Bayesian models for macroevolutionary studies

Transcription

1 Bayesian models for macroevolutionary studies Nicolas Lartillot February 28, 2012 Nicolas Lartillot (Universite de Montréal) Integrative models of macroevolution February 28, / 47

2 The molecular clock 8%&9%:&'9%+.*;:-(+ "#$%&$'()*+'()+,'"*-(./+0123/+4-5"&'+/ ρ = µ f 0 substitution rate = mutation rate fraction of neutral mutations

3 Variation of the substitution rate among lineages AARDVARK GOLDENMOLE TENRECID ELEPHANTULUS MACROSCELIDES ELEPHANT HYRAX SIRENIAN ANTEATER SLOTH ARMADILLO CAT DOG PANGOLIN FLYINGFOX PHYLLOSTOMID HORSE RHINO TAPIR COW DELPHINOID WHALE HIPPO PIG LLAMA HEDGEHOG SHREW MOLE CAVIOMORPH MOUSE RAT SCIURID PIKA RABBIT FLYINGLEMUR HUMAN LEMUR TREESHREW 0.1 subs per site concatenation of 13 nuclear genes, 38 placentals

4 Variation of the substitution rate among lineages Possible causes generation-time effect time metabolic rate effects selection for longevity (reviewed in Lanfear et al, 2010) = AARDVARK GOLDENMOLE TENRECID ELEPHANTULUS MACROSCELIDES ELEPHANT HYRAX SIRENIAN ANTEATER SLOTH ARMADILLO CAT DOG PANGOLIN FLYINGFOX PHYLLOSTOMID HORSE RHINO TAPIR COW DELPHINOID WHALE HIPPO PIG LLAMA HEDGEHOG SHREW MOLE CAVIOMORPH MOUSE RAT SCIURID PIKA RABBIT FLYINGLEMUR HUMAN LEMUR TREESHREW 0.1 subs per site concatenation of 13 nuclear genes, 38 placentals

5 Introduction Tree shape and diversification patterns Nee et al, 1994 modeling speciation-extinction processes using time-calibrated phylogenies to fit and compare models Nicolas Lartillot (Universite de Montréal) Integrative models of macroevolution February 28, / 47

6 tion event, a new 10 l 2 is drawn from the dis- (ii) Cope s rule with tinction alone, and (v timal body size, has the best empirical support a probability calculated only from the species size. produced size distrib [model selection by likelihood ratio test theandcretaceous-tertiary We specified a basal extinction boundary rate b by(19, assuming 20, 25). close to the empirical Bayesian information criterion (24)]. ThisFurther, model that a limit the number in this of vicinity Recent terrestrial is supported mammal species by both dicts a particular exti includes both a strengthening of Cope s rule for small-bodied species (x ~ < 32 g) and a small but is close to a putative carrying capacity. We then let extinction risk per unit time increase logarithmically that could be tested data. with body size (24, 28). uniformly positive bias for larger species, resulting Diffusion This model and leaves To further discrim in an average body-size growth of 4.1 ± 1.0% only the rate r by which riskshort term increases with size planations for the sp selective advantages tested simpler diffus rameters estimated fr A B ing (i) unbiased diffu 10 (iii) Cope s rule alon that omits the incre 2 Long term risk species (x < ~ 32 g). We x A of extinction 1 predicted size distrib Lower 0.5 times dramatically so x D boundary bution (Fig. 3, B and effects Additionally, we found for large-bodied sp Ancestor descendant data extinction risk increa Estimated model (µ, σ) Body size (g) results support the i lower limit, the diffu Ancestor body (g) increasing risk of ext Clauset Fig. 1. et Smoothed al, 2008 species body-size distribution of Fig. 2. (A) A schematic illustrating a simple4002 cladogenetic Recent diffusion terrestrial model of mammals species body-size [dataevolution, from (21)], an increased bias tow where the size of a descendant species x D is related to its ancestor s size x A by a multiplicative factor l.(b) bodied species (x ~ < 3 Empirical data on 1106 changes in North American showing mammalian the three body size macroevolutionary [data from (20)], as a function processesthus, the shape of ancestor size, overlaid with the estimated that model shape of within-lineage the relative changes, abundances where the average of different logchange can be interpreted in log l varies piecewise as a function of body size (24). macroevolutionary pr n body size (17) could also produce a simape. Furthermore, different mechanisms ive body-size evolution on spatial and temscales (3), and the importance of interic competition to the macroevolutionary ics of species body size is not known. developed a generalized diffusion model ies body-size evolution, in which the size ution is the product of three macroevoluprocesses (Fig. 1). We combine these ses, each of which has been independently Extinction and body size d (1, 2, 17, 18), in a single quantitative ork, estimate its parameters from fossil n extinct terrestrial mammals from before te Quaternary (19, 20), and determine er this model, or simpler variants, can ree the sizes of the 4002 known extant and terrestrial mammal species from the late nary (Recent species) (21, 22). is model makes three assumptions: (i) s size varies over evolutionary time as a enetic Equilibrium multiplicative between diffusion process ; the size of a descendant species x D is the t of a stochastic growth factor l and its or s size x A, that is, x D = lx A. For each coupling between tree shape and body size evolution A Empirical data intra-lineage trend towards larger 1 body B size Diffusion model higher risk of extinction in larger animals ion Multiplicative change in Log body Density size, λ sizes. The left tail of the distribution is created by diffusion in the vicinity of a taxon-specific lower limit near 2 g, whereas the long right tail is produced by the interaction of diffusion over evolutionary time (including trends like Cope s rule) and the long-term risk of extinction 10 2 from increased body size. ion ion 10 1 C 10 2 Downloaded

7 Introduction Motivation Macro-evolutionary studies reconstructing divergence times testing diversification models testing models about life-history evolution understanding driving forces of molecular evolution correlation diversification / life-history / substitution patterns Potential methodological problems current approaches proceed sequentially problems of bias / error propagation lack of flexibility calls for more integrative approaches Nicolas Lartillot (Universite de Montréal) Integrative models of macroevolution February 28, / 47

8 Estimating divergence times: the relaxed clock model r t sequence alignment &'(#'('#('&#')'#***# &'&#'&'#('&#')'#***# &'(#'&'#()&#')'#***# &'(#'&'#()&#')'#***# %# $# "# Data and constraints multiple alignment D (here, nuclear coding genes in mammals) tree topology T, and fossil calibrations Φ

9 Estimating divergence times: the relaxed clock model r t sequence alignment &'(#'('#('&#')'#***# &'&#'&'#('&#')'#***# &'(#'&'#()&#')'#***# &'(#'&'#()&#')'#***# %# $# "# Hierarchial Bayesian model diversification process (e.g. birth-death, parameters λ, µ, ρ) substitution rate: Brownian log-normal process (variance σ 2 ) substitution process (4x4 substitution matrix Q) parameters: θ = (λ, µ, ρ, σ, t, r)

10 Estimating divergence times: the relaxed clock model r t sequence alignment &'(#'('#('&#')'#***# &'&#'&'#('&#')'#***# &'(#'&'#()&#')'#***# &'(#'&'#()&#')'#***# %# $# "# Diversification process diversification process (e.g. birth-death, parameters λ, µ, ρ) tree topology T, fossil constraints Φ t: vector of divergence times p(t λ, µ, ρ, Φ, T ) = p(t λ, µ, ρ) Kendall 1948, Nee et al 1994, Yang and Rannala, 2006

11 Molecular dating Brownian process lnr j ~ N(ln r jup,"#t) r j r j up l = r "t %# $# "# "t = t 2 # t 1 joint probability: p(d T,l,Q)p(r t,")p(t)p(")p(q) x t = ln r t dx t = σdb t x t N(x 0, σ 2 t) P taxa, j = 1..2P 2 branches p(r r 0, σ 2, t) = j p(r j r jup, t j, σ 2 ) Nicolas Lartillot (Universite de Montréal) Integrative models of macroevolution February 28, / 47

12 Molecular dating Substitution process sequence alignment r j &'(#'('#('&#')'#***# r j up l = r "t &'&#'&'#('&#')'#***# &'(#'&'#()&#')'#***# &'(#'&'#()&#')'#***# %# $# "# "t = t 2 # t 1 probability of transition between nucleotides a and b over time t: r = 1 t t1 r t dt r j + r jup t 2 2 p(a b r, t, Q) = [exp(r t Q)] ab Nicolas Lartillot (Universite de Montréal) Integrative models of macroevolution February 28, / 47

13 Molecular dating Relaxed clock model lnr j ~ N(ln r jup,"#t) r j r j up l = r "t %# $# "# "t = t 2 # t 1 joint probability: joint probability: p(d T,l,Q)p(r t,")p(t)p(")p(q) p(t λ, µ, ρ) p(r t, σ 2 ) p(d r, t, Q) Nicolas Lartillot (Universite de Montréal) Integrative models of macroevolution February 28, / 47

14 Molecular dating Bayes theorem: general formulation p(θ D) = p(d) = p(d θ)p(θ) p(d) p(d θ)p(θ)dθ θ model parameters D Data p(θ) prior distribution p(d θ) likelihood p(d) evidence, or marginal likelihood p(θ D) posterior distribution Nicolas Lartillot (Universite de Montréal) Integrative models of macroevolution February 28, / 47

15 Sampling from the posterior: the Metropolis algorithm Histogram of out2[[1]] 1 "out2" Density Metropolis algorithm draw U Uniform[0, 1] random walk set θk = θ k + δ(u 0.5), possibly reflecting back into [0, 1] { } accept with probability q = min iterate 1, p(θ k D) p(θ k D) (θ k ) k N is a Markov chain with stationary distirbution p(θ f )

16 Molecular dating Relaxed clock model lnr j ~ N(ln r jup,"#t) r j r j up l = r "t %# $# "# "t = t 2 # t 1 joint probability: posterior proportional to joint probability: p(d T,l,Q)p(r t,")p(t)p(")p(q) p(λ, µ, ρ) p(σ 2 ) p(t λ, µ, ρ) p(r t, σ 2 ) p(d r, t, Q) Nicolas Lartillot (Universite de Montréal) Integrative models of macroevolution February 28, / 47

17 Molecular dating Relaxed clock model r j " r j # %# $# "# Metropolis Hastings on rates α = p(d r, t, Q) p(r t, σ 2 ) p(d r, t, Q) p(r t, σ 2 ) α > 1: accept move α < 1: accept with prob. α Nicolas Lartillot (Universite de Montréal) Integrative models of macroevolution February 28, / 47

18 Molecular dating Relaxed clock model %# $# "# t j " t # j Metropolis Hastings on divergence times α = p(d r, t, Q) p(r t, σ 2 ) p(t λ, µ, ρ) p(d r, t, Q) p(r t, σ 2 ) p(t λ, µ, ρ) α > 1: accept move α < 1: accept with prob. α Nicolas Lartillot (Universite de Montréal) Integrative models of macroevolution February 28, / 47

19 Molecular dating Relaxed clock model lnr j ~ N(ln r jup,"#t) r j r j up l = r "t %# $# "# "t = t 2 # t 1 joint probability: p(d T,l,Q)p(r t,")p(t)p(")p(q) Metropolis Hastings on σ 2 α = p(r t, σ 2 ) p(σ 2 ) p(r t, σ 2 ) p(σ 2 ) α > 1: accept move α < 1: accept with prob. α Nicolas Lartillot (Universite de Montréal) Integrative models of macroevolution February 28, / 47

20 Molecular dating Relaxed clock model lnr j ~ N(ln r jup,"#t) r j r j up l = r "t %# $# "# "t = t 2 # t 1 joint probability: Metropolis Hastings on λ, µ, ρ p(d T,l,Q)p(r t,")p(t)p(")p(q) α = p(t λ, µ, ρ ) p(λ, µ, ρ ) p(t λ, µ, ρ) p(λ, µ, ρ) α > 1: accept move α < 1: accept with prob. α Nicolas Lartillot (Universite de Montréal) Integrative models of macroevolution February 28, / 47

21 Posterior mean times and rates Divergence times and substitution rat rate time CAT DOG PANGOLIN FLYINGFOX PHYLLOSTOM HORSE RHINO TAPIR COW DELPHINOID WHALE HIPPO PIG LLAMA HEDGEHOG SHREW MOLE CAVIOMORPH MOUSE RAT SCIURID PIKA RABBIT FLYINGLEMU HUMAN STREPSIRRH TREESHREW GOLDENMOLE TENRECID LOEARELESH SHEARELESH AARDVARK ELEPHANT HYRAX SIRENIAN ANTEATER SLOTH ARMADILLO DIDELPHIS MONODELPHI PLATYPUS 100 KT 0 Myrs (Thorne et al 1998, Lepage et al 2007, Rannala and Yang 2007) Multidivtime, PhyloBayes, MCMCtree

22 Substitution-calibrated versus time-calibrated trees AARDVARK GOLDENMOLE TENRECID ELEPHANTULUS MACROSCELIDES ELEPHANT HYRAX SIRENIAN ANTEATER SLOTH ARMADILLO CAT DOG PANGOLIN FLYINGFOX PHYLLOSTOMID HORSE RHINO TAPIR COW DELPHINOID WHALE HIPPO PIG LLAMA HEDGEHOG SHREW MOLE CAVIOMORPH MOUSE RAT SCIURID PIKA RABBIT FLYINGLEMUR HUMAN LEMUR TREESHREW 0.1 subs per site

23 Correlating rates and life-history traits rate / mass regression log mass log subs. rate correcting for phylogenetic inertia (independent contrasts) sequential method: error propagation no feedback of rate variations on life-history evolution

24 Coupling substitution process with life-history evolution &'#"()# *+,-#./00# 01*02#3/4# r 3 r 2 r 1 sequence alignment $ " = 2 #1 ' & ) %#1 1 ( covariance matrix l 2 = r 2 "t "()# )2(5# 5)# 789#898#987#8:8#222# 787#878#987#8:8#222# 789#878#9:7#8:8#222# (6))# 789#878#9:7#8:8#222# %# $# "# kg (Lartillot and Poujol, 2011, Molecular Biology and Evolution) Data and constraints multiple alignment D (nuclear coding genes in mammals) matrix of quantitative characters (C) (life-history traits) tree topology (T ), and fossil calibrations (Φ)

25 Coupling substitution process with life-history evolution &'#"()# *+,-#./00# 01*02#3/4# r 3 r 2 r 1 sequence alignment $ " = 2 #1 ' & ) %#1 1 ( covariance matrix l 2 = r 2 "t "()# )2(5# 5)# 789#898#987#8:8#222# 787#878#987#8:8#222# 789#878#9:7#8:8#222# (6))# 789#878#9:7#8:8#222# %# $# "# kg (Lartillot and Poujol, 2011, Molecular Biology and Evolution) Hierarchial Bayesian model (parameter estimation by MCMC) diversification process t (birth-death, parameters λ, µ, ρ) Brownian multivariate process X (covariance matrix Σ) time-dependent codon model Q

26 Codon model Mutation matrix U (4 x 4) A C G T A γ κγ 1 C 1 γ κ G κ γ 1 T 1 κγ γ κ: transition-transversion ratio γ = GC /(1 GC ) (GC : equilibrium GC) Codon substitution matrix Q (61 x 61) Q c1 c 2 = U n1 n 2, Q c1 c 2 = U n1 n 2 ω, c 1, c 2 synonymous, c 1, c 2 non-synonymous. Muse and Gaut 1994

27 Phylogenetic covariance model Generalization time-dependent substitution parameters rate of synonymous substitution (r) non-synonymous / synonymous ratio (ω) equilibrium GC (γ) time-dependent quantitative traits sexual maturity (proxy of generation time) adult body mass maximum recorded lifespan (proxy of longevity) metabolic rate genome size karyotypic number (number of chromosomes 2n) Nicolas Lartillot (Universite de Montréal) Integrative models of macroevolution February 28, / 47

28 Coupling substitution process with life-history evolution &'#"()# *+,-#./00# 01*02#3/4# r 3 r 2 r 1 sequence alignment $ " = 2 #1 ' & ) %#1 1 ( covariance matrix l 2 = r 2 "t "()# )2(5# 5)# 789#898#987#8:8#222# 787#878#987#8:8#222# 789#878#9:7#8:8#222# (6))# 789#878#9:7#8:8#222# %# $# "# kg (Lartillot and Poujol, 2011, Molecular Biology and Evolution) posterior proportional to joint probability: p(λ, µ, ρ) p(t λ, µ, ρ) p(σ) p(x t, Σ) p(d X, t)

29 Phylogenetic covariance model Conjugate sampling Data augmentation: substitution mappings resample mapping conditional on current model parameters resample parameters conditional on current mapping Lartillot, 2006, J. Comput Biol. Conjugacy on covariance matrix - Brownian multivariate process Σ W 1 (Σ 0, q) p(σ Σ 0, q) Σ 0 q 2 Σ q+m+1 2 e 1 2 tr(σ 0Σ 1), p(σ): Inverse-Wishart of parameters Σ 0 = κi, q d.f. p(x Σ, t): Multivariate normal p(σ X, t): Inverse-Wishart of parameters Σ + A, q + 2P 2 d.f. Lartillot and Poujol 2011, Mol. Biol. Evol. Nicolas Lartillot (Universite de Montréal) Integrative models of macroevolution February 28, / 47

30 Phylogenetic covariance model Conjugate sampling Conjugacy on covariance matrix - Brownian multivariate process p(σ): Inverse-Wishart of parameters Σ 0 = κi, q d.f. p(x Σ, t): Multivariate normal p(σ X, t): Inverse-Wishart of parameters Σ + A, q + 2P 2 d.f. A: empirical cov. matrix of branchwise contrasts: (X j X jup )/ t j. Integrating the joint probability over Σ: p(λ, µ, ρ) p(t λ, µ, ρ) ( ) p(x t, Σ)p(Σ)dΣ p(d X, t) MCMC marginalized over Σ for each point θ k of the MCMC: Σ k p(σ k X) Lartillot and Poujol 2011, Mol. Biol. Evol. Nicolas Lartillot (Universite de Montréal) Integrative models of macroevolution February 28, / 47

31 Results Rates, dates and traits 1. Nuclear data: correlates of synonymous rate ds ds dn/ds mat. long. mass met. dn/ds maturity longevity mass red: blue: light shade: positive negative not significant metabolic rate strong correlations between life-history traits ds correlates negatively with body mass, gen. time and longevity R 2 : life-history variations explain 35% of synonymous rate. dn/ds positively correlated with body size (nearly neutral effect?) Nicolas Lartillot (Universite de Montréal) Integrative models of macroevolution February 28, / 47

32 Inferring divergence times and body size evolution Manis Ailuropoda Canis Felis Panthera Equus Ceratotherium Tapirus Tadarida Antrozous Myotis Artibeus Nycteris Megaderma Pteropus Rousettus Sus Bos Tragelaphus Hippopotamus Megaptera Tursiops Lama Vicugna Solenodon Erinaceus Sorex Galemys Talpa Tarsius Callithrix Macaca Pongo Gorilla Homo Pan Otolemur Lemur Microcebus Cynocephalus Galeopterus Ptilocercus Tupaia Castor Dipodomys Pedetes Mus Rattus Hystrix Erethizon Cavia Hydrochoerus Muscardinus Spermophilus Tamias Ochotona Oryctolagus Sylvilagus Orycteropus Amblysomus Echinops Elephantulus Macroscelides Loxodonta Procavia Trichechus Dasypus Chaetophractus Euphractus Choloepusdi Choloepusho Myrmecophaga Tamandua Myrs KT

33 The evolution of body size CAT 1 kg 10 kg DOG PANGOLIN FLYINGFOX PHYLLOSTOMID HORSE Pakicetids 100 kg RHINO TAPIR 1000 kg COW DELPHINOID WHALE HIPPO PIG LLAMA HEDGEHOG SHREW MOLE (Thewissen et al, 2001) CAVIOMORPH MOUSE RAT SCIURID PIKA RABBIT Hippo Whale ancestor FLYINGLEMUR HUMAN LEMUR TREESHREW GOLDENMOLE TENRECID ELEPHANTULUS MACROSCELIDES AARDVARK ELEPHANT HYRAX SIRENIAN ANTEATER SLOTH ARMADILLO DIDELPHIS post. density coupled < KT uncoupled MONODELPHIS PLATYPUS log 10 Mass (g) 100 KT 0 Myrs

34 Systematic trends substitution rate body mass Cope s or Stanley s rule intra-lineage drive towards larger body size more frequent extinction of large-bodied mammals needs to be explicitely modeled (directed Brownian motion) possible impact in estimated divergence times (Welch 2008) connections with mass-dependent extinction (FitzJohn, 2010).

35 Results GC landscapes and biased genes conversion 2. Equilibrium GC (GC ) in nuclear genomes ds dn/ds GC* mat. mass long. # chrom. ds dn/ds GC* maturity red: blue: light shade: positive negative not significant mass longevity # chromosomes negative correlation between GC and body size positive correlation between GC and number of chromosomes Nicolas Lartillot (Universite de Montréal) Integrative models of macroevolution February 28, / 47

36 Results GC landscapes and biased genes conversion Biased gene conversion (BGC) during meiosis GC is overtransmitted GC-biased mismatch repair A A T = T A T C G C G C G C G C G adapted from Duret and Galtier 2009 x GC = 1 + b 2 x AT = 1 b 2 meiotic distorsion bias b positive selection for GC b proportional to local recombination rate Nicolas Lartillot (Universite de Montréal) Integrative models of macroevolution February 28, / 47

37 Biased gene conversion explains variations of GC ds ds dn/ds gc mat. mass long. # chrom. dn/ds gc maturity red: blue: light shade: positive negative not significant mass longevity # chromosomes Negative correlation GC / body size larger animals = smaller population = less efficient selection also less efficient BGC (lower GC )

38 Biased gene conversion explains variations of GC F. Pardo-Manuel de Villena, C. Sapienza: Recombination and chromosome arms ds ds dn/ds gc mat. mass long. # chrom. dn/ds gc maturity mass longevity # chromosomes Fig. 1. Plot of mammalian recombination frequency as a function of haploid number of chromosome arms (FN/2). a) Recombination estimated as number of chiasma de Villena (NC). Each and circlesapienza, represents a species: , Dasyuroides byrnei; 2, Dasyurus viverrinus; 3, Sarcophilus harrissi; 4, Smithopsis crassicaudata; 5, Paremeles gunnii; 6, Isoodon macrourus; 7, Dasypus novemcinctus; 8, Oryctolagus cuniculus; 9, Cricetus cricetus; 10, Lagurus lagurus; 11, Meriones ungiculatus; 12, Apodemus sylvaticus; 13, Rattus norvegicus; 14, Mus musculus; 15, Cebuella pygmamaea; 16, Sanguinus oedipus; 17, Macaca fuscata; 18, Macaca mulatta; 19, Macaca nemestrina; 20, Pan troglodytes; 21, Homo sapiens; 22, Homo sapiens; 23, Mandrillux sphinx; 24, Cebus capucinus; 25, Lemur fulvus; 26, Lemur fulvus collaris; 27, Lemur fulvus albocollaris; 28, Akodon arviculoides; 29; Akodon arviculoides; 30, Akodon sp; 31, Akodon nigris; 32, Zygodontomys lasiurus; 33, Clyomys laticeps; 34; Nectomys squamipes; 35, Nectomys squamypes; 36, Oxymicterus sp; 37, Euryzygomalomys guiara; 38, Proechimys iheringi; 39, Mus musculus; 40, Mesocricetus auratus; 41, Positive correlation GC / chromosome number conversion bias proportional to recombination rate 1 recombination event per chromosome arm per meiosis recombination rate inversely proportional to chromosome size linkage maps are provisional, they are in good agreement with the regression line. Both the regression line for all species in Fig. 1a (NC 0.85(NF/2) + 6.2; R ; F < "17, in Fig. 1a) and the average NC per chromosome arm (1.06 and 1.16 in Dutrillaux (1986) and Burt and Bell (1987), respectively) suggest that there is stronger gene conversion bias in more fragmented karyotypes Cricetulus griseus data in species re data reported by number of haploid data in species rep the regression lin data is denoted as map. Each filled c 1, cattle; 2, dog; species not includ 9, cat; 10, horse; a each species is as which we estimate correcting for the used in their stud ingly, the centro combination an and human (Do Mathani and W establishes imp crossovers for a

39 Results GC landscapes and biased genes conversion Mutation selection model Kimura 1982 Substitution process (low mutation approx.) Substitution rate = mutation rate x fixation probability r = 2Nu p = u 2Np = up u: mutation rate p: fixation probability N: effective population size P = 2Np: scaled fixation probability (relative to neutral) Nicolas Lartillot (Universite de Montréal) Integrative models of macroevolution February 28, / 47

40 Results GC landscapes and biased genes conversion Fixation probability of a mutation CARTWRIGHT, LARTILLOT, AND THORNE STUDYING ANCESTRAL LINEAGES 23 FIGURES (a) Ancestral Lineage (b) Ancestral Lineages Relating Three Species FIGURE 1. neutral case p 0 = 1 2N general case p = 2s 1 e 4Ns Scaled fixation probability P = 2Np = 4Ns 1 e 4Ns = S 1 e S S = 4Ns: scaled selection coefficient Nicolas Lartillot (Universite de Montréal) Integrative models of macroevolution February 28, / 47

41 Results GC landscapes and biased genes conversion Scaled fixation probability as a function of S = 4Ns P = 2Np = S 1 e S P S neutral case S = 0: P = 1 deleterious S < 0: P < 1 advantageous S > 0: P > 1 Nicolas Lartillot (Universite de Montréal) Integrative models of macroevolution February 28, / 47

42 Neutral fixation probability in the presence of BGC CARTWRIGHT, LARTILLOT, AND THORNE STUDYING ANCESTRAL LINEAGES 23 FIGURES (a) Ancestral Lineage (b) Ancestral Lineages Relating Three Species FIGURE 1. GC overtransmission A T A T C G C G A T C G C G C G x GC = 1 + b 2 x AT = 1 b 2 Scaled conversion coefficient B = 4Nb mutation from AT to GC P = B 1 e B > 1 mutation from GC to AT P = B 1 e B < 1

43 A mechanistic phylogenetic covariance model substitution rate = mutation rate x fixation probability µ AC µ AG µ AT µ CA µ CG µ CT µ GA µ GC µ GT µ TA µ TC µ TG + B = µ AC B 1 e B µ AG B 1 e B µ AT µ CA B 1 e B µ CG µ CT B 1 e B µ GA B 1 e B µ GC µ GT B 1 e B µ TA µ TC B 1 e B µ TG B 1 e B B = 4N e b : scaled conversion coefficient

44 A mechanistic phylogenetic covariance model substitution rate = mutation rate x fixation probability µ AC µ AG µ AT µ CA µ CG µ CT µ GA µ GC µ GT µ TA µ TC µ TG + B = µ AC B 1 e B µ AG B 1 e B µ AT µ CA B 1 e B µ CG µ CT B 1 e B µ GA B 1 e B µ GC µ GT B 1 e B µ TA µ TC B 1 e B µ TG B 1 e B B = 4N e b : scaled conversion coefficient Predicted scaling of B = 4N e b with mass (M) and # chrom (2n) N e M γ M, (γ M < 0) b = b 0 r r 2n therefore, B M γ M 2n. ln B = γ M ln M + ln 2n + N(0, σ 2 t)

45 9#:;<'*2# &'()#*+,,# -./0&# M (kg) 2n sequence alignment (syn. positions) " = [ 3# 3] covariance matrix B 1 B 2 B 3 "/1# 12/3# 31# %=# 3=# $/# #222# #222# #222# /411# /$# #222# %# $# "# overall modeling strategy only 4-fold degenerate third codon positions modeling joint variation in B, body mass (M) and karyotype (2n) modeling among gene variation (recombination landscapes)

46 Results GC landscapes and biased genes conversion Allometric scaling of B = 4N e b B M γ M 2n. ln B = γ M ln M + γ n ln 2n + N(0, σ 2 t) predicted: γ M < 0 and γ n = 1. Estimated scaling coefficients γ M γ n 73 taxa 17 genes (-0.19, -0.03) 1.28 ( 0.54, 2.03) 33 taxa 115 genes (-0.52, -0.01) 0.21 (-1.20, 1.56) Nicolas Lartillot (Universite de Montréal) Integrative models of macroevolution February 28, / 47

47 A history of biased gene conversion in placentals reconstruction of B = 4N e b Dasypus Choloepus Procavia Loxodonta Echinops Oryctolagus Ochotona Rattus Mus Dipodomys Cavia Spermophilus Otolemur Microcebus Pan Homo Gorilla Pongo B < 1: effectivelymacaca neutral Callithrix Tarsius Tupaia Sorex Erinaceus B > 1: selective regime B > 10: likely deleterious Canis Felis Equus Pteropus Myotis Tursiops Bos Sus Vicugna Dasypus Choloepus Procavia Loxodonta Echinops Oryctolagus Ochotona Rattus Mus Dipodomys Cavia Spermophilus Otolemur Microcebus Pan Homo Gorilla Pongo Macaca Callithrix Tarsius Tupaia Sorex Erinaceus Felis Canis Equus Pteropus Myotis Tursiops Bos Sus Vicugna BGC very weak (B 0.2) in anthropoids BGC above the nearly neutral threshold (B > 1) in many taxa in some lineages (microbats, insectivores) > 5% exons under B > 10

48 GC and genome rearrangements GC and genome rearrangements Biased clustered substitutions in the human genome atterns of substitution bias are nearly identical in human and chimp. (A) Unexpected biased clustered substitutions (UBCS) (fa Dreszer et al, 2007 Figure 3. Exceptions to genome-wide patterns of bias. (A) There is little evidence of UBCS on either human or chimp sex chromosomes. There is also poor agreement between the human and chimp smoothed UBCS curves ( = 0.25 on chrx). The pseudo-autosomal regions (PAR) are shown in green. (B) Human chromosome 2 shows an atypical central peak, which is likely due to the fusion of two ancestral chromosomes (red, human chr2; blue, chimp chr2a and chr2b). The two smoothed curves are in remarkable agreement ( = 0.84). The UBCS signal for hypothetical telomeres (if no fusion had occurred) was predicted (green) by using 16 Mb of distal sequence (yellow). chromosome fusion dated at 0.74 Myr in the human lineage. Dreszer et al, 2007 beit reduced relative to the autosomes) both the human and significant (P 0). This level of correlation is high, especially

49 Perspectives Perspectives on biased gene conversion Perspectives joint reconstruction of GC and genome rearrangements teasing out population size, recombination landscapes and BGC modeling overdispersion due to recombination hotspots turnover understanding the (mal)adaptive value of BGC population genetics models (modifier theory) is there a selective regulation (buffering) of BGC intensity? Nicolas Lartillot (Universite de Montréal) Integrative models of macroevolution February 28, / 47

50 Perspectives Conclusions integrative approach for correlating substitution patterns and quantitative traits can yield mechanistic insights about causes of molecular evolution potential source of information for reconstructing evolution of life-history, population size, karyotype, and genetic systems Perspectives further into mechanistic modeling (dn/ds, BGC) including data about body size of fossil taxa modeling bursts (punctuated equilibria) and trends (Cope s rule) including other diversification models modeling trait-dependent speciation and extinction modeling correlation with discrete characters Nicolas Lartillot (Universite de Montréal) Integrative models of macroevolution February 28, / 47

51 Perspectives Acknowledgments Raphael Poujol Nicole Uwimana Frédéric Delsuc Nicolas Rodrigue Hervé Philippe many others... Software availability (coevol) Nicolas Lartillot (Universite de Montréal) Integrative models of macroevolution February 28, / 47

52 Perspectives Nicolas Lartillot (Universite de Montréal) Integrative models of macroevolution February 28, / 47

53 Perspectives dn/ds, Kr/Kc and the nearly neutral theory 2. Mitochondrial data: correlates of dn/ds ds dn/ds mat. mass long. ds dn/ds maturity mass fit unfit coding sequence 1/N 2 1/N 1 longevity positive correlation between dn/ds and body size compatible with a nearly-neutral interpretation via negative correlation body size population size (N) (Ohta, 1972, Kimura, 1979, Popadin, 2007) Nicolas Lartillot (Universite de Montréal) Integrative models of macroevolution February 28, / 47

54 Radical-conservative amino-acid replacement model (adapted from Livington and Barton, 1993) ω = K r /K c Q ab = R ab if a b conservative, Q ab = R ab ω if a b radical. R ab : a general time reversible 20x20 process. conservative = conserving volume and/or polarity (and/or charge)

55 Perspectives dn/ds, Kr/Kc and the nearly neutral theory Mitochondrial data K r /K c (volume + polarity) Kc Kr/Kc mat. mass long. Kc Kr/Kc maturity mass red: blue: light shade: positive negative not significant longevity positive correlation between K r /K c and body size similar to that observed for dn/ds (but higher R 2 ) charge: no significant effect polarity + volume : strongest correlation (highest R 2 ) Nicolas Lartillot (Universite de Montréal) Integrative models of macroevolution February 28, / 47

56 Reconstructed variations of K r /K c Acinonyx jubatus Felis catus Herpestes javanicus Arctocephalus forsteri Eumetopias jubatus Odobenus rosmarus rosmarus Halichoerus grypus Phoca vitulina Ursus americanus Ursus arctos Ursus maritimus Canis familiaris Ceratotherium simum Rhinoceros unicornis Tapirus terrestris Equus asinus Equus caballus Manis tetradactyla Balaena mysticetus Eubalaena australis Eubalaena japonica Balaenoptera acutorostrata Balaenoptera bonaerensis Balaenoptera borealis Balaenoptera brydei Balaenoptera musculus Balaenoptera physalus Megaptera novaeangliae Eschrichtius robustus Caperea marginata Berardius bairdii Hyperoodon ampullatus Platanista minor Inia geoffrensis Pontoporia blainvillei Lagenorhynchus albirostris Monodon monoceros Phocoena phocoena Kogia breviceps Physeter catodon Hippopotamus amphibius Bos grunniens Bos indicus Bos taurus Bubalus bubalis Capra hircus Ovis aries Cervus nippon centralis Cervus nippon yesoensis Muntiacus crinifrons Muntiacus muntjak Muntiacus reevesi Lama pacos Sus scrofa Artibeus jamaicensis Mystacina tuberculata Chalinolobus tuberculatus Pipistrellus abramus Pteropus dasymallus Pteropus scapulatus Rhinolophus monoceros Rhinolophus pumilus Crocidura russula Episoriculus fumidus Sorex unguiculatus Mogera wogura Talpa europaea Urotrichus talpoides Echinosorex gymnura Erinaceus europaeus Hemiechinus auritus Cavia porcellus Thryonomys swinderianus Jaculus jaculus Mus musculus Mus musculus molossinus Rattus norvegicus Volemys kikuchii Nannospalax ehrenbergi Myoxus glis Sciurus vulgaris Lepus europaeus Oryctolagus cuniculus Ochotona collaris Ochotona princeps Cebus albifrons Cercopithecus aethiops Macaca mulatta Macaca sylvanus Papio hamadryas Colobus guereza Trachypithecus obscurus Gorilla gorilla Homo sapiens Pan paniscus Pan troglodytes Pongo pygmaeus Pongo pygmaeus abelii Hylobates lar Cynocephalus variegatus Tarsius bancanus Lemur catta Nycticebus coucang Tupaia belangeri Bradypus tridactylus Choloepus didactylus Tamandua tetradactyla Dasypus novemcinctus Chrysochloris asiatica Orycteropus afer Elephantulus sp Macroscelides proboscideus Echinops telfairi Dugong dugon Elephas maximus Loxodonta africana Procavia capensis "#$%&'#"( 4)#%55',"-*./"( )*"#+',"-*./"( 0%#'1*)#"( 23/.1'*.10/"( 6',)$+"( 7"8'9'#10"( 4#%9"*)5( :)$"#*0#"( ;<#'*0)#%"(