Transcript of José Alexandre Felizola Diniz-Filho Departamento de Ecologia, UFG Tópicos Avançados em Ecologia...
- Slide 1
- 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
- Slide 11
- ((((homo: 0.22,pongo: 0.22): 0.25,macaca:0.47):0.14,ateles:
0.62): 0.38,galago: 1.00): 0.00; 1.000.780.530.380.00
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
- Slide 12
- This is an ultrametric tree...distance from root to TIP is
constant for all species Main diagonal Phylogenetic
variance-covariance (vcv) matrix ( )
- Slide 13
- This ultrametric tree has a total lenght of 1.0 PHYLOGENETIC
CORRELATION = Standardized Variance-Covariance = Shared proportion
of branch lenght
- Slide 14
- 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
- Slide 15
- 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
- Slide 18
- Evolutionary models Mechanisms (selection, drift, mutations)
Interspecific data 3. EVOLUTIONARY MODELS
- Slide 19
- The analytical core of comparative analysis
- Slide 20
- 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...
- Slide 26
- 50 time-steps Speciation WHAT ABOUT PHYLOGENY?
- Slide 27
- 50 time-steps 100 time-steps 1 0.3331 001 00 1 00 0.6661
Expected VCV matrix
- Slide 28
- Slide 29
- 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...
- Slide 32
- > 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
- 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 `
+
- Slide 85
- colourPhyl1% YELLOWGR019.77 BLUEcomb22.06 REDbal30.61
GREENnorm32.49 ORANGEgr5078.03
- Slide 86
- Slide 87
- 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
- Slide 121
- >library(motmot) primbw