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Individual Growth and Comparison among Matrix and Integral Prokection Models with Data from 18 Species of Tropical Trees...

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Title:
Individual Growth and Comparison among Matrix and Integral Prokection Models with Data from 18 Species of Tropical Trees at Los Tuxtlas, Mexico Statistical and Simulation Analysis
Physical Description:
1 online resource (47 p.)
Language:
english
Creator:
Palmas Perez, Sebastian
Publisher:
University of Florida
Place of Publication:
Gainesville, Fla.
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Thesis/Dissertation Information

Degree:
Master's ( M.S.)
Degree Grantor:
University of Florida
Degree Disciplines:
Forest Resources and Conservation
Committee Chair:
Cropper, Wendell P, Jr
Committee Members:
Gezan, Salvador
Kainer, Karen A
Ricker, Martin

Subjects

Subjects / Keywords:
cedar -- cedrela -- dbh -- mamey -- pouteria -- zapote
Forest Resources and Conservation -- Dissertations, Academic -- UF
Genre:
Forest Resources and Conservation thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract:
Development of sustainable management plans require reliable growth models to determine long-term timber yield and analysis of population dynamics. However, growth model estimation is challenged by slow growth rates, low densities and high variability, which result in high parameter uncertainty. Diameter at Breast Height (DBH) measurements from 18 species populations were taken at Los Tuxtlas, Mexico. Two Periodic Annual Increments (PAId) models were statistically tested with nonlinear regression analysis. Using the ?tted growth models, Matrix (MPM) and Integral Projection Models (IPM) were compared to determine the difference in the projected outcomes from the models. PAId values ranged from 0.1 for Pimenta dioica to 4.86 in Cordia megalantha. Cordia alliodora, C. megalantha and Cedrela odorata presented the highest growth rates. Populations presented highly variable PAId among sizes. Overall, there is low correlation between DBH and PAId and between DBH and survival probability. The population projection for the IPM returns lower population sizes, probably due to class grouping in MPMs. There is high sensibility to the number of classes and the growth model chosen for matrix models. We suggest that, when dealing with small population samples, using IPM can result in better projections.
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.
Statement of Responsibility:
by Sebastian Palmas Perez.
Thesis:
Thesis (M.S.)--University of Florida, 2013.
Local:
Adviser: Cropper, Wendell P, Jr.
Electronic Access:
RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2015-08-31

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Applicable rights reserved.
Classification:
lcc - LD1780 2013
System ID:
UFE0045978:00001

MISSING IMAGE

Material Information

Title:
Individual Growth and Comparison among Matrix and Integral Prokection Models with Data from 18 Species of Tropical Trees at Los Tuxtlas, Mexico Statistical and Simulation Analysis
Physical Description:
1 online resource (47 p.)
Language:
english
Creator:
Palmas Perez, Sebastian
Publisher:
University of Florida
Place of Publication:
Gainesville, Fla.
Publication Date:

Thesis/Dissertation Information

Degree:
Master's ( M.S.)
Degree Grantor:
University of Florida
Degree Disciplines:
Forest Resources and Conservation
Committee Chair:
Cropper, Wendell P, Jr
Committee Members:
Gezan, Salvador
Kainer, Karen A
Ricker, Martin

Subjects

Subjects / Keywords:
cedar -- cedrela -- dbh -- mamey -- pouteria -- zapote
Forest Resources and Conservation -- Dissertations, Academic -- UF
Genre:
Forest Resources and Conservation thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract:
Development of sustainable management plans require reliable growth models to determine long-term timber yield and analysis of population dynamics. However, growth model estimation is challenged by slow growth rates, low densities and high variability, which result in high parameter uncertainty. Diameter at Breast Height (DBH) measurements from 18 species populations were taken at Los Tuxtlas, Mexico. Two Periodic Annual Increments (PAId) models were statistically tested with nonlinear regression analysis. Using the ?tted growth models, Matrix (MPM) and Integral Projection Models (IPM) were compared to determine the difference in the projected outcomes from the models. PAId values ranged from 0.1 for Pimenta dioica to 4.86 in Cordia megalantha. Cordia alliodora, C. megalantha and Cedrela odorata presented the highest growth rates. Populations presented highly variable PAId among sizes. Overall, there is low correlation between DBH and PAId and between DBH and survival probability. The population projection for the IPM returns lower population sizes, probably due to class grouping in MPMs. There is high sensibility to the number of classes and the growth model chosen for matrix models. We suggest that, when dealing with small population samples, using IPM can result in better projections.
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.
Statement of Responsibility:
by Sebastian Palmas Perez.
Thesis:
Thesis (M.S.)--University of Florida, 2013.
Local:
Adviser: Cropper, Wendell P, Jr.
Electronic Access:
RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2015-08-31

Record Information

Source Institution:
UFRGP
Rights Management:
Applicable rights reserved.
Classification:
lcc - LD1780 2013
System ID:
UFE0045978:00001


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INDIVIDUALGROWTHANDCOMPARISONAMONGMATRIXANDINTEGRALPROJECTIONMODELSWITHDATAFROM18SPECIESOFTROPICALTREESATLOSTUXTLAS,MEXICO:STATISTICALANDSIMULATIONANALYSISBySEBASTIANPALMASPEREZATHESISPRESENTEDTOTHEGRADUATESCHOOLOFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENTOFTHEREQUIREMENTSFORTHEDEGREEOFMASTEROFSCIENCEUNIVERSITYOFFLORIDA2013

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c2013SebastianPalmasPerez 2

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ToF&F,intensemusicians,hauntingdemonsandotherfunpeople 3

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ACKNOWLEDGMENTS ThisstudywasnancedbyUSAIDsHigherEducationforDevelopmentTIESPartnership,throughthegrantBridgingacademiaandpractice:Integrativeleadershipforbiodiversityconservationinmanagedlandscapes,managedbyDr.KarenKainer.SpecialthankstotheSchoolofForestResourcesandConservationattheUniversityofFloridaandtheInstituteofFoodandAgriculturalSciences.Besidessupportingmethroughoutmystudies,SFRCprovidedadditionalfundingformylastyearofstudies.FieldresearchinMexicowasfundedbyaTinkerTravelGrantawardedbytheTropicalConservationandDevelopmentProgramatUF.IamalsothankfultoTCDfortheirsupportwithbureaucraticaffairs.ToWendellCropperforhispatienceandadvice.ToKarenKainerwhogavemetheopportunitytobehere.ToSalvadorGezanwhohelpedmeduringthisthesisandmorewithmoreworktocome.ToMartinRickerforprovidingthedataandadvice.TotheNationalAutonomousUniversityofMexicothroughtheirBiologicalStationatLosTuxtlas,fortheirsupportoneldinsidetheBiosphereReserve.ToMr.MiguelAngelSinacaandEladioSinacafortheirsupportontheeldmeasurements. 4

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TABLEOFCONTENTS page ACKNOWLEDGMENTS .................................. 4 LISTOFTABLES ...................................... 6 LISTOFFIGURES ..................................... 7 ABSTRACT ......................................... 8 CHAPTER 1INTRODUCTION ................................... 9 2DIAMETERGROWTHMODELSANDPOPULATIONDYNAMICSFOR18TROPICALTREESPECIESINVERACRUZ,MEXICO .............. 10 2.0.1Growthmodelsandtropicaltrees ................... 11 2.0.2Matrixprojectionmodels ........................ 12 2.0.3IntegralProjectionModels ....................... 13 2.1Methods ..................................... 14 2.1.1StudySite ................................ 14 2.1.2Speciesdatadescription ........................ 14 2.1.3GrowthanalysisandRegressionmodel ............... 17 2.1.4Evaluationofmodels .......................... 18 2.1.5Transitionmatrices ........................... 19 2.2Results ..................................... 20 2.2.1Growthmodels ............................. 24 2.2.2SurvivalprobabilityforCedrelaodorata,DiospyrosdigynaandPouteriasapota ............................. 24 2.2.3Populationmodels ........................... 29 2.3Discussion ................................... 38 2.3.1Growthanalysis ............................. 38 2.3.2Growthmodels ............................. 38 2.3.3MatrixandIntegralProjectionModels ................. 39 2.4Summary .................................... 40 3CONCLUSIONS ................................... 41 REFERENCES ....................................... 42 BIOGRAPHICALSKETCH ................................ 47 5

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LISTOFTABLES Table page 2-1Scientic,commonnameandusesofthe13speciesoftropicaltreesstudied. 16 2-2SummarydataofmeasuredDBHandPAIdforthe18studiedspecies ..... 22 2-3Gompertzfunctioncoefcientsandtnessmeasuresforthe18studiedspecies. 26 2-4BRCregressioncoefcientsandtnessmeasuresforthe18studiedspecies. 27 2-5LesliematrixforCedrelaodorata .......................... 36 2-6LesliematrixforDiospyrosdigyna ......................... 36 2-7LesliematrixforPouteriasapota .......................... 36 6

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LISTOFFIGURES Figure page 2-1MeasuredPAIdresultsforeachspeciesandpairwisecomparisonresultsbetweenspecies. ........................................ 23 2-2SurvivalprobabilitiesforCedrelaodorata,DiospyrosdigynaandPouteriasapota. 28 2-3PAIddata,GompertzandBRCregressionts.Residualplotandresidualhistogramforbothmodels. ................................... 30 2-4PopulationprojectionsforMPMandIPMandestimatedpassagetimeinyearsforCedrelaodorata,DiospyrosdigynaandPouteriasapota ........... 37 7

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AbstractofThesisPresentedtotheGraduateSchooloftheUniversityofFloridainPartialFulllmentoftheRequirementsfortheDegreeofMasterofScienceINDIVIDUALGROWTHANDCOMPARISONAMONGMATRIXANDINTEGRALPROJECTIONMODELSWITHDATAFROM18SPECIESOFTROPICALTREESATLOSTUXTLAS,MEXICO:STATISTICALANDSIMULATIONANALYSISBySebastianPalmasPerezAugust2013Chair:WendellCropperMajor:ForestResourcesandConservationDevelopmentofsustainablemanagementplansrequirereliablegrowthmodelstodeterminelong-termtimberyieldandanalysisofpopulationdynamics.However,growthmodelestimationischallengedbyslowgrowthrates,lowdensitiesandhighvariability,whichresultinhighparameteruncertainty.DiameteratBreastHeight(DBH)measurementsfrom18speciespopulationsweretakenatLosTuxtlas,Mexico.TwoPeriodicAnnualIncrements(PAId)modelswerestatisticallytestedwithnonlinearregressionanalysis.Usingthettedgrowthmodels,Matrix(MPM)andIntegralProjectionModels(IPM)werecomparedtodeterminethedifferenceintheprojectedoutcomesfromthemodels.PAIdvaluesrangedfrom0.1forPimentadioicato4.86inCordiamegalantha.Cordiaalliodora,C.megalanthaandCedrelaodoratapresentedthehighestgrowthrates.PopulationspresentedhighlyvariablePAIdamongsizes.Overall,thereislowcorrelationbetweenDBHandPAIdandbetweenDBHandsurvivalprobability.ThepopulationprojectionfortheIPMreturnslowerpopulationsizes,probablyduetoclassgroupinginMPMs.Thereishighsensibilitytothenumberofclassesandthegrowthmodelchosenformatrixmodels.Wesuggestthat,whendealingwithsmallpopulationsamples,usingIPMcanresultinbetterprojections. 8

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CHAPTER1INTRODUCTIONItisestimatedthat75%ofpermanenttropicalforestestatesproductionandprotectionforestscarryouttheiroperationswithoutmanagementplans( Blaseretal. 2011 ).Soundforestmanagementplansrequirereliablegrowthpredictionstodeterminetimberyieldandlong-termsustainabilityofforeststructureanddynamicstoselectivelogging.However,tropicaltreesusuallylackpreciseestimatesofgrowthand,inturn,limitedunderstandingofpopulationdynamicswhichcanresultinunsustainableextractionoftimberandotherforestproducts.In2011,Mexicoreported31.3millionhaoftropicalforests,48%ofthetotalforestedareainthecountry( Blaseretal. 2011 ).DeforestationreportsshowthatdeforestationratesintheMexicantropicshavebeendecreasinginthelast15years.Annualdeforestationfrom1990averaged354000hayear)]TJ /F7 7.97 Tf 6.59 0 Td[(1andwasreducedto235000and155000hayear)]TJ /F7 7.97 Tf 6.59 0 Td[(1fortheperiods2000and2005respectively( FAO 2010 ).Thedecreaseindeforestationrateshasbeenattributedtoasuccessofconservationpoliciestohaltillegallogging,increaseofareaandhigherprotectionofprotectedareas,afforestationprogramsandsuccessinpaymentforenvironmentalservicesprograms( KolbandGalicia 2012 ).AttheLosTuxtlasBiosphereReserve,regulationsforbidlogginginsidecoreareaswithuseofnaturalresourcesonlyallowedinsidebufferareaswhenconsistentwithconservationandsustainabledevelopmentvalues( DiarioOcialdelaFederacion 2009 ).However,duetolimitingmonitoringandenforcement,illegalharvestingcontinueswithinallareasinLosTuxtlas.ThisthesisresearchestheparticularitiesofgrowthandpopulationdynamicsofspeciesattheLosTuxtlasBiosphereReserve.ItaimstoprovideinformationusefultothecreationofmanagementplansconsistentwiththecharacteristicsofthisforestandtheMexicantropics. 9

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CHAPTER2DIAMETERGROWTHMODELSANDPOPULATIONDYNAMICSFOR18TROPICALTREESPECIESINVERACRUZ,MEXICOMosttropicaltimberisstillharvestedatunsustainablerates.Additionally,mostloggingoperationsinthetropicsareconductedwithoutsustainablemanagementstrategies( Blaseretal. 2011 ).Withoutprecisegrowthmodels,forestmanagementplansifexistingarecommonlydependentonunreliablegrowthestimates,resultingofteninunsustainableremovaloftimber.Individualgrowthandpopulationmodelsestimatetimberyieldandpredictlong-termforeststructureanddynamics( Weiskitteletal. 2011 ).Dynamicsstudiescanalsoshowifthepopulationisstableenoughtosupportharvest( Holmetal. 2008 ; Klimasetal. 2012 )orthreatenedenoughtorequirespecialrestorationforitsmaintenance.Despitetheimportanceofgrowthandpopulationpredictions,modelingtropicaltreegrowth,however,facesmanychallenges.Tropicaltreespresentslowindividualgrowth,lowspeciespopulationdensities,andoftenlackofannualgrowthringstodetermineage.Tropical-treeresearcherscommonlyestablishpermanentplotsandrepeatedlymeasureindividualstoobtainlong-termmeasurements.Despitethechallengesofcollectingsuchlong-termdata,thisapproachcanproducereliableestimatesforspeciesspecicgrowthrates( Condit 1998 ; HeroldandSchiller 2009 ).Tomodelgrowth,datafrompopulationsof18speciesoftropicaltreeswasmeasuredatLosTuxtlasinVeracruz,Mexicobetween1994and1999.DiameteratBreastHeight(DBH)observedfromthese18tropicaltreespecieswasusedtotgrowthmodelsandevaluatetheirgoodness-of-t.TheresultinggrowthmodelsdeneIntegralProjectionModels.AcomparisonbetweenIntegralProjectionModelsandclassicMatrixPopulationModelsismadetodeterminesensitivityofpopulationmodelstoclassdenition,specicallyrelatedtosmalldatasets.Thepopulationanalysiswasmadeforthreespecies:Cedrelaodorata,DiospyrosdigynaandPouteriasapota. 10

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2.0.1GrowthmodelsandtropicaltreesDiametergrowthpredictionisrequiredfortimberyieldmodelscommonlyusedinforestmanagement.Additionally,thesemodelsapplytoresearchonselectivelogging( Heraultetal. 2010 ),reforestationplans( Rickeretal. 2008 ),carbonstocksestimation( Salimonetal. 2011 ),populationdynamics( FortiniandZarin 2011 ),speciesresponsestoclimatechange( Lauranceetal. 2004 )andforesteconomicmodels( Rickeretal. 1999 ).Developinggrowthmodelsfortropicaltreesfacesuniquechallenges.Fluctuatinggrowthratesofmillimetersperyearcansignicantlyaffectmodelcalibration.Smallgrowthincrementsrequirehighprecisionandlong-termmeasurements.Aswithmanylong-termcensuses,dataisoftenmissingandmeasurementerrorsvaryduetochangesinprotocol( Condit 1998 ).Becausepopulationsoftropicaltreespresentlowdensities(e.g. Wadtetal. 2005 ),tropicaltreeinventoriesareoftenlimitedtoindividualswithDBH10cm,resultinginlackofearlylife-historyinformation.Finally,lackofstrongclimaticcuesinthetropicsfrequentlyfailstoproducereliableannualgrowthrings( Worbes 2002 ).Notwithstanding, Brienenetal. ( 2006 )showedthattropicaltreesmaypresentdiscernablegrowthrings;however,furtherstudiesarerequiredtoassessthereliabilityofthesegrowthringsoneachsite.Thesechallengespotentiallyresultindataoutliers,highparameteruncertainty,biasedgrowthestimates( Vanclay 1994 )andquestionableextrapolation(intimeandspace)oftheresultinggrowthmodelsfortropicaltreespecies( Clarketal. 2007 ).Extrapolationisproblematicbecauseestimatesdoesnottakeintoaccountclimatevariationandchangesinmacroandmicroforeststructurethatproducedifferentgrowthrates.Forthesereasons,long-termhighprecisionmeasurementsofferabetterbasisformodeling.Manymodelsexistforgrowthandyield.Treelistmodels( Weiskitteletal. 2011 ),Treelevelmodels( PorteandBartelink 2002 )orSingle-treemodels( Vanclay 1994 ). 11

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Thelatterarethemostappropriatefornaturalmixedforestsastheyhavetheexibilityandabilitytodescribecomplexstandstructures,ensuringreliablepredictionsforarangeoftreesizes,sitesandstandconditions( Zhaoetal. 2004 ).Treelistmodelskeeptrackofeachindividualinthestandtotgrowthcurvesbasedonparameterssuchasageandsize.Theyprovidethehighestresolutionofpredictionsandcansimulatearangeofstandcompositionsandstructures.However,theseempiricalmodelsdescribegrowthwithnocausalexplanationoftheunderlyingbiologicalprocesses,reducingitsvalidityindifferentareas.Sinceindividualsofthesamespeciescanhavedifferentgrowthratesdependingonclimatevariations( ClarkandRoad 1999 ),lackofspatialdatarequirestoalsoassumethatgrowthpatternsareuniformbetweenrecordlocations.Whileageandsizecontributetoreducinggrowthratesoftrees(byage-dependentgeneticchangeslikeaccumulationofmutationoralteredphysiologicalstresses),treegrowthcorrelatesmorestronglywithsizethanwithage( Steppeetal. 2011 ).DBHiseasilymeasuredandisprobablythebestvariableforexplaininggrowthratesinforests.Currentdiametersizehighlycorrelateswithdiametergrowthifthestandremainsunmanagedandifthereareminimumnaturaldisturbances(see Weiskitteletal. 2011 ,p.85). 2.0.2MatrixprojectionmodelsMatrixPopulationModels(MPMs)aremathematicalmodelswidelyusedinpopulationdynamicsstudies( Caswell 2001 ; Leslie 1945 ).Thesestudiestranslateindividualgrowth,andotherpopulationvitalrates,intopredictedchangesinthepopulationusingmatrixalgebra.Amongthese,populationresearcherscommonlyuseMPMsandhaverecentlyfocusedonIntegralProjectionModels(IPMs, Easterlingetal. 2000 ; EllnerandRees 2006 ).MPMsallowindividualsizetobethemainfactorthatinuencesindividualandpopulationgrowth. Lefkovitch ( 1965 )extendedtheLeslieMPM,whichreliesonagegrouping,intoonewithsizeorstagegrouping,assuming 12

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thateachindividualinsidethepopulationhavethesamediametergrowthrate.Thepopulationstructurechangesfromtimettot+1dependingonthenumberofindividualsineachsizeclassattimet,representedwiththevectornt,andatransitionmatrixM.Thistransitionmatrixisusedtoupdatethenumberofindividualsateachtimestep,resultinginanewvectornt+1. Mnt=266666664m1,1m1,2m1,sm2,1m2,2m1,s......mx,y...ms,1ms,2ms,s377777775266666664n1n2...ns377777775t=266666664n1n2...ns377777775t+1=nt+1(2)ThetransitionmatrixMcorrespondtotheproportionofindividualsatsizestagexthatpasstostagey.Thepopulationvectornincludesthenumberofindividualsateachstage.SinceDBHisacontinuousvariable,MPMsrequiretodiscretizethisvariable.Denitionofclassescanbedonewithdifferentapproaches,eachhavinganspeciceffectandconsequenceintheresultsandinterpretations( Gonzalezetal. 2013 ; Laturietal. 2012 ).Toavoiderroneouspredictions,sizeclassesshouldbedenedtorepresentgroupswithsimilarlifehistoryparameters.Largeclassintervalscombineindividualsofdifferentsizesandaveragingtheseindividualsmayresultinbiasedpredictions.WithMPMs,wecanestimate,theintrinsicgrowthrateofthepopulation. 2.0.3IntegralProjectionModelsIPMsmaintainacontinuousstatevariablestructure,avoidingstageclassicationgroupingbystages( Easterlingetal. 2000 ; EllnerandRees 2006 ).IPMsdenetransitionprobabilitiesbasedonthegrowthregressionsfromthedata.LikeMPMs,populationdynamicsareprojectedindiscretetimes.IPMscanbeestimatedusingfewerparameters,makingitpossibletobuildmodelswithsparserdata( EllnerandRees 2006 ).WhileIPMsstillhaveasizeclassication,thenumberofstagesisgreatly 13

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increased.Thisresultsinanalmostcontinuousdistribution.Ithasbeensuggestedthathighernumberofclassesresultsinincreasedaccuracyofpredictions( Enrightetal. 1995 ; Laturietal. 2012 )andcouldperformbetterthanMPMsforsmallpopulationsizes( Ramulaetal. 2009 ).ThisthesiswillcomparebothpopulationmodelsusingLosTuxtlastreepopulationstondouttheirprojectiondifferences. 2.1Methods 2.1.1StudySiteThevolcanicregionofLosTuxtlasliesonacoastalplatformattheGulfofMexicoandrisesfromsealevelto1680m.a.s.l.inelevation( Gutierrez-Garcaetal. 2011 ; Vazquez-Torresetal. 2010 ).MidlandsandlowlandsatLosTuxtlasareclassiedashumidtropical(typeA)bytheKoppen'sclimaticclassication.Highelevationsaremoistwithmildwinters.Thetemperaturevariesfrom24Cand18C,fromthelowesttothehighestareas,respectively.Averageannualprecipitationatthelocationofthetreesrangesfrom2000200mm,witharainyseasonfromJunetoDecember( Gutierrez-Garcaetal. 2011 ).LosTuxtlashostsseveralvegetationtypes:highevergreentropicalforest,mediumevergreentropicalforest,cloudforest,pineforest,oakforest,savanna,mangroves,coastdunes,andinundatedlowtropicalforest( Castillo-CamposandLaborde 2004 ).VegetationatLosTuxtlashasexperiencedextensivedeforestationinfavorofpastureinthelast30years( Mendozaetal. 2005 ),leavinglessthan21%oftheoriginalforestcoverby2011( Gutierrez-Garcaetal. 2011 ),mostlyconcentratedathigheraltitudeareas. 2.1.2SpeciesdatadescriptionLocaleldassistantsmeasuredDBHfrommarkedindividualsfrom18speciesatLosTuxtlas(seeTable 2-1 forspeciesdescription)overseveralyears.Treesweremeasuredduringdryseason(OctobertoFebruary).Allofthemeasuredindividualsbelongtoprimaryorsecondaryhighevergreentropicalforests.SometreesofPouteria 14

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sapotaarelocatedinsidepastureelds.ForCedrelaodorata,DiospyrosdigynaandPouteriasapota,individualsweremeasuredyearlyfrom1994to1998.Therestofthespecieswereonlymeasuredtwice(in1997and1999).DuringanadditionalvisitontheSummerof2012,mosttreeswerenotfoundduetologging,lackofprecisedescriptionofthelocationandlackofpropernumberingidentication.OnlytwotreesofP.sapotawerefoundinthisvisit.Todealwithoutliers,negativeincrementsandincrementsabove6cmwereremovedfromthedatabase.Whileshrinkagehasbeenfoundintropicalforestsasaresultofdryseasonsordecayofdyingtrees( Gourlet-FleuryandHoullier 2000 ),shrinkagehasnotbeendocumentedatLosTuxtlas.ThenalnumberofindividualsandmeasurementstakenisdetailedonTable 2-2 .Becausethemeasurementswerenottakenexactlyoneyearapart,DBHvalueswereinterpolatedtoaone-yeargrowth.Forexample,atreeDBHwasrstmeasuredwitha12.5cminDBH.Then395dayslater,thetreehadaDBHof13.2.Thismeansthattheincrementinterpolatedto365days,orPAId,is(13.2-12.5)*365/395=0.647cm.PopulationmodelswereconstructedforpopulationsofCedrelaodorata,DiospyrosdigynaandPouteriasapota.Unliketherestofthespeciesconsideredforthegrowthregressions,thesethreespecieshadgrowthandsurvivaldatafor4years.Thislongermeasurementspansgivesalargequantityoftransitionprobabilitiesfromwhichtoestimatepopulationmatricesmoreprecisely.Cedrelaodorataisafastgrowingspeciesthatisdistributedacrosstheneotropics.ItisexploitedforitsvaluedtimberfromeasternMexicotoSouthAmericaandtheCaribbean.GrowthratesforC.odorataarehighlyvariable.YoungindividualsinsecondaryforestsofCampeche,Mexico,andplantationsinTamaulipas,Mexico,presentedgrowthratesof1.26and1.72cmyear)]TJ /F7 7.97 Tf 6.58 0 Td[(1,respectively( Alderete-Chavezetal. 2010 ; Ramirez-Garciaetal. 2008 ).However,individualsinunmanagedtropicalforestsofMexicopresentedgrowthrates0.6.4cmyear)]TJ /F7 7.97 Tf 6.58 0 Td[(1( BurnsandHonkala 1990 ). 15

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Table2-1. Scientic,commonnameandusesofthe13speciesoftropicaltreesstudied.TheediblecategoriesareF:fruit;S:seeds,L:leaves.SpeciesCommonnameTimberEdibleFSL AmpelocerahottleiGuayadeMonteAspidospermamegalocarponNazareno,PaloVoladorBrosimumalicastrumOjoche,Ojite,RamonCalophyllumbrasilienseOcu,BarCedrelaodorataCedroCordiaalliodoraSuchil(acahualero),Bojon,SolerilloCordiamegalanthaSuchil,Nopo,XulaxuchitlDialiumguianensePaque,Guapaque,TamarindilloDiospyrosdigynaZapotenegroorprietoGuareagrandifoliaSabinoNectandraambigensLaurelchilpatilloPerseaschiedeanaChinine,Pagua,AguacatedeMontePimentadioicaPatololote,pimientagordaPouteriasapotaMamey,zapotePseudolmediaglabrataTomatilloRolliniamucosaChirimoyaRoupalamontanaAjilloSideroxylonportoricensePionche See PenningtonandSarukhan ( 2005 ), Vazquez-Torresetal. ( 2010 ) 16

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Diospyrosdigynaisfoundatlowlands.ItiscultivatedfromMexicotoCostaRicaandintheCaribbeanforitsvaluedediblefruits(zapotenegro)( Pacheco 1981 ).ThewoodfromD.digynahasbeenusedformedicinalpurposes( Rickeretal. 2000 ).Pouteriasapotaisacanopyspeciesnativetotheevergreenandsemi-evergreentropicalforestsfromsouthMexicotoNicaragualocatedbetween0m.a.s.l.( Pennington 1990 ).Itsfruit,themamey,isedibleandhighlyvalued(see Rickeretal. 1999 ).Inaddition,timberisusedlocally. 2.1.3GrowthanalysisandRegressionmodelToanalysegrowth,anANOVAofthemeasuredPAIdwasperformed.Twoanalyseswereperformed:oneincludingonlysmalltrees(0cminDBH)andotherwithlargetrees(40cminDBH).ApairwisecomparisonwastestedwithTukeyHSD.TopredictPeriodicAnnualIncrementsofDiameter(PAId),twononlinearmodelswheretted:Gompertzcurve(GM)andaBertalanffy-Richards-Chapmanmodel(BRC).TheGMhasanexponenttoamaximum,whereitreachesanasymptote.GMfollowstheexpression: PAId=1e)]TJ /F5 7.97 Tf 6.58 0 Td[(e2)]TJ /F13 5.978 Tf 5.76 0 Td[(3DBH+(2)where1,2,3andarethethreeregressioncoefcientsandthemeasurementserror,respectively.1representsthemaximumpredictedPAId(asymptote)and2are3shapeparameters.TheBRCmodelassumesalogisticgrowthrate.Thistrendconsidersajuvenileperiodwheregrowthisexponential,alongperiodofmaturationwheregrowthisnearlylinear,andalatestagewheregrowthisreducedtoaneventualasymptote.ThismodelisamodicationofthefrequentlyusedBertalanffy-Chapman-Richards(BRC)model. Rickeretal. ( 1999 )derivedtheformulaoftheBRCgrowthfunctiontoaccountforthelackofageandrelaterelativegrowthorannualincrementtoDBH. 17

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TheoriginalformulaoftheBRCmodelis: DBH=DBHmax[1)]TJ /F4 11.955 Tf 11.95 0 Td[(e)]TJ /F17 7.97 Tf 6.59 0 Td[(1Age]2(2)DBHmaxisaregressioncoefcientthatcanbeinterpretedasmaximumdiameter,1isagrowthrateparameter,and2isashapeparameter.Equation 2 canbesolvedforageas: Age=ln[1)]TJ /F9 11.955 Tf 11.95 0 Td[((DBH=DBHmax)1=2]=)]TJ /F12 11.955 Tf 11.95 0 Td[(1(2)Aninstantaneousrelativegrowth(RG),equationcanbederivedfrom 2 bytakingthederivativewithrespecttoAgeanddividingbyDBH: RG=ln[dDBH=dAge]=[DBHmax(1)]TJ /F4 11.955 Tf 11.96 0 Td[(e)]TJ /F17 7.97 Tf 6.58 0 Td[(1Age)2)]TJ /F7 7.97 Tf 6.59 0 Td[(1=e1Age]=[DBHmax(1)]TJ /F4 11.955 Tf 11.96 0 Td[(e)]TJ /F17 7.97 Tf 6.58 0 Td[(1Age)2]=12=(e1Age)]TJ /F9 11.955 Tf 11.95 0 Td[(1)Here,ageisreplacedwithEq. 2 .ThelogarithmtransformationforRGisusefultospreadthedatapointsandtoavoidunrealisticallypredictednegativevaluesofrelativegrowth.Equation 2 requiresthatDBHmax>DBH. ln[PAId]=ln[12=((1=(1)]TJ /F9 11.955 Tf 11.95 0 Td[((DBH=DBHmax)1=2))))]TJ /F9 11.955 Tf 11.95 0 Td[(1]+(2)ThettingprocesswasadjustedusingOrdinaryLeastSquares(OLS)anditerativemethodsusingR3.0( RCoreTeam 2013 ). 2.1.4EvaluationofmodelsToevaluatebothmodels,residualanalysisandthreestatisticalcriteriawereobtained:R2emp,BIAS%andtheRoot-meansquareerrorpercentage,orRMSE%(Figures 2 2 ).Calculatedasfollow: R2emp=1)]TJ /F5 7.97 Tf 17.71 27.73 Td[(nPi=1(yi)]TJ /F9 11.955 Tf 12.24 0 Td[(^yi)2 nPi=1(yi)]TJ /F9 11.955 Tf 12.24 0 Td[(yi)2(2) 18

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BIAS%=100 ynPi=1(yi)]TJ /F9 11.955 Tf 12.24 0 Td[(^yi)2 n(2) RMSE%=100 yvuuut nPi=1(yi)]TJ /F9 11.955 Tf 12.24 0 Td[(^yi)2 n)]TJ /F4 11.955 Tf 11.96 0 Td[(p(2)Whereyi,^yiandyiarethemeasured,estimatedandaveragevaluesofthedependentvariable,respectively;nisthetotalnumberofobservationsusedandpisthenumberofmodelparameters.R2emp(Equation 2 ),alsocalledEmpiricalCorrelationCoefcientorModelef-ciency,istheadjustedcoefcientofdetermination( VanclayandSkovsgaard 1997 ).R2empprovidesasimpleindexofperformanceonarelativescale,where1indicatesaperfectt,0revealsthatthemodelisnotbetterthanasimpleaverage,andnegativevaluesindicateaworsethananaveragemodel.WhileR2empcanquantifythebettert,itdoesn'taccountforthecomplexityofthemodelbyfavoringparameterrichmodels.BIAS%(Equation 2 )representstherelativebias.BIAS%isanabsolutemeasureofamodelreportedintheoriginalunits(unlikeempiricalR2emp);assuch,thismeasurecannotbeuniversallycompared.BIAS%doesn'tpenalizeforthenumberofparametersinamodel.RMSE%(Equation 2 )isthepercentagesquaredrootofthevarianceoftheresiduals( Weiskitteletal. 2011 ).RMSE%canheavilybeinuencedbyoutliersinthedata. 2.1.5TransitionmatricesBecausethesamplingofCedrelaodorata,DiospyrosdigynaandPouteriasapotapopulationsincluded4yearsofmeasurements,population'sprojectionswereonlyestimatedforthesethreespecies.BothMPMandIPMwereestimatedindividuallyusingDBHtoclassifythepopulation.Formodelcomparison,survivalprobabilitieswereestimatedtogetherwithpopulationprojectionsandpassageoftime.Passagetime 19

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referstotheaveragetime(inyears)whichtakesforatreetoreachacertainsize.Thepopulationprojectionstartedwiththepopulationstructurefoundontheeld.Thepopulationwasclassiedtoensureatleast10individualsineachclasswhichresultedin10cmclasswidths.Duetosmallsamplesizesforsmallindividuals,theclassicationforD.digynastartedwitha15cmwidesizeclass.Toavoidclasseswith0%or100%survival,thepercentagewaschangedtomatchthelastclassprobability.Forinstance,asurvivalprobabilityof1wasestimatedforthepreviousclassof50cmDBHforC.odorata(Table 2-5 ),however,thisprobabilitywaschangedto0.842,thesamesurvivalasthelastclass.ThebesttforgrowthineachofthesethreespeciesenteredtheIPMasthegrowthfunction.Theobservedpopulationdistributionwasusedasthestartingpointforeachoftheprojections.Tohavesurvivalprobabilitiesforthetransitionmatrix,theIPMrequiresamodeldescribingsurvivalintermsofDBH.Alogisticregressionwasttedtondanadequatemodeltodescribesurvival.Thesurvivalmodelfollowstheexpression: surv=e0+1DBH 1+e0+1DBH(2)wheresurvistheprobabilityofsurvival.Tofullyintegratetheindividualgrowthmodels,evaluationofmodels,thematrixestimationandprojectionswerecodedinR3.0( RCoreTeam 2013 ),usingIPMpack( Metcalfetal. 2013 )fortheIPMestimation. 2.2ResultsTherewere1610measuredtreeswithalittleover3700measurements(seeTable 2-2 ).Thenumberofindividualsperspeciesrangedfrom50individualsofAspidospermamegalocarponto119ofCordiamegalantha.AllofthespeciesincludedindividualswithDBH8cm.ThebiggesttreesfoundwereindividualsfromSideroxylonportoricense,DiospyrosdigynaandPouteriasapota 20

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measuring141,139and133cm,respectively.SomespeciessuchasBrosimumalicastrumandCalophyllumbrasiliensehadseveralindividualswithsmallsizes,whileotherslikeCedrelaodorataorDialiumguianensehadaDBHdistributionclosertonormal.Maximumincrementsrangedfrom1cmyear)]TJ /F7 7.97 Tf 6.58 0 Td[(1tovaluesabove5cmyear)]TJ /F7 7.97 Tf 6.59 0 Td[(1forCedrelaodorataandPouteriasapota,respectively.MinimumPAIdwasconsistentlysmallerthan3cmyear)]TJ /F7 7.97 Tf 6.59 0 Td[(1forallspecies.ThelowestmeangrowthratecamefromPerseaschiedeanawith0.25cmyear)]TJ /F7 7.97 Tf 6.58 0 Td[(1.C.odorataaveragedaPAIdof1.34cmyear)]TJ /F7 7.97 Tf 6.58 0 Td[(1.IntermsofmeanPAId,CordiamegalanthaandCordiaalliodorashowedthehighestgrowthrateswithmeansof2.00and1.83cmyear)]TJ /F7 7.97 Tf 6.58 0 Td[(1,respectively(Figure 2-1 ).Cordiaalliodora,AmpelocerahottleiandRolliniamucosapresentedthehighestmaximumPAIdvalues.PotentialoutliersofPAIdandinstancesofnegativegrowthwerecommoninthedataset.OneindividualfromDialiumguianensepresentedaPAIdof3cmyear)]TJ /F7 7.97 Tf 6.58 0 Td[(1,whilealloftheother67measurementsofindividualsofthesamespecieshadincrementsbelow2cmyear)]TJ /F7 7.97 Tf 6.59 0 Td[(1.SimilarobservationscanbemadeforindividualsfromRolliniamucosaandRoupalamontana. 21

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Table2-2. Numberofmeasurements(n)andsummarydataofmeasuredDBH(cm)andPAId(cmyear)]TJ /F7 7.97 Tf 6.59 0 Td[(1)forthe18studiedspecies nminmedmaxmeans.d. Ampelocerahottlei69DBH1.5929.2895.4931.717.63PAId0.10.72.460.830.55Aspidospermamegalocarpon47DBH7.9926.972.4531.2716.47PAId0.120.440.920.450.23Brosimumalicastrum91DBH4.319.191.4222.8416.45PAId0.120.381.770.530.44Calophyllumbrasiliense110DBH1.3416.35102.6923.120.91PAId0.120.671.960.750.48Cedrelaodorata276DBH4.7723.3671.6824.9211.32PAId0.111.053.991.320.94Cordiaalliodora114DBH1.4311.3363.0315.7613.51PAId0.141.434.811.811.02Cordiamegalantha119DBH3.0222.03126.7532.6528.73PAId0.471.74.862.011.03Dialiumguianense66DBH7.7745.2695.8746.4117.39PAId0.10.521.280.590.3Diospyrosdigyna265DBH4.5232.02139.0440.8928.41PAId0.110.552.570.620.42Guareagrandifolia87DBH7.4833.982.1636.6818.71PAId0.110.511.840.590.4Nectandraambigens94DBH1.9160.3893.8456.0423.54PAId0.10.461.470.540.35Perseaschiedeana66DBH0.6419.89106.3531.2433.29PAId0.10.220.780.250.13Pimentadioica67DBH5.0944.2577.745.6517.41PAId0.10.230.50.260.11Pouteriasapota252DBH1.7839.44133.0541.7529.48PAId0.050.82.70.940.6Pseudolmediaglabrata97DBH2.3918.7847.1718.9710.11PAId0.110.360.840.410.19Rolliniamucosa81DBH6.6821.6851.6624.3311.05PAId0.110.441.820.530.37Roupalamontana81DBH0.6720.0575.521.7419.22PAId0.120.450.970.470.24Sideroxylonportoricense81DBH2.8618.59141.3926.1826.29PAId0.110.481.680.610.43 22

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A BFigure2-1. MeasuredPAIdresultsforeachspeciesandpairwisecomparisonresultsforindividualswithA)10cmandB)40cminDBH. 23

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2.2.1GrowthmodelsMostGMregressionsconvergedtothedata;however,severalspeciesdidnotconvergedwiththeBRCmodel(seeTables 2-3 and 2-4 ).Mostparameterswerenotstatisticallysignicant(P>0.05).TheGMmodeldidnotconvergedforGuareagrandifolia.ForGM,thehighestR2empwasforCalophyllumbrasiliensewithavalueof0.388.Thisstatisticshowedlargevariabilitybetweenthespecies,reachingvaluesfrom1.006toabove1forCordiamegalantha.BIAS%rangedfrom4.4%forPimentadioicato62.67%inCedrelaodorata.TheBRCmodelreturnedlowandevennegativevaluesfortheempiricalcorrelation.ThehighestempiricalR2empreached0.34forCalophyllumbrasiliense.BIAS%valuesrangedfrom4to70%forPimentadioicaandCedrelaodorata,respectively.TheNLmodelnotconvergedforDialiumguianense,DiospyrosdigynaandPerseaschiedeana.ForAspidospermamegalocarpon,Dialiumguianense,Diospyrosdigyna,Perseaschiedeana,Pimentadioica,Pouteriasapota,Rolliniamucosa,RoupalamontanathereislowcorrelationbetweenDBHandPAId.Fortherestofthespecies,thereisapositivecorrelationbetweenDBHandPAId.Theresidualhistogramforeachmodelttendedtobecenteredonzero(Figure 2-3 ).However,forCedrelaodorataandRolliniamucosa,theresidualsfortheGompertzmodeltendedtonegativenumbers,evidencinggrowthunderestimation.Duetothelowcorrelationvalues,thegrowthmeanenteredtheIPMmatrixasthegrowthfunctionforthepopulationanalysisofCedrelaodorata,DiospyrosdigynaandPouteriasapota. 2.2.2SurvivalprobabilityforCedrelaodorata,DiospyrosdigynaandPouteriasapotaThepopulationsforCedrelaodorata,DiospyrosdigynaandPouteriasapotadidnotpresentacorrelationbetweendiametersizeandsurvivalprobability(seeFigure 2-2 ) 24

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withp-valuesof0.09,0.671and0.378,respectively.TheC.odoratapopulationhadanaveragesurvivalprobabilityof97.19%.ThemortalityeventsrecordedweretreeswithaDBH<35cm.smallertrees.TheD.digynaandP.sapotapopulationshadanaveragesurvivalprobabilityof88.93%and93.17%,respectively.Thesurvivalprobabilityforthesetwospeciesdidnotshowevidentcorrelationwithsize,withsurvivalprobabilitybeingpresentevenlyamongallsizes.WhilethesurvivalprobabilityinsideMPMscomedirectlyfromthedata,theaveragesurvivalprobabilityresultingfromtheregressionwasusedtodetermineIPMmatrices. 25

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Table2-3. Gompertzfunctioncoefcientsandtnessmeasuresforthe18studiedspecies.Signicanceindicationsforeachcoefcientare:**:P<0.001,*:P<0.01.Regressionresultsthatdidnotconvergedarenotshown. 1SE2SE3SER2empRMSE%BIAS% A.hottlei1.207**0.2260.7360.5160.0630.0370.2090.49628.433A.megalocarpon0.466**0.042.0784.7260.3250.520.0360.22710.708B.alicastrum0.787**0.1280.7230.4950.0930.0550.1830.429.316C.brasiliense1.164**0.0950.4540.2020.081*0.0260.3880.38118.732C.odorata1.639**0.2180.2110.480.0810.050.0510.91662.67C.alliodora2.338**0.242)]TJ /F9 11.955 Tf 9.3 0 Td[(0.150.2830.1120.0640.1590.9447.512C.megalantha2.432**0.1250.6110.4230.154*0.0560.2410.90339.554D.guianenseD.digyna0.9291.656)]TJ /F9 11.955 Tf 9.3 0 Td[(0.6333.1240.0070.0340.010.42428.731G.grandifolia5.03833.4121.0382.2280.0070.0240.1840.36621.901N.ambigens0.6**0.0610.3710.6670.0630.0450.0940.33520.251P.schiedeana0.321**0.059)]TJ /F9 11.955 Tf 9.3 0 Td[(0.6870.3890.0360.0450.1350.1276.182P.dioica0.268**0.019)]TJ /F9 11.955 Tf 9.3 0 Td[(11.35516.101)]TJ /F9 11.955 Tf 9.3 0 Td[(0.1320.2150.0210.114.444P.sapota0.967**0.0393.1923.0071.4411.1390.030.59236.895P.glabrata0.48**0.0390.2360.4920.1540.0870.1670.1767.312R.mucosa0.542**0.076)]TJ /F9 11.955 Tf 9.3 0 Td[(0.8616.7650.1530.7150.0020.37225.229R.montana0.562**0.0320.2850.3720.2940.130.2650.218.946S.portoricense0.879**0.0860.5530.3510.1030.0470.30.36520.948 26

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Table2-4. BRCregressioncoefcientsandtnessmeasuresforthe18studiedspecies.Signicanceindicationsforeachcoefcientare:**:P<0.001,*:P<0.01.Regressionresultsthatdidnotconvergedarenotshown. DBHmaxSE1SE2SER2empRMSE%BIAS% A.hottlei246.603264.0190.0110.01128.893354.1480.1490.57530.565A.megalocarpon95.099**20.7360.0120.00710.1354.645neg0.56111.331B.alicastrum148.12578.0680.0130.008)]TJ /F9 11.955 Tf 9.3 0 Td[(7.00121.1990.1110.67931.904C.brasiliense254.733197.8150.0110.0084.5014.1090.3480.58119.936C.odorata303.176632.8050.010.022.7883.343neg0.78270.07C.alliodora221.156259.8690.0160.021.577**0.3710.1090.54950.326C.megalantha203.057**47.7550.023*0.0082.158**0.5390.1820.46842.642D.guianenseD.digynaG.grandifoliaN.ambigens409.654599.9240.0020.0031.8380.7820.0090.66422.172P.schiedeanaP.dioica223.666191.5930.0020.0021.229*0.44neg0.4584.714P.sapota343.977232.1110.0020.0020.978**0.084neg0.75441.275P.glabrata201.069309.420.0040.0071.8630.916neg0.46529.368R.mucosa217.452711.5840.0030.0131.4121.423neg0.6827.325R.montana266.778266.2620.0030.0041.489**0.2440.1920.5189.833S.portoricense305.19224.3390.0070.0053.4292.4430.2540.63122.339 27

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A B CFigure2-2. SurvivalprobabilitiesforA)Cedrelaodorata,B)DiospyrosdigynaandC)Pouteriasapota.PointsrepresentmortalityobservationsdependingonDBH.Greenlineistheaveragesurvivalprobability,usedintheIPM. 28

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2.2.3PopulationmodelsSmallnumbersofmeasuredindividualsresultedin100%transitionprobabilitiesatlargerclassesforDiospyrosdigynaandPouteriasapota.Theseprobabilitieswerechangedtomatchthesurvivalprobabilityforthelastclass(seeTables 2-5 to 2-7 ).WhileMPMprobabilitiescomedirectlyfromdata,IPMsprobabilitiescomefromregressions,givingthematrixacontinuoussurvivalprobability.ThiscontinuoussurvivalprobabilityforD.digynaandP.sapotaishigherthanthevaluesestimatedintheMPM.Allprojectionsdecreaseexponentiallyduetothelackoffecundityvaluesinthematrices(Figure 2-4 A).ThepopulationprojectionfortheIPMreturnslowerpopulationsizes.Thiscouldbebecausethegrowthratesareoverestimatedduetoclassgrouping.Asshownabove,individualshavedemonstratehighlyvariablegrowthrates,andwiththerequirementforhighprecisiononthemeasurements,overestimationiscommon.Additionally,thepassagetimeforthespeciesisvariable(Figure 2-4 B).ForC.odorata,passagetimesarelowerintheIPMmodel,whichmeanshighergrowthrates.Thesehighergrowthratesarenotreectedinthepopulationprojection,givinglesspopulationsizesfortheIPM.AlthoughIPMshowshighersurvivalcomparingittosomeclassesattheMPM,theseclasseswithhighersurvivalthantheIPMsurvivalmayhavemoreweightforthenalprojections.Thesamplingdesignmayhaveoverlookedsmalltrees,mostlikelytodifcultiesinlocatingandidentifyingthespeciesinahighdensitytropicalforest.Withoutproperdataonsmallclasses,theestimatesfortransitionandregressionanalysismayhaveresultedinbiasedprobabilitiesandpredictions. 29

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Figure2-3. Firstcolumn:PAIddataandGompertz(dash),BRC(point)ts.Secondandcolumn:ResidualplotandresidualhistogramfortheGompertzModel.Thirdcolumn:ResidualplotandresidualhistogramfortheBRCModel. 30

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Figure 2-3 .Continued.Firstcolumn:PAIddataandGompertz(dash),BRC(point)ts.Secondcolumn:ResidualplotandresidualhistogramfortheGompertzModel.Thirdcolumn:ResidualplotandresidualhistogramfortheBRCModel. 31

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Figure 2-3 .Continued.Firstcolumn:PAIddataandGompertz(dash),BRC(point)ts.Secondcolumn:ResidualplotandresidualhistogramfortheGompertzModel.Thirdcolumn:ResidualplotandresidualhistogramfortheBRCModel. 32

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Figure 2-3 .Continued.Firstcolumn:PAIddataandGompertz(dash),BRC(point)ts.Secondcolumn:ResidualplotandresidualhistogramfortheGompertzModel.Thirdcolumn:ResidualplotandresidualhistogramfortheBRCModel. 33

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Figure 2-3 .Continued.Firstcolumn:PAIddataandGompertz(dash),BRC(point)ts.Secondcolumn:ResidualplotandresidualhistogramfortheGompertzModel.Thirdcolumn:ResidualplotandresidualhistogramfortheBRCModel. 34

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Figure 2-3 .Continued.Firstcolumn:PAIddataandGompertz(dash),BRC(point)ts.Secondcolumn:ResidualplotandresidualhistogramfortheGompertzModel.Thirdcolumn:ResidualplotandresidualhistogramfortheBRCModel. 35

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Table2-5. LesliematrixforCedrelaodorata 0)]TJ /F9 11.955 Tf 11.96 0 Td[(1010)]TJ /F9 11.955 Tf 11.96 0 Td[(2020)]TJ /F9 11.955 Tf 11.95 0 Td[(3030)]TJ /F9 11.955 Tf 11.95 0 Td[(4040)]TJ /F9 11.955 Tf 11.96 0 Td[(50>50 0)]TJ /F9 11.955 Tf 11.96 0 Td[(100.85710)]TJ /F9 11.955 Tf 11.96 0 Td[(200.0950.74420)]TJ /F9 11.955 Tf 11.96 0 Td[(300.2070.84230)]TJ /F9 11.955 Tf 11.96 0 Td[(400.1390.92640)]TJ /F9 11.955 Tf 11.96 0 Td[(500.0560.842>500.1580.842 Table2-6. LesliematrixforDiospyrosdigyna 0)]TJ /F9 11.955 Tf 11.96 0 Td[(1515)]TJ /F9 11.955 Tf 11.96 0 Td[(2525)]TJ /F9 11.955 Tf 11.95 0 Td[(3535)]TJ /F9 11.955 Tf 11.95 0 Td[(4545)]TJ /F9 11.955 Tf 11.96 0 Td[(55>55 0)]TJ /F9 11.955 Tf 11.96 0 Td[(150.85215)]TJ /F9 11.955 Tf 11.96 0 Td[(250.0740.83325)]TJ /F9 11.955 Tf 11.96 0 Td[(350.1000.77835)]TJ /F9 11.955 Tf 11.96 0 Td[(450.0860.86745)]TJ /F9 11.955 Tf 11.96 0 Td[(550.0330.870>550.0330.870 Table2-7. LesliematrixforPouteriasapota 0)]TJ /F9 11.955 Tf 11.96 0 Td[(1515)]TJ /F9 11.955 Tf 11.96 0 Td[(3030)]TJ /F9 11.955 Tf 11.95 0 Td[(4545)]TJ /F9 11.955 Tf 11.95 0 Td[(6060)]TJ /F9 11.955 Tf 11.96 0 Td[(75>75 0)]TJ /F9 11.955 Tf 11.96 0 Td[(150.88215)]TJ /F9 11.955 Tf 11.96 0 Td[(300.0440.88930)]TJ /F9 11.955 Tf 11.96 0 Td[(450.0830.95245)]TJ /F9 11.955 Tf 11.96 0 Td[(600.0240.93260)]TJ /F9 11.955 Tf 11.96 0 Td[(750.0230.830>750.0230.941 36

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A B Figure2-4. A).PopulationprojectionsforMPMandIPM.BlueandgreenlinesrepresenttheMPMandIPMprojectionsrespectively.B).Estimatedpassagetimeinyears.BlueandgreenlinesforMPMandIPMrespectively.RedlinerepresentsthetargetDBH. 37

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2.3DiscussionTheresultssummarizetheobservedgrowthincrementsamongspeciesandtheestimatedgrowthmodels.TheresultinggrowthmodelsarereliableestimatesforthesepopulationsatLosTuxtlas.Theprovidedanalysisofgrowthincrementscanhelpdeterminefastandslow-growspecies,whicharehelpfulformanagementplans. 2.3.1GrowthanalysisCloseto75%ofthemeasurementsaveragedgrowthlowerthan1.19cmyear)]TJ /F7 7.97 Tf 6.59 0 Td[(1and50%ofallgrowthincrementsobservedarelowerthan0.62cmyear)]TJ /F7 7.97 Tf 6.59 0 Td[(1.Mostspeciesdidn'thavestatisticallydifferentgrowthratesinsmallorlargetrees(Figure 2-1 ).PopulationsofCordiaalliodorainChiapas,Mexico( Brienenetal. 2009 )andCedrelaodoratainBolivia( BrienenandZuidema 2006 )hadsimilargrowthrates.HoweverthePAIdvaluesreportedinthisthesisareconsiderablylargerthanthosereportedby Anguiano ( 2002 ),whoworkedwiththesamedata.Hereportedannualincrementsof0.5,0.37and0.0007cmyear)]TJ /F7 7.97 Tf 6.59 0 Td[(1forAspidospermamegalocarpon,DiospyrosdigynaandBrosimumalicastrum,respectively.TheanalysisshowthatCordiamegalantha,Cordiaalliodora,C.odoratacanbeconsideredasfast-growspecies(Figure 2-1 ),withstatisticaldifferenceatsmallandlargesizes.ThehighPAIdofC.megalanthacanberesultofitsadaptabilitytodisturbances( Bongersetal. 1988 )andC.alliodoraandC.odorataareknownfortheirfastgrowrates( Greaves 1990 ; Zuidemaetal. 2009 ). 2.3.2GrowthmodelsAlmosteveryspeciespresentedhighvarianceofPAIdwithintheirsizeranges.ThisresultedinnoclearrelationshipbetweensizeandPAId.LowcorrelationbetweenPAIdandsizehasbeenfoundinothertropicalforests(e.g. ClarkandRoad 1999 ).Someauthorssuggestthatpreviousgrowthmayhaveahigherinuenceongrowththansize( Brienenetal. 2006 ).PAIdvaluesforAmpelocerahottlei,CordiaAlliodora,GuareagrandifoliaandPseudolmediaglabratashowedaclearerpatternwherethelargestindividualstendedtohavehighergrowthrates.Neitherearly-stagesnorlargeradults 38

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wereconsistentlycharacterizedbyslowgrowth.Atallstages,thespeciespopulationspresentedafullvariationofgrowthcapacities.Largevarianceofannualincrementscouldcomefromageorenvironmentalvariablesnotconsideredinthemodels(likesoilconditions,lightavailability,competition,climatevariationorlocationwithinthelandscape),aswellasfrommeasurementerrorwhenmeasuringtrunkperimeterofirregularshapedtrees.Includingamong-treeautocorrelatedgrowthmayexplainsomeofthehighvariance( Brienenetal. 2006 )andfutureeffortsshouldtrytoincludethis.Thereislowcorrelationbetweentreesizeanddiametergrowthforthe18studiedspeciesasseenbythelowandevennegativeR2empvalues.Thislackofcorrelationiscommonamongtropicalforeststudies(see ClarkandRoad 1999 ).Forthosespecieswithlowcorrelationandhighmeansquarederror(e.g.DialiumguianenseandPimentadioica),asimpleaveragegrowthrateoutperformsaGompertzorBRCmodels.Whiletheuseofaveragegrowthratestopredictfuturegrowthisquestionableduetothelackofecologicalmeaning,withoutadditionalhighqualitydata(includingcovariables)andpropersampling,averagegrowthcouldperformsignicantlybetterthantheunderperforminglinearandnon-linearmodelsobtainedinthesepopulationsatLosTuxtlas. 2.3.3MatrixandIntegralProjectionModelsMPMandIPMprojecteddifferentoutcomesforthepopulations.Thedifferenceintheprojectionsiscloseto10years.MeaningthattheMPMmodelprojectsthatthecurrentpopulationwithoutanyrecruitmentcouldpersistforlongertime. Ramulaetal. ( 2009 )comparedMPMsandIPMmodelswithtwoperennialherbaceousspecieswithlowpopulations.Oppositetowhatispresentedinthisthesis,theyfoundthatMPMtendedtounderestimate.Thisdifferencemaybeexplainedbythelackofmortalityobservationsonthispopulationwhichmayhaveinatedthesurvivalestimates.Thislackofmortalitydatacanonlyimprovedwithlongerspanofmeasurements. 39

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Thisdiscrepancyofthemodelsevidencesthatpopulationprojectionsaresensitivetothedenitionofclassesandtheuseofempiricalormodeledgrowth.InthecaseofIPMsthematrixisdenedbythegrowthandsurvivalprobabilitymodelused.WhileinthisworkitisnottestedthesensitivityoftheIPMprojectionstothechosenmodel,wecanexpectadifferentresultbyusingaverageoraGompertzmodel. 2.4SummaryForthisstudy,itwasevidentthatusingthedatasettoestimatetransitionprobabilitiesinsteadofestimatingagrowthmodel,wouldhaveresultedinlackoftransitionsandsurvivalprobabilitieswhencalculatingtheMPM.Evenwhenusingonlyveclasses,somesurvivalprobabilitiesresultedinunrealistic100%values.Forthisreason,thisworksuggeststhatforsmallsamplesizepopulations,usingIPMscouldresultinbetterprojectionsforthepopulations.However,sincesmalldatasetsusuallycomewithhighuncertaintyofgrowthandsurvivalmodels,anIPMcanbealsolimitedbythelackoftnessofmodels. 40

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CHAPTER3CONCLUSIONSThisworkrepresentsanefforttoimprovetheunderstandingabouttropicaltreegrowthandpopulationdynamics.Theseresultscanbeusedtoprojectgrowthforthese18speciesfordetailingmanagementplansforthesespeciesandfortheforestandtosupportsustainablemanagementoftheseforests.However,theseresultscomefrompopulationsinsideLosTuxtlas,Veracruz,Mexico.Ifspecicmodelswanttobeestimated,researchersneedtoconsiderpopulationsindifferentlocations.Ifgeneralizationsaboutthegrowthofthesespeciesarerequired,comparisonwithdifferentlocationsisrequired.Long-termforestinventoryplotsareoneofthestrongesttoolsavailablefortropicaltreeresearchandhavereturnedmanyimportantresultsfrommanyplacesacrossthetropics.Implementingalargenetworkoflong-termpermanentinventoryplotsacrossMexicoiskeytogatherinformationaboutspeciesdynamicsintropicalandtemperateforests. 41

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BIOGRAPHICALSKETCH BorninMexicoCity,SebastianspentmostofhischildhoodinMexicoCity,withsomeyearsinSaltillo,MexicoandRiodeJaneiro,Brazil.Comingfromaheavilymathematicalfamily,Sebastianshowedinterestinsciencesinceearlyyears.Sebastianchangedhismajortwicewhileatcollege.HestartedEngineering,thenAgronomy,beforenallysettlingandndinghisplaceinBiology.HemajoredinBiologysummacumlaudefromtheMetropolitanAutonomousUniversityin2010.Duringhiscollegestay,hebecameinterestedinNaturalResourceManagementinthetropics.HismajorthesisdescribedtheMexicanMarcgraviaceae,apoorlyknownplantfamilyfromtheneotropics.BytheendofhiscollegedegreehewasworkingcloselywithresearchersattheCenterforTropicalResearch(CITRO)oftheUniversityofVeracruzinXalapa.AtCITRO,SebastiangaveseminarsonhisworkwithSpeciesDistributionModels.IsatthisCenter,wherehegotintouchwithKarenKainer,whowasavisitingscholarfromUF.Dr.Kainerwasofferingagraduatepositionforamaster'sdegreeattheSchoolofForestResourcesandConservationatUF.In2011,Sebastianstartedthismaster'sdegreeatUFundertheguidanceofDr.WendellCropper.HebecameincreasinglyinterestedinForestModeling,specicallyformanagementoftropicalforests.InAugust2012,hevisitedtheMaxPlanckInstituteforDemographicResearchatRostock,GermanytostudyIntegralProjectionModels.AthisnalsemesteratUFhestartedworkingwithAgentBasedModelsforSocioecologicalSystemswiththeREDD+WorkingGroup.DuringhisMaster'sstudies,hehasactivelyparticipatedintheTropicalConservationandDevelopmentProgramandtheMexicansinGainesvilleAssociation.SebastianwillstartadoctoratedegreeatSFRCinAugust2013.HewillworkwithForestInventorydataandForestModelinginsidetheCommunityForestsofQuintanaRoo. 47