LatinamericanMacroevolutionworkshopUNAM2018

AlejandroGonzalez-VoyerInstitutodeEcología

UNAM

Altitude

SVL

s1s2s3s4s5s6s7s8s9s10s11s12s13s14s15s16s17s18s19s20s21s22s23s24s25s26s27s28s29s30s31s32s33s34s35s36s37s38s39s40s41s42s43s44s45s46s47s48s49s50

0

12.5

25

37.5

50

TypeIErrorSinfilogenia FilogenéJco

500simulationsofphenotypicevolutionfor2independenttraitsalongthephylogeny

%Significantcorrelations

Risksofignoringphylogeneticnon-independence

PhylogeneticGeneralizedLeastSquares(PGLS)

• Generalizedleastsquaresmodelwherethephylogeneticrelationshipsamongspeciesareincorporatedintheerrorterm

• Variancecovariancematrixdescribestheexpectedsimilarityamongspeciesbasedonthedegreeofsharedancestry

• Moreprecisely:expectedcovarianceamongresidualsduetosharedancestry(phylogeneticrelationships)amongspecies

Grafen1989;Martins&Hansen1997

Covarianceandphylogeneticrelationships

A

B

CD

EFG

H

I

J

L

K

A&B:Expectedcovariance=high

A&D:Expectedcovariance=low

A&K:Expectedcovariance=null

A B C D E F G H I J K LA δ2 + + + + - - - 0 0 0 0B δ2 + + + - - - 0 0 0 0C δ2 + + - - - 0 0 0 0D δ2 + - - - 0 0 0 0E δ2 - - - 0 0 0 0F δ2 + + 0 0 0 0G δ2 + 0 0 0 0H δ2 0 0 0 0I δ2 + + +J δ2 + +K δ2 +L δ2

Variancecovariancematrix

�8

A B C D E F G H A B C D E F G H

A B

CD

EF

GH

A

B

C

D

E

F G

H

• AdvantagesofPGLS:–Modeloftraitevolutionisdeterminedbythevariancecovariancematrix,hencecanaccomodatedifferentevolutionarymodels–Canincorporateanestimateofintraspecificmeasurementerrorinthemodel–Cancombinecontinuousanddiscretetraitssimplyinasinglemodel–Canobtaintheinterceptvalue

Phylogeneticgeneralizedleastsquares

• UseofPGLSdoesnot“remove”partofthecorrelationduetothephylogeny

• Theeffectoftakingphylogenyintoaccountistoreducethevariancearoundtheestimatedslope

• Theirmeansarenotbecausesinceestimatesofregressioncoefficientsareunbiasedwhetherornotthecorrectphylogenyistakenintoaccount.

Rohlf2006

ModelsofEvolution

• PGLSmethodestimatesanevolutionaryparametersimultaneouslywithmodelfit

• Evolutionaryparameter(λ,α)describesthemodelofevolution&adjuststhevariancecovariancematrixtothemodel– λ:adjuststhevariancecovariancematrixtoaBrownianevolutionmodel– 1:evolutionfollowsaBrownianmodel– 0:evolutiondoesnotfollowaBrownianmodel,thereisnophylogeneticsignalintheresiduals

PICvsPGLS• IfcovarianceintheresidualsfollowsastrictBrownianmodelPIC&PGLSshouldconvergeinthesameresult

• RegressionsthroughtheoriginofPICsareidenticaltothoseobtainedusingPGLSwithaninterceptincluded

• HoweverwhenevolutionisnotBrownianPGLSoutperformsPICs

• Maximumlikelihoodestimateoflambdaallowsfornecessarycorrectionforestimatedcovarianceofresiduals

Rohlf2001;Revell2010

The7deadlysinsofcomparativeanalyses

1. PuttingunduefaithinmodelswithlowR2–OnlyasinglepackageinRestimatesR2forphylogenticGLSmodels–SomequestiontheaccuracyofR2estimatesinphylogeneticGLS

Freckleton2009

2. Reportingtheresultsofphylogeneticallyindependentandphylogeneticanalyses:– thetwomodelsmakedifferentassumptions

aboutthedistributionofdata– atbestregardedasalternativemodelsofthe

samedata– assuchtheyshouldNOTbetreatedequally

3. Nottestingdistributionalassumptions:– Phylogeneticanalysesmakeassumptionsabout

thedistributionofresidualsthatarethesameasthosemadeinnonphylogeneticanalyses

– Roffersdifferentwaysoftestingresidualdistributions(incapersimplyuseplot()function)

Freckleton2009

4. Datadredging:– becausedataarenotgeneratedexperimentally,

therelationshipsfoundareonlycorrelative– possibilityofhiddenvariablesmeanthat

significantcorrelationsmaybemistakenlytakenasimplyingacausalrelationshipwhennosuchrelationshipexists

– shouldavoidthetemptationofincludingalargenumberofpredictorsto“seewhatcomesout”

Freckleton2009

5. Treatingresidualsasdata:– Useofresidualstocontrolforconfoundingvariablesis

wrong– Canresultinbiases– UseANCOVAtocontrolforallometriceffectsor

confoundingvariables6. Ignoringalternativemodels:– UsemodelcomparisonwithAICorAICC

7. Ignoringqualitycontrolofdata:– Datafromdisparatesourcesmaybeofdifferent

quality– Lowqualitydatacompromisesstatisticalpower– Missingdatacanleadtobiasesintheoutcomeof

analysesFreckleton2009

Correlatesofspeciesrichness

• Intrinsicorextrinsicspeciescharacteristicsmayinfluencespeciationrates

• CanusePGLSmodelstoanalyzethecorrelationbetweenspeciescharacteristicsandspeciesrichness

• Dependentvariableinsuchmodelsisrateofdiversificationorspeciesrichness