Applied Hierarchical Modeling in Ecology. Analysis of distribution, abundance and species richness in R and BUGS: Volume 1: Prelude and Static Models

792 Pages·2016·35.856 MB·English

by  Kéry, Marc, Royle, J. Andrew

Applied Hierarchical
Modeling in Ecology
Analysis of distribution, abundance
and species richness in R and BUGS
Volume 1
Prelude and Static Models
Marc Ke´ry
Swiss Ornithological Institute,
Sempach, Switzerland
J. Andrew Royle
USGS Patuxent Wildlife Research Center,
Laurel MD, USA
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J.A.Roylewastheprincipalauthorofchapters2,7,8,9.Useofproductnamesdoesnotconstitute
endorsementbytheU.S.Government.
For Jim Nichols, who changed the way in which we think about Ecology
Foreword
Istartedgraduateschoolin2003workingonasimpleprojecttounderstandhowforestmanagement
practicesaffectbirdpopulationsintheWhiteMountainNationalForestinNewHampshire,USA.As
withmanyprojectsofitskind,wecollectedpointcountdatatocharacterizeabundanceatacollection
ofsitesthathadreceiveddifferentmanagementactions.Knowingthatwewouldfailtodetectmanyof
theindividualspresentatseveralsites,andthatdetectionprobabilitymightcovarywithhabitat vari-
ables, my adviser David King recommended that we survey each site multiple times and record the
distance to each individual detected. When the field season came to an end, I had my data in hand
andwasreadytoknockoutaquickanalysis.Thatiswhenthedifficultiesbegan.ThefirstthingItried
wasamultipleregression,butIwasimmediatelystumpedastowhattheappropriateresponsevariable
was.Shoulditbethemeannumberofindividualsdetectedateachsite,themaximumnumberdetected,
orperhapsthemedian?Differentauthoritiesrecommendeddifferentstrategies,andtomydismay,the
resultsdifferedwitheachapproach.Inadditiontothisproblem,itwasapparentthatthemodelmadeno
distinction between the explanatoryvariables that I had collected todescribevariationin abundance
andthevariablesthatIhadcollectedtoexplainvariationindetection.Asaresult,Icouldusemymodel
topredicttheeffectofmanagementonobservedcounts,butnotonabundance,thestatevariablethatI
was actuallyinterested in.
Isoonabandonedtheregressionapproachandturnedmyattentiontodistancesamplingmethods.
Hereagain,IwasquicklysurprisedtofindthatalthoughIcouldpoolmydatatoaccountfortheeffect
of distance on detection probability, I couldn’t directly model the effects of management variables
(someofwhichwerecontinuous)onabundance.Eventhetwo-stageapproachesthatwererecommen-
dedatthetimewerenotpossiblebecauseofthesparsenessofmydata,whichincludedmanysiteswith
nodetections.Moreover,evenifIhadbeenabletocorrectfordetectionandthenmodelmyestimates,
itwouldhavebeenverydifficulttoproperlyaccountforthecovarianceoftheestimates.AsIsearched
for solutions to these problems, my despair continued to grow as I read several distance sampling
papers proclaiming that the data I had worked so hard to collect might be impossible to use for my
purpose. Theonly option seemed to beto study somethingelse!
Andthenin2004,AndyRoyleandcolleaguespublishedtwopapersthatseemedtohavebeenwrit-
ten with exactly my problem in mind. Royle (2004b, Biometrics) demonstrated how repeated count
datacouldbeusedtomodelspatialvariationinabundancewhileaccountingforvariousfactorsinflu-
encingdetectionprobability,andRoyleetal.(2004,Ecology)explainedhowspatialvariationinabun-
dance could be modeled using distance data collected using standard point count survey methods.
UnlikeallothermethodsIhadseen,therewasnoneedtodoatwo-stageanalysis,anditwasstraight-
forwardtomodelcovariatesofbothabundanceanddetection.Herewerehierarchicalmodelsthatnot
onlyprovidedconceptualclarity,butallowedmetomakefulluseofmydatasothatIcouldtestthe
hypotheses I was interested in.
There was only one problem with the exciting models that I was reading aboutdI had no clue
howtofitthemtomydata.Ihadtakenacoupleofstatisticscourses,butIhadneverheardofmar-
ginallikelihood,andIcertainlyhadnoideahowtowritecodetomaximizeanintegratedlikelihood
function.Theverynextyear,however,MarcKe´ry,AndyRoyle,andHansSchmidpublishedapaper
in Ecological Applications that provided additional details about these models, and the paper
included an appendix with a short R script that demonstrated how to obtain maximum likelihood
ix
x FOREWORD
estimates. It’s no exaggeration to say that I learned more about statistics and programming by
trying to understand this one bit of code than I did from any formal education up to that point.
From there, I quickly began modifying the code to make it more general and to deal with other
typesofdatathatIhadgathered.Thiseventuallyledmetodevelopsomegeneralfunctions,which
werecomingtogetherjustasIlearnedaboutanRpackagebeingdevelopedbyIanFisketo fitthis
class of models. I offered to help, and even though I never met Ian in person, we had a couple of
good years of collaboration that resulted in the R package unmarked.
The reason for conveying this bit of personal history is not just to make the point that Marc and
Andyhavehadahugeimpactonmyowncareer,buttoconveyastorythatIknowappliedecologists
aroundtheworldcanrelateto.Simplepracticalproblemsturnouttoposeseriouschallengeswhenwe
areunabletodirectlyobservetheprocessesofinterest.Indicesofabundanceandpopulationtrendsare
nearly useless when we’re concerned about absolutes like extinction risk or harvest limits. Applied
ecologistshaverecognizedtheseproblemsforalongtime,andhierarchicalmodelsprovideasolution
byenablingresearcherstodirectlymodeltheecologicalprocess,ratherthansomepoorlydefinedin-
dex,whilealsomodelingtheobservationprocess.Moreover,thesemodelsallowpractitionerstosolve
problemsinsuchawaythattheresultscanbeclearlycommunicatedtomanagersandpolicymakers.
Butwhydidittakesolongforthesemethods,thefoundationsofwhichweredevelopedalongtime
ago,tomaketheirwayintothehandsofpractitioners?Inmyopinion,thepowerofhierarchicalmodels
wouldneverhavebeenrealizedhaditnotbeenforresearcherslikeMarcandAndy,whohavedelib-
eratelyworkedtomakethesetoolsaccessibletothoseofuslackingadvanceddegreesinstatistics.This
bookisaphenomenalsynthesisofthateffort.Unlikemanybooksonstatisticalmodelingthatseemto
havebeenwrittenbystatisticiansforstatisticians,themainaudienceofthisvolumeisclearlytheprac-
ticing ecologist. The writing style is clear and engaging, and for virtually every technical problem,
workedexamplesandcodeareprovided.Thisaccomplishment,ofdistillingadvancedmodelingtech-
niquesintoanaccessibleformat,isinmyviewoneofthetwogreatcontributionsofthisworktoecol-
ogyand related environmentalsciences.
Thesecond great contributionofthisworklies outside thecontextofappliedresearch.Thehier-
archicalmodelingapproachthathasbeendevelopedandillustratedhereispartofanemergingtrend,
one that is far moregeneral and in someways far more consequential for ecology as a science. The
methods covered in this book provide a framework for advancing knowledge of ecological systems
by narrowing the chasm between theoretical and statistical models. It has always struck me as trou-
bling that the mathematical models covered in ecology textbooks often fall by the wayside when
we get our hands on data. As soon as the data are facing us on the computer, the instinct arises to
turn toward the latest development in statistics and leave theory behind. For example, we have
>100yearsoftheoryonthefactorslimitingspeciesdistributionsdfactorssuchascompetition,Allee
effects,andphysiologicalconstraintsdyetwecramdata,oftencollectedforotherpurposes,intospe-
ciesdistributionmodelsthatignoredemographicprocessesandbioticinteractions,nottomentionthe
observationprocessesthatwillcauseseverebiasifignored.Or,weoftenhavedatafrommetapopula-
tionsthatwerunthroughamachinelearningalgorithmortowhichwefitsomesortofGAMwithloads
of random effects. The tools described in this book provide an alternative. They offer a framework
thatallowsonetofitmetapopulationmodelstometapopulationdata,toestimatethestrengthofbiotic
interactions, and to test for effects of abiotic covariates on abundance, occurrence, or population
growth rates. This is the power of hierarchical modeling: that we can tailor our statistical models to
the scientific questionat hand and notthe otherway around.
FOREWORD xi
This is not to say that this book is full of theory. Rather, it provides the tools necessary to build
hierarchical models based on theory instead of relying on purely phenomenological approaches.
Why is this so important at this point in time, when focus is increasingly shifting to prediction?
Why don’t we just hire a team of Netflix data miners to forecast the future of ecological systems?
In my view, prediction without mechanism falls well outside the realm of science. For instance, we
knowthatwecandevelopgoodpredictivemodelsbysimplymodelingspatialandtemporalautocor-
relation.Abundanceatonelocationcanoftenbeaccuratelypredictedasafunctionofabundanceatan
adjacentlocation,justasvotinghabitsinonecountycanbepredictedfromthebehaviorofneighboring
counties,andjustastheweathertodayoftentellsussomethingabouttheweathertomorrow.Butwhat
islearned about the underlying processes fromfitting modelslacking mechanism?Very little,inmy
estimation,whichiswhyI’mhappytohavethisnewbookthatpresentssuchapowerfulalternative.
Asgreatasthehierarchicalmodelingframeworkis,Ithinkitisimportanttoemphasizethatitisnot
meanttobeanalternativetoclassical methods ofexperimental designandanalysis.Infact, Iwould
suggest that it is only via manipulative experiments that can we achieve the ultimate goal of causal
inference. The problems we face in ecology, however, are that we often cannot bring our system
into the lab, and we can’t always manipulate one component while holding the others constant. To
complicatemattersfurther,processesthatholdatonepointinspaceandtimemayoperatedifferently
atanother.Wearethereforeforcedtocombineexperimentalapproacheswithobservationalonesifwe
wishtoadvanceknowledgeandinformconservationefforts.Onceagain,themethodspresentedinthis
bookprovideaformalwayofbuildingmechanismsintoourmodelssothatwecanunifytheinsights
gained from experimental studies with the information contained in field data. It is this unified
approachthatIthinkoffersthegreatestpromiseforadvancingourfield,anditisexcitingtobeworking
inatimewhenwefinallyhavethetoolsavailableforthetask.SoitiswithgreatpleasurethatIcongrat-
ulateMarcandAndyonafantasticbook,onethat,aslargeasitis,isjustthebeginning.I’llbelooking
forward tothe nextvolumeand allthe excellent work thatissure tobenefit from it.
Richard Chandler
UniversityofGeorgia
Preface
Thisisvolume1ofournewbookontheappliedhierarchicalmodelingofthethreecentralquantitiesin
ecologydabundance,ordensity,occurrence,andspeciesrichnessdaswellasofparametersgoverning
theirchangeovertime,especiallysurvivalandrecruitment.Hierarchicalmodelingisagrowthindustryin
ecology.Inthelast10yearstherehavebeenadozenormorebooksfocusedonhierarchicalmodelingin
ecology including Banerjee et al. (2004), Clark and Gelfand (2006), Clark (2007), Gelman and Hill
(2007),McCarthy(2007),RoyleandDorazio(2008),Kingetal.(2009),LinkandBarker(2010),Ke´ry
and Schaub (2012), Hobbs and Hooten (2015), etc. How can we possibly add 700þ more pages (and
perhaps1500ifyoucountvolume2)towhatisknownonthistopic?That’sagoodquestion!
Inthis bookwe cover severalclasses ofmodelsthat havepreviouslyreceivedonly cursoryorno
treatmentatallinthehierarchicalmodelingliterature,andyettheyareextremelyimportantinecology
(e.g., distance sampling). Moreover, we give complete recipes for analyzing these models and all
otherscoveredinthebook,usingprogramRingeneralandtheRpackageunmarkedinparticular,and
very extensively using the generic Bayesian modeling software BUGS. The use of unmarked is
completely novel compared to these other books. Some models that we cover here and especiallyin
volume2weresimplyunimaginableacoupleyearsago,e.g.,theopenhierarchicaldistancesampling
models, the metacommunity abundance models and models with explicit population dynamics (i.e.,
the famousmodelof Dail and Madsen, 2011), which can be fittocountsand relateddata,including
evendistancesamplingdata.Muchofthismaterialisextremelynew,andsomehasonlyjustappeared
intheliteratureinthelastyearorso.Thus,thisbookrepresentsatimelysynthesisandextensionofthe
state of hierarchical modeling in ecology that builds on previous efforts, but covers much new and
importantterritory,andprovidesimplementationsusingboththelikelihood(unmarked)andBayesian
(BUGS)frameworks.
A BOOK OF MONOGRAPHS
In a sense, Applied Hierarchical Modeling for Ecologists (AHM) is a book of books, or a book of
monographs.Volume1containsthefirsttwoparts,aprelude,whichintroducesthenecessaryconcepts
andtechniquesinfivechapters,followedbysixchaptersthatdealwithstaticdemographicmodelsof
distribution, abundance, and species richness and other descriptors of communities and meta-
communities. Volume 2 will contain two further parts on dynamic models and on advanced
demographicmodelsforpopulationsandcommunities;seebelowformoreinformationonthedivision
of topics betweenvolumes1 and2 of AHM andon the content that we envision for volume2.
Looking back at volume 1 now, at the time of writing of this preface, we feel as if we have
packaged almost a dozen independent books into this one book. There are general, introductory
“monographs”ontheconceptsofdistribution,abundance,andspeciesrichnessandtheirmeasurement
andmodelinginpractice(Chapter1),onhierarchicalmodelsandtheiranalysis(Chapter2),onlinear,
generalized linear, and mixed models (Chapter 3), on data simulation in R (Chapter 4), and on the
celebrated BUGS language and software (Chapter 5). After that, there are six comprehensive
monographsondemographicmodelsfordistribution,abundance,andspeciesrichnessinthecontextof
whatwecalla“meta-populationdesign,”thatis,theextremelycommonsituationwhereyoumeasure
something in apopulation ora community at morethan asingle point inspace.
In the prelude, and following the introductory Chapter 1, we have one monograph to cover hi-
erarchical models (HMs) and their Bayesian and frequentist analyses (Chapter 2). The next
xiii
xiv PREFACE
monograph (Chapter 3) provides a highly accessible review of that “heart” of applied statistics:
linearmodels,generalizedlinearmodels(GLMs),andsimplemixedmodels,allofthemillustrated
in the context of one extremely simple ecological data set. Data simulation is one of the defining
featuresofthisbookbecauseitprovidessuchimmensebenefitsfortheworkofecologists(andalso
for statisticians). Hence, the next monograph (Chapter 4) is dedicated to this essential topic and
walks you through the R code necessary for the generation of one simple type of data set that is
fundamentaltotheclassesofmodelscoveredinthisbook:thecasewhereonegoesoutandcounts
birds(oranyotherspecies)atmultipleplaces(e.g.,20,100,or267)andrepeatsthesecountsateach
site multiple times (e.g., 2 or 3).
The BUGS model definition language is implemented in three currently used BUGS engines for
Bayesian inference: WinBUGS (Lunn et al., 2000), OpenBUGS (Thomas et al., 2006), and JAGS
(Plummer, 2003). It has also just been adopted in the exciting new R package NIMBLE (NIMBLE
DevelopmentTeam,2015;deValpineetal.,inreview),whichisageneralmodelfittingsoftwarethat
uses and extends the BUGS language for flexible specification of HMs and allows analysis of HMs
with both maximum likelihood and Bayesian posterior inference.
Over the first 25 years of its existence, BUGS has been instrumental in the surge of Bayesian
statisticsinallkindsofsciencesincludingecology(Lunnetal.,2009).Ithasgrownbyfarintothemost
importantgeneral,Bayesianmodelinglanguage,anditsuserpopulationkeepsgrowingatarapidrate
(andofcoursewehopetoincreasethatrateevenmorewiththisbook).BUGSisuniqueingivingyou
asa nonstatistician amodeling freedom that lets you develop, test,and fit models that you wouldn’t
even have dared to dream of in the pre-BUGS era of ecological modeling (which we might call the
ecological Stone Age;.). Although there are now many useful introductory books on BUGS (e.g.,
McCarthy, 2007; Ke´ry, 2010; Lunn et al., 2013; Korner-Nievergelt et al., 2015), we have decided to
writeyetanotherpracticalBUGSintroductionandpackageitintoChapter5.Itisourlatestandbest
attemptatcoveringasmuchaspossibleonthistopicandincludingsomeofthelatesttricksinBUGS
modelinginamere70bookpages,illustratingtheuseofallthreeBUGSenginesandfocusingonthe
models covered in Chapter 3, i.e., linear models, GLMs, and simple mixed models. By introducing
BUGSforexactlythekindsofmodelsthatyouarelikelytobefamiliarwithalready,wehopetomake
itespeciallyeasy for youtograspthe Bayesiansideofthe analysisandthe implementationofthese
essential models inthe BUGS language.
Inthesecondpartofthebook,wepresentsixmonographsthatcontainacomprehensivetreatment
ofimportantclassesofmodelsforinferenceaboutdistribution,abundance,andspeciesrichness,and
relateddemographicpopulationorcommunitymetricsinso-called“meta-populationdesigns”(Royle,
2004a;Ke´ryandRoyle,2010),i.e.,forthefrequentcasewhereyouareinterestedinthesethingsnotat
a single place but have studied them at multiple sites. Specifically, in Chapter 6 we cover binomial
mixture, or N-mixture, models (Royle, 2004b), which are a unique type of model for count data on
unmarkedindividuals(thatis,youdonotneedtokeeptrackofwhichindividualiswhichacrossthe
repeatedmeasurementsofabundanceatasite)andthatcontainsanexplicitmeasurementerrormodel,
whichcorrectsyourinferencesforthebiasesthatwouldotherwisebecausedbyundercountingdueto
imperfect detection probability. Chapter 7 covers a “sister-type” of model, the multinomial mixture
model(Royle,2004a;Dorazioetal.,2005),whichonlydiffersfrombinomialmixturemodelsinthe
typeofdatatowhichitisfitted:typicallyyouneedindividualrecognition,thatis,youhavecapture-
recapture-type of data, but again collected not at a single site but at multiple places. Both types of
mixture models havebeen around for about 10yearsnowandpreviouslythey havebeen featured in
PREFACE xv
someoftheabove-citedhierarchicalmodelingbooks(mostlyinRoyleandDorazio,2008),butnever
beforehavetheybeencoveredinsuchdetailand,especially,inamannerthatmakesthemsoaccessible
to youas anecologist.
Chapters 8 and 9 are special in that they provide perhaps the first large, and yet practical and
applied, synthesis in distance sampling more than 10years after the two classics by Buckland et al.
(2001,2004a)werepublished.Inourtwodistancesamplingmonographs,weprovideafresh,newlook
atdistancesamplinginthecontextofhierarchicalmodelsinanessentiallybook-lengthtreatment.We
hopethatthiswillhelptomakethisimportanttypeofmodelevenmorewidelyunderstoodandusedby
ecologists.Whilewecovermainlystaticmodelsinvolume1andthencoverdynamicmodelsinmore
detailinvolume2ofAHM,wehavedeviatedslightlyfromthisruleinChapters8and9,wherewehave
preferred topical unity over conceptual unity by keeping all of distance sampling (closed and open)
together.Nevertheless,weplantocoverseveralmorecutting-edgeopenandothernovelextensionsof
hierarchical distance sampling (HDS) models involume2.
These two monographs, and more specifically the wealth of material on hierarchical distance
sampling,areperhapsthosewithmostnoveltyinourbook.Thoughagaininventedjustover10years
ago(around2004),HDShasrecentlyexperiencedaboostwiththewidespreadrealizationthatthistype
of specification of distance sampling models enables extremely flexible modeling of spatially or
temporally replicated distance sampling data or combined analyses of data sets collected under
differingprotocols(“integratedmodels”),whichwasthoughtimpossiblebeforeoratleastwasnever
achieved.Forinstance,itisperfectlydoable(oreventrivial)tomodelpopulationdynamics(Sollmann
et al., 2015) or community size and composition (Sollmann et al., in press) from distance sampling
data within the context of hierarchical models. And, the power of BUGS nowadays makes the
implementation of such models possible even for ecologists, since really such models differ in only
relatively minor waysfrom similarmodels for otherdata types (e.g., of the capture-recapture type).
Hence, we hope that we contribute to change your view of “capture-recapture” and “distance
sampling”asbeingtwowidelyseparatedfieldstoanewwayofseeingthemasreallyrelativelyminor
variations on the overarching theme of hierarchical models, which have one model component for
abundance,ordensity,andinanothermodelcomponentdescribethemeasurementerrorthatinduces
imperfectdetectionandthereforeundercounting(Borchersetal.,2015).Theonlythingthatchanges
whenyoumovefromacapture-recapturetoadistancesamplingmodelisthespecificparameterization
ofthemeasurementerrorunderlyingtheobserveddataandofcoursethetypeofdatathatyouneedto
estimate the parameters of that measurement error model. This wonderful, unifying power of
describing statistical models in a hierarchical way lets youmuch bettergrasp the similaritiesamong
large numbers of models that were often thought as totally distinct hitherto. It is one of the main
themesofthisbookandoneonwhichwewillsaymuchmorethroughoutthebook.Forinstance,we
hope that you will recognize that there are really only quite minor differences between a binomial
mixturemodelforcountsofunmarkedindividuals,amultinomialmixturemodelforcapture-recapture
data,andahierarchicaldistancesamplingmodeldtheonlydifferenceisagainthemeasurementerror
model,whilethestatemodel,thatis,thedescriptionoftheessentialbiologicalquantity(abundanceor
density), is exactly the sameinall three types ofmodels.
Thepenultimatemonograph(Chapter10)isonoccupancymodeling(MacKenzieetal.,2002;Tyre
et al., 2003). This powerful type of model for occurrence or distribution comes with an explicit
measurement error component model for both false-negatives and false-positives (models by Royle
andLink,2006;Aingetal.,2011;Milleretal.,2011,2013b;Sutherlandetal.,2013;Chambertetal.,
xvi PREFACE
2015) or with a measurement error model for false negatives only (all other types of occupancy
models).Occupancymodelshavebecomehugeinecologyandhaveexperiencedasteepgrowthcurve
in both the number of papers that further develop the theory of these models and especially also in
studiesthatapplythisdesignandtheassociatedmodels.(Wehaveevenheardrumorsthatthevigorous
growthofthefieldhas“scared”someecologyjournaleditorssothattheyputacaponthenumberof
occupancy papers they acceptda strange way of stifling progress one would think.) Occupancy
modelshavereceivedonebook-lengthtreatisesofar(MacKenzieetal.,2006),withasecondedition
that is in preparation, and several customized software products that specialize in them, especially
PRESENCE(Hines,2006)andMARK(WhiteandBurnham,1999;CoochandWhite,2014).Inthis
firstAHMvolume,wedealwithsingle-speciesoccupancymodelsingreatdetailandcoversometopics
(e.g.,somemodelsfordatacollectedalongspaceortime“transects”)thathaven’tbeencoveredinany
bookbefore.Involume2,wewilladdseveralmoremonographsonalargevarietyofoccupancymodel
types; see below.
The final monograph involume 1 covers community models, that is, community or multispecies
variants of all the previous models. Specifically, we cover the community variant of an occupancy
model (Chapter 10) and the community variant of a binomial N-mixture model (Chapter 6). These
powerfulhierarchicalmodelsenableinferencesatmultiplescales,thatoftheindividualspecies,thatof
alocalcommunity,andthatofanentiremetacommunity.Asalwaysinthisbook,bothcomewithan
explicitmeasurementerrormodelforthedesiredstateofinference,presence/absence,orabundanceof
eachindividualspeciesateverysiteinthe“meta-population.”Thesemodelshaveexperiencedmuch
increasedattentionintheveryrecentpast(Iknayanetal.,2014;Yamauraetal.,2012,inpress),andwe
provideamuchneeded,comprehensiveandyetsupremelypracticalmonographonboththeabundance
andon the occupancy-basedcommunity models.
Ofcourse,apartfromservingasastandaloneintroductiontothislargerangeofpowerfulanduseful
hierarchical models, the material in volume 1 also lays the groundwork for more models and more
advanced material in volume 2. See below for more about the division of content between the two
volumes.
UNIFYING THEMES
AHM is not just a hodgepodge of models that have not previously been covered in detail or at all.
Rather, our developmentand organization ofthese models has a number ofunifying themes that we
emphasize throughout the book:
(cid:129) hierarchical modeling
(cid:129) data simulation
(cid:129) measurement error models
(cid:129) dual inference paradigmapproach (Bayesianismand frequentism)
(cid:129) accessible andgentle style (including hierarchical likelihood construction and data simulation)
(cid:129) “cookbookrecipes”
(cid:129) predictions
One, we advocate hierarchical modeling as a unifying concept and overarching principle in
modelingandalsoconceptually;aswehaveemphasizedbefore,whenseenasHMsallthesemodels
almostlookthesame(orverysimilar)anditisquitetrivialtomovefromonetoanother,e.g.,froma
capture-recapturemodeltoadistancesamplingmodeltoanoccupancymodeloreventoacommunity