Overview
This lecture explains how the classic univariate Breeder’s equation is expanded to the multivariate case to account for selection acting on multiple traits, focusing on the role of genetic variance and covariance in evolutionary responses.
Multivariate Breeder’s Equation
- Selection rarely acts on single traits; most traits are genetically linked to others.
- The Breeder’s equation can be expanded to a multivariate form to predict evolutionary changes across multiple traits.
- The multivariate equation calculates Δz (change in mean phenotype) as a vector for all traits considered.
- The G matrix summarizes additive genetic variances (on the diagonal) and covariances (off-diagonal elements).
G Matrix and Trait Covariances
- G11, G22, etc. (diagonals) represent additive genetic variances for individual traits; these drive direct selection responses.
- Off-diagonal terms (e.g., G12) represent additive genetic covariances between pairs of traits; these cause indirect selection responses.
- Indirect selection means a trait can evolve due to selection on a genetically correlated trait.
Constraints on Evolutionary Response
- Lack of additive genetic variance for a trait limits its evolutionary potential, even under strong selection.
- Genetic covariances between traits can constrain or alter the direction of evolutionary change.
- With no genetic correlation, traits can evolve freely toward their fitness optima.
- Positive genetic correlations cause traits to change together, potentially constraining direct adaptation if selection is only on one trait.
- Negative genetic correlations may prevent a population from reaching the optimal trait combination, regardless of selection strength.
Key Terms & Definitions
- Multivariate Breeder’s Equation — An extension of the Breeder’s equation accounting for selection on multiple traits via vector and matrix algebra.
- G Matrix — A matrix representing additive genetic variances (diagonal) and covariances (off-diagonal) for multiple traits.
- Direct Selection — Evolutionary response due to variance in the trait itself.
- Indirect Selection — Evolutionary response in a trait due to selection acting on a genetically correlated trait.
Action Items / Next Steps
- Read relevant chapters in “A Primer of Ecological Genetics” by Conner and Hart.
- Review the provided web link for more on the G matrix.
- Prepare for next lecture by considering examples of trait correlations in real populations.