Inferring the Ancestral Origin of Sockeye Salmon, Oncorhynchus nerka, in The Lake Washington Basin: A Statistical Method in Theory and Application

Master's Thesis: Eric C. Anderson

It was once held that any native populations of anadromous sockeye salmon in the Lake Washington Basin were extirpated by the changes in the lake following the completion of the Lake Washington Ship Canal in the early 1900's, and were replaced by sockeye planted from Baker or Cultus lakes in the 1930's and 1940's. The authors of two surveys of neutral genetic markers in Lake Washington sockeye populations, however, suggest that the sockeye spawning in Bear Creek and its tributaries are of native origin. I argue that one cannot prove that the fish in Bear Creek are of native origin, but it may be possible to statistically exclude the possibility that sockeye in Bear Creek derive exclusively from Baker Lake or Cultus Lake. I present a likelihood ratio test of the hypothesis that Bear Creek fish could have derived exclusively from Baker (or Cultus) Lake against the alternative hypothesis that at least some of the ancestry of the Bear Creek population must be from a source other than Baker (or Cultus) lake. The test is based on a probability model which includes uncertainty in the data due both to sampling error and to the error due to random genetic drift.

Several different formulations and approximations are used to compute the likelihood ratio as appropriate for four different loci on which data are available. The method requires independent knowledge of the historical effective sizes of the populations in Bear Creek, Cultus Lake, and Baker Lake. I perform simulations based on very good historical data suggesting that a lower bound on effective size for the Baker Lake population is about 250 individuals and for the Cultus Lake population is about 800. Early run-size data for Bear Creek are not available, so I perform simulations based on a reasonable scenario that show how the Bear Creek population might have grown from the early 1940's so as to have an effective size of 100. If these numbers for effective size are accurate, it is unlikely that the sockeye inhabiting Bear Creek could have descended exclusively from fish introduced from either Baker Lake or Cultus Lake. Unfortunately, this result depends highly on the assumed run sizes in Bear Creek in years with little or no data.