Pacific Salmon and the Coalescent Effective Population Size

Abstract

Pacific salmon include several species that are both commercially important and endangered. Understanding the causes of loss in genetic variation is essential for designing better conservation strategies. Here we use a coalescent approach to analyze a model of the complex life history of salmon, and derive the coalescent effective population (CES). With the aid of Kronecker products and a convergence theorem for Markov chains with two time scales, we derive a simple formula for the CES and thereby establish its existence. Our results may be used to address important questions regarding salmon biology, in particular about the loss of genetic variation. To illustrate the utility of our approach, we consider the effects of fluctuations in population size over time. Our analysis enables the application of several tools of coalescent theory to the case of salmon.

Coalescence theory for a general class of structured populations with fast migration

“…This extends the results of, e.g. Sagitov and Jagers (2005); see also Cenik and Wakeley (2010). The approach of Engen et al (2005aEngen et al ( ), (2005b, on the other hand, can be used to calculate the variance effective population size using forward diffusion approximations.…”

Phylogeny and phylogeography of Atlantic oyster species: evolutionary history, limited genetic connectivity and isolation by distance

“…Standard coalescent models may not be applicable to species with extremely high fecundities (Eldon & Wakeley 2006) and high variance in the cross-generation contribution to the gene pool (the sweepstakes hypothesis; Hedgecock 1994, Hedgecock et al 2007), like those observed in oysters. However, estimates of effective population size through different approaches can give results that are fairly well correlated even under extreme fluctuations in reproductive effort and overlapping generations (Cenik & Wakeley 2010).…”

Coalescence theory for a general class of structured populations with fast migration

“…Sagitov and Jagers (2005); see also Cenik and Wakeley (2010). The approach of Engen et al (2005aEngen et al ( ), (2005b, on the other hand, can be used to calculate the variance effective population size using forward diffusion approximations.…”

“…For instance, Engen et al (2005a) derived the variance effective population size for age-structured diploid models. It would be interesting to obtain expressions for the coalescent effective diploid population size in our context of age and spatial structures.…”