Adaptation and Fitness in Animal Populations pp 83-101 | Cite as

# Spherical Cows Grazing in Flatland: Constraints to Selection and Adaptation

## Abstract

The vector of traits that a breeder is trying to improve and/or natural selection is acting upon has a distribution of phenotypic and breeding values that lives in a complex space. This space is not simply a sphere with equal variation in all dimensions, but rather a much more constrained structure and these constraints have critical implications for selection responses. Here we emphasise the importance of the resurgence of interest in Fisher’s geometric model of adaptation, and the necessity of taking a multivariate view of selection. We review basic matrix tools, such as the angle between two vectors, the projection of a vector into a matrix subspace, and more recent advances such as the estimation of the dimensionality of a covariance matrix, that provide different ways to quantify potential constraints on evolutionary change. A key goal of quantitative genetics is to now understand the geometry of the genetic covariance matrix **G** from both the point of view of mutation generating genetic variance and from selection depleting it. Initial studies using *Drosophila* have suggested that **G** may be very ill-conditioned, with a number of phenotypic dimensions displaying very little genetic variance. Such multivariate constraints may be quite important, potentially resulting in very little usable genetic variation in the direction of persistent directional selection, despite significant heritabilities in each of the component traits.

### Keywords

Selection adaptation G matrix genetic constraints matrix subspace projection## Preview

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