Quantitative evolution of morphology

Quantitative evolution of morphology

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)

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))! }!!

Quantitative evolutionary theory Change in phenotype Selection coefficients can be: Random Directional Stabilizing Etc. Selection coefficients Additive genetic variance covariance matrix Lande, R. 1979. Quantitative genetic analysis of multivariate evolution, applied to brain: body size allometry. Evolution, 33: 402-416.

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.)

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

Brownian motion analogous to evolution on a flat adaptive landscape where random bumps appear and disappear Shape model in landmark space PC scores in shape space Procrustes distance from 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

Directional selection analogous to a flat adaptive landscape that is tilted up in one direction Shape model in landmark space PC scores in shape space Procrustes distance from 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

Stabilizing selection analogous to classic adaptive peak Shape model in landmark space PC scores in shape space Procrustes distance from 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

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 landmark space PC scores in shape space Procrustes distance from 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

The curvature and slope of a divergence graph depend on the type of selection and the rate of evolution Mode of selection Rate

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.

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

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 Homologous landmarks Homology free outline semilandmarks Homology free surface semilandmarks Polly, 2008

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.

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.