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ContentslistsavailableatSciVerseScienceDirect
Ecological
Modelling
j ou rna l h o m e pa ge :w w w . e l s e v i e r . c o m / l o c a t e / e c o l m o d e l
Modelling
the
spatio-temporal
pattern
of
primary
dispersal
in
stone
pine
(
Pinus
pinea
L.)
stands
in
the
Northern
Plateau
(Spain)
Rubén
Manso
a,∗,
Marta
Pardos
a,
Christopher
R.
Keyes
b,
Rafael
Calama
a aDpto.SelviculturayGestiónForestal,CIFOR-INIA,Ctra.LaCoru˜nakm7.5,28040Madrid,SpainbDepartmentofForestManagement,CollegeofForestry&Conservation,UniversityofMontana,Missoula,MT59812,USA
a
r
t
i
c
l
e
i
n
f
o
Articlehistory: Received19April2011 Receivedinrevisedform 21November2011 Accepted25November2011
Keywords: Inversemodelling Fecundity Crowneffect Seedlimitationindexes Climatecontrol Regenerationfellings
a
b
s
t
r
a
c
t
Naturalregenerationinstonepine(PinuspineaL.)managedforestsintheSpanishNorthernPlateauis notachievedsuccessfullyundercurrentsilviculturepractices,constitutingamainconcernforforest managers.Wemodelledspatio-temporalfeaturesofprimarydispersaltotestwhether(a)presentlow standdensitiesconstrainnaturalregenerationsuccessand(b)seedreleaseisaclimate-controlledprocess. Thepresentstudyisbasedondatacollectedfroma6yearsseedtrapexperimentconsideringdifferent regenerationfellingintensities.Fromaspatialperspective,weattemptedalternateestablishedkernels underdifferentdatadistributionassumptionstofitaspatialmodelabletopredictP.pineaseedrain.Due toP.pineaumbrella-likecrown,modelswereadaptedtoaccountforcrowneffectthroughcorrectionof distancesbetweenpotentialseedarrivallocationsandseedsources.Inaddition,individualtreefecundity wasassessedindependentlyfromexistingmodels,improvingparameterestimationstability.Seedrain simulationenabledtocalculateseeddispersalindexesfordiversesilviculturalregenerationtreatments. Theselectedspatialmodelofbestfit(Weibull,Poissonassumption)predictedahighlyclumpeddispersal patternthatresultedinaproportionofgapswherenoseedarrivalisexpected(dispersallimitation) between0.25and0.30forintermediateintensityregenerationfellingsandover0.50forintensefellings. Todescribethetemporalpattern,theproportionofseedsreleasedduringmonthlyintervalswasmodelled asafunctionofclimatevariables–rainfallevents–throughalinearmodelthatconsideredtemporal autocorrelation,whereasconeopeningtookplaceoveratemperaturethreshold.Ourfindingssuggest theapplicationoflessintensiveregenerationfellings,tobecarriedoutafteryearsofsuccessfulseedling establishmentand,seasonally,subsequenttothemainrainfallperiod(latefall).Thisschedulewould avoiddispersallimitationandwouldallowforacompleteseedrelease.Thesemodificationsinpresent silviculturepracticeswouldproduceamoreefficientseedshadowinmanagedstands.
© 2011 Elsevier B.V. All rights reserved.
1. Introduction
Pinuspinea is an essential species of Mediterranean
ecosys-temsthatprovidesimportanteconomicbenefitstolocalpopulation fromitsedibleseedproductionandtimberproduction.Inaddition, thespeciesplaysavaluableecologicalroleasitsnatural distribu-tionoccupieschallengingsitesthatexhibitgeneralMediterranean weatherconditions,continental wintersand highly sandysoils, wherefewarborealspeciespersist.Suchanenvironmentcanbe oftenfoundthroughouttheSpanishNorthernPlateau(Pradaetal.,
1997), which accounts for more than 50,000ha of indigenous
∗Correspondingauthor.Tel.:+34913471461;fax:+34913476767. E-mailaddresses:manso.ruben@inia.es,rmgforestal@hotmail.com
(R.Manso),pardos@inia.es(M.Pardos),christopher.keyes@cfc.umt.edu(C.R.Keyes), rcalama@inia.es(R.Calama).
P.pineaforests.Thesestandshavebeenmanagedforoveracentury
throughmodernsilviculturetechniques.
P.pineanaturalregenerationhasbecomeaprimaryconcernfor
forestmanagement.LikeotherMediterraneanspecies(e.g.species ofgenusQuercus),naturalregenerationiscommonlyunsuccessful undercurrentlyappliedsilviculturalsystems(seedtreemethod, and,increasingly,shelterwoodmethod),whichleadtolow den-sitiestooptimizeconeproductionpertree.Regenerationfellings derivedfromthesetreatmentsproduceeven-agednon-coetaneous standsastheyintendtoimitatenaturalforestdecayleading gen-erallytothesestructures(Schütz,2002).Severalfactorshavebeen notedasdeterminantsofthisregenerationfailure,including: cli-mate,andspecificallyseveresummerdroughtsandhighsummer temperaturesthatleadtoestablishmentfailure;mastinghabitand lackofsynchronywithregenerationfellingsandadequateyears forseedlingestablishment;intensiveconeharvesting,resultingin depauperateseedbanksprior toregenerationfelling;long rota-tions,inducingpoorseedcropsduringtheregenerationperioddue
totreevigourdecline;thespecies’ gravity-basedseed dispersal strategy,resultinginpatchyseeddistribution;andpost-dispersal seedpredation(CalamaandMontero,2007;Barbeitoetal.,2008;
Mansoetal.,2010).
The study of primary seed dispersal spatial patterns has focused on understanding the general mechanisms that con-trolfundamentalpopulationdynamics(Clarketal.,1998,1999b;
Nathan et al., 2002; Levin et al., 2003; Muller-Landau et al.,
2008; Martínezand González-Taboada, 2009),or their
ecologi-cal consequencesin localcircumstances (Ordó ˜nez et al., 2006;
Santoset al., 2006; Debain et al., 2007; Gómez-Aparicio et al.,
2007;Sagnard et al., 2007). Similarly, moststudies aboutcone
openingprocesseshavemainlyaimedtotesttherelative impor-tanceofpyriscenceandxeriscence strategiesfromanecological perspective (Nathan et al., 1999, 2000), evolutionary perspec-tive(Tapiasetal.,2001)andstructuralperspective(Nathanand
Ne’eman,2004).Withfewexceptions(suchasTsakaldimi etal.
(2004)or Ganatsas and Thanasis (2010)),little effort hasbeen
undertaken to apply the valuable information generated from ecologicalstudiestoinformpracticesofpromotingnatural regen-eration.
Thedensityofseedsdepositedinaparticularlocationwithina standisafunctionofstandstockingandthespatialarrangement oftrees(source),andofseedproductionandthecapacityforseed dispersaloverlongdistances(Clarketal.,1998).Providedthatthe latterisaseriousconstraintforcolonizationinP.pinea,duetothe species’largewinglessseed(Magini,1955),adeeperknowledge ofseeddispersalspatialtraitscanofferessentialinformationwith referencetothesuitabilityofcurrentdensitiesinstandsafterseed fellingsfornaturalregeneration.Lowstockingspromoteahigher coneproductionpertree(Calamaetal.,2008)butmayresultin aseedarrivallimitation(dispersallimitation).Ontheotherhand, densestandslargelyfavoranevendistributionofseedsbutmay contributetoinsufficientseedproduction(seedlimitation). Opti-maldensitieswouldleadtoacompromisebetweenbothsituations, withacceptabletrade-offsinbothseedproductionandseed disper-sal.Becauseconeopeningisrelatedtophysicalvariables(Dawson etal.,1997),accuratepredictionsofseedreleaseratesbasedon cli-matevariableswouldallowforoptimizedtemporalregeneration fellingschedules.
In thepresentstudy,anestablishedmethodology toanalyze thespatialpatternofseeddispersalwasused.Themethodology, introducedbyRibbensetal.(1994)tostudythespatialdistribution ofseedlingsfromseedsourcelocations,utilizesinversemodelling proceduresinordertoestimatethesummedseedshadowfrom datacollectedinaseedtrapexperiment.Althoughbroadlyapplied (Clarketal.,1998,1999b;Uriarteetal.,2005;Debainetal.,2007;
Sagnardetal.,2007;Nanosetal.,2010),theapproachisnot
with-outcontroversy,especiallywithregardtotheexperimentaldesign (Clarketal.,1999a).Recently,comparisonscarriedoutwithseed dispersalkernelsattainedfromgeneticanalysisdemonstratedthat traplocationcandramaticallybiasparameterestimation
(Robledo-ArnuncioandGarcía,2007).Furthermore,amorestableandreliable
estimationisachievedifthefittingprocessisindependentofthe fecundityparameter.Ithasalsobeenarguedthatother consider-ations,suchasthebiasintroducedbyimmigrantseeds(i.e.from nomapped sources), should be taken into account (Jones and
Muller-Landau,2008).ForP.pinea,however,therelativelyshort
dispersaldistance(Rodrigoetal.,2007)andtheavailabilityof exist-ingmodelstoindependently estimateseed production(Calama
etal.,2008)severelyreduceparameterizationstabilityproblems,
andimmigrantseedsoccurrencecanbesafelyconsidered negligi-ble.Inaddition,potentialbiasderivedfromtraplocationcanbe minimizedwithasensibletrapdeploymentinordertoobtaina largerrepresentationofcritical(andmorerelevant)dispersal dis-tances.
Alternativekernelsestimatedbyinversemodellinghavebeen recentlyproposedbasedondifferentassumptionsthatdeal bet-terwithspeciesspecificdispersalfeatures.Mechanisticapproaches (GreeneandJohnson,1989;StoyanandWagner,2001;Wrightetal.,
2008)werespecificallydevelopedtomodelwinddispersedspecies
kernels. From a non-mechanistic perspective, different variants of the Weibull distribution have been assessed (Ribbens et al.,
1994; Clark et al., 1998),while improvementson those
meth-ods were attained to manage its specific rigid behavior (Clark
etal.,1999b;BullockandClarke,2000).Eventually,otherempirical
approachescomprisinggeneticprocedureshavebeendevelopedto obtainmoreaccuratepredictions(González-Martínezetal.,2006;
Robledo-ArnuncioandGarcía,2007).Forourstudy,wetestedand
compared theperformance of alternative models,sensu Debain
etal.(2007),selectedaccordingtoP.pineaspecificdispersal
syn-drome,asausefulprotocoltoachievethebestfitand,consequently, acorrectinterpretationofthephenomena.Additionally,from sim-ulationsassessedthroughthemodelofbestfit,wecalculatedand comparedsourceabundanceanddispersallimitationindexvalues (Clarketal.,1998;Muller-Landauetal.,2002)underP.pinea’stwo mostcommonregenerationfellingsystemsandacontrolstand(i.e. priorfellings).
Themainaimsofthepresentworkweretounderstand,model andpredictthespatio-temporalpatternsoftheprimarydispersal
inP.pineamanagedstandsintheSpanishNorthernPlateau.The
purposewastoidentifythelikelybottlenecksoccurringduringthe firststepofthenaturalregenerationprocess.Ourhypotheseswere (a)thatcurrentstanddensitiesatrotationageinmanagedP.pinea forestsconditionnaturalregenerationsuccess,and(b)thereexists a climatecontrolonthetemporal patternof primarydispersal, similartothephenomenondrivingconeproduction(Mutkeetal.,
2005a;Calamaetal.,2011).Ourfindingswillserveasanessential
toolforforestmanagersattemptingtoachievesatisfactorynatural regenerationofP.pinea.
2. Materialsandmethods
2.1. Studysite
The study site is located at 700m a.s.l. in a representative
P. pinea stand onthe flat sandy soils of the Northern Plateau,
Spain.Thestudywasperformedina120-year-oldeven-agedpure standin CorbejónyQuemadospublicforest(41◦28N,4◦43W). Site location was selected and regeneration felling treatments designedtorepresenttypicalconditionsinamaturemanaged for-est,whenrestrictionsonconecollectionforcommercialpurposes arecommonlyimposedtoallowforseedrainandregeneration. Regenerationfellingscommencedduring2002–2003followingthe highly intensive seed tree method(ST) and the more progres-siveshelterwoodmethod(SW).Bothsystemshavebeenbroadly applied as regeneration treatments for the species. Pre-felling and post-felling standdensities are shown in Table1. Climate iscontinental-Mediterranean.Meanmonthlytemperaturesrange from4.0◦C inJanuaryto21.7◦CinJuly.Meanannual precipita-tionis435mm,withaperiodofsummerdrought(July–September meanprecipitationof66mm).Siteindexis15–16mat100years, characteristicofaIIclassquality(Calamaetal.,2003).Thisindex definesthequalityofastandasafunctionofitsdominantheight ataparticularage.Theconsidereddominantheightcriterionwas theheightofthosetreeswhosediameteratbreastheight(1.3m; “dbh”)wasincludedamongthe20%ofthethickesttreesofthestand (Weise,1880).
Table1
Summaryofstanddensities.
Plot Treatment Nb/fc(ha−1) Nd(ha−1) BAe(m2/ha) Dgf(cm) Hg(m) FCCh(%)
1 STa 144 46 8.17 47.6 13.6 19
2 ST 115 48 9.37 49.9 15.5 22
3 ST 156 46 6.99 44.1 12.6 14
4 SWb 192 73 10.82 43.4 14.1 31
5 SW 233 75 9.70 40.6 12.9 30
6 SW 169 75 12.26 45.6 15.8 34
7 Control 149 149 18.42 40.1 13.8 70
aST—seedtreemethod. b SW—shelterwoodmethod.
c Nb/f—densitypriorfellings.Afterfellings. d N—remainingdensity.
eBA—basalarea.
f Dg—quadraticmeandiameter. gH—averageheight.
h FCC—forestcanopycover.
2.2. Experimentaldesign
Theprimarydispersaltrialwasinstalledin2005,toallowfor astandresponsetofellingsinconeproduction.Itconsistedofsix 60m×80m(0.48ha)sampleplotsthatwereestablishedunder dif-ferentstanddensitiesproducedbyregenerationfellings.Densities inplots1–3wererepresentativeoftheSTmethod,whereasthose inplots4–6weredistinctiveoftheSWmethod.Ontheonehand, thesetreatmentsprovidedaconvenientrangeofstanddensities, essentialformodellingpurposes.Ontheotherhand,theyofferan excellentframeworkforfurthermodelsimulation.A7.5mbuffer areawasincludedaroundeachplot,increasingtheoverallplot sur-faceupto0.7ha.Anavailablecontrolplot(nofellings)ofidentical dimensionswasusedexclusivelyforsimulationpurposes.Graphic informationaboutplotscanbefoundinFig.A.1inAppendixA.
Alltreeswithinplotswerestemmappedandmeasured.Tree measurements included dbh, total height, and 4 perpendicular crownradiiincardinaldirections.
InMay2005,asystematicgrid(17.7m×17.7m)often circu-larseedtrapsof0.25m2 wasestablishedwithineach ofthesix plots(controlexcluded).Twotrapsinplot1weredestroyedatthe beginningoftheexperimentandwerediscardedfromthe analy-sis.Theshortestdistancefromatraptoplotboundarywas12m. Thetrapdesignwasabagmadeoftextilefinemeshstapledon threewoodensticksat1mabovetheground(topreventrodent predation).Trappedseedswerecollectedon60occasionsfromtrap deploymenttoJanuary2011atintervalsaveraging34.6days(range from19to70,standarderror1.26),withlongestintervals corre-spondingtolowintensityseedrainmonthsordifficultaccessto plots(winter).
2.3. Modellingthespatialpattern
2.3.1. Theinversemodellingapproach
In order to determine the spatial pattern of dispersal, an approach based on non-mechanistic models involving inverse modellingprocedureswasattempted(sensuRibbensetal.,1994). Withthistypeofmodel,theseedshadowiscalculatedasthe prod-uctoftwofactors:thekernelandsourcefertility.Thefirstfactor, thekernel(kij),representstheprobabilitythataseedisprimary dispersedtolocationi,givenasourcejandtravelling,isotropically, adistancerij(m).Thekernelimpliesparameterstobeestimated whichcontroltheshapeofthecurveasafunctionofdistance.The secondfactoris thefertilityofthesource.Inourapproach, the modeldevelopedbyCalamaetal.(2008)isusedtoestimateaverage coneweight(wcj)duringthestudiedperiod(2005–2010)foreach individualtreej.Ratherthanestimateaparametertoobtainthe numberofseedsfromtheresponsevariableoftheaforementioned
model,weusedthemodeldevelopedbyMorales(2009)topredict thenumberofseedsperkgofcones(P).Pwascalculated consider-ingaconstantfractionofconeweightattributabletoseeds(0.259) andassuminganaverageseedweightof0.615g.Consequently,the valueNij(seeds/m2)ofthegenericseedshadowforasingletreej atalocationiisdefinedas:
Nij=P·wcj·k(rij) (1)
Inthecaseofnon-discretesources(e.g.astand),thenumberof seedsreachingalocationiiscomputedasthesumoftheexpected numberofseedsdispersedtothislocationfromtheTtrees con-sidered.Inthatcase,thesummedseedshadowcanbeexpressed as:
Ni=P· T
j=1
wcj·k(rij) (2)
Notethatdefinitionofthesummedseedshadowleadsto indi-vidualtreekernelparameterization.
2.3.2. Sourcedetermination
Formodellingpurposes,weoptimizedthenumberofsources T tocontribute tothesummedseed shadowata specific loca-tion.Therefore,weinitiallyplottedtheinversecumulativerateof seedarrivaltoeachtrapalongnormalizeddistances(totaldistance betweenatrapiandatreej(dc)/crownradiusdimension(db))to thenearesttree.Crownradiiwerecalculatedasthedistancefrom thecrowncentroidjtodriplineinthedirectionofthetrapi(Fig.1). Suchsimplificationindicatesboththedegreeofclumpingofdata andtherelativedistanceoftrapsnoreceivingseedstotheclosest tree.Thelatterdefinesthemaximumrelativedispersaldistance foundfromthedataavailable(2crownradii).Thus,theprocedure tooptimizetheTcontributorseedsourceswastoexcludefrom analysistreeslocatedoveradistanceof2crownradiifromtraps.
Fig.2.Histogramsoffrequencyforrelativedistancesfromtrapitotheclosest1st,2nd,3rdand4thtreej.Distancesbelow2crownradiiaregreycolouredforclarity.Note thatthe4thnearesttreewasalwaysfurtherthan2crownradii.Meancrownradiuswas3.5m.
Todoit,wecalculatedtheempiricaldistributionofdistancesin crownradiifromeachtraptothestemofthenearest1sttoTth tree.Then, Twasconsideredoptimumwhenthedistributionof distancesbetweentrapsandtheTth+1nearesttreeonlyincluded figuresover2crownradii,resultinginT=3(Fig.2).
2.3.3. Distancedefinition
Inordertoaccountforcrowneffectinthekernelvalue assign-ment, we computed standardized distances between traps and sources,normalizingthebeneath-crownsegmentdbtoan aver-agecrownradius(R),leavingtherest(beyondcrown)unaltered. Whenatrapwaslocatedbeneathacrownshadow,itsdistanceto sourcewasassessedasthecorrespondingproportionofR.Inturn, beneath-crowndistancesareslightlyrescaled,whereastwopoints locatedatthesamedistancetodriplineofequallyproductivetrees ofdifferentcrownsizesareconsideredtobereachedbythesame numberofseeds.Correcteddistancerij(m)analyticdefinitionis then:
(dc−db)+R¯ (dc/db)·R¯
ifthetrapisbeyondcrown
ifthetrapisbeneathcrown (3)
wheredbistherealcrownradiuslength;dcisthedistancebetween thecentroidoftreejandthetrapi.
2.3.4. Kernelformulation
Inordertoestimatetheseedshadowthatbestfitthedata,two kernelsweretested:theWeibull(Clarketal.,1998),andthe2Dt model(Clarketal.,1999b).Parameterestimationwasperformed throughthe optimizationof the log-likelihood functionfor the assumedtheoreticaldistributionofdata,throughavariantofthe simulatedannealingalgorithm(Belisle,1992).
TheWeibullkernelcanbere-formulatedas:
kij= 1 nexp
−
rij ˛
c(4)
where˛isthedispersalparameter,cistheshapeparameter,nis thenormalizer:
n=2··˛2·(2/c) c
with(·),thegammadistribution.
Shape parameter c is assessed together with ˛ in the log-likelihood maximization. Nevertheless, whenever optimization becomesunstableweassumed,likeClarketal.(1998),aGaussian curve(c=2).
Ontheotherhand,the2Dtkernelconsistsofareformulationof theWeibullcurvewithc=2,allowing˛tovaryalongrij:
kij= u
·p·(1+(r2ij/p))(u+1)
(5)
whereuisthescaleparameter,pistheshapeparameter.
2.3.5. Likelihoodfunctions
Parameters involvedin both kij formulations were achieved throughlog-likelihoodmaximizationofEq.(2),undertwo alter-nativehypotheses(Poissonandnegativebinomial)withrespectto thestochasticprocessofseedarrival.Inthecaseofthe2Dtmodel, onlythePoissonhypothesiswasused.Poissonandnegative bino-miallog-likelihoodsadaptedbyRibbensetal.(1994)andClarketal.
(1998),respectively,areexpressedas:
log=
i
log=
i
(log(yi+)−log(yi+1)−log()+yi·logNi
+·log−(yi−)·log(Ni+)) (7)
whereisthelikelihoodfunctiontomaximize,yiistheobserved numberofseedscollectedfromthetrapi,Niistheexpected num-berof seedsin trapi, is theclumping parameter,(·)is the gammadistribution.Maximizationofthelog-likelihoodfunctions wasassessedusingthedatafromalltrapssimultaneously.
2.3.6. Modelevaluation
Comparisons between models were performed through the AkaikeInformationCriterion(AIC)totestmodelaccuracyandselect thatonewhichbestfittedthedata.Wealsocomputeda regres-sionbetweenobservedandexpectedseeddensityvalues,testing whethertheinterceptandslopedifferedsignificantlyfrom0and1, respectively(H0:intercept=0,slope=1),asameasureofthelevelof concordancebetweendataandmodel.Inaddition,thecoefficient ofdeterminationforthisregressionwascalculated,assuggested byClarketal.(1998).
2.3.7. Seedlimitation
Forthetwoproposedregenerationfellingtreatmentsand con-trol,wetestedwhetherchangesindensity(post-harvestingbasal area)couldleadtoseverevariationsinseedavailability(inregard toboth abundance and occurrence).Thiswas accomplishedby computingthesourcelimitationindex,orSL,andthedispersal lim-itationindex,orDL(Clarketal.,1998;Muller-Landauetal.,2002). SLisexpressedastheproportionofsiteswherenoseedsarrive assumingthatthetotalamountofseedsisdistributeduniformly:
SL=1−Pr
ˆ
Ni>0|Poisson Nˆi
⁄
l=e− Nˆi
⁄
l(8)
with ˆNi,theexpectednumberofseedsreachingthelocationi,andl, thenumberoflocationstakenintoconsideration.DLcanbedefined asthecomparisonbetweentheproportionofsitesactuallyreached bydispersedseedsandtheproportionoflocationswhereseeds wouldarriveifdispersalwereuniform,whereaisthenumberof pointsreachedbyatleastoneseed:
DL=1−
a/l 1−SL
(9)
Usingthebestmodel,weassessedasimulatedseedrainat1m2 scalethroughout2501points(l)locatedin aregulargridinthe central41m×61mrectangleofeachplot.Regardingmodel con-sistence,distancesbetweensimulationpointsandtreesmustbe modifiedsimilarlytoEq.(2).ThesesimulationsallowedforSLand DLcalculationthroughoutallplots,includingthecontrol.
2.4. Modellingthetemporalpattern
Inordertomodelseeddispersalfromatemporalperspective, thetotalseedcollectedintrapsduringeachdatacollectioninterval wasgraphicallycomparedwiththatperiod’smeanclimate vari-ables,includingmeantemperature,maximumtemperature,mean relativehumidityandtotalprecipitation.Basedonthisanalysis,the mostsuitablevariableswereselectedtocontroltheprocessofcone opening.AllclimatedatawereachievedfromOlmedo meteorolog-icalstation(coordinates41◦1734N,4◦4058W).
Concerningseedrelease,weconstructedaresponsevariable(sr) relatedtothetotalamountofcollectedseedsthatalsoaccounted fortheseasonallydecreasingaerialseedbankovertime, asthe percentageofseedsreleasedin aparticularperiodwithrespect tothetotalamountofseedsremainingin thecone.Thenature oftheresponsevariable(apercentage)rendersit insensitiveto
extremelylowconecrops,thusweonlyconsideredyearsof appre-ciablecropsintheanalysis(i.e.2006–2007,2007–2008,2008–2009 and2010–2011).Significantdifferencesamongyieldswere deter-minedviathenon-parametricKruskal–Wallistestfornon-normal data(˛=0.05).
Agraphicalanalysiswasalsoundertakentoidentifyprior rela-tionships betweenclimatevariables and sras a basis tomodel srthrough asimplelinearregression.In ordertoprevent unre-alisticconfidenceintervalsfortheparameters,anauto-regressive errorstructurewasappliedwithindispersal periods,due tothe fact that theobservations oftheresponse variable are intrinsi-callyautocorrelatedfromatemporalperspective.Inaddition,those caseswheresr=100werenotusedintheregressionasitisa con-stantthroughoutallterminalvaluesofeverydispersalperiodwith no ecologicalmeaning. Eventually,potential transformations in explanatoryvariableswerecarriedoutwhennecessarytolinearize therelationship.Modelevaluationwasperformedcomparingthe AICofalternativemodels.
Allstatisticalanalysesandcalculationsinthisstudywere per-formedinR2.12.0(RDevelopmentCoreTeam,2009).
3. Results
3.1. Seedrain
During the dispersal periods from 2005to 2010, 753seeds werecollectedintheseedplots.Thespatialdistributionoftrapped seedswasnotuniform.24traps(41%)werenotreachedbyany seed during all periods. The Kruskal–Wallistest indicated sig-nificant differences among years in number of seedscollected (2=48.6924, p-value<0.0001). Dispersal was especially scarce (non-appreciable)during2005–2006(6seeds)and2009–2010(7 seeds);higheryieldsoccurredduring2008–2009(29seeds)and 2010–2011 (73seeds). In contrast, 2006–2007(237 seeds) and 2007–2008(401seeds)werestrongmastingyears.Statisticsper traparesummarizedinTable2.
ConeopeningtookplaceduringJuneandJulyallyears,when seedsreachingtrapsincreasedconsiderably.Concerningthe pro-gressiveseed releaseafteropening,although a strongdispersal peakoccurredatthebeginningofeachdispersalperiod,arelative maximumatadvancedstagesoftheprocessaroseasacommon featurefor allyears holdingappreciableyields(Fig.3).Notably, in2006alargeportionoftheyear’sdispersedseedsfellduring November.Thesametrendoccurredin2007,whenahigh percent-ageoftheyear’sseedfallwascollectedduringSeptember.In2008, thepeakoccurredinOctober,whilein2010twolatemaximawere recordedinSeptemberandNovember.Duringtheyearsof appre-ciableconecrop,thosedatacollectionintervalsoflesserseedrain intensityshowedaresidual(non-null)dispersalrate,withonlyfour lagswherenotrappedseedswerefound.
3.2. Spatialpattern
TheWeibullmodelconsideringaPoissondistributionofdata (henceforthW.P)provedthemostaccurate,withthelowestAIC value,togetherwiththe2Dtmodel(Table3).Themaximizationof thenegativebinomiallog-likelihoodfunctionfortheWeibullcurve (hereafterW.NB)presentedhighinstabilityinparameter estima-tionevenfixingc.Theclumpingparameterinthenegativebinomial hadatrendtolargevalues(>100),meaninglackofoverdispersion inthedata.
Table2
Mainannualseeddispersalstatisticspertrapandseedraindensity(seeds/ha).
Period 2005–2006 2006–2007 2007–2008 2008–2009 2009–2010 2010–2011
Mean 0.10 4.09 6.91 0.50 0.12 1.26
SDa 0.36 9.24 11.65 1.23 0.46 2.57
CIb(95%) ±0.09 ±2.38 ±3.00 ±0.32 ±0.12 ±0.66
Seeds/ha 4137.93 163448.28 276551.72 20000.00 4827.59 50344.83
aSD:standarddeviation. bCI:confidentintervals.
Fig.3.Numberofseedstrapped(solidline),monthlymeanrelativehumidity(dottedline)andmonthlymeantemperature(dashedline)during2005–2010.
Table3
Estimatedparameters,AICandlog-likelihood(log)forthefittedmodels.Inbolds,thelowestAIC.Coefficientofdetermination(r2)amongobservedandpredictedvalues foreachmodelisalsoshown.
˛ c u p AIC r2 log
W.P 3.308 2.065 – – 2358.300 0.428 −1177.150
2Dt – 2a 24.837 253.6 2358.758 0.424 −1117.379
aFixedparameter.
proposedapproaches.Basically,themodelsdifferedinseed disper-salestimationatshortdistances(beneathcrown)withexpected densityatsourcerangingfrom39.89(2Dt)to37.71seeds/m2(W.P), asillustratedinFig.4foranaveragetreewitha3.5mcrownradius. Theprobabilitythataseedisdispersedbeyondcrownvariedfrom 0.312(W.P)to0.310(2Dt).Beyond3.5mfromthedripline(2mean crownradii),theprobabilitywaslessthan0.01forallmodels, indi-catingahighlyaggregatedspatialpattern(Fig.5).
Ahighlevelofagreementbetweenmodelanddatawasfoundin thecaseoftheW.Pmodel.AsshowninFig.6andTable3,therewere
Fig.4. Comparisonofseeddensitycurvesproducedbythefittedmodelsforan averagetreewithcrownradiusR.
noevidencesforrejectingthenullhypothesisofalinear relation-shipwithslope=1(p-value>0.05)andintercept=0(p-value=0.24) amongobservedandexpectedvalues.Coefficientsofdetermination betweenthemintheW.Pand2Dtmodelsweresimilar(Table3), exhibitingrelativelylowvalues.
Simulations to calculate limitation indexes were performed withtheW.Pmodel(Fig.4).Sourcelimitationindex(Fig.7) indi-catedthatlimitationduetoseedavailabilitywasnegligibleforall plots(SL<0.005),implyingthatunderauniformseedrain,mostof thespacewould bereached. Dispersallimitationshoweda ten-dency for lower values as basal area increased(Fig.6). Atlow densities(basalarea<9m2/ha;plots3and1),DLwas0.58and0.49, respectively;itwas0.32(plot5),0.29(plot2),0.28(plot4)and0.25 (plot6),wherebasalareawasbetween9and13m2/ha.DLinthe controlplotwas0.13(basalarea=18.4m2/ha).
3.3. Temporalpattern
Anexploratoryanalysisofdifferentclimatevariablesshowed thatconeopenedwhenmeantemperatureofdatacollection inter-vals(mostlymonthly)reached19–20◦C(Fig.3).However,when consideringthesubsequentseedrelease,therewasnoapparent relationshipofthenumberofharvestedseedstotemperature vari-ablesormeanrelativehumidity.
Onthecontrary,whentakingintoaccountthepercentageof seeds fallen during the collecting interval related to the over-all amountof seeds tobe released at theend of thedispersal period(sr),asynchronicpatternwithtotalprecipitationwasfound (Fig.8;anomalousvaluesinthistrendwerethosecorresponding toFebruaryandMarchof2007).
Fig.5.Examplesofseedshadowmapsforplot1(STtreatment),plot4(SW treat-ment)andplot7(control).Crossescorrespondtostemslocations.Linesrepresent levelsofequalpredictedseeddensity(valueindicatedbythefigurewithinlines).
as the explanatory variable (see Table 4, Fig. 9). A slight improvementintheAICvaluewasobtainedwhenan autoregres-sivestructure (AR-1) wasapplied withineach dispersal period (rangingfrom285.939withoutstructure to284.538with struc-ture).
Fig.6.Observedvsexpectedseedshadowintrapsi.Solidlineindicatesatheoretical perfectagreementbetweenmodelanddata(slope=1,intercept=0).Dottedline showstherealdegreeofaccordance(slope=0.858;intercept=2.361).
4. Discussion
4.1. Theinversemodellingapproach
We attempted to fit empirical models using inverse mod-elling procedures todescribe and predictseed shadowand, by implication,thespatialpatternofprimaryseeddispersalandits consequencesinnaturalregenerationinP.pinea.Ourmain con-cern wasshortdispersaldistance,particularly,thescopeofthe crown.Therefore, weusedtwocompetingmodels(Weibulland 2Dt) that workproperly atthis scale. Eventhoughthe flexibil-ityofthe2Dtkernelwasdevelopedtoaccountforlongdistance events (Clark et al., 1999b), those models have been reported to underestimatelongdispersal distances (Debain etal., 2007), incomparisonwiththemixturemodelproposedbyBullockand
Clarke(2000).Similarly,mechanisticapproacheswerenottaken
into consideration,as theyhavebeen developedusing physical variables specificallyrelatedtowinddispersalmechanisms(e.g.
GreeneandJohnson,1989;BullockandClarke,2000;Stoyanand
Wagner,2001;butseealsoMartínezandGonzález-Taboada,2009)
oreven tomodelsecondarydispersal byanimals(Greeneetal., 2004).
Aseriousconstraintofinversemodellingisthatplotsizeand spatialdistributionofseedtrapsmayleadtounderestimationof mean dispersal distancewhen leptokurtic dispersal takes place (Robledo-ArnuncioandGarcía,2007).However,thisproblemdoes notseverelyapplytothisstudy,asanextremelyhighkurtosisisnot expectedinP.pinea,providedgravityprimarydispersalstrategyin thespecies.Inaddition,ourregulargridmaximizesthenumber oftrapsbetweenoneandtwocrownradii,wheredroppedseeds intrapscommencetobeuncommon(deficientsamplinginthose circumstancescouldresultinanunreliableparameterestimation). Anindirectconsequenceofdispersalfeatureisthatthearrivalof
Table4
Summaryoftheestimatedcoefficientsforthefittedmodelbetweenvariablesrand thecubicrootofpp(precipitation).ϕistheauto-regressiveparameteroforder1 indicatingcorrelationbetween2consecutiveobservations.
Coefficient Standarderror t p-value
Intercept −0.0989 9.2157 −0.0107 0.9915
3
√
pp 10.1624 2.7346 3.7162 0.0008
Fig.7. Sourcelimitation(SL)anddispersallimitation(DL)indexesvsBA(m2/ha)forthesevenplots.Circlesindicateseedtreetreatment;crosses,shelterwoodtreatment;
andthesquaredsymbolcorrespondstothecontrol.
0 20 40 60 80 100 120
Jun-0 5 Sep-0
5 Dec-0
5 Mar-0
6 Jun-0
6 Sep-0
6 Dec-0
6 Mar-0
7 Jun-07Sep-0
7 Dec-0
7 Mar-0
8 Jun-0
8 Sep-0
8 Dec-0
8 Mar-0
9 Jun-09Sep-0
9 Dec-0
9 Mar-1
0 Jun-1
0 Sep-1
0 Dec-1
0
sr (%)
0 50 100 150 200 250
pp (mm)
Fig.8.Variablesr(solidline)andtotalprecipitationperdispersalperiod(dashedline)intime.Forclarity,wedonotshowsrdatafrom2005to2006and2009to2010 dispersalperiods(negligible).Notethatsr=100correspondstothelastvalueofeachdispersalperiod.
immigrantseedsisexpectedtobeahighlyunlikelyeventinthis case,consideringalsothespatialdispositionofthegridinregard totheplotboundaries.
Ontheotherhand,althoughgeneticanalysisdealswiththese difficulties,dispersalkernelestimationthroughparentage analy-sisrequirestheuseofhighlyvariablemolecularmarkers,which
Fig.9.Regressionmodelforthetemporalpatternofseedrelease (solidline) betweensrandthecubicrootoftotalprecipitation(pp).Datafromthedispersal yearsusedtofitthemodelaredisplayedseparately.
provide an exact identification of all potential seed sources
(Robledo-Arnuncio and García, 2007; Jones and Muller-Landau,
2008).Thisinterestingandpowerfultechniqueisunfeasibletobe
appliedinthecaseofP.pinea,duetotheextremelylowgenetic diversityinthespecies(Vendraminetal.,2008).
Dependingonthenatureofthedata,severalauthorshave pro-poseddifferenttheoreticaldistributionstofitthedispersalmodels. TheobviousapproachisthePoissondistribution,astheresponse variableisobtainedfromcounts(Ribbensetal.,1994;Sagnardetal.,
2007).However,Clarketal.(1998)firstappreciatedthe
unsuit-abilityofthePoissonprocesswhenclumpingofdatawaspresent, suggestingtheuseofthenegativebinomialdistributioninstead. Thisinterestingfindingandthesubsequentproposalmaydealwith clumping,atcostofanextraparameter(),being,inpractice,a generalizationofthePoissonapproach.Indeed,tendstobelarge whendataaccommodatesaPoissonprocess.
The2DtmodelinvolvesthePoissonassumptionbydefinition. Thisvery flexible Gaussianmodeldealsreasonably wellwitha clumpeddatadistribution,notbeingessentialtoconstructcomplex likelihoodfunctions(Clarketal.,1999b).However,weattempted thenegativebinomialfortheWeibullmodel.Parameterestimation became unstable and the clumping parameter frequently pro-duced high figures (>100; in contrast to Clark et al. (1998)). Consequently,weusedthePoissonlikelihoodasaparticularcase ofthenegativebinomialtoachieveaccurateestimates. Difficul-tiesinfittingandlackofstabilityarenotuncommonforpoorly primarydispersedspecies(zoochorousandbarochorusdispersal syndromes)asreportedbyClarketal.(1998)andMartínezand
Eventually,giventhespecificfeaturesofP.pineaspatialprimary dispersal,allmodelsshowedasimilarbehaviorintermsof predic-tion(comparabler2),withslightdifferencesnearbythestem.In addition,thecoefficientofdeterminationwasrelativelylow,asa resultofincreasingvariancewithmeanvalues(Poisson assump-tion),especiallyatshortdistances(belowcrown).
4.2. Modelimprovements
InaccordancewiththefindingsofRodrigoetal.(2007),through ourpreliminaryanalysistoestimatethemaximumrelative disper-saldistance(crownradii),itwasobservedthatseedtrapslocated furtherthantwocrownradiifromthenearesttreeseldomreceived anyseed,dropping 80%ofseedsunderthecrown.This circum-stance,duetotheaforementionedgravitydispersalpatternandto thelowstanddensities,allowedustoassumealimitednumber ofsources associatedwitheach trap.Consequently, itwas pos-sibletoimprovecomputing efficiencytoassess highresolution distancesand,inturn,tosupplymoreaccurateinputsformodel fit.Inaddition,oursystematictrapdesign,deployedthroughouta varietyofstanddensities,providedahighrangeofdistancesunder thisassumption,whichconstitutesadesirablecircumstance(Clark etal.,1998).
Commonly,inversemodellingproceduresreduceseedsources to points. To our knowledge, there is no study where crown sizehasbeentakenintoaccountinkernelparameterization,but
Sagnardetal.(2007)inadifferentcasestudy.Nevertheless,due
totheumbrella-likeshapeofP.pineacrownsandconeoccurrence throughouttheupperfractionofthecrown(Mutkeetal.,2005b), thewholecrownmust beconsideredasa seedsource.Besides, asitssizemaystronglyinfluenceprimaryseedarrival(Barbeito etal.,2008),itisofgreatinteresttopredicttheproportionofseeds droppedbeneathcrowns.Weproposeamethodthatsuccessfully accomplishesthisobjective.Providingthatasummedseedshadow modelimpedesusingrelativedistances(crownradii)betweentrees andtraps,duetodimensionalinconsistence,distancesfromtrap tosourcearecorrected,implyingadoublescale:beyondcrown, distancetothedriplineisknownandunaltered,whereasbeneath crown, relative distances are assessed in terms of crown radii (1crownradius=3.5m,meancrownradiusatourexperimental plots).BeyonditsapplicationinP.pineastands,theapproach pro-videsaninterestingtooltoaccuratelystudyprimarydispersalin large-seededspecieswithbroadcrowns(e.g.genusQuercus),with modestchangestocustomizethemodel(meancrownradius).
Oneofthemaindrawbacksinclassicseedshadowestimation usinginversemodellingisthatitrequiressourcefecundityfigures. Frequently,thesevaluesaredifficulttoachieveandaredefinedas theproductofsomeknownvariablerelatedtoseedproductivity. Forexample,dbh(Ribbensetal.,1994;Clarketal.,1998;Uriarte
etal.,2005)ornumberofcones(Sagnardetal.,2007)plusa
param-etertoestimatenumberofseedsperdbhunitorcone.Adifferent approachwasproposedbyNanosetal.(2010),wherefecunditywas allowtovaryamongtreeswithoutrestrictions.Thesimultaneous estimationoffecundity anddispersalparameters maycomprise highinstabilityintheprocess(Clarketal.,2004;Nanosetal.,2010). Inourapproach,wereducedmodelcomplexityderivedfromthis issuebyestimatingfecundityviatheexistingmodeldevelopedby
Calamaetal.(2008)andthedimensionalcorrectionsassessedby
Morales(2009),whichenableaccuratepredictionofseed
produc-tioninP.pineaasafunctionofdbhandsiteindex.
4.3. Spatialpatternofseeddispersal
The seed shadow estimated from the selected model (W.P) showedahighlyaggregatedspatialpatternofprimaryseed dis-persalfor P.pinea. Therefore,the presenceof dropped seedsis
boundedbeneathcrownsorinnearbyareas(uptotwocrownradii foranaveragetree),infullaccordancewiththefindingsofRodrigo
etal.(2007).Simulationsproducedbytheselectedmodelallowed
toattainsourceanddispersallimitationindexes.Comparisonsof theseindexeswiththecorrespondingbasalareavalueswithineach plotshowedthatsourcelimitationwasnegligibleforallplots con-sidering thewholeperiod,althoughdue tothespecies’masting habit,limitationwouldoccurfrequentlyinnomastyears(Calama
etal.,Unpublisheddata).Nevertheless,theresultssupportedour
hypothesis thatcurrent managementdensitiesare inefficientin regardtodispersallimitation.Forpost-harvestbasalareavalues underbothregenerationfellings(especiallytheseedtreemethod), thecurrentseedshadowsproducedanotablepercentageofgaps wheredispersedseedsarenotexpectedtoarrive.Theseresultsare consistentwiththose fromDallingetal.(2002)when consider-inglarge-seeded,non-zoochorusspecieswithlowdensitieswithin astand.Thisissuecouldlimitnaturalregenerationifstand den-sityisreducedpriortoseedlingestablishment,particularlywhen basalareaisreducedbelowacriticalvalueof10m2/ha(seedtree method).Inthatcircumstance,theremainingtreesareinsufficient tosuccessfullyregeneratethestand,evenifhighlyfavorable disper-saleventstakeplace,andthusnecessitatingartificialregeneration (directseeding).Thisscenarioconstitutesacommoncircumstance givencurrentfellingschedules,involvingdensitiesthatrangefrom 50 to75stems/haduring thefirst 10 years oftheregeneration period(Monteroetal.,2008).
4.4. Temporalpatternofseeddispersal
From a temporal perspective, the results also support our hypothesisthatclimatecontrolsconeopeningandseedreleaseinP.
pinea.Duringourstudy,conesopenedinresponsetoatemperature
threshold(19–20◦C).Accordingly,Tapiasetal.(2001),ina compar-ativestudyundercontrolledconditions,foundthatP.pineacones openingtookplaceasapunctualprocessat28◦C(thelowest tem-peraturetested).Ontheotherhand,therelationshipbetweensrand totalprecipitationcouldbeconnectedtopassivephysicalprocesses involvingscaletissuesstructureandchangesinrelativehumidity (Dawsonetal.,1997).Thatwouldpromoteconescalesmovements, alternativelyopeningand closing thecone,which would facili-tate seed release.Contrastingly, Masettiand Mencussini (1991) observeddispersalpeaksforP.pineaduringthedriestmonthin twocorrelativeyearsinToscana(Italy),althoughthatanalysiswas performedwithouttakingintoaccounttheseasonallydecliningof thecanopyseedbank.In ourcase, suchaneffectwasobserved onlyduringthedispersalpeakthatbeganinMarch2007.Adaily analysisofprecipitationratesshowsthatmostoftherainfalltook placeattheendofthepreviousinterval(February)along correl-ativedays.However,thedispersalpeakwasrecordednextmonth (March,whichwasdrier).Thisdiscrepancymightindicatethatseed releasecanbecontrolledbyalternatedryandhumideventsin cli-matescharacterizedbyalowerandmoreunevenprecipitationthan inToscana,suchastheSpanishNorthernPlateau.Similarly,Nathan
etal.(1999)claimedthatPinushalepensisseedreleasewasstrongly
relatedtoextremelydryandhotclimateevents.Althoughrainfall wasnotinvolvedintheprocess,shortchangesinhumiditywith respecttopriordailyvaluesproducedtherelease.
4.5. Managementimplications
OurfindingssuggestthatunderthecurrentmanagementofP.
pineastandsintheNorthernPlateau,primarydispersalcould
outpoorphysiologicalperformance ofseedlingslocatedbeyond thecrown influence,whereas Calama et al.(Unpublished data) observedhighermortalityinseedlingslocatedbeyondtwocrown radiifromtrees.Inaddition,Awadaetal.(2003)establishedthat
P.pinearesponsetolateshadereleasingdidnotconditionfurther
plantdevelopment.Therefore,theabsenceoflongdispersal dis-tanceeventscouldapparentlybeneficiatethespecies.Themodels developedinthisstudyshowedahighlyclumpeddispersal spa-tialpattern,wheretheoccurrenceofseedrainisintimatelyrelated torainfallevents.Seedlimitationindexesobtainedfromselected modelsimulationssuggestthatnaturalregenerationfailureisdue to,atleastinpart,dispersallimitation.Inaddition,asseedrelease provedclimate-controlled,currentfellingschedulesfollowingno ecologicalcriteriacanresultinunsuitabledensityreductionbefore dispersaltakesplace.Thesespatialandtemporalconstrictionslimit dispersalthroughspaceandtime,andindicatethatpresent silvicul-turepracticesinP.pineastandscanbemodifiedinordertooptimize seedarrival.Areductionintheintensityofregenerationfellings andtheirschedulingafewyearsaftertheoccurrenceoffavorable recruitmenteventswouldreducetheprobabilityofregeneration failurethroughamoreevenlydistributeddispersal.Becausethe controldispersal limitationindexshowedanegligibleseed lim-itationwithrespect tobasal area, theresidual densities atthe beginningoftheregenerationperiodshouldexceed16–18m2/haof basalarea.Regenerationfellingsshouldbelimitedtopost-dispersal periods,aftertherainfallsthatfollowcone openinginthis area (i.e.October–December)inordertoguaranteethereleaseofallthe seeds.Inconclusion,silviculturalrecommendationsbasedonthe modelsdevelopedinthepresentstudywouldincreasethe avail-ableseedinthesoilbanknecessaryforthenextprocessesinnatural regeneration.
Acknowledgements
WearegratefultotheForestServiceoftheJuntadeCastillay LeónandinparticulartoAyuntamientodeElPortilloforpermission toconductthefieldexperiment.WealsowishtothankGuillermo Madrigal and Enrique Garriga for their help in data collection. Finally,wewouldliketoexpressourgratitudetoDavidAffleckfor hissuggestionsonRprogrammingandJuanJoséRobledo-Arnuncio for hishelpful comments that improved notably the text.This researchwassupportedbyINIAprojectRTA2007-00044.
AppendixA. Supplementarydata
Supplementarydataassociatedwiththisarticlecanbefound,in theonlineversion,atdoi:10.1016/j.ecolmodel.2011.11.028.
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