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SOULE/CHAPTER 9 THRESHOLDS FOR SURVIVAL packs, this means that only about 10 animals are breeding in any given year. Thus, the rate of inbreeding is about five percent. Situations of this kind call for immediate and continuous preventative management (that is, artificial gene flow). Fluctuations in population size are another fly in the ointment, as Franklin points out. We once believed that tropical species, especially vertebrates, hardly fluctuated at all, but the discussion by Foster (Chap- ter 5) puts this pleasant fantasy to rest. Overlapping generations, as occur in perennial plants and in most vertebrates, may also shrink the effective number of breeding adults. Hill (1977) states that "with overlapping generations, even if there are no fer- tility differences among survivors and there is random death of breeding individuals, the inbreeding rate will be higher than [expected] since the distribution of lifetime family size is not Poisson. With an exponential distribution of deaths the rate can be nearly three times as high as in the simple formula (Felsenstein, 1971)." Here, it might be heuristic to estimate the minimum size of a nature reserve dedicated to the short-term conservation of a canid species, for example, the wolf. The necessary parameters might he as follows: the density of wolves is about one adult per 20 square kilometers (Rutter and Pimlott, 1968), but only about one-third of the adults actually breed. Say that the population fluctuates, reaching an ebb of about 10 percent of the carrying capacity on the average of once in 10 years. Employing the basic rule, we would start out with an absolute minimum effective size of 100 adults, since many adults fail to breed in a given season, and probably in a given generation. Next, it would be advisable to double the minimum tolerable size to at least 200 because of the problem of overlapping generations. Finally, we assume that the population increases by 50 percent each year following a crash. A little experimentation with formula 3 in Chapter 8 will show that the minimum bottleneck size is about 60 (that is, 1/ Nt ~ 0.0167). Bottleneck sizes below this, given the assumed conditions, prevent ~ from reaching 200. Therefore, the carrying capacity must be 600 or more, and the size ofthe reserve would have to be at least 12,000 square kilome- ters, or substantially larger than Yellowstone National Park. In Chapter. 8, an effective size of 500 is suggested as the lower limit for the preserva- tion of variation and evolution in a changing environment. If we apply Franklin's estimate of a long-term criterion to the wolf example, the min- imum size of the reserve would be an order of magnitude larger. Genetic considerations, therefore, raise the issue of the minimum sizes for reserves in quite a different light than it exists in the biogeographic literature (Chapter 6). That is, most existing parks are too small to ulti- 163