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adequate for flatheads. Pristine rivers must have supported numbers of other native fishes adequate to feed Colorado squawfish as well. Genetics. Conserving genetic variation has been a major fo- cus of recovery efforts for many endangered species, includ- ing Colorado River fishes (Wydoski 1994). It is important to retain the variation that will permit adaptation to environ- mental change, particularly because many imperiled taxa are in recently altered habitats and thus exposed to new biolog- ical threats, including nonnative predators, competitors, and parasites. In general, the amount of genetic variation within a population results from a balance between mutation, which introduces new variation, and genetic drift, which reduces it. Also, selection may reduce the frequency of detrimental vari- ants or increase the frequency of advantageous alleles. Franklin (1980) suggested that for neutral variants, if the effect of new mutations is about a thousandth of the envi- ronmental variance in fitness per generation, then loss of genetic variation in a finite population is balanced when ef- fective population size (N? see Hedrick 2000) is 500. N can be thought of as the size of a theoretical, randomly breeding population with the same rate of genetic drift as the popula- tion in question. This was the basis for Franklin's very gen- eral choice of N = 500 for maintaining genetic variation. How- ever, N equals the adult breeding number only if, from generation to generation, individuals at the same life stage are produced at random, that is, if all parents are equally likely to contribute gametes. For most organisms, there typically is higher variance in contribution than predicted from ran- dom breeding because of unequal sex ratio, high variance in mating success, fecundity or progeny survival over individ- uals, and other factors. Further, IV over time (i.e., generations) depends on the harmonic mean of the number of individu- als for each generation, which may be far lower than the arithmetic mean (Hedrick 2000). Lande (1995) suggested up to 90% of the inacasc in gcnctic variant by mutation ovcr time may be caused by changes that unconditionally reduce fitness, so most new variation is unavailable for adaptive change. Thus, he thought that N. = 5000 may be required to maintain potentially adaptive genetic variation. Franklin and Frankham (1998) suggested that this number may be too high, largely because heritability may be lower than Franklin (1980) and Lande (1995) assumed. Lynch and Lande (1998) noted that the mutation rate for some traits (e.g., genes that may confer disease resistance) may be 1000-fold lower than for quantitative traits, making the numbers needed to main- tain their variation 1000-fold higher. Caution should be used in discussing N because impor- tant parameters-mutation rates, selection on new mutants, and N. itself-are poorly uAderstood in general and are un- known for Colorado River fishes. Also, the actual N may be a fraction of the total adult population. Frankham (1995) re- viewed published estimates and suggested that N is only about 10% of the adult population size. Within-generation estimates of the ratio of N to adult numbers often appear higher than 0.10 (Vucetich et al. 1997), but for long-term maintenance of genetic variation, temporal variance in N should be included. In other words, to maintain genetic vari- ation in a population with N. of 500 would require a census population (N) size of approximately 5000 adults per gen- eration. With N. of 1000 (e.g., USFWS 2002a, 2002b, 2002c, 2002d), an adult N of approximately 10,000 would be required. Large populations of the four endangered fishes were present in the lower Colorado River as late as the mid-20th century. Because generation time is long (4 to 8 years or more) and the age span of reproduction is large in all four species, there probably have been few recruitment failures where genetic variation could be lost to the succeeding gen- eration. Thus, we expected extensive variation to remain in today's wild adults. One way to examine this is to explore the amounts of variation for molecular variants. An estimate of long-term N can be derived from mitochondrial DNA (mtDNA) sequence data (Garrigan et al. 2002), using a max- imum likelihood approach. This method assumes, as above, that new sequence variants appear by mutation and are elim- inated by genetic drift. For a given mutation rate and NP a sample of mtDNA sequences thus should exhibit an appro- priate pattern of pairwise differences. However, these long- term estimates of the effective population size for a species throughout a substantial portion of its evolutionary history do not necessarily reflect the historical or recent effective population size. Other approaches can be used to estimate con- temporary effective population size (Hedrick 2000), a topic we do not consider here. Examination of mtDNA sequence variation in bonytail, humpback chub, and razorback sucker showed substantial variation (Garrigan et al. 2002): 5, 3, and 10 haplotypes were found in samples of 16,18, and 49 individuals, respectively (table 3). In a sample of 16 bonytail, 4, 7, and 5 individuals exhibited three haplotypes: Zx, Zz, and Yy, respectively (figure 4b). Humpback chub and razorback sucker genealo- gies are similar in that rare haplotypes are most divergent and common haplotypes are closely related. Humpback chub and razorback sucker showed similar divergence over all sequences of about 1.5 nucleotides between all pairwise com- parisons, while bonytail averaged 2.8 nucleotide differences. Assuming a mutation rate of 2 x 10' per nucleotide, we can estimate the long-term female effective population size from these data (table 3). If population size is constant over evo- lutionary time, estimates are 97,500, 89,500, and 669,000 for humpback chub, bonytail, and razorback sucker, respectively. Overall effective population size should be about twice this value if sex ratios are equal. Taking population growth into account, estimates suggest bonytail has been declining and ra- zorback sucker expanding in numbers over evolutionary time (table 3). Overall, this analysis suggests the three species historically existed in large numbers. Although there is less genetic variation for bonytail, and estimates of effective population size are smallest for it, the March 2003 / VoL 53 No. 3 • BioScience 225