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Jos Alexandre Felizola Diniz-Filho Departamento de Ecologia, UFG Tpicos Avanados em Ecologia Filogentica e Funcional Modelos evolutivos, sinal filogentico, conservao de nicho

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1.Introduo (programas de pesquisa) 2.Filogenias e matrizes de relao entre taxa 3.Modelos de Evoluo 3.1. Conceitos gerais 3.2. Mtodos Estatisticos 3.3. Abordagens baseadas em modelos de evoluo 3.4. Comparao de mtodos 4. Conservao de nicho 4.1. Conceitos gerais 4.2. Sinal filogentico e conservao de nicho Modelos evolutivos, sinal filogentico, conservao de nicho

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Phylogenetic Comparative Methods Phylogenetic Diversity Community Phylogenetics 1. Introduction: on the research traditions... Paul Harvey (1980s) Campbell Webb (2002) Dan Faith (1992)

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Marc Cadotte (University of Toronto)

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Ecophylogenetics Assemblages Traits

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1985

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Traits Correlated Evolution Phylogenetic Signal TRAITS

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A B C 2 2 3 5 2. Phylogenies and relationship matrices

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ABC A010 B 04 C 40 Pairwise (patristic) distances >primcor

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ABC A1.000 B0 0.39 C0 1.0 Shared proportion of branch lenght from root to tips

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((((homo: 0.22,pongo: 0.22): 0.25,macaca:0.47):0.14,ateles: 0.62): 0.38,galago: 1.00): 0.00; 1.000.780.530.380.00 0.781.000.530.380.00 0.530.531.000.380.00 0.380.380.381.000.00 0.000.000.000.001.00 >primcor

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This is an ultrametric tree...distance from root to TIP is constant for all species Main diagonal Phylogenetic variance-covariance (vcv) matrix ( )

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

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t4t5t2t8t6t3t1t7 t41.8301.2150.761 0.000 t51.2151.7610.761 0.000 t20.761 1.8181.1150.774 0.000 t80.761 1.1151.5360.774 0.000 t60.761 0.774 1.8461.4120.000 t30.761 0.774 1.4121.5240.000 t10.000 1.0290.558 t70.000 0.5580.816

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The species covary, but in terms of what? PHENOTYPES! So, the phylogenetic vcv matrix gives na EXPECTED covariance based on traits species (which is actually similarity of mean values) among the species...

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ERM (Expected Relationship Matrix; Martins 1995)

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

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

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The analytical core of comparative analysis

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Evolutionary models Mechanisms (selection, drift, mutations) Interspecific data ? 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...

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I = selection intensity R = response T = time h 2 = heritability Vp = phenotypic variance Mechanistic versus phenomenological evolutionary models

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Statistical models that capture the expectation of alternative evolutionary processes or mechanisms

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

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

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The distribution of Y at time step 1000, replicated 2000 times...

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50 time-steps Speciation WHAT ABOUT PHYLOGENY?

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50 time-steps 100 time-steps 1 0.3331 001 00 1 00 0.6661 Expected VCV matrix

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

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

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sp1sp2sp3sp4sp5 trait1-0.928-3.0100.246-0.433-0.422 trait2-2.9140.7882.4863.3081.628 trait36.6312.5904.2002.3943.227 trait4-6.380-5.593-2.0741.013-0.208 trait5-0.5939.7250.9683.5462.101 trait62.627-4.5491.953-1.2083.152 trait74.411-2.0700.5135.0436.609 trait8-1.565-9.055-1.1182.523-3.547 trait91.3291.3155.062-1.551-0.145 trait10-0.292-1.601-2.935-5.727-5.107 trait11-1.430-3.896-2.4940.280-0.925 trait12-0.5852.413-1.444-1.901-0.052 trait13-2.029-2.192-3.938-2.575-5.659 trait14-1.281-1.8633.187-0.340-1.974 trait154.1049.415-0.2054.2107.856 trait16-2.212-3.050-4.495-6.210-6.638 trait17-0.649-7.015-0.971-2.8232.670 trait18-3.0460.229-4.418-1.7671.183 trait191.1341.4650.842-2.1050.011 trait201.241-1.303-0.0914.4910.607... trait1000-3.2460.329-4.418-2.767-1.827 1 0.5391 0.3410.3501 0.3540.3600.3331 0.2740.2850.3330.6661 Observed matrix (10000 traits) Calculate a Pearson (or covariance) matrix among Taxa (in R mode) Each line is a simulation that gives Y values for each species...

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> simbw [,1][,2][,3][,4][,5] [1,]-0.04001-0.0530.07408-0.05225-0.13472 [2,]0.2469950.1883680.2105390.161954-0.04256 [3,]0.0343130.015872-0.025370.042092-0.03787 [4,]0.024264-0.08208-0.07415-0.05169-0.02666 [5,]-0.07504-0.09173-0.05418-0.090410.091738 [6,]0.2811380.2109350.1212050.1625390.081836 [7,]0.1529360.169856-0.01267-0.00268-0.00039 [8,]0.009934-0.09725-0.08152-0.207570.099189 [9,]-0.037260.026658-0.17218-0.14235-0.0787 [10,]-0.33382-0.20617-0.17718-0.294380.061293 [11,]-0.05479-0.167420.064186-0.033450.003819 [12,]0.046365-0.08393-0.11845-0.196070.107281 [13,]-0.15355-0.10313-0.19682-0.24950.07867 [14,]0.1850260.1305590.0174910.1112120.033344 [15,]0.0897260.0312120.035245-0.087060.059088 [16,]0.009616-0.01897-0.009930.08443-0.15238 [17,]-0.010190.009079-0.041080.0721250.119902... [98,]0.1156720.0915170.213318-9.59E-03-0.0636 [99,]0.018725-0.00479-0.125211.13E-01-0.0851 [100,]-0.10961-0.11279-0.08101-1.66E-01-0.11171 ntimes=100 nsp=5 simbw

Several options to transform branch lenghts 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 plot(primtreeOU)

Slide 44 primcorOU write.table(primcorOU, file="primcorOU.txt") homopongomacacaatelesgalago homo1.0000.3280.0890.0400.000 p">

>primcorOU write.table(primcorOU, file="primcorOU.txt") homopongomacacaatelesgalago homo1.0000.3280.0890.0400.000 pongo0.3281.0000.0890.0400.000 macaca0.089 1.0000.0400.000 ateles0.040 1.0000.000 galago0.000 1.000 THIS IS THE EXPECTED VCV UNDER OU PROCESS WITH = 2.5! BM OU

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COMPARATIVE versus NON- COMPARATIVE ANALYSIS: The STAR-PHYLOGENY -This is actually what you assume when you say that did not use comparative methods (so, they actually use, but with a particular vcv matrix) -Doing a standard regression or correlation is a particular form of comparative analyses assuming a Star-Phylogeny - This assumption indicates that the trait has no pattern (the interspecific variation is random in respect to phylogeny) This does not indicate that there is no phylogenetic relationships among species, of course, only that the processes driving trait variation occurred in such a way that the patterns is completely lost. 10000 01000 00100 00010 00001

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PHYLOGENETIC SIGNAL: BASIC CONCEPTS Relationship between species similarity for a trait and phylogenetic distance - phylogenetic pattern; - phylogenetic component; - phylogenetic signal; - phylogenetic correlation; - phylogenetic inertia Patterns and processes...

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Metrics Model Based Statistical ? MEASURING PHYLOGENETIC SIGNAL

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Number of spp Matrix W with weights Species trait Z centered for the species i e j Sum of weights in W Morans I coefficient for phylogenetic autocorrelation Phylogenetic covariance variance

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Sokal, R. R. & Oden, N. L. 1978. Spatial autocorrelation in biology: 1. methodology 2. Some biological implications and four applications of evolutionary and ecological interest Biological Journal of Linnean Society 10: 199-249. Robert Sokal (1924-2012) CORRELOGRAMS IN POPULATION GENETICS

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Matrix Zi * Zj (Z)

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Matriz W (1/Dij) Patristic distances Sum of W = 10.38333

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W Z ZijWij Sum ZijWij = 8.400781

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Morans I Numeratorphylogenetic covariance = 8.400781 / 10.3833 = 0.809 Denominator variance = 23.375 / 8 = 2.984 I = 0.809 / 2.984 = 0.276 -1.0 < Morans I < 1.0 Maximum and minimum are a function of eigenvalues of W (see Lichstein et al. 2002)

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What is wrong?

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W ij = 1 / d ij W Phylogenetic distance Gittleman used something like this, but this is empirical... The W matriz: inverting the relationship between W and D

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Wij = 1/ Dij Wij = 1/ (Dij ^ 2)

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-W ij = 1 / D ij 2 I de Moran = 0.72

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Other possible functons linking W and D -W ij = 1 / d ij -W ij = 1 / d ij 2 -W ij = e (- d ij ) W Phylogenetic distance Or we can use directly any VCV matrix, previously defined...!!!!

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The R matrix (shared branch lenghts when root age is 1.0) is already a W matrix that can be used directly in Morans I

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Testing significance: the analytical solution... Standard normal deviate, (SND, or Z) assuming normal distribution of the statistics If | Z | > 1.96, then Morans I is significant at P < 0.05

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Permutation test Randomize the tip values in the phylogeny... 4.0 3.5 3.0 6.0 7.5 8.0 5.0 6.0 and recalculate Morans many times... The P-value (Type I error) is given by how many times the Morans I was higher than the randomized values

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The PRIMATE example (Lynch 1991): Body weight and Longevity (log-scale) Lets use R as a weighting matrix 1.000.780.530.380.00 0.781.000.530.380.00 0.530.531.000.380.00 0.380.380.381.000.00 0.000.000.000.001.00 sppbwlong homo4.0944.745 pongo3.6113.332 macaca2.3703.367 ateles2.0282.890 galago-1.4702.303

Slide 67 primtree primcor diag(Rprim) Moran.I(primlog[,c(1)],primcor) Significant phylogenetic signal... Not significant phylogenetic signal... The matriz W is wrongly defined in Paradis book">

Morans I results Body weight: I = 0.200 0.217; E(I) = (-1/(n-1) = -0.25 Z = 2.07 P = 0.038 Longevity: I = -0.121 0.209; E(I) = (-1/(n-1) = -0.25 Z = 0.617 P = 0.537 > primlog primtree primcor diag(Rprim) Moran.I(primlog[,c(1)],primcor) Significant phylogenetic signal... Not significant phylogenetic signal... The matriz W is wrongly defined in Paradis book

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ntimes

> chev209 1-var(chev209$residuals)/var(bs209)

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Phylogenetic Eigenvector Regression (PVR)

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Diniz-Filho`s et al. (1998) Phylogenetic eigenVector Regression (PVR) (Evolution 52: 1247-1262.) Phylogenetic distances Phylogeny Multiple regression Y Double centering Eigenvectors (V) S P X Estimated values Regression residuals R2R2

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Diniz-Filho`s et al. (1998) phylogenetic eigenvector regression (PVR) Phylogeny Eigenvectors (V) - Eigenvalues Phylogenetic eigenvectors represent linearly different cuts of phylogeny, allowing evaluation of phylogenetic effects at different `scales ` +

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colourPhyl1% YELLOWGR019.77 BLUEcomb22.06 REDbal30.61 GREENnorm32.49 ORANGEgr5078.03

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Pierre Legendre Daniel Griffith Principal coordinate analysis of truncated geographic distances W (PCNM) Eigenvectors of double centered binary (0/1) connectivity matrix

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70 species of Carnivora in New World Body size, geographic range size Supertree (12 first eigenvectors) Diniz-Filho & Torres (2002, Evol.Ecol. 16: 351-367)

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PVR Geographic range R 2 = 0.28 (P = 0.06) Body size R 2 = 0.75 (P

K = 1.018437 0.388 ntimestransformPhylo.ML(primbw,primtree,model="> transformPhylo.ll(primbw,primtree,model="OU",alpha=2) >library(motmot) FITTING GENERAL MODELS OF TRAIT EVOLUTION USING PGLS Get the maximum likelihood of trait given the tree (the tree can be transformed into trees reflecting other models (in GEIGER), or... It can find the parameter alpha that maximize the likelihood Gives the likelihood for a model and parameter Gavin Thomas Rob Freckleton"> transformPhylo.ll(primbw,primtree" title=">primbw likTraitPhylo(primbw,primtree) >transformPhylo.ML(primbw,primtree,model="OU") > transformPhylo.ll(primbw,primtree">

>primbw likTraitPhylo(primbw,primtree) >transformPhylo.ML(primbw,primtree,model="OU") > transformPhylo.ll(primbw,primtree,model="OU",alpha=2) >library(motmot) FITTING GENERAL MODELS OF TRAIT EVOLUTION USING PGLS Get the maximum likelihood of trait given the tree (the tree can be transformed into trees reflecting other models (in GEIGER), or... It can find the parameter alpha that maximize the likelihood Gives the likelihood for a model and parameter Gavin Thomas Rob Freckleton

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>library(motmot) primbw