Population selection to maximize value in an environmental gradient

A theory for determining optimum planting and breeding zones is described. The theory is based on a model consisting of Gaussian response functions for traits that vary in a gradient for a single environmental variable. Environments are assumed to be normally distributed with known mean and variance. Methods are presented for determining parameters of response functions that maximize the expected value for such a trait when two, three and four populations are selected for breeding or as sources of propagules. Expected value is maximized only when the populations selected have response functions symmetrically arrayed about the mean of the environmental variable. Maximum expected value was shown to increase with increasing number of selected populations at a rate that depends upon the ratio of homostasis to environmental variability. The methods presented are illustrated with data on performance of Scots pine provenances in Sweden.