UNIVERSIDADE FEDERAL DE GOIS INSTITUTO DE CINCIAS BIOLGICAS MESTRADO ECOLOGICA & EVOLUO

Jos Alexandre Felizola Diniz-Filho

Departamento de Ecologia, UFG

Tpicos Avanados em Ecologia Filogentica e Funcional

Modelos evolutivos, sinal filogentico, conservao de nicho

Introduo (programas de pesquisa)Filogenias e matrizes de relao entre taxaModelos de Evoluo3.1 . Conceitos gerais3.2. Mtodos Estatisticos3.3. Abordagens baseadas em modelos de evoluo3.4. Comparao de mtodos4. Conservao de nicho4.1. Conceitos gerais4.2. Sinal filogentico e conservao de nichoModelos evolutivos, sinal filogentico, conservao de nicho

Phylogenetic Comparative MethodsPhylogenetic DiversityCommunity Phylogenetics

1. Introduction: on the research traditions...

Paul Harvey(1980s)

Campbell Webb(2002)

Dan Faith (1992)

Marc Cadotte(University of Toronto)EcophylogeneticsAssemblagesTraits

1985TraitsCorrelated EvolutionPhylogenetic SignalTRAITSA B C22352. Phylogenies and relationship matrices

ABCA01010B1004C1040Pairwise (patristic) distances>primcor

ABCA1.000B01.00.39C00.391.0Shared proportion of branch lenght from root to tips

((((homo: 0.22,pongo: 0.22): 0.25,macaca:0.47):0.14,ateles: 0.62): 0.38,galago: 1.00): 0.00;1.000.780.530.380.000.781.000.530.380.000.530.531.000.380.000.380.380.381.000.000.000.000.000.001.00>primcor

This is an ultrametric tree...distance from root to TIP is constant for all speciesMain diagonalPhylogenetic variance-covariance (vcv) matrix ( )

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

t4t5t2t8t6t3t1t7t41.8301.2150.7610.7610.7610.7610.0000.000t51.2151.7610.7610.7610.7610.7610.0000.000t20.7610.7611.8181.1150.7740.7740.0000.000t80.7610.7611.1151.5360.7740.7740.0000.000t60.7610.7610.7740.7741.8461.4120.0000.000t30.7610.7610.7740.7741.4121.5240.0000.000t10.0000.0000.0000.0000.0000.0001.0290.558t70.0000.0000.0000.0000.0000.0000.5580.816

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...

ERM (Expected Relationship Matrix; Martins 1995)The same phylogeny can generate different OBSERVED vcv matrices, for different traits, for example...

EVOLUTIONARY MODELSEvolutionary modelsMechanisms (selection, drift, mutations)Interspecific data3. EVOLUTIONARY MODELS

The analytical core of comparative analysisEvolutionary modelsMechanisms (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...

I = selection intensityR = responseT = timeh2 = heritabilityVp = phenotypic variance

Mechanistic versus phenomenological evolutionary models21

Statistical models that capture the expectation of alternative evolutionary processes or mechanismsBROWNIAN MOTION

After Robert Brown (1827)

Simplest continuous-time stochastic process

Simple discrete Random walks...

=A1+(ALEATRIO()-0.5)In Excel, when A1=0...

15 replications of the same process through timeUniform distribution (0-1)UNDERSTANDING BROWNIAN MOTION

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

50 time-steps50 time-steps50 time-stepsSpeciationWHAT ABOUT PHYLOGENY?50 time-steps50 time-steps50 time-steps50 time-steps50 time-steps100 time-steps100 time-steps100 time-steps10.3331001000.3331000.3330.6661Expected VCV matrix

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

If we repeat this many times...But how?????sp1sp2sp3sp4sp5trait1-0.928-3.0100.246-0.433-0.422trait2-2.9140.7882.4863.3081.628trait36.6312.5904.2002.3943.227trait4-6.380-5.593-2.0741.013-0.208trait5-0.5939.7250.9683.5462.101trait62.627-4.5491.953-1.2083.152trait74.411-2.0700.5135.0436.609trait8-1.565-9.055-1.1182.523-3.547trait91.3291.3155.062-1.551-0.145trait10-0.292-1.601-2.935-5.727-5.107trait11-1.430-3.896-2.4940.280-0.925trait12-0.5852.413-1.444-1.901-0.052trait13-2.029-2.192-3.938-2.575-5.659trait14-1.281-1.8633.187-0.340-1.974trait154.1049.415-0.2054.2107.856trait16-2.212-3.050-4.495-6.210-6.638trait17-0.649-7.015-0.971-2.8232.670trait18-3.0460.229-4.418-1.7671.183trait191.1341.4650.842-2.1050.011trait201.241-1.303-0.0914.4910.607...............trait1000-3.2460.329-4.418-2.767-1.82710.53910.3410.35010.3540.3600.33310.2740.2850.3330.6661Observed matrix (10000 traits)Calculate a Pearson (or covariance) matrix amongTaxa (in R mode)

Each line is a simulation that gives Y values for each species...> 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-01-0.11171ntimes=100nsp=5simbw primtreeOU plot(primtreeOU)>primcorOU write.table(primcorOU, file="primcorOU.txt")homopongomacacaatelesgalagohomo1.0000.3280.0890.0400.000pongo0.3281.0000.0890.0400.000macaca0.0890.0891.0000.0400.000ateles0.0400.0400.0401.0000.000galago0.0000.0000.0000.0001.000

This is the expected vcv under OU process with = 2.5!BMOU

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.1000001000001000001000001PHYLOGENETIC 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...MetricsModel BasedStatistical?Measuring Phylogenetic Signal

Number of sppMatrix W with weightsSpecies trait Z centered for the species i e jSum of weights in WMorans I coefficient for phylogenetic autocorrelationPhylogenetic covariancevariance

Sokal, R. R. & Oden, N. L. 1978. Spatial autocorrelation in biology:1. methodology2. Some biological implications and four applications of evolutionary and ecological interestBiological Journal of Linnean Society 10: 199-249. Robert Sokal (1924-2012)CORRELOGRAMS IN POPULATION GENETICS

50

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Matrix Zi * Zj (Z)

Matriz W (1/Dij)Patristic distancesSum of W = 10.38333

WZZijWijSum ZijWij = 8.400781Morans 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)

What is wrong?56Wij = 1 / dij

WPhylogenetic distanceGittleman used something like this, but this is empirical...The W matriz: inverting the relationship between W and D

Wij = 1/ DijWij = 1/ (Dij ^ 2)Wij = 1 / Dij2

I de Moran = 0.72Other possible functons linking W and D

Wij = 1 / dij

Wij = 1 / dij2

Wij = e (- dij)

WPhylogenetic distanceOr we can use directly any VCV matrix, previously defined...!!!!

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

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

64Permutation test

Randomize the tip values in the phylogeny...4.03.53.06.07.58.05.06.0and recalculate Morans many times...

The P-value (Type I error) is given by how many times the Morans I was higher than the randomized values65The PRIMATE example (Lynch 1991):

Body weight and Longevity (log-scale)

Lets use R as a weighting matrix

1.000.780.530.380.000.781.000.530.380.000.530.531.000.380.000.380.380.381.000.000.000.000.000.001.00sppbwlonghomo4.0944.745pongo3.6113.332macaca2.3703.367ateles2.0282.890galago-1.4702.303Morans 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 = 0.617P = 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 bookntimes