How to compute the effective size of spatiotemporally structured populations using separation of time scales

Selection on age-specific survival: Constant versus fluctuating environment

According to a classic result in evolutionary biodemography, selection on age-specific survival invariably declines with reproductive age. The result assumes proportional changes in survival and a constant environment. Here, we look at selection on age-specific survival when changes are still proportional but the environment fluctuates. We find that selection may or may not decline with reproductive age depending on how exactly survival is proportionally altered by mutations. However, interpreted in neutral terms, the mathematics behind the classic result capture a general property that the genetics of populations with age structure possess both in a constant and in a fluctuating environment.

Contemporary effective population and metapopulation size (N e and meta-N e): comparison among three salmonids inhabiting a fragmented system and differing in gene flow and its asymmetries

We estimated local and metapopulation effective sizes ([Formula: see text] and meta-[Formula: see text]) for three coexisting salmonid species (Salmo salar, Salvelinus fontinalis, Salvelinus alpinus) inhabiting a freshwater system comprising seven interconnected lakes. First, we hypothesized that [Formula: see text] might be inversely related to within-species population divergence as reported in an earlier study (i.e., FST: S. salar> S. fontinalis> S. alpinus). Using the approximate Bayesian computation method implemented in ONeSAMP, we found significant differences in [Formula: see text] ([Formula: see text]) between species, consistent with a hierarchy of adult population sizes ([Formula: see text]). Using another method based on a measure of linkage disequilibrium (LDNE: [Formula: see text]), we found more finite [Formula: see text] values for S. salar than for the other two salmonids, in line with the results above that indicate that S. salar exhibits the lowest [Formula: see text] among the three species. Considering subpopulations as open to migration (i.e., removing putative immigrants) led to only marginal and non-significant changes in [Formula: see text], suggesting that migration may be at equilibrium between genetically similar sources. Second, we hypothesized that meta-[Formula: see text] might be significantly smaller than the sum of local [Formula: see text]s (null model) if gene flow is asymmetric, varies among subpopulations, and is driven by common landscape features such as waterfalls. One 'bottom-up' or numerical approach that explicitly incorporates variable and asymmetric migration rates showed this very pattern, while a number of analytical models provided meta-[Formula: see text] estimates that were not significantly different from the null model or from each other. Our study of three species inhabiting a shared environment highlights the importance and utility of differentiating species-specific and landscape effects, not only on dispersal but also in the demography of wild populations as assessed through local [Formula: see text]s and meta-[Formula: see text]s and their relevance in ecology, evolution and conservation.

Pacific salmon and the coalescent effective population size

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.

The neutral effective migration rate in a mainland-island context

Genetic influx into a population often does not correspond to the real migration rate (m) of individuals, due to class structure within the population. The effective migration rate (m(e)) is a concept to measure gene flow in such a situation. The ratio of the effective migration rate to the real migration rate (m(e)/m) is called the gene flow factor, and represents the degree of gene flow modification. Prior authors proposed different definitions of the effective migration rate. These may be categorized into two groups: the neutral effective migration rate and the selective effective migration rate. In this article, we construct a general model of a class-structured population with a mainland-island structure. Using the model, we prove that the gene flow factor of the neutral effective migration rate converges to the mean reproductive value of immigrants if the limit is taken with the real migration rate converging to zero. This limit theorem provides a novel interpretation of gene flow and can be used to derive approximation formulae of the neutral effective migration rate. We illustrate this method analyzing two examples, sex ratio distortion due to extrinsic factors and hybrid zones with underdominance.