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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:[email protected],[email protected]
(R.Manso),[email protected](M.Pardos),[email protected](C.R.Keyes), [email protected](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.
References
Awada,T.,Radoglou,K.,Fotelli,M.N.,Constantinidou,H.I.A.,2003.Ecophysiologyof seedlingsofthreeMediterraneanpinespeciesincontrastinglightregimes.Tree Physiol.23,33–41.
Barbeito,I.,Pardos,M.,Calama,R.,Ca ˜nellas,I.,2008.Effectofstandstructureon stonepine(PinuspineaL.)regenerationdynamics.Forestry81,617–629. Belisle,C.J.P.,1992.Convergencetheoremsforaclassofsimulatedannealing
algo-rithmsonR(d).J.Appl.Prob.29,885–895.
Bullock,J.M.,Clarke,R.T.,2000.Longdistanceseeddispersalbywind:measuring andmodellingthetailofthecurve.Oecologia124,506–521.
Calama,R.,Canadas,N.,Montero,G.,2003.Inter-regionalvariabilityinsiteindex modelsforeven-agedstandsofstonepine(PinuspineaL.)inSpain.Ann.Forest Sci.60,259–269.
Calama,R.,Gordo,F.J.,Mutke,S.,Montero,G.,2008.Anempiricalecological-type modelforpredictingstonepine(PinuspineaL.)coneproductionintheNorthern Plateau(Spain).For.Ecol.Manage.255,660–673.
Calama,R.,Manso,R.,Barbeito,I.,Madrigal,G.,Garriga,E.,Gordo,F.J.,Montero,G., Ca ˜nellas,I.,Pardos,M.,Unpublisheddata.Doesinter-specificdifferencesinseed sizedeterminenaturalregenerationtraitsinPinuspineaandPinussylvestris? Calama,R.,Montero,G.,2007.Coneandseedproductionfromstonepine(Pinuspinea
L.)standsinCentralRange(Spain).Eur.J.ForestRes.126,23–35.
Calama,R.,Mutke,S.,Tomé,J.,Gordo,J.,Montero,G.,Tomé,M.,2011.Modelling spatialandtemporalvariabilityinazero-inflatedvariable:thecaseofstone pine(PinuspineaL.)coneproduction.Ecol.Model.222,606–618.
Clark,J.S.,Beckage,B.,Camill,P.,Cleveland,B.,HilleRisLambers,J.,Lichter,J., McLach-lan,J.,Mohan,J.,Wyckoff,P.,1999a.Interpretingrecruitmentlimitationin forests.Am.J.Bot.86,1–16.
Clark,J.S.,LaDeau,S.,Ibanez,I.,2004.Fecundityoftreesandthe colonization-competitionhypothesis.Ecol.Monogr.74,415–442.
Clark,J.S.,Macklin,E.,Wood,L.,1998.Stagesandspatialscalesofrecruitment limi-tationinsouthernAppalachianforests.Ecol.Monogr.68,213–235.
Clark,J.S.,Silman,M.,Kern,R.,Macklin,E.,HilleRisLambers,J.,1999b.Seed disper-salnearandfar:patternsacrosstemperateandtropicalforests.Ecology80, 1475–1494.
Dalling,J.W.,Muller-Landau,H.C.,Wright,S.J.,Hubbell,S.P.,2002.Roleofdispersal intherecruitmentlimitationofneotropicalpioneerspecies.J.Ecol.,90. Dawson,J.,Vincent,J.F.V.,Rocca,A.M.,1997.Howpineconesopen.Nature390,
668.
Debain,S.,Chadoeuf,J.,Curt,T.,Kunstler,G.,Lepart,J.,2007.Comparingeffective dispersalinexpandingpopulationofPinussylvestrisandPinusnigraincalcareous grassland.Can.J.For.Res.37,705–718.
Ganatsas,P.,Thanasis,G.,2010.PinushalepensisinvasioninPinuspineahabitatin Strofyliaforest(SiteofNATURA2000network),southernGreece.J.Nat.Conserv. 18,106–117.
Gómez-Aparicio,L.,Gómez,J.M., Zamora,R.,2007. Spatiotemporalpatterns of seeddispersal inawind-dispersedMediterranean tree(Aceropalussubsp granatense):implicationsforregeneration.Ecography30,13–22.
González-Martínez,S.C.,Burczyk,J.,Nathan,R.,Nanos,N.,Gil,L.,Alía,R.,2006. Effec-tivegenedispersalandfemalereproductivesuccessinMediterraneanmaritime pine(PinuspinasterAiton).Mol.Ecol.15,4577–4588.
Greene,D.F.,Canham,C.D.,Coates,K.D.,Lepage,P.T.,2004.Anevaluationof alterna-tivedispersalfunctionsfortrees.J.Ecol.92,758–766.
Greene,D.F.,Johnson,E.A.,1989.Amodelofwinddispersalofwingedorplumed seeds.Ecology70,339–347.
Jones,F.A.,Muller-Landau,H.C.,2008.Measuringlong-distanceseeddispersalin complexnaturalenvironments:anevaluationandintegrationofclassicaland geneticmethods.J.Ecol.96,642–652.
Levin,S.A.,Muller-Landau,H.C.,Nathan,R.,Chave,J.,2003.Theecologyand evolu-tionofseeddispersal:atheoreticalperspective.Annu.Rev.Ecol.Evol.Syst.34, 575–604.
Magini,E.,1955.Sullecondizionidigerminazionedelpinod’Aleppoedelpino domestico.ItaliaForestaleeMontana,AnnoX:,106–124.
Manso,R.,Calama,R.,Madrigal,G.,Garriga,E.,DeBlas,S.,Gordo,F.J.,Pardos,M. Dis-persiónprimaria,dispersiónsecundariaypredaciónpost-dispersiónenPinus pineaL.In:J.Gordo,R.Calama,M.Pardos,F.BravoandG.Montero(Eds.),La regeneraciónnaturaldePinuspineaL.yPinuspinasterAit.enlosarenalesde laMesetaCastellana.ActasdelasIJornadasdeTransferenciaTecnológicay Científica,inpress.
Manso,R.,Pardos,M.,Garriga,E.,DeBlas,S.,Madrigal,G.,Calama,R.,2010.Modelling thespatial–temporalpatternofpost-dispersalseedpredationinstonepine (PinuspineaL.)standsintheNorthernPlateau(Spain).In:FrugivoresandSeed Dispersal:MechanismsandConsequencesofaKeyInteractionforBiodiversity, Montpellier,France.
Martínez,I.,González-Taboada,F.,2009.Seeddispersalpatternsinatemperate for-estduringamastevent:performanceofalternativedispersalkernels.Oecologia 159,389–400.
Masetti,C.,Mencussini,M.,1991.Régénérationnaturelledupinpignon(Pinuspinea L.)danslaPinetaGranducalediAlberese(ParcoNaturalledellaMaremma, Toscana,Italie).Ecol.Mediterr.17,103–188.
Montero,G.,Calama,R.,RuizPeinado,R.,2008.SelviculturadePinuspineaL.In: Montero,G.,Serrada,R.,Reque,J.(Eds.),CompendiodeSelviculturadeEspecies. INIA—FundaciónCondedelValledeSalazar,Madrid,pp.431–470.
Morales,L.,2009.Modelosparalaprediccióndelcontenidoycalidaddepi ˜nónen pi ˜nasdePinuspineaL.enlosvallesdelTiétarydelAlberche.MasterThesis, UniversidadPolitécnicadeMadrid,Madrid.
Muller-Landau,H.C.,Wright,S.J.,Calderon,O.,Condit,R.,Hubbell,S.P.,2008. Inter-specificvariationinprimaryseeddispersalinatropicalforest.J.Ecol.96, 653–667.
Muller-Landau,H.C.,Wright,S.J.,Calderón,O.,Hubbell,S.P.,Foster,R.B.,2002. Assess-ingrecruitmentlimitation:concepts,methodsandcase-studiesfromatropical forest.In:Levey,D.J.,Silva,W.R.,Galetti,M.(Eds.),SeedDispersaland Fru-givory:Ecology,EvolutionandConservation.CABInternational,Wallingford, pp.35–53.
Mutke,S.,Gordo,J.,Gil,L.,2005a.VariabilityofMediterraneanstonepinecone pro-duction:yieldlossasresponsetoclimatechange.Agric.ForestMetereol.132, 263–272.
Mutke,S.,Sievanen,R.,Nikinmaa,E.,Perttunen,J.,Gil,L.,2005b.Crownarchitecture ofgraftedstonepine(PinuspineaL.):shootgrowthandbuddifferentiation.Trees 19,15–25.
Nanos,N.,Larson,K.,Milleron,M.,Sjostedt-deLuna,S.,2010.Inversemodelingfor effectivedispersal:doweneedtreesizetoestimatefecundity?Ecol.Model.221, 2415–2424.
Nathan,R.,Katul,G.G.,Horn,H.S.,Thomas,S.M.,Oren,R.,Avissar,R.,Pacala,S.W., Levin,S.A.,2002.Mechanismsoflong-distancedispersalofseedsbywind. Nature418,409–413.
Nathan,R.,Safriel,U.N.,Noy-Meir,I.,Schiller,G.,1999.Seedreleasewithoutfire inPinushalepensis,aMediterraneanserotinouswind-dispersedtree.J.Ecol.87, 659–669.
Nathan,R.,Safriel,U.N.,Noy-Meir,I.,Schiller,G.,2000.Spatiotemporalvariationin seeddispersalandrecruitmentnearandfarfromPinushalepensistrees.Ecology 81,2156–2169.
Ordó ˜nez,J.L.,Molowny-Horas,R.,Retana,J.,2006.AmodeloftherecruitmentofPinus nigrafromunburnededgesafterlargewildfires.Ecol.Model.197,405–417. Pardos,M.,Puertolas,J.,Madrigal,G.,Garriga,E.,deBlas,S.,alama,R.,2010.
Sea-sonalchangesinthephysiologicalactivityofregenerationunderanaturallight gradientinaPinuspinearegularstand.ForestSyst.19,367–380.
Prada,M.A.,Gordo,J.,DeMiguel,J.,Mutke,S.,Catalán,G.,Iglesias,S.,Gil,L.,1997. LasregionesdeprocedenciadePinuspineaL.enEspa ˜na.MinisteriodeMedio Ambiente,Madrid.
Ribbens, E., Silander, J.A., Pacala, S.W., 1994. Seedling recruitment in forests—calibratingmodels topredictpatterns oftree seedlingdispersion. Ecology75,1794–1806.
Robledo-Arnuncio,J.J.,García,C.,2007.Estimationoftheseeddispersalkernelfrom exactidentificationofsourceplants.Mol.Ecol.16,5098–5109.
Rodrigo,A.,Quintana,V.,Retana,J.,2007.FirereducesPinuspineadistributioninthe northeasternIberianPeninsula.Ecoscience14,23–30.
Sagnard,F.,Pichot,C.,Dreyfus,P.,Jordano,P.,Fady,B.,2007.Modellingseeddispersal topredictseedlingrecruitment:recolonizationdynamicsinaplantationforest. Ecol.Model.203,464–474.
Santos,B.A.,Melo,F.P.L.,Tabarelli,M.,2006.Seedshadow,seedlingrecruitment,and spatialdistributionofBuchenaviacapitata(Combretaceae)inafragmentofthe BrazilianAtlanticForest.Braz.J.Biol.66,883–890.
Schütz,J.P.,2002.Silviculturaltoolstodevelopirregularanddiverseforest struc-tures.Forestry45,329–337.
Stoyan,D.,Wagner,S.,2001.Estimatingthefruitdispersionofanemochorousforest trees.Ecol.Model.145,35–47.
Tapias,R.,Gil, L.,Fuentes-Utrilla,P.,Pardos, J.A.,2001.Canopy seedbanksin Mediterranean pines of southeasternSpain: a comparison betweenPinus halepensis Mill., P.pinaster Ait., P.nigra Arn. and P. pinea L. J. Ecol. 89, 629–638.
RDevelopmentCoreTeam,2009.R:ALanguageandEnvironmentforStatistical Computing.RFoundationforStatisticalComputing,Vienna,Austria. Tsakaldimi,M.N.,Tsitsoni,T.K.,Zagas,T.,Ganatsas,P.P.,2004.Aleppopine(Pinus
halepensis)naturalregeneration,withoutfire,intheKassandraPeninsula, north-ernGreece.In:Papanastasis,A.(Ed.),MEDECOSConference.25thApril–1stMay. Millpress,Rhodes,Greece.
Uriarte, M., Canham, C.D., Thompson, J., Zimmerman, J.K.,Brokaw, N., 2005. Seedlingrecruitmentinahurricane-driventropicalforest:lightlimitation, density-dependenceandthespatialdistributionofparenttrees.J.Ecol.93, 291–304.
Vendramin,G.G.,Fady,B.,Gonzalez-Martinez,S.C.,Hu,F.S.,Scotti,I.,Sebastiani,F., Soto,A.,Petit,R.J.,2008.Geneticallydepauperatebutwidespread:thecaseofan emblematicmediterraneanpine.Evolution62,680–688.
Weise,W.,1880.ErtragstafelnfürKiefer.J.Springer.
