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1 SEEDS MOVE BUT TREES STAND STILL: SPATIAL POPULATION DYNAMICS OF TROPICAL TREES By TIMOTHY TREVOR CAUGHLIN A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIR EMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2013
2 2013 T. Trevor Caughlin
3 To my sister Hannah for reteaching me how to look at nature with wonder
4 ACKNOWLEDGMENTS First and fo remost, I would like to thank my amazing collaborators. Jessica H. Wheeler was instrumental in designing the sampling scheme and carrying out the field work for Chapter 2, and her undergraduate thesis on post dispersal seed fate of Miliusa provided many essential natural history details for Chapters 3 and 4. Jake M. were enormous, and Jake was very patient and encouraging even during the lengthy debugging periods for th e individual based models. Jeremy W. Lichstein was a great mentor and taught me how to write engaging descriptions of models. My adviser, Douglas J. Levey, was an amazing supporter during the course of my PhD. Doug has been patient, insightful and critic al when necessary. Committee members Robert Dorazio, Emilio Bruna, Kaoru Kitajima were central to my intellectual development, always challenging me to think deeper and be a better scientist. My academic collaborators and friends in Thailand, including Ge orge Gale, (KMUTT), provided me with a homebase in Thailand, giving me a sense of security and belonging that enabled me to overcome the challenges of field work in a remot e area. Daphawan Khamcha graciously and patiently helped me translate my research permits into Thai. Wirong Chantorn provided friendship and intellectual companionship.. Sarayudh Bunyavejchewin at the Thai Royal Forest Department lended his field staff, d ata and decades of knowledge on forest dynamics to my research. My many field under challenging conditions. The staff at the Huai Kha Khaeng Wildlife Sanctuary provided food, shelter and kind encouragement during my field work.
5 Funding was provided by the J. William Fulbright Foundation, a student research grant from the Florida Exotic Pest Plant Council (FLEPPC), a research grant from the Sigma Xi Foundation, and the Nat ional Science Foundation under Grant No. 0801544 in the Quantitative Spatial Ecology, Evolution and Environment Program (QSE 3 ) and a Graduate Research Fellowship. In particular, the Fulbright grant and the QSE 3 IGERT fellowship provided many opportunities for professional growth and training in new skills, languages and cultures. Many friends, including Anand Roopsind, Chris Wilson, Nick and Cori Ruktanonchai, Rosana Zenil, Michael Jones, Kristen Sauby, Sami Rafi, Sarah Graves and many others, provided int ellectual and social support throughout graduate school. Finally, the love and encouragement of my mother and sister, Karen and Hannah Smith, have given me confidence throughout graduate school.
6 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIS T OF ABBREVIATIONS ................................ ................................ ........................... 10 ABSTRACT ................................ ................................ ................................ ................... 11 CHAPTER 1 GENERAL INTRODUCTION ................................ ................................ .................. 13 2 URBANIZED LANDSCAPES FAVORED BY FIG EATING BIRDS INCREASE INVASIVE BUT NOT NATIVE JUVENILE STRANGLER FIG ABUNDANCE ......... 18 Background ................................ ................................ ................................ ............. 18 Materials And Methods ................................ ................................ ........................... 21 Study region ................................ ................................ ................................ ..... 21 Study species ................................ ................................ ................................ ... 22 Stud y design ................................ ................................ ................................ ..... 22 GIS dataset and classification of favorable bird habitat ................................ .... 24 Modeling juvenile abundance ................................ ................................ ........... 25 Seed addition experiment ................................ ................................ ................. 29 Results ................................ ................................ ................................ .................... 30 Summary statistics for observational plots ................................ ....................... 30 Model fit and comparison ................................ ................................ ................. 30 F. microcarpa ................................ ................................ ............................. 30 F. aurea ................................ ................................ ................................ ..... 31 Seed addition experiment ................................ ................................ ................. 31 Discussion ................................ ................................ ................................ .............. 32 3 THE IMPORTANCE OF LONG DISTANCE SEED DISPERS AL FOR THE DEMOGRAPHY AND DISTRIBUTION OF A CANOPY TREE SPECIES ............... 40 Background ................................ ................................ ................................ ............. 40 Materials And Methods ................................ ................................ ........................... 43 Study site ................................ ................................ ................................ .......... 43 Study species ................................ ................................ ................................ ... 43 Study design ................................ ................................ ................................ ..... 44 Establishment ................................ ................................ ................................ ... 44 Seed arrival ................................ ................................ ................................ ...... 46 Individual based model (IBM) ................................ ................................ ........... 47 Results ................................ ................................ ................................ .................... 50 Seed arrival ................................ ................................ ................................ ...... 51 IBM results ................................ ................................ ................................ ....... 52 Experime nt 1: ................................ ................................ ............................. 52
7 Experiment 2: ................................ ................................ ............................. 52 Discussion ................................ ................................ ................................ .............. 53 4 THE DEMOGRAPHIC IMPORTANCE OF SPATIAL STRUCTURE THROUGHOUT THE LIFE CYCLE OF A TROPICAL TREE SPECIES ................. 62 Introduction ................................ ................................ ................................ ............. 62 Materials A nd Methods ................................ ................................ ........................... 65 Study site ................................ ................................ ................................ .......... 65 Study species ................................ ................................ ................................ ... 66 Demographic data ................................ ................................ ............................ 66 Models ................................ ................................ ................................ .............. 67 Statistical models ................................ ................................ ............................. 67 Individual based model ................................ ................................ .................... 70 Population Viability Analysis ................................ ................................ ............. 72 Results ................................ ................................ ................................ .................... 73 IBM results ................................ ................................ ................................ ....... 74 PVA ................................ ................................ ................................ .................. 75 Discussion ................................ ................................ ................................ .............. 76 5 GENERAL CONCLUSIONS ................................ ................................ ................... 87 APPENDIX A DERIV ING FIG EATING BIRD HABITAT QUALITY FROM FRUITING TREE OBSERVATIONS AND GIS DATA ................................ ................................ ......... 91 B PARAMETER ESTIMATES AND 95% CONFIDENCE INTERVALS FOR TOP FITTING MODELS OF JUVENILE FIG ABUNDANCE ................................ ........... 98 C ADDITIONAL DETAILS ON STUDY SPECIES AND FIELD METHODOLOGY FOR CHAPTER 3 ................................ ................................ ................................ ... 99 D ADDITIONAL DETAILS ON STATISTICAL METHODS AND IBM FOR CHAPTER 3 ................................ ................................ ................................ .......... 105 E ADDITIONAL DETAILS ON MODELS IN CHAPTER 4 ................................ ........ 120 F ADDITIONAL DETAILS ON SENSITIVITY ANALYSIS ................................ ......... 131 REFERENCE LIST ................................ ................................ ................................ ...... 135 BIOGRAPHICAL SKETCH ................................ ................................ .......................... 145
8 LIST OF TABLES Table page 2 1 Data used to determine terms in Equation 2 1 ................................ ................... 36 2 2 Model selection results for F. microcarpa and F. aurea ................................ ...... 37 4 1 ............................ 82 A 1 Summary of bir d visitation to fig trees. ................................ ................................ 95 A 2 Habitat categories and values after reclassification for fig eating bird abundance. ................................ ................................ ................................ ......... 96 B 1 Parameter estimates and 95% confidence intervals for top fitting F. microcarpa model ................................ ................................ ............................... 98 B 2 Parameter estimates and 95% confidence intervals for top fitting F. aurea model. ................................ ................................ ................................ ................. 98 D 1 Data sources for response variables used in used in model ............................ 105 D 2 Prior distributions for parameters used in s tatistical models. ............................ 113 D 3 Parameter estimates and 95% credible intervals ................................ .............. 115 E 2 Prior distributions for parameter s in IBM. ................................ ......................... 127 E 3 Parameter estimates for parameters in IBM ................................ ..................... 128
9 LIST OF FIGURES Figure page 2 1 Map of study region and scale of observational plots ................................ ........ 37 2 2 Predictors of j uvenile fig abundance. ................................ ................................ .. 38 2 3 Predicted contribution of adult trees to j uvenile fig abundance. .......................... 39 3 1 Overview of study design ................................ ................................ ................... 57 3 2 Map of study region ................................ ................................ ........................... 58 3 3 Miilusa demography and distribution along transect. ................................ .......... 59 3 4 Seedling density and predicted rates of sapling establishment and seed arrival along transect. ................................ ................................ ......................... 60 3 5 Mean squared predicted error (MSPE) for IBM prediction of seedling distributio n along transect. ................................ ................................ .................. 61 4 1 Effects of size structure on tree vital rates. ................................ ......................... 82 4 2 Spatial scale, magnitude and uncertainty of seed dispersal and NDD for Miliusa. ................................ ................................ ................................ .............. 83 4 3 Asymmetric effects of neighbor size on Miliusa vital rates ................................ .. 84 4 4 Population dynamics from IBM model. ................................ ............................... 85 4 5 Results of population viability analysis for the IBM runs with and without animal seed dispersal. ................................ ................................ ........................ 86 A 1 Illustration of the raster reclassification process for a single fig plot. .................. 97 D 1 Spatial variation in light availability ................................ ................................ 118 D 2 Parameter estimates for effect of covariates on demographic models ............. 119 F 1 Comparison of analytical sensitivity for a beta binomial distribution to numerical approximation. ................................ ................................ .............. 133 F 2 Main sensitivities for parameters in the IBM as a function of histogram bins. 134
10 LIST OF ABBREVIATIONS HKK The Huai Kha Khaeng Wildlife Sanctuary, a research site in Thailand. IBM Individual Based Model, a dynamic model used for simulating individual behavior, including growth, survival and reproduction. LDD Long Distance Dispersal, seed dispersal outside of the local patch. For most tree species, LDD refers to seed dispersal on the scale of kilometers. NDD Negative Density Dependence, a demographic disadvantage for individual organisms in conditions of high conspe cific density.
11 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy SEEDS MOVE, BUT TREES STAND STILL: SPATIAL POPULATI ON DYNAMICS OF TROPICAL TREES By Timothy Trevor Caughlin August 2013 Chair: Douglas J. Levey Major: Zoology Because seed dispersal sets the spatial template for all future tree life stages, seed dispersal is considered important for ecological theory and conservation. Nevertheless, studies that link seed dispersal to later tree life stages at large spatial and temporal scales are rare, and the question of when tree populations are likely to be limited by seed arrival remains largely unanswered. Quanti fying the degree of seed limitation for tree populations is necessary to address many applied issues, such as how many seeds are required to reforest a degraded area, how rapidly trees could migrate if climate change renders existing habitat unsuitable, an d the threat of invasive species to otherwise intact forests. I determined the demographic importance of tree seed dispersal over large areas and long time periods, using an approach that combines seed addition experiments, observational data, and quantit ative models. Chapter 2 quantifies the importance of seed limitation for the distribution of invasive strangler figs in South Florida. I found strong support for the hypothesis that invasive, but not native, strangler fig abundance is higher in habitats w ith high human land use because fig eating birds that disperse fig seeds are more abundant in these habitats.
12 Consequently, managing invasive fig trees should involve removing adult fig trees from areas of high human land use, rather than targeting all fi g trees equally or reducing seedling survival and growth. In Chapter 3, I determined how long distance seed dispersal (LDD) influences the distribution of a canopy tree species ( Miliusa horsfieldii) across a landscape mosaic of evergreen and deciduous for est in Western Thailand. Results suggest that although Miliusa individuals of all life stages are most abundant in evergreen forest, Miliusa is rare in the deciduous forest because arrival of seeds there is limited by low rates of LDD. Thus I conclude th at LDD plays a pivotal role in the distribution of this tree species in its native habitat. Finally, in Chapter 4, I used spatially explicit data on Miliusa vital rates, from seed production to adult tree survival, to parameterize an individual based mode l (IBM) to simulate Miliusa population dynamics over multiple decades. This model suggests that seed dispersal to low density neighborhoods is critically important for population dynamics, and if the mammalian seed dispersers of Miliusa are hunted to exti nction, the probability of extinction for Miliusa populations increases by an order of magnitude. These results demonstrate that when dispersal allows individuals to reach unoccupied patches or arrive in locations with long term benefits for survival and g rowth, seed dispersal is likely to have high demographic importance for trees.
13 CHAPTER 1 GENERAL INTRODUCTION I have great faith in a seed. Convince me that you have a seed there and I Henry David Thoreau A tree can produce millions of seeds in its lifetime, most of which will die as seeds, seedlings or saplings before becoming reproductive adults. Yet, whether a tree lives for two weeks or two h undred years, seed dispersal represents the only time when movement is possible, and thus sets the spatial template for all future life stages. Understanding the demographic importance of the spatial template set by seed dispersal is the motivating questi on of this dissertation. Relating events between seed arrival and adult recruitment to the spatial dynamics of tree populations is necessary to answer many pressing environmental questions, such as how best to manage the spread of invasive species, how ra pidly trees could migrate if climate change renders existing habitat unsuitable, and how loss of animal seed dispersers due to overhunting will impact tropical forest dynamics. If range expansion of invasive tree species is limited by seed dispersal, opt imal management will involve restricting seed arrival, however, if range expansion is limited by establishment of dispersed seeds into adults, the best management action may be to reduce survival and growth of existing plants. Chapter 2 addresses the role of seed limitation in the distribution of invasive and native strangler fig seedlings in south Florida. This study began with the observation that invasive figs were more abundant in urban areas, while native figs were more abundant in natural habitats, a pattern that
14 could either be a result of increased establishment or increased seed dispersal of invasive figs in urban habitats. I addressed these hypotheses using a large scale dataset on seedling fig abundance, spanning the entire range of human land use, from urban parking lots to native forest. Using spatially explicit models to combine data on seedling fig abundance with the distribution of reproductive adult fig trees, fig eating bird habitat preferences and GIS data on land use, I found strong s upport for the hypothesis that invasive fig seedlings are most abundant in urban habitats due to higher bird seed dispersal in those habitats. These results were corroborated with a seed addition experiment, which revealed high rates of seed limitation for both species of strangler fig. From a management perspective, these results provide an unexpected strategy to reduce invasion: remove adult invasive fig trees in urban landscapes with high fig eating bird abundance. The third and fourth chapters take pla ce in a very different landscape than suburban Florida: a primary forest in a wilderness area of western Thailand. The Huai Kha Khaeng Wildlife Sanctuary is part of the largest intact forest complex in mainland southeast Asia, and contains intact populati ons of large mammals hunted to extinction elsewhere, including sun bears, tigers and gibbons. Understanding the role of animal seed dispersers in tree demography is central for tropical forest conservation, because if seed dispersal plays an important rol e in determining tree abundance and distribution, maintaining populations of animal seed dispersers should be a conservation priority. The focal species for these two chapters is Miliusa horsfieldii, a dominant canopy tree species in Huai Kha Khaeng. Seed s of Miliusa are dispersed by large, wide ranging mammals, including civets, bears, macaques and gibbons, providing the opportunity to
15 study the demography of an animal dispersed tree species in a site where the dispersers are still abundant. The third cha pter applies the concepts of dispersal and establishment limitation to assess the impact of long distance dispersal (LDD) on the distribution of Miliusa The landscape in Huai Kha Khaeng is a mosaic of deciduous and evergreen forest, with stark differences in species composition, understory vegetation and forest structure between forest types. Miliusa is abundant in evergreen forest and rare in deciduous forest. This distribution could be due to dispersal limitation, with few seeds arriving in the deciduou s forest, or to establishment limitation, if low survival and growth in deciduous forest restrict recruitment to evergreen forest. I combined a seed addition experiment with data on the distribution of Miliusa on a landscape scale to quantify the importan ce of LDD for this tree population. This analysis extends the methods developed to understand dispersal limitation in Chapter 2, by directly combining data on seedling abundance with the seed addition experiment to infer seed arrival. Results reveal that Miliusa is rare in the deciduous forest because arrival of seeds into the forest is much more important for explaining observed seedling distributions than spatial differences in survival and growth between forest types. By using dynamic models to link d emographic data to spatial patterns, I conclude that LDD plays a pivotal role in the distribution of this tree in its native habitat. While the second and third chapters focus on seed dispersal at large spatial scales, the fourth chapter quantifies the dem ographic importance of seed dispersal within a single patch over a time scale of several decades. Results from Chapter 3 suggested strong negative effects of conspecific density (negative density dependence,
16 hereafter NDD) on Miliusa seedling establishmen t, and I hypothesized that if these negative effects were consistent across the entire tree life cycle, seed dispersal into low density neighborhoods would have significant demographic consequences. I used spatially explicit on vital rates for seeds, seed lings and trees >1 cm DBH to parameterize statistical models for the effects of NDD and size on tree survival and growth. Next, these statistical models were integrated into a dynamic individual based model (IBM). The IBM was used to quantify the sensitivi ty of population dynamics to parameters for size structure, NDD and seed dispersal after 100 years of spatially explicit demography. I found NDD effects were prevalent for seeds, seedlings and trees, although the magnitude, spatial scale and demographic i mportance of NDD varied between life stages. These results indicate the importance of spatial structure at multiple points throughout the life cycle for population dynamics of a long lived tree species. Finally, I conducted a simulation experiment to comp are the probability of extinction of Miliusa with natural seed dispersal to a scenario with no animal seed dispersal. In these simulations, loss of animal seed dispersal increases the probability of extinction by an order of magnitude, indicating the crit ical importance of seed dispersal for this tree population. The demographic importance of the spatial template of seed dispersal for tree populations has been identified as a major research gap with consequences for ecological theory and conservation. Thi s dissertation provides unique insight on when and why seed dispersal will play a key role in tree spatial population dynamics. First, the spatial pattern of LDD is likely to have a major impact on the distribution of tree species over large spatial scale s. Alterations to LDD, either through an increase in
17 human land use and seed dispersing bird abundance (Chapter 2) or the potential extinction of wide ranging animal dispersers (Chapter 3), will likely result in major changes in the range of animal dispers ed tree species. Chapter 4 demonstrates that if demographic effects of being located in particular sites are consistent across tree life stages, seed dispersal to these sites is likely to have demographic consequences even for long lived species with mult iple life stages. The ultimate consequence of these results is that managing seed dispersal, either through decreasing seed arrival of invasive plants into sensitive ecosystems, promoting tree migration in the face of climate change via assisted migration or maintaining animal seed disperser abundance to protect tropical tree populations, is likely to be a crucial component of biodiversity conservation in a changing world.
18 CHAPTER 2 URBANIZED LANDSCAPES FAVORED BY FIG EATING BIRDS INCREASE INVASIVE BUT NOT NATIVE JUVENILE STRANGLER FIG ABUNDANCE Background Propagule pressure, which reflects both seed production and dispersal, can have major impacts on plant population and community dynamics. Many of the processes that motivate interest in propagule pr essure, such as regional beta diversity, range expansion of invasive species and metapopulation dynamics, occur at large scales and encompass a variety of land cover types (Condit et al. 2002, Levine and Murrell 2003, Simberloff 2009) Landscape context, including the proportion of different land cover types in a landscape, and the spatial distribution of propagule sources in relation to land cover, could change the strength of propagule pressure, with consequences for plant distribution and abundance. Seed dispersal by animals may be particularly dependent upon landscape context, since landscape composition and configuration can affec t animal movement and abundance, potentially changing both seed dispersal distances and removal rates (Buckley et al. 2006, Uriarte et al. 2011) However, few studies have quantified how landscape context might alter seed dispersal, causing increases or decreases in propagule pressure in different l andscapes. Propagule pressure is particularly crucial for invasive species range expansion. Propagule addition experiments reveal propagule input is often a stronger determinant of invasion success than microhabitat characteristics, including patch biodiv ersity and disturbance regime (Levine 2000, Von Holle and Simberloff 2005) However, if Reprinted with permission from Caughlin, T., J. H. Wheeler, J. Jankowski, and J. W. Lichstein. 2012. Urbanized landscapes favored by fig eating birds increase invasive but not native juvenile strangler fig abundance. Ecology 93:1571 1580.
19 favorable microhabitats for recruitment are limited, propagule a ddition may increase invader abundance only if propagules arrive in favorable microhabitats (Britton Simmons and Abbott 2008) These mechanistic propagule addition studies are usually constrained to a small number of habitats, so metimes a single forest type. However, range expansion of invasive species often occurs over multiple landscapes, from introduction sites in human inhabited areas to recruitment sites in undisturbed forest. While propagule addition experiments have provi ded valuable insight into the relative importance of microhabitat characteristics and propagule pressure at small spatial scales, we lack an understanding of how habitat characteristics at the landscape scale may mediate the effects of propagule pressure o n invasive plant abundance. Variation in human land use is a component of landscape context with the potential to alter the impact of propagule pressure on plant invasion. Many studies have coupled GIS land use data sets with mapped distributions of inva sive plants to reveal a positive correlation between human disturbance and invasive species abundance (Burton et al. 2005, Bradley and Mustard 200 6, Seabloom et al. 2006) However, these large scale observational studies are usually unable to identify the mechanism behind this correlation, which could be explained by several different biological hypotheses. Intrinsic characteristics of habitats wi th high human land use, such as increased light and nutrient availability, could increase establishment of invasive species regardless of propagule pressure (Leishman and Thomson 2005) Alternatively, propagule pressure could increase in human dominated l andscapes due to increased abundance of reproductive individuals of invasive species deliberately planted by people (Colautti et al. 2006) Finally, human land use could amplify propagule pressure by increasing seed
20 dispersal distances in disturbed landscapes (With 2002) Distinguishing among these hypotheses has implications for management of invasive species, because restricting propagule input requires di fferent actions than manipulating environmental conditions to decrease survival of established plants (Reaser et al. 2008) In Florida, native and i nvasive strangler figs ( Ficus aurea and F. microcarpa ) provide an unusually tractable system for understanding how propagule pressure and landscape context influence the distribution of an invasive species. In Florida, see dling figs establish primarily in the canopy of a single species of common native palm, the cabbage palm ( Sabal palmetto ). As the figs reach maturity, they eventually become rooted in the ground. Consequently, suitable sites for seedling establishment are different than suitable sites for adult growth and survival, and the relationship between juvenile fig abundance in cabbage palms and adult fig abundance in soil is more likely to be influenced by seed dispersal than habitat effects on growth and survival F. aurea and F. microcarpa have similar habitat preferences, growth forms and dispersal mode, but F. microcarpa is in the process of rapid range expansion (Gordon 1998) while F. aurea is common throughout South Florida (Serrato et al. 2004) As a result, comparing the two species provides a rare opportunity to explore how the spatial distribution of adult trees may affect propagule pressure, and ultimately, juvenile abundance. Invasive fig abu ndance appears to be positively correlated with urban land use in Florida ( EDDMapS 2011) We hypothesized that increased juvenile F. microcarpa abundance in urban landscapes can be explained by increased seed dispersal due to a higher abundance of seed di spersing birds in urban environments. We also considered
21 two alternative hypotheses: that presence of reproductive adults increases juvenile fig abundance regardless of human land use, and that human land use affects fig abundance by increasing juvenile f ig survival. Additionally, we predicted that in our study area which is within the established range of F. aurea but on the range boundary of F. microcarpa spatial distribution of juveniles is associated with adult locations) would be greater for the latter species. We tested these hypotheses by modeling juvenile fig abundance in relation to adult fig abundance and landscape scale habitat suitability for fig eating birds. To better understand the mechanisms behind our model results, we conducted a seed addition experiment. Our study bridges the knowledge gap between large scale observational studies relating land cover to invasive plant abundance and more mechanistic propagule addition studies limited to small spatial scales. Consequently, we are able to provide novel insight into how landscape context may alter propagule pressure and, ultimately, t he abundance of an invasive species in different landscapes. Materials And Methods Study region Our study region is located on the west coast of South Florida (Fig 2 1). Existing figs were surveyed in plots across a 250 km transect from Anne Marie Island ( 27.471 N, 82.689 W) to Chokoloskee Island (25.838 N, 81.380 W), and the seed addition experiment was conducted at the northern edge of this transect in Sarasota (27.382, 82.564). The average annual precipitation for five sites within the 250 km transec t is range of natural habitats, including longleaf pine forest, mangrove swamp and dry
22 prairie (Table 2 1). Invasive plant species are considered a major conservation threat in the region (Gordon 1998) Study species Ficus aurea and F. microcarpa are the most common fig species in Florida and share a similar niche, with 90% of F. aurea and 92% of F. microcarpa juveniles occurring in cabbage palm leaf bases (Wheeler and Caughlin unpublished data), probably as a result of the relatively high moisture of this microhabitat (Swagel et al. 1997) Ficus aurea is native to the Caribbean Bas in, with Florida representing the northern range limit (Serrato et al. 2004) F. microcarpa is native to South Asia and has become invasive around the world including South America, Australia and Pacific Islands (McPherson 1999, Corlett 2006) In Florida, F. microcarpa trees were deliberately planted as ornamental trees and have been present since at least 1912, but around 1975 (Gordon 1998). The northernmost point in our study region was approximately 60 km south of the zone where winter temperatures limit the range of F. aurea, which otherwise occurs throughout South Florida. In contrast, the current range boundary of F. microcarpa appears centered around human settlements on the coa st of South Florida (EDDMaps 2011). Study design We quantified the distribution of fig trees in 52 plots, surveying each plot once between June, 2006 and January, 2009. Plots were distributed across the entire gradient of human disturbance, from downtown parking lots to native forest. Plot locations were selected using a stratified random approach to ensure equal
23 representation of different habitats. Once a random location was selected, the 30 m x 30 m area with at least five cabbage palms nearest to the random point was used for the plot. All plots were located at least one km apart. Each plot consisted of a 30 m x 30 m juvenile plot where all juvenile figs were counted, centered within a larger circular adult plot with a radius of 300 m, where adult fi gs were surveyed (Fig 2 1). We define a juvenile as a fig <25 cm dbh (diameter at breast height), a reproductive threshold for F. microcarpa (Caughlin and Wheeler, unpublished data). When fig trees are large enough to be reproductive, they are generally rooted in the ground, so we were able to measure dbh from the ground. Within the juvenile plots, we recorded the number of cabbage palms >2 m tall, since an increased number of cabbage palms is likely to result in a higher chance of sampling juvenile fig t rees. We also quantified canopy cover within the juvenile plots, because canopy cover alters microhabitat characteristics likely to affect fig establishment, such as light availability. We recorded canopy cover by visually estimating the amount of sky cov ered by vegetation >2 m high in five categories from 0 20% to 81 100% coverage. Canopy cover was recorded at 12 points, located every 5 m on two randomly selected parallel edges of the juvenile plot. We calculated the average value of these 12 points for use in analyses. Canopy cover was aggregated at the 30 m x 30 m scale, because this scale best reflects the overall differences between the wide range of habitats our juvenile plots sample. The larger 300 m radius adult plot surrounding the juvenile plot was used to sample adult fig trees as potential seed sources. The total area of each of these adult plots is 28.27 ha, which is larger than the territories of most of the fig eating birds in our
24 study region (see Appendix A for more details). Because la rger fig trees are likely to receive more frugivore visits (Korine et al. 2000) we assumed that larger trees would have a higher chance of dispersing seeds than smaller trees, and we sampled trees accordingly. Within 50 m of the juvenile plot we recorded the location and dbh of all fig trees >25 cm dbh, within 100 m all fig trees >50 cm dbh, within 200 m all fig trees >100 cm dbh and within 300 m all fig trees >200 cm dbh. The location of each fig tree and juvenile plot was measured with a Garmin 60Csx GPS unit with six meter accuracy. The 52 observational plots included a total area sampled of 4.68 ha for juvenile figs and 1470.27 ha for adult figs. GIS dataset and classification of favorable bird habitat We created an ind ex to describe habitat favorable to fig eating birds by combining a satellite derived land cover map with data on the abundance of fig eating birds. We determined which resident bird species were potential fig seed dispersers by quantifying bird visitatio n rates to seven F. aurea and five F. microcarpa fruiting trees, during February June 2006 (see Appendix A for details). The synconium (hereafter sized (6 11 mm) and there were no significant differences in bird visitati on between fig species (Appendix A). A total of fourteen resident bird species were recorded visiting fig trees, with Northern Mockingbirds ( Mimus polyglottos ), Blue Jays ( Cyanocitta cristata ) and Red Bellied Woodpeckers ( Melanerpes carolinus ) as the top three visitors, accounting for 38.7, 20.8 and 12.8 percent of visitation, respectively. We combined the bird visitation data with an independent set of bird abundance data (Stracey and Robinson 2012) to direct a classification of GIS land use data. These abundance data were collected in 2005 from auditor y visual counts of birds at 185 points across Florida. During each bird count, the
25 surrounding habitat was visually classified (using categories similar to the land cover classification in the GIS dataset; Table A2). fig species to fruiting fig trees, and used this value as an index of fig eating bird habitat quality (see Appendix A for more details). Favorable habitat for fig eati ng bird species largely reflects human land use: high and low impact urban land cover classes had the highest values for fig eating bird abundance (1.19 and 1.11, respectively), while the lowest value, 0.07, was found in pinelands habitat (Table A2). We pa ired the bird data with Landsat Enhanced Thematic Mapper+ Satellite Imagery at 30 m x 30 m resolution (Stys et al. 2004) This initial GIS dataset with 28 habitat categories was reclassified into rasters representing fig eating bird habitat quality (see above ). Next, we took a weighted average of all fig eating bird habitat rasters within 300 m of every adult fig and juvenile plot. We assumed that effects of the landscape would decline with distance and calculated the weighted average of fig eating bird habit at quality using the inverse distances between rasters and adult figs or juvenile plots as the weights. Modeling juvenile abundance Observed plant distributions represent a combination of seed dispersal and survival (Clark et al. 1999) We assumed that seed dispersal and survival were negative binomially and binomially distributed processes, respectively. Compounding these two distributions results in a negative binomial distribution for the number of juveniles in a 30 m 30 m plot (the response variable in all models), with expectation equal to expected seed rain multiplied by survival probability. We parameterized the
2 6 negati ve binomial distribution with a mean, and a variance equal to where the parameter k determines the degree of overdispersion. Our basic model structure is: ( 2 1) The data used to represent each of these terms is shown in Table 2 1. The substrate term is the number of cabbage palms in the 30 x 30 m plots. We assume that cabbage palm abundance affects the chances of sampling juvenile figs, rather than im pacting seed dispersal or seedling survival. Thus, the number of cabbage palms in the model is included as a multiplicative term, independent of survival and seed dispersal. The second term represents the seed dispersal process, considered here as: (2 2) Here, f is a parameter representing long distance seed dispersal from beyond the 300 m radius plots where adult figs were surveyed The term AT represents seed dispersal from trees within the 300 m radius plot and is weighted by the parameter g We considered three different forms for AT In the first form, AT is 0 or 1, respectively, for 300 m radius plots where no adults or at le ast one adult exceeded our distance dependent dbh threshold. Hereafter, we refer to this first form of AT absence data as we did not perform a complete census of adult tree s. In the presence absence form of AT expected seed rain is either f or f + g respectively, for plots with or without at least one sampled adult. The second two forms were based on the following expression: (2 3)
27 Here, AT includes a term for seed dispersal from individual adult trees i to the juvenile plot, summed over the n adult trees in the plot. In (3 ), dis i is the distance from adult i to the plot center, f is the long distance dispersal term, g and are fitted parameters; and is either one or (the fig eating bird habitat index in a 300 m radius around adult tree i ), depending on the version of the model. If seed arrival depends strongly on fig eating bird habitat qual ity in the surrounding landscape, then the model with should outperform the model with In preliminary analyses, we also considered models that accounted for the dbh of adult figs, as well as models based on alterna tive dispersal kernels (including lognormal and 2dt kernels; Clark et al. 1999). These alternatives did not improve the fit to the data and are not considered further. The third term in our model (E quation 2 1) is: ( 2 4) This survival term consists of a parameter representing baseline survival and two survival covariates, canopy cover and the fig eating bird habitat index within a 300 m radius of the juvenile pl ot, with fitted parameters and We do not include a temporal component for survival, because our seed addition experiment revealed that the vast majority (>99%) of mortality occurs during the first four months after seed dispersal, while annua l survival for established seedlings is relatively high (see below). We considered four possibilities for the covariates within the survival term: including both canopy cover and juvenile plot habitat ( and both treated as free parameters); se tting either or equal to zero so that only canopy cover or only juvenile plot habitat affects survival; and setting both and equal to zero, indicating no effect of
28 covariates. A consequence of this model structure is that canopy co ver and fig eating bird habitat around juvenile plots can affect juvenile fig abundance regardless of adult tree abundance within adult plots. If fig eating bird habitat is correlated with unmeasured environmental variables which directly affect juvenile fig survival, models with fig eating bird habitat around juvenile plots should fit better than models with fig eating bird habitat around adult trees. In total, we used combinations of the three seed arrival terms and the four survival terms to construct 10 models for each fig species. Models were fit in a maximum likelihood context in R version 2.10.1 using simulated annealing, a global the seed dispersal parameters f and g resulted in extremely large confidence intervals. g or f significantly degraded the fit. Therefore, for the remainder of t Repeating the annealing algorithm several times with different initial conditions yielded very similar results, suggesting that the parameter estimates we obtained are close to the true maximum l ikelihood estimates. Model fit was evaluated using the small sample c, (Burnham and Anderson 2010) We used R 2 to evaluate the predictive capacity of each model by calculating the proportion of variance in log(x+1) transformed juvenile fig abundance explained by each model (Lichstein et al. 2010) All analyses were conducted using R version 2.11.1 (R Development Core Team 2010).
29 Seed addition experi ment Because modeling observational data on plant distributions may confound seed dispersal and seedling establishment, we supplemented our observational data with a seed addition experiment. If seed arrival limits population growth rates, experimental see d addition should result in an increase in seedling abundance, while if establishment represents the main bottleneck for the population, adding seeds should not result in an increase in abundance (Clark et al. 2007) In May 2009, we added F. microcarpa and F. aurea seeds to cabbage palms in Sarasota, FL (Fig 2 1). We implemented the experiment at a site with a high abundance of F. mi crocarpa adults, where seed limitation was expected to be weak relative to other locations. Thus, the experiment constitutes a conservative test of seed limitation for F. microcarpa We randomly selected 72 cabbage palms, embedded in an urban landscape w ith a variety of microhabitats, to serve as seed addition sites for each fig species. In each cabbage palm we placed five mesh pockets containing 0, 5, 10, 20 and 40 fig seeds, collected from at least six different individuals of each fig species in the s tudy area, resulting in a total of 5,400 seeds per species. Pockets were sewn closed on the bottom to prevent rain from displacing fig seeds but open at the top, to allow naturally dispersed seeds to arrive in the pocket. Seeds were processed using the f loat method and a sieve to remove non viable seeds. Germination rates of seeds processed using this technique were ~79% (Patel and Doan unpublished data). Within each mesh pocket, we placed two tablespoons of humus collected from cabbage palm leaf bases, approximately equivalent to the amount naturally found in cabbage palm leaf bases. The number of seedlings in palms was recorded four, nine, and sixteen months after initial seed placement. We compared seedling establishment in treatments with zero seeds added
30 to treatments with seeds added after the first census using a non parametric Monte Carlo test because zero seeds emerged from packets with zero seeds added. In a separate test, we used a logistic mixed model with survival of individual seeds as the r esponse variable, fig species and number of seeds added as predictor variables and nested random effects at the mesh pocket and cabbage palm levels. The Monte Carlo analysis addresses the question of whether adding seeds increases seedling abundance, whil e the logistic mixed model analyzes survival effects on seeds that were added. Results Summary statistics for observational plots Our plots sampled a wide range of fig eating bird habitat. Invasive fig adults were more closely associated with fig eating b ird habitat than native fig adults: the mean (standard deviation) fig eating bird habitat quality within 300 m of F. microcarpa and F. aurea adults, respectively, was 0.76 (0.21) and 0.58 (0.29). In the 300 m radius circles around juvenile plots, the mea n number of F. aurea adults was 5.6911.41 individuals, compared to a mean of 4.45.23 F. microcarpa adults. F. aurea juvenile abundance in juvenile plots had a higher mean and standard deviation (4.795.26 individuals) than that of F. microcarpa (2.963. 66 individuals). Model fit and comparison F. microcarpa The best model for juvenile F. microcarpa abundance included distance to adult trees, fig eating bird habitat around adult trees, and canopy cover (Table 2 2). Both models incorporating fig eating c <3.5, in contrast to the four models with fig eating bird habitat in the survival term, which all had
31 AIC c >5. Inverse models that did not include the distance based dispersal term performed poorly: the best m odel without distance appeared in the model set with AIC c =13.42. The R 2 values revealed a good fit to the data for F. microcarpa, with the model including distance, canopy cover, and fig eating bird habitat around adult trees having the highest R 2 value of 73%. Figure 3 shows the relative strength of the two seed dispersal effects: distance to adult and fig eating bird habitat quality around adults. While the predicted number of juvenile figs declines exponentially with distance from adults, adult tree s with high fig eating bird habitat contribute more to juvenile abundance than trees with low fig eating bird habitat, even at long distances. F. aurea In contrast to the invasive F. microcarpa the best fit model for F. aurea included only presence/absen ce of adult trees within 300 m of juvenile plots and canopy cover (Table 2 2). The first model with a distance based dispersal term had a AIC c =11.46, indicating almost no empirical support for distance dependent dispersal limitation. Predictive power of models for F. aurea was relatively low compared to F. microcarpa with an R 2 value of 43% for the best model. Parameter estimates and 95% confidence intervals for the best fitting F. microcarpa and F. aurea models are presented as Tables B2 and B3 in App endix B. Seed addition experiment In the first seedling census, four months after seed placement, 41 F. aurea and 20 F. microcarpa seedlings had established out of a total of 5400 seeds of each species added. However, after this initial four month period, survival was relatively high, with 41% annual survival for F. aurea and 70% annual survival for F. microcarpa seedlings. Zero seedlings emerged from pockets with zero seeds added, suggesting that few
32 viable seeds were dispersed into the cabbage palm boot s after experimental seed placement. Statistical tests were performed on seedlings from the first post dispersal census in October 2009, since the number of seedlings was highest during this census, resulting in more statistical power to detect effects. There was a statistically significant difference in seedling emergence between pockets with seeds added and pockets with no seeds added (p=0.036; non parametric Monte Carlo test). Comparing only pockets with seeds added, logistic mixed models of seedling s urvival showed no significant differences between fig species (p=0.78) or between different levels of seed addition (p=0.82). Discussion Propagule pressure is increasingly recognized as a key process underlying invasion, and understanding how landscape context can alter dispersal distances and propagule availability is a research priority in invasion biology (Hastings et al. 2005) Two recent studies have suggested that mic rohabitat characteristics can amplify the impact of propagule pressure by increasing the number of favorable sites available for recruitment (Britton Simmons and Abbott 2008, Eschtruth and Battles 2011) Our result s support another possibility: at a large scale, landscape context could boost the effect of propagule pressure by increasing seed dispersal distances (With 2001). Our best models for the invasive fig species, F. microcarpa, support the hypothesis that ju veniles are more abundant in landscapes with high human land use because of increased seed dispersal from fig eating birds in urban habitats. However, our best models for the native fig species, F. aurea, did not include characteristics of individual adul t trees, suggesting that effects of landscape context on seed dispersal may depend on the regional distribution of adult trees.
33 Determining whether environmental heterogeneity impacts invasive plant populations through seed or establishment limitation has consequences for invasive control strategies (Reaser et al. 2008). While our analysis partitions juvenile fig abundance into seed dispersal and survival components, we cannot make strong inferences on the relative importance of these two components from o bservational data alone. An ideal way to untangle factors related to seed limitation for invasive species would be a large scale seed addition experiment over a range of habitats and seed availability (Denslow and DeWalt 2008) H owever, such an experiment would be logistically challenging and ethically questionable. Instead, we supplemented our large scale observational study with a small scale seed addition experiment. Our experiment revealed that natural recruitment of fig seed lings of both F. aurea and F. microcarpa is extremely rare, supporting the interpretation of our models that juvenile fig abundance largely reflects seed limitation. We observed a positive correlation between invasive plant abundance and human land use, c onsistent with many previous studies (Burton et al. 2005, Bradley and Mustard 2006, Seabloom et al. 2006) We incorporated fig eating bird habita t quality, reflective of human land use, into either the dispersal or the survival term of our models for juvenile fig abundance. For F. microcarpa, models with fig eating bird habitat around individual adult trees in the dispersal term fit better than mo dels with fig eating bird habitat around the juvenile plot in the survival term. These results are reflected in Fig 2 2 (top left panel), which shows that an increase in fig eating bird habitat results in increased juvenile F. microcarpa abundance only if adult trees are present. Examination of the parameterized dispersal term for F. microcarpa reveals that adult
34 trees surrounded by little favorable bird habitat contribute almost nothing to juvenile abundance, even if the adult is close to the juvenile pl ot (Fig 2 3). Previous studies on wind dispersed plants have shown that local neighborhood effects of tree density (Schurr et al. 2008) and spatial distribution of gaps (Bergelson et al. 1993) may change seed dispersal distances and ultimately rates of range expansion In both of these studies, the scale used to examine the effects of environment on dispersal was less than 10 m. In comparison, when F. microcarpa adults are located in landscapes with high fig eating bird habitat, our models suggest that even trees 300 m away from the juvenile plot have an effect on juvenile F. microcarpa abundance (Fig 2 3). For animal dispersed species, the scale at which landscape configuration affects dispersal may be much larger than for wind dispersed species, highlighting the nee d to consider frugivory as a component of invasive plant spread (Buckley et al. 2006) A limitation of our study is that data on seed dispersal by the bird species we observed eating figs, including quality of seed disper sal provided by each species, and daily movement patterns in different landscapes, were not available. More research on bird seed dispersal, including seed dispersal kernels for bird species that disperse invasive plants (e.g. Weir and Corlett 2007) could lead to more mechanistic models for invasive plant spread. The best models predicting the abundance of juvenile F. aurea were very different than the best models for F. microcarpa Instead of models incorporating favorable bird habitat and distance to ad ult trees, models with presence/absence of conspecific adults best predicted juvenile F. aurea abundance. The best models for F. aurea had relatively poor fits to the data, with the highest R 2 values for predicted vs.
35 observed values less than 40%, compar ed to 74% for the top F. microcarpa models. The relatively weak correlation between adult F. aurea trees and juveniles can also be observed in Fig 2 2. Out of 16 plots with zero adult F. microcarpa within 300 m, only one plot contained a single F. microca rpa juvenile, while out of 18 plots with zero F. aurea adults, seven contained F. aurea juveniles. How can these results be reconciled with our seed addition experiment which showed no significant differences in seed limitation between F. aurea and F. mic rocarpa? Seed limitation is a combination of multiple factors, including tree fecundity, the density and dispersion of seed sources and seed dispersal (Clark et al. 1998) For F. microcarpa, an invasive plant at the edge of its rapidly exp anding range, distance to individual seed sources, which are comparatively few, may be crucial for juvenile abundance. For F. aurea with a higher mean density of adult trees within an established range, seed arrival into cabbage palms may still be limite d by the overall fecundity and density of adult trees, but less limited by distance to any single individual tree. These results highlight the potential complexities underlying the concept of seed limitation; although seed addition experiments are a usefu l tool for quantifying the degree of seed limitation, observational data may still be valuable for determining whether seed limitation is a result of adult tree density, fecundity, or seed dispersal. Range expansion of many invasive plants requires seed d ispersal by animals, which are likely to deposit most seeds less than a kilometer from the parent plant (Clark et al. 1999) Yet, invasive plant range expansion also entails distributional shifts at much larger scales as populations move from the locus of introduction, often an urban area, into other landscapes. Ultimately, quantifying the relationship between landscape
36 context and seed dispersal could lead to better techniques for controlling invasive species. Our study suggests that the most effective strategy to reduce invasive fig recruitment would be to remove F. microcarpa adult trees located in landscapes with a high amou nt of fig eating bird habitat, rather than targeting all adult trees equally or restricting human land use regardless of adult tree abundance Table 2 1. Data used to determine terms in Equation 2 1 Term 1. Data used to represent term Scale of data Subs trate Number of cabbage palms 30 m x30 m juvenile plots Seed dispersal Distance to adult trees (Dist) 300 m radius centered around juvenile plot Fig eating bird habitat around adult trees (Adult.hab) 300 m radius centered around every adult tree Pres ence/absence of adult trees (PA) 300 m radius centered around juvenile plot Survival Canopy cover (CC) 30 m x 30 m juvenile plots Fig eating bird habitat around center plot (Juv.hab) 300 m radius centered around juvenile plots
37 Table 2 2. Model sele ction results for F. microcarpa and F. aurea Model F. microcarpa F. aurea Seed dispersal term Survival term df AIC c R 2 AIC c R 2 Adult.hab/Dist CC 5 0.00 0.73 14.86 0.18 1/Dist 4 2.96 0.70 14.44 0.22 Adult.hab/Dist 4 3.34 0.69 12.43 0.21 1/Dist Juv.hab+ CC 6 5.37 0.7 11.46 0.32 1/Dist 4 8.45 0.65 13.05 0.17 1/Dist Juv.hab 5 9.69 0.68 14.93 0.24 PA CC 4 13.42 0.48 0.00 0.43 PA Juv.hab+CC 5 14.99 0.55 2.63 0.43 PA 3 24.38 0.29 0.63 0.39 PA Juv.hab 4 24.87 0.37 1.79 0.41 Note : Abbreviations correspond to terms presented in Table 2 intercept only survival term. The total num ber of parameters in the model is indicated by the column labeled df. Figure 2 1. Map of study region and scale of observational plots
38 Figure 2 2. Predictors of j uvenile fig abundance. A) F. microcarpa abundance and fig eating bird habitat, B ) F. microcarpa juvenile and adult presence, C) F. aurea abundance and fig eating bird habitat, D) F. aurea juvenile and adult presence. Filled and open circles indicate plots where adult conspecific figs were present and absent, respectively. A B C D
39 Figure 2 3. Predicted contribution of adult trees to j uvenile fig abundance Each curve, eating bird habitat quality, spanning the range of values observed in the data.
40 CHAPTER 3 THE IMPORTANCE OF LONG DISTANCE SEED DISPERSAL FOR THE DEMOGRAPHY AND DISTRIBUTION OF A CANOPY TREE SPECIES Background Adult recruitment of seeds dispersed long distances can have major consequences for plant population and community dynamics. For example, historic rates of lo ng distance seed dispersal (LDD) may explain the current distribution and diversity of many tree species (Svenning and Skov 2007, Lesser and Jackson 2013) Because LDD can enable range expansion of invasive species (Neubert and Caswell, 2000) plant migration in response to climate change (Corlett 2009) and species persistence in fragmented landscapes (Uriarte et al. 2011) understanding LDD is also relevant for conservation and management (McConkey et al. 2012 Trakhtenbrot et al. 2005). Recent advances in quantifying seed dispersal have revealed that LDD on the scale of kilometers may be r elatively common (Cain et al. 2000, Nathan 2006) However, any effects of LDD on plant distributions depend on the establishment of long distance dispersed seeds into adults, a process spanning many years and transitions between multiple life stages for long lived plants. LDD, which we define as dispersal beyond the spatial scale of the local patch (sensu Muller Landau et al. 2003) could have both costs and benefits for adult recruitment. Movement beyond the local patch may allow seeds to escape high resource competition (Amarasekare 2003) or specialized pests (Fragoso et al. 2003, Muller Landau et al. 2003 ) leading to higher establishment for seeds dispersed long distances. However, LDD may be costly if seeds are dispersed out of favorable habitats and into unfavorable habitats, leading to lower establishment compared to seeds dispersed short distances (Snyder and Chesson 2003, Kremer et al. 2012) As an
41 extreme example, long distance dispersal for terrestrial plants on oceanic islands would be disadvantageous because most seeds dispersed into the ocean would di e (Cody and Overton 1996) Lower survival and growth for seeds dispersed into habitats with few conspecifics present has been observed in forest and savannah (Hoffmann et al. 2004) landward and seaward habitats in sand dunes (Keddy 1982) and forest habitats in different successional states (Losos 1995) Thus, while paleoecological data, theoretical models and data from invasive plant range expansion d emonstrate the consequences of successful LDD events, there are also likely to be many cases where LDD fails to result in established adults. Connecting the fate of LDD seeds to the distribution and abundance of plants requires estimating the degree to whi ch populations are limited by rates of seed arrival vs. establishment (Muller Landau et al. 2002) If low seed arrival limits adult abundance, the population is considered seed limited: i.e., some sites remain unoccupied due to lack of seed arrival rather than competition or suitable habitat (Hurtt and Pacala 1995, Turnbu ll et al. 2000, Clark et al. 2007) On the other hand, if survival and growth after seed arrival limit adult abundance, the population is considered establishment limited. Seed limitation is typically estimated from seed addition experiments, (Munzbergova et al. 2006, Clark et al. 2007) or by comparing spatial patterns of natural seed arrival to spatial patterns of plant abundance, with the degree of positive correlation indicating the degree of seed limitation (Muller Land au et al. 2002) Both of these methods are logistically challenging at spatial scales relevant to LDD. Seed addition experiments at large spatial scales require collecting and placing huge amounts of seed, and quantifying natural rates of seed arrival a t long distances from
42 source populations is hindered by the rarity of LDD events (Clark et al. 1998) Consequently, few studies have quantified the relative importance of seed and establishment limitation at varying distances from a source population, the essential question underlying the potential for LDD to impact plant distributions (Diez 2007, Moore et al. 2011) Patchy distributions of a given species could be a result of either seed or establishment limitation (Moore et al. 2011) This distinction is important for theoretical questions of species coexistence because if spatial patterns of dispersal alone can generate patchiness, there is no need to invoke habitat specialization (increased establishment in particular habitats) as a mechanism for coexistence (Clark et al. 2007). Understanding the causes of patchiness also relates to biod iversity conservation in heterogeneous landscapes, such as managing woody encroachment into savannah (H offmann et al. 2012) If LDD seeds are able to establish into adults outside the source patch in these landscapes, chance LDD events and local extinction could result in stochastic shifts in tree distributions over time. One example of a tree population in a landscape with distinct habitat boundaries is Miliusa horsfieldii, a canopy tree species, which at our study site in Thailand is abundant in evergreen forest and rare in deciduous forest (Baker 1997) This distribution could be due to spatially heterogeneous seed arrival, with low rates of LDD leading to seed limitation in the deciduous forest, or to spatially heterogeneous establishment, with low survival and growth in deciduous forest restricting recruitment to evergreen forest. We quantified the importance of LDD in t he current distribution of Miliusa by using a unique large scale dataset on demography to estimate seed and establishment
43 limitation at varying distances from a source population of trees in evergreen forest. We then used an individual based model (IBM) t o integrate our spatial data on demography and dispersal into a dynamic framework, allowing us to conduct simulation experiments and compare results to the observed distribution of plants. We use the IBM to ask two questions: (1) how does the probability of sapling establishment differ between seeds dispersed long vs. short distances? And, (2) is the current distribution of seedlings better predicted by observed rates of seed arrival or establishment? Our novel approach provides new insight into the demogr aphic mechanisms that underlie the importance of LDD for tree distributions, enabling us to fill the knowledge gap between long distance seed arrival and abundance of established plants. Materials And Methods Study site The study site, the Huai Kha Khaeng Wildlife Sanctuary (HKK), located in western Thailand, is part of the largest intact forest complex in mainland Southeast Asia, and still contains viable populations of large mammalian seed dispersers (Bunyavejchewin et al. 2004) The landscape is a mosaic of three forest types: seasonally dry evergreen forest, mixed deciduous forest, and dry deciduous forest. These forest types are characterized by differences in canopy height and openness, understory vegetation and tree diversity (Baker 1997) Mosaics of these forest types are characteristic of many other sites in mainland Southeast Asia (Blanc et al. 2000, Tani et al. 2007) Study species Miliusa horsfieldii is one of the dominant species in seasonally dry evergreen forest at HKK (Buny avejchewin et al. 2004) reaching heights to 35 meters (Baker 1997)
44 and fruiting from June July. Each roughly spherical fruit is ~20 mm diameter and contains 1 5 seeds (average = 3.8) with an average diameter of 8.13 mm. Seeds are dispersed by mammals, including civets, macaque s and bears, with daily movement patterns on the scale of kilometers (Kitamura et al. 2002, Ngoprasert et al. 2011) Thus, we consider the scale of LDD for Miliusa to be >1 km. Rates of secondary seed dispersal for Miliusa at our study site are negligible (Wheeler 2009) For further details on the stu dy site and species, see Appendix C. Study design Our study consisted of three steps (Fig. 3 1). First, we collected demographic data on seeds and seedlings across a gradient from evergreen to deciduous forest. We then used these demographic data to para meterize statistical models for demographic transitions, and finally, we used the statistical models as input for a dynamic individual based model (IBM) to predict seedling distributions. Data were collected in 93 24 x 24 m plots, randomly located along a 5 kilometer transect (Fig. 3 2). Because statistical models and IBM output incorporated plot specific predictor variables, we were able to examine changes in seed arrival, sapling establishment and seedling distribution at varying distances from a source population of Miliusa in seasonally dry evergreen forest. Establishment We consider establishment as the sequence of demographic transitions beginning with seed germination and ending at the sapling stage, with saplings defined as trees >1.6 m high, a siz e threshold for surviving ground fires that occur roughly every 5 10 years at our study site (Baker et al. 2008) A challenge for quantifying seedling demography where adult trees are absent is that seedlings are extremely rare.
45 Therefore, in June 2009 we experimentally added the same number of seeds (65), in piles o f 5, 15 and 45, to each of the 93 plots. A pilot study in which the fate of individual seeds was tracked over time revealed that three months after seed dispersal in June July, all seeds have either died or become seedlings (Appendix C). Thus, we checke d experimentally placed seeds for germination three months after seed placement and Because seedlings generated from the seed addition experiment constitute a small siz e, we also monitored survival and growth of naturally occurring seedlings using an adaptive sampling scheme, such that area sampled increased in plots where seedlings were rare. This scheme enabled us to census naturally occurring seedlings across a range of sizes from all regions of the gradient, even in the deciduous forest where natural abundance was very low. We measured these naturally occurring seedlings annually from 2009 2011, yielding n=1443 for survival data and n=819 for growth data. We used a hierarchical Bayesian approach to model germination, new recruit height, seedling survival and growth as a function of environmental covariates measured within each plot, including presence of grass, light availability and conspecific density (see Appendi x C for description of covariates). These variables were selected because they strongly influence seedling demography in similar systems (Hoffmann et al. 2004, Comita et al. 2010) We included plot as a random effect in all models, representing unaccounted for spatial variation. For seedling survival and growth, we also included seedling height as a continuous predictor variabl e. Germination and survival were modeled as binomial random variables, and new recruit height and growth
46 were modeled as normal random variables. A full description of these statistical models is provided in Appendix D. Seed arrival Estimates of plot spe cific seed arrival are required to understand and model the dynamics of seedling distributions. However, direct estimates of seed dispersal are impractical at long distances (> 1 km) from source trees, due to the low density of seeds dispersed long distan ces. Indirect estimates based on counts of established seedlings are also problematic because different combinations of establishment probability and seed rain can result in similar seedling abundance (Caughlin et al. 2012) We addressed this problem using direct observations of germination probability (from the seed addition experiment described above) and fruit product ion (see below), in addition to counts of naturally established recruits, to simultaneously estimate parameters describing seedling establishment, fecundity, and seed dispersal using a hierarchical Bayesian modeling approach. The combined model predicts t he abundance of naturally established recruits in 1723 1 m x 1 m quadrats, with 737 quadrats located within the 93 plots along the 5 km transect, and an additional 986 quadrats located within 124 plots in an adjacent 50 ha forest dynamics plot (Fig. 3 2; Appendix D). Abundance of newly recruited seedlings (three months after seed arrival) was modeled as a Poisson distributed random variable with a mean equal to a germination probability multiplied by seed arrival where the index k represents quadrats, and the index j represents plots. ( 3 1)
47 In E quation ( 2 1), is directly estimated from the seed addition experiment data. The seed arrival term includes seed arrival from nearby adult trees in a 20 m neighborhood ( ) and from seed sources outside of the local neighborhood ( ), and a plot level random effect : ( 3 2) The Nhood term was parameterized with data on counts of fruit production in fruit count quadrats beneath trees, scaled to represent total fruit p roduction by tree canopy area (Appendix D). The second component in E quation 3 2 represents dispersal from seed sources outside the 20 m neighborhood. Because adult tree abundance decreased along the transect, was a Gaussian function of linear distance along the transect. Finally, the sum of the Bath and Nhood terms was multiplied by a random effect, distributed as a lognormal random variable with a mean of 0 on the log scale. This plot level random effe ct, represents unexplained plot scale variation in seed arrival (e.g., due to plot location relative to movement paths of seed dispersing animals). We used a Markov Chain Monte Carlo algorithm in JAGS v. 3.2.0 (Plummer 2003) to generate samples from the joint posterior distribution of the seed arrival model ( Equation 3 1). Posterior samples for seed arrival to each plot ( ), which propagate uncertainty in seedling establishment and fruit production, were one of the key inputs to the IBM described below (see Appendix D for more details). Individual based model (IBM) The purpose of the IBM was to combine the s tatistical models for seed arrival, germination, new recruit height, and seedling survival and growth into a single dynamic
48 model for seedling abundance. All of these components stochastically simulate individual behavior. The IBM tracks size and survival of individual seedlings in 737 of the 1 m x 1 m quadrats at the center of the 93 plots across the 5 km transect. Each quadrat is matched with environmental covariates (grass, light, conspecific adult density, and plot level random effects), measured in 2 011. With the exception of conspecific seedling density, these environmental covariates were assumed to remain constant throughout the IBM simulations. During each time step, the IBM simulates seed arrival in each quadrat, followed by germination of thes e seeds, assignment of new recruit height to new recruits (3 month old seedlings), first year survival of new recruits and survival and growth of existing seedlings (those seedlings surviving from the previous time step) (Fig. 3 1). All parameters used in the IBM come from the demographic models and were estimated with field data. For each IBM experimental treatment (see below), we randomly drew 1000 parameter sets from the posterior distribution of parameters, and ran the IBM 100 separate times for each of these 1000 unique parameter sets (see Appendix D for more details). Thus, IBM output accounts for both parameter uncertainty and demographic stochasticity (Clark 2005, Evans et al. 2010) We used the IBM for two separate simulation experiments. The first projected the probability of sapling establishment in a 15 year time period fo r a single seed added to each quadrat. At the end of the period, we determined whether the seed had become a 1.6 m high sapling. This first experiment allowed us to combine the statistical models for germination, new recruit height and seedling survival and growth to estimate sapling establishment rates per plot, while propagating uncertainty in parameter estimation.
49 The second simulation experiment was designed to test whether seed or establishment limitation best explains the current distribution of se edlings. This simulation experiment had three treatments: (1) a full treatment with quadrat specific establishment and seed arrival, (2) a homogenous establishment treatment in which seed arrival was quadrat specific, but establishment (including survival growth, germination and new recruit height) was averaged across all quadrats, and (3) a homogenous seed arrival treatment, in which establishment was quadrat specific but each quadrat received the average number of seeds per quadrat. If differences in s eed arrival, and hence seed limitation, are most important for determining the observed pattern of seedling distribution, we would expect the treatment with homogenous seed arrival to have a worse fit to the observed data than the model with homogenous est ablishment but variable seed arrival. In contrast, if the observed pattern of seedling distribution is better explained by differences in establishment, we would expect the treatment with homogenous establishment to perform worse than the model with homog enous seed arrival but variable establishment. We compared output from the simulation experiment to observed abundance of both new recruits and older seedlings of a range of sizes. For comparison with the distribution of new recruits, we ran the IBM for a single time step, including only seed arrival and germination. For comparison with the distribution of older seedlings, we initialized the IBM with zero seedlings in all quadrats, and then simulated seed arrival and establishment for fifteen years. Com paring the relative predictive power of the full, homogenous seed, and homogenous establishment treatments for seedlings at multiple ages allowed us to leverage all our data and statistical models to determine the relative importance of seed arrival and es tablishment
50 for the distribution of seedlings. To compare IBM model output to observed data, we used mean squared predicted error (MSPE) as a minimum posterior predictive loss criterion (Gelfand and Ghosh 1 998) Results Conspecific seedling and adult density were highest in evergreen forest ~1 km along the transect, and then declined; after 3.2 km (in deciduous forest), no adults were recorded in any plots (Fig. 3 3), and after 2.1 km, seedling density sha rply decreased (Fig. 3 4). Hereafter, we refer to the region of high adult and seedling abundance light and grass presence showed high spatial heterogeneity within forest t ypes, but values of both covariates increased in deciduous forest (Appendix D). Vital rates of individual plants, including germination, new recruit height, and seedling survival and growth, revealed benefits for plants in deciduous forest at long distanc es from the source population in evergreen forest (Fig. 3 3). While effects of environmental covariates varied in significance and magnitude between life stages, models generally revealed a positive effect of grass presence and light, and a negative effec t of conspecific seedling and adult density (Appendix D). LDD had the strongest positive effect on germination rates; of the 6105 seeds in the seed addition experiment, 615 germinated to become new recruits, and most (>80%) of these new recruits were loca ted in deciduous forest plots at distances >2 km from the source population (Fig. 3 3). In contrast, new recruit height showed only a small increase in deciduous forest, with a mean of 5.21.42 cm, compared to a mean of 4.711.60 cm in evergreen forest. The 1443 naturally established seedlings represented sizes from new recruits to saplings, with a range of height from 3.5 cm to 180 cm, and a mean (SD) height of
51 18.314.0 cm. Seedling survival and growth were highest in deciduous forest and lowest in e vergreen forest (Fig. 3 3). However, models for seedling survival revealed that effect of seedling height outweighed any effect of location on survival. For example, in the plot with the lowest predicted survival, located within evergreen forest, estimate d survival probability of a 3 cm seedling had a median annual survival of 0.42 (CI 0.19 to 0.68), but for a 30 cm tall seedling in this plot, estimated annual survival increased to a median value of 0.97 (CI 0.90 to 0.99). Seed arrival Predicted seed arr ival was very heterogeneous, with several plots receiving many seeds and most receiving close to zero (Fig. 3 4). Specifically, seed arrival was low in deciduous forest at distances >2.26 km, with 308 out of 340 of these quadrats predicted to receive a me dian of <1 seed/m 2 Median seed production per tree ranged from 65 seeds (CI 39 133) for a 20 cm DBH tree to 14582 seeds (CI 10085 18875) for a 100 cm DBH tree. Only a small proportion of seeds per tree, 7.90e 05 (CI 1.90e 05 2.24e 04), were predicted to reach a 1 x 1 m quadrat within 20 m, reflecting the small size of this sampling unit. While the contribution to seed arrival from adult tree neighborhoods and sources >20 m from quadrats ( Bath term) was similar, with means of 0.3 (CI 0 1.5) and 0.4 (CI 0 0.6) seeds, respectively, the plot level random effect disproportionately increased seed arrival for quadrats with few adult trees within 20 m, leading to several plots with large numbers of seeds predicted to arrive from the Bath term (Fig. 3 4).
52 IBM results Experiment 1: After simulating survival and growth of single seeds for fifteen years, 45% of quadrats had a mean probability of sapling establishment > 0.01. Strikingly, 85% of the 261 quadrats located in evergreen forest had a mean probability of sapling establishment <1%, suggesting that sapling establishment in this habitat is highly unlikely, even though evergreen forest is where adults and seedlings are most abundant (Fig. 3 4). Sapling establishment was highest in deciduous forest long dis tances from the source population, with a mean establishment probability >1% for 75% of 340 quadrats >2.26 km, and 29 long distance quadrats had mean establishment probabilities >10%. Experiment 2: Comparison of predicted seedling distribution from the IB M suggests that seed arrival is a more important determinant of seedling abundance than is establishment for both new recruits and older seedlings (Fig. 3 5). For both of these life stages, the full model, with quadrat specific estimates of seed arrival a nd establishment, had the lowest mean squared predicted error (MSPE), with a relatively small increase in MSPE for homogenous establishment but quadrat specific seed arrival, and large increases in MSPE for models with homogenous seed arrival but quadrat s pecific establishment. The proportional increase in MSPE between the full model and the homogenous seed model was 4.32 for the 15 year simulation, compared to a proportional increase of 3.05 for the new recruit simulation, meaning that spatially heterogen eous seed arrival was more important for explaining the abundance of older plants than new recruits.
53 Discussion Our results suggest that the distribution of Miliusa horsfieldii, a canopy tree species in a landscape mosaic of forest types, is constrained by low rates of long distance seed dispersal (LDD). At our study site, Miliusa seedlings and adults are abundant in evergreen forest and near absent in deciduous forest. Individuals in deciduous forest, far from the source population, experienced multiple benefits -increased germination rate, new recruit height, seedling survival and growth -from being in a habitat where conspecifics were almost absent (Fig. 3 3). The net effect of these spatial differences in demographic processes is that estimated sapling establishment probabilities 15 years after seed dispersal are highest for seeds dispersed long distances (Fig. 3 4). Nevertheless, Miliusa is rare in the deciduous forest because the spatial pattern of seed arrival is much more important for expl aining observed seedling distributions than is the spatial pattern of establishment, even after fifteen years (Fig. 3 5). These results demonstrate that LDD is likely to play a major role in structuring the distribution of this long lived tree in its nativ e landscape. The IBM experiments suggest that arrival of even single seeds long distances from the source population can impact Miliusa distributions, with a mean probability of sapling establishment 15 years after seed dispersal of 0.5% for LDD seeds (Fi g. 3 4). Consequently, quantifying rates of rare long distance seed dispersal events is critical for understanding plant population dynamics (Cain et al. 2000, Nathan 2006) Direct estimates of such events are logistically difficult, r egardless of method (Nathan et al. 2008) Our approach demonstrates a solution: use of hierarchical Bayesian models to estimate seed arrival from data on seedling abundance and germination Our model fo r seed dispersal reveals that while overall rates of LDD are very low, random plot level
54 variability in seed arrival is high, suggesting that some plots are likely to receive far larger numbers of seeds than other plots, regardless of neighboring trees or distance from source population. These results could be explained by movement patterns of the large mammals that disperse Miliusa seeds, including civets, and bears, which can have daily movements >5 km (Rabinowitz 1991, Corlett 2009) and heterogeneous patterns of dispersal with high seed deposition under trees where some of these dispersers sleep, in latrines or along game trails (Corlett 1998, Nakashima et al. 2010) A common criticism of using seed addition experiments to detect seed limitation is that the importance of seed arrival is likely to decrease over time for long lived species, due to spatial differences in demographic performance between life stages (Schupp 1995) density dependence at later life stages (Kauffman and Maron 2006) or simply the loss of the pattern of initial seed dispersal from accumulation of chance mortality over time (Clark et al. 2007) We used an IBM to compare observed seedling distributions with predicted seedling distributions and evaluated how much worse model fit would be if seed arrival or establishment was homogenous across quadrats, rather than spatially variable. We found that even after 15 years of simulated demography, homogenous seed arrival resulted in a worse fit to the observed distribution of seedlings than homogenous establishment, suggesting that spatial patterns of seed dispersal have ecological relevance for at least 15 years. This surprising result is a consequence of both low rates of LDD (Fig. 3 4) and high rates of establishment for L DD seeds (Fig. 3 3). If establishment rates were highest where most seeds arrived, homogenizing seed arrival across plots would not result in drastic differences from the observed
55 distribution of seedlings because low establishment would limit seedling ab undance in long distance plots, even if seeds arrived. Understanding the dynamics of tree distributions in heterogeneous landscapes, such as the seasonally dry forests of Southeast Asia, is crucial for maintaining landscape biodiversity (Rabinowitz 1990 p. 199) Although our results suggest that the seedling distribution of Miliusa is determined largely by where seeds arrive, they raise a larger question: why is the population of Miliusa, including adult tree s, found in evergreen but not in deciduous forest at our study site? One possibility is that rare events such as fire or drought may have a larger negative effect in deciduous forest than in evergreen forest, ultimately restricting seedling and adult esta blishment in the former habitat. Our period of demographic monitoring did not include any such events; consequently, our models assume a constant environment and we cannot make inferences about stochastic events. Nevertheless, our results suggest that sa pling establishment in the deciduous forest is possible in a 10 15 year time period under current conditions, a period that is within the realm of possibility for a fire free interval, considering there has been no wildfire at our site since 2004 (Baker et al. 2008) Alternately, the distribution of Miliusa trees in t he landscape could be driven by a stochastic combination of historic fire occurrence and chance seed dispersal events, an expectation supported by a disparate set of studies including remote sensing (Johnson and Dearden 2009) seedling transplant experiments (Baker 1997) and tree ring analysis (Baker et al. 2005) Our study provides insight into how LDD may be a demographic mechanism underlying stochastic changes in plant specie s distributions at HKK.
56 The importance of LDD for biodiversity conservation is expected to increase with habitat fragmentation and shifts in habitat suitability as a consequence of climate change (Trakhtenbrot et al. 2005, Corlett 2009) For East Asia, climate change projections for the next 100 years suggest that movement on the scale of 1 3 km per century may be required for plant species to successfully track climatic conditions (Corlett 2009) Our results demonstrate that even for a species dispers ed by long ranging mammals, the rarity of LDD may be a major barrier to distributional shifts. Finally, our results directly show that changes in the spatial pattern of LDD can have a large effect on seedling distributions. Human actions that alter rates of LDD, such as overhunting of seed dispersing mammals with long range movements, will likely have significant consequences for plant species
57 Figure 3 1. Overview of study design, showing data and statistical models used as input to the individual bas ed model (IBM) that simulated seedling distributions. Thin black arrows between the three large rectangles represent connections between the data, statistical models and IBM. Gray dotted arrows in the statistics rectangle represent connections between the statistical models used to estimate seed dispersal. The bottom rectangle shows the processes (diamonds) and counts of seeds, seedlings and saplings (small rectangles) simulated by the IBM.
58 Figure 3 2. Map of study region including the transect with the 93 demographic plots, and additional 124 plots located within the 50 ha forest dynamics plot that were used for natural seedling demography and new recruit abundance data. The labels 0 and 5 km indicated the beginning and end of the transect, and corr espond to the x axis in Figures 3 3 and 3 4.
59 Figure 3 3. Miilusa demography and distribution along transect. A) Observed adult abundance, B) G ermination rate, C) A nnual seedling survival and D) A nnual seedling growth Dashed gray lines represent boundaries between evergreen and deciduous forest types. A B C B D
60 Figure 3 4. Seedling density and predicted rates of sapling establishment and seed arrival along transect. A) naturally established seedling density/m 2 with gray dots representing new rec ruits and black dots representing older seedlings, B) median probability of sapling establishment 15 years from present for each of 737 quadrats, C) number of seeds/m 2 predicted to arrive along the transect in a single fruiting season, with the black polyg on indicating total seed arrival and the gray polygon indicating contribution of adult trees within 20 m to seed arrival (term Nhood in Equation 3 2). Dashed gray lines represent boundaries between forest types. Distances > 3 km along the transect can be considered long distance dispersal. A C B
61 Figure 3 5. Mean squared predicted error (MSPE) for IBM prediction of seedling distribution along transect A) new recruits, B) older seedlings. Boxplots represent how well the IBM treatments predicted the distribut ion of newly recruited seedlings and older seedlings from the 15 year simulation. MSPE was calculated for each of 100,000 runs of the IBM, and variation in the MSPE values is a result of parameter uncertainty and demographic stochasticity. Large MSPE val ues represent a worse fit between predicted and observed data. The thick black line represents the median, the top and bottom of the box represent the minimum and maximum observations within 1.5 times the upper quartile, and circles represent outliers. B A
62 CH APTER 4 THE DEMOGRAPHIC IMPORTANCE OF SPATIAL STRUCTURE THROUGHOUT THE LIFE CYCLE OF A TROPICAL TREE SPECIES Introduction The role of seed dispersal in tree population dynamics has crucial implications for the species composition of forests in a changing w orld (Corlett 2009, Harrison et al. 2013) Seed dispersal determines the location a tree will experience for the rest of its life and thus sets the spatial template for all subsequent vital rates (Wang and Smith 200 2, Howe and Miriti 2004) Yet the demographic importance of seed dispersal remains uncertain, and few studies have quantified how the spatial template set by seed dispersal affects multiple life stages, and ultimately, population dynamics, for long live d plant species (Brodie et al. 2009, Swamy and Terborgh 2010) Size structured population models for long lived plants nearly always lead to the e stablishment is low, compared to adult survival (Alvarez Buylla et al. 1996, Franco and Silvertown 2004) However, models that consider size as the only determinant of tree vital rates may yield deceptive results because there can be large differences in survival, growth, and contribution to population growth rate between similar sized individuals (Zuidema et al. 2009) Persistent differences i n vital rates between individuals of the same size can result from tree location; the initial light environment of saplings, for example, can result in large differences in life expectancy among individuals (Metcalf et al. 2009) In such cases, the minority of seeds that are dispersed to favorable locations (e.g. tree fall gaps) may have a far larger im pact on population growth rate than all other seeds Alternately, if size determines vital rates reg ardless of location or if some locations are advantageous for certain life stages but
63 disadvantageous for others (Schupp 1995) the spatial template set by seed dispersal may have only minimal effects on demography. Distinguishing between these possibilities requires evaluating spatial differences in vital rates acr oss multiple tree sizes and stages. A spatial variable likely to have a strong effect on tree vital rates is conspecific density (Terborgh 2012). Negative density dependence (NDD) here defined as a reduction in growth or survival or both with increased conspecific density at spatial scales of 0 20 m is expected to play a large role in regulating populations of tropical trees (Janzen 1970, Harms et al. 2000, Peters 2003) Seed dispersal sets the spatial structure on which NDD initially operates, with strongest effects close to the parent tree, where most se eds are dispersed (Clark et al. 1999, Muller Landau et al. 2008) For subsequent life stages, spatial structure is determined both by the initial template of seed dispersal and by the spatial pattern of mortality. Spatially explicit models for plant population dynamics without size structure have shown that the spatial scale of seed dispersal relative to the spatial scale of NDD is crucial for determining plant population d ensity (Bolker and Pacala 1 999, Law et al. 2003) A recent theoretical model with two discrete stage classes has revealed that aggregation can either increase or decrease for later stages, depending on rates of growth, fecundity and neighborhood competition, indicating the potenti al importance of size structure for spatial population dynamics (Murrell 2009) Despite the expectation from size structured models that early li fe stages should be relatively unimportant for population dynamics (Franco and Silvertown 2004) empirical research on NDD in tropical forests has mostly focused on seeds ( e.g. Harms et al. 2000) and seedlings ( e.g. Comita and Hubbell 2009) although
64 several studies have also detected NDD for later tree life stages, including saplings (Peters 2003, Uriarte et al. 2004) and adult trees (Hurst et al. 2011) However, no empirical study that we are aware o f has compared the demographic consequences of NDD among seeds, seedlings and trees. Determining the importance of spatial processes for tree population dynamics has critical implications for conservation because overhunting of large bodied frugivores in t ropical forests reduces seed dispersal, increases spatial aggregation, and decreases recruitment rates for animal dispersed trees (Corlett 2007, Cordeiro et al. 2009, Harrison et al. 2013) The long generation time of trees necessitates model projections to assess consequences of disperse r loss for population dynamics. A matrix model analysis of an animal dispersed tree species in which loss of seed dispersal was assumed to affect vital rates of only seeds and seedlings, concluded that local extinction of large bodied dispersers resulted in only slight decreases in the population growth rate (Brodie et al. 2009) If increases in spatial aggregation due to loss of dispersers increase NDD and de crease survival and growth throughout the entire life cycle, this type of matrix model may greatly underestimate the impact of disperser loss. Because the problem of disperser loss is inherently spatial, spatially explicit models will be required to unders tand the demographic consequences of changes in seed dispersal. We quantified the demographic importance of spatial structure for a canopy tree in a tropical forest of western Thailand. Our study species, Miliusa horsfieldii (Annonaceae), is a dominant c omponent of the canopy at our study site, and has seeds dispersed by long ranging, large bodied mammals, including bears, civets and primates, which have been extirpated from many other forests in the region (Corlett 2007) Our
65 stud y is unique because we combine spatial and demographic data on early life stages of Miliusa, including seed production by adult trees, seed dispersal, seed germination and seedling growth and survival, with a dataset spanning 10 years of census data on tre es > 1 cm DBH. We used these data to parameterize statistical models for the effect of NDD and size structure on vital rates for all life history stages, from seeds to adults. We then used our statistical results to construct a spatially explicit individu al based model (IBM), which we used to evaluate the relative importance of seed dispersal, NDD and size structure for tree population dynamics. Finally, we constructed a version of the IBM with no animal seed dispersal, representing a scenario in which ani mal seed dispersers are hunted to extinction, and compared the probability of extinction between natural (observed) dispersal and no dispersal scenarios. By evaluating the importance we aim to provide novel insight into the link between seed dispersal and tree population dynamics. Materials A nd Methods Study site The study site, the Huai Kha Khaeng Wildlife Sanctuary (HKK), is located in western Thailand and part of the largest intac t forest complex in mainland Southeast Asia. It still contains viable populations of large mammalian seed dispersers, including gibbons, bears and elephants (Bunyavejchewin et al. 2004) Mean annual rainfall is ~1500 mm, with a 5 6 month dry season from November April. Our study site is centered around a 50 ha Forest Dynamics Plot in which all w diameter at breast height (DBH) have been tagged, mapped, and measured every five years since 1994, according to Center for Tropical Forest Science standard protocols (Bunyavejchewin et al. 2004)
66 Study species Miliusa horsfieldii is a canopy tree species in the Annonaceae family that reaches heights of 35 meters (Baker 1997). It is a dominant species in the 50 ha Forest Dynamics Plot, with the most stems >10 cm DBH of any tree species and the second highest basal area (Bunyavejchewin et al. 2004) From June July, Miliusa produces roughly spherical fruits ~20 mm in diameter, each with 1 5 seeds and an average seed diameter of 8.13 mm (Wheeler, 2009). Seeds are disper sed by large mammals, including gibbons, civets and bears (Kitamura et al. 2002, Wheeler 2009, Ngoprasert et al. 2011) Rates of secondary seed dispersal at our study site are negligible, and there is no seed bank: three months after dispersal, all seeds have either germina ted or died (Wheeler 2009) Miliusa produces shade tolerant seedlings which form a long lived seedling bank in the understory (Baker, 1997; Caughlin in review) Demographic data We parameterized our statistical models using spatially explicit data on Miliusa seed germination, and survival and growth of seedlings and trees >1cm DBH. We any individual> 1 cm DBH. Survival and growth data on trees come from a 1 5 year dataset from the 50 ha forest dynamics plot in which 2,049 Miliusa individuals were marked, measured and mapped to the nearest 0.1 centimeter in between 1994 and 2009. Survival and growth of seedlings were determined from 1,600 tagged seedlings cen sused annually from 2009 to 2011. Seedling growth was measured as the annual change in seedling height (cm). Data on seed germination were collected using a seed addition experiment in 2009, in which 6,500 marked seeds were added to 95 plots and monitore d for survival until all seeds had either germinated or died (see Caughlin et al.
67 2013 for details). We quantified conspecific neighborhoods by mapping reproductive trees within 10 m of every seed addition plot, 20 m of every tagged seedling, and 25 m for all Miliusa trees. All conspecific seedlings were counted in 1 m x 1 m quadrats containing focal marked seeds and seedlings. Seed production was determined by counting fruit peels (indicating dispersed seeds) beneath adult trees to create a fecundity m odel (Appendix E, Equation E 7). These fecundity data were then paired with data on new seedling recruits and germination to parameterize a seed dispersal model (see Caughlin et al in review for details). We used a two T distributio n to model the seed dispersal kernel, with the degrees of freedom parameter set to three, because this distribution has previously been shown to provide a good fit to seed dispersal data from animal dispersed trees in tropical forests (Clark et al. 1999, Muller Landau et al. 2008) Models We used Bayesian statistical models to parameterize spatially explicit models for vital rates. These statistical models provided input to an IBM to simulate population dynamics. The IBM was used to quantify the demographic importance of seed dispersal, NDD and size structure as well as the probability of extinction in a scenario with no animal seed dispersal. Statistical models For each lif e stage (seeds, seedlings and trees), the goal of statistical analysis was to parameterize models for vital rates which included conspecific neighborhood and size as predictor variables. For all models, we included a term for conspecific neighborhood as a function of distance to each neighborhood tree and its DBH, scaled by the height or DBH of the focal individual ( Equation 4 1). This neighborhood function
68 has previously been used to quantify NDD for saplings in a tropical forest (Uriarte et al. 2004) and provided a better fit to the data than ot her funct ional forms. In the following E quation 4 1 represents the size of the focal individual, represents the DBH of the i th neighbor tree, represents distance from the i th neighbor tree to the focal individual, and and are free parameters determined from the data. Based on preliminary analyses, we parameterized the neighborhood function for tree survival and growth, using data on neighbors within a 25 m radius, seedling survival and growth using data on neigh bors within a 20 m radius, and seed germination using data on neighbors within a 10 m radius. (4 1) Fo r models of seed germination and seedling growth and survival, we also included conspecific seedling density (counts of seedlings in 1 m x 1m plots) as a predictor variable. We assumed that seedling density would have a negligible effect on trees and so d id not include conspecific seedling density in models of tree survival and growth. We modeled the effect of tree size on growth and survival of trees using the Hossfeld function ( Equation 4 2), which allows exponential increases in growth and survival for small to mid sized trees and declining growth and survival for large sized trees, a commonly observed pattern in tree populations (Hurst et al. 2011). High correlations between parameters R and P in Equation ( 4 2) resulted in extremely large credibility intervals for these parameters for both the survival and growth models. Consequently, we set R=2, based on a previous study of size dependent demography for six tropical tree species (Zuidema et al. 2010)
69 (4 2) For seedling survival and growth, statistical models included the heig ht of seedlings as a linear size term. Survival of trees, seedlings and seed germination were modeled as Bernoulli trials, with probability of survival equal to the logit transformed sum of the size function (for seedlings and trees), conspecific tree neig hborhood (for all life stages) and conspecific seedling density (for seedlings and seeds): Growth of trees and seedlings was skewed towards positive growth, but with some finite probability of negative values, and was thus modeled as a skew normal distributi on. We parameterized the skew normal distribution with mean, variance and skewness terms. Mean growth was assumed to be the product of functions for size (Hossfeld function for trees and linear for seedlings), tree neighborhood (all life stages) and consp ecific seedling density (seedlings): This model formulation provided a better fit to the data than additive models. Finally, we parameterized intercept terms (for seed and seedling models) and the P term in the Hossfe ld equation (tree models) as random effects to account for non independence between census periods (for tree data) and plots (for seed and seedling data). All random effects were modeled as draws from a normal distribution with a mean and standard deviati on estimated from the data. We parameterized each model using an MCMC algorithm run for 110,000 iterations with a burn in period of 10,000 iterations and 4 chains. We used non informative prior distr ibutions for parameters (Table E 2). Model convergence was
70 assessed by visually comparing output from chains and by using the Gelman Rubin diagnostic with a threshold of 1.1. We evaluated whether or not including NDD terms improved model fit by using a model selection procedure based on posterior predictive l oss (Gelfand and Ghosh, 1997). Individual based model The IBM connects the data, statistical models and initial spatial distribution of trees into a single dynamical framework. The IBM simulates the location, size and stage of individuals within a 200x 200 m (4 ha) plot in annual time steps. The IBM is set in continuous space, with x and y coordinates for each tree individual, using a toroidal surface. During each time step, the IBM stochastically determines survival and growth of existing trees and see dlings, production and dispersal of seeds, germination of seeds into seedlings, and the transition between seedlings and trees. All parameters in the IBM come directly from the statistical models (see previous section). The IBM was initialized with the s ize and location of trees in eight 4 ha subplots from the 1994 census of the 50 ha plot. Because seedlings were not censused over the entire plot, seedling density was initialized by running the IBM for eight years with dynamic seed production, dispersal, and seedling survival and growth, while leaving size and location of trees DBH unchanged. The IBM was run for 100 annual time steps. At each step, we recorded three different outputs: total population size, basal area and spatial aggregation. Total popul ation size includes the total number of seedlings and trees: thus, changes in total population size are equivalent to the (transient) population growth omass. Finally, we quantified spatial aggregation as the average density
71 population size, (see C ondit et al. 2000) This metric of spatial aggregation has the advantage of being simple to calculate over hundreds of thousands of runs of the IBM, and has been widely used for comparisons of spatial aggregation between tropical tree species (Condit et a l. 2000, Flgge et al. 2012) We used sensitivity analysis of IBM output to determine the relative importance of parameters representing NDD, seed disper sal, and size structure, for spatial population dynamics. Sensitivity analysis addresses the question of how perturbations in model parameters contribute to variability in model output. Local sensitivity analyses, such as taking the partial derivative of output with respect to an input parameter, are often used for analyzing matrix and integral projection models in demographic research (e.g., Franco and Silvertown 2004) but have the disadvantage of assuming linear rela tionships between parameters and output, which may lead to misleading results when relationships between parameters and output are non linear (Morris and Doak 2002) Thus, we used a global sensitivity analysis to perturb all parameters simultaneously, including input from the full parameter space and non linear responses (Ellner and Fieberg 2003, Fieberg and Jenkins 2005) We used variance based methods to decompose the variance in IBM output into main effects of parameters, r epresenting the additive effect of each parameter on output (Ellner and Fieberg 2003) Variance in parameter inputs for a global sensitivity analysis can be arbitrarily set at a particular scale, determined by expert opinion, or can originate from variability in the data (Fieberg and Jenkins 2005) Because all of the parameters used in our IBM come from Bayesian statistical models parameterized with field data, we used samples from
72 the posterior distribu tion of each parameter as input to the global sens itivity analysis. We ran the IBM for 10,000 times, each with a set of parameters randomly drawn from samples of the parameter posterior distributions, recording total population size, basal and IBM output both have a probabilistic interpretation, we were able to obtain sensitivities using numerical methods to marginalize parameter inputs over the IBM output. For these sensitivities ( we marginalized each parameter input, ove r the output and divided variance in this marginal distribution by the total variance in output Equation 4 3. Additional details on this method are provided in Appendix F. (4 3) These main sensitivities can be interpreted as a correlation ratio between parameters and output, and thus sum to one. Population Viability Analysis The sensitivity analysis provides insight into how population dynamics vary with the current biologically plausible scales of variation in parameters. To explore a future scenario in which animals no longer disperse Miliusa seeds, we constructed a version of the IBM in wh ich seeds are assumed to fall beneath the canopy of parent trees, using estimates of canopy allometry from the data (Appendix E, Equation E 10). We ran this extinction ov er 100 years between the no seed dispersal IBM and IBM with animal seed dispersal. The simulated area (4 ha) is too small to represent a tree population and our models do not include environmental stochasticity, such as year to year variation in vital rat es or occasional catastrophes. Therefore, following Morris and Doak (2003), we
73 interpret the population via bility analysis in terms of the relative risk of extinction between the two scenarios, rather than absolute extinction risk. Results Statistical mod els revealed the importance of both size and NDD for Miliusa vital rates. Fecundity increased with size, with a predicted median of 132 (95% CI 126 145) seeds produced for a 20 cm DBH tree, compared to a median of 7372 (95% CI: 7158 7584) seeds produced f or a 100 cm DBH tree (Fig. 4 1). Seedling survival and growth also increased with seedling height, with seedling survival reaching an asymptote near 100% for large seedlings. In contrast, the model for survival and growth of trees showed rapid increases in growth and survival for trees 1 20 cm DBH, then gradual declines in growth and survival for large trees (Fig. 4 1). Parameter estimates with 95% CI for all parameters are shown in Appendix E (Table E 3 ). We detected NDD for all sizes and life stages, a lthough the magnitude and spatial scale of NDD effects varied greatly between life stages (Fig 4 2.). Survival and growth models revealed a significant negative effect of tree neighborhood for all life stages except seedling survival, for which the model with tree neighborhood fit the data worse than the model with only size and conspecific seedling density. Consequently, the model used for seedling survival in the IBM did not include tree neighborhood. Conspecific neighbor trees caused the largest decre ases in germination rate and seedling growth, and statistical models predicted suppressed growth and germination even at distances >20 m from a large neighbor (Fig. 4 2). Growth and survival of trees also showed significant NDD, however, even for a large neighbor (90 cm DBH), NDD effects were predicted to be negligible at distances >15 m for tree growth and >5 m for tree survival. In general, larger individuals within stage classes were predicted to be
74 much less affected by NDD effects. One exception was tree growth mid sized trees (5 30 cm DBH) were predicted to experience the largest cost in growth near a neighbor, a pattern explained by the multiplicative interaction between the non linear Hossfeld term for size structure and the exponential term for N DD (Fig. 4 3). The spatial scale of seed dispersal was much larger than the spatial scale of NDD. While most seeds were predicted to be dispersed <50 m from neighbor trees, there was an appreciable amount of probability density of seed dispersal for distan ces>100 m (Fig. 4 2). For seeds and seedlings, conspecific seedling density in 1 x 1 m plots had strong effects on survival and growth, with germination predicted to be completely suppressed at conspecific seedling densities >10 seedlings/m 2 and seedli ng growth greatly suppressed at densities >20 seedlings/m 2 (Fig. 4 2). Seedling survival models predicted an appreciable negative effect of conspecific seedlings on seedling survival only at densities >100 seedlings/m 2 IBM results A consequence of th e larger spatial scale of seed dispersal than of NDD is that recruitment is suppressed around large trees, but areas with few reproductive adults quickly fill with seedlings and saplings (Fig. 4 4). Total population size tended to increase rapidly in the first 40 years, and then stabilized at ~25,000 individuals in the 4 ha plot (Fig. 4 5). Basal area generally declined over the 100 year per generally remained near one. However, parameter uncertainty generated wide variance in IBM output over 10,000 runs, with some runs exhibiting exponential population growth, overcompensatory dynamics and extinction (Fig. 4 5). The global sensi tivity analysis suggests that parameters for size structure contribute the most variance to IBM output, followed by parameters for NDD, with
75 relatively small contributions from parameters related to seed dispersal (Table 4 1). Sensitivity of output to par ameter values exhibited non linear relationships with time, although the ranking of parameters remained similar over time. Here, we present the sensitivity values for the 99 th time step of the IBM runs. Main sensitivities suggest that parameters for NDD size. Within parameters for NDD, the effect of tree neighborhood on adult survival was variance to the se outputs respectively, while effects of conspecific seedling density on seedling growth were most important for basal area, contributing 4.7% of variance to this output. Within size structured parameters, the most important parameter for adult survival a while the parameter determining the linear effect of seedling height on seedling growth was most import ant for basal area, contributing 10.3% of variance in basal area. PVA The IBM simulation without animal seed dispersal exhibited fundamental differences from the IBM with animal seed dispersal, with lower total population size and median basal area and m uch higher spatial aggregation. For the no dispersal simulation, median total population size was 2840 (95% CI: 0 12251), median basal area (m 2 / ha) was 6.25e 06 (95% CI: 0 6e 111.75). In contrast, the simulation with dispersal yielded median total population size of 22537 (95% CI: 3 55993), median basal area of 1.175e 05 (95% CI: 8e 09 1e 04) and of 1.14 (95% CI: 1.01 42.4). Without animal seed dispersal, the probability of
76 extinction increased by an order of magnitude from 0.5% in the simulation with natural seed dispersal to 7% in the simulation with no animal seed dispersal (Fig. 4 5). Discussi on A Miliusa tree can live for hundreds of years and produce >100,000 seeds. The vast majority of these seeds will die before reaching reproductive maturity, and for this size structured population, larger seedlings and mid sized trees are far more importa nt for producing the next generation of trees than smaller individuals. Yet, our data show that Miliusa demography is also structured by space, with decreased survival and growth for seeds, seedlings and trees in neighborhoods with high conspecific densit y. Consistent effects of spatial structure across the tree life cycle mean that not all individuals of a given size are equal; a small individual in a low density neighborhood may have a much higher chance of establishing into a reproductive adult than a larger individual in a high density neighborhood. Consequently, Miliusa population dynamics, including changes in total population size, spatial aggregation, and basal area, are sensitive to parameters for both size and space (Table 4 1). Seed dispersal plays a crucial role in Miliusa population dynamics because it sets the template for spatial structure, and if animal seed dispersal ceases, our model predicts that the probability of extinction for Miliusa would increase by an order of magnitude. While mo st other studies have examined the consequences of NDD for only a single life stage ( e.g. Harms et al. 2000, Peters 2003, Uriarte et al. 2004, Comita and Hubbell 2009, Hurst et al. 2011) we used the same neighborhood model ( Equation 4 1 ) for NDD in all life stages, enabling us to directly compare the magnitude of neighborhood effects across Miliusa's life cycle. Generally, the magnitude of NDD effects w as lower for larger individuals in later stages, with the strongest measured
77 effects of NDD for seed germination and seedling growth (Fig. 4 2). For seedling growth and tree survival, effects of NDD on large individuals became negligible (Fig. 4 3), possi bly because these individuals have more resources to resist and recover from NDD (Chanthorn et al. 2013) In contrast, models for tree growth revealed an interaction between neighborhood and size, such that mid sized individuals between 10 and 30 cm DBH had the most to lose fr om being in high conspecific density neighborhoods (Fig 4 3). The spatial scale of NDD due to tree neighborhoods also varied between vital rates, with almost no detectable effects beyond 5 m for tree survival, but strong effects even at 20 m for seedling growth and seed germination. Whether these differences in the spatial scale of neighborhood effects indicate differences in the mechanisms underlying NDD between life stages remains an important, unanswered research question. NDD in tropical tree populat ions could be dependent on both distance from adult trees and/or density of seeds and seedlings (Janzen 1970) Whether distance or density responsive NDD is more prevalent for tropical tree seedlings has been widely debated, with some evidence suggesting seedling seedling interactions are significant determinants of seedling mortal ity and growth (Poulsen et al. 2012) while other evidence suggests only a weak role for seedling interactions (Paine et al. 2008, Chanthorn et al. 2013) In addition to distance responsive effects of the tree neighborhood within 20 m, we also found evidence for d ensity responsive NDD from conspecific seedlings at scales of <1 m from seeds and seedlings (Fig. 2). NDD from conspecific seedling density differs from tree neighborhood NDD, because it is symmetric, with a large neighbor having an equal negative effect on seedling vital rates
78 as a small neighbor. The magnitude of conspecific seedling density varied between vital rates, with the strongest effect on germination, and the weakest effect on seedling survival (Fig. 2). Population dynamics provided evidence f or the importance of both density responsive and distance responsive NDD (see below). Statistical models enable us to evaluate the magnitude and spatial scale of size and NDD for vital rates, but their output does not provide insight into the relative impo rtance of parameters for population dynamics. To evaluate the demographic importance of parameters, we used an IBM to establish how sensitive population dynamics were to changes in parameters. The input to this IBM was samples from parameter posterior dis tributions, and the output was three emergent properties of the sensitivity analysis is directly connected to uncertainty in parameter estimation. Parameter uncertaint y could be related to biological variability between individual trees, due to unmeasured genetic, phenotypic, and microhabitat differences, or could be a result of sampling error (Zuidema and Franco 2001) Because our data on vital rates for seeds, seedlings and adult trees incorporated large, equivalent sample sizes (> 1000 individuals), our sensitivity analysis is uniquely able to address the question of how a reduction in variance for a parameter would reduce variance in IBM output. The effect of tree neighborhoods on tree survival provides an example of how statistical significance does not equal demographic significance. Many authors have argued that the most important effects of NDD will be on early life stages, because these early life stages are likely a demographic bottleneck, in which especially high mortality limits abundance of later life stages (Harms et al. 2000, Comita and Hubbell
79 2009, Poulsen et al. 2012, Terborgh 2012) Indeed, our statistical models for empirical data detected the strongest magnitude and largest spatial scale of NDD for seed germination and seedling growth, with relatively weak ma gnitude and small spatial scale (<5 m) for tree survival (Fig. 4 2). However, out of all the NDD effects, both total of trees >1 cm DBH. This result reflects the gene ral demographic importance of stasis of large individuals for long lived plant species (Franco and Silvertown 2004) Our research suggests ecological questions relating to tree population regulation, such as the Janzen Connell hypothesis (Terborgh 2012) may bene fit from an increased focus on NDD induced mortality of larger trees. Degree of conspecific aggregation plays a crucial role in theories for plant population dynamics (Bolker and Pacala 1999, Law et al. 2003) community structure (Cond it et al. 2000, Bagchi et al. 2011) and forest dynamics (Seidler and Plotkin 2006) Our spatially explicit IBM enabled us to quantify the degree of aggregation for simulated populations using the same metric which has been used to measure aggregation within natural populations of tropical trees (Condit et al. 2000, Seidler and Plotkin 2006) Consequently, we are able to link data to theory that suggests when the spatial scale of seed dispersal is much larger than that of NDD, the distribution of plants should be increasingly ra ndom, rather than clustered (Law et al. 2003) Indeed, we found that for most of our simulated populations, which had rates of seed dispersal on a scale of hundreds of 1.15 (95% CI 1.00 63.66) after 100 years of simulation. Previous research has found that interspecific levels of conspecific aggregation in tree populations are closely linked
80 to b etween species seed dispersal syndromes (Seidler and Plotkin 2006) In contrast, for a natural range of variance in seed dispersal within a single species, differences in the scale of seed disp Instead, parameters for survival and NDD for trees >1 cm DBH played the most sensitivity of total p opulation size and aggregation to perturbations in parameters were very similar in magnitude and rank (Table 1). This result supports recent research that suggests population growth rate and spatial aggregation are closely linked for trees, with informati on on one potentially providing information on the other (Flgge et al. 2012, Detto and Muller Landau 2013) While total population and spatial aggregation are important metrics for tree population and community dynamics, basal area, which weights abundance by tree DBH, is more importa nt for biomass and carbon storage (Brown 2002) Sensitivity of basal area to parameter perturbations differed from the s ensitivity of total population area output, compared to 15% for total population s reflects the increased importance of growth to larger sizes for determining basal area, as the magnitude of NDD effects was generally greater for growth than survival (Fig. 1). Second, out of all NDD effects, the effe ct of conspecific seedlings on seedling growth contributed the most variance to basal area. This result is surprising because basal area does not incorporate information on seedlings. One explanation of this result is that for Miliusa as a tree species w ith a long lived, shade tolerant seedling bank, lower
81 NDD enables seedlings to spend less time in the seedling bank, become saplings faster and contribute more to basal area than seedlings in populations with higher seedling NDD. This result highlights the potential importance of the seedling bank for determining tree biomass, and suggests that data on seedling dynamics may contribute to our understanding of carbon dynamics in tropical forests. In light of the many size and space dependent processes that oc cur after seed dispersal, how important is seed dispersal for tree population dynamics? In the IBM with natura l levels of seed dispersal, dispersal distance was relatively unimportant for 1). While variance in seed dispersal was high, none of the posterior samples from the seed dispersal model included a peak in se ed dispersal <10 m from the parent tree (Fig ure 4 1), demonstrating a high degree of confidence that most seeds are currently dispersed far from the parent tree. Extinction of large bodied mammals that disperse Miliusa seeds from Thai forests is a real possib ility (Corlett 2007, Brodie et al. 2009) and an IBM that assumes seeds are dispersed only near the canopie s of the parent tree reveals the importance of animal factor of four. Because conspecific density has consistent negative effects for all life stages (seeds, seedlings and trees), the loss of seed dispersal has effects that propagate throughout the entire tree lifespan, increasing the probability of extinction by an order of magnitude. Assuming these results are at least partially generalizable to other species, we sugg est that NDD across the life cycle is likely a demographic mechanism underlying observed declines in abundance of animal dispersed tree species after extirpation of seed dispersers ( Corlett 2007, Cordeiro et al. 2009, Harrison
82 et al. 2013) More generally, these results demonstrate the c ritical importance of spatial structure for tree population dynamics. z Table 4 1. Model component Total population Basal area aggregation) Size structure 0.7 0.41 0.67 NDD 0.15 0.26 0.15 Seed dispersal 0.01 0.02 0.02 Figure 4 1. Effects of size structure on tree vital rates. A) Seed production, B) Seedling growth, C) Seedling survival, D) Tree growt h, E) Tree survival. Each panel represents a separate vital rate, displaying the effects of size for a target individual in the absence of conspecific individuals. Black lines represent median values for functions,, and gray lines represent 1000 draws fro m the posterior distribution of parameters. A E C D B
83 Figure 4 2. Spatial scale, magnitude and uncertainty of seed dispersal and NDD for Miliusa. A) Seed dispersal, B)Tree effect on Germination, C) Tree effect on seedling growth, D) Tree effect on tre e growth, E) Tree effect on tree survival, F) Seedling effect on germination, G) Seedling effect on seedling growth, H) Seedling effect on seedling survival. Each panel shows results from statistical models for seed dispersal (top left), effects of distanc e from a 90 cm DBH conspecific adult tree on survival and growth as a function of distance (top right panels), and effects of conspecific seedling density on survival and growth. For seedlings, we effects are illustrated for a 5 cm high seedling, the mini mum size observed in the data, and for trees effects are illustrated for a 1 cm DBH tree. Black lines represent median values for spatial functions, the dotted green line represents the baseline growth or survival rate in the absence of NDD, and gray line s represent 1000 draws from the posterior distribution of parameters. Gray lines represent uncertainty which was directly propagated into the dynamic IBM. A B C D E F G H
84 Figure 4 3. Asymmetric effects of neighbor size on Miliusa vital rates, including A) seedling growth and B) tree growth Each line represents median growth of 6 target individuals spanning the range of seedling and tree sizes, 1 m away from a neighbor tree A B
85 Figure 4 4. Population dynamics from IBM model. These figures show the location and size of seedlings and reproductive trees (DBH>20 cm) for the IBM model with natural seed dispersal (top) and the model without animal seed dispersal, in which seeds fall beneath the canopy of parent trees (bottom). In these figures, red circles represent reproductive trees and size of the circle is proportional to tree size. Green dots represent seedlings. The model begins with initial conditions determined by the 50 ha data (Initial conditions panel), then shows the initial pattern of seed arrival duri ng the first year of the run (Seed arrival panel), followed by the location of those first year seedlings immediately after germination (Germination), and final adult trees and seedlings 17 years and 97 years into the model runs.
86 Figure 4 5. Results o f population viability analysis for the IBM runs with and without animal seed dispersal. A) The IBM with natural seed dispersal, B) An IBM in which seeds fall under the canopy of the parent tree (no animal seed dispersal) Red lines reveal populations whi ch have gone extinct. Losing animal seed dispersal results in a 7% chance of extinction in 100 years, compared to a 0.5% chance of extinction in the original model. A B
87 CHAPTER 5 GENERAL CONCLUSIONS Trees are rooted in place, yet spatial structure underli es both vital rates of individual trees and dynamics of tree populations. Seed dispersal provides a link between stationary trees and all future spatial structure. However, seed dispersal is separated from the eventual distribution of adult trees by comp lex abiotic and biotic processes which kill the vast majority of seeds, seedlings and saplings, and are poorly understood in most tropical forests. I relate events between seed arrival and adult recruitment to the spatial dynamics of tree populations. Du e to the large spatial scale of animal seed dispersal, the vast number of seeds produced by trees during their lifetimes, and the long generation time of trees, quantitative models are required to understand the importance of seed dispersal in the context of tree life cycles. However, models quantifying the impact of seed dispersal on the spatial distribution and demography of multiple tree life stages are rare. In this dissertation, I developed quantitative models for seed dispersal and tree demography an d applied those models to understand when seed dispersal is likely to be important for tree spatial population dynamics. In Chapter 2, I quantified the importance of seed arrival for the distribution of an invasive plant. Invasive plant range expansion ta kes place at large spatial scales, often encompassing many types of land cover, yet the effect of landscape context on seed dispersal remains largely unknown. Many studies have reported a positive correlation between invasive plant abundance and human lan d use and increased seed dispersal in these landscapes may be responsible for this correlation. I tested the hypothesis that increased rates of seed dispersal by fig eating birds, which are more common in urban
88 habitats, result in an increase in invasive strangler fig abundance in landscapes dominated by human land use. I used data on strangler fig abundance to parameterize spatially explicit models that predicted juvenile fig abundance from distance to adult fig seed sources and fig eating bird habitat q uality. The best model for invasive figs suggested that landscape effects on invasive fig abundance are mediated by seed dispersing birds. Understanding seed dispersal as a demographic mechanism of plant invasion may lead to better management techniques, in this case prioritizing the removal of adult fig trees in sites with high human land use. Long distance seed dispersal (LDD) is considered a crucial determinant of tree distributions, but its effects depend on demographic processes that enable seeds t o establish into adults and that remain poorly understood at large spatial scales. In Chapter 3, I quantified the importance of LDD for the distribution of a canopy tree species ( Miliusa horsfieldii ), in a landscape of western Thailand, spanning evergreen absent. I used field data to determine rates of seed arrival, germination, and survival and growth across this habitat gradient, then used an individual based model to com pare the relative importance of seed arrival and establishment in explaining the observed distribution of seedlings. A lthough sapling establishment was significantly higher for seeds dispersed long distances into deciduous forest, results suggest that Mil iusa is rare in the deciduous forest due to the rarity of long distance dispersal of seeds into this habitat This chapter demonstrates that dispersal limitation at the landscape scale is likely to have crucial importance for the distribution of a tropica l tree species in its native habitat.
89 While Chapters 2 and 3 demonstrate the importance of seed dispersal for tree demography in landscapes with unoccupied patches, Chapter 4 focuses on the role of dispersal in within patch tree population dynamics. Seed dispersal and negative density dependent (NDD) mortality generate spatial structure in tree populations within stands, with potential consequences for forest dynamics and species coexistence. However, any effect of the spatial template set by seed dispers al on population dynamics could be overwhelmed by the importance of growth and survival of larger individuals, regardless of their location. I evaluated the demographic consequences of spatial structure for a canopy tree species, Miliusa horsfieldii, in a tropical forest of western Thailand by collecting spatially explicit data on vital rates for seeds, seedlings and trees>1 cm DBH. This data was used to compare the magnitude of NDD between vital rates, and quantify the sensitivity of an individual based model (IBM) for population dynamics to perturbations in size structure, NDD and seed dispersal. Because Miliusa seeds are dispersed by large mammals, which have been hunted to extinction in many Asian forests, I conducted a simulation experiment to compare the probability of extinction with natural seed dispersal to a scenario with no animal seed dispersal. Results reveal that NDD effects were prevalent for seeds, seedlings and trees and consequently, loss of animal seed dispersal increases the probability of extinction of simulated Miliusa populations by an order of magnitude. This dissertation demonstrates that the role of seed dispersal in tree population dynamics has important consequences for biodiversity conservation. By relating the spatial pattern of seed arrival at large spatial scales to tree distributions in Chapter 2 and 3, we show that LDD is likely to have a major impact on the distribution of both
90 invasive trees undergoing rapid range expansion and native trees in patchy landscapes. A take home message of these first two chapters is that although rare LDD events are difficult to measure, quantitative estimates of seed arrival at large scales are worthwhile, because even very low rates of seed arrival at long distances can significantly affec t tree distributions. Chapters 1 and 2 demonstrate that changes in LDD by seed dispersing animals, including increases in abundance of invasive fig dispersing birds in urban habitats (Chapter 2) and the potential extinction of wide ranging animal disperse rs (Chapter 3), will likely result in major changes in the distribution of animal dispersed tree species. Chapter 4 demonstrates seed dispersal to beneficial sites within a single forest stand is likely to have demographic consequences even for long lived species with multiple life stages. Consequently, accounting for seed dispersal will be important for conserving tree populations in changing landscapes.
91 APPENDIX A DERIVING FIG EATING BIRD HABITAT QUALITY FROM FRUITING TREE OBSERVATIONS AND GIS DATA B ird visitation rates to fig trees. We determined which bird species were likely to disperse fig trees by observing bird visitation to five F. microcarpa and seven F. aurea adults, all near peak fruiting. Visitation was observed from February June, 2007. Each tree was observed from 6:45 to 8:45 AM, on two consecutive days. During each observation period, we recorded the number and species of every resident bird that entered the tree. For analysis, we used the average of bird visitation for the two days pe r tree. The bird visitation data suggest similar rates of visitation between the two fig species, with Northern Mockingbirds ( Mimus polyglottos ) Blue Jays ( Cyanocitta cristata ) and Red bellied Woodpeckers ( Melanerpes carolinus ) as the most common visitor s for both species (Table A 1). One apparent difference between the two fig species was the higher rates of visitation by European Starlings ( Sturnus vulgaris ) and Boat tailed Grackles ( Quiscalus major ) to F. aurea (mean and standard deviation of 2.215.2 3 and 2.865.28 for visits of the two bird species, respectively, to F. aurea compared to 0.20.45 and 0.50.5 visits to F. microcarpa ) However, this difference was the result of visitation by large flocks of European Starlings to a single tree and of B oat tailed Grackles to two F. aurea trees. To formally test for differences in bird visitation between F. microcarpa and F. aurea we conducted a one way multivariate analysis of variance (MANOVA), using visitation rates of the top five bird species as res ponse variables and fig species as a predictor. The MANOVA revealed no significant difference between F. aurea and F. microcarpa in bird visitation rates (df=1, 10, F = 1.46, P = we pooled bird visitation data from the two fig tree species.
92 Using bird visitation rates of resident species as a proxy for seed dispersal requires several assumptions and is subject to practical limitations in data collection. First, we assume that the nu mber of visits of each bird species to fig trees reflects disperser effectiveness (S chupp 1993) However, if some bird species visit trees infrequently, but are high quality dispersers (for example, a bird species that rarely eats fig fruits but deposits a high proportion of seeds in cabbage palms), our disperser index would be artifici ally low for those species. Second, while some migratory bird species visit fig trees, we did not include these species in our analyses because they occur sporadically in large flocks that are practically impossible to monitor on the temporal scale of our study. Third, in Florida, fig fruits are also eaten by several mammal species, including gray squirrels and raccoons (T. Caughlin, personal observation). Understanding the relative contributions of mammalian and avian seed dispersers to plant demography is an important research gap, but beyond the scope of the current study. Finally, F. microcarpa seeds are apparently adapted for secondary dispersal by ants (Kaufmann et al. 1991) while F. aurea seeds are not; however this difference is unlikely to affect the results of the study sin ce ants rarely disperse seeds long distances (Gomez and Espadaler 1998) Whether the spatial sca le of fig eating bird movements is within the range of the plots used to determine adult fig locations and fig eating bird habitat quality is another important question for this analysis. The circular plots used for adult fig locations and fig eating bird habitat quality had a 300 m radius corresponding to an area of 28.27 ha. The top three bird visitors to fig trees, accounting for 72% of all visits, have territories within 28.27 ha. The breeding and year round territory of Northern Mockingbirds, the
93 bir d species with the highest visitation to fig trees (Table A1), ranges from 0.25 ha (Logan, 1987) to 1.27 ha ( Derrickson and Breitwisch, 1992). Territories of Blue Jays, the second most common visitor to fruiting fig trees, range from 3 20 ha in south cent ral Florida (Tarvin, 1998). Red bellied woodpeckers, the third most common visitors to fig trees, have territories ranging from 1.6 to 16 ha (Poole, 2005). Territories of Northern Cardinals, Brown Thrashers, Mourning Doves, Great crested Flycatchers, Ca rolina Wrens, Rock Doves, and Downy Woodpeckers, which together account for 8% of visitation, are also likely to be well below the 28 ha scale of our plots (Poole, 2005). In contrast, European Starlings, Boat tailed Grackles, Pileated Woodpeckers and Amer ican Crows, which accounted for 19% of visitation to fruiting fig trees, are likely to have territories larger than the scale of our 300 m radius plots (Mellen et al. 1992; Poole, 2005). Our 300 m radius plots may underestimate the scale of seed dispersal by this minority of wide ranging bird species, as well as occasional long distance movements by bird species with relatively small territories. Quantifying adult plant seed sources at a scale large enough to match the scale of these long distance seed di spersal events represents a major challenge for plant ecology (Cain et al. 2000) Quantifying fig eating bird habitat quality. We combined three separate sources of information to produce a GIS layer representing fig eating bird abundance: bird visitation to fruiting fig trees (see ab ove), point count surveys of bird abundance in different Florida habitats (Stracey and Robinson 2012) and a GIS layer of discrete habitat types derived from satellite imagery (Stys et al. 2004) First, we determined the relative importance of each bird species for fig seed dispersal by dividing the total num ber of visits to fig trees for each bird species by the total number of visits for all
94 by the average number of detections per survey point for that species in each ha bitat represented in the bird survey dataset. We then matched these habitats to the habitat categories in the original GIS layer (Table A 2). Most habitat types in the bird survey dataset could be directly matched to a habitat category in the GIS layer; h owever, bird abundance data were not available for twelve of the twenty eight habitat categories present in the GIS dataset. These unavailable habitats were either habitats in which fig eating birds are mostly absent (e.g., open water) or habitats that co mprised only a small proportion of the total study area (e.g., sand pine scrub). We removed rasters for those habitat categories without a clear equivalent in the bird survey dataset from the final fig eating bird habitat quality layer. The ultimate produ ct of these analyses was a dataset consisting of 30x30 m rasters of habitat types, each with a value representing fig eating bird abundance, ranging from 0.07 to 1.19 (Figure A 1). Alternative methods of producing the fig eating bird habitat raster datase t, including using only the top two to five fig eating bird species and classifying rasters on a binary scale, representing favorable and unfavorable habitat for fig eating birds, did not qualitatively change the results of our statistical models.
95 Table A 1. Summary of bird visitation to fig trees. Bird Species F.microcarpa F. aurea Percent of Total Visits Northern Mockingbird 8.15.21 7.647.93 38.7% Blue Jay 5.34.4 3.434.75 20.8% Red bellied Woodpecker 1.31.89 3.52.02 12.8% Boat tailed Grackl e 0.50.5 2.865.28 9.3% European Starling 0.20.45 2.215.23 6.8% Northern Cardinal 0.60.89 11.32 4.1% American Crow 0.30.45 0.711.68 2.7% Brown Thrasher 0.61.34 0.140.24 1.6% Mourning Dove 0.50.71 0.070.19 1.2% Pileated Woodpecker 0.30.45 0.140.38 1% Great crested Flycatcher 0.20.27 00 0.4% Carolina Wren 0.10.22 00 0.2% Rock Dove 00 0.070.19 0.2% Downy Woodpecker 00 0.070.19 0.2%
96 T able A 2. Habitat categories and values after reclassification for fig eating bird abundance. Ha bitat category % of land cover class within 600 m of plots Fig eating bird abundance High Impact Urban 42.5% 1.19 Low Impact Urban 6.8% 1.11 Row/Field Crops 0.4% 0.98 Other Agriculture 0.2% 0.98 Coastal Strand 1.1% 0.56 Shrub and Brushland 0.4% 0.49 Xeric Oak Scrub 0.2% 0.49 Dry Prairie 2.4% 0.44 Improved Pasture 0.4% 0.44 Unimproved Pasture 0.4% 0.44 Grassland 0% 0.44 Mangrove Swamp 4.6% 0.26 Hardwood Hammocks 3.7% 0.19 Bare Soil/Clearcut 0.6% 0.15 Mixed Pine Hardwood Forest 1.6% 0.13 Pin elands 9.9% 0.07 Open Water 15.3% NA Salt Marsh 2.2% NA Mixed Wetland Forest 1.6% NA Cypress Swamp 1.3% NA Hardwood Swamp 1.1% NA Freshwater Marsh 1% NA Cypress/Pine/Cabbage Palm 0.6% NA Shr b Swamp 0.3% NA Brazilian Pepper 0.2% NA Exotic Plants 0.1% NA Sand Pine Scrub 0% NA Note: H abitat category represents the original habitat categories from the land cover GIS layer (Stys et al. 2004). Fig eating bird habitat quality represents the value of the categories in the final raster dataset used for original GIS dataset with no equivalent in the bird abundance dataset
97 Figure A 1. Illustration of the raster reclassification process for a single fig plot. The first panel illustrates the scale of the plot in relation to houses, streets and other Mapping Service. The second panel represents t he GIS data layer from Stys et al. (2004), with each 30x30 m raster representing a discrete habitat category. The rightmost panel represents the final raster dataset, processed to reflect fig eating bird abundance.
98 APPENDIX B PARAMETER ESTIMATES AND 95% CONFIDENCE INTERVALS FOR TOP FITTING MODELS OF JUVENILE FIG ABUNDANCE Table B 1. Parameter estimates and 95% confidence intervals for top fitting F. microcarpa model Parameter MLE Lower CI Upper CI f 0.06 0.02 0.84 g 35.44 11.54 108.87 72.85 9.07 584.87 1 0.49 0.81 0.17 k 3.01 1.27 7.16 Table B2 Parameter estimates and 95% confidence intervals for top fitting F. aurea model. Parameter MLE Lower CI Upper CI f 0.36 0.19 0.70 g 1.24 0.60 2.53 k 1.40 0.78 2.54 1 0.46 0.78 0.14
99 APPENDIX C ADDITIONAL DETAILS ON STUDY SPECIES AND FIELD METHODOLOGY FOR CHAPTER 3 Study site The study site is located in the Huai Kha Khaeng Wildlife Sanctuary (HKK), in rt of the largest intact forest complex in mainland Southeast Asia, with viable populations of tigers, elephants and other threatened mammals, and a minimal history of human disturbance (Bunyavejchewin et al. 2004) Mean annual rainfall in HKK is ~1500 mm, with a 5 6 month dry season from November April. The landscape at our study site is a mo saic of three forest types, including seasonal dry evergreen forest, characterized by a tall canopy up to 60 m in height and an understory dominated by woody seedlings; mixed deciduous forest with a main canopy of deciduous trees between 30 and 40 m tall, a mixture of evergreen and deciduous trees in the midstory, and an understory which includes grasses, gingers (Zingiberaceae) and bamboo; and dry deciduous forest, with a 15 20 m canopy dominated by a few species of Dipterocarpacaeae and an understory of g rass (Baker 1997) St udy species Miliusa horsfieldii syn. Miliusa lineata, and previously described in the Thai forestry literature as Saccopetalum lineatum (Mols and Kessler 2003) is one of the dominant species in season ally dry evergreen forest at HKK. In a 50 ha Forest Dynamics Plot located within the seasonally dry evergreen forest at our study site, in according to Center for Tropical Forest Scien ce (CTFS) standard protocols, Miliusa has the most stems>10 cm DBH of any tree species (Bun yavejchewin et al. 2004) Miliusa
100 is a canopy tree species, reaching maximum heights up to 35 meters, and is semi deciduous, remaining at maximum leaf fall in HKK for ~1 month (Baker 1997, Williams et al. 2008) Additional details on sampling protocol The purpose of our field data collec tion and statistical analyses was to produce dynamic models for seedling distributions. Seedling distributions are the product of multiple demographic processes, beginning with seed arrival in plots, followed by seed germination, resulting in newly recrui ted seedlings, which can then grow and survive as part of the seedling bank. We collected data on these demographic processes from 93 plots spanning the five kilometer transect between forest types. Transitions between the forest types are gradual, and th e landscape is characterized by heterogeneity in terms of forest age and structure (Baker et al. 2005) complicating attempts to assign a categorical forest type to any particular location. Consequently, we model demographic rates as functions of plot specific environmental covariates including presence of grass, light availability and conspecific density. We measured light availab ility during the wet season using hemispherical photographs, following protocol to minimize errors associated with automatic exposure (Zhang et al. 2005) and analyzed photos f or percent transmitted light using Gap Light Analyzer v. 2 (Frazer et al. 1999) Grass was quantified as the presence or absence of under story grass (excluding bamboos). We quantified conspecific seedling density as counts of conspecific seedlings in 1 m x 1 m quadrats and adult density as summed DBH of all conspecific trees within 10 m neighborhoods. Finally, because plots contained mul tiple seedlings, seeds or new
101 recruits, we included plot as a random effect in all models, representing unaccounted for plot specific variation. Fecundity We collected data on fruit production and canopy area to estimate seeds produced as a function of t ree size. Fruit production was measured for 14 randomly selected trees, with DBH>20 cm, a reproductive threshold for Miliusa (Caughlin, unpublished data), during a single fruiting season in June July 2011. Fruit production was estimated by counting peels a nd pedicels discarded by frugivores. Observations of frugivore feeding behavior at fruiting trees suggest that ingestion of these peels is rare (Caughlin, personal observation). Beneath each tree, discarded fruit peels and pedicels were counted in three ra ndomly placed 3 m x 3 m quadrats, resulting in a total of 42 quadrats, each of which yielded an estimate of fruit production per unit adult tree canopy area. Peels and pedicels were counted three separate times during the fruiting season. A pilot study in which peels and pedicels were experimentally placed on the forest floor revealed high rates of recovery (>95%), so observation error is likely to be small for this method of measuring seed production (Caughlin, unpublished data). Undispersed fruits (frui ts that fall beneath the tree without being eaten) have an almost zero probability of germination (Caughlin, unpublished data), so we did not include undispersed fruits in our analyses of fruit production. In order to scale predicted fruit production per quadrat to fruit production per tree, we multiplied fruits per square meter of quadrat times tree canopy area. For the 14 trees with fruit production quadrats, we determined canopy area by measuring canopy width in the four cardinal directions and then t aking the average of four circle areas calculated with these width measurements.
102 Seed germination Data on germination and new recruit height comes from a seed addition experiment in which 6,175 seeds were added to 281 1 m x 1 m seed addition quadrats wit h piles of 0,5,15, or 45 seeds in June July, 2009. Each of the 93 plots had 4 of these seed addition quadrats, representing each of the levels of seed addition, and seed addition quadrats were arranged so that each quadrat was 12 m in one of four cardinal directions from the center of the plot. The numbers of seeds added to seed addition quadrats span the range of Miliusa seeds counted in frugivore dung (n=36 dung piles, Caughlin unpublished data). Zero seedlings emerged from seed addition quadrats with zero seeds added, and this treatment is not considered further. We marked seeds with a small dot of red paint, allowing us to track the fate of individual seeds, and monitored seeds monthly. Three months after seed addition all seeds had either died or g erminated and become seedlings (new recruits). Environmental covariates were measured at the center of the seed addition quadrats at the time of seed addition. Abundance of newly recruited seedlings Our model for seed arrival uses data on newly recruited seedlings, from natural arrival of seeds in plots, collected in 217 3 m x 3 m subplots. 93 of these 3 m x 3 m subplots were located at the center of the plots along the gradient, supplemented with an additional 124 3 m x 3 m subplots outside the 93 plot s, within the 50 ha plot. For the purposes of analysis,each subplot was separated into eight 1 m x 1 m new recruit quadrats (the center square 1 m x 1 m quadrat in the 3 m x 3 m subplot was not included), resulting in a total of 1723 1 m x 1 m new recrui t quadrats with data on the abundance of new recruits. In order to parameterize the neighborhood term, we
103 measured the size and location of all conspecific reproductive sized trees within 20 m of each new recruit quadrat, as well as environmental covariat es at the center of each new recruit quadrat. All covariates were measured at the time of seed addition. Survival and growth of naturally occurring seedlings To develop survival and growth models representing a range of seedling size, we censused naturally occurring seedlings. All seedlings (n = 101) were located and tagged during June July 2009 within the 1 m x 1 m seed addition quadrats and the 3 m x 3 m center subplots, and then recensused a year later. In 2010, we expanded our census of tagged seedlin gs to include an additional 124 randomly selected 3 m x 3 m subplots within the 50 ha forest dynamics plot in the evergreen forest region and additional seedlings in the 93 plots along the transect. For the additional seedlings in the 93 plots along the t ransect, we found seedlings using an adaptive sampling procedure, in which size of the plots used to search for seedlings was increased from the original 3 x 3 m plots, by adding additional seedling census quadrats to the edges of the existing subplot, unt il either 10 seedlings were found and tagged or the total area reached 24 x 24 m. The adaptive sampling scheme resulted in a total of 1342 newly tagged seedlings in July 2010. We recorded survival for all of these seedlings and measured growth for a subs ample of 726 seedlings in June July 2011. Consequently, our total sample size for seedling survival across both years is 1443 seedlings and total sample size for growth is 819 seedlings. Presence or absence of grass was measured at the stem of each of the se seedlings, and the number of conspecific adult trees was measured within a 10 m radius beginning from the stem of each seedling. Conspecific seedling abundance was counted in each seedling census quadrat. Hemispherical
104 photographs were taken either dir ectly above the seedling or when multiple seedlings were within 3 m from one another, at the estimated center of the seedling cluster; consequently, no seedling was > 3 m from a hemispherical photograph.
105 APPENDIX D ADDITIONAL DETAILS ON STATISTICAL METH ODS AND IBM FOR CHAPTER 3 Statistical models The following text describes the statistical models used as input for the IBM (Fig. 1). For each statistical model, parameters are presented with superscripts representing the process to which the parameter belo ngs. For example, the mean of the fruit production process is indicated by the variable: where the superscript fr indicates fruit production. Data sources, sample sizes and indices used in submodels are shown in Table D 1. Table D 1. Data sourc es for response variables used in used in model Response variable Data Sample size Index used in model New recruit abundance Quadrats with counts of naturally arrived new recruits (seedlings<3 months old) 1723 k Adult tree fecundity Canopy area per tre e 14 g Fruit production in three 3 m x 3m fruit count quadrats beneath each tree 42 h Germination Survival of seeds in quadrats from seed addition experiment 281 i New recruit height Height of new recruits from seed addition experiment, 3 months after seed placement 628 p Seedling growth Censuses of natural seedlings 819 m Seedling survival Censuses of natural seedlings 1443 s Plot level random effects Natural seedlings, seed addition experiment, new recruit counts 75 219 j
106 Fruit production The p urpose of the fruit production statistical model was to estimate seeds produced as a function of tree size. Fruit production (number of pedicels plus peels per m 2 canopy area) in fruit count quadrat h (42 total quadrats) was modeled as a Poisson random var iable whose mean ( was a sigmoid function of tree size (DBH) with three free parameters ( ( D 1) This function allowed us to predict the fruit prodcution per unit canopy area of all adult Miliusa trees in our plots, while propagating uncertainty in individual fruit production (see below). We assumed that canopy area was proportional to DBH, which fit the data as well as power law allometry. Thus, our canopy area function consisted of a single proportionality constant The resulting statistical model for canopy area ( for tree g (14 total trees) is: (D 2) Consequently, the model for total fecundity of tree g is a product of canopy area Equation D 2 ) and fruit production ( Equation D 3) (D 3)
107 Seedling establishment We modeled experimental new recruits as a binomial random variable with the number of trials equal to the number of experimentally a dded seeds ( ) and the success rate equal to the probability of germination ( ) in quadrat i within plot j For the seed addition experiment data, seed arrival is known (seeds added to each seed addition qua drat). As with all other demographic models we assumed that depended on the following covariates light, grass presence, conspecific seedlings and conspecific adult trees. Hemispherical photographs were not available for 72/281 quadrats, s o we used a latent variable approach to propagate uncertainty in the 72 missing light values. Specifically, we assumed that the unknown light values were normally distributed random variables with plot level mean, Similarly, we included a no rmally distributed plot level random effect for seedling establishment probability, The model is formally described as follows for seed addition quadrat i (281 total quadrats) in plot j (93 plots): (D 4) New recruit height, for the seedlings which emerged from the seed addition experiment after 3 months (new recrui ts), was modeled as a normally
108 distributed random variable, with a mean ( equal to a linear function of an intercept term environmental covariates, and a normally distributed plot level random effect ( ). W e did not include transmitted light as a predictor in this analysis, because a large number of new recruits (297 out of 628) had missing light data, and preliminary analysis of the subset of data with light values suggested that including this covariate di d not improve model fit. The model for new recruit height of new recruit p (out of 628) in plot j (75 plots) is as follows: ( D 5) Seed arrival We modeled abundance of naturally arrived new recruits (originating from naturally dispersed seeds, in contrast to new recruits originating from experimentally added seeds) as a function of seed dispersal and germination. The statistical model simultaneously estimates seed arrival from data on from counts of naturally arrived new recruits, fruit production, and experimental new recruits from the seed addition experiment New recruit abundance in quadrat k (17 23 quadrats) within plot j (219 plots) was modeled as a Poisson distributed random variable with a mean equal to a germination probability multiplied by expected seed arrival In this model, the abundance of naturally arrived new recruits is a binomial random variable:
109 (D 6) The first expression is equivalent to the Binomial model for experimental new recruits (germination section, above). However, unlike the experimental new recruits, the number of naturally arrived seeds in new rec ruit quadrat k and plot j is unknown. Marginalizing over results in a Poisson random variable, with a mean equal to the the probability of success from the Binomial random variable multiplied by expected seed arrival (Lavine et al. 2002) : (D 7) This model jointly estimates from data which includes both the seed addition experiment and counts of naturally arrived new recruits. Expected seed arrival is t he sum of expected seed rain from adult trees within a 20 m neighborhood ( ) and expected seed rain from sources outside of the 20 m neighborhood, ( ), multiplied by a plot level random effect : ( D 8) ( D 9) ( D 10) The Nhood term includes the model for fecundity per tree g ( D 3) su mmed over all trees in a 20 m radius around quadrat k in plot j and a dispersal parameter which describes the proportion of seeds
110 from the neighborhood which arrive in a quadrat. More complicated dispersal kernels, including the logno (Clark et al. 1999) did not improve the fit to the data. The second component in Equation D 8 is a term representing dispersal from seed sources outside the 20 m neighborhood around each quadrat, Because our plots were located along a transect running from an area of high adult abundance, to low adult abundance, the Bath term is a function of distance along this transect. We evaluated several different functions for the Bath term and found that a Gaussian function of linear distance from the southeastern most plot on the transect provided the best fit to the data. Based on the observed distribution of reproductive Miliusa trees in the landscape, we set the location parameter of the Gaussian function to 1.88 kilometers, the mean of the distance from the starting point of the transect for each plot. Because we standardize d transect distance by dividing by two standard deivations and centering around the mean (Gelman 2008) the location parameter is equal to zero in Equation D 11. Survival and growth of naturally occurring seedlings We modeled survival of seedling s (1443 total seedlings) in plot j (136 plots) as a Bernoulli distributed random variable, with a logit transformed probability ( ) equal to a linear function of an intercept term ( additive covariates and a plot level normally distributed random effect ( (D 11)
111 Growth was modeled as a normally distributed random variable, with linear and non linear components in the mean ( ) : a l inear term with an intercept ) plot level random effect ( ) and grass and light covariates multiplied by exponential functions for the effect of conspecific seedling and adult covariates. The consequence of this model formulation is that high conspecific density can result in reduced but not negative growth. For m seedlings (819 total) in 93 plots, growth was modeled as follows: (D 12) Priors We assigned non informative priors to most parameters, with parameters of these non informat ive priors constrained to biologically reasonable values. We used informative priors for the intercept ( ) and the variance term in the plot level random effect ( in the germination model, because we had prior data on seed germination for our study species from similar seed addition experiments at our study site conducted in 2008 (Wheeler 2009) and 2011 (Caughlin, unpublished data). Environmental covariates were not measured for these seed addition experiment s, limiting our ablity to use the data directly in our models. Thus, we parameterized intercept only models for these additional years of data and used the posterior
112 distributions from this analysis as informative priors in the germination model. Similar ly, we used an informative prior for the plot level variance term in the light submodel ( based on additional years of transmitted light data from hemispherical photographs collected from the same plots. The use of these informative pr iors did not qualitatively affect model results, but greatly improved model convergence. A full table of prior distributions for all parameters is available in Table D 2 below.
113 Table D 2. Prior distributions for parameters used in statistical models. Pa rameter Submodel Prior distribution Parameter 1 Parameter 2 Fecundity Uniform 0 100 Fecundity Uniform 0 100 Fecundity Uniform 100 0 Canopy area Uniform 0 1000 Canopy area Uniform 0 100 Germination Normal 4.94 17 Establishm ent Normal 0 1e 06 Establishment Normal 0 1e 06 Establishment Normal 0 1e 06 Establishment Normal 0 1e 06 Establishment Uniform 0 100 Establishment Uniform 0 100 Establi shment Log normal 0.31864 112.85 Establishment Log normal 0.5395103 17.9006 Seed dispersal Uniform 0 10 Seed dispersal Normal 0 1e 06 Seed dispersal Normal 0 1e 06 Seed dispersal Uniform 0 10 New recruit height Normal 0 1e 06 New recruit height Normal 0 1e 06 New recruit height Normal 0 1e 06 New recruit height Normal 0 1e 06 New recrui t height Uniform 0 10 New recruit height Uniform 0 10 Survival Normal 0 1e 06 Survival Normal 0 1e 06 Survival Normal 0 1e 06 Survival Normal 0 1e 06 Survival Normal 0 1e 06 Survival Normal 0 1e 06 Survival Uniform 0 1000 Growth Normal 0 1e 06 Growth Normal 0 1e 06 Growth Normal 0 1e 06 Growth Normal 0 1e 06 Growth Normal 0 1e 06 Growth Uniform 0 1000 Growth Uniform 0 1000 Note: For normally and lognormally distributed priors, parameter 1 is the mean and parameter 2 is the standard deviation. For unifor m priors, parameter 1 and 2 are the minimum and maximum of the distribution, respectively
114 Parameter estimation Parameters in the submodels for vital rates were estimated using Markov Chain Monte Carlo simulations in JAGS v. 4.3.0 (Plummer 2003) with three chains, each run for 250,000 iterations with a burn in of 50000 iterations. To reduce autocorrelation, we retained every 200 th iteration from each chain. Convergence was assessed using t he Gelman Rubin diagnostic with a threshold of 1.1 (Gelman and Rubin 1992) and by visually examining output from the chains. Parameter estimates are shown below in Table D 3.
115 Table D 3. Parameter estimates and 95% credible intervals Parameter Submodel Lower CI Median Upper CI Fecundity 0.02 0.52 2.28 Fecundity 1.30e 03 1.34e 3 1.38e 03 Fecundity 0.13 0.12 0.12 Canopy area 1.21 1.75 2.25 Canopy area 29.09 42.05 66.13 Germination 4.62 4.26 3.90 Establishment 0.45 0.03 0.34 Establishment 1.10 0.60 0.06 Establishment 0.18 0.54 0.90 Establishment 2.10 2.51 3.04 Establishment 4.4e 03 0.09 0.27 Establishment 0.76 0.88 1.02 Establishment 0.47 0.52 0.59 Establishment 0.99 1.34 1.72 Seed dispersal 1.90e 05 7.9e 5 2.24e 04 Seed dispersal 0.21 0.53 1.22 Seed dispersal 7.30 3.40 1.29 Seed dispersal 1.55 2.16 2.83 Height 4.46 4.75 5.02 Height 1.32 0.49 0.25 Height 0.02 0.30 0.61 Height 0.50 0.17 0.20 Height 1.31 1.38 1.46 Height 0.37 0.55 0.75 Survival 0.33 0.30 0.91 Survival 0.10 0.14 0.18 Survival 0.66 0.42 0.15 Survival 0.48 0.14 0.22 Survival 0.21 0.18 0.63 Survival 0.65 0.25 0.14 Survival 0.35 0.69 1.08 Growth 0.57 1.69 2.90 Growth 0.09 0.12 0.15 Growth 0.47 0.28 1.11 Growth 0.48 0.65 1.79 Growth 3.02 1.87 0.90 Growth 6.29 6.61 6.96 Growth 2.31 3.23 4.37
116 Additional details on the individual based model (IBM) The IBM has an annual time step. At the beginning of each time s tep, the number of seeds arriving to quadrat k in plot j is drawn from a Poisson distribution with a mean equal to Establishment of these seeds to the new recruit stage (three months old) is stochastic (independent Bernoulli trials), with the germination probability equal to ; thus, the number of surviving seeds is a binomial random variable. Each surviving new recruit q in quadrat k is assigned an initial height, drawn from a Normal distribution with parameters from t he new recruit height model. Because resulting new recruits are three months old, simulating survival and growth of new recruits for eight additional months is required to produce year old seedlings. New recruit survival is thus drawn from a Bernoulli di stribution with a probability of survival equal to annual seedling survivorship scaled to 8 months by raising seedling survivorship to the power of 8/12. Similarly, growth of new recruits into year old seedlings is drawn from a Normal distribution with a mean equal to the mean from the seedling growth model multiplied by 8/12. Survival of pre existing seedlings (those seedlings surviving from the previous time step) is simulated as Bernoulli trials with probability equal to seedling survivorship ), where the index q specifies an individual seedling. Growth of each pre existing (and surviving) seedling q in quadrat k in plot j at time t is drawn from a normal distribution with parameters from the seedling growth model. The demographic processes which occur in a single run of the IBM are shown below:
117 Seedlings which die or shrink to a height< 0 are removed from the simulation. We used minimized posterior predictive loss (Gelfand and Ghosh 1998) to compare IBM model output from three different simulation experiments (full model, homog enous seed arrival model and homogenous establishment model) to observed data. This model selection approach uses a loss function to measure the discrepancy between the posterior predictive distribution from a Bayesian analysis and observed data. Similar to information criterion approaches (e.g. AIC, DIC), the posterior predictive loss approach incorporates both a goodness of fit term and a penalty term for model complexity. However, unlike information criterion approaches, posterior predictive loss does not require specifying model dimensions or asymptotic justification (Gelfand and Ghosh 1998) making it an ideal tool for evaluating complex, hierarchical models. Following (Ghosh and Norris 2005) we use mean squared predict ed error (MSPE) on the log scale, adding 0.5 to avoid log(0), to compare IBM predictions of both new recruits and total seedling abundance to observed counts in each k of N quadrats: (D 13) Each run of the IBM model results in a unique MSPE value, resulting in a distribution of MSPE values for each treatment of the simulation experiments.
118 Figure D 1. Spatial variation in light availabili ty (A) and grass presence (B) across the habitat gradient. Each dot represents the plot level mean for multiple measurements of percent transmitted light and presence/absence of grass (1=present). Dashed black lines represent boundaries between evergreen and deciduous forest types. A B
119 Figure D 2 Parameter estimates for effect of covariates on demographic models for A) New Recruit Height, B) Growth, C) Germintaion, D) Survival. Each panel shows the point estimate (black dot) and 95% credible interval (thin line) for parameters associated with particular environmental covariates and the plot level random effect. The horizontal dashed line represents zero. To facilitate interpretation of parameter estimates, environmental covariates were standardized by dividing by two standard deviations and centered around the mean, following (Gelman 2008) In this figure, con.seedlings and con.adults stand for conspecific seedling and adult density, respectively. A B C D
120 APPENDIX E: ADDITIONAL DETAILS ON MODE L S IN CHAPTER 4 The following equation sec tion presents the submodels for survival, growth, seed production and dispersal and scheduling of submodels in the IBM. All submodels were parameterized with data using Bayesian models, resulting in 1000 draws from the posterior distribution of each param eter. Parameters, prior distributions for parameters, parameter estimates with 95% CI and main sensitivities for each parameter are pre sented in Supplementary Tables E1,E2, E3 and E 4. The IBM is initialized with data on trees> 1 cm DBH from eight 4 ha se ctions from the 50 ha forest dynamics plot, using the 1994 census. During the first eight years of simulation, growth and survival of trees>1 cm DBH is held constant, while seed production, dispersal, germination and seedling growth and survival are simul ated, in order to approximate the initial distribution of seedlings in the plot. After the first eight years of simulation, one time step in the IBM begins with tree growth and survival ( Equation s E 1 and E 2). In these equations, represents the DBH of the i th individual, with and representing the size and distance of neighbor tree j in a 25 m radius around the target individual. Note that because tree census data was collected on a 5 year time step and th e IBM runs on an annual time step, we scale survival and growth to an annual time step by raising the probability of survival to the power of and divide centimeters of growth by 5. (E 1)
121 (E 2) The next step in the IBM is simulating seedling growth and survival. Equation s E 3 and E 4 show the submodels for seedling growth and survival. In these equations, indicates the height (in cm) of the i th seedling. Note that the tree neighborhood, and is calculated for seedling growth using the location and size of trees from the previous time step, before current year tree growth and survival. In these equations, represents the density of conspecific seedlings in 1 m x 1m plots. (E 3) (E 4) After seedling growth and survival, the probability of seedlings reaching 1 cm DBH and the size of those seedlings which have reac hed 1 cm DBH is also
122 stochastically simulated. In reality, there is no such discrete transition between a seedling stage and a tree stage, however, this step was necessary in the IBM because of the difference in time and spatial scale between seedling and tree data. (E 5) (E 6) The next step in the IBM is to simulate the production of new seedlings, beginning with seed production. Seed production for the i th tree is drawn from a Poisson distribution, with a sigmoid function of tree DBH: ( E 7) For IBM simulations w ith natural dispersal, the distance each seed is dispersed from the parent tree is drawn from a two T distribution, with a single free parameter, u.dispersal : (E 8) In addition to seeds arriving from trees within the IBM plot, we also had a term for seeds arriving outside the plot, We do not refer to the Bat Bath term refers to dispersal from seed sources from outside the plot, regardless of distance (thus a seed arriving from a tree 1 m outside the plot
123 would still be included in the Bath term). For each of th e 40,000 1 x 1 m quadrats in the 200 x 200 m simulated area, the number of Bath seeds arriving in each quadrat is drawn from a Poisson distribution: (E 9) The IBM scenario with no animal dispersal assumes that all seeds are dispersed beneath parent tree canopies and does not include a bath term. In th is version of the IBM, seed production remains identical to Eq 7, but dispersal distance of seed i from parent tree j, is drawn from a Uniform distribution with a minimum value equal to the anopy radius: (E 10) The canopy radius is drawn from a submodel for canopy allometry, which assumes that canopy radius is a power law of tree DBH: (E 11) After seed dispersal, the tree neighborho od in a 20 m radius and conspecific seedling density in 1 m x 1 m quadrats around each individual seed is determined from the distribution of trees and seedlings from the previous time step of the IBM. Next, seed germination of the i th seed is determined as: (E 12)
124 The germination submodel determines whether or not a seed survives to beco me a seedling. Surviving seedlings must then be assigned an initial height, which for the i th seedling is drawn stochastically from a skew normal distribution with a mean, shape and scale: (E 13) Germination and initial height of new seedlings occur three months after seed dispersal, leaving a gap of nine months between these processes and the next time step of the IBM. Consequen tly, we simulate survival and growth of newly germinated seedlings using the submodels for seedling survival and growth scaled by raising the probability of survival ( in Eq 3 to the power of 9/12, and multiplying growth term in Equation E 4 by 9/12. After simulating new seedling establishment, the IBM begins the next time step, starting with adult survival and growth ( Equation E 1 and E 2).
125 Table E 1. Key to parameters in IBM Parameter Role in model Shape of dispers al kernel Adult tree seed production Adult tree seed production A dult tree seed production Mean seed arrival (m 2 ) from outside plot Intercept in germination model Effect of consp ecific seedlings on germination Magnitude of tree neighborhood effect on germination Distance decay of tree neighborhood on germination Mean initial height of newly germinated seedlings Shap e of initial height of newly germinated seedlings Scale of initial height of newly germinated seedlings Seedling survival intercept Effect of conspecific seedlings on seedling survival Effect of seedling size on seedling survival Seedling growth intercept Magnitude of tree neighborhood effect on seedling growth Distance decay of tree neighborhood on seedling growth Effect of seedling size on seedling growth Effect of conspecific seedlings on seedling growth Scale of seedling growth Shape of seedling growth Intercept for DBH of new trees Slope relating DBH of new trees to seed ling height
126 Table E 1. Continued Parameter Role in model Variance of DBH of new trees Intercept for transition from seedlings to trees Slope relating height of seedlings to probability of transitioning to a tree Magnitude of tree neighborhood on tree survival Magnitude of tree neighborhood on tree growth Distance decay of tree neighborhood for tree survival Distance decay of tree neighborhood for tree growth Hossfeld function for tree growth Hossfeld function for tree growth Hossfeld function for tree survival Hossfeld function for tree survival Size dependent shape of tree growth Size dependent varian ce in tree growth Size dependent shape of tree growth Size dependent variance in tree growth
127 Table E 2. Prior distributions for parameters in IBM. Parameter Distribution Prior 1 Prior 2 Normal 0 1.00E 06 Uniform 0 100 Uniform 0 100 Uniform 100 0 Normal 0 1.00E 06 Normal 0 1.00E 06 Normal 0 1.00E 06 Normal 0 1.00E 06 Normal 0 1 .00E 06 Normal 0 1.00E 06 Normal 0 1.00E 06 Normal 0 1.00E 06 Normal 0 1.00E 06 Normal 0 1.00E 06 Normal 0 1.00E 06 Normal 0 1.00E 06 Normal 0 1.00E 06 Normal 0 1.00E 06 Normal 0 1.00E 06 Gamma 0.01 1.00E 02 Exponential 0.01 Normal 0 1.00E 06 Normal 0 1.00E 06 Uniform 0 1.00E+03 Normal 0 1.00E 06 Normal 0 1.00E 06 Normal 0 1.00E 02 Normal 0 1.00E 02 Normal 0 1.00E 02 Normal 0 1.00E 02 Uniform 50 5.00E+01 Normal 0 1.00E 02 Normal 0 1.00E 02 Normal 0 1.00E 02 Normal 0 1.00E 02 Exponential 1.00E 02 Normal 0 1.00E 02
128 Table E 3. Parameter estimates for parameters in IBM Parameter 2.5 % 50% 97.5 % 77 6.9 1915.8 4590.7 3 1.0 1 1.42 2.93 0 0 0 0.13 0.12 0.12 0.1 4 0.32 0.5 2.86 2.49 2.17 1.29 0.8 0.39 0.05 0.03 0.02 0.0 1 0.21 0.56 4.7 1 4.91 5.1 0.8 3 0.9 0.97 0.1 0 0.1 0.24 0.35 0.91 0.06 0.04 0.02 0.1 0.14 0.19 2.8 1 5.46 8.14 15.4 3.9 0.83 0.6 9 1.3 1.84 0.1 3 0.17 0.21 0.22 0.15 0.08 20. 62 22.17 23.79 0.0 5 0.14 0.25 1.04 0.85 0.64 0.0 1 0.01 0.01 0.1 2 0.15 0.19 78.42 36.52 14.61 6.27 15.86 34.19
129 Table E 3. Continued Parameter 2.5 % 50% 97.5 % 1.65 0.74 0.1 0.29 0.15 0.04 0.38 0.82 1.21 1.18 1.56 2.06 1.89 12.75 24.38 4.85 4.92 4.98 6.79 0.06 9.05 3. 17 3.26 3.37 23.4 9.28 3.25 0.07 0.08 0.09 19.34 0.14 18.71 0.86 0.89 0.92
130 Table E 4. Main sensitivities to output of IBM for parameters Parameter Total population Basal area 0.006 0.009 0.006 0.005 0.013 0.009 0.013 0.043 0.018 0.007 0.018 0.013 0.008 0.012 0.01 0.021 0.014 0.008 0.011 0.053 0.008 0.013 0.02 0.013 0.013 0.02 0.013 0.011 0.028 0.016 0.004 0.014 0.007 0.007 0.019 0.01 0.019 0.019 0.017 0.007 0.025 0.016 0.009 0.015 0.009 0.01 0.01 6 0.012 0.009 0.005 0.01 0.012 0.024 0.011 0.015 0.103 0.017 0.01 0.048 0.013 0.009 0.041 0.02 0.007 0.022 0.008 0.006 0.017 0.015 0.005 0.037 0.00 8 0.01 0.021 0.019 0.01 0.01 0.006 0.008 0.027 0.018 0.036 0.025 0.024 0.008 0.02 0.013 0.023 0.002 0.011 0.007 0.021 0.017 0.039 0.004 0.019 0.011 0.022 0.021 0.56 0.037 0.488 0.01 0.015 0.014 0.007 0.01 0.007 0.01 0.075 0.016 0.013 0.054 0.022 0.009 0.025 0.019
131 APPENDIX F. ADDITIONAL DETAILS ON SENSITIVITY ANALYSIS Our sensitivity analysis builds off of previous variance based sensitivity analyses (reviewed in Saltelli et al. 2008) Variance base d methods for global sensitivity analysis calculate main sensitivities ( ) of output Y to parameter as: Previous variance based methods for global sensitivity analysis in ecology have used Monte Carlo based numerical procedures for computing main and total sens itivities (Ellner and Fieberg 2003, Fieberg and Jenkins 2005) For the sensitivity of a given parameter, this numerical procedure involves generating two matrices containing p arameter values ( A and B), in which each column represents variation in a single parameter. Next, a third matrix ( C ) is built using all columns of A, except the column representing the parameter of interest, which is drawn from B. Using matrices A, B and C as input for a model results in three vectors of output: Y a Y b and Y c Each matrix has dimensions (N,k), where N is the number of samples of each parameter and k is the number of parameters. The main sensitivities can be estimated as: (F 1) This Monte Carlo method for determining sensitivities requires a total cost of N(k+2) runs of the model. With typical values of N <1000, this method can be computationally prohibitive for complex, memory and time intensive models. Our method of sensitivity analysis takes advantage of the fact that all of the parameters used as input for our IBM have a probabilistic interpretation as samples from the posterior distribution of parameters. This approach discretizes the distribution
132 of Y and values using histograms to bin these vectors. We then determine the numerator in Equation F 1 by subtracting the mean value for output Y in bin j of the histogram of from the mean of all of the output values and sc ale by the probability of bin j : ( F 3) We tested the validity of this method by comparing sensitivities calculated using our method to sensitivities calculated analytically for a simple example: sensitivity in a beta binomial distribution. In this example, output Y is distributed as a binomial distribution with size parameter N and probability parameter p : (F 4) The probability in the binomial distribution is itself distributed as a beta random variable: (F 5) The variance of p is given by: (F 6) The variance of Y conditional on parameters is given by: (F 7) Consequently, (F 8) is given by Equatio n F 8 and V[Y] is given by Equation F 8 After some algebra, including these expressions in the numerator and denominator of Equation F 1 results in an analytical expression for the sensitivity of output Y to p:
133 (F 9) To compare our numerical method for calculating main sensitivities to we simulated 10,000 draws from a beta binomial distributio n with n=100, and a range of values for a and b. We then calculated the sensitivity of Y to p with a range of histogram bins, from 2 to 500. Results demonstrate that our numerical method converges to the analytical solution with >10 histogram bins (Figur e F 1). Figure F 1. Comparison of analytical sensitivity for a beta binomial distribution to numerical approximation. Each panel of this figure shows the sensitivity of the beta binomial distribution to p, for beta distribution with different shape para meters (shown at the top of each panel). The black line indicates the numerical solution for a given number of histogram bins and the red line indicates the analytical solution from Equation F 9
134 In addition to this analytical check, we also determined ho w our results for sensitivities changed with number of histogram bins. For each output, main sensitivities for each parameter converged at ~500 bins (Figure F 2). Thus, for our analysis of main sensitivities, we used 500 bins in the histogram for each par ameter. Figure F 2. Main sensitivities for parameters in the IBM as a function of histogram bins. Each colored line represents the sensitivity of the model to a different parameter.
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145 BIOGRAPHICAL SKETCH Trevor Caughlin was born in Gunnison, Colorado in 1984. He received his Bachelor of Arts with a reas of c oncentration in b io logy and environmental s tudies from the New College of Florida in 2007. Af ter graduating from New College, Trevor received a Fulbright Research Grant to conduct research in Thailand from 2007 2008. During the ten month Fulbright period, Trevor conducted research on the natural history of seed dispersal and frugivory in Thai for ests. This preliminary research formed the basis for his Ph D 2008. He received his Ph.D. from the University of Florida in the summer of 2013. His main area of interest lies in understand ing spatial pattern and process in tropical plant communities.