Genetic covariance between plant biparental populations: concept and estimation

Covariances between relatives, between traits evaluated in the same environment, and between the values for the same trait in different environments have long been exploited in plant and animal breeding. An assumption underlying these covariances is that individuals belong to a single population or that populations have homogeneous covariances. This assumption is routinely violated, yet a framework for defining and estimating the covariance between populations is lacking. Our objective was to develop and validate a framework for estimating the genetic covariance between plant biparental populations via their molecular marker effects. We derived an analytical method to estimate variances and covariances between such populations, then validated it in simulated datasets and in a maize (Zea mays L.) dataset from a commercial breeding program. The simulated populations confirmed the method's expected behavior, whereas the maize dataset showed trait- and population-specific patterns in (co)variance. Our method requires the following inputs that can all be estimated or approximated: marker effects for each population; a linkage map; linkage phase information; and the inbreeding coefficient of the populations. The covariance between populations has potential applications not only in genomewide prediction, but also in non-breeding fields such as ecology and domestication.