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DRAFT 1 Introduction The objective of this report is to assess the quality of the preliminary genetic data available for Gila cypha and, if possible, use these data to answer two questions regarding the broodstock fish held at Willow Beach. If the data quality are sufficient, I should be able to determine if the Willow Beach broodstock adequately represent the genetic variation present in the Little Colorado River. Depending on the answer to this question, I will make recommendations on how the utility of this broodstock can best be enhanced. I will first use a simple power analysis to evaluate whether the three wild collected samples adequately represent the genetic variation in these populations. I will then compare populations sampled in the wild to the captive population to determine how much of the variation in the wild is present in the captive population. It is important to note that these analyses focus on neutral markers and not on the quantitative traits that are much more likely to influence performance in the wild. 2 Theoretical analysis: Proportion of variation collected in field To satisfy the objectives listed above, it is important to adequately characterize variation in both wild and broodstock populations. Characterizing variation in the broodstock is rela- tively straightforward: all (or a majority of the) fish in the broodstock should be genotyped. Characterizing variation in the wild is more problematic, because any inference will always be based upon samples rather than all the fish in a drainage. As a result, it is important to determine how large a sample is necessary to develop a wild reference to which to compare broodstock. This section is essentially a power analysis that attempts to determine a sample's ability to represent genetic variation present in natural populations. In this analysis, I focus on rare alleles and contrast them against all of the more common alleles present. This focus allows the use of the binomial distribution to model power. In the analysis below I assume a diploid locus in a population that is randomly mating. The figure below gives the results of this analysis. The solid line refers to the probability of detecting an allele at a frequency of 0.05. The dashed line refers to the probability of detecting an allele at a frequency of 0.1.