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Exact estimates of the effective population size are complicated. For <br />example, the formula given above for the effect of sex ratios assumes <br />random mating, constant population size through time, and variance in <br />fertility that approaches the Poisson distribution. Effective population <br />' size can be maximized by non-random matings of paired individuals and <br />equalizing the sizes of family lots (Allendorf 1993). <br /> <br /> <br />The effective population size should be maximized in every hatchery <br />generation to reduce the risk of loss of within-population genetic <br />variation (Kapuscinski et al. 1993). Strategies for conserving genetic <br />diversity in captive-reared endangered fish are summarized in Box 9. <br />Box 9. Strategies for conserving genetic diversity of endangered fish <br />in the Upper Colorado River Basin. <br />1. The genetic diversity of wild endangered fish stocks should be <br />characterized by genetic markers. <br />2. Captive propagation and stocking should be considered temporary <br />management tools to facilitate development of self-sustaining <br />wild endangered fish stocks. <br />3. Broodstocks should be developed from an appropriate donor source <br />in an artificial genetic refuge that offers maximum control. <br />4. Appropriate breeding strategies should be used to maintain genetic <br />diversity similar to the wild donor stock or population. <br />5. The genetic diversity of captive broodstocks and their progeny <br />will be monitored and compared to the genetic diversity of wild <br />stocks. <br />6. The number of captive-reared fish that are to be stocked should be <br />limited to prevent potential risks to severely depleted wild stocks <br />from genetic swamping. <br />The rate of inbreeding ( O F) can be calculated if the Ne is known using <br />the formula: <br />?F= <br />2 1 Ne <br />By applying this formula, the estimated rate of inbreeding for an <br />effective population size of 50 (equal sexes) is 1 %. For an effective <br />population size of 10 (equal sexes), the estimated rate of inbreeding <br />is 5%. Therefore, it is advantageous to use as many adult fish as <br />possible in developing broodstocks. <br />' It has been suggested that a minimum effective population size of 50 is <br />required to prevent inbreeding depression (Soule 1980) and a minimum <br />effective population size of 500 is required to reduce long-term genetic <br />' drift (Franklin 1980). The acceptability of the "50" value is empirical <br />from broad experience of animal breeders. Animal breeders have not <br />25