Provisional breeding zone determination modeled as a maximal covering location problem

Abstract

This study was a first attempt to model the problem of delineating breeding zones as a maximal covering location problem. The method involves two steps. First, a comprehensive set of candidate breeding zones is generated for a region using the focal point seed zone method. This method allows for control over the adaptive difference of genetic material within each zone. A grid of points is used to create the set of candidate breeding zones: one zone per point. Next, candidate zones are entered into a maximal covering location model formulated to suit this problem. The objective of this model is to select a subset of candidate zones that maximally covers the area of the region, given a limit on the number of zones to be selected and on the adaptive dissimilarity allowed within zones. Through use of this method, decision-makers can gain insight into how many breeding zones are needed to cover the region. Using different inputs from the focal point seed zone method, it is also possible to explore the trade-offs between the quantity and the quality of breeding zones. The method was tested on data from a series of jack pine (Pinus banksiana Lamb.) common garden trials of 102 seed sources from northwestern Ontario.