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<br /> <br />increasing the maintenance population size results in proportional . <br />creases in survival. As seen in Figures B and 9, however, effort put intd <br />increasing initial size leads to diminishing returns. <br /> <br />Manipulation That Increases NtJ <br /> <br />Can anything be done to improve the chances of survival once the <br />animals have been collected and have reached captivity? Given an upper <br />limit for the actual number of animals that can be maintained, one varia. <br />ble with a great impact on effective population size (NtJ) is the distribu. <br />tion of offspring among individuals (Chapters B and 9). The simulations <br />discussed above all used random-mating sexual populations with PoiSSon <br />distributed numbers of gametes per animal. This means that neutral <br />heterozygosity is lost approximately at the rate of 1/2NtJ. The more gen. <br />eral formula is <br /> <br />NtJ- <br /> <br />(N,-2R- 2) <br />82 <br />(8'-1 + -.!..) <br />R <br /> <br />where N 1_ 2 is the number of grandparents of the ith generation, g is the <br />number of gametes per individual, and where R and s: are the mean and <br />variance of gamete production, respectively. <br />Because a Poisson distribution of offspring has been assumed so far, <br />for which s: - 8, it follows that when the population is of constant size, <br />NtJ - N - 1 where N is the population (census) size. But if it is possible <br />to manipulate the offspring distribution so that all parents have equal <br />numbers of offspring, then s: - 0, and N, - 2(N - 1). That is, by the <br />expedient of managing reproduction so that all parents contribute <br />equally to the next generation, one can double the effective population <br />size. <br />Another approach to increasing N, (thereoy decreasing the rate of in- <br />breeding) is to exercise control over mate selection. Such control requires <br />the calculation of inbreeding coefficients. Exact coefficients of inbreeding <br />can be calculated from pedigree infonnation (Wright, 1977), but these are <br />not particularly useful in this general model. Exact coefficients of in- <br />breeding in each generation can also be calculated when matings follow a <br />regular scheme (for example, circular half-sib mating, double first cousin <br />mating). These schemes require complete control over the pattern of mat- <br />ing and fixed population sizes. They will not be very useful to the ZOO <br />breeder unless breeding pairs can be closely managed. One such system is <br />maximum avoidance of inbreeding as shown in scheme A of Figure 12 (for <br />a population size of four). In this scheme as in the elimination of differen- <br />tial reproduction, there is a doubling of the effective size over randoJ1l <br />mating and N, - 2N. <br /> <br />"218 <br /> <br />SENNER/CHAPTER 12 <br />INBREEDING DEPRESSION AND THE SURVIVAL OF ZOO POPULATIONS <br /> <br />B <br /> <br /> <br />FIGURE 12. Mating schemes used to decrease the rate of inbreeding in <br />captive populations. <br /> <br />Scheme B in Figure 12 is an example of circular half-sib mating. Al- <br />though it starts out deliberately breeding half.sibs, this scheme eventu- <br />ally and paradoxically results in less loss of heterozygosity. Robertson <br />(1964) shows that for circular half-sib mating <br /> <br />N _ 2(N + 2)2 <br />tJ '11'2 <br /> <br />Circular half-sib mating does not improve on maximum avoidance of <br />inbreeding until after generation 16 in this example, and then only <br />slowly. By this time many groups will be extinct. For this reason alone, <br />circular half-sib mating will not be of practical value to the captive <br />breeder. In addition, both this breeding scheme and the former require <br />specific matings which could be highly disruptive in social species, partic- <br />ularly where there are pair bonds and dominance hierarchies. <br />Finally it should be noted that much of the increase in effective size <br />produced by such schemes can be accounted for by the schemes' inherent <br />enforcement of equal genetic contribution of parents to the next genera- <br />tion. Therefore, there is little to be gained by the use of such protocols so <br />long as the variance of the progeny distribution is kept low. <br /> <br />SUMMARY <br /> <br />1. Extinction of small populations is inevitable; its probability de- <br />Pends on fecundity, viability and sex ratio. These in turn depend <br />on population size which roughly determines the rate of inbreeding. <br /> <br />219 <br />