Rather complex theoretical considerations are sometimes required to predict the genetic dynamics of a population under supportive breeding, and for the purpose of this presentation, we confine the discussion to illustrating the basic problems by means of some worked examples. We focus on inbreeding (F) and on the corresponding parameter inbreeding effective size that is related to the rate of inbreeding per generation (ΔF) through ΔF = 1/(2Ne) (see Ryman et al. [1995b] or Wang and Ryman [2001 for details). The results presented below have been generated using the equations for inbreeding effective size of Wang and Ryman (2001).

Model: We consider a wild population with an even sex ratio that in a particular generation (t) consists of N individuals. Before mating, these N individuals (breeders) are distributed at random into a captive (c) and a wild (w) group of size Nc and Nw, which reproduce in captivity and in the wild, respectively (Nc + Nw = N; “enumeration” takes place at sexual maturity, and the unit of measurement refers to adults that are potential breeders). The mean and variance of the number of (adult) progeny per wild individual is μw and σ2w, respectively, and the corresponding quantities for the captive segment are μc and σ2c. The captive offspring are released into the natural habitat where they mix and breed with wild individuals. Mating is random within each of the wild and captive groups, and the entire process of selecting breeders for captive propagation and releasing their progeny may be repeated in generation t + 1 and subsequent generations. The wild population is of constant size when μw = 2, it grows when μw > 2, and it is declining if μw < 2. When considering the effect of supportive breeding on the total population size (N), the operation is successful when μc > μw, it has no effect when μc = μw, and it is unfavorable when μc < μw.

Binomial distribution of family size: As an example, we consider a natural population of N = 50 individuals that is constant in size (μw = 2). The organism can be bred in captivity, and under captive conditions, the average number of progeny is typically around 10 (μc = 10). Ecological studies indicate that the present population size is far below carrying capacity, and the manager wants to raise the number through captive propagation of some of the individuals. It is assumed that the removal of some individuals will not affect the reproductive rate of those that are left to reproduce in the wild. A supportive breeding program is initiated, and during each of 10 generations, five randomly selected breeders are caught in the wild and brought into captivity for reproduction and subsequent release of all their offspring (initial N = 50, Nc = 5, and Nw = N – 5 = 45).

The number of progeny per individual (family size) follows a binomial distribution within each of the wild and captive groups. Under such

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