Quick viewing(Text Mode)

Quantitative Evolution of Morphology

Quantitative Evolution of Morphology

G562 Geometric

Quantitative 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 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: size . 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

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

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. and quantitative characters. Annual Review of Ecology and Systematics, 19: 445-471.

Lande, R. 1976. 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 , 35, 83-96.

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