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Potential Effects of Diurnal Temperature Oscillations on Potato Late Blight under Climate Change

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Title:
Potential Effects of Diurnal Temperature Oscillations on Potato Late Blight under Climate Change Results from Experiments and Simulation Modeling
Creator:
Shakya, Shankar K
Place of Publication:
[Gainesville, Fla.]
Florida
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University of Florida
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english
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1 online resource (11 p.)

Thesis/Dissertation Information

Degree:
Master's ( M.S.)
Degree Grantor:
University of Florida
Degree Disciplines:
Plant Pathology
Committee Chair:
VANBRUGGEN,ARIENA HENDRIKA
Committee Co-Chair:
GOSS,ERICA M
Committee Members:
DUFAULT,NICHOLAS S
Graduation Date:
8/9/2014

Subjects

Subjects / Keywords:
Blight ( jstor )
Climate change ( jstor )
Disease models ( jstor )
Diseases ( jstor )
Infections ( jstor )
Lesions ( jstor )
Modeling ( jstor )
Phytophthora ( jstor )
Sporulation ( jstor )
Trucks ( jstor )
Plant Pathology -- Dissertations, Academic -- UF
climatechange -- lateblight -- modeling -- simulation
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bibliography ( marcgt )
theses ( marcgt )
government publication (state, provincial, terriorial, dependent) ( marcgt )
born-digital ( sobekcm )
Electronic Thesis or Dissertation
Plant Pathology thesis, M.S.

Notes

Abstract:
Global climate change is associated with increased average temperatures and changes in diurnal temperature ranges. To enable prediction of effects of diurnally oscillating versus constant temperatures on potato late blight (Phytophthora infestans) detached potato leaves were inoculated with two P. infestans isolates (clonal lineages US-8 and US-23), and disease cycle components were monitored. Number of lesions, incubation period, latent period, radial lesion growth and sporulation intensity were assessed at seven constant and/or two diurnally oscillating temperatures around the same means. Optimum curves were obtained by fitting the data to a thermodynamic model. We tested and confirmed the hypothesis that the optimum temperature curve for growth and development rates of P. infestans was steeper under constant conditions than oscillating temperatures. A new mechanistic model (BLIGHTSIM) was developed to simulate and predict late blight development under climate change. BLIGHTSIM is a modified Susceptible (S), Exposed (E), Infectious (I) and Removed (R) compartmental model with hourly temperatures and relative humidities as input variables. A new approach of parallel box car trains was introduced in the model to simulate and limit lesion growth. The model was fitted to data obtained from the controlled temperature experiments with the isolate of the US-23 lineage of P. infestans. The model provided a good fit to the data except for constant 10 degree Celsius. BLIGHTSIM, when incorporated in a potato growth model, can be an effective tool to study effects of changes in average temperature and diurnal oscillations on potato late blight. ( en )
General Note:
In the series University of Florida Digital Collections.
General Note:
Includes vita.
Bibliography:
Includes bibliographical references.
Source of Description:
Description based on online resource; title from PDF title page.
Source of Description:
This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Thesis:
Thesis (M.S.)--University of Florida, 2014.
Local:
Adviser: VANBRUGGEN,ARIENA HENDRIKA.
Local:
Co-adviser: GOSS,ERICA M.
Electronic Access:
RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2015-02-28
Statement of Responsibility:
by Shankar K Shakya.

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UFRGP
Rights Management:
Applicable rights reserved.
Embargo Date:
2/28/2015
Resource Identifier:
968131610 ( OCLC )
Classification:
LD1780 2014 ( lcc )

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1 POTENTIAL EFFECTS OF DIURNAL TEMPERATURE OSCILLATIONS ON POTATO LATE BLIGHT UNDER CLIMATE CHANGE: RESULTS FROM EXPERIMENTS AND SIMULATION MODELING By SHANKAR KAJI SHAKYA A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIV ERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2014

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2 © 2014 Shankar Kaji Shakya

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3 To my family

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4 ACKNOWLEDGMENTS I owe my deepest gr atitude to the chair of my thesis committee Ariena van Bruggen for her tremendous support throughout my study. This thesis would not have been complete without your recurrent advice and guidance. I would also like to thank Erica Goss (Co Chair) and Nichola s Dufault for their continuous encouragement and serving on my committee. I am very grateful to Pamela Anderson and Andre Devaux of the International Potato Centre (CIP) for developing the research proposal and Walter Bowen of International Programs (UF/I FAS) and Rosemary Loria, chair of the Plant Pathology department, for providing me the opportunity to come to UF. I am thankful to Peter Kromann of CIP for his help during my visit to Ecuador. I would like to acknowledge Jorge Andrade Piedra (CIP), Senthol d Asseng (UF) and Daniel Wallach from the Institut National de la Recherche Agronomique (INRA) for their assistance in developing the model. I want to thank Shouan Zhang (UF) and Bill Fry (Cornell University) for providing late blight infected leaves from Homestead and clonal lineage US 8 from Pennsylvania, respectively, and Nik Grünwald (USDA) for genotyping the Homestead isolate. I must thank all the lab members, Ellen Dickstein, Hong Ling Er, Mpoki Shimwela and Kalpana Sharma, for their support. How can I forget my friends Deepak Shrestha, Sujan Timilsina, Naweena Thapa, Kshitij Khatri and Sanju Kunwar? Two years of graduate school would not have been so fun without you guys. Nothing could have been accomplished without the advice, love, care and patie nce of my mom, dad, sisters and lovely wife Sujata. Thank you everyone for being always with me.

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ ............... 4 LIST OF TABLES ................................ ................................ ................................ ........................... 7 LIST OF FIGURES ................................ ................................ ................................ ......................... 8 LIST OF ABBREVIATIONS ................................ ................................ ................................ .......... 9 ABSTRACT ................................ ................................ ................................ ................................ ... 11 CHAPTER 1 GENERAL INTRODUCTION ................................ ................................ .............................. 13 Global Climate Change ................................ ................................ ................................ ........... 13 Climate Change and Diseases ................................ ................................ ................................ . 16 Climate Change in the A ndes ................................ ................................ ................................ . 17 Potato, Late Blight and its Causal Agent Phytophthora infestans ................................ .......... 18 Origin and Migration of P.infestans ................................ ................................ ....................... 20 Epidemiology of P.infestans ................................ ................................ ................................ ... 21 Late Blight Models ................................ ................................ ................................ ................. 22 Research Objectives ................................ ................................ ................................ ................ 23 Outline of Thesis ................................ ................................ ................................ ..................... 24 2 POTENTIAL EFFECTS OF DIURNAL TEMPERATURE OSCILLATIONS ON POTATO LATE BLIGHT UNDER CLIMATE CHANGE ................................ .................. 25 Introduction ................................ ................................ ................................ ............................. 25 Materials and Methods ................................ ................................ ................................ ........... 28 Clonal Lineages of Phytophthora infestans ................................ ................................ .... 28 Plant Production ................................ ................................ ................................ .............. 28 Inoculum Production ................................ ................................ ................................ ....... 29 Inoculation and Incubation ................................ ................................ .............................. 29 Comparison of Growth Chamber and Incubators at Constant Temperatures .................. 30 Comparison of Effects of Constant and Oscillating Temperatures on Late Blight ......... 31 Measurements of Epidemic Components ................................ ................................ ........ 31 Model Fitting and Statistical Analysis ................................ ................................ ............ 32 Results ................................ ................................ ................................ ................................ ..... 34 Comparison of Incubators and Growth Chamber ................................ ............................ 34 Nonlinear Regressions ................................ ................................ ................................ ..... 34 Effects of Average Temperatures and Their Daily Amplitudes ................................ ...... 34 Discussion ................................ ................................ ................................ ............................... 37

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6 3 BLIGHTSIM: A NEW SEIR MODEL FOR POTATO LATE BLIGHT SIMULATING THE RESPONSE OF Phytophthora infestans TO CLIMATE CHANGE UNDER DIURNAL TEMPERATURE OSCILLATIONS ................................ ................................ ... 51 Introduction ................................ ................................ ................................ ............................. 51 Materials and Methods ................................ ................................ ................................ ........... 56 Model Assumptions ................................ ................................ ................................ ......... 56 Basic Structure of Model BLIGHTSIM ................................ ................................ .......... 57 Model Equations ................................ ................................ ................................ .............. 58 Estimation of Relative Lesion Growth Rate ................................ ................................ .... 59 Effect of Temperatur e on Relative Sporulation*Infection and Derivation of Function f1 ................................ ................................ ................................ ................... 60 Effect of Relative Humidity on Sporulation and Derivation of Function f2 ................... 60 Effect of Temperature on Relative Lesion Growth and Derivation of Function f3 ........ 60 Effect of Temperature on Latency Progression Rate and Derivation of Function f4 ...... 61 Driving Variables ................................ ................................ ................................ ............ 61 Model Fitting ................................ ................................ ................................ ................... 61 Results ................................ ................................ ................................ ................................ ..... 63 Effects of Temperature and Relative Humidity on Model Parameters ........................... 63 Model Calibration ................................ ................................ ................................ ............ 63 Model Output at Con stant and Oscillating Temperatures ................................ ............... 64 Discussion ................................ ................................ ................................ ............................... 65 4 SUMMARY AND CONCLUSION ................................ ................................ ....................... 81 APPENDIX: BLIGHTSIM MODEL CODE IN R ................................ ................................ ........ 84 LIST OF REFERENCES ................................ ................................ ................................ ............... 88 BIOGRAPHICAL SKETCH ................................ ................................ ................................ ......... 99

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7 LIST OF TABLES Table page 2 1 Preliminary experiments comparing epidemic components of late blight on potato with two isolates of P. infestans in two incubators and one growth cham ber ................... 45 2 2 Values of the approximate coefficients of determination (R 2 ) for duplicate nonlinear regressions of five epidemic components of late blight ................................ ..................... 46 2 3 Multivariate analysis of variance (MANOVA) for the effects of isolate (I), temperature amplitude (AMP) and the interaction between isolate and amplitude on epidemic components of late blight. ................................ ................................ .................. 47 3 1 Variables and parameters used in the BLIGHTSIM model ................................ ............... 73 3 2 Initial values of the proportions of healthy (H) and latently infected sites (L1a) at different tempera ture amplitude combinations for the BLIGHTSIM model.* .................. 74 3 3 Estimated parameter values for the reducing functions (f1 f4) obtained by fitting a thermodynamic model to epidemic components of an isolate of Phytophthora infestans clone US 23 on potato cv. Red Lasoda ................................ .............................. 74 3 4 Values of slope and coefficients of determination (R 2 ) for simulated versus observed disease severities at different temperature amplitude combinations for late blight .......... 74

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8 LIST OF FIGURES Figure page 2 1 Effect of constant and oscillating temperat ures on number of late blight lesions mm 2 zoospore 1 (NL) ................................ ................................ ................................ .................. 48 2 2 Effect of constant and oscillating temperatures on late blight epidemic components incubation progression rate, h 1 (IPR) and l atency progression rate, h 1 (LPR) ................. 49 2 3 Effect of constant and oscillating temperatures on the late blight epidemic components lesion growth rate in cm day 1 (LGR) and sporulation intensity a s sporangia cm 2 (SI) ................................ ................................ ................................ ............. 50 3 1 Relational diagram of the model BLIGHTSIM for simulation of potato late blight ( Phytophthora infestans ) with all compartments and rate variables. ................................ . 75 3 2 Optimum curves for parameter estimates used in the model BLIGHTSIM ...................... 76 3 3 Observed (Dots) and simulated (continuous line) disease progress curve s of an isolate of Phytophthora infestans clone US 23 at different constant temperatures ........... 77 3 4 Simulated versus observed late blight severities (dotted lines) and expected 1:1 relationships (so lid lines) at different temperature amplitude combinations .................... 78 3 5 Observed (Dots) and simulated (continuous line) disease progress curves of and isolate of Phytophthora infestans clone US 23 at different oscillating temperatures ....... 79 3 6 Observed (Dots) and simulated (continuous line) disease progress curves of and isolate of Phytophthora infestans clone US 23 at different oscillating te mperatures ....... 80

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9 LIST OF ABBREVIATIONS AgMIP ANOVA BSL CaCO 3 cal cv DILFAC ENSO GCM GHG GLM Gt HMF HSP IP IPCC IPR K LA LAI LGR LP LPR LWR The Agricultural Model Intercomparison and Improvement Project Analysis of Variance Biosafety level Calcium Carbonate Calorie Cultivar Dilution factor El nino Southern oscillation General Climate Model Green House Gas Generalized Linear Model Giga ton Ho urly Multiplication Factor Hourly Spore Production Incubation Period Intergovernmental Panel on Climate Change Incubation Progression Rate Potassium Lesion Area Leaf Area Index Lesion Growth Rate Latent Period Latency Progression Rate Long Wave Radiation

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10 MANOVA m.a.s.l N NL NLIN P PARP ppb ppm R 2 REMRATE RH RLGR SI SSR SWR UNFCCC M ultivariate Analysis of Variance meter above sea level Nitrogen Number of lesions per mm 2 per zoospore Non Linear Regression Phosphorus Pimaricin, Ampicillin, Rifampicin, Pentachloronitrobenzene parts per billion parts per million Coefficient of determinat ion Removal Rate Relative Humidity Relative Lesion Growth Rate Sporulation Intensity Simple Sequence Repeat Short Wave Radiation United Nations Framework Convention on Climate Change Pi (Mathematical constant)

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11 Abstract of Thesis Presented to th e Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science POTENTIAL EFFECTS OF DIURNAL TEMPERATURE OSCILLATIONS ON POTATO LATE BLIGHT UNDER CLIMATE CHANGE: RESULTS FROM EX PERIMENTS AND SIMULATION MODELING By Shankar Kaji Shakya August 2014 Chair: Ariena H.C. van Bruggen Cochair: Erica Goss Major: Plant Pathology Global climate change is associated with increased average temperatures and changes in diurnal temperature ra nges. To enable prediction of effects of diurnally oscillating versus constant temperatures on potato late blight ( Phytophthora infestans ) detached potato leaves were inoculated with two P. infestans isolates (clonal lineages US 8 and US 23), and disease c ycle components were monitored. Number of lesions, incubation period, latent period, radial lesion growth and sporulation intensity were assessed at seven constant and/or two diurnally oscillating temperatures around the same means. Optimum curves were obt ained by fitting the data to a thermodynamic model. We tested and confirmed the hypothesis that the optimum temperature curve for growth and development rates of P. infestans was steeper under constant conditions than oscillating temperatures. A new mechan istic model (BLIGHTSIM) was developed to simulate and predict late blight development under climate change. BLIGHTSIM is a modified Susceptible (S), Exposed (E), Infectious (I) and Removed (R) compartmental model with hourly temperatures and relative humid ities as input variables. A new approach of parallel box car trains was introduced in the model to simulate and limit lesion growth. The model was fitted to data obtained from the controlled temperature experiments with the isolate of the US 23 lineage of P.

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12 infestans . The model provided a good fit to the data except for constant 10 degree Celsius. BLIGHTSIM, when incorporated in a potato growth model, can be an effective tool to study effects of changes in average temperature and diurnal oscillations on p otato late blight.

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13 CHAPTER 1 GENERAL INTRODUCTION Global Climate Change Climate change refers to observable and measurable changes in the climatic pattern over a long period of time due to increased concentrations of Green House Gases (GHGs) in the atmosphere. According to the Intergovernmental Panel on Climate Change (IPCC), climate change is defined as a change in the state of the climate that can be identified (e.g. using statistical tests) by changes in the mean and/or the variability of its properties and that persists for an extended period, typically decades or longer (Field et al. 2014). The above definition does not make a clear distinction between the human induced (anthropogenic) climate change and climate change due to natural variability, and thus includes both components as drivers of climate change. This definition of climate change is different from the United Nations Framework Convention on Climate Change (UNFCCC), where climate change refers to a cha nge of climate, which is attributed directly or indirectly to human activity that alters the composition of the global atmosphere in addition to natural climate variability observed over comparable time periods. This definition distinguishes between climat e change induced by human activities and that due to natural causes (Field et al. 2014). Climate change is caused by an increase in concentration of greenhouse gases (GHGs), resulting in an increase in average global temperature and changes in extreme weat her events like drought and rain storms. These changes in global weather patterns are also leading to a rise in global surface and sea temperatures, melting of the snow and rising sea levels. Long lived GHGs, primarily carbon dioxide (CO 2 ), methane (CH 4 ), nitrous oxide (N 2 O) and fluorinated gases (F gases), are responsible for the rise in temperature of the atmosphere. The incoming short wave radiation (SWR) is partially reflected from the atmosphere or clouds, partially

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14 transmitted and absorbed by the ear th surface (land and oceans), and partially reradiated into space. There exists equilibrium between incoming and outgoing radiation with SWR coming (LWR) from the earth surface to the atmosphere and beyond. These long wavelength infrared rays are partially trapped by GHGs and re emitted in all directions. The radiation directed towards the earth surface cause an increase in the surface temperature; this phenomenon is well known as greenhouse effect. The global atmospheric concentration of carbon dioxide , methane and nitrous oxide has increased from a pre industrial value of a bout 278 ppm to 390.5 ppm, 722 ppb to 1803 ppb and 271 ppb to 324.2 ppb, respectively, by the year 2011 (Stocker et al. 2013). The increment in the amount and concentration of GHGs is primarily due to human activities that involve burning of fossil fuels for energy and transportation, deforestation, land clearance for agriculture, industrial p rocessing, waste management and agricultural practices. The increase in GHGs is the primary driving force for the observed temperature change. Global avera g e sur f a c e and ocean temper a tu r es have increased b y 0.85°C (0.65 to 1.06 °C ) during 1880 2012 ( Stocke r et al. 2013), which coincides with the increasing GHG concentrations. The temperature change is observed more in the northern latitudes and warming of the earth surface is faster than oceans (Salinger 2005; Field et al. 2014). Besides the changes in con centration of GHGs and temperature, rising sea level, melting of the snow and observed extreme events are the other indicators of climate change. Globally average sea level has increased at an average rate of 2.0 mm year 1 (1.7 to 2.3 mm year 1 ) over 1971 to 2010 (Stocker et al. 2013). On an average 226 Gt (91 361 Gt year 1 ) ice was lost from glaciers every year from 1971 to 2009 (Stocker et al. 2013). Since 1950 extreme weather events have been observed more

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15 frequently. The number of extremely warm days an d nights has increased globally. Increases in frequency of heat waves and heavy rainfall have also been observed (Stocker et al. 2013). Global surface temperatures are expected to increase between 1.5°C and 2.0°C by the end of the 21 st century (Field et al . 2014). However, the changes in temperature are not uniform over the globe. The change in surface temperature is expected to be greater than ocean temperature. By the end of 21 st century the ocean temperature is expected to rise by 0.3 0.6°C at a depth of 1 km. Frequency, duration and magnitude of hot weather extremes are expected to increase with occasional cold winter extremes in the future. Arctic sea ice cover is expected to decrease (43 94%) in September with the increase in temperature. Global glacie r volume, excluding glaciers on the periphery of Antarctica, is expected to decrease by 15 85%. Northern Hemisphere spring snow cover is projected to decrease by 7 25% (Stocker et al. 2013). Global climate change is also associated with differences in dail y temperature amplitudes and shifts in the frequency of meteorological extremes ( Ramirez Villegas et al. 2013; Scherm 2004; Scherm and van Bruggen 1994b). Th e uncertainty associated with predictions of diurnal variations in temperature is currently still v ery large (Ramirez et al. 2013). On average, the diurnal amplitudes in temperature are expected to decrease (Salinger 2005; Stocker et al. 2013). However, for some locations, the amplitudes may be underestimated by current climate models. On high plains, t he amplitudes may increase under global warming because of reduced cloud cover (Anonymous 2011; Perez et al. 2010). The daily temperature oscillations are expected to deviate more from sinusoidal with maximum temperatures later in the afternoon (Knappenber ger et al. 1996), so that dew periods and high relative humidities may last longer in the morning (Scherm and van Bruggen 1993b; Scherm and van Bruggen 1994b).

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16 Climate Change and Diseases Climate change is likely to affect plant disease development and i s well described in various reviews (Coakley et al. 1999; Garrett et al. 2006; Garrett et al. 2011; Ghini et al. 2008; Gregory et al. 2009; Juroszek and von Tiedemann 2013; Luck et al. 2011; Pautasso et al. 2012; Roos et al. 2011; Savary et al. 2011; West et al. 2012). Increased CO 2 concentration, temperature and changes in rainfall pattern may modify the physiology and resistance of host, shift the geographical distribution of host and pathogen (migration), affect the rate of pathogen development, and the evolution of new races of pathogens (Bebber et al. 2013; Coakley et al. 1999; Chakraborty 2013; Evans et al. 2008). Effect of elevated CO 2 on plant disease has received less attention compared to the temperature effect. Increase in CO 2 is known to increase the plant canopy size and density (Manning and von Tiedemann 1995) resulting in increased humidity. This increase in humidity is likely to promote diseases like rusts, powdery mildews, leaf spots and blights (Manning and von Tiedemann 1995). Chakraborty a nd Datta (2003) demonstrated increased fecundity of Colletotrichum gloeosporoides with doubling of CO 2 concentration. Besides the effect of elevated CO 2 on plant disease , increase in temperature has gained more attention in recent years. Temperature plays an important role in the disease cycle and is associated with infection, symptom development, propagule production, dispersion and survival. Warm winters with high night temperatures may increase the survival of pathogens, accelerate life cycles of vector s and fungi, and increase sporulation and aerial fungal infection, resulting in an overall increase in disease pressure (Harvell et al. 2002; Kaukoranta 1996). Elevation in temperature is associated with modification of host physiology and resistance (Coak ley et al. 1999). Poleward shift in pests and pathogens have been observed under increasing temperatures (Bebber et al. 2013). Californian forest is becoming more susceptible to Phytophthora ramorum (Pautasso et al. 2012). A climate model combined with a P homa stem

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17 canker forecasting model predicts the increase in range and severity of this disease (Evans et al. 2008). Late blight epidemics were observed 2 4 weeks earlier in Finland ( Hannukkala et al. 2007). However, the interrelationships between plant pat hogens, their hosts, climatic factors and ecosystem managers are likely complex with multiple interactions, non linearities and feedback loops (Coakley et al. 1999; Garrett et al. 2011; De Wolf and Isard 2007). Thus, prediction of plant disease development under climate change is difficult, and will be specific for the pathosystem and its immediate environment. Climate Change in the Andes Glacial retreat is one of the most important indicators of climate change in the Andes region (Vuille et al. 2003; Urru tia and Vuille 2009; Rabatel et al. 2013). This phenomenon is most likely associated with the observed increase in temperature and El Nino events rather than changes in precipitation (Vuille et al. 2003; Urrutia and Vuille 2009; Rabatel et al. 2013). It is well documented now that the average temperature has increased in the tropical Andes (Vuille et al. 2003; Vuille et al. 2008). Based on a number of weather stations, the temperature in the Andes has increased by 0.68°C on average and 0.1°C per decade sinc e 1939 (Vuille et al. 2008). This result is consistent with earlier studies predicting the change in temperature (Vuille and Bradley 2000; Vuille et al. 2003). Increases in both maximum and minimum temperatures were observed between 1918 1990 although th e increase in minimum temperature was much larger and thus reducing the diurnal temperature range in certain areas of the Andes (Vuille et al. 2008). On the other hand, the daily temperatures amplitudes may increase under global warming on the high plains of the Andes, because reduced cloud cover will likely raise the daily maximum temperature more than the daily minimum temperature (Perez et al. 2010). Unlike changes in temperature, documentation of rainfall has been very difficult due to unavailability of sufficient long term data. The precipitation trend was not clear in the Andes (Vuille et al. 2003) until

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18 recently.It is now known that precipitation has slightly increased in certain areas in the second half of the century (Vuille et al. 2008). The El Nin o Southern Oscillation (ENSO) is likely to influence the amount and intensity of precipitation but is also responsible for drought periods (Salinger 2005). During the period of 1950 1995 a significant increase in relative humidity ranging from 0.5 per ce nt to 2.5 per cent per decade was observed (Vuille et al. 2003). Climate change predictions for the Andes region is primarily focused on changes in temperature and precipitation. Climate projections for the Andes show an increasing trend in temperature thr oughout the century (Urrutia and Vuille 2009). The temperature increase is predicted to be more in high mountains of Ecuador, Peru and Bolivia (Bradley et al. 2006; Urrutia and Vuille 2009). The predictions are different for the eastern and western slope o f the Andes. Increase in temperature is predicted to be more on the western slopes and may be insignificant for the eastern slopes (Vuille et al. 2003). Under the high emission scenario, the temperature change is expected to be 4 5°C and is positively corr elated with altitude (Urrutia and Vuille 2009). Due to this increase in temperature many glaciers are at risk especially the ones that are 5400 m.a.s.l. Precipitation tends to increase in the tropical Andes under A2 scenario with some uncertainties. A2 sce nario describes a heterogeneous world with regional economic development. Variation in precipitation is predicted depending on the slopes. Eastern slopes are expected to have increased precipitation up to 2000 m.a.s.l and decreases beyond that altitude wh ere as precipitation is expected to increase in general in the western slopes with exception at 1000 3000 m.a.s.l (Urrutia and Vuille 2009). Potato, Late Blight and its Causal Agent Phytophthora infestans P otato ( Solanum tuberosum L .) is the third mo s t i m port a nt food c rop a ft e r w h ea t a nd r i ce with global production of more than 300 million metric tons . I t is c ul t ivat e d und e r t e mpe ra te, subtropi ca l a n d tropi ca l c ondi t ions. More than half (52%) of the potato production is in

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19 developing countries. The c ul t iva t e d potato o r i g inat e d in the And e s in P e ru a round L a ke Tit i ca c a , wh e r e a w i de v a ri e t y of p r i m i t ive c ul t iva r s a nd wild s p ec i es r e latives st i ll e x is t (Spooner et al. 2005) . L a t e bl i g ht is one of the most i m port a nt a nd ec o nom i c dise a s e s o f the potato c rop, a n d h a ve t he potential of destr o ying a whole potato f i e ld in a w e e k und e r f a vo r a ble c ondi t ion s . T h e dis e a se is ca used b y an oo m y c e te, Phytophthora infestans (Mont.) de B a r y . The pathogen is more closely related to brown algae and diatoms than to fungi, as ev ident from the molecular phylogenies ( Baldauf et al. 2000; Sogin and Silberman 1998; Thines and Kamoun 2010). P. infestans belongs to the Kingdom Stramenopiles, Phylum Oomycota, Order Peronosporales , Family Peronosporaceae , and Genus Phytophthora. P. infes tans can reproduce both sexually and asexually. It is a heterothallic oomycete and requires two opposite mating types (A1 and A2) and produces a thick walled sexual resting structure called oospore. Oospores can survive from one season to another in soil ( Drenth et al. 1995; Mayton et al. 2000; Fernández Pavía et al. 2004) and serve as primary inoculum when the conditions are favorable. Oospores are also known to survive high temperatures up to 44°C (Singh et al. 2004) and can remain in soil for many years ( Andersson et al. 1998; Lehtinen and Hannukkala 2004). The production of oospores is not very common as it requires both mating types (A1 and A2); instead, P. infestans commonly produces asexual spores called sporangia. A single lesion could have as many as 300,000 sporangia (Mayton et al. 2000) which are distributed through wind. Sporangia do not survive for a long time in the atmosphere ( Fernández Pavía et al. 2004; Mizubuti et al. 2000; Sunseri et al. 2002) as their survival is dependent on temperature, relative humidity and solar radiation (Minogue and Fry 1981). High relative humidity, 15 20°C temperature and overcast

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20 conditions increase the chances of survival of sporangia ( Mizubuti et al. 2000). The survival of sporangia in moist soil is much greater than in the atmosphere (Andrivon 1995). Origin and Migration of P.infestans The origin of P.infestans is still a controversy (Ristaino 2002; Goss et al. 2014). Different lines of evidence support each hypothesis about its origin. The first hypothesis pro poses central Mexico as the centre of origin (Goss et al. 2014; Grünwald and Flier 2005; Goodwin et al. 1994a). This theory is based on facts that the pathogen populations are highly diverse for genotypic and phenotypic markers (Goodwin et al. 1992), both mating types (A1 and A2) are found in Mexico, and the host resistance genes are present in wild Solanum species in Mexico. A recent study that included sequencing the four nuclear genes from different populations supports the Mexican origin of P. infestans (Goss et al. 2014). Another hypothesis proposes the South American Andes as the centre of origin (Gómez Alpizar et al. 2007). This theory is based on the fact that late blight may have been endemic to the Andes region. Sequencing and analysis of mitochond rial and nuclear loci of the pathogen supports this hypothesis (Gómez Alpizar et al. 2007). Another ongoing debate is about the migration of the pathogen that caused the Irish famine. Prior to early 1980s, the sexual reproduction of the pathogen was limite d to the highlands of central Mexico (Goodwin et al. 1994b). A single clonal lineage (A1 mating type) was dominant all round the world (Goodwin et al. 1994b). Three theories have been proposed regarding the migration and distribution of the pathogen. First , the pathogen moved from central Mexico to US and then to Europe (Fry et al. 1993). Second, the pathogen migrated from the Andes to the US and then to Europe (Tooley et al. 1989). Third, the pathogen migrated from Mexico to Peru and then to the US and Eur ope (Andrivon 1996).

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21 Epidemiology of P.infestans P. infestans is a hemibiotroph and thus requires living tissue for infection. When sporangia land on healthy leaf surface in the presence of enough moisture and optimum temperature conditions, infection take s place. Depending on temperature, the germination of sporangia is via a germ tube at temperatures more than 15°C and/or production of 6 12 motile zoospores below that temperature (Crosier 1934). The zoospore has two types of flagella to swim in free water , tinsel type and whiplash type (Thines and Kamoun 2010). Effects of temperature on mode of germination have been studied intensively (Crosier 1934; Maziero et al. 2009; Melhus 1915; Mizubuti and Fry 1998). Differences in germination have been reported for different clonal lineages (Mizubuti and Fry 1998; Maziero et al. 2009). Crosier (1934) reported direct germination of sporangia at 18 20°C, possibly with the isolate of clonal lineage US 1. Recent work by Mizubuti and Fry (1998) reported that the work of Crosier still holds true for US 1 but the newer clonal lineage US 8 germinates directly at 10 15°C, but not at 18 20°C. A Brasilian isolate (BR 1) is reported to have higher indirect germination percentage compare to US 1 when tested at 10°C and 15°C (Mazi ero et al. 2009). Temperatures above 26°C are reported to have detrimental effects on sporangia germination (Crosier 1934; Maziero et al. 2009; Melhus 1915). Once the sporangia or zoospore has penetrated colonization of the host tissue takes place. Tiny le sions are visible within 2 3 days upon infection depending on temperature (Andrade Piedra et al. 2005b; Crosier 1934; Hartill et al. 1990; Maziero et al. 2009; Mizubuti and Fry 1998). Average temperatures ranging from 20 22°C favor symptom development (And rade Piedra et al. 2005b Crosier 1934; Hartill et al. 1990; Maziero et al. 2009; Mizubuti and Fry 1998). The latent period, from infection to sporulation, is also extremely dependent on the atmospheric conditions and is optimum about 20 22°C (Andrade Piedr a et al. 2005b; Crosier 1934; Hartill et al. 1990; Maziero et al. 2009; Mizubuti and Fry 1998).

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22 Sporangiophores are formed on the under surface of the leaves under high moisture conditions, protruding out of stomates. This process usually happens after sy mptom development. The lesion continues to produce spores under favorable conditions and grows until it reaches the margin. Sporulation takes place at low temperature and high RH (Andrade Piedra et al. 2005b; Crosier 1934; Harrison 1992; Hartill et al. 199 0) i.e usually at night. Optimum temperature for sporulation is around 12 14°C with high RH of more than 90%. Saturated conditions do not favor spore production. The produced spores are liberated in the morning when the dew dries out or the RH decreases an d are carried away by wind over shorter or longer distances. Wind speed of 1 2 ms 1 can remove the spores and disperse up to 20 km in less than 3 hours (Aylor et al. 2001). Survival of sporangia in atmosphere is only for couple of hours (Fernández Pavía et al. 2004; Mizubuti et al. 2000; Sunseri et al. 2002) and is sensitive to temperature, moisture and solar radiation. Part of the surviving spores can land on susceptible host tissue and initiate new infections. The disease cycle of the old clones of P. inf estans took about a week to complete, but that of the newer clones can take less than a week (Fry et al. 2013; Kato et al. 1997). Late Blight Models Various simulation and forecasting models have been described in literature for potato late blight caused by P. infestans (Apel et al. 2003; Aylor et al. 2001; Bruhn and Fry 1981; Garcia et al. 2006; Grünwald et al. 2002; Henshall et al. 2006; Hijmans et al. 2000; Iglesias et al. 2010; Kaukoranta 1996; Michaelides 1985; Raymundo et al. 2002; Shtienberg et al. 1989; Skelsey et al. 2009a, 2009b, 2010; Van Oijen 1991). Most of the simulation models are based on different stages in the infection cycle (Apel et al. 2003; Bruhn and Fry 1981; Raymundo et al. 2002; Skelsey et al. 2009b; Van Oijen 1991) or on spore rele ase, survival and aerial transport (Aylor et al. 2001; Michaelides 1985; Skelsey et al. 2009a). Some of these models include weather forecasts rather than past weather (Raposo et al. 1993). The LATEBLIGHT simulation

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23 model of Bruhn and Fry (1981) was param eterized for use in the Andean highlands (Andrade Piedra et al. 2005a, 2005b, 2005c). Unlike simulation models, empirical forecasting models are based on the accumulation of late blight risk units under various temperature and humidity conditions (Grünwald et al. 2002; Henshall et al. 2006; Hijmans et al. 2000; Iglesias et al. 2010; Kaukoranta 1996) and are mostly derived from the BLITECAST model (Krause et. al., 1975). Few of these simulation and forecasting models have been used to predict late blight r isk under climate change conditions (Andrade Piedra et al. 2005b and 2005c; Kaukoranta 1996; Sparks et al. 2014). Most of these models have a daily time step. Several researchers have indicated the need for an hourly time step as the various epidemic compo nents may respond strongly to daily temperature variations (Olanya et al. 2007; Raymundo et al. 2002). Research Objectives Global climate change is not only associated with an increase in mean daily temperature but also with changes in diurnal temperature amplitudes (Stocker et al. 2013). A simple mathematical model indicated that fungal pathogens respond differently in terms of growth and development to changes in average temperature depending on the diurnal temperature amplitude (Scherm and van Bruggen 1 994b). This model was based on observed differences in the effects of constant versus oscillating temperatures on lettuce downy mildew development (Scherm and van Bruggen 1993b). The pathogen causing lettuce downy mildew, Bremia lactucae , is an oomycete wi th a similar epidemiology as P. infestans . Thus, our first objective was to test the hypothesis about differences in disease development depending on the diurnal temperature amplitude put forward by Scherm and van Bruggen (1994b) with experimental data for potato late blight. Most of the late blight simulation models are possibly too complex to be linked to crop models simulating effects of climate change. Moreover, they use a daily time step ignoring diurnal oscillations in temperature that may affect diff erent processes in the disease cycle.

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24 Therefore, our second objective was to develop and validate a simple hourly simulation model (BLIGHTSIM) for potato late blight enabling simulation of effects of diurnal temperature oscillations on late blight developm ent under climate change scenarios. Outline of Thesis In chapter 2 the effects of constant and diurnally oscillating temperatures on the epidemic components of late blight, namely zoospore infection efficiency (as evidenced from the number of lesions forme d), incubation and latent periods, lesion growth rate and sporulation intensity, are described. Chapter 3 presents a modified Susceptible, Exposed, Infectious, Removed (SEIR) model for late blight with an hourly time step. Chapter 4 summarizes the findings and discusses the implications of the research work presented here.

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25 CHAPTER 2 POTENTIAL EFFECTS OF DIURNAL TEMPERATURE OSCILLATIONS ON POTATO LATE BLIGHT UNDER CLIMATE CHANGE Introduction The effect of temperature on plant disease development has retur ned to the limelight as the impacts of global warming are increasingly felt (Coakley et al. 1999; Garrett et al. 2006; Garrett et al. 2011; Garrett et al. 2013; Ghini et al. 2008; Gouache et al. 2013; Harvell et al. 2002; Scherm 2004; Shaw 2009). The most recent predictions of increases in global surface temperatures range between 1.5°C and 2.0°C by the end of the 21st century compared to last century (Stocker et al. 2013). These projected average increases are lower than those predicted six years earlier ( Solomon et al. 2007), but changes in climate are unevenly distributed over the globe, with the highest increases in average temperatures at high latitudes in the Northern hemisphere and at high altitudes. Overall, the numbers of extreme temperature and rai nfall events as well as the number of drought periods are expected to increase, although the predictions of seasonal and inter annual variations in temperatures and precipitation are still erratic (Stocker et al. 2013). Predictions of the daily variations in temperature at particular locations are similarly erratic (Ramirez et al. 2013). Climate change will likely influence plant disease development. Thus far, researchers have mainly made educated guesses about potential effects of climate change on plant diseases (Garrett et al. 2013; Roos et al. 2011). Due to the complexity of potential effects, most predictions have been based on the average future climate. For example, in Northern countries a milder and more humid climate would stimulate the production of warmer climate crops, but many pathogens and pests may survive better in the winter and reproduce faster during the cropping season, resulting in an overall increase in pest and disease pressure (Bebber et al. 2013,

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26 Harvell et al. 2002; Juroszek and von Tiedemann 2013). Climate change could also affect life history trade offs, for instance selecting for sexual reproduction in the late blight pathogen Phytophthora infestans , which would result in thick walled overwintering oospores and greater genetic va riation (Garrett et al. 2006). Potential effects of climate change on plant disease development have seldom been assessed using detailed quantitative models that take various epidemic components into account (Garrett et al. 2011; Juroszek and von Tiedemann 2013; Kaukoranta 1996; Luck et al. 2011). Models predicting the risk of establishment of foliar pathogens in a new area are typically based on average climatic variables such as temperature, rainfall, and humidity. For potato late blight, an empirical mod el was based on thermal time (in degree days) to predict the date of planting and emergence of potato, and thermal time on rainy days to predict the first late blight outbreak of the season (Kaukoranta 1996). Results from this model indicate that an increa se in mean temperature in northern Europe of 1°C will extend the period when chemical control for potato late blight is necessary by 10 20 days (Kaukoranta 1996). Moreover, a simulation model has been used to assess potato late blight development in the An des under climate change scenarios, including expected mean temperature and rainfall (Andrade Piedra et al. 2005b). However, global warming will not only change average temperature and rainfall but also the magnitude (amplitude) of daily oscillations in t emperature and the frequency of meteorological extremes (Stocker et al. 2013). In some areas, the daily minimum and maximum temperatures are both expected to increase; in many areas the daily minimum temperature is expected to increase whereas the daily ma ximum temperature will remain unchanged resulting in a decrease in temperature amplitude. In some other areas, like high altitude regions, the daily maximum temperature may increase more than the daily minimum temperature if cloud cover is

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27 reduced, increas ing the daily temperature amplitude (Stocker et al. 2013). Thus, modeling effects of diurnal variation in temperature and relative humidity or leaf wetness on disease development may be at least as important as average daily temperature and humidity (Harri son 1992; Scherm and van Bruggen 1994a, Scherm and van Bruggen 1994b). Based on the results of a simple mathematical model, it was hypothesized that when temperature amplitude is high, the change in relative growth and development rates of plant pathogens in response to an increase in average temperature would be less than that expected under constant temperatures (Scherm and van Bruggen 1994b). However, this hypothesis has never been tested by experimental data. To the best of our knowledge, all controlled experiments to determine the optimum temperature for in vitro growth, infection and sporulation of plant pathogens have been conducted under constant or alternating high and low temperatures, but not under realistic oscillating temperatures (Andrade Piedr a et al. 2005b; Hartill et al. 1990; Kato et al. 1997; Mizubuti and Fry 1998). Potato late blight has become increasingly problematic in many parts of the world. One reason may be the appearance of more aggressive isolates of P. infestans (Fry et al. 2013 ). Another reason may be a change in climate, particularly in regions highly sensitive to the changing climate such as the Andes region in Latin America (Garcia et al. 2008; Kaukoranta 1996). To better predict potential effects of climate change on potato production systems, we examined the effect of changes in diurnal temperatures on all stages of the infection cycle of P . infestans . A total of 42 short term experiments were carried out in growth chambers with constant or oscillating temperatures to determ ine temperature effects on number of lesions formed, incubation and latent periods, lesion expansion rates and sporulation intensities of two isolates of P. infestans on a susceptible potato (Solanum tuberosum L.) cultivar, Red Lasoda. The objective of thi s research was to confirm or refute, for P. infestans , the general hypothesis

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28 put forward by Scherm and van Bruggen (1994b) that the optimum temperature curve for various growth and development rates of plant pathogens would be steeper under conditions of constant compared to oscillating daily temperatures. We also discuss the implications of our results for predicting the potential effects of global climate change on late blight epidemics. Materials and Methods Clonal Lineages of Phytophthora infestans Two isolates representing clonal lineages US 8 and US 23 were used in the experiments. The US 8 clonal lineage was first detected in the U.S. in 1992, whereas US 23 is a relatively new and currently dominant clonal lineage (Fry and Goodwin 1997; Fry et al. 20 13). The US 8 isolate US110063 was collected in 2011 from potato in Erie County, PA, and obtained from the P. infestans culture collection at Cornell University, Ithaca, NY. The US 23 strain was isolated from a tomato leaf from Homestead, Florida, in the s pring of 2013. Tomato leaves with typical late blight lesions were cut and plated in rye PARP (Anonymous 2007) for isolation. When the colony covered half of the medium, it was transferred to freshly prepared 1.5 % pea agar (120 gram frozen pea; 15 gram ag ar, 1000 ml water) for sporulation. The clonal lineage was confirmed by genotyping SSR loci (Li et al. 2013). Both clonal lineages were transferred to freshly prepared 1.5 % pea agar in a laminar flow biosafety cabinet (BSL2) and maintained at 18°C. Plant Production Berne, IN, USA) was used for all experiments. The plants were grown in a greenhouse at temperatures ranging from 18 25°C without supplemental light. The day length ranged from 10 to 14 h and the relative humidity from 41 to 98% depending on the time of the year. Plants were

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29 watered daily and fertilized with a tablespoon of slow release pellets of Osmocote (N:P:K = 14:14:14) once per month. Inoculum Production Inocul um was produced on leaflets of cv. Red Lasoda incubated for one week in an incubator at 18°C with 12 h of light. Fully expanded non terminal leaflets of 4 to 6 month old plants were placed abaxial surface up in a moist chamber (9 cm diameter petri plate w ith moistened filter paper on the bottom) and inoculated with sporangia collected from a 2 week old culture maintained on pea agar (as described above). Sporangia for inoculation were collected from leaflets that had been inoculated 7 days earlier, and the concentration of sporangia per ml was adjusted to 20,000 ml 1 using a haemocytometer. Sporangial suspensions were placed in a refrigerator at 4°C for 40 minutes to initiate zoospore production and release. The numbers of zoospores per sporangium were dete rmined using a light microscope. Inoculation and Incubation For measurement of five epidemic components of late blight (Table 2 1), 6 to 8 week old leaves were inoculated in a petri plate moist chamber with the sporangial suspension produced as described earlier. Each petri plate contained two leaflets with the abaxial surface placed upward. Three to four petri plates per isolate were used. The drop inoculation method was followed where each leaflet was inoculated with 50 µl of sporangial suspension. The n umber of zoospores per sporangium was calculated separately for US 8 and US 23 isolates to get an approximate estimate of zoospore release. The US 23 isolate had a slightly higher average zoospore release (8.2 zoospores/sporangium) compared to the US 8 iso late (7.7 zoospores/sporangium). Four additional leaflets in two plates were inoculated with the same volume of deionized water as controls. Inoculated leaflets were then placed in an incubator at 18°C without lights for 14 hours to promote infection (pre incubation). After the pre incubation

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30 period the petri plates were transferred (at 7.00 am) to different incubators or a growth chamber at constant or fluctuating temperatures, respectively, as described below. Petri plates were kept open (12 h) during th e day and closed at night to mimic changes in relative humidity (RH) and leaf wetness. The filter paper was moistened before closing the petri plates without wetting the leaves. Comparison of Growth Chamber and Incubators at Constant Temperatures Two contr olled environment incubators (Thermo Scientific Precision, Model 818, Waltham, MA, USA) and a single growth chamber (Percival, Model PGC 10, S/N 14732.01.10, Percival Scientific, Inc., Perry, IA) were used for the experiments. The incubators were equipped with fluorescent lights. The growth chamber had both fluorescent and incandescent lights, but only the fluorescent lights were used. All were programmed for a daily cycle of 12 hours light (6 am to 6 pm) and 12 hours dark. Only the growth chamber could be programmed to attain oscillating temperatures. To ascertain that the three chambers performed equally well, preliminary experiments were conducted to compare the five epidemic components of late blight (Table 2 1), using both isolates of P. infestans , in t he two incubators and one growth chamber at two constant temperatures (12°C and 18°C). Both isolates and water control were evaluated simultaneously and were randomized in each incubator or growth chamber. Three or four petri plates were used with two leav es each. The measured temperatures were not significantly different in the growth chamber and two incubators (12.38°C + 0.09 and 18.375°C + 0.03 in the incubators and 12.40°C + 0.22 and 18.24°C + 0.21 in the growth chamber). The light intensity was 2200 240 0 Lux. The relative humidity in the incubators ranged between 65% and 94%, and that in the growth chamber between 70 and 95%.

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31 Comparison of Effects of Constant and Oscillating Temperatures on Late Blight Seven different constant temperatures (10, 12, 15, 17, 20, 23, 27°C) and two amplitudes of oscillating temperatures (±5°C and ±10°C) around the same means were tested for their effects on late blight development. Each average temperature and amplitude combination was tested twice in independent experiments with different inoculation dates, considered true replications. Both of the isolates and water control were tested simultaneously in each incubator or growth chamber and randomized for each experiment. There were three or four petri plates (pseudoreps) wi th two leaflets for each isolate and the water control within each chamber/incubator. Constant temperature experiments were conducted in the two controlled environment incubators, while the fluctuating temperature experiments were conducted in the single g rowth chamber as described above. Each incubator/chamber was programmed for a daily cycle of 12 h light (6 am to 6 pm) and 12 h dark. Oscillating temperatures in the growth chamber were programmed using a modified sine wave equation adjusting the temperatu re every hour based on the provided maximum and minimum temperature at 1600 h and 0400 h, respectively. T H = A Sin (15*H + 210) + M (2 1) where T H = temperature at hour H, A = amplitude (T max T min )/ 2, H = time in 24 hours, M = mean temperature. The relati ve humidity in the chamber was set at 60 70% during the day and 90 95% at night. Measurements of Epidemic Components Number of initial lesions/ mm 2 / zoospore (NL), incubation period (IP), latent period (LP), lesion growth rate (LGR) and sporulation intensi ty (SI) were measured on each leaflet. NL and IP were assessed every 6 hours starting 24 hours after inoculation. NL was calculated by dividing the number of initial lesions (as determined under a stereo microscope) by the leaf surface area that was in con tact with the sporangial suspension and by the number of zoospores applied. The

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32 contact area between a droplet and the leaf surface was determined from the CaCO 3 deposit remaining after placing ten 50 µl droplets with a CaCO 3 suspension on the abaxial surf ace of account, the number of lesions per mm 2 of contact area per zoospore (NL) was calculated. IP was calculated as hours since inoculation when the first lesions we re visible under the binocular light microscope. LP was calculated as time required from inoculation to first sporulation observed under the same microscope. For LGR, it was assumed that a lesion grows in a circular fashion and has a constant radial growth rate after IP. LGR was calculated as described by Andrade Piedra et al. 2005b. (2 2) where LA is lesion area. Sporulation intensity was determined at 168 h (7 d) after inoculation. The lesion area was cut and transferred to a 15 ml vial co ntaining 5 ml of distilled water. The vial was vortexed for 10 seconds to dislodge the sporangia. The number of sporangia per ml was determined using a haemocytometer and multiplied by the volume of water to determine the sporangia produced up to the sampl ing time. Sporulation intensity was calculated by dividing the sporangia produced by lesion area. Model Fitting and Statistical Analysis The original Sharpe and De Michele model (Sharpe and DeMichele 1977) describes how changes in temperature affect the ra te of biological processes. The model assumes that the development rate is determined by a single rate controlling enzyme and this enzyme is reversibly denatured at high and low temperatures, but maintains a constant total concentration independent of temp erature. Here, we describe the relationship between the epidemic components of P. infestans and temperature using a modified Sharpe and De Michele four parameter model also

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33 known as thermodynamic model without changing the original theory of the model (Sch oolfield et al. 1981). (2 3) 25 = development rate at 25°C assuming no enzyme activation, = enthalpy of activation of the reaction catalyzed by enzyme (cal/mol), ation of the enzyme (cal/mol) and T1/2H = temperature at which the enzyme is half active and high temperature inactive. For IP and LP, development rate was calculated by using the reciprocal of the time period. The four rate controlling parameters were e stimated for each temperature amplitude isolate 9.3 (Statistical Analysis System, SAS Institute Inc., Cary, NC). For the initial constant temperature test, comparison of incubator and growth chamber test for each of the two temperatures separately. For the comparison of constant and oscillating temperatures, we performed MANOVA in PROC GLM on the four rate parameters using the three ampli tudes (±0°C, ±5°C, ±10°C) and two isolates as independent variables and the two repetitions as blocks, in order to determine the significance of isolate, amplitude and their interaction. PROC MIXED was also carried out to confirm our results for individual rate parameters (as MANOVA was not possible in PROC MIXED), but no major differences were detected between the test statistics of the different procedures. When quantification of differences in optimum values of epidemic components was needed for the comp arison of constant versus oscillating temperatures, ANOVAs were carried out for the values at the same mean temperatures. To compare the values of an epidemic component of the two

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34 isolates under a particular set of temperature conditions, a two sided paire d t test was carried out in Excel. Results Comparison of Incubators and Growth Chamber At constant temperatures (12ºC and 18ºC) there were no significant differences between the two incubators and the growth chamber in any of the late blight epidemic comp onents on individual potato leaves, justifying comparison of data at oscillating temperatures in the growth chamber with those at constant temperatures in the incubators. Although the numbers of lesions induced by the US 8 isolate seemed to be lower in the growth chamber than in the two incubators at 12°C, this difference was not statistically significant (Table 2 1), and was probably due to variation among leaves in the experiment at 12°C as no such difference was observed at 18°C. Nonlinear Regressions Th e four parameter thermodynamic model provided a good fit to most of the observed data. The approximate coefficients of determination ranged from 0.57 to 0.99 for all epidemic components (Table 2 2). The lowest coefficients of determination were observed fo r number of lesions per zoospore by the US 23 isolate under high temperature amplitude conditions (±10ºC, R 2 = 0.57 0.68). Effects of Average Temperatures and Their Daily Amplitudes Number of lesions mm 2 zoospore 1 (NL). There was a significant interacti on ( P = 0.0007) between isolate and amplitude for number of lesions formed per zoospore (Table 2 3). A right hand skewed curve was observed for the US 8 isolate with peak lesion formation around 12ºC for all amplitudes (Figure 2 1A). In contrast, the highe st number of lesions was observed at 15±5ºC for the US 23 isolate (Figure 2 1B). For both isolates a small fluctuation (±5ºC) in

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35 temperature around the same mean increased the number of lesions while the larger fluctuation (±10ºC) in temperature resulted in reduced numbers of lesions. The difference in peak lesion formation between constant and fluctuating temperatures was significant (P<0.0001) for US 8 only. Specifically, a significant difference was observed when the temperature fluctuation was 10°C com pared to 0°C at a mean temperature of 10°C (t test at one mean temperature; P<0.0001). The highest number of lesions was at 12±5°C for this isolate. Incubation period and incubation progression rate (IPR). The reciprocal of incubation period, incubation pr ogression rate (IPR), was used for analysis. Overall, there was no significant difference between the isolates ( P =0.6194) or interaction between isolate and amplitude (P=0.1105), but the effect of amplitude on IPR was highly significant ( P <0.0001 ) (Table 2 3). When plotted against temperature, the highest IPR was around 24°C under constant temperature conditions (Figure 2 2). Under oscillating temperature conditions, the optimum IPR shifted towards lower average temperatures (12 14°C) such that the curves f or constant and oscillating temperatures crossed around 17°C, the apparent inflection point of the constant temperature curve. The IPR values increased at larger amplitudes below this point and decreased compared to constant temperatures above this point. The effect of temperature on IPR was greater when temperature was constant as compared to oscillating and the IPR curves were flatter as the amplitude increased. Latent period and latency progression rate (LPR). The latent period and its reciprocal, the l atency progression rate, followed a similar pattern in relation to temperature as that of the incubation progression rate (Figure 2 2C and 2 2D). Again, no significant difference was observed between isolates ( P = 0.5394) and the amplitude effect was highly significant ( P = 0.0042) for LPR (Table 2 3). The shortest latent period or the highest LPR was observed at

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36 around 22°C under constant temperature. The LPR curves under constant temperatures showed an inflection point around 16 17°C, where the curves for o scillating temperatures crossed the constant temperature curve. Below this point, increasing daily amplitudes resulted in faster development rates compared with constant temperatures, while at higher mean temperatures, the optimum curves for oscillating te mperatures flattened out such that temperature oscillations resulted in reduced LPR values compared to constant temperatures. This reduction was greater at 10°C than at 5°C amplitudes (P<0.0001). Lesion growth rate (LGR). Under constant temperatures, the LGR was at its maximum at 23°C for both isolates (Figure 2 3A and 2 3B). A shift in optimum temperature from 23°C to 20°C was observed for LGR when the temperature oscillated by ±5ºC. For LGR, there was a significant interaction between isolate and amplitu de ( P = 0.0005) (Table 2 3). This interaction was due to a differential effect of temperature oscillations ( ± 10°C) on the isolates at medium and high mean temperatures. When temperatures oscillated ± 10°C , the LGR for the US 8 isolate peaked at a lower mean t emperature (~19ºC) and then decreased (Figure 2 3A), whereas the LGR for the US 23 isolate increased up to 23ºC and then declined (Figure 2 3B). Thus the isolates showed significantly different LGRs (P<0.0001) at a mean temperature of 23ºC under oscillatin g (±10ºC) temperatures. Sporulation intensity (SI). Under constant temperature, the sporulation intensity per unit lesion area of the US 8 isolate did not have a clear maximum temperature, but decreased sharply at temperatures above 20°C (Figure 2 3C). Th e US 23 isolate had a clear maximum SI at a constant temperature of 12°C, and produced more spores than the US 8 isolate at higher temperatures (Figure 2 3D). There was a significant interaction ( P = 0.001) between isolate and amplitude (Table 2 3). Small fl uctuations in temperature ( ±5ºC) resulted in higher numbers of

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37 sporangia per unit lesion area irrespective of mean temperature, except at the temperature extremes. For both isolates, 15±5ºC resulted in peak production of sporangia per unit area. Higher tem perature oscillations ( ±10ºC) had different effects on the sporulation intensities of the two isolates. Under those oscillating conditions, the sporulation intensity of the US 8 isolate was optimal at 15ºC, while that of the US 23 isolate was optimal at 12 ºC. Discussion In this paper we demonstrate that the growth and development rates during different phases of the infection cycle of two isolates of P. infestans respond to a wide range of temperatures in the form of typical optimum curves consistent with previous studies (Andrade Piedra et al. 2005b; Crosier 1934; Hartill et al. 1990; Mizubuti and Fry 1998). Optimum curves were obtained under both constant and oscillating temperatures. Two basic types of curves can be distinguished: curves that are skewed to the left for processes that take place inside plant tissues (colonization during the incubation period, the latent period and lesion growth) and those that are skewed to the right for processes that are influenced by leaf surface temperature (spore ger mination, initial infection and sporulation). This distinction has not been mentioned explicitly in the literature, but can be gleaned from various figures for in plant development rates (Andrade Piedra et al. 2005b; Crosier 1934; Hartill, 1990; Mizubuti a nd Fry 1998; Scherm and van Bruggen 1994a) and sporulation, germination and infection (Andrade Piedra et al. 2005b; Bonde et al. 1985; Melhus 1915; Mizubuti and Fry 1998; Scherm and van Bruggen 1993a) of low temperature foliar pathogens. Although optimum curves were obtained for both constant and diurnally oscillating conditions, effects of oscillating temperatures differed significantly from those of constant temperatures on all measured epidemic components of potato late blight. The differences between o scillatory and constant conditions were similar for the incubation and latency

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38 progression rates, while they were different for infection efficiency, sporulation intensity and lesion growth rate. During the incubation and latency periods the late blight de velopment rates were faster under oscillating than under constant conditions at relatively low average temperatures, while these rates were slower under oscillating conditions at relatively high average temperatures, rendering the optimum curves less steep under oscillating temperatures (Figure 2 2). The differences between oscillating and constant temperatures increased progressively at increasing amplitudes. The optimum curves for oscillating and constant temperatures crossed over around 17°C, which seems to be the inflection point on the left side of the constant temperature curves. Theoretically, the curves should cross over at the inflection point, because the curve is symmetrical around that point. This would need to be proven mathematically. In contra st to the clear patterns in incubation and latency progression rates, the results were more complex for the other epidemic components. For infection efficiency, lesion growth rate and sporulation, small oscillations in temperature ( + 5°C) increased these v ariables whereas large oscillations ( + 10°C) brought them back at or below the constant temperature values (Figure 2 1 and 2 3). This difference in response to temperature amplitude compared to that of the incubation and latency progression rates can be as cribed to the fact that sporulation and initial infection occur mostly at night or in the early morning, when temperatures are low and relative humidities are high. This may be associated with an evolutionary adaptation to night temperatures, resulting in low temperature optima. Although the average temperature over a 24 h period is for example 15°C for processes that take more than one day, the actual average during the sporulation and infection period (usually less than 12 h at night) is lower than 15°C and closer to the constant temperature optimum if the amplitude is 5°C, enhancing sporulation

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39 and infection. The actual average for sporulation and infection is even lower and below the optimum temperature if the amplitude is 10°C, explaining the low leve ls of the optimum curve for this amplitude compared to the optimum curve at constant temperatures (Figure 2 1 and 2 3). Lesion growth rate is also stimulated by small temperature fluctuations ( + 5°C), but not by large oscillations ( + 10°C). This is differe nt from the incubation and latency progression rates, even though all these processes take place inside the leaves and have optimum curves skewed to the left. Visible lesions may primarily increase during the day after spores die under high temperature con ditions. This would need to be verified experimentally, but if this is true, lesion growth rate is affected more by the day time temperatures than the night temperatures, and at + 10°C amplitudes the average temperature is above the optimum at constant tem peratures, and may be detrimental to lesion growth. This could be an explanation for the difference in response to large oscillations between lesion growth rate and incubation or latency progression rate. The effects of oscillating and constant temperat ures on incubation and latent periods were similar for the two isolates used. Clonal lineage US 8 is being gradually replaced by US 23, which produces more devastating epidemics than US 8 (Cooke et al. 2012; Fry et al. 2013). If the isolates used for this research are representative of the clonal lineages, then the displacement of US 8 by US 23 is not due to differences in generation time driven by the incubation and latent period. Rather, the faster epidemic development with US 23 may be explained by diffe rences in sporulation intensities, infection efficiency, and lesion growth rate. Although the in plant development rates of the US 8 and US 23 isolates were similar, the sporulation intensity of US 23 was higher under both constant and fluctuating (±5°C) t emperatures than that of US 8 in the temperature range of 12 to 20°C. The infection efficiency of the zoospores was greater for US 8 than US 23, at low temperatures, but not at high temperatures. Finally, at high fluctuating

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40 (±10°C) temperatures, the US 23 isolate also had a higher rate of lesion growth at high temperatures. Thus, while we did not find epidemic components that clearly explain the displacement of US 8 by US 23, we did find differences among these two isolates that may represent fitness trade offs in the clonal lineages. However, the current experiments were not set up to test potential differences in relative fitness of the two isolates. To our knowledge, this is the first study examining the effects of diurnal temperature oscillation on the l atent and incubation periods, the number of lesions, the lesion growth rate and sporulation intensity of P. infestans . Melhus (1915) reported that germination of P. infestans spores was faster in cultures at constant temperature compare to those held for f ive minutes at 20°C and then placed at low temperature. Differences in the incubation period were also reported by Crosier when the pathogen was exposed to three combinations of intermittent high and low temperatures (Crosier 1934). Thus, we have known tha t developmental rates are affected by average temperatures and temperature extremes but most epidemiological studies to date have failed to incorporate the notion of diurnal oscillations in temperature. Our results support the hypothesis put forward by Sch erm and van Bruggen (1994b) that the in planta development rates of plant pathogens (with the exception of lesion growth rate) respond less steeply to an increase in average daily temperature with increasing daily amplitudes. However, this hypothesis does not hold for processes taking place at the leaf surface like sporulation, spore germination and initial infection. Similarly, insect development rates accelerate with increasing magnitude of daily oscillations at low average temperatures and decelerate wit h increasing amplitudes at high average temperatures (Behrens et al. 1983; Carrington et al. 2013). The response of insects to oscillating temperatures in terms of egg production is similarly complex as spore production by P. infestans (Behrens et al. 1983 ; Carrington et al. 2013).

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41 Potential mechanisms underlying the different responses to fluctuating versus constant temperatures have been discussed extensively by entomologists, who studied effects of oscillating temperatures on the development rates of eg gs and larvae, as well as on oviposition and survival (Behrens et al. 1983; Carrington et al. 2013; Worner 1992). The differences in development rates under oscillating compared to constant temperatures have been ascribed to the nonlinearity of the optimum curves for insect development rates (Worner 1992), and in one case for fungal plant pathogens (Scherm and van Bruggen 1994b). These differences in development rates were first described by Kaufmann and are hence called Kaufmann effect or rate summation ef fect (Worner 1992). In addition to the Kaufmann effect, physiological differences under constant versus oscillating conditions have been postulated, in that energy expenditure would be higher (slowing down development) under oscillating than under constant temperatures at mean temperatures close to the optimum of the constant temperature curve (Behrens et al. 1983; Carrington et al. 2013). At relatively low mean temperatures, oscillations generally stimulate insect development as well as egg production, pos sibly by temporarily exceeding an enzyme activity threshold that may not be reached at low constant temperatures (Behrens et al. 1983). On the other hand, at high average temperatures, oscillations may result in temporary inhibitory conditions resulting in decreased survival as observed for insects (Behrens et al. 1983) and bacteria (Semenov et al. 2007). The observed differences in the response of epidemic components to oscillating versus constant temperatures will have a profound effect on predictions ma de for plant disease development under global climate change (Garrett et al. 2011; Scherm and van Bruggen 1994b). Unfortunately, the uncertainty associated with predictions of diurnal variations in temperature is very large (Ramirez et al. 2013). On averag e, the diurnal amplitudes in temperature are expected

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42 to decrease according to predictions by the Intergovernmental Panel on Climate Change (Stocker et al. 2013). However, for some locations, the amplitudes may be underestimated by current climate models. For example, on high plains, the amplitudes may increase under global warming because reduced cloud cover will raise the daily maximum temperature more than the daily minimum temperature, increasing the diurnal temperature amplitude. As the average tempera ture is generally lower at high than at low altitudes, the late blight development rate will likely be increased when the daily amplitudes are large compared to constant low temperatures (Figure 2 2), depending on humidity and leaf wetness conditions. Thus , our results may be particularly relevant to high altitude regions. Moreover, the daily temperature oscillations are expected to deviate more from sinusoidal with maximum temperatures later in the afternoon (Knappenberger et al. 1996), so that dew periods and high relative humidities will last longer in the morning (Scherm and van Bruggen 1994b). This might result in faster epidemic development of late blight, but differences in dew periods or relative humidities have not been taken into account during our experiments, as the relative humidity was lowered and increased at fixed time periods each day. In addition to the absence of realistic day night changes in relative humidity in our experiments, only two incubators and a growth chamber were available for these experiments, so that not all temperature combinations could be compared simultaneously. However, the treatments were controlled as much as possible: the growth chamber and incubators were adjusted to give the same results under constant temperatures, and the leaflets used for inoculation had the same age by using leaflets from plants with different planting dates. Moreover, 6 8 leaflets were used as pseudo replicates to minimize variability. Here we assumed that the detached leaf experiments in contro lled conditions reflect late blight development under

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43 field conditions. We used 20,000 sporangia ml 1 and 50 µl drop volume as standard for inoculation, although studies (Kato and Naito 2001; Perez et al. 2001) suggest that 3,000 to 5,000 sporangia ml 1 an d 10 µl drop volume would be sufficient for inoculation. Thus, our infection efficiency (number of lesions per zoospore), may have been underestimated due to on leaf competition among zoospores. To limit underestimation, lesions were counted under a micros cope after the incubation period was complete. Although inoculations were controlled in our experiments, sporulation started on different days as a result of the temperature treatments. Nevertheless, sporulation was measured 168 h after inoculation for all treatments. Thus, the phase in the sporulation period when spores were harvested varied as the leaves did not start sporulating at the same time. This could have resulted in an underestimation of the sporulation intensity at mean temperatures optimal for the latency progression rate (around 22°C). This would likely be a more severe problem under constant than under oscillating conditions, because the latent period is shorter under constant than oscillating conditions at a mean temperature around 22°C. To a void this problem, multiple samples would need to be taken throughout the sporulation period to estimate spore production over time. However, this would only be possible for a few temperature treatments. Despite the limitations of our study, it is a critic al first step towards understanding the importance of oscillating temperatures for the epidemiology of late blight. We showed that the initial growth and development rates of P. infestans respond less drastically to an increase in average temperatures unde r diurnal oscillations than to a similar increase under constant temperatures at high average temperatures. In contrast, our results suggest that if climate change is accompanied by greater temperature amplitudes at high altitudes with relatively low mean temperatures, the epidemic development rate could be increased. Moreover moderate

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44 fluctuations in temperature cause an increase in lesion growth rate and sporulation intensity compared to constant temperatures, especially at relatively low mean temperature s. It is hard to predict what the implications of these results would be in potato growing areas at high altitudes, like the Andes, where average temperatures have increased and are expected to increase even further, but rainfall and relative humidity hav e remained the same over the past 50 years (Perez et al. 2010; Vuille et al. 2003). Until recently, late blight was limited by relatively low temperatures at high altitudes, but the disease is expanding in those areas (Perez et al. 2010). A recent meta mod el to predict late blight severity based on the accumulation of blight units indicated that there would be little effect of global change on potato late blight risk, except at very high altitudes (Sparks et al. 2014). Diurnal temperature amplitudes were no t explicitly taken into account. As a large part of the population in the high Andes relies on potatoes for their livelihood, it is important to accurately predict the risk of potato late blight under weather conditions expected for specific climatic zones . The results presented in this paper will be used for the development of a late blight model that can be coupled to a potato crop model under construction in the framework of the Agricultural Model Intercomparison and Improvement Project, or AgMIP (van Br uggen et al. 2014)

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45 Table 2 1. Preliminary experiments comparing epidemic components of late blight on potato with two isolates of P. infestans in two incubators and one growth chamber at two different temperatures under the same lighting conditions (12 h light and 12 h darkness; light intensity 2200 2400 Lux). Isolates are designated by their clonal lineage. Shown are the mean and standard deviation of six leaves (two leaves per petri plate) for each variable. No significant differences were detected betw een incubators and growth chamber. Clonal Lineage of Isolate Variable a 12°C 18°C Incubator 1 Incubator 2 Growth Chamber Incubator 1 Incubator 2 Growth Chamber US 8 NL 22.75 (4.77) 21.25 (16.06) 16.63 (4.00) 10.33 (1.75) 10.83 (0.98) 11.50 (1.97) IP 72.00 (10.64) 72.75 (11.76) 73.50 (9.49) 63.00 (9.10) 66.00 (5.37) 67.00 (10.33) LP 111.75 (5.50) 108.75 (2.12) 110.25 (3.11) 76.00 (9.80) 78.00 (6.57) 77.00 (9.61) LGR 0.20 (0.02) 0.23 (0.05) 0.20 (0.02) 0.23 (0.01) 0.24 (0.02) 0.24 (0.04) SI(×10 5 ) 1.74 (0.47) 1.71 (0.65) 1.70 (0.32) 1.34 (0.27) 1.30 (0.16) 1.36 (0.25) US 23 NL 21.88 (6.79) 23.75 (15.42) 20.25 (4.59 ) 13.00 (2.19) 12.00 (1.67) 12.33 (1.86) IP 74.25 (12.80) 75 (13.22) 75.00 (9.62) 56.00 (6.20) 57.00 (6.29) 58.00 (3.10) LP 108.50 (1.41) 108.75 (2.12) 108.00 (0) 70.00 (3.10) 69.00 (3.29) 71.00 (2.45) LGR 0.18 (0.04) 0.18 (0.03) 0.16 (0.04 ) 0.26 (0.01) 0.26 (0.01) 0.26 (0.01) SI(×10 5 ) 2.95 (0.75) 2.89 (1.36) 2.88 (1.28) 1.74 (0.40) 1.75 (0.47) 1.72 (0.29) a Variables are the epidemic components that were assessed during the experiments. NL, number of lesions (lesions mm 2 zoospor e 1 ); IP, incubation period (h); LP, latent period (h); LGR, lesion growth rate (cm day 1 ); SI, sporulation intensity (sporangia cm 2 )

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46 Table 2 2. Values of the approximate coefficients of determination (R 2 ) for duplicate nonlinear regressions of five epide mic components of late blight on temperature using three daily amplitudes (0°C, 5°C and 10°C). Isolates are designated by their clonal lineage. Clonal Lineage of Isolate Variables a ±0°C b ±5°C b ±10°C b US 8 NL 0.73, 0.82 0.85, 0.91 0.87,0.80 IPR 0.86, 0.93 0.89, 0.91 0.89, 0.84 LPR 0.95, 0.98 0.91, 0.96 0.95, 0.79 LGR 0.81, 0.81 0.94, 0.94 0.88, 0.86 SI 0.77, 0.72 0.90, 0.92 0.93, 0.88 US 23 NL 0.71, 0.82 0.93, 0.90 0.68, 0.57 IPR 0.96, 0.98 0.95, 0.93 0.93, 0.96 LPR 0.98, 0.97 0.95, 0.97 0. 86, 0.90 LGR 0.83, 0.84 0.87, 0.88 0.99, 0.98 SI 0.89, 0.91 0.97, 0.98 0.96, 0.96 a Components of epidemic development. NL, number of lesion mm 2 zoospores 1 ; IPR, incubation progression rate (h 1 ); LPR, latency progression rate (h 1 ); LGR, lesion gro wth rate (cm day 1 ); SI, sporulation intensity (sporangia cm 2 ) b Amplitudes of daily temperature oscillations

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47 Table 2 3. Multivariate analysis of variance (MANOVA) for the effects of isolate (I), temperature amplitude (AMP) and the interaction between isolate and amplitude on epidemic components of late blight on detached potato leaflets (6 8 leaflets per treatment) in two incubators and one growth chamber. Variables a Treatments b P value c NL I 0.0012 AMP 0.0001 I*AMP 0.0007 IPR I 0.6194 AMP <0.0001 I*AMP 0.1105 LPR I 0.5394 AMP 0.0042 I*AMP 0.9582 LGR I 0.0010 AMP <0.0001 I*AMP 0.0005 SI I 0.0046 AMP 0.0022 I*AMP 0.0010 a Variables are the epidemic components of potato late blight. NL, number of lesion mm 2 zoospores 1 ; IPR, incubation progression rate (h 1 ); LPR, latency progression rate (h 1 ); LGR, lesion growth rate (cm day 1 ); SI, sporulation intensity (sporangia cm 2 ). b Treatments are P. infestans isolate (I), temperature amplitude (AMP) and the interaction between I and AMP (I*AMP). Isolates were from clonal lineages US 8 and US 23, and temperature amplitudes were 0ºC, 5ºC and 10ºC. c

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48 Figure 2 1. Effect of constant and oscil lating temperatures on number of late blight lesions mm 2 zoospore 1 (NL). The amplitudes of daily temperature oscillations were 0°C, 5°C and 10°C. Each data point represents the average of two repetitions at each mean (or constant) temperature. Lines sho w the fitted thermodynamic model for each amplitude. The graph on the left shows results for a P. infestans isolate from clonal lineage US 8 A) and that on the right an isolate from clonal lineage US 23 B). Vertical bars represent the standard deviations o f means.

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49 Figure 2 2. Effect of constant and oscillating temperatures on late blight epidemic components incubation progression rate, h 1 (IPR) and latency progression rate, h 1 (LPR). Each data point represents the average of two repet itions at each constant or oscillating temperature. Lines show the fitted thermodynamic model for each amplitude. Graphs on the left represent P . infestans clonal lineage US 8 (A and C) and those on the right clonal lineage US 23 (B and D). Vertical bars r epresent the standard deviations of means.

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50 Figure 2 3. Effect of constant and oscillating temperatures on the late blight epidemic components lesion growth rate in cm day 1 (LGR) and sporulation intensity as sporangia cm 2 (SI). Each data point rep resents the average of two repetitions at each constant or oscillating temperature. Lines show the fitted thermodynamic model for each amplitude. Graphs on the left represent P. infestans clonal lineage US 8 (A and C) and those on the right clonal lineage US 23 (B and D). Vertical bars represent the standard deviations of means.

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51 CHAPTER 3 BLIGHTSIM: A NEW SEIR MODEL FOR POTATO LATE BLIGHT SIMULATING THE RESPONSE OF Phytophthora infestans TO CLIMATE CHANGE UNDER DIURNAL TEMPERATURE OSCILLATIONS Intr oduction Climate change refers to changes in climatic factors like temperature and rainfall that can be detected statistically by changes in their mean and/or variability over an extended period of time (Salinger 2005). Global surface temperatures are expe cted to increase between 1.5°C and 2.0°C by the end of the 21 st century (Field et al. 2014). Moreover, the numbers of extremely high temperature and rainfall events as well as the numbers of drought periods are expected to increase (Field et al. 2014). Pre dictions of the seasonal and inter annual variations in temperature and precipitation are still erratic (Ramirez Villegas et al. 2013), and will be affected by the El Nino Southern Oscillation (ENSO) in the tropical pacific (Field et al. 2014; Salinger 200 5). For example, the western side of the Andes will experience significant increases in temperature and enhanced glacier melts, which are strongly influenced by sea surface temperatures as affected by ENSO (Vuille et al. 2003; Perez et al. 2010). Global climate change is not only associated with a change in average temperature and rain fall but also with differences in daily amplitudes and shifts in the frequency of meteorological extremes ( Ramirez Villegas et al. 2013; Scherm 2004; Scherm and van Bruggen 1994b). Th e uncertainty associated with predictions of diurnal variations in temperature is currently still very large (Ramirez et al. 2013). On average, the diurnal amplitudes in temperature are expected to decrease (Stocker et al. 2013). However, for so me locations, the amplitudes may be underestimated by current climate models. For example, on high plains, the amplitudes may increase under global warming because reduced cloud cover will raise the daily maximum temperature more than the daily minimum tem perature, increasing the diurnal temperature

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52 amplitude (Anonymous 2011; Perez et al. 2010). Moreover, the daily temperature oscillations are expected to deviate more from sinusoidal with maximum temperatures later in the afternoon (Knappenberger et al. 199 6), so that dew periods and high relative humidities may last longer in the morning (Scherm and van Bruggen 1993b, 1994c). Global climate change will likely have profound effects on plant disease development. Potential direct and indirect effects of globa l change on plant diseases have been discussed in several review papers (Garrett et al. 2006; Garrett et al. 2011; Ghini et al. 2008; Juroszek and von Tiedemann 2013; Luck et al. 2011; Pautasso et al. 2012; Roos et al. 2011; Savary et al. 2011; West et al. 2012). The interrelationships between plant pathogens, their hosts, climatic factors and ecosystem managers are likely complex with multiple interactions, non linearities and feedback loops (Garrett et al. 2011; De Wolf and Isard 2007). Thus, prediction o f plant disease development under climate change is difficult, and will be specific for the pathosystem and its immediate environment. Nevertheless, several attempts have been made to predict how climate change might affect particular plant pathogens or pa thogen ecotypes (Savary et al. 2011; Sparks et al. 2014; West et al. 2012). In these studies, the emphasis has been on average changes in temperature over large climatic and ecological regions. For example, in Northern Europe a milder and more humid climat e would stimulate the production of warmer climate crops, but many pathogens and pests may survive better in the winter season and reproduce faster in the cropping season (Bebber et al. 2013; Roos et al. 2011). Warm winters with high night temperatures wou ld facilitate the survival of pathogens; accelerate life cycles of vectors and fungi, and increase sporulation and aerial fungal infection, resulting in an overall increase in disease pressure (Harvell et al. 2002; Kaukoranta 1996). Plant disease developme nt is not only affected by

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53 average daily weather conditions but possibly even more by the diurnal variation in temperature, relative humidity, leaf wetness and light conditions (Garrett et al. 2011; Scherm and van Bruggen 1993b, 1994a, 1994b; Wu et al. 200 0 and 2002). However, with a few exceptions (Garrett et al. 2011; Scherm and van Bruggen 1994b), diurnal variation in weather conditions have generally not been considered when potential effects of climate change are discussed (Ghini et al. 2008; Pautasso et al. 2012; Savary et al. 2011; West et al. 2012). Also, when models are employed for the prediction of future plant disease epidemics average values of weather variables have been used as input in the mo dels (Bergot et al. 2004; Er et al. 2013; Garrett et al. 2006; Orlandini et al. 2008; Papastamati et al. 2001; Scherm and van Bruggen 1993a; Shaw 2009 ). Various simulation and forecasting models have been developed for potato late blight caused by Phytophthora infestans (Apel et al. 2003; Aylor et al. 20 01; Bruhn and Fry 1981; Garcia et al. 2006; Grünwald et al. 2002; Henshall et al. 2006; Hijmans et al. 2000; Iglesias et al. 2010; Kaukoranta 1996; Michaelides 1985; Raymundo et al. 2002; Shtienberg et al. 1989; Skelsey et al. 2009a, 2009b, 2010; Van Oijen 1991 ). Most simulation models are based on different stages in the infection cycle (Apel et al. 2003; Bruhn and Fry 1981; Raymundo et al. 2002; Skelsey et al. 2009b; Van Oijen 1991 ) or on spore release, survival and aerial transport (Aylor et al. 2001; Mi chaelides1985; Skelsey et al. 2009a). Many of the late blight modeling studies, including those with weather forecasts (Raposo et al. 1993) and adaptation to a wide range of ecoclimates including the Andean highlands (Andrade Piedra et al. 2005a, 2005b, 20 05c), are based on the LATEBLIGHT model by Bruhn and Fry (1981). The empirical forecasting systems are mostly derived from BLITECAST (Krause et. al. 1975), and are based on the accumulation of late blight risk units under various temperature and humidity c onditions (Grünwald et al. 2002; Henshall et al. 2006; Hijmans et al. 2000; Iglesias et al. 2010; Kaukoranta

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54 1996). Only few of these simulation and forecasting models have been used to predict late blight risk under climate change conditions (Andrade Pied ra et al. 2005b and 2005c; Kaukoranta 1996; Sparks et al. 2014). The late blight simulation models listed above typically have a daily time step, while several researchers already indicated that an hourly time step would be preferable, as the various epid emic components respond strongly to daily temperature variations (Olanya et al. 2007; Raymundo et al. 2002; Shakya et al. 2014 (submitted)). Because recent climate change predictions still had a relatively low temporal and spatial resolution, a late blight metamodel was developed based on the Simcast forecasting model (Grünwald et al. 2002), so that aggregated daily or even monthly weather data could be used as input data (Sparks et al. 2011). The blight units calculated with the metamodel using aggregated weather data corresponded reasonably well with aggregated blight units from the Simcast model based on accumulations of hourly data (Sparks et al. 2011). Thus, the metamodel could be used to predict the risk of late blight in various climatic regions despi te the lack of geographic detail in predicted climate and disease distribution and the lack of accuracy in predicting temporal variation in weather patterns (Sparks et al. 2014). According to this metamodel, with aggregated weather data as input, there wou ld be little effect of global climate change on potato late blight risk (Sparks et al. 2014). Recently however, the general circulation models (GCMs) have significantly improved in both temporal and spatial scales (Field et al. 2014), and better disease p redictions could perhaps be obtained when the diurnal temperature range is taken into account. We recently showed that the duration and intensity of the various stages in the infection cycle of P. infestans are very different under constant than under osci llating temperatures with the same means (Shakya et al. 2014 (Submitted)). At increasing daily amplitudes over the whole temperature range, the

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55 relative growth rates respond less drastically to an increase in average temperature than under constant temper ature conditions (Scherm and van Bruggen 1994b, Shakya et al. 2014 (Submitted) ). At relatively low average temperatures, the incubation and latency progression rates are faster under oscillating than under constant conditions , while these rates are slower under oscillating conditions at relatively high average temperatures. The differences between oscillating and constant temperatures increase progressively at increasing amplitudes (Shakya et al. 2014 (Submitted)). For infection efficiency, lesion growth ra te and sporulation, small oscillations in temperature ( + 5°C) increase these variables whereas large oscillations ( + 10°C) reduce them below the constant temperature values. These differences in the response of epidemic components to oscillating versus con stant temperatures will have profound effects on predictions made for plant disease development under global climate change (Garrett et al. 2011; Scherm and van Bruggen 1994b). If climate change is accompanied by greater temperature amplitudes at high alti tudes, for example in the Andes, with relatively low mean temperatures, the epidemic development rate could be increased at those locations due to shorter latent periods, enhanced lesion growth rate and infection efficiency, and greater sporulation intensi ty compared to constant temperatures, especially at relatively low mean temperatures. Besides an increase in daily amplitude, the maximum temperature is expected to occur later in the afternoon (Knappenberger et al. 1996), potentially resulting in longer m orning leaf wetness periods that may enable spore release and infection to occur in the same morning, reducing the risk of spore desiccation or death due to UV radiation in the afternoon (Scherm and van Bruggen 1993b and 1994 c; Su et al. 2000 and 2004; Sun seri et al. 2002; Wu et al. 2000 and 2002). On the Western side of the Andes, average temperatures have increased and are expected to increase even further, while rainfall and relative humidity have remained the same over the

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56 past 50 years (Perez et al. 20 10; Vuille et al. 2003). Until recently, late blight was limited by relatively low temperatures at high altitudes, but the disease is expanding rapidly in those areas (Perez et al. 2010). As a large part of the population in the Andes relies on potatoes fo r its livelihood, it is important to accurately predict the risk of potato late blight and the associated yield gaps under weather conditions expected for specific climatic zones in that region. The best option for prediction of crop loss by plant diseases under climate change is the use of coupled simulation models for crop growth and disease development (Raymundo et al. 2002; Savary et al. 2011; van Bruggen et al. 2014). For this purpose, a relatively simple disease model will be needed, if possible simpl er than the widely used LATEBLIGHT model (Bruhn and Fry 1981; Andrade Piedra et al. 2005b), but with hourly rather than daily time steps. Such a model is currently not available. Thus, the objective of this research was to develop and validate an hourly si mulation model (BLIGHTSIM) for potato late blight enabling simulation of effects of diurnal temperature oscillations. Materials and Methods Model Assumptions The model BLIGHTSIM is a compartmental model with Healthy (H), Latently infected (L x ), Infectious (I) and Removed (R) compartments, which are equivalent to Susceptible (S), Exposed (E), Infectious (I) and Removed (R) model described in the literatures (Chiyaka et al. 2012). A site is the basic unit of the model and is assumed to be 1mm 2 in area. Total susceptible sites are distributed over H, L x , I and R compartments and the total is constant throughout the epidemic. Susceptible sites are randomly distributed over a plot area of 16m 2 planted to potatoes. The leaf area index (LAI) is 2 (m 2 .m 2 ) (Gordon et al. 1997) and we assume only a single leaf layer without vertical distribution. A single leaflet has a maximum of 2,000 infection sites. Stems are not considered to have susceptible sites.

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57 The minimum latent period is 57 h for the US 23 isolate of P. i nfestans used in a growth chamber study (Shakya et al. 2014 (Submitted)); however, the value ranges from 57.5 h 118.5 h depending on temperature. New infections are directly related to the proportion of infectious sites; sporulation is not modeled explicit ly. Thus, no distinction is made between infection by zoospores or sporangia. The hourly multiplication factor (HMF) is the product of hourly spore production per mm 2 (HSP) and the dilution factor (DILFAC). HSP is 45 at 15±5 o C (Shakya et al. 2014 (Submitte d)). The dilution factor is assumed to be 0.01, meaning that 99 per cent of the spores do not land on susceptible sites. In addition, there is a reduction factor for the infection efficiency, which is related to temperature. New latent sites originate from two sources: infectious sites (through infection by spores) and day old latent sites (through lesion growth). All latent sites are divided into two categories: one day old latent sites and older latent sites. Only one day old latent sites contribute to le sion growth. The lesion grows with a constant radial lesion growth rate from the latent edge of each lesion. Lesion growth takes place for 72 h at decreasing rates to avoid lesion growth beyond the leaf margin. After a site moves through the second latenc y category, it becomes infectious. The infectious period of a sporulating ring of a lesion (internal to the ring of latent tissue) is assumed to be 24 h (Parlevliet 1979). The previously sporulating sites turn necrotic and belong to the removed category. B asic Structure of Model BLIGHTSIM BLIGHTSIM is a modified SEIR compartmental model (Figure 3 1). The compartments are healthy sites (H), latent sites (L x ), infectious sites (I) and removed sites (R) (Table 3 1). Latently infected sites are divided into 8 l atent compartments: L1a and L1b are formed from infection of H by spores, and the other latent compartments (L2a and b, L3a and b, and L4a and b) originate from lesion growth on three successive days. L1a, L2a, L3a and L4a are up to one

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58 day old, while the latent b compartments are more than one day old, until the total latent period has passed. The model starts with the initial number of healthy susceptible sites and latently infected sites at 7 am in the morning (Table 3 2). Healthy susceptible sites decr ease in two ways: (i) through new infection determined by the number of infectious sites, and (ii) through the growth of the latently infected sites. The rate of transition from latent to infectious state is determined by latency progression rate LPR which is the inverse of latent period and is temperature dependent as described by a thermodynamic model (Shakya et al. 2014 (Submitted)). Two latency progression rates are distinguished: LPR1 is 1/24 h 1 , based on the notion that only 24 h old latent lesions c ontribute to lesion growth, and LPR2 is 1/33 h 1 , the latency rate for the remaining period assuming that the optimum latent period is 57 h at 23°C. The rate of change from the infectious to the removed state is determined by the removal rate, 1/24 h 1 , wh ich is the inverse of the infectious period. BLIGHTSIM uses hourly temperature and RH data as input to simulate the disease severity, which is considered as the sum of infectious and removed sites. Temperature and RH are the primary driving variables of th e system which affect the latency progression and relative lesion growth rates. The whole program is developed in R software. The change in each state variable of the system is governed by the following equations. Model Equations The model equations for th e model are described below. dH=( HMF*f1*f2*H[hour]*I[hour]) (RLGR1*f3* H[hour]*L1a[hour]) (RLGR2*f3* H[hour]*L2a[hour]) (RLGR3*f3* H[hour]*L3a[hour]) (3 1) dL1a=(HMF*f1*f2*H[hour]*I[hour]) (L1a[hour]*LPR1*f4) (3 2) dL2a=(RLGR1*f3* H[hour]*L1a[h our]) ( L2a[hour]* LPR1*f4) (3 3) dL3a= (RLGR2* f3* H[hour]*L2a[hour] ) (L3a[hour]* LPR1*f4) (3 4) dL4a= (RLGR3*f3* H[hour]*L3a[hour]) (L4a[hour]* LPR1*f4) (3 5) dL1b=(L1a[hour]*LPR1*f4) (L1b[hour])*LPR2*f4) (3 6)

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59 dL2b=(L2a[hour]* LPR1*f4) (L2b[hour]* LPR2*f4) (3 7) dL3b=(L3a[hour]* LPR1*f4) (L3b[hour]* LPR2*f4) (3 8) dL4b=(L4a[hour]* LPR1*f4) (L4b[hour]* LPR2*f4) (3 9) dI=(L1b[hour])*LPR2*f4)+ (L2b[hour]* LPR2*f4)+ (L3b[hour]* LPR2*f4)+ (L4b[hour]* LPR2*f4) (REMRATE*I[hour]) (3 10) dR=((REMRATE)*I[hour]) (3 11) dY=dI+dR (3 12) where, f1= a reducing function that describes the effect of temperature on sporulation and infection f2= a reducing function that describes the effect of relative humidity on s porulation f3= a reducing function that describes the effect of temperature in radial lesion growth f4= a reducing function that describes the effect of temperature on the latency progression rate. Estimation of Relative Lesion Growth Rate Lesion growth is assumed to take place for 72 h. Under optimal conditions, a lesion will reach the margin of a leaf in 72 h. To avoid growth beyond the leaf margin, lesion growth is assumed to stop after 72 h. The relative lesion growth rate declines according to a power function as the lesion area increases proportionally to the square of the radius. The relative lesion growth rates were calculated in Excel. First, the hourly increase in radius and lesion area was plotted using the data for the above mentioned US 23 isola te (Shakya et al. 2014 (Submitted)). The increase in area over time was fitted to a power function. Next, the derivative of the area increase (the absolute growth rate) was calculated and plotted against time, which resulted in a straight line. Further, th e derivative of the area increase was divided by the observed area at each specific hour and plotted against time to estimate the relative lesion growth rates. As nothing is known about relative lesion growth rates during the day versus the night, it was a ssumed that the relative lesion growth rate is constant during 24 h. Thus, the decline curve for the relative lesion growth rate was divided into three discrete sections (every 24 h), and the average relative growth rates were calculated for three consecut ive 24 h periods (Table 3 1).

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60 Effect of Temperature on Relative Sporulation*Infection and Derivation of Function f1 A four parameter thermodynamic model (Schoolfield et al. 1981) was used to describe the combined effect of temperature on relative sporulati on and infection (Equation 2 2) . Independent sporulation and infection efficiency curves described in Shakya et al 2014 (Submitted)for an isolate of P. infestans clone US 23 were merged by multiplying relative sporulation and inf ection efficiency to produce a single optimum curve (Figure 3 2A). All the parameters and their values are described in Table 3 3. Effect of Relative Humidity on Sporulation and Derivation of Function f2 The function f2 was derived using the sporulation d ata from Harrsion and Lowe (1989) (Figure 3 2B) on detached potato leaflets at 0.3 mms 1 air speed and 15°C. Leaflets were incubated at 80, 85, 90, 95 and 100% relative humidity. Sporulation was assessed 10 days after inoculation. The same thermodynamic mo del was fitted to estimate the parameters for the sporulation function (Table 3 3). Effect of Temperature on Relative Lesion Growth and Derivation of Function f3 The relative lesion growth rates for three consecutive days were derived using the data from growth chamber experiments for the US 23 isolate as described above. These rates were adjusted for the effect of temperature using function f3 for each of the relative lesion growth rates in three consecutive 24 h periods. To obtain function f3, the increa se in lesion radius per hour was calculated at different constant temperatures and fitted to the thermodynamic model (Figure 3 2C). The parameters of this model (Table 3 3) were used in the simulation model. An alternative approach, fitting the increase in lesion area per hour to the same thermodynamic model and using those parameter values in the model, did not result in a good fit.

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61 Effect of Temperature on Latency Progression Rate and Derivation of Function f4 Relative latent period progression rates wer e fitted to the same thermodynamic model. Growth chamber data for and isolate of US 23 (Shakya et al 2014 (Submitted)) were used to produce an optimum curve for the relative latency progression rate (Figure 3 2D) and parameters were estimated (Table 3 3). Driving Variables The model uses hourly temperature and relative humidity data in an Excel spread sheet (.csv format) as driving variables. These data were obtained from growth chamber experiments (Shakya et al. 2014 (Submitted)). Hourly temperature in the growth chamber was modeled using a modified sine wave equation given below. T H = A Sin (15*H + 210) + M where T H = temperature at hour H, A = amplitude (T max T min )/ 2, H = time in 24 hours, M = mean temperature, T max = Maximum temperature in 24 hours, T min = minimum temperature in 24 hours. The relative humidity of the chamber was set for 60 70% during day and 90 95% at night. Model Fitting The model was fitted to disease progress curves for lesion growth of an isolate of P. infestans clone US 23 in a growth chamber set at 21 different temperature amplitude combinations (Shakya et al. 2014 (Submitted)). Six potato leaflets (about 2000 mm 2 each) had been inoculated with P. infestans zoospores for each temperature amplitude combination, and infection efficiency , incubation and latency progression, lesion growth and sporulation were followed over time. Re infection from sporangia or zoospores was avoided. Disease progress curves were constructed taking the incubation period (from transfer of the leaves to various temperatures to first lesion appearance) and observed lesion growth into account. The model was run only for 154 h starting at 7 am in the morning, so that secondary cycles of the pathogen were

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62 avoided. Therefore, the number of initial infectious sites an d hourly multiplication factor were set to zero. The model was initiated with the proportion of latent sites in the L1a compartment (Table 3 2). The number of initial latent sites (L1a) was estimated for each temperature amplitude combination, converted t o proportion of leaf area latently infected and subtracted from 1 to get the proportion of healthy sites at the starting hour. The proportion of initial L1a sites at 23°C was determined by estimating the proportion of the contact area of the inoculation dr oplet (14 mm 2 ) occupied by initial lesions (approximately 0.1%).The proportions of initial latent sites at other temperatures were estimated similarly using the numbers of lesions counted under the microscope at the various temperatures. The proportions of initial L1a sites were then optimized to obtain a good fit of the simulated to the observed disease progress curves at each temperature amplitude combination. The ultimate i nitial L1a sites used in the simulation model were plotted against temperature to check if the relationship was similar to that of the number of lesions formed mm 2 zoospore 1 versus temperature as described in Shakya et al. 2014 (Submitted) . The simulated diseased area was considered to be the sum of infectious (I) and removed (R) site s. Simulated disease severity was calculated by dividing I plus R sites on six leaves by the maximum number of sites on six leaves (12,000 sites of 1 mm 2 each). Simulated and observed disease severities were plotted over time for each of the 21 temperature amplitude combinations. Simulated and observed disease severities were also plotted against each other and linear regression equations were calculated in Excel. The slopes of the regression lines were compared to 1.0, and the R 2 was considered as a measur e of the goodness of fit.

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63 Results Effects of Temperature and Relative Humidity on Model Parameters A right hand skewed optimum curve was obtained for relative sporulation*infection efficiency, similar to the individual optimum curves for sporulation and infection efficiency versus temperature (Shakya et al. 2014 (Submitted)). The relative sporulation*infection efficiency was maximal at 12°C and gradually reduced beyond that temperature (Figure 3 2A). The sporulation opportunity at 15°C plotted versus rel ative humidity resulted in a left hand skewed curve with an optimum around 95% relative humidity (Figure 3 2B). A left hand skewed optimum curve was also obtained for relative lesion growth rate versus temperature (Figure 3 2C). This temperature function w as optimal at 22 23°C. Fitting the relative latency progression rate to the thermodynamic model resulted in a left hand skewed optimum curve (Figure 3 2D). This temperature function also had an optimum at 22 23°C. The parameter values for the thermodynamic models are given in Table 3 3. Model Calibration Because there was no secondary cycle of disease development in the calibration data set (Shakya et al. 2014 (Submitted)), the hourly multiplication factor was set to zero. Only the initial proportion of la tent sites (L1a) was adjusted for each temperature amplitude combination to simulate the disease severity over time (Table 3 2). Almost significant positive correlations between proportion of initial latent sites (L1a) and infection efficiency (the number of lesions mm 2 zoopsore 1 ) were observed for constant (r=0.69; P=0.08) and fluctuating temperatures with amplitude + 5°C (r=0.73; P=0.06). There was no significant correlation between the optimized proportion of initial latent sites and fluctuating tempera tures with amplitude + 10 o C.

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64 Model Output at Constant and Oscillating Temperatures When the model was run for 154 hours at seven constant temperatures ranging from 10°C to 27°C, a very good fit was obtained to the observed disease severity data except at 1 0°C (Figure 3 3 and 3 4). The poor fit at constant 10°C is reflected in the low value for the slope and R 2 for the observed versus simulated linear regression (Table 3 4). The observed and predicted disease severities were maximum (74%) at 23°C and minimum (1.7%) at 10°C. The simulated disease severity increased at increasing average temperatures from 10°C to 23°C as observed in a growth chamber experiment and decreased beyond that temperature. When the model was run for 154 hours under oscillating tempera tures with amplitude ±5°C, the fit was better compared to the constant temperature predictions (Figure 3 5) as indicated by the slope and coefficient of determination for the observed versus simulated linear regression (Table 3 4). The simulated and observ ed final maximum disease severities (25%) were low compared to those at constant temperatures. The maximum disease severity (25%) was observed at 17±5°C and the minimum disease severity (6%) at 10±5°C. Disease severity increased with increasing average tem peratures ±5°C up to 17°C. Low final disease severities were observed at the temperature extremes. When the model was run for 154 hours at oscillating temperatures ranging from 10°C to 27°C with amplitude ±10°C, the final maximum disease severity (36%) was again low compared to simulated disease severities at constant temperatures but higher than those at oscillating temperatures with amplitude ±5°C. Maximum disease severity (36%) was observed at 23±10°C whereas minimum disease severity (4%) was observed at 10±10°C (Fig 3 6). Disease severity values increased with increasing average temperatures with this amplitude up to 23°C and declined at higher average temperatures.

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65 The deviations of the simulated disease severity data from the observed data were greate r at increasing amplitudes when the average temperatures were above 10°C, especially at 23°C (Figure 3, 4, 5 and 6). The deviations from the 1:1 line for observed versus simulated data were always greater at the lower disease severities, in the beginning o f the disease progress curves (Figure 3 4), because latently infected sites moved continuously into infectious sites and simulated disease severity, consisting of I and R sites, did not start after a discreet incubation period. Nevertheless, the slopes of the regression lines of observed versus simulated disease severities were mostly close to 1.0, with R 2 values ranging from 0.772 to 0.984 (Table 3 4). Discussion The primary objective of this research was to develop a relatively simple simulation model for potato late blight that uses hourly temperature and relative humidity data as driving variables. We were able to simulate late blight disease progression at different temperature amplitude combinations using the model BLIGHTSIM. The model described here uses a parallel box car train approach for relative lesion growth rate. The number of parallel series is dependent on the number of days each lesion continues to grow before it reaches the leaf margin. In the current version of BLIGHTSIM four series we use d one series for new lesions and three for expanding lesions. We restricted the number of box cars in each parallel series to two, assuming two classes of latent sites: one contributing directly to lesion growth (at the margin of each late blight lesion) a nd one needed to pass through the rest of the latent period without contributing to lesion growth (a ring of latent sites behind those at the lesion margin). This approach has not been described before in plant disease simulation publications. BLIGHTSIM wa s calibrated to fit observed disease progress curves for an isolate of the US 23 clone of Phytophthora infestans on potato cv. Red Lasoda by adjusting the initial latent sites (L1a) for different temperatures. This adjustment was deemed justified as the in fection

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66 efficiency is dependent on temperature (Shakya et al. 2014 (Submitted)); so that the effective spore density and initial number of latent sites were not the same for each temperature. Indeed, for constant temperatures and oscillating temperatures w ith +5ºC the relationship between the fitted initial latent sites and temperature was similar to that of the calculated infection efficiency and temperature. The correlation coefficients between initial latent sites and infection efficiency was almost sign ificant (P=0.06 0.08). However, there was no relation between fitted initial latent sites and infection efficiency when the amplitude was +10ºC. Optimization of the initial latent sites was done visually. A better fit may be obtained by using an automated optimization package. Despite these discrepancies, the model BLIGHTSIM provided a good fit to the observed disease severities calculated for the US 23 isolate in growth chamber experiments (Shakya et al. 2014 (Submitted)). The slope of the simulated versu s the observed disease severities was close to 1 for most temperatures, and the coefficients of determination were generally high. The difference between the slope and 1.0 was negligible in most of the cases (Table 3 4). The model over predicted the initia l disease development but under predicted the final disease severity after 154 h at constant 10°C. One of the reasons could be the longer incubation period at 10°C in the growth chamber, while simulated disease development progressed continuously as soon a s the first latent sites developed into infectious sites. Moreover, final disease evaluations were always done at 154 h after transfer of inoculated leaflets to the various temperatures (Shakya et al. 2014 (Submitted)), so that the time left over for lesio n expansion was limited at 10°C and the estimated lesion expansion rate used in the model might have been too low. Without a time limit for lesion expansion at 154 h, a better fit at 10°C could probably be obtained by increasing the

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67 number of latent box ca r series in the model allowing lesions to grow for some additional days until the leaf margin would be reached. Contrary to the relatively poor fit at a constant average temperature of 10°C, the fit was improved under oscillating temperatures around 10°C ( Figure 3 4). At this low average temperature, the incubation and latency progression rates were progressively greater at increasing amplitudes (Shakya et al. 2014 (Submitted)). As a result, there was more time for lesion growth until 154 h. On the other ha nd, the incubation and latency progression rates were reduced at increasing amplitudes around higher mean temperatures, particularly 23°C (Shakya et al. 2014 (Submitted)). The longer incubation and latent periods under oscillating compared to constant 23°C and 27°C, and the associated shorter time for lesion expansion, explains the greater deviation of simulated from observed disease severities under oscillating temperatures at relatively high mean temperatures (Table 3 4; Figure 3 4). Another reason for th e slightly increased deviations between simulated and observed disease severity at increasing temperature amplitudes could be the fact that the model functions (f1, f3 and f4) were derived from constant temperature experiments, which resulted in slightly l ess perfect predictions under oscillating than under constant temperatures. Finally, the deviations between simulated and measured disease severities occurred especially at the beginning of the epidemics. This is because latently infected sites move conti nuously into infectious sites and infectious sites into removed sites, resulting in shorter simulated than observed incubation periods. Based on the results presented here and previously (Shakya et al. 2014 (Submitted)), diurnal oscillations determine to a large extent the development of potato late blight similar to that of lettuce downy mildew (Scherm and van Bruggen 1994a and b). The BLIGHTSIM model is the first simulation model that uses diurnal oscillations in temperature and the associated

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68 relative hu midity to simulate plant disease progress. There are many late blight simulation and forecasting models. The first and widely accepted late blight model is LATEBLIGHT described by Bruhn and Fry (1981). This is a matrix model where lesions pass through 15 age classes and at the same time expand in area. The age classes represent different stages of pathogen development from sporangial or zoospore germination to microscopic lesion, expanded lesion, sporulating lesion and necrotic lesion after spore dispersal . Daily integrated measures of temperature, relative humidity and leaf wetness are the driving variables for sporulation and infection, but not for latent period. This model was modified by Andrade Piedra et al. (2005b and c) by including the effect of tem perature on latent period, and modifying the temperature effect on lesion expansion and sporulation; this modified model is referred to as LB2004. Similar daily temperature and moisture variables were used in LB2004 as in LATEBLIGHT. The constant temperatu re functions of BLIGHTSIM are based on thermodynamic models that have similar shapes as the polynomial models of LB2004 (Andrade Piedra et al. 2005b), but BLIGHTSIM has an hourly time step so that diurnal oscillations in temperature and relative humidity c an be simulated. The LATEBLIGHT and LB2004 models are quite complex due to the many lesion categories and separate categories for sporangia and zoospore production and germination. SEIR models, where a minimal number of successive categories of potential i nfection sites are distinguished, can be quite simple and easily integrated into crop growth models. Only few SEIR models for late blight development have been published (Apel et al. 2003; Van Oijen 1992). All these models use daily time steps. BLIGHTSIM i s a simple modified SEIR model that simulates both new infections and lesion growth with an hourly time step, so that effects of diurnal temperature oscillations on disease development can be simulated accurately.

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69 Lesion expansion has been identified as a n important resistance component and primary determinant of disease progression (Van Oijen 1992, Berger and Jones 1985). Lesion growth has mostly been modeled by assuming a constant radial growth rate (mday 1 ) at one or more constant temperatures (Van Oije n 1992; Andrade Piedra et al. 2005b; Skelsey et al. 2009b). For BLIGHTSIM constant radial growth rates (mm h 1 ) at constant temperatures between 10°C and 27°C (Shakya et al. 2014 (Submitted)) are converted to two dimensional relative lesion growth rates (h 1 ) that decrease as lesions expand, resulting in an excellent fit of simulated to measured final lesion size. Lesion expansion has seldom been included in other disease simulation models, except for a 3D virtual wheat model with a submodel for Septoria bl ight where each lesion was modeled up to a maximum size (Robert et al. 2008). This spatial approach to limiting lesion size was not possible here, as BLIGHTSIM does not keep track of individual leaves. Therefore, lesion growth is limited in time rather tha n space in BLIGHTSIM. Although lesion growth is also limited in time in LATEBLIGHT, this limitation is obtained in a different way compared to BLIGHTSIM (Bruhn and Fry 1981). So far, the BLIGHTSIM model has been tested only for a short epidemic period (15 4 h) using late blight progression data from growth chamber experiments (Shakya et al. 2014 (Submitted)). Secondary disease cycles have not been considered yet and therefore the hourly multiplication factor was set at zero. The hourly multiplication factor consists of two components: spore production and a dilution factor. The first component is related to temperature and humidity, but the dilution factor is constant. However, spore release, dispersal and survival are strongly affected by environmental cond itions (Su et al. 2000 and 2004; Sunseri et al. 2002; Wu et al. 2000 and 2002). Thus, the next logical step in the development of BLIGHTSIM is incorporation of additional environmental variables affecting the hourly multiplication factor,

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70 besides model cal ibration and validation with field data. In addition, a sensitivity analysis will be carried out on the effects of model parameters and initial input values on model output, and scenario analysis for effects of average weather variables versus the amplitud e of diurnal oscillations of these variables. BLIGHTSIM was developed to study late blight development under future climate change scenarios. Potential effects of climate change on potato late blight has been studied using various forecasting models where risk units are accumulated depending on temperatures during periods of high relative humidity suitable for infection (Hijmans et al. 2000; Kaukoranta 1996; Shtienberg et al. 1989; Sparks et al. 2011 and 2014). Contrary to simulation models, these models do not take into account that different stages in pathogen development respond differentially and instantaneously to changing environmental conditions. Such models can only give very coarse predictions of changes in late blight severity in response to large trends in climate change. Thus, late blight severity was predicted to increase at high latitudes (Kaukoranta 1996) or high altitudes in some tropical regions (Hijmans et al. 2000; Sparks et al. 2014). However, regional variability in climate and extreme we ather events is expected to be considerable with differential effects on late blight development depending on particular locations. Sparks et al. (2011) developed a metamodel based on the SIMCAST forecasting model for late blight (Grünwald et al. 2002) tha t allowed coarse predictions of effects of climate change despite the lack of accurate prediction of regional weather at that time (Sparks et al. 2014). However, in the latest IPCC report (Field et al. 2014) global climate predictions have improved conside rably, including the prediction of regional and inter annual variation in average daily weather, as well as the daily temperature range.

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71 These improvements in climate predictions combined with the constantly increasing computing capacity will ultimately a llow inclusion of the effects of diurnal oscillations in weather variables in simulation models to predict the effects of climate change on plant pathogens with short generation times like P. infestans . Another reason for using simulation models rather tha n forecasting models for disease prediction under climate change is the sheer impossibility to couple outputs of forecasting models to crop growth models to arrive at yield loss predictions. For this purpose, simple simulation models are needed. SEIR model s in which all state variables are expressed as proportion of potentially susceptible plant tissue are particularly appropriate for integrated crop disease yield models intended to predict effects of climate change on crop productivity (Savary et al. 2011) . Thus, BLIGHTSIM can play an important role in the prediction of effects of climate change on potato production, particularly in the Andes where human populations depend heavily on potatoes as a staple crop. Average temperatures and their diurnal amplitud es are expected to increase in the Andean highlands under climate change scenarios (Perez et al. 2010). Late blight used to be restricted at high altitudes due to low temperatures, but changes in potato cultivars, cultural practices and weather patterns (i ncreasing temperature) have extended the occurrence of this disease into areas where it was limited previously (Perez et al. 2010). The late blight model LB2004 has been validated under a broad range of field conditions, including the Andes (Andrade Piedra et al. 2005a and 2005c; Blandón Díaz et al. 2011), but has not been related to potato yield loss under climate change scenarios. We expect that BLIGHTSIM can be easily coupled to a potato crop model after adjusting and validating the model for field condi tions. This model will enable the study of effects of changes in average temperatures and diurnal oscillations on late blight development in the Andean highlands under climate change. A combined BLIGHTSIM potato

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72 model will allow comparison of adaptation st rategies and their economic impacts, so that farming communities can better adjust to the impending changes in their environment.

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73 Table 3 1. Variables and parameters used in the BLIGHTSIM model and their initial val ues for simulation of potato late blight caused by an isolate of Phytophthora infestans clone US 23 on potato cv. Red Lasoda. State variables Description (units) Initial values H Healthy susceptible sites Table 2 L x Latently infected sites Table 2 I I nfectious sites 0 R Removed sites 0 Y Sum of infectious and removed sites 0 Driving variables T Hourly temperature (°C) 0 37 RH Hourly relative humidity (%) 60 95 Parameters LPR1 Latency progression rate 1 (h 1 ) 1/24 at 23°C LPR2 Latency prog ression rate 2 (h 1 ) 1/33 at 23°C RLGR1 Relative lesion growth rate 1(h 1 ) 0.3136 RLGR2 Relative lesion growth rate 2(h 1 ) 0.0568 RLGR3 Relative lesion growth rate 3(h 1 ) 0.0334 REMRATE Relative rate of removal (h 1 ) 1/24 HSP Hourly spore production (mm 2 h 1 ) 45 DILFAC Dilution factor 0.01 HMF (=HSP*DILFAC) Hourly multiplication factor (h 1 ) 0.45

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74 Table 3 2. Initial values of the proportions of healthy (H) and latently infected sites (L1a) at different temperature amplitude c ombinations for the BLIGHTSIM model.* Temperature a ±0°C b H L1a ±5°C H L1a ±10°C H L1a 10 0.9995 0.0005 0.9950 0.0050 0.9970 0.0030 12 0.9930 0.0070 0.9850 0.0150 0.9950 0.0050 15 0.9920 0.0080 0.9900 0.0100 0.9950 0.0050 17 0.9930 0.0070 0.9930 0.0070 0.9920 0.0080 20 0.9900 0.0100 0.9970 0.0030 0.9850 0.0150 23 0.9900 0.0100 0.9960 0.0040 0.9800 0.0200 27 0.9940 0.0060 0.9960 0.0040 0.9900 0.0100 a Average temperature in °C b Amplitudes of daily temperature oscillations *The initial values of all the other latent sites are zero Table 3 3. Estimated parameter values for the reducing functions (f1 f4) obtained by fitting a thermodynamic model to epidemic components of an isolate of Phytophthora infestans clone US 23 on potato cv. Red Lasoda (Shakya et al. 2014 (Submitted)). Parameter Sporulation*inf. eff. vs. temperature (f1) Sporulation vs. relative humidity (f2) Radial lesion growth rate vs. temperature (f3) Relati ve latency progression rate vs. temperature (f4) 1.013*10 10 4.371*10 8 123.8 1.7168 292131 55763.5 390540 14275.4 331573 77245.3 402880 49087.1 284.9 365.3 300.1 298.85 Table 3 4. Values of slope and coefficients of determination (R 2 ) for s imulated versus observed disease severities at different temperature amplitude combinations for late blight caused by an isolate of Phytophthora infestans clone US 23 on potato cv. Red Lasoda. Temperature a ±0°C b Slope R 2 ±5°C Slope R 2 ±1 0°C Slope R 2 10 0.337 0.772 0.966 0.843 1.124 0.954 12 1.000 0.920 1.096 0.952 1.118 0.972 15 0.894 0.951 1.138 0.967 1.014 0.970 17 1.020 0.964 1.038 0.967 1.0586 0.966 20 0.782 0.950 1.015 0.960 1.151 0.936 23 1.016 0.984 1.148 0.961 1.0 78 0.911 27 1.040 0.955 1.190 0.953 1.038 0.907 a Average temperature in °C b Amplitudes of daily temperature oscillations

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75 Figure 3 1. Relational diagram of the model BLIGHTSI M for simulation of potato late blight ( Phytophthora infestans ) with all compartments and rate variables. Material flow and information flow are indicated by solid and dashed arrows respectively. Healthy Removed Latent 3a Latent 2a Latent 1a Latent 1b Latent 2b Latent 3b Infectious Latent 4b Latent 4a Disease severity RLGR1 *f3 RLGR2*f3 RLGR3*f3 LPR1*f4 LPR 1 *f 4 LPR 1 *f4 LPR 1 *f4 LPR2*f4 LPR2*f4 LPR2*f4 LPR2*f4 REMRATE HMF*f1*f2

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76 Figure 3 2. Optimum curves for parameter estimates used in the model BLIGHTSIM. All data except those in B were obtained from growth chamber experiments performed on potato cv Red Lasoda using an isolate of Phytophthora infestans clone US 23 (Shakya et al. 2014 (Submitted)). The data were fitted with a four par ameter thermodynamic model (Table 3 3). A= Effect of temperature on relative sporulation*infection efficiency. B= Effect of relative humidity on sporulation of P. infestans race 4,10,11 on potato cv Bintje (Harrison and Lowe 1989). C= Effect of temperature on relative radial lesion growth rate. D= Effect of temperature on relative latency progression rate.

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77 Figure 3 3. Observed (Dots) and simulated (continuous line) disease progress curves of an isolate of Phytophthora infestans clone US 23 at different c onstant temperatures (T), A: T =10°C, B: T =12°C, C: T =15°C, D: T =17°C, E: T =20°C, F: T =23°C, G: T=27°C. The simulated disease progress curves were obtained with BLIGHTSIM and the observed disease severities in a growth chamber experiment at Gainesvill e, Florida (Shakya et al. 2014 (Submitted)).

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78 Figure 3 4. Simulated versus observed late blight severities (dotted lines) and expected 1:1 relationships (solid lines) at different temperature amplitude combinations. A: T=10±0°C, B: T=20±0°C, C: T=27±0°C, D: T=10±5°C, E: T=20±5°C , F: T=27±5°C , G: T=10±10°C, H: T=20±10°C, I: T=27±0°C.

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79 Figure 3 5. Observed (Dots) and simulated (continuous line) disease progress curves of and isolate of Phytophthora infestans clone US 23 at different oscillating temperatur es, A: T=10±5°C, B: T=12±5°C, C: T=15±5°C, D: T=17±5°C, E: T=20±5°C, F: T=23±5°C, G: T=27±5°C. The simulated disease progress curves were obtained with BLIGHTSIM and the observed disease severities in a growth chamber experiment at Gainesville, Florida (Sh akya et al. 2014 (Submitted)).

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80 e Figure 3 6. Observed (Dots) and simulated (continuous line) disease progress curves of and isolate of Phytophthora infestans clone US 23 at different oscillating temperatures, A: T=10±10°C, B: T=12±10°C, C: T=15±10°C, D: T=17±10°C, E: T=20±10°C, F: T=23±10°C, G: T=27±10°C. The simulated disease progress curves were obtained with BLIGHTSIM and the observed disease severities in a growth chamber experiment at Gainesville, Florida (Shakya et al. 2014 (Submitted)).

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81 CHAPTER 4 SUMMARY AND CONCLUSION Global climate change is a fact as it is evident from average surface temperature, rising sea level, change in rainfall intensity and quantity and increase in frequency of extreme events (Stocker et al. 2013). These changes are assoc iated with increases in the concentrations of greenhouse gases in the atmosphere. Global climate change is expected to have effects on crop production partially determined by disease development. However, the impacts of climate change on plant pathogens an d disease development are not straightforward (Coakley et al. 1999) and difficult to quantify. There are complex interrelationships between host, pathogen and their immediate environment, which are all affected by climate change (Coakley et al. 1999; Garre tt et al. 2011). Most of the climate change studies on plant diseases have predicted increased activity of pathogens (Chakraborty and Datta 2003), a shift in geographical distribution (Chakraborty 2013), modifications in physiology and resistance of host p lants (Coakley et al. 1999) and evolution of new races (Chakraborty 2013). Late blight of potato ( Phytophthora infestans ) is an important disease and is responsible for yield losses up to 21 per cent (Oerke 2006). To date most simulation models predicting late blight development are rather complex, while typical descriptive forecasting models are simpler but based on the accumulation of average daily or monthly temperatures (Apel et al. 2003; Bruhn and Fry 1981; Garcia et al. 2006; Grünwald et al. 2002; Kau koranta 1996). Diurnal oscillations in temperature are barely taken into account. Research has shown that pathogens respond differently to temperature variation (Scherm and van Bruggen 1994a) and GCMs mostly predict a decrease in temperature amplitude. How ever, diurnal amplitudes may increase in highland areas (Perez et al. 2010). Thus it was extremely important to study the effect of diurnal temperature oscillations on growth and development of P. infestans and develop a model that takes temperature oscill ations into account.

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82 Using a temperature and humidity controlled growth chamber and incubators, we tested and confirmed the hypothesis that the growth and development rates of P. infestans are quite different under diurnally oscillating temperatures compar ed to constant temperatures. Our measurements of incubation and latency progression rates proved accelerated growth under oscillating temperatures with low daily means and reduced development rates under oscillating temperatures with high daily means as pr edicted by Scherm and van Bruggen (1994a). Small fluctuations in temperature (±5°C) were shown to have increased infection efficiencies, lesion growth rates and sporulation capacities whereas large temperature fluctuations (±10°C) had a detrimental effect on these components. There was a clear distinction between the optimum curves for the processes that take place inside the plant tissue (skewed to left) and outside of plant tissue (skewed to right). These results clearly show that oscillations in temperat ure need to be considered when predicting late blight under climate change scenarios instead of just using the change in average temperature. Incorporation of the effects of temperature oscillations on epidemic components in a simulation model is another i mportant aspect of studies of climate change impacts on disease development. A new simulation model for potato late blight (BLIGHTSIM) was developed which uses hourly temperatures and relative humidities to simulate infection by P. infestans and late bligh t lesion growth. The model was calibrated using the observed disease severity data from the growth chamber and incubator experiments. Besides temperature and relative humidity, increases in CO 2 concentration and changes in rainfall patterns are also assoc iated with climate change. Modeling the combined effect of changes in temperature, relative humidity, CO 2 concentration and rainfall pattern together might reflect the actual impact of climate change on late blight. Although we only studied and tested

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83 for variation in temperature and humidity to model late blight, the next logical step would be to add other variables into the model. The research work presented here opens new avenues for further research. Sensitivity analysis to input parameters and validati on of the model (BLIGHTSIM) with the field data will need to be done in the near future. The model is not as complex as existing late blight models and thus linking the model to a potato growth model could be done easily. Climate change is expected to hav e a substantial impact on Andean highlands. Average temperature and diurnal oscillations are expected to increase in this region (Perez et al. 2010). Large part of Andean population is dependent on potatoes. Thus, it becomes quite necessary to predict late blight accurately and make appropriate management decisions to adjust to climate change. The research work presented here might be helpful to study the impact of climate change on late blight in Andes region and provide suggestions how potato farmers coul d adjust their cropping practices to the expected changes in climate.

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84 APPENDIX BLIGHTSIM MODEL CODE IN R The user has to create an excel file (.csv format) with three columns. First column is the number of hours for a simulation run ( input value from 1 to 154); second and third column requires the temperature and relative humidity data at specific hour. rm(list=ls()) BLIGHTSIM=function(HMF,LPR1,LPR2,LGR1,LGR2,LGR3,REMRATE,shour,lhour,weather) { H=rep(NA,lhour) L1a=rep(NA,lhour) L1b=rep (NA,lhour) L2a=rep(NA,lhour) L2b=rep(NA,lhour) L3a=rep(NA,lhour) L3b=rep(NA,lhour) L4a=rep(NA,lhour) L4b=rep(NA,lhour) I=rep(NA,lhour) R=rep(NA,lhour) Y=rep(NA,lhour) H[shour]=0.99 L1a[shour]=0.01 L2a[shour]=0 L3a[shour]=0 L4a[shour]=0 L1b[shour]=0 L2b[sh our]=0 L3b[shour]=0 L4b[shour]=0 I[shour]=0 R[shour]=0 Y[shour]=0 for(hour in shour:(lhour 1)){ T=weather$Thour[hour] RH=weather$RHhour[hour] dH=(( HMF )*( 1.013*10^10*((T+273.2)/298)*exp((292131/1.987)*(1/298 1/(T+273.2)))/(1+(exp((331573/1.987)*(1/284.9 1/(T+273.2))))))*( 4.371*10^ 8*((RH+273.2)/298)*exp((55763.5/1.987)*(1/298 1/(RH+273.2)))/(1+(exp((77245.3/1.987)*(1/365.3 1/(RH+273.2))))))*(H[hour]*I[hour]))

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85 ((LGR1)*( 123.8*((T+273.2)/298)*exp(( 390540/1.987)*(1/298 1/(T+273.2)))/(1+(exp(( 402880/1.98 7)*(1/300.1 1/(T+273.2)))))) *H[hour]*L1a[hour]) ((LGR2)*( 123.8*((T+273.2)/298)*exp(( 390540/1.987)*(1/298 1/(T+273.2)))/(1+(exp(( 402880/1.987)*(1/300.1 1/(T+273.2)))))) *H[hour]*L2a[hour]) ((LGR3)*( 123.8*((T+273.2)/298)*exp(( 390540/1.987)*(1/298 1/ (T+273.2)))/(1+(exp(( 402880/1.987)*(1/300.1 1/(T+273.2)))))) *H[hour]*L3a[hour]) dL1a=((HMF )* ( 1.013*10^10*((T+273.2)/298)*exp((292131/1.987)*(1/298 1/(T+273.2)))/(1+(exp((331573/1.987)*(1/284.9 1/(T+273.2))))))*( 4.371*10^ 8*((RH+273.2)/298)*exp((5576 3.5/1.987)*(1/298 1/(RH+273.2)))/(1+(exp((77245.3/1.987)*(1/365.3 1/(RH+273.2))))))*(H[hour]*I[hour])) (L1a[hour]*LPR1*( 1.7168*((T+273.2)/298)*exp((14275.4/1.987)*(1/298 1/(T+273.2)))/(1+(exp((49087.1/1.987)*(1/298.85 1/(T+273.2))))))) dL2a=((LGR1)*( 12 3.8*((T+273.2)/298)*exp(( 390540/1.987)*(1/298 1/(T+273.2)))/(1+(exp(( 402880/1.987)*(1/300.1 1/(T+273.2)))))) *H[hour]*L1a[hour]) (L2a[hour]* LPR1*( 1.7168*((T+273.2)/298)*exp((14275.4/1.987)*(1/298 1/(T+273.2)))/(1+(exp((49087.1/1.987)*(1/298.85 1/(T+27 3.2))))))) dL1b=(L1a[hour]*LPR1*( 1.7168*((T+273.2)/298)*exp((14275.4/1.987)*(1/298 1/(T+273.2)))/(1+(exp((49087.1/1.987)*(1/298.85 1/(T+273.2))))))) (L1b[hour])*(LPR2*((1.7168*((T+273.2)/298)*exp((14275.4/1.987)*(1/298 1/(T+273.2)))/(1+(exp((49087.1/1.9 87)*(1/298.85 1/(T+273.2)))))))) dL2b=(L2a[hour]* LPR1*( 1.7168*((T+273.2)/298)*exp((14275.4/1.987)*(1/298 1/(T+273.2)))/(1+(exp((49087.1/1.987)*(1/298.85 1/(T+273.2))))))) (L2b[hour]* LPR2*( 1.7168*((T+273.2)/298)*exp((14275.4/1.987)*(1/298 1/(T+273.2) ))/(1+(exp((49087.1/1.987)*(1/298.85 1/(T+273.2))))))) dL3a= ((LGR2)*( 123.8*((T+273.2)/298)*exp(( 390540/1.987)*(1/298 1/(T+273.2)))/(1+(exp(( 402880/1.987)*(1/300.1 1/(T+273.2)))))) *H[hour]*L2a[hour]) (L3a[hour]* LPR1*( 1.7168*((T+273.2)/298)*exp((142 75.4/1.987)*(1/298 1/(T+273.2)))/(1+(exp((49087.1/1.987)*(1/298.85 1/(T+273.2))))))) dL3b=(L3a[hour]* LPR1*( 1.7168*((T+273.2)/298)*exp((14275.4/1.987)*(1/298 1/(T+273.2)))/(1+(exp((49087.1/1.987)*(1/298.85 1/(T+273.2))))))) (L3b[hour]* LPR2*( 1.7168*(( T+273.2)/298)*exp((14275.4/1.987)*(1/298 1/(T+273.2)))/(1+(exp((49087.1/1.987)*(1/298.85 1/(T+273.2))))))) dL4a= ((LGR3)*( 123.8*((T+273.2)/298)*exp(( 390540/1.987)*(1/298 1/(T+273.2)))/(1+(exp(( 402880/1.987)*(1/300.1 1/(T+273.2)))))) *H[hour]*L3a[hour]) (L4a[hour]* LPR1*( 1.7168*((T+273.2)/298)*exp((14275.4/1.987)*(1/298 1/(T+273.2)))/(1+(exp((49087.1/1.987)*(1/298.85 1/(T+273.2))))))) dL4b=(L4a[hour]* LPR1*( 1.7168*((T+273.2)/298)*exp((14275.4/1.987)*(1/298 1/(T+273.2)))/(1+(exp((49087.1/1.987)*(1/29 8.85 1/(T+273.2)))))))

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86 (L4b[hour]* LPR2*( 1.7168*((T+273.2)/298)*exp((14275.4/1.987)*(1/298 1/(T+273.2)))/(1+(exp((49087.1/1.987)*(1/298.85 1/(T+273.2))))))) dI=(L1b[hour])*(LPR2*((1.7168*((T+273.2)/298)*exp((14275.4/1.987)*(1/298 1/(T+273.2)))/(1+(exp( (49087.1/1.987)*(1/298.85 1/(T+273.2))))))))+ (L2b[hour]* LPR2*( 1.7168*((T+273.2)/298)*exp((14275.4/1.987)*(1/298 1/(T+273.2)))/(1+(exp((49087.1/1.987)*(1/298.85 1/(T+273.2)))))))+ (L3b[hour]* LPR2*( 1.7168*((T+273.2)/298)*exp((14275.4/1.987)*(1/298 1/( T+273.2)))/(1+(exp((49087.1/1.987)*(1/298.85 1/(T+273.2)))))))+ (L4b[hour]* LPR2*( 1.7168*((T+273.2)/298)*exp((14275.4/1.987)*(1/298 1/(T+273.2)))/(1+(exp((49087.1/1.987)*(1/298.85 1/(T+273.2))))))) (REMRATE*I[hour]) dR=((REMRATE)*I[hour]) dY=dI+dR H[ho ur+1]=H[hour]+dH L1a[hour+1]=L1a[hour]+dL1a L1b[hour+1]=L1b[hour]+dL1b L2a[hour+1]=L2a[hour]+dL2a L2b[hour+1]=L2b[hour]+dL2b L3a[hour+1]=L3a[hour]+dL3a L3b[hour+1]=L3b[hour]+dL3b L4a[hour+1]=L4a[hour]+dL4a L4b[hour+1]=L4b[hour]+dL4b I[hour+1]=I[hour]+dI R[ hour+1]=R[hour]+dR Y[hour+1]=Y[hour]+dY } results=data.frame(hour=shour:lhour,H=H[shour:lhour], L1a=L1a[shour:lhour], L1b=L1b[shour:lhour], L2a=L2a[shour:lhour], L2b=L2b[shour:lhour], L3a=L3a[shour:lhour], L3b=L3b[shour:lhour], L4a=L4a[shour:lhour], L4b= L4b[shour:lhour], I=I[shour:lhour], R=R[shour:lhour], Y=Y[shour:lhour]) return(results) } shour=1 lhour=154 HMF=0 LPR1=1/24 LPR2=1/33 LGR1=0.3136 LGR2=0.0568 LGR3=0.0334 REMRATE=1/24 hour=1:lhour tempdata=read.csv(file.choose(),h=T)

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87 Thour=tempdata$t RHhour =tempdata$RH weather=data.frame(cbind(hour,Thour,RHhour)) head(weather) results=BLIGHTSIM(HMF,LPR1,LPR2,LGR1,LGR2,LGR3,REMRATE,shour,lhour,weather) par(mfrow=c(3,4)) plot(results$hour,results$H) plot(results$hour,results$L1a) plot(results$hour,results$L2a) plot(results$hour,results$L3a) plot(results$hour,results$L4a) plot(results$hour,results$L1b) plot(results$hour,results$L2b) plot(results$hour,results$L3b) plot(results$hour,results$L4b) plot(results$hour,results$I) plot(results$hour,results$R) plot(result s$hour,results$Y) results

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98 West, J. S., Townsend, J.A. , Stevens, M., and fit, B. D. L. 2012. Comparative biology of different plant pathogens to estimate the effects of climate change on crop diseases in Europe. Eur. J. Plant Pathol. 133:315 331. Worner, S. P.1992. Performance of phenological models under var iable temperature regimes: Consequences of the Kaufmann or rate summation effect. Environ. Entomol. 21:689 699. Wu, B.M., Subbarao, K.V., and van Bruggen, A.H.C. 2000. Factors affecting the survival of Bremia lactucae sporangia deposited on lettuce leaves. Phytopathology 90:827 833. Wu, B.M., van Bruggen, A.H.C., Subbarao, K.V., and Scherm, H. 2002. Incorporation of temperature and solar radiation thresholds to modify a lettuce downy mildew warning system. Phytopathology 92:631 636.

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99 BIOGRAPHICAL SKETCH Shankar Kaji Shakya, native to Nepal, was born in 1987. Mr. Shakya completed his high school education from his home town Butwal. He has an undergraduate degree with major in plant pathology from Institute of Agriculture and Animal Sciences (IAAS), Tribhuw an University (TU) Nepal. He worked as an instructor at Gokuleshwor Agriculture and Animal Science College, TU (2011 2012) before starting his graduate studies in University of Florida. mathematical modeling.