A general multilocus two-allele model for epistatic selection

Observations show that evolutionary processes often relate to multilocus epistatic selection. Here we develop further the approach suggested earlier by Zhivotovsky and Gavrilets to admit arbitrary multilocus epistasis. The obtained dynamic equations for allelic frequencies and gametic disequilibria are represented in a simple form. If selection is weak, this result extends Wright’s evolutionary equation to the case of cis-trans effects and sex differences in both recombination rates and genotypic fitnesses. Additionally to Wright’s equations for allelic frequencies, we derive equations for the gametic disequilibrium terms. We also give a general expression for the gametic disequilibria in a quasi-linkage state.     

Stochastic fluctuations in frequency-dependent selection: a one-locus, two-allele and two-phenotype model

Stochastic fluctuations in a simple frequency-dependent selection model with one-locus, two-alleles and two-phenotypes are investigated. The steady-state statistics of allele frequencies for an interior stable phenotypic equilibrium are shown to be similar to the stochastic fluctuations in standard evolutionary game dynamics [Tao, Y., Cressman, R., 2007. Stochastic fluctuations through intrinsic noise in evolutionary game dynamics. Bull. Math. Biol. 69, 1377-1399]. On the other hand, for an interior stable phenotypic or genotypic equilibrium, our main results show that the deterministic model cannot be used to predict the expectation of phenotypic frequency. The variance of phenotypic frequency for an interior stable genotypic equilibrium is more sensitive to the expected population size than for an interior stable phenotypic equilibrium. Furthermore, the stochastic fluctuations of allele frequency and phenotypic frequency can be considered approximately independent of each other for these genotypic equilibria, but not for phenotypic.     

Further properties of Gavrilets' one-locus two-allele model of maternal selection

I derive several properties of the model proposed by Gavrilets for maternal selection at a single diallelic locus. Most notably, (i) stable oscillations of genotype frequencies (i.e., cycling) can occur and (ii) in the special case in which maternal effects and standard viability selection act multiplicatively, maternal selection effectively acts on maternally derived alleles only.     

A numerical solution to the equilibria of the two-locus two-allele selection model.

Examination of the equilibria of the standard two-locus two-allele selection model leads to the construction of a polynomial with coefficients derived from selective values in the genotypic fitness matrix. This polynomial can be partially factored algebraically and numerical techniques are available to extract the roots of the remainder. Each root provides a possible value of the disequilibrium coefficient and the gametic frequencies at equilibrium, and these can be readily checked for stability.     

Maximization principles for frequency-dependent selection I: the one-locus two-allele case

In this article we study the one-locus two-allele version of the pairwise-interaction model of frequency-dependent selection in discrete and continuous time. Our main aim is to provide necessary and sufficient conditions for the validity of maximization principles. We provide a systematic approach that covers all possible facets of the dynamical behavior of the model, and we illustrate our results by concrete examples. We show that the mean fitness of the population is nondecreasing if the interaction coefficients are symmetric and positive. Moreover, monotonic convergence to the set of equilibria always occurs, which is not true if we also consider negative interaction coefficients. For asymmetric interaction, we provide necessary conditions when the mean fitness is nondecreasing and sufficient conditions when it is not. Furthermore, in discrete time, we show that limit cycles cannot occur, unless some interaction coefficients are negative.     

Sexual selection and temporal phenotypic variation in a damselfly population

Temporal variation in selection can be generated by temporal variation in either the fitness surface or phenotypic distributions around a static fitness surface, or both concurrently. Here, we use within- and between-generation sampling of fitness surfaces and phenotypic distributions over 2 years to investigate the causes of temporal variation in the form of sexual selection on body size in the damselfly Enallagma aspersum. Within a year, when the average female body size differed substantially from the average male body size, male body size experienced directional selection. In contrast, when male and female size distributions overlapped, male body size experienced stabilizing selection when variances in body size were large, but no appreciable selection when the variances in body size were small. The causes of temporal variation in the form of selection can only be inferred by accounting for changes in both the fitness surface and changes in the distribution of phenotypes.     

Spatial and temporal demographic variation drives within-season fluctuations in sexual selection

Our understanding of selection in nature stems mainly from whole-season and cross-sectional estimates of selection gradients. These estimates suggest that selection is relatively constant within, but fluctuates between seasons. However, the strength of selection depends on demographics, and because demographics can vary within seasons, there is a gap in our understanding regarding the extent to which seasonal fluctuations in demographics may cause variation in selection. Here we use two populations of the golden orb-web spider (Nephila plumipes) that differ in density to examine how demographics change within a season and whether there are correlated shifts in selection. We demonstrate that there is within-season variation in sex ratio and density at multiple spatial and temporal scales. This variation led to changes in the competitive challenges that males encountered at different times of the season and was correlated with significant variation in selection gradients on male size and weight between sampling periods. We highlight the importance of understanding the biology of the organism under study to correctly determine the relevant scale in which to examine selection. We also argue that studies may underestimate the true variation in selection by averaging values, leading to misinterpretation of the effect of selection on phenotypic evolution.     

Some population genetic models combining artificial and natural selection pressures: I. One-locus theory

A series of one-locus genetic models involving the combined effects of artificial and natural selection forces are analyzed. Other factors incorporated in this work include the influence of the imposed or inherent mating system, the relevance of timing in application of the two types of selection forces, the importance of multiallelism and dominance relations.     

Natural selection on floral traits of Lobelia (Lobeliaceae): spatial and temporal variation

The strength and direction of natural selection on floral traits can vary spatially and temporally because of variation in the biotic and abiotic environment. High spatial variation in selection should lead to differentiation of floral traits among populations. In contrast, high temporal variation in selection should retard the evolution of population-specific floral phenotypes. To determine the relative importance of spatial vs. temporal variation in natural selection, we measured phenotypic selection on seven floral traits of the wildflowers Lobelia cardinalis and L. siphilitica in 1999 and 2000. Lobelia cardinalis experienced significant temporal variation in selection, whereas L. siphilitica experienced spatial variation in selection on the same traits. This variation in selection on floral traits was associated with spatial and temporal differences in the soil microenvironment. Although few studies of natural selection include spatial or temporal replicates, our results suggest that such replication is critical for understanding the distribution of phenotypes in nature.     

Random genetic drift and selection in a triallelic locus: a continuous diffusion model.

The Kolmogorov forward diffusion equation is used to examine the evolution of three alleles at one locus under viability selection and random genetic drift. Separation of variables and Chebyschev approximations are employed to solve this equation for long times. As an example, one artificial viability set is examined in detail; its general implications for the evolution at a triallelic locus are discussed.     

Evaluating temporal variation in Citizen Science Data against temporal variation in the environment

Citizen Science Data (CSD) is increasingly contributing to the assessment of biodiversity and ecosystems. However, there is a need to evaluate the usefulness of CSD for different purposes. Ideally, CSD from populations should be evaluated against independent population data collected using a proper sampling design, but such data are lacking for almost all species. We propose an approach for evaluating CSD against environmental data. First, an evaluation model is formulated based on knowledge of how environmental variables affect population dynamics. Second, the hypotheses of the evaluation model are tested statistically. Support for the evaluation model is interpreted as support for the CSD. We applied the approach to six longhorn beetle species using Swedish data from 1930–2000. The evaluation model assumed that early summer temperature affects larval development time. We found support for the evaluation model in two species, and some evidence in its favour in one species. This suggests that the CSD from these species reflect true inter‐annual variation. We also found statistical evidence for population trends in three to four species. In two of these, the evaluation model was supported thus providing particular support for the trend estimates. Lack of support for the evaluation model may be due to biological inaccuracy, the general characteristics of CSD, or low resolution of the environmental evaluation data. We also discuss alternative environmental data for evaluating CSD.     

Fruit selection by Andean forest birds: influence of fruit functional traits and their temporal variation

Fruit selection, i.e., the consumption of fruits disproportionately to their availability, results from the interaction between diet preferences and ecological factors that modify them. We assessed the importance of functional fruit traits to explain fruit selection by birds in Andean subtropical forests, taking into account temporal variation in trait distribution in the assembly of available fruits. During 2 yr, we measured the abundance of ripe fruits and their consumption by birds in a 6‐ha plot during 11 bimonthly samplings, and we used 17 phenological, morphological, and nutritional traits to characterize fruits selected by four bird species. Fruit selection was pervasive year‐round, highly variable over time and across bird species. Fruit species were selected over time periods shorter than their ripening phenology, and the selection of fruits with particular traits was specific to the fruit‐eating species. Maximization in pulp reward per consumed fruit seems to be the main driving force behind fruit selection, indicating that birds select fruits with traits that directly affect net energy gain. Our results can be interpreted in a framework of a hierarchy of foraging decisions, under which the spatiotemporal context of the fruiting environment modifies the relative intake rates of a particular fruit, while the ability to discriminate fruit contents becomes increasingly important on a smaller dimension. We show that fruit‐selection properties are contingent on specific fruit traits and particular spatiotemporal conditions, which modify the structure of mutualistic interactions.     

Temporal and microspatial variation in the intensities of natural and sexual selection in the yellow dung fly Scathophaga stercoraria

Studies of phenotypic selection in natural populations often concentrate only on short time periods and do not quantify selection intensities. We quantified temporal and microspatial variation in the intensities of natural and sexual selection for body size in the yellow dung fly over 2 years. Female fecundity selection intensity remained approximately constant over the season with an overall mean ± SE of 0.187 ± 0.014. Selection intensity for male reproductive success, defined as eggs obtained by mating males, did not differ from zero, indicating there was no assortative mating by size. Sexual selection intensity for male mating success favouring large males was variable but overall strong in the two years (0.499 ± 0.053 and 0.510 ± 0.051). As theoretically expected for male–male competition, sexual selection intensity increased with competitor density and reached an asymptote at about 250 males per pat; it also decreased with time in spring and increased again in autumn as a function of density. Small males had the best chance of obtaining a female at very low male densities. Greater selection intensity for large size in males than females is consistent with, and might be responsible for, the observed sexual size dimorphism in this species, as males are larger. The seasonal pattern of mean male body size (smallest at the beginning and end of the season) most likely reflects mere environmental (primarily temperature) influences on phenotypic size.     

A coalescent model of background selection with recombination,demography and variation in selection coefficients

There is increasing evidence that background selection, the effects of the elimination of recurring deleterious mutations by natural selection on variability at linked sites, may be a major factor shaping genome-wide patterns of genetic diversity. To accurately quantify the importance of background selection, it is vital to have computationally efficient models that include essential biological features. To this end, a structured coalescent procedure is used to construct a model of background selection that takes into account the effects of recombination, recent changes in population size and variation in selection coefficients against deleterious mutations across sites. Furthermore, this model allows a flexible organization of selected and neutral sites in the region concerned, and has the ability to generate sequence variability at both selected and neutral sites, allowing the correlation between these two types of sites to be studied. The accuracy of the model is verified by checking against the results of forward simulations. These simulations also reveal several patterns of diversity that are in qualitative agreement with observations reported in recent studies of DNA sequence polymorphisms. These results suggest that the model should be useful for data analysis.