Environment-sensitive epigenetics and the heritability of complex diseases.

Genome-wide association studies have thus far failed to explain the observed heritability of complex human diseases. This is referred to as the "missing heritability" problem. However, these analyses have usually neglected to consider a role for epigenetic variation, which has been associated with many human diseases. We extend models of epigenetic inheritance to investigate whether environment-sensitive epigenetic modifications of DNA might explain observed patterns of familial aggregation. We find that variation in epigenetic state and environmental state can result in highly heritable phenotypes through a combination of epigenetic and environmental inheritance. These two inheritance processes together can produce familial covariances significantly higher than those predicted by models of purely epigenetic inheritance and similar to those expected from genetic effects. The results suggest that epigenetic variation, inherited both directly and through shared environmental effects, may make a key contribution to the missing heritability.

Selection at work in self-incompatible Arabidopsis lyrata. II. Spatial distribution of S haplotypes in Iceland.

We survey the distribution of haplotypes at the self-incompatibility (SI) locus of Arabidopsis lyrata (Brassicaceae) at 12 locations spread over the species' natural distribution in Iceland. Previous investigations of the system have identified 34 functionally different S haplotypes maintained by frequency-dependent selection and arranged them into four classes of dominance in their phenotypic expression. On the basis of this model of dominance and the island model of population subdivision, we compare the distribution of S haplotypes with that expected from population genetic theory. We observe 18 different S haplotypes, recessive haplotypes being more common than dominant ones, and dominant ones being shared by fewer populations. As expected, differentiation, although significant, is very low at the S locus even over distances of up to 300 km. The frequency of the most recessive haplotype is slightly larger than expected for a panmictic population, but consistent with a subdivided population with the observed differentiation. Frequencies in nature reflect effects of segregation distortion previously observed in controlled crosses. The dynamics of the S-locus variation are, however, well represented by a 12-island model and our simplified model of dominance interactions.

Selection at work in self-incompatible Arabidopsis lyrata: mating patterns in a natural population.

Identification and characterization of the self-incompatibility genes in Brassicaceae species now allow typing of self-incompatibility haplotypes in natural populations. In this study we sampled and mapped all 88 individuals in a small population of Arabidopsis lyrata from Iceland. The self-incompatibility haplotypes at the SRK gene were typed for all the plants and some of their progeny and used to investigate the realized mating patterns in the population. The observed frequencies of haplotypes were found to change considerably from the parent generation to the offspring generation around their deterministic equilibria as determined from the known dominance relations among haplotypes. We provide direct evidence that the incompatibility system discriminates against matings among adjacent individuals. Multiple paternity is very common, causing mate availability among progeny of a single mother to be much larger than expected for single paternity.

Influenza drift and epidemic size: the race between generating and escaping immunity.

Influenza in humans is characterised by strongly annual dynamics and antigenic evolution leading to partial escape from prior host immunity. The variability of new epidemic strains depends on the amount of virus currently circulating. In this paper, the amount of antigenic variation produced each year is dependent on the epidemic size. Our model reduces to a one-dimensional map and a full mathematical analysis is presented. This simple system suggests some basic principles which may be more generally applicable. In particular, for diseases with antigenic drift, vaccination may be doubly beneficial. Not only does it protect the population through classical herd immunity, but the overall case reduction reduces the chance of new variants being produced; hence, subsequent epidemics may be milder as a result of this positive feedback. Also, a disease with a high innate rate of antigenic variation will always be able to invade a susceptible population, whereas a disease with less potential for variation may require several introduction events to become endemic.

MATE AVAILABILITY AND FECUNDITY SELECTION IN MULTI-ALLELIC SELF-INCOMPATIBILITY SYSTEMS IN PLANTS.

We investigate mate availability in different models of multiallelic self-incompatibility systems in mutation-selection-drift balance in finite populations. Substantial differences among self-incompatibility systems occur in average mate availability, and in variances of mate availability among individual plants. These differences are most pronounced in small populations in which low mate availability may reduce seed set in some types of sporophytic self-incompatibility. In cases where the pollination system causes a restriction in the number of pollen genotypes available to an individual plant, the fecundity of that plant depends on the availability of compatible pollen, which is determined by its genotype at the incompatibility locus. This leads to an additional component of selection acting on self-incompatibility systems, which we term "fecundity selection." Fecundity selection increases the number of alleles maintained in finite populations and increases mate availability in small populations. The strength of fecundity selection is dependent on the type of self-incompatibility. In some cases, fecundity selection markedly alters the equilibrium dynamics of self-incompatibility alleles. We discuss the population genetic consequences of mate availability and fecundity selection in the contexts of conservation management of self-incompatible plant species and experimental investigations on self-incompatibility in natural populations.