EstimatingtrophicdiscriminationfactorsusingBayesian
inferenceandphylogenetic,ecologicalandphysiologicaldata.
DEsiR:DiscriminationEstimationinR.
KevinHealy1.,SeánB.A.Kelly1,ThomasGuillerme2,RichardInger3,Stuart
Bearhop3andAndrewL.Jackson1.
TrinityCollegeDublin,DepartmentofZoology,SchoolofNaturalSciences,Dublin,IrelandandtheTrinityCentrefor
BiodiversityResearch,TrinityCollegeDublin,Dublin2,RepublicofIreland.2ImperialCollegeLondon,SilwoodPark
Campus,DepartmentofLifeSciences,BuckhurstRoad,AscotSL57PY,UnitedKingdom.3CentreforEcologyand
Conservation,CollegeofLifeandEnvironmentalSciences,UniversityofExeter,CornwallCampus,PenrynTR109EZ,UK.
1
Abstract
1. Stable isotope analysis is a widely used tool for the reconstruction and
interpretation of animal diets and trophic relationships. Analytical tools
have improved the robustness of inferring the relative contribution of
different prey sources to an animal’s diet by accounting for many of the
sources of variation in isotopic data. One major source of uncertainty is
Trophic Discrimination Factor (TDF), the change in isotopic signatures
between consumers’ tissues and their food sources. This parameter can
haveaprofoundimpactonmodelpredictions,butoften,itisnotfeasible
toestimateaspecies’TDFvalueandsoresearchersoftenuseaggregated
or taxon level estimates, an assumption that in turn has major
implicationsfortheinterpretationofsubsequentanalyses.
2. We collected extensive carbon (δ13C) and nitrogen (δ15N) TDF data on
mammals and birds from published literature. We then used a Bayesian
linearmodellingapproachtodetermineif,andtowhatextent,variationin
TDF values can be attributed to a species’ ecology, physiology,
phylogenetic relationships and experimental variation. Finally, we
developed a Bayesian imputation approach to estimate unknown TDF
values and compared the accuracy of this tool using a series of crossvalidationtests.
3. Ourresultsshowthat,forbirdsandmammals,TDFvaluesareinfluenced
byphylogeny,tissuetypesampled,dietofconsumer,isotopicsignatureof
PeerJ Preprints | https://doi.org/10.7287/peerj.preprints.1950v3 | CC BY 4.0 Open Access | rec: 17 Apr 2017, publ: 17 Apr 2017
food source, and the error associated with the measurement of TDF
withinaspecies.Furthermore,ourcross-validationtestsdeterminedthat,
our tool can (i) produce accurate estimates of TDF values with a mean
distanceof0.2‰fromobservedTDFvalues,and(ii)provideanestimate
oftheprecisionassociatedwiththeseestimates,withspeciespresencein
thedataallowingforareducedlevelofuncertainty.
4. Byincorporatingvarioussourcesofvariationandreflectingthelevelsof
uncertaintyassociatedwithTDFestimatesournoveltoolwillcontribute
to more accurate and honest reconstructions and interpretations of
animaldietsandtrophicinteractions.Thistoolcanbeextendedreadilyto
includeothertaxaandsourcesofvariationasdatabecomesavailable.To
facilitate this, we provide a step-by-step guide and code for this tool:
DiscriminationEstimationinR(DEsiR)
Keywords(10):TrophicDiscriminationFactor,stableisotopes,trophic
enrichmentfactor,trophicecology,mixingmodels,discriminationfactor,
mammals,birds,DEsiR,BayesianImputation.
Intro
Theuseofstableisotopeanalysistoreconstructanimaldietsordetermine
trophicrelationshipshasgrownsubstantiallyovertheprevioustwodecades
(Post2002,Hussey,MacNeiletal.2014).Inrecentyearsthisgrowthhasbeen
boostedbythedevelopmentofmixingmodelsthatallowfordietreconstruction
insystemsthatoftenhavegreaterthantwosourcesmorethanthenumberof
isotoperatiosmeasured(PhillipsandGregg2003,MooreandSemmens2008,
Parnell,Ingeretal.2010,HopkinsIIIandFerguson2012,Fernandes,Millardet
al.2014).Theabilityoftheseapproachestopredictaccuratelythedietary
proportionsandhencetrophicrelationshipsdependsontherelativegeometryof
themixtures(usuallytheconsumers)andtheirsources(theirfood)(Phillipsand
Gregg2003,Phillips,Ingeretal.2014)inisotopicspace.Furthermore,variation
inthesedata,arisingfrombothnaturalvariationamongsamplesandalso
throughuncertaintyinparameters,cantogetherreduceboththeaccuracyand
PeerJ Preprints | https://doi.org/10.7287/peerj.preprints.1950v3 | CC BY 4.0 Open Access | rec: 17 Apr 2017, publ: 17 Apr 2017
precisionofpredictionsmadebythesemixingmodelsbyalteringtherelative
geometricpositionofconsumersandtheirsources.Onekeysourceofvariation,
thatcancausefarmoreproblemsforusersthansample-dependentvariationis
theparameterthatdescribestheaveragechangeinisotopicratiosbetween
consumersandtheirdiets;thetrophicdiscriminationfactor(TDF).
Trophicdiscriminationisthechangeinisotopicsignaturesattributedtothe
biologicalandbiochemicalprocessesassociatedwiththeuptakeand
assimilationoffoodsourcesbyconsumers(DeNiroandEpstein1981,Peterson
andFry1987,FranceandPeters1997).Inthecaseofthecommonlyused
elementsindietarystudies(C,N,S&H),thesechangesinisotoperatiosbetween
sourcesandconsumersariseusuallyfromthepreferentialretentionofheavier
isotopesbyconsumersleadingtoachangeintheratioofheavytolightisotopes
ofagivenelement(Olive,Pinnegaretal.2003).WhileTDFcantypicallyvary
fromspeciestospecies,theyalsovaryaccordingtoarangeofotherfactors
includingconsumertissuetype,thetypeoffoodsource,theisotopicratioofthe
foodsource,thenutritionalstatusofboththeconsumerandthefoodsourceand
theforagingenvironmentoftheconsumer(Caut,Anguloetal.2009).Hence,in
ordertoaccuratelyestimatetheTDFforagivenconsumer-preyrelationship,one
mustconductanexperimentalstudythatcontrolsforthesemultiplesourcesof
variation(Greer,Hortonetal.2015).
Thehighcostsanddifficultyofperformingthesestudiesandasmanyspeciesare
notamenabletocontrolledcaptiveenvironmentshasresultedinarelativelylow
coverageofspeciesforwhichTDFestimatesareavailable(Caut,Anguloetal.
2009).Hence,moststableisotopestudiesondietaryproportionsandtrophic
relationshipshavereliedongeneralapproximatelymeanestimatesacross
multiplestudies,forexampletheadditionof+3.4‰fornitrogenand+0.4‰for
carbon(DeNiroandEpstein1978,DeNiroandEpstein1981,Post2002);
estimatesaggregatedforcertaintissuetypesorathightaxonomiclevels
(McCutchan,Lewisetal.2003,Caut,Anguloetal.2009);ortheuseofestimates
fromcloselyrelatedspecies(Bodey,Wardetal.2014).Whilesomeapproaches
attempttoprovidegeneralTDFvaluesforhightaxonomiclevels(Caut,Anguloet
PeerJ Preprints | https://doi.org/10.7287/peerj.preprints.1950v3 | CC BY 4.0 Open Access | rec: 17 Apr 2017, publ: 17 Apr 2017
al.2009)noneoftheseapproachesfullyincorporatesthetruevariationinTDFs
associatedwithphylogeneticrelatedness;physiology;ecology;ortheerrorand
naturalindividuallevelvariationassociatedwiththeexperimentalmeasureof
thesevalues(McCutchan,Lewisetal.2003,DelRioandWolf2005,Robbins,
Felicettietal.2005).Theseunaccountedsourcesofvariationmayimpactthe
resultinganalysismainlythroughpropagatingerrorintothefinalresultsleading
tooverlyconservativeresults(BondandDiamond2011),butonly,wewould
argue,ifonespecifiesTDFswithverysmalluncertaintiesaroundthem(i.e.
assumingoverlypreciseestimates).Inanycase,bybetteracknowledgingand
accountingforthesesourcesinTDFvariation,moreaccurateestimatesand
associatederrorscanbecalculatedwhichinturnwillyieldmorehonestand
encompassingdescriptionsofconsumers’dietsandtrophicrelationships.
HereweassesssourcesofvariationinTDFanddevelopatoolimplementinga
BayesianlinearmodellingapproachthatincorporatesthevariationinTDF
associatedwithphylogeny;physiology;ecologyandstudymeasurementerror.
Bayesiantechniquesallowfortheimplicitimputation(i.e.estimation)ofmissing
values,andhavebeendevelopedinseveralfields(Fagan,Pearsonetal.2013,
Swenson2014,JetzandFreckleton2015,Schrodt,Kattgeetal.2015).Herewe
exploitthisimputationapproachtoestimatevaluesforspeciesthathaveno
currentTDFvalues:predictedestimateswilldrawinferencefromtheincluded
explanatoryvariables,andwillreturnadistributionofestimatesratherthana
singlepoint-estimate.Wetestourapproachbycollectingcarbon(δ13C)and
nitrogen(δ15N)TDFvaluesfromtheliteratureforbothbirdsandmammalsand
comparingtheseobservedvaluesagainstourestimates.
OverallweshowthatTDFvaluesareinfluencedbyphylogeny,tissuetype,source
isotopicsignature,diettypeandtheerrorassociatedwithmeasurementswithin
aspecies,withtheimportanceofeachsourceofvariationdependentonthe
element(Nitrogen,Carbon)andtaxonomicclass(Aves,Mammalia).Wethen
exploittheabilityofBayesianInferencetoimputemissingvaluesinorderto
predictwithuncertaintytheTDFforun-quantifiedspeciesandtestthese
estimatesusingaseriesofcrossvalidationtestswherebothindividualsamples,
PeerJ Preprints | https://doi.org/10.7287/peerj.preprints.1950v3 | CC BY 4.0 Open Access | rec: 17 Apr 2017, publ: 17 Apr 2017
andentirespeciesareomittedfromthemodelfittingprocessandtheirimputed
valuescomparedwiththeirobservedvalues.Finally,weprovideastep-by-step
guideofusingtheDEsiRpackage(https://github.com/healyke/DEsiR).
Methods
Datacollection
Followingthemethodsof(Caut,Anguloetal.2009),wecollecteddataonTDFof
stablecarbon(δ13C)andnitrogen(δ15N)isotopesinmammalsandbirdsas
thesewerethetaxonwiththelargestamountofavailabledata(SeeDEsiR
packageforupdatesthatincludefurthertaxa).Ourdatacollectioncovered
publicationsfrom2007to2015andwassupplementedby(Caut,Anguloetal.
2009)whichcoveredtheperiodof1983-2007usingthesameselectioncriteria.
Onlystudieswithisotopicratiosmeasuredonboththetissuesamplesandthe
foodsourcewereused.ForalldatarelatingtoTDF,correspondingdataondiet,
tissuetypesampledandforagingenvironmentwerealsocollected.Dietwas
definedbytheanimalfeedusedduringthestudyandwascategorisedaseither
omnivore,carnivore,herbivoreorpellet.Tissuetypewascategorisedaseither
blood,whichincludedwholebloodandallitsconstituentssuchasplasma;
keratinclaws;collagen;feathers;hair(includingwhiskers);kidney;liver;milk;
andmuscle(withtissuesasappropriateforbirdsandmammals).Environment
wasdefinedbasedonwhetheraspeciespredominantlyfedprimarilyina
terrestrial(includingfreshwater)ormarineenvironments.Forfulldetailsonthe
methodsused,includingsearchtermsanddatastandards,see(Caut,Anguloetal.
2009).
Ascommonancestryamonggroupscanaffecttraitvariationweincluded
phylogeneticinformationforbothbirdsandmammalsinourmodels.Rather
thanbasingouranalysesonasinglephylogenetictree,wefollowedprevious
approaches(Healy,Guillermeetal.2014,Healy2015),ofusingadistributionof
treestoincorporatetheinherentuncertaintyinthephylogenies.Weextracted
threetreesfromtheposteriordistributionofarecentbirdphylogenygenerated
underaBayesianinferenceframework(Jetz,Thomasetal.2012),andusedthe
mammaltreesconstructedby(Kuhn,Mooersetal.2011)wereeachindividual
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treecomprisesoneresolutionofthepolytomiesofapreviouslypublished
supertreeandtheseasequivalenttoaBayesianposteriordistributionoftrees.
Analysisofsourcesofvariation
ToestimatevaluesofTDFwefittedmodelsusingBayesianphylogeneticmixed
modelsfromtheMCMCglmmpackage(Hadfield2010).Separatemodelswere
fittedforbothnitrogenandcarbonandalsoforbothAvesandMammaliadueto
theuseofdistincttissuetypestomeasureTDFinbothgroups.Wefiteachmodel
withtermsknownorexpectedtodetermineTDFincluding;foodsourceisotopic
ratio;diettypeandenvironmenttypeasfixedtermsandtissuetypeandspecies
levelvariationfittedasrandomterms.Toincludethenon-independence
betweenspeciestraitsduetocommondecentweincludedphylogenyasa
randomtermusingtheanimaltermintheMCMCglmmpackageandrunthese
modelsoveradistributionofphylogenetictreesusingtheMultreepackage
(GuillermeandHealy2014).Wedeterminedthenumberofiterations,thinning
andtheburn-inperiodforeachmodelrunacrossalltreesusingdiagnosticsin
thecodapackage(Plummer,Bestetal.2006)andwecheckedforconvergence
betweenmodelchainsusingtheGelman-Rubinstatistic,thepotentialscale
reductionfactor(PSR),withallmodelsrequiredtohaveaPSRbelow1.1(Brooks
andGelman1998).FollowingtherecommendationsofHadfield(Hadfield2010),
weusedanuninformativeinverse-Wishartdistribution(withvariance,V,setto
0.5andbeliefparameter,nu,setto0.002)andaparameterexpandedprior,with
ahalf-Cauchydistribution(describedbytheparametersV.0.5,nu.1,theprior
meanalpha.mu.0,andalpha.V.102,whichrepresentsthepriorstandard
deviationwithascaleof10),fortherandomfactortoimprovemixingand
decreaseautocorrelationamongiterations.
Whileweincludeisotopicratioasafixedeffectinthemainanalysis,asitisfound
tobeastrongpredictorofTDFinpreviousstudies(Caut,Anguloetal.2009),we
alsoruneachmodelwithoutthefixedtermsoffoodsourceisotopicratioas
informationrelatingtothisfactorisunlikelytobeavailableoutsideofcontrolled
experiments.Thisresultedinfourmodels(CarbonforAvesandMammaliaand
NitrogenforAvesandMammalia)usingthefullmodel
PeerJ Preprints | https://doi.org/10.7287/peerj.preprints.1950v3 | CC BY 4.0 Open Access | rec: 17 Apr 2017, publ: 17 Apr 2017
1. TDF~Fixedterms:Sourceisotopicratio+Diettype+Environment
Randomterms:Phylogeny+Tissuetype+Specieslevel
andfoursimilarmodelswithoutincludingsourceisotopicratio.
2. TDF~Fixedterms:Diettype+Environment
Randomterms:Phylogeny+Tissuetype+Specieslevel
Usingthesemodels,wethenavailoftheabilitytoimputemissingvaluesina
BayesianframeworkbyusingtheMCMCglmmpackagetoestimateTDFvalues
fornewspecies(Hadfield2010).
Analysis(Crossvalidation)
TotesttheaccuracyofthismethodwecomparedestimatesofTDFcalculated
usingBayesianimputationstovaluesmeasuredincontrolledexperiments.We
madethesecomparisonsbyrunningmodelswereanobservedTDFvalueinthe
datasetwasreplacedwithaNAcodinglabelwhichisthenestimatedimplicitly
duringmodelfittingusingtheimputationmethoddescribedabove.Thiswas
repeatedforeachvaluewithinthedatasetsothatanTDFestimatewas
calculatedforeachindividualobservedTDFvaluewerethatwastheonly
missingvalueinthemodel.
TotestourmodelforscenarioswerenoTDFvaluesarepresentforanentire
specieswealsosequentiallyreplacedallvaluesforeachspeciesinturnwiththe
sameNAcodinglabelwithinthedataset.Henceinthespeciesreplacement
analyseseachvalueisestimatedfromadatasetthatdoesnotcontainanyTDF
estimatesforthatspecies.AllcodeisavailableaspartoftheFestRpackage
(https://github.com/healyke/DEsiR).
PeerJ Preprints | https://doi.org/10.7287/peerj.preprints.1950v3 | CC BY 4.0 Open Access | rec: 17 Apr 2017, publ: 17 Apr 2017
Results
Overallourdatasetincludes328TDFvaluesandassociateddata(diettype,etc)
for24speciesofmammalsand24birdspecies.Forcarbonthereare94TDF
valuesfor21mammalspecies,and76TDFvaluesacross23birdspecies.For
nitrogenthereare89valuesacross21mammalspeciesand69TDFvalues
across24birdspecies.
SourcesofTDFvariation
Forbothelementsandtaxonomicclasses,theisotopicratioofthesourcehada
negativeeffectontheTDFrangingfrom-0.2to-0.29(Table.1).Forboth
elementsinbirds,butonlyfornitrogenisotoperatiosinmammals,TDFfrom
terrestrialhabitatswerefoundtobelowerthanmarinehabitats(Table.1).Diet
typeinmammalsshowedsignificantlylowercarbonTDFforpelletdiets,in
comparisontocarnivorousdiets.Wealsoobservedsignificantlylowernitrogen
TDFforherbivores,omnivoresandpelletdietsincomparisontocarnivorediets.
Inbirdsonlyomnivorousdietswerefoundtohavesignificantlylowernitrogen
TDFswithrespecttocarnivorousdiets.
PeerJ Preprints | https://doi.org/10.7287/peerj.preprints.1950v3 | CC BY 4.0 Open Access | rec: 17 Apr 2017, publ: 17 Apr 2017
Table1.SummaryoffactorsaffectingTDFinAvesandMammaliaforboth
CarbonandNitrogen.Estimatesforeffectsaremodalestimateswithlower5%
confidenceintervalandhigher95%credibleintervals(CI).Fixedeffects
estimatesinboldindicatethatthe95%credibleinterval(CI)doesnotcontain
zero.
Model
Carbon
Terms
Aves
Mammalia
Estimate LowerCI UpperCI Estimate LowerCI UpperCI
Fixed
Terms
Intercept
-3.59
-7.12
-0.167 -2.55
-4.59
-0.43
Source13C
-0.29
-0.47
-0.11 -0.20
-0.28
-0.13
DietType
Herbivore
-0.28
-2.08
1.56
-0.61
-1.58
0.44
Omnivore
-1.01
-2.56
0.28
0.11
-0.71
0.99
Pellet
-0.14
-1.83
1.50
-1.33
-2.41
-0.04
HabitatType
Terrestrial -1.79
-3.42
-0.33 0.58
-1.15
2.07
Random
Terms
Phylogeny
0.01
0.00
0.87
0.08
0.00
2.83
TissueType
0.36
0.13
3.04
0.11
0.00
1.54
Specieslevel
0.83
0.31
2.63
0.24
0.00
1.97
Residuals
0.47
0.33
0.79
0.84
0.62
1.35
Nitrogen
Aves
Mammalia
Estimate LowerCI UpperCI Estimate LowerCI UpperCI
Fixed
Terms
Intercept
5.92
4.01
7.94
6.74
4.69
8.72
Source15N
-0.24
-0.40
-0.07
-0.28
-0.40
-0.16
DietType
Herbivore 0.022
-2.50
2.48
-1.81
-3.06
-0.68
Omnivore -1.44
-3.00
-0.13
-0.90
-1.82
-0.02
Pellet
0.44
-1.87
1.10
-1.48
-2.68
-0.18
HabitatType
Terrestrial -1.36
-2.66
-0.22
-0.50
-2.18
0.90
Random
Terms
Phylogeny
0.19
0.00
2.02
0.26
0.00
2.55
TissueType
0.20
0.05
1.72
0.002
0.00
0.17
Specieslevel
0.12
0.00
1.22
0.06
0.00
1.10
Residuals
0.31
0.22
0.53
0.68
0.50
1.01
PeerJ Preprints | https://doi.org/10.7287/peerj.preprints.1950v3 | CC BY 4.0 Open Access | rec: 17 Apr 2017, publ: 17 Apr 2017
Theimportanceandeffectoftherandomtermsofphylogeny;tissuetype;species
levelvariationandresidualvariation,variedacrosselementsandclass.
Phylogenyaccountedfor1%and23%oftheresidualvariationinbirdsand6%
and26%inmammalsforcarbonandnitrogenrespectively.Tissuetypewasa
moreimportantterminbirdsaccountingfor22%and24%oftheresidual
variationforcarbonandnitrogencomparedto9%and1%inmammals.Finally,
withinspecieslevelvariationwasfoundtoaccountforasmuchas19%and50%
ofresidualvariationforcarbonand12%and6%fornitrogeninmammalsand
birds(Table1).
Modelvalidation
Theabilityofourmethodandtheassociatedpackage(DEsiR)toaccurately
estimateTDFvalueswashigh.Acrossallanalysesthemodedifferencebetween
estimatedandobservedvalueswasfoundtobe0.21forindividualreplacement
and-0.15forspeciesreplacementforcarboninbirds(Figure1a);-0.15
(individual)and0.31(species)fornitrogeninbirds(Figure1b);-0.09
(individual)and0.09(species)forcarboninmammals(Figure1c);and0.15
(individual)and0.22(species)nitrogeninmammals(Figures1d).
PeerJ Preprints | https://doi.org/10.7287/peerj.preprints.1950v3 | CC BY 4.0 Open Access | rec: 17 Apr 2017, publ: 17 Apr 2017
Bird Carbon TDF
Figure1.aTDFestimatesforCarbonforbirdsinbothindividualandspecies
replacementanalyses.Blackdotsrepresentmodelestimates,blackbars
represent50%CIanddashedbarsrepresent95%CI.Reddotsindicateobserved
TDFderivedfromreportedcontrolleddietexperiments.
PeerJ Preprints | https://doi.org/10.7287/peerj.preprints.1950v3 | CC BY 4.0 Open Access | rec: 17 Apr 2017, publ: 17 Apr 2017
Bird Nitrogen TDF
Figure1.bTDFestimatesfornitrogenforbirdsinbothindividualandspecies
replacementanalyses.Blackdotsrepresentmodelestimates,blackbars
represent50%CIanddashedbarsrepresent95%CI.Reddotsindicateobserved
TDFderivedfromreportedcontrolleddietexperiments.
PeerJ Preprints | https://doi.org/10.7287/peerj.preprints.1950v3 | CC BY 4.0 Open Access | rec: 17 Apr 2017, publ: 17 Apr 2017
Mammal Carbon TDF
Figure1.cTDFestimatesforcarbonformammalsinbothindividualandspecies
replacementanalyses.Blackdotsrepresentmodelestimates,blackbars
represent50%CIanddashedbarsrepresent95%CI.Reddotsindicateobserved
TDFderivedfromreportedcontrolleddietexperiments.
PeerJ Preprints | https://doi.org/10.7287/peerj.preprints.1950v3 | CC BY 4.0 Open Access | rec: 17 Apr 2017, publ: 17 Apr 2017
Mammal Nitrogen TDF
Figure1.dTDFestimatesfornitrogenformammalsinbothindividualand
speciesreplacementanalyses.Blackdotsrepresentmodelestimates,blackbars
represent50%CIanddashedbarsrepresent95%CI.Reddotsindicateobserved
TDFderivedfromreportedcontrolleddietexperiments.
Whilethegeneralaccuracyoftheseestimateswashightheseestimatesvaried
acrossspecieswithunderestimatesaslowas-4.11inLarusheermanniand
overestimatesashighas4.63inLarusdelawarensis(Figure1a).Theuncertainty
associatedwithTDFestimateswaslowerintheindividualreplacementanalysis
incomparisontothespeciesanalysiswith95%oftheestimatesfallingwithin
PeerJ Preprints | https://doi.org/10.7287/peerj.preprints.1950v3 | CC BY 4.0 Open Access | rec: 17 Apr 2017, publ: 17 Apr 2017
theintervalsof-1.71and1.70oftheindividualanalysisandbetweenthe
intervalsof-2.57and2.65forthespeciesintervals(Figure2).
Aves
4
-4
-2
0
2
4
-2
0
2
4
0.30
0.10
0.00
-4
-2
0
2
4
-4
-2
0
2
4
-4
-2
0
2
4
0.10
0.10
0.00
0.00
0.00
0.05
0.10
0.10
0.20
0.20
0.30
0.10
0.00
-4
0.20
2
0.20
0
0.00
Density
0.20
0.30
0.20
0.1
0.00
-2
0.15
-4
Nitrogen
Carbon
0.40
0.40
0.30
0.20
Density
0.10
0.00
Individual
replacement
Species
replacement
Mammalia
Nitrogen
Carbon
Difference between Estimated and Observed TDF
50% CI =
95% CI =
99% CI =
Figure2.Densityhistogramsofthedifferencebetweenestimatedvaluesusing
Bayesianimputationandobservedvaluesfromexperimentallycontrolled
dietarystudies.Thetoprowgivesdifferencesforestimatescalculatedfor
individualreplacementsforbothAvesandMammaliagroups,andCarbonand
Nitrogenelements.Thebottomrowgivesdifferencesforthespecies
replacementanalysis.Greenbarsrepresent50%,redbars95%andbluebars
99%confidenceintervals.
Theaccuracyanduncertaintyinmodelsrunwithouttheinclusionofsource
isotopicratioasafixedfactorwithamodedifferencebetweenestimatedand
observedvaluesfoundtobe0.19forindividualreplacementand0.05forspecies
replacementforcarboninbirds;-0.14(individual)and0.16(species)for
nitrogeninbirds;0.23(individual)and0.01(species)forcarboninmammals;
and0.003(individual)and0.42(species)nitrogeninmammals.
SimilartothemainanalysistheuncertaintyassociatedwithTDFestimatesin
modelswithoutsourceisotopicratioincludedwaslowerintheindividual
replacementanalysisincomparisontothespeciesanalysiswith95%ofthe
PeerJ Preprints | https://doi.org/10.7287/peerj.preprints.1950v3 | CC BY 4.0 Open Access | rec: 17 Apr 2017, publ: 17 Apr 2017
estimatesfallingwithintheintervalsof-1.96and1.94oftheindividualanalysis
andbetweentheintervalsof-2.72and2.90forthespeciesintervals(Figure3).
Aves
Individual
replacement
Density
Species
replacement
Density
Carbon
Mammalia
Nitrogen
Carbon
Nitrogen
Difference between Estimated and Observed TDF
50% CI =
95% CI =
99% CI =
Figure3.Densityhistogramsofthedifferencebetweenestimatedvaluesusing
Bayesianimputationwithoutsourceisotopicratioincludedandobservedvalues
fromexperimentallycontrolleddietarystudies.Thetoprowgivesdifferencesfor
estimatescalculatedforindividualreplacementsforbothAvesandMammalia
groups,andCarbonandNitrogenelements.Thebottomrowgivesdifferencesfor
thespeciesreplacementanalysis.Greenbarsrepresent50%,redbars95%and
bluebars99%confidence
Discussion
Here,wepresentDEsiRanapproachfortheestimationofunknowncarbonand
nitrogenTrophicDiscriminationFactor(TDF)valuesinbirdandmammal
species.Ourapproachbuildsonpreviousstudiesthatidentifiedvarioussources
ofvariationinTDF(DeNiroandEpstein1978,DeNiroandEpstein1981,Caut,
Anguloetal.2009)(McCutchan,Lewisetal.2003,Olive,Pinnegaretal.2003)
andextendsthembyincludingadditionalstudiesmeasuringTDFandby
incorporatingimportantadditionalsourcesofvariationincludingphylogenetic
structureandtheerrorassociatedwithmeasurementswithinaspecies.Ofthe
additionalsourcesofvariationthatweinvestigated,phylogenywasfoundtobe
PeerJ Preprints | https://doi.org/10.7287/peerj.preprints.1950v3 | CC BY 4.0 Open Access | rec: 17 Apr 2017, publ: 17 Apr 2017
particularlyimportantfornitrogenTDFforbothbirdsandmammalsbut
accountedforlittlevariationforcarbonTDFs.Thissuggeststhatwhileclosely
relatedspeciesarelikelytoshareasimilarnitrogenTDFs,nearest-neighbour
estimatesarenotasuitablemethodforestimatingcarbonTDFs.Incontrast,a
largeproportionofthevariationincarbonTDFestimatesforbirds,andtoa
lesserextentinmammals,wasattributedtovariationamongtissuesbutalsowas
simplyleftasresidualerrorforspeciesacrossstudies(i.e.theerrorassociated
foraspeciesaftercontrollingfortissuetype,diettypeetc).Foraging
environmentwasasourceofsignificantvariationforbothcarbonandnitrogen
TDFestimatesinbirds,andfornitrogenestimatesinmammals,withspecies
foraginginterrestrialenvironmentsexhibitinglowerTDFvaluesthanthosein
marineenvironments.Whileenvironmenthasbeenfoundtobeasignificant
factorinpreviousstudies(Caut,Anguloetal.2009)forstableisotoperatios,
theseeffectshavenotbeenpreviouslyrecordedfornitrogenTDFs.Furtherdata
willallowformoredetailedcomparisonoftheeffectsofenvironmentswiththe
terrestrialbiome,mainlyfreshwaterenvironments.
IncomparisontopreviouslydevelopedapproachesforestimatingTDF(Caut,
Anguloetal.2009),ourmodelsallowthephylogeneticrelationshipofspecies
withavailabledatatoinfluenceTDFestimationalongwithothersourcesofTDF
variation.Theaccuracyofthismethodwasvalidatedboththroughleave-one-out
crossvalidationreplacementofsingleobservationsandreplacementofwhole
species.Asexpectedtheaccuracyofsingleobservationreplacementwashigher
thanwholespeciesreplacementowingtotheadditionallossofinformationin
thespeciesremovalprocess.However,theprimarydifferencebetweenthe
performancesofthetwovalidationmodelsisasonewouldexpect.Ifyou
estimateaspeciesthatispresentinthedatasetusedtofitthemodel(i.e.the
speciesremovalvalidation)thentheestimatedTDFismoreprecisethanifyou
estimateaspeciesthatisnotpresentinthedatasetusedtofitthemodel(i.e.the
speciesremovalvalidation).
Allmodelsarebutanapproximationoftherealworldandareonlyasgoodas
thedataavailable;thus,underourapproach,TDFestimatesforsomespeciesare
PeerJ Preprints | https://doi.org/10.7287/peerj.preprints.1950v3 | CC BY 4.0 Open Access | rec: 17 Apr 2017, publ: 17 Apr 2017
likelytobemoreaccuratethanothers.Forexample,inoursinglespecies
replacementmodel,ourestimatesofcarbonTDFfortwoNorthAmericangulls,
LarusdelawarensisandL.heermanni,areamongtheleastaccurateinthemodel.
Thismayreflectpeculiaritiesin,oralackofdetaileddatarelatingto,theecology
andphysiologyofthesespecies,suchasthehighlevelofterrestrialforagingin
manygullspeciesorthephysiologicalprocessofsaltexcretionusedbythese
species(Douglas1970).Nonetheless,asmoredataonTDFbecomesavailable,
ourapproachtoTDFestimationwillbecomeincreasinglypowerful.
Irrespectiveofimprovementsinaccuracy,theabilitytocalculateanappropriate
errorassociatedwiththemcaninturnbeappliedtocurrentBayesianisotope
mixingmodels(MooreandSemmens2008,Parnell,Ingeretal.2010),which
encourageinclusionofallsourcesofuncertaintysoastopropagatethis
uncertaintytowardsthefinaldietaryortrophicestimates(Phillips,Ingeretal.
2014).Ourapproachalsoallowsforflexibilityinthemodelappliedtoestimate
TDFvalues,whichisparticularlyimportantasmanyofthefactorsinfluencing
TDFarestilldebated,suchastheisotopicratioofthesourceitself(Phillips,Inger
etal.2014).Similarly,whileourapproachiscurrentlyconfinedtobirdsand
mammals,itcanalsoeasilybeadaptedandextendedtoothertaxonomicgroups
asfurtherdataontheTDFand/orphylogeneticrelationshipsofthetaxabecome
availableandmoreinformationfromcontrolleddietstudiesonbothnewspecies
aswellasthosealreadyincludedinthedataset.
WeprovideRcode(https://github.com/healyke/DEsiR)fortheestimationof
carbonandnitrogentrophicenrichmentfactorsforanybirdormammalspecies,
whichcaneasilyfitintotheinputofcurrentstableisotopemixingmodelsand
alsobeextendedtoothertaxonomicgroupsinthefuture.Byincorporating
phylogeny,ecologyandtheerrorassociatedwithTDFestimates,ourapproach
canprovidemoreaccuratedietaryproportionestimatesalongwithamore
honestrepresentationoftheirprecision.Akeyfeatureofourmethodisthatit
providesaframeworkwhichlendsitselftorefinementandimprovedestimates
asmoreTDFdatafromexperimentalstudiesbecomesavailable.
PeerJ Preprints | https://doi.org/10.7287/peerj.preprints.1950v3 | CC BY 4.0 Open Access | rec: 17 Apr 2017, publ: 17 Apr 2017
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