José Alexandre Felizola Diniz-Filho Departamento de Ecologia, UFG Tópicos Avançados em Ecologia...
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José Alexandre Felizola Diniz- Filho Departamento de Ecologia, UFG Tópicos Avançados em Ecologia Filogenética e Funcional Modelos evolutivos, sinal filogenético, conservação de nicho
José Alexandre Felizola Diniz-Filho Departamento de Ecologia, UFG Tópicos Avançados em Ecologia Filogenética e Funcional Modelos evolutivos, sinal filogenético,
Jos Alexandre Felizola Diniz-Filho Departamento de Ecologia,
UFG Tpicos Avanados em Ecologia Filogentica e Funcional Modelos
evolutivos, sinal filogentico, conservao de nicho
Slide 2
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
Slide 3
Phylogenetic Comparative Methods Phylogenetic Diversity
Community Phylogenetics 1. Introduction: on the research
traditions... Paul Harvey (1980s) Campbell Webb (2002) Dan Faith
(1992)
Slide 4
Marc Cadotte (University of Toronto)
Slide 5
Ecophylogenetics Assemblages Traits
Slide 6
1985
Slide 7
Traits Correlated Evolution Phylogenetic Signal TRAITS
Slide 8
A B C 2 2 3 5 2. Phylogenies and relationship matrices
Slide 9
ABC A010 B 04 C 40 Pairwise (patristic) distances
>primcor
Slide 10
ABC A1.000 B0 0.39 C0 1.0 Shared proportion of branch lenght
from root to tips
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...
Slide 16
ERM (Expected Relationship Matrix; Martins 1995)
Slide 17
The same phylogeny can generate different OBSERVED vcv
matrices, for different traits, for example... EVOLUTIONARY
MODELS
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...
Slide 21
I = selection intensity R = response T = time h 2 =
heritability Vp = phenotypic variance Mechanistic versus
phenomenological evolutionary models
Slide 22
Statistical models that capture the expectation of alternative
evolutionary processes or mechanisms
Slide 23
BROWNIAN MOTION -After Robert Brown (1827) - Simplest
continuous-time stochastic process Simple discrete Random
walks...
Slide 24
=A1+(ALEATRIO()-0.5) In Excel, when A1=0... 15 replications of
the same process through time Uniform distribution (0-1)
UNDERSTANDING BROWNIAN MOTION
Slide 25
The distribution of Y at time step 1000, replicated 2000
times...
Here we assumed that species are INDEPENDENT (the started all
at the root) Here species are PHYLOGENETICALLY STRUCTURED
Slide 30
If we repeat this many times... But how?????
Slide 31
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...
>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
Slide 45
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
Slide 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 Patterns
and processes...
Slide 47
Metrics Model Based Statistical ? MEASURING PHYLOGENETIC
SIGNAL
Slide 48
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
Slide 49
Slide 50
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
Slide 51
Slide 52
Matrix Zi * Zj (Z)
Slide 53
Matriz W (1/Dij) Patristic distances Sum of W = 10.38333
Slide 54
W Z ZijWij Sum ZijWij = 8.400781
Slide 55
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)
Slide 56
What is wrong?
Slide 57
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
Slide 58
Wij = 1/ Dij Wij = 1/ (Dij ^ 2)
Slide 59
-W ij = 1 / D ij 2 I de Moran = 0.72
Slide 60
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...!!!!
Slide 61
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
Slide 62
Slide 63
Slide 64
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
Slide 65
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
Slide 66
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
Slide 68
ntimes
> chev209 1-var(chev209$residuals)/var(bs209)
Slide 82
Phylogenetic Eigenvector Regression (PVR)
Slide 83
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
Slide 84
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 `
+
Pierre Legendre Daniel Griffith Principal coordinate analysis
of truncated geographic distances W (PCNM) Eigenvectors of double
centered binary (0/1) connectivity matrix
Slide 88
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)
Slide 89
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