An Integer Programming Approach to Selecting Individuals for Transfer in Pedigreed Populations

Abstract

Extinctions of various species are becoming more prevalent and as a result, zoos now play an active role in the conservation of endangered species. It is widely recognized that responsible population management practices are necessary to ensure the long term survival of species residing in zoos. A central concern is to preserve genetic diversity of captive populations in order to avoid detrimental effects on reproductive fitness, as well as to maintain the adaptive potential of the population.

When given the task of selecting individuals to transfer to new or existing populations, zoo managers must take into consideration the genetic effects on all involved populations. This is a challenge because the addition and removal of individuals change the genetic composition of the population. The proposed integer program identifies a group of individuals to transfer that maximizes genetic diversity within all populations. This model is based on a measure of genetic diversity, proportional gene diversity, which is deduced from pedigree analysis.

First, an intuitive, quadratic integer program is presented which considers transferring a given number of individuals from one source population to a transfer site that does not contain existing individuals. This model is reformulated as a linear IP, which in tum lends itself to further simplification. Two extensions of this model allow for (1) the specification of demographic constraints and (2) the consideration of preexisting individuals at the transfer site.

Data is obtained from the California condor studbook and performances of the presented models are compared. Both the linear model and the simplified linear model achieve optimality for a small demand. For larger demand, the latter comes close to optimality in a reasonable amount of time. The performance of the linear IP models is compared to that of an existing program used to balance genetic diversity between two populations, MetaMK. MetaMK employs an iterative, user-based method that is sensitive to user input, and is an individual rather than group approach that does not guarantee optimality. For the considered demand values, the IP model outperforms that of MetaMK, although one selection procedure in MetaMK comes close to optimality.