José Alexandre Felizola Diniz-Filho Departamento de Ecologia , UFG

1. Tópicos Avançados em Ecologia Filogenética e Funcional Modelos evolutivos, sinal filogenético, conservação de nicho José AlexandreFelizolaDiniz-Filho Departamentode Ecologia, UFG

2. Modelos evolutivos, sinal filogenético, conservação de nicho • Introdução (programas de pesquisa) • Filogenias e matrizes de relação entre taxa • Modelos de Evolução • 3.1 . Conceitos gerais • 3.2. Métodos Estatisticos • 3.3. Abordagens baseadas em modelos de evolução • 3.4. Comparação de métodos • 4. Conservação de nicho • 4.1. Conceitos gerais • 4.2. Sinal filogenético e conservação de nicho

3. 1. Introduction: ontheresearchtraditions... Phylogenetic Comparative Methods Paul Harvey (1980’s) Phylogenetic Diversity Community Phylogenetics Campbell Webb (2002) Dan Faith (1992)

4. Marc Cadotte (University of Toronto)

5. Traits Ecophylogenetics Assemblages

6. 1985

7. TRAITS Phylogenetic Signal Traits Correlated Evolution

8. 2.Phylogeniesandrelationshipmatrices A B C 2 2 5 3

9. Pairwise (patristic) distances >primcor <- cophenetic(primtree) >

10. Shared proportion of branch lenght from root to tips

11. ((((homo: 0.22,pongo: 0.22): 0.25,macaca:0.47):0.14,ateles: 0.62): 0.38,galago: 1.00): 0.00; 1.00 0.78 0.53 0.38 0.00 0.78 1.00 0.53 0.38 0.00 0.53 0.53 1.00 0.38 0.00 0.38 0.38 0.38 1.00 0.00 0.00 0.00 0.00 0.00 1.00 >primcor <- vcv.phylo(primtree, cor=TRUE) >

12. Phylogenetic variance-covariance (vcv) matrix ( ) Thisisanultrametrictree...distancefrom root to TIP isconstant for allspecies Main diagonal

13. PHYLOGENETIC CORRELATION = Standardized Variance-Covariance = Shared proportion of branch lenght This ultrametric tree has a total lenght of 1.0

15. The species“covary”, but in termsof “what”? PHENOTYPES! So, thephylogeneticvcvmatrixgives na EXPECTED covariancebasedontraitsspecies (whichisactuallysimilarityofmeanvalues) amongthespecies...

16. ERM (Expected Relationship Matrix; Martins 1995)

17. The same phylogeny can generate different OBSERVED vcv matrices, for different traits, for example... EVOLUTIONARY MODELS

18. 3. EVOLUTIONARY MODELS Mechanisms (selection, drift, mutations…) Evolutionary models Interspecific data

19. Theanalytical core ofcomparativeanalysis

20. Mechanisms (selection, drift, mutations…) ? The path from evolutionary mechanisms (selection, drift, mutation and so on) to interspecific variation is a conceptual idea, but it may be hard (or even impossible) to reverse it and actually recover such processes from empirical data... Evolutionary models Interspecific data

21. I = selection intensity R = response T = time h2 = heritability Vp = phenotypic variance ‘Mechanistic’ versus phenomenological evolutionary models

22. Statistical models that “capture” the expectation of alternative evolutionary processes or mechanisms

23. BROWNIAN MOTION • After Robert Brown (1827) • Simplest continuous-time stochastic process Simple discrete Random walks...

24. UNDERSTANDING BROWNIAN MOTION In Excel, when A1=0... =A1+(ALEATÓRIO()-0.5) Uniform distribution (0-1) 15 replications of the same process through time

25. The distributionof Y at time step 1000, replicated 2000 times...

26. WHAT ABOUT PHYLOGENY? 50 time-steps 50 time-steps Speciation 50 time-steps

27. 100 time-steps 50 time-steps 100 time-steps 50 time-steps 100 time-steps 50 time-steps 50 time-steps 50 time-steps Expected VCV matrix

29. Here we assumed that species are INDEPENDENT (the started all at the root) Here species are PHYLOGENETICALLY STRUCTURED

30. If we repeat this many times... But how?????

31. Each line is a simulation that gives Y values for each species... Calculate a Pearson (or covariance) matrix among Taxa (in “R mode”) “Observed” matrix (10000 “traits”)

32. ape > rTraitCont(phy, model = "BM", sigma = 0.1, alpha = 1, theta = 0, ancestor = FALSE, root.value = 0, ...) ntimes=100nsp=5simbw <- matrix(data=NA,nrow=ntimes,ncol=nsp) for(i in 1:ntimes){ simbw[ i, ]<-rTraitCont(primtree) }

33. 100 time-steps 95 time-steps 100 time-steps 5 time-steps 100 time-steps 95 time-steps 75 time-steps 25 time-steps Expected VCV (standardized) matrix

34. Expected VCV (standardized) matrix r = 0.991!!!! Observed matrix (10000 “traits”)

35. PropertiesorBrownianmotion in comparativeanalysis • Normal distributionofphenotypes (tips) • Meanconstantthrough time (absenceoftrends) • Varianceincreaseslinearlywithtime (butrememberthatwe do notknowtheabsoluteexpectedvariance) • The evolutionaryinterpretationofBrownianmotion • Geneticdrift + Mutation = Neutral (sensu Kimura) evolution • Stochasticadaptation in eachlineageateach time step (multipleindependentadaptive forces)

36. ConstrainedBrownianmotion: Ornstein-Uhlenbeck (O-U) process …The Ornstein–Uhlenbeck (O-U) process (named after Leonard Ornstein and George Eugene Uhlenbeck), is a stochastic process that, roughly speaking, describes the velocity of a massive Brownian particle under the influence of friction. Stabilizing selection...

39. Brownian motion e Ornstein-Uhlenbeck (OU) processes…

42. Creatingalternativemodelsbywarpingthebranchlenghts... The tipisto move from a “real” phylogeny (thesequenceofbranchingevents in time) to a “trait” or “model” phylogeneticstructurethat must beused in thestatisticalanalyses....

43. Severaloptions to transformbranchlenghts in GEIGER deltaTree(phy, delta, rescale = T) lambdaTree(phy, lambda) kappaTree(phy, kappa) ouTree(phy, alpha) tworateTree(phy, breakPoint, endRate) linearchangeTree(phy, endRate=NULL, slope=NULL) exponentialchangeTree(phy, endRate=NULL, a=NULL) speciationalTree(phy) rescaleTree(phy, totalDepth) BM OU > primtreeOU <-ouTree(primtree,2.5) > plot(primtreeOU)

44. >primcorOU <-vcv.phylo(primtreeOU,cor=TRUE) > write.table(primcorOU, file="primcorOU.txt") This is theexpectedvcvunder OU processwith = 2.5! OU BM

45. “COMPARATIVE” versus “NON-COMPARATIVE” ANALYSIS: The “STAR-PHYLOGENY” • This is actuallywhatyou assume whenyousaythatdidnot use comparativemethods (so, theyactually use, butwith a particular vcvmatrix) • Doing a standard regressionorcorrelation is a particular formofcomparativeanalysesassuming a Star-Phylogeny • - Thisassumptionindicatesthatthetraithas no pattern (the interspecific variation is random in respect to phylogeny) • This does notindicatethatthere is no phylogenetic relationshipsamongspecies, ofcourse, onlythatthe processes drivingtraitvariationoccurred in such a waythatthepatterns is completelylost.

46. PHYLOGENETIC SIGNAL: BASIC CONCEPTS • Relationship between species’ similarity for a trait and phylogenetic distance • phylogenetic pattern; • phylogenetic component; • phylogenetic signal; • phylogenetic correlation; • phylogenetic inertia Patternsand processes...

47. Measuring Phylogenetic Signal Statistical ? Metrics Model Based

48. Moran’sI coefficient for phylogenetic autocorrelation MatrixW withweights Numberofspp Speciestrait Z centered for thespecies i e j Phylogenetic covariance variance Sumofweights in W

50. CORRELOGRAMS IN POPULATION GENETICS Robert Sokal (1924-2012) Sokal, R. R. & Oden, N. L. 1978. Spatialautocorrelation in biology: 1. methodology 2. Some biologicalimplicationsand four applications ofevolutionaryandecologicalinterest BiologicalJournalofLinneanSociety 10: 199-249.