Allele frequencies and selection coefficients in locally adapted populations.

Understanding the role of natural selection in driving evolutionary change requires accurate estimates of the strength of selection acting at the genetic level in the wild. This is challenging to achieve but may be easier in the case of populations in migration-selection balance. When two populations are at equilibrium under migration-selection balance, there exist loci whose alleles are selected different ways in the two populations. Such loci can be identified from genome sequencing by their high values of FST. This raises the question of what is the strength of selection on locally-adaptive alleles. To answer this question we analyse a 1-locus 2-allele model of a population distributed between two niches. We show by simulation of selected cases that the outputs from finite-population models are essentially the same as those from deterministic infinite-population models. We then derive theory for the infinite-population model showing the dependence of selection coefficients on equilibrium allele frequencies, migration rates, dominance and relative population sizes in the two niches. An Excel spreadsheet is provided for the calculation of selection coefficients and their approximate standard errors from observed values of population parameters. We illustrate our results with a worked example, with graphs showing the dependence of selection coefficients on equilibrium allele frequencies, and graphs showing how FST depends on the selection coefficients acting on the alleles at a locus. Given the extent of recent progress in ecological genomics, we hope our methods may help those studying migration-selection balance to quantify the advantages conferred by adaptive genes.

Sexual imprinting leads to speciation in locally adapted populations.

Sexual imprinting is widespread in birds and other species but its existence requires explanation. Our results suggest that sexual imprinting leads to speciation in locally-adapted populations if a neutral mating cue-e.g., novel plumage coloration-arises through mutation. Importantly, the mating cue locus is not linked to adaptation loci. Local adaptation is a necessary precursor to speciation and occurs when evolution results in stable genetic polymorphisms with one allele predominating in some areas while others predominate elsewhere. Here we use a deterministic two-niche population genetic model to map the set of migration and selection rates for which polymorphic evolutionary outcomes, i.e., local adaptations, can occur. Approximate equations for the boundaries of the set of polymorphic evolutionary outcomes were derived by Bulmer (American Naturalist, 106, 254, 1972), but our results, obtained by deterministic simulation of the evolutionary process, show that one of Bulmer's equations is inaccurate except when the level of dominance is 0.5, and fails if one of the alleles is dominant. Having an accurate map of the set of migration and selection rates for which polymorphic evolutionary outcomes can occur, we then show using the model of Sibly et al. (Ecology and Evolution, 9, 13506, 2019) that local adaptation in all analyzed cases leads to speciation if a new neutral mating cue arises by mutation. We finish by considering how genome sequencing makes possible testing our model and its predictions.

How phenotypic matching based on neutral mating cues enables speciation in locally adapted populations.

Maynard Smith's (American Naturalist, 1966, 100, 637) suggestion that in some cases a prerequisite for speciation is the existence of local ecological adaptations has not received much attention to date. Here, we test the hypothesis using a model like that of Maynard Smith but differing in the way animals disperse between niches. In previous studies, males disperse randomly between niches but females stay put in their natal niche. As a first step toward generalizing the model, we here analyze the case that equal proportions of the two sexes disperse between niches before breeding. Supporting Maynard Smith's (1966) hypothesis, we find that once local adaptations are established, a neutral mating cue at an independent locus can rapidly enable speciation in populations with a suitable mechanism for phenotype matching. We find that stable ecological polymorphisms are relatively insensitive to the strength of selection, but depend crucially on the extent of dispersal between niches, with a threshold of ~5% if population sizes in two niches are equal. At higher levels of dispersal, ecological differentiation is lost. These results contrast with those of earlier studies and shed light on why parapatric speciation is limited by the extent of gene flow. Our testable model provides a candidate explanation for the rapid speciation rates, diversity of appearance and occurrence of "species flocks" observed among some African cichlids and neotropical birds and may also have implications for the occurrence of punctuational change on phylogenies.

Genetic polymorphisms between altruism and selfishness close to the Hamilton threshold rb = c.

Genes that in certain conditions make their carriers altruistic are being identified, and altruism and selfishness have shown to be heritable in man. This raises the possibility that genetic polymorphisms for altruism/selfishness exist in man and other animals. Here we characterize some of the conditions in which genetic polymorphisms may occur. We show for dominant or recessive alleles how the positions of stable equilibria depend on the benefit to the recipient, b, and the cost to the altruist, c, for diploid altruists helping half or full sibs, and haplodiploid altruists helping sisters. Stable polymorphisms always occur close to the Hamilton threshold rb = c. The position of the stable equilibrium moves away 0 or 1 with both increases in c, the cost paid by the altruist, and increasing divergence from the Hamilton threshold, and alleles for selfishness can reach frequencies around 50%. We evaluate quantitative estimates of b, c and r from field studies in the light of these predictions, but the values do not fall in the regions where genetic polymorphisms are expected. Nevertheless, it will be interesting to see as genes for altruism are discovered whether they are accompanied by alternate alleles for selfishness.

Evolution of discrimination in populations at equilibrium between selfishness and altruism.

Where there is genetically based variation in selfishness and altruism, as in man, altruists with an innate ability to recognise and thereby only help their altruistic relatives may evolve. Here we use diploid population genetic models to chart the evolution of genetically-based discrimination in populations initially in stable equilibrium between altruism and selfishness. The initial stable equilibria occur because help is assumed subject to diminishing returns. Similar results were obtained whether we used a model with two independently inherited loci, one controlling altruism the other discrimination, or a one locus model with three alleles. The latter is the opposite extreme to the first model, and can be thought of as involving complete linkage between two loci on the same chromosome. The introduction of discrimination reduced the benefits obtained by selfish individuals, more so as the number of discriminators increased, and selfishness was eventually eliminated in some cases. In others selfishness persisted and the evolutionary outcome was a stable equilibrium involving selfish individuals and both discriminating and non-discriminating altruists. Heritable variation in selfishness, altruism and discrimination is predicted to be particularly evident among full sibs. The suggested coexistence of these three genetic dispositions could explain widespread interest within human social groups as to who will and who will not help others. These predictions merit experimental and observational investigation by primatologists, anthropologists and psychologists.

Detecting non-multiplicative genotype relative risks from transmissions of parental alleles to affected children.

The differential transmission of alleles from parents to affected children indicates that the locus under investigation is either directly involved in the occurrence of the disease or that there are allelic associations with other loci that are directly involved. Conditional logistic regression applied to a diallelic locus leads to a test with two degrees of freedom. The power of a single degree of freedom test to detect non-multiplicative allelic effects is discussed here.