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Quantitative Evolution of Morphology

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Quantitative Evolution of Morphology G562 Geometric Morphometrics Quantitative evolution of morphology Department of Geological Sciences | Indiana University (c) 2012, P. David Polly G562 Geometric Morphometrics Properties of Brownian motion evolution of a single quantitative trait Most likely outcome = starting value Variance of the outcomes = number of step * (rate parameter)2 Outcomes are normally distributed (reason is Central Limit Theorem: each step adds a random variable, sum of many random variables forms a normal distribution) Department of Geological Sciences | Indiana University (c) 2012, P. David Polly G562 Geometric Morphometrics Brownian motion function for 2 traits ! #################################################################! #! # This function generates a Brownian-motion random walk! # in two traits for n number of generations. The default step! # variance is 1. Written by David Polly, 2008.! #! #################################################################! ! randomwalk <- function(n,r=1) { ! scores <- matrix(ncol=3, nrow=n)! scores[1,] <- c(1,0,0)! for (i in 2:n) {! scores[i,1]=i! scores[i,2]=scores[i-1,2]+rnorm(1, mean=0, sd=sqrt(r)) ! scores[i,3]=scores[i-1,3]+rnorm(1, mean=0, sd=sqrt(r)) ! }! return(as.data.frame(scores)) ! }! ! Department of Geological Sciences | Indiana University (c) 2012, P. David Polly G562 Geometric Morphometrics Quantitative evolutionary theory Change in phenotype Additive genetic variance – covariance matrix Selection coefficients can be: Random Selection coefficients Directional Stabilizing Etc. Lande, R. 1979. Quantitative genetic analysis of multivariate evolution, applied to brain: body size allometry. Evolution, 33: 402-416. Department of Geological Sciences | Indiana University (c) 2012, P. David Polly G562 Geometric Morphometrics To properly model evolution Additive genetic covariance matrix of traits for a single species Normally this is estimated from parent-offspring data Phenotypic covariance matrix (for a single species) can arguably be substituted Don’t use covariance matrix based on multiple species because this confounds phenotypic covariances and phylogenetic covariances Use this covariance matrix to construct shape space Estimate step rates from phylogeny (e.g., Martins and Hansen, 1997; Gingerich, 1993, etc.) Department of Geological Sciences | Indiana University (c) 2012, P. David Polly G562 Geometric Morphometrics Department of Geological Sciences | Indiana University (c) 2012, P. David Polly G562 Geometric Morphometrics Adaptive landscape Wright, 1932 (original concept for allele frequency and reproductive fitness) Simpson 1944 (phenotypic concept for macro evolution) Lande, 1976 (quantitative theory for phenotypes) Polly, P. D. 2004. On the simulation of the evolution of morphological shape: multivariate shape under selection and drift. Palaeontologia Electronica, 7.2.7A: 28pp, 2.3MB. http://palaeo-electronica.org/2004_2/evo/issue2_04.htm Department of Geological Sciences | Indiana University (c) 2012, P. David Polly G562 Geometric Morphometrics Brownian motion analogous to evolution on a flat adaptive landscape where random bumps appear and disappear Shape model in PC scores in Procrustes distance from landmark space shape space ancestral (consensus) shape Polly, P. D. 2004. On the simulation of the evolution of morphological shape: multivariate shape under selection and drift. Palaeontologia Electronica, 7.2.7A: 28pp, 2.3MB. http://palaeo-electronica.org/2004_2/evo/issue2_04.htm Department of Geological Sciences | Indiana University (c) 2012, P. David Polly G562 Geometric Morphometrics Directional selection analogous to a flat adaptive landscape that is tilted up in one direction Shape model in PC scores in Procrustes distance from landmark space shape space ancestral (consensus) shape Polly, P. D. 2004. On the simulation of the evolution of morphological shape: multivariate shape under selection and drift. Palaeontologia Electronica, 7.2.7A: 28pp, 2.3MB. http://palaeo-electronica.org/2004_2/evo/issue2_04.htm Department of Geological Sciences | Indiana University (c) 2012, P. David Polly G562 Geometric Morphometrics Stabilizing selection analogous to classic adaptive peak Shape model in PC scores in Procrustes distance from landmark space shape space ancestral (consensus) shape Polly, P. D. 2004. On the simulation of the evolution of morphological shape: multivariate shape under selection and drift. Palaeontologia Electronica, 7.2.7A: 28pp, 2.3MB. http://palaeo-electronica.org/2004_2/evo/issue2_04.htm Department of Geological Sciences | Indiana University (c) 2012, P. David Polly G562 Geometric Morphometrics Drift Perfectly flat landscape where change occurs by chance sampling from one generation to the next. Change is small and a function of population size (where population size is average number of breeding individuals in the species through the period of interest) Shape model in PC scores in Procrustes distance from landmark space shape space ancestral (consensus) shape Polly, P. D. 2004. On the simulation of the evolution of morphological shape: multivariate shape under selection and drift. Palaeontologia Electronica, 7.2.7A: 28pp, 2.3MB. http://palaeo-electronica.org/2004_2/evo/issue2_04.htm Department of Geological Sciences | Indiana University (c) 2012, P. David Polly G562 Geometric Morphometrics The curvature and slope of a divergence graph depend on the type of selection and the rate of evolution Rate Mode of selection Department of Geological Sciences | Indiana University (c) 2012, P. David Polly G562 Geometric Morphometrics Applied to hominin tooth shape Gómez-Robles, A. and P.D. Polly. 2012. Morphological integration in the hominin dentition: evolutionary, developmental, and functional factors. Evolution, 66: 1024-1043. Department of Geological Sciences | Indiana University (c) 2012, P. David Polly G562 Geometric Morphometrics Possible issues with this kind of modeling: • Does not model the gain or loss of features • Presumes that trait covariances don’t change • Presumes that evolutionary transitions in phenotypes are continuous Department of Geological Sciences | Indiana University (c) 2012, P. David Polly G562 Geometric Morphometrics Department of Geological Sciences | Indiana University (c) 2012, P. David Polly G562 Geometric Morphometrics New Frontiers: Alternative approaches “Homology free” geometric methods that can accommodate gain and loss of features Non-linear shape spaces that can be used to model interactions of genetic, developmental, and environmental effect “Homology free” “Homology free” Homologous outline surface landmarks semilandmarks semilandmarks Polly, 2008 Department of Geological Sciences | Indiana University (c) 2012, P. David Polly G562 Geometric Morphometrics Estimated trajectory of pinniped calcaneum evolution Polly, P. D. 2008. Adaptive Zones and the Pinniped Ankle: A 3D Quantitative Analysis of Carnivoran Tarsal Evolution. In (E. Sargis and M. Dagosto, Eds.) Mammalian Evolutionary Morphology: A Tribute to Frederick S. Szalay. Springer: Dordrecht, The Netherlands. Department of Geological Sciences | Indiana University (c) 2012, P. David Polly G562 Geometric Morphometrics Further reading Adams, D. C. and M. L. Collyer. 2009. A general framework for the analysis of phenotypic trajectories in evolutionary studies. Evolution, 63: 1143-1154. Arnold, S. J., M. E. Pfrender, and A. G. Jones. 2001. The adaptive landscape as a conceptual bridge between micro- and macroevolution. Genetica, 112-113: 9-32. Felsenstein, J. 1988. Phylogenetics and quantitative characters. Annual Review of Ecology and Systematics, 19: 445-471. Lande, R. 1976. Natural selection and random genetic drift in phenotypic evolution. Evolution, 30: 314-334. Lande, R. 1986. The dynamics of peak shifts and the pattern of morphological evolution. Paleobiology, 12: 343-354. Martins, E.P. and T.F. Hansen. 1997. Phylogenies and the comparative method: a general approach to incorporating phylogenetic information into the analysis of interspecific data. The American Naturalist, 148: 646-667. Polly, P. D. 2004. On the simulation of the evolution of morphological shape: multivariate shape under selection and drift. Palaeontologia Electronica, 7.2.7A: 28pp, 2.3MB. http://palaeo-electronica.org/2004_2/evo/issue2_04.htm Polly, P.D. 2008. Developmental dynamics and G-matrices: Can morphometric spaces be used to model evolution and development? Evolutionary Biology, 35, 83-96. Department of Geological Sciences | Indiana University (c) 2012, P. David Polly .
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