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Genomic imprinting is a form of epigenetic modification involving parent-of-origin-dependent gene expression, usually the inactivation of one gene copy in some tissues, at least, for some part of the diploid life cycle. Occurring at a number of loci in mammals and flowering plants, this mode of non-Mendelian expression can be viewed more generally as parentally-specific differential gene expression. The effects of natural selection on genetic variation at imprinted loci have previously been examined in a several population-genetic models. Here we expand the existing one-locus, two-allele population-genetic models of viability selection with genomic imprinting to include sex-limited imprinting, i.e., imprinted expression occurring only in one sex, and differential viability between the sexes. We first consider models of complete inactivation of either parental allele and these models are subsequently generalized to incorporate differential expression. Stable polymorphic equilibrium was possible without heterozygote advantage as observed in some prior models of imprinting in both sexes. In contrast to these latter models, in the sex-limited case it was critical whether the paternally inherited or maternally inherited allele was inactivated. The parental origin of inactivated alleles had a different impact on how the population responded to the different selection pressures between the sexes. Under the same fitness parameters, imprinting in the other sex altered the number of possible equilibrium states and their stability. When the parental origin of imprinted alleles and the sex in which they are inactive differ, an allele cannot be inactivated in consecutive generations. The system dynamics became more complex with more equilibrium points emerging. Our results show that selection can interact with epigenetic factors to maintain genetic variation in previously unanticipated ways., (Copyright © 2017 Elsevier Inc. All rights reserved.)

Population geneticists have long been interested in the ability of natural selection to maintain the levels of standing variation observed in natural populations. Here, we study the polymorphism-maintaining properties of maternal selection, in which the fitness of an individual is a function of its own and its mother's genotype. Using a model proposed by Gavrilets, we first estimate the proportion of parameter/state space that preserves allelic variation, before investigating the construction of polymorphism over time through the joint action of mutation and selection. These two methods, the "parameter-space" and "constructionist" approaches, respectively, enable us to draw some general conclusions. We argue that, even though the proportion of parameter-state space allowing multiallele polymorphism is greater under maternal selection than under the standard model of constant viability selection, the former is, in fact, less likely to maintain large numbers of alleles. Nevertheless, variation that is balanced by maternal selection is likely to show elements of heterozygous advantage and be resistant to depletion by genetic drift. We observe that the population mean fitness frequently decreases after the successful invasion of a new mutation, but such declines are usually temporary., (Copyright © 2015 Spencer and Chiew.)

Paramutation involves an interaction between homologous alleles resulting in a heritable change in gene expression without altering the DNA sequence. Initially believed to be restricted to plants, paramutation has recently been observed in animal models, and a paramutation-like event has been noted in humans. Despite the accumulating evidence suggesting that trans-acting epigenetic effects can be inherited transgenerationally and therefore generate non-genomic phenotypic variation, these effects have been largely ignored in the context of evolutionary theory. The model presented here incorporates paramutation into the standard model of viability selection at one locus and demonstrates that paramutation can create long-term biological diversity in the absence of genetic change, and even in the absence of the original paramutagenic allele. Therefore, if paramutation is present, attributing evolution to only a traditional genetic model may fail to encompass the broad scope of phenotypic differences observed in nature. Moreover, we show also that an unusual mathematical behaviour, analogous to "Ewens' gap" of the two-locus two-allele symmetric-selection model, occurs: when the rate of one parameter-for example, the rate of paramutation-is increased, a pair of equilibria may disappear only to reappear as this parameter increases further. In summary, by incorporating even the simplest epigenetic parameters into the standard population-genetic model of selection, we show how this type of inheritance system can profoundly alter the course of evolution., (Copyright © 2013 Elsevier Inc. All rights reserved.)

There is increasing evidence that epigenetic modifications can be passed from one generation to the next. The population-level consequence of these discoveries, however, remains largely unexplored. In this paper, we introduce and analyze some simple models of constant viability selection acting on such heritable epigenetic variation. These "population-epigenetic" models are analogous to those of traditional population genetics, and are a preliminary step in quantifying the effect of non-genomic transgenerational inheritance, aiming to improve our understanding of how this sort of environmental response may affect evolution., (Copyright © 2011 Elsevier Inc. All rights reserved.)

Rafting has long been invoked as a key marine dispersal mechanism, but biologists have thus far produced little genetic evidence to support this hypothesis. We hypothesize that coastal species associated with buoyant seaweeds should experience enhanced population connectivity owing to rafting. In particular, invertebrates strongly associated with the buoyant bull-kelp Durvillaea antarctica might be expected to have lower levels of population-genetic differentiation than taxa mainly exploiting nonbuoyant substrates. We undertook a comparative genetic study of two codistributed, congeneric chiton species, assessing population connectivity at scales of 61-516 km, using ≥ 186 polymorphic AFLP loci per species. Consistent with predictions, population-genetic differentiation was weaker in the kelp-associated Sypharochiton sinclairi than in the rock-associated S. pelliserpentis. Additionally, while we found a significant positive correlation between genetic and oceanographic distances in both chiton species, the correlation was stronger in S. pelliserpentis (R(2) = 0.28) than in S. sinclairi (R(2) = 0.18). These data support the hypothesis that epifaunal taxa can experience enhanced population-genetic connectivity as a result of their rafting ability., (© 2011 Blackwell Publishing Ltd.)

The evolutionary effects of Southern Hemisphere Pleistocene oceanographic conditions - marked by fluctuations in sea levels and water temperatures, and redirected currents - are poorly understood. The southeastern tip of Australia presents an intriguing model system for studying the biological impacts of palaeoceanography. In particular, contrasting oceanographic conditions that existed on eastern vs. western sides of the Bassian Isthmus during Pleistocene glacial periods allow for natural comparisons between putative refugial vs. re-invading populations. Whereas many western Tasmanian marine taxa were likely eliminated by cold subantarctic water during the last glacial period, eastern Tasmanian populations would have persisted in relatively warm temperatures mediated by the ongoing influence of the East Australian Current (EAC). Here we test for the effects of contrasting palaeoceanographic conditions on endemic bull kelp, Durvillaea potatorum, using DNA sequence analysis (COI; rbcL) of more than 100 individuals from 14 localities in southeastern Australia. Phylogenetic reconstructions reveal a deep (maximum divergence 4.7%) genetic split within D. potatorum, corresponding to the 'eastern' and 'western' geographical regions delimited by the Bassian Isthmus, a vicariant barrier during low Pleistocene sea levels. Concordant with the western region's cold glacial conditions, samples from western Tasmania and western Victoria are genetically monomorphic, suggesting postglacial expansion from a mainland refugium. Eastern samples, in contrast, comprise distinct regional haplogroups, suggesting the species persisted in eastern Tasmania throughout recent glacial periods. The deep east-west divergence seems consistent with earlier reports of morphological differences between 'western' and 'eastern' D. potatorum, and it seems likely that these forms represent reproductively isolated species.

Frequency-dependent selection remains the most commonly invoked heuristic explanation for the maintenance of genetic variation. For polymorphism to exist, new alleles must be both generated and maintained in the population. Here we use a construction approach to model frequency-dependent selection with mutation under the pairwise interaction model. The pairwise interaction model is a general model of frequency-dependent selection at the genotypic level. We find that frequency-dependent selection is able to generate a large number of alleles at a single locus. The construction process generates multiallelic polymorphisms with a wide range of allele-frequency distributions and genotypic fitness relationships. Levels of polymorphism and mean fitness are uncoupled, so constructed polymorphisms remain permanently invasible to new mutants; thus the model never settles down to an equilibrium state. Analysis of constructed fitness sets reveals signatures of heterozygote advantage and positive frequency dependence.

The outcome of selection in structured populations with spatially varying selection pressures depends on the interaction of two factors: the level of gene flow and the amount of heterogeneity among the demes. Here we investigate the effect of three different levels of spatial heterogeneity on the levels of genetic polymorphisms for different levels of gene flow, using a construction approach in which a population is constantly bombarded with new mutations. We further compare the relative importance of two kinds of balancing selection (heterozygote advantage and selection arising from spatial heterogeneity), the level of adaptation and the stability of the resulting polymorphic equilibria. The different levels of environmental heterogeneity and gene flow have a large influence on the final level of polymorphism. Both factors also influence the relative importance of the two kinds of balancing selection in the maintenance of variation. In particular, selection arising from spatial heterogeneity does not appear to be an important form of balancing selection for the most homogeneous scenario. The level of adaptation is highest for low levels of gene flow and, at those levels, remarkably similar for the different levels of spatial heterogeneity, whereas for higher levels of gene flow the level of adaptation is substantially reduced.

At a small number of mammalian loci, only one of the two copies of a gene is expressed. Just which copy is expressed depends on the sex of the parent from which that copy was inherited. Such genes are said to be imprinted. The functional haploidy implied by imprinting has a number of population genetic consequences. Moreover, since diploidy is widely believed to be advantageous, the evolution of this non-Mendelian form of expression requires an explanation. Here I examine some of the theoretical and mathematical models investigating these two aspects of imprinting. For instance, the dynamics and equilibrium properties of many models of natural selection at imprinted loci are formally equivalent to models without imprinting. And different approaches to modeling the problem of the evolution of imprinting reveal the weakness of several of the apparent predictions of various verbal hypotheses about why imprinting has evolved.

Many single-locus, two-allele selection models of genomic imprinting have been shown to reduce formally to one-locus Mendelian models with a modified parameter for genetic dominance. One exception is the model where selection at the imprinted locus affects the sexes differently. We present two models of maternal inactivation with differential viability in the sexes, one with complete inactivation, and the other with a partial penetrance for inactivation. We show that, provided dominance relations at the imprintable locus are the same in both sexes, a globally stable polymorphism exists for a range of viabilities that is independent of the penetrance of imprinting. The conditions for a polymorphism are the same as in previous models with differential viability in the sexes but without imprinting and in a model of the paternal X-inactivation system in marsupials. The model with incomplete inactivation is used to illustrate the analogy between imprinting and dominance by comparing equilibrium bifurcation plots for fixed values of dominance and penetrance. We also derive a single expression for the dominance parameter that leaves the frequency and stability of equilibria unchanged for all levels of inactivation. Although an imprinting model with sex differences does not formally reduce to a nonimprinting scheme, close theoretical parallels clearly exist.

The study examines the distinction between assortative and selective mating made by Lewontin, Kirk, and Crow in 1968 and finds it unproductive. Not only has the difference been ignored on many occasions even as it was invoked, but maintaining it obscures several useful properties of both nonrandom mating schemes and some formally equivalent systems such as fertility selection. The elucidation of these similarities could have accelerated the work of population biologists.

The phenomenon of genomic imprinting has recently excited much interest among experimental biologists. The population genetic consequences of imprinting, however, have remained largely unexplored. Several population genetic models are presented and the following conclusions drawn: (i) systems with genomic imprinting need not behave similarly to otherwise identical systems without imprinting; (ii) nevertheless, many of the models investigated can be shown to be formally equivalent to models without imprinting; (iii) consequently, imprinting often cannot be discovered by following allele frequency changes or examining equilibrium values; (iv) the formal equivalences fail to preserve some well known properties. For example, for populations incorporating genomic imprinting, parameter values exist that cause these populations to behave like populations without imprinting, but with heterozygote advantage, even though no such advantage is present in these imprinting populations. We call this last phenomenon "pseudoheterosis." The imprinting systems that fail to be formally equivalent to nonimprinting systems are those in which males and females are not equivalent, i.e., two-sex viability systems and sex-chromosome inactivation.