quantitative evolution of morphology - morphometrics 4b... · department of geological sciences |...

Department of Geological Sciences | Indiana University (c) 2012, P. David Polly

G562 Geometric Morphometrics

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

Lande, R. 1979. Quantitative genetic analysis of multivariate evolution, applied to brain: body size allometry. Evolution, 33: 402-416.

Change in phenotype

Selection coefficients

Additive genetic variance – covariance matrix

Selection coefficients can be: Random Directional Stabilizing Etc.



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.)



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

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)



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



Directional selection analogous to a flat adaptive landscape that is tilted up in one direction








Stabilizing selection analogous to classic adaptive peak






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)







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



Polly, 2008

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



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. 2008. Developmental dynamics and G-matrices: Can morphometric spaces be used to model evolution and development? Evolutionary Biology, 35, 83-96.

quantitative evolution of morphology - morphometrics 4b... · department of geological sciences |...

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