Since its discovery in 1907, polyploidy has been recognized as an important phenomenon in vascular plants, and several lines of evidence indicate that most, if not all, plant species ultimately have a polyploid ancestry. However, previous estimates of the frequency of polyploid speciation suggest that the formation and establishment of neopolyploid species is rare. By combining information from the botanical community's vast cytogenetic and phylogenetic databases, we establish that 15% of angiosperm and 31% of fern speciation events are accompanied by ploidy increase. These frequency estimates are higher by a factor of four than earlier estimates and lead to a standing incidence of polyploid species within genera of 35% (n ‫؍‬ 1,506). Despite this high incidence, we find no direct evidence that polyploid lines, once established, enjoy greater net species diversification. Thus, the widespread occurrence of polyploid taxa appears to result from the substantial contribution of polyploidy to cladogenesis, but not from subsequent increases in diversification rates of polyploid lines.

Transgenerational plasticity (TGP) occurs when offspring exhibit plasticity in traits induced by the environments experienced by their parents, and represents a nongenetic mechanism of inheritance. Evidence that traits can be transmitted to future generations by means other than genetic inheritance has caused a surge of interest in epigenetic inheritance, but evidence for epigenetic modifications being both adaptive and heritable remains scarce. What features would make a species most prone to evolve a system of epigenetically mediated adaptive TGP? Here, we use population‐genetic models modified to include epigenetic induction and inheritance to investigate if and when epigenetically mediated adaptive TGP would be expected to evolve for a population subdivided between two habitats connected by migration. We show that differences in the direction of selection between the two habitats drives the evolution of epigenetically mediated adaptive TGP. With low migration, the strength of indirect selection in favor of epigenetically mediated adaptive TGP increases with migration rate. Yet, with higher migration, the opposite trend is observed. We predict that species subdivided between habitats that differ in the direction of selection with moderate migration rates between the habitats would be most likely to evolve epigenetically mediated adaptive TGP if costs of producing such systems are not too high.

Most models of Fisherian sexual selection assume haploidy. However, analytical models that focus on dynamics near fixation boundaries and simulations show that the resulting behavior depends on ploidy. Here we model sexual selection in a diploid to characterize behaviour away from fixation boundaries. The model assumes two di-allelic loci, a male-limited trait locus subject to viability selection, and a preference locus that determines a female's tendency to mate with males based on their genotype at the trait locus. Using a quasi-linkage equilibrium (QLE) approach, we find a general equation for the curves of quasi-neutral equilibria, and the conditions under which they are attracting or repelling. Unlike in the haploid model, the system can move away from the internal curve of equilibria in the diploid model. We show that this is the case when the combined forces of natural and sexual selection induce underdominance at the trait locus. Sexual selection is considered to be responsible for many striking and bizarre ornaments and mating behaviors found across the animal kingdom. Although there is a large body of theoretical treatment of sexual selection, most studies make simplifying genetic assumptions, such as haploidy or infinitesimally small polygenic inheritance, to make the math more tractable. However, most animal species that exhibit the ornaments attributed to evolution by sexual selection are diploid. This would not concern us if haploid and diploid models behaved identically. However, the small number of studies that have considered sexual selection in diploids have shown that different and unexpected behavior can occur.Using computer simulations, Heisler and Curtsinger (1990) studied a model of diploid Fisherian sexual selection. Among the cases that they considered is a two-locus diploid model analogous to the haploid model considered by Kirkpatrick (1982) in his seminal paper on sexual selection. Unlike Kirkpatrick (1982) who showed the existence of neutrally stable curves, Heisler and Curtsinger (1990) showed that neutrally stable curves do not exist for any of the parameter sets considered, except under a special case of complete dominance at the trait locus. In some cases, trait and preference frequencies tended toward a curve but then moved slowly along it, whereas in other cases the system appeared to move away from a curve. The latter behavior was associated with heterozygote disadvantage of the trait in the numerical examples considered, but the exact conditions under which these two types of behaviors arise remained unclear, and the authors concluded that there was "a definite need for further analysis of diploid sexual selection models."Two studies have made analytical progress by describing the behavior of the diploid two-locus model when either the trait or preference locus is nearly fixed. Gomulkiewicz and Hastings (1990) studied dynamics near fixation at the trait locus. They found that the stability properties of the fixation boundaries were similar in their diploid model and the haplo...

By constantly selecting for novel genotypes, coevolution between hosts and parasites can favour elevated mutation rates. Models of this process typically assume random encounters. However, offspring are often more likely to encounter their mother's parasites. Because parents and offspring are genetically similar, they may be susceptible to the same parasite strains and thus, in hosts, maternal transmission should select for mechanisms that decrease intergenerational genetic similarity. In parasites, however, maternal transmission should select for genetic similarity. We develop and analyse a model of host and parasite mutation rate evolution when parasites are maternally inherited. In hosts, we find that maternal transmission has two opposing effects. First, it eliminates coevolutionary cycles that previous work shows select for higher mutation. Second, it independently selects for higher mutation rates, because offspring that differ from their mothers are more likely to avoid infection. In parasites, however, the two effects of maternal transmission act in the same direction. As for hosts, maternal transmission eliminates coevolutionary cycles, thereby reducing selection for increased mutation. Unlike for hosts, however, maternal transmission additionally selects against higher mutation by favouring parasite offspring that are the same as their mothers.

Speciation is less likely to occur when there is gene flow between nascent species. Natural selection can oppose gene flow and promote speciation if there is variation in ecological conditions among the nascent species' locations. Previous theory on ecological speciation with gene flow has focused primarily on the role of genetic variation in ecological traits, largely neglecting the role of nongenetic inheritance or transgenerational plasticity. Here, we build and analyze models incorporating both genetic and epigenetic inheritance, the latter representing a form of nongenetic inheritance. We investigate the rate of speciation for a population that inhabits two patches connected by migration, and find that adaptively biased epigenetic induction can speed up or slow down speciation, depending on the form of the map from genotype and epigenotype to phenotype. While adaptively relevant epigenetic variation can speed up speciation by reducing the fitness of migrants and hybrids, it can also slow down speciation. This latter effect occurs when the epialleles are able to achieve adaptation faster than the genetic alleles, thereby weakening selection on the latter.