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tions at population size N (Frankel and Soule 1981). This formula, and the concept of genetic drift, simply represents a chronic bottleneck. However, whereas a bottleneck may do little harm in one generation, a prolonged bottleneck can seriously reduce variance (Fig. 3). The longer the period of drift, and the smaller the population, the greater will be the loss of variance. For example, only 60% of original variance will remain in a population of 10 after 10 generations. A population of 100 will retain 95% in that time, but if followed for 100 generations (only 100 years in an "annual" fish), variance is reduced to 60.6%. For 1000 years this value drops to 0.67%. Clearly, drift can be quite detrimental to long-term genetic health in small populations. Even in the short term, drift can significantly reduce proportion of polymorphic loci (P), average number of alleles per locus (Ma), and average heterozygosity per individual (H). For example, a hatchery stock of Montana west-slope cutthroat trout (Sabno clarki lewist); derived 14 years earlier frost approximately 60 wild individuals, exhibited reductions of 57% (P), 29%a (Ma), and 21% (H) compared with the original stock (Allendorf and Phelps 1980). Other studies of natural (Avise and Selander 1972; Vrijenhoek 1979; Vrijenhoek and Lerman 1982) and captive (Ryman and Stahl 1980; Cross and King 1983; Tan- iguchi et al. 1983) populations of fishes also illustrate the importance of drift. Inbreeding Depression. Inbreeding depression is possibly the most serious and yet most nebulous problem facing managers of endangered fishes. Inbreeding, or consanguin- ity, is defined as the mating of individuals related by com- mon ancestry (Jacquard 1975; Falconer 1981), that is, those U Z Z Q W !r 100 Ne= 1000 N =100 90 ? Ne = 50 601 N e W 50 U Z 40 Q 30 Q 20 Ne=1 0 that share more genes in common due to descent than in- dividuals randomly selected from the population. It is a relative concept because the degree of consanguinity is con- sidered relative to that of a base population, and thus there is no absolute measure of inbreeding. The most useful meas- urement is the increase in inbreeding per generation, expressed as AF = (2II . This formula illustrates that a smaller effec- tive population size is more susceptible to inbreeding effects (Fig. 4). Contrary to random drift and bottlenecks, inbreeding does not affect overall genetic variance in the population per se. Rather, inbreeding results in a predictable increase in homo- zygous genotypes (Frankel and Soule 1981) differentially affecting different traits. Fitness characters (those related to reproduction, Robertson 1955) and others with low herita- bilities (Falconer 1981) are most affected by consanguinous matings. Consequently, such traits as fecundity, fertility, age at maturity, clutch size, growth, or survivorship will be greatly depressed by inbreeding (Bowman and Falconer 1960; Wright 1977; Senner 1980). Data from domesticated animals demonstrate that a OF of 10% will result in a 5-10% decline in individual reproductive traits; if total reproductive per- formance is considered in aggregate, this may amount to an overall 25% decrease (Frankel and Soule 1981). This is an unacceptable level of depression, particularly if it occurs over an extended number of generations. Franklin (1980) and Soule (1980) suggest that a 1% level of inbreeding is tolerable in the short term, amounting to an effective pop- ulation size of 50. Population sizes in excess of 500 are sug- gested for the long term. tl d Ne 1 2 3 4 5 6 7 8 9 10 GENERATION Figure 3. Proportion of original genetic variance remaining in pop- ulations of various sizes after 1 to 10 generations. Figure 4. Inbreeding depression as a function of Ne. A selfing hermaphrodite would have 50% of its heterozygous loci become homozygous each generation as a result of inbreeding. A popu- lation of 10 would experience a 5% increase in homozygosity each generation. January - February 1986 17 1 10 100