A fundamental relationship between genotype frequencies and fitnesses

The set of possible postselection genotype frequencies in an infinite, randomly mating population is found. Geometric mean heterozygote frequency divided by geometric mean homozygote frequency equals two times the geometric mean heterozygote fitness divided by geometric mean homozygote fitness. The ratio of genotype frequencies provides a measure of genetic variation that is independent of allele frequencies. When this ratio does not equal two, either selection or population structure is present. Within-population HapMap data show population-specific patterns, while pooled data show an excess of homozygotes.     

Genetic Variation in Heterogeneous Environments

A model of population structure in heterogeneous environments is described and conditions sufficient for maintaining a polymorphism are derived.

The absolute fitness of any genotype is regarded as a function of location in the niche space and the population density at that location. Two modes of habitat selection are examined: (1) organisms are distributed uniformly over the environment; and (2) each organism selects to occupy that habitat in which it is most fit ("optimal habitant selection").—Sufficient conditions for maintenance of genetic polymorphisms are derived for both models. In populations which do not practice habitat selection heterozygote superiority averaged over the environment is sufficient to guarantee the existence of polymorphisms. Comparable conditions for populations which practice optimal habitat selection are much less restrictive. If the heterozygotes are superior to one homozygote in any one part of the niche and to the other homozygote in any other part of the niche then a polymorphism will be defined.—A positive correlation between genetic and environmental variation follows from the model with habitat selection, but not from the other. The adaptive significance of polymorphisms thus depends on how animals behave.

     

Genetic Variation in a Heterogeneous Environment. I. Temporal Heterogeneity and the Absolute Dominance Model

The conditions for a stable polymorphism and the equilibrium gene frequency in an infinite population are compared when there is spatial or temporal environmental heterogeneity for the absolute dominance model. For temporal variation the conditions for stability are more restrictive and the equilibrium gene frequency is often at a low gene frequency. In a finite population, temporal environmental heterogeneity for the absolute dominance model was found to be quite ineffective in maintaining genetic variation and is often less effective than no selection at all. For comparison, the maximum maintenance for temporal variation is related to the overdominant model. In general, cyclic environmental variation was found to be more effective at maintaining genetic variation than where the environment varies stochastically. The importance of temporal environmental variation and the maintenance of genetic variation is discussed.     

EVOLUTION AND EXTINCTION IN A CHANGING ENVIRONMENT: A QUANTITATIVE-GENETIC ANALYSIS

Because of the ubiquity of genetic variation for quantitative traits, virtually all populations have some capacity to respond evolutionarily to selective challenges. However, natural selection imposes demographic costs on a population, and if these costs are sufficiently large, the likelihood of extinction will be high. We consider how the mean time to extinction depends on selective pressures (rate and stochasticity of environmental change, and strength of selection), population parameters (carrying capacity, and reproductive capacity), and genetics (rate of polygenic mutation). We assume that in a randomly mating, finite population subject to density-dependent population growth, individual fitness is determined by a single quantitative-genetic character under Gaussian stabilizing selection with the optimum phenotype exhibiting directional change, or random fluctuations, or both. The quantitative trait is determined by a finite number of freely recombining, mutationally equivalent, additive loci. The dynamics of evolution and extinction are investigated, assuming that the population is initially under mutation-selection-drift balance. Under this model, in a directionally changing environment, the mean phenotype lags behind the optimum, but on the average evolves parallel to it. The magnitude of the lag determines the vulnerability to extinction. In finite populations, stochastic variation in the genetic variance can be quite pronounced, and bottlenecks in the genetic variance temporarily can impair the population's adaptive capacity enough to cause extinction when it would otherwise be unlikely in an effectively infinite population. We find that maximum sustainable rates of evolution or, equivalently, critical rates of environmental change, may be considerably less than 10% of a phenotypic standard deviation per generation.     

Fitness and adaptation in a novel environment: effect of inbreeding, prior environment, and lineage

Abstract. The ability of populations to undergo adaptive evolution depends on the presence of genetic variation for ecologically important traits. The maintenance of genetic variation may be influenced by many variables, particularly long-term effective population size and the strength and form of selection. The roles of these factors are controversial and there is very little information on their impacts for quantitative characters. The aims of this study were to determine the impacts of population size and variable versus constant prior environmental conditions on fitness and the magnitude of response to selection. Outbred and inbred populations of Drosophila melanogaster were maintained under benign, constant stressful, and variably stressful conditions for seven generations, and then forced to adapt to a novel stress for seven generations. Fitness and adaptability were assayed in each replicate population. Our findings are that: (1) populations inbred in a variable environment were more adaptable than those inbred in a constant environment; (2) populations adapted to a prior stressful environment had greater fitness when reared in a novel stress than those less adapted to stress; (3) inbred populations had lower fitness and were less adaptable than the outbred population they were derived from; and (4) strong lineage effects were detectable across environments in the inbred populations.     

The Genetic Structure of Natural Populations of Drosophila melanogaster. Xx. Comparison of Genotype-Environment Interaction in Viability between a Northern and a Southern Population

In order to examine the operation of diversifying selection as the maintenance mechanism of excessive additive genetic variance for viability in southern populations in comparison with northern populations of Drosophila melanogaster, two sets of experiments were conducted using second chromosomes extracted from the Ogasawara population (a southern population in Japan) and from the Aomori population (a northern population in Japan). Chromosomal homozygote and heterozygote viabilities were estimated in eight kinds of artificially produced breeding environments. The main findings in the present investigation are as follows: (1) Significant genotype-environment interaction was observed using chromosomes extracted from the Ogasawara population. Indeed, the estimate of the genotype-environment interaction variance for heterozygotes was significantly larger than that of the genotypic variance. On the other hand, when chromosomes sampled from the Aomori population were examined, that interaction variance was significant only for homozygotes and its value was no more than one quarter of that for the chromosomes from the Ogasawara population. (2) The average genetic correlation between any two viabilities of the same lines estimated in the eight kinds of breeding environments for the chromosomes sampled from the Ogasawara population was smaller than that for the chromosomes from the Aomori population both in homozygotes and in heterozygotes, especially in the latter. (3) The stability of heterozygotes over homozygotes against fluctuations of environmental conditions was seen in the chromosomes from the Ogasawara population, but not from the Aomori population. (4) From the excessive genotype-environment interaction variance compared with the genotypic variance in heterozygotes, it was suggested for the chromosomes from the Ogasawara population that the reversal of viability order between homozygotes took place in some environments at the locus level. On the basis of these findings, it is strongly suggested that diversifying selection is operating in a southern population of D. melanogaster on some of the viability polygenes which are probably located outside the structural loci, and the excessive additive genetic variance of viability in southern populations is maintained by this type of selection.     

Fluctuating Environments Maintain Genetic Diversity through Neutral Fitness Effects and Balancing Selection

Genetic variation is the raw material upon which selection acts. The majority of environmental conditions change over time and therefore may result in variable selective effects. How temporally fluctuating environments impact the distribution of fitness effects and in turn population diversity is an unresolved question in evolutionary biology. Here, we employed continuous culturing using chemostats to establish environments that switch periodically between different nutrient limitations and compared the dynamics of selection to static conditions. We used the pooled Saccharomyces cerevisiae haploid gene deletion collection as a synthetic model for populations comprising thousands of unique genotypes. Using barcode sequencing, we find that static environments are uniquely characterized by a small number of high-fitness genotypes that rapidly dominate the population leading to dramatic decreases in genetic diversity. By contrast, fluctuating environments are enriched in genotypes with neutral fitness effects and an absence of extreme fitness genotypes contributing to the maintenance of genetic diversity. We also identified a unique class of genotypes whose frequencies oscillate sinusoidally with a period matching the environmental fluctuation. Oscillatory behavior corresponds to large differences in short-term fitness that are not observed across long timescales pointing to the importance of balancing selection in maintaining genetic diversity in fluctuating environments. Our results are consistent with a high degree of environmental specificity in the distribution of fitness effects and the combined effects of reduced and balancing selection in maintaining genetic diversity in the presence of variable selection.     

Emergence of long‐term balanced polymorphism under cyclic selection of spatially variable magnitude

A fundamental question in evolutionary biology is what promotes genetic variation at nonneutral loci, a major precursor to adaptation in changing environments. In particular, balanced polymorphism under realistic evolutionary models of temporally varying environments in finite natural populations remains to be demonstrated. Here, we propose a novel mechanism of balancing selection under temporally varying fitnesses. Using forward‐in‐time computer simulations and mathematical analysis, we show that cyclic selection that spatially varies in magnitude, such as along an environmental gradient, can lead to elevated levels of nonneutral genetic polymorphism in finite populations. Balanced polymorphism is more likely with an increase in gene flow, magnitude and period of fitness oscillations, and spatial heterogeneity. This polymorphism‐promoting effect is robust to small systematic fitness differences between competing alleles or to random environmental perturbation. Furthermore, we demonstrate analytically that protected polymorphism arises as spatially heterogeneous cyclic fitness oscillations generate a type of storage effect that leads to negative frequency dependent selection. Our findings imply that spatially variable cyclic environments can promote elevated levels of nonneutral genetic variation in natural populations.     

A General Model to Account for Enzyme Variation in Natural Populations

Approximate conditions for genetic polymorphism in temporally and spatially varying environments are presented for loci which are intermediate at the level of fitness or at the level of gene function. The conditions suggest that polymorphism will be more likely in more variable environments while unlikely in constant environments. Biochemical evidence is presented to justify the assumption of heterozygote intermediacy. Observations on natural populations are cited which substantiate the claim that allozymic polymorphism is primarily due to selection acting on environmental variation in gene function.     

Heterozygote advantage and the maintenance of polymorphism for multilocus traits

Explaining how polymorphism is maintained in the face of selection remains a puzzle since selection tends to erode genetic variation. Provided an infinitely large unsubdivided population and no frequency-dependance of selective values, heterozygote advantage is the text book explanation for the maintenance of polymorphism when selection acts at a diallelic locus. Here, we investigate whether this remains true when selection acts at multiple diallelic loci. We use five different definitions of heterozygote advantage that largely cover this concept for multiple loci. Using extensive numerical simulations, we found no clear associations between the presence of any of the five definitions of heterozygote advantage and the maintenance of polymorphism at all loci. The strength of the association decreases as the number of loci increases or as recombination decreases. We conclude that heterozygote advantage cannot be a general mechanism for the maintenance of genetic polymorphism at multiple loci. These findings suggest that a correlation between the number of heterozygote loci and fitness is not warranted on theoretical ground.     

Degeneracy allows for both apparent homogeneity and diversification in populations

Trait diversity - the substrate for natural selection - is necessary for adaptation through selection, particularly in populations faced with environmental changes that diminish population fitness. In habitats that remain unchanged for many generations, stabilizing selection maximizes exploitation of resources by reducing trait diversity to a narrow optimal range. One might expect that such ostensibly homogeneous populations would have a reduced potential for heritable adaptive responses when faced with fitness-reducing environmental changes. However, field studies have documented populations that, even after long periods of evolutionary stasis, can still rapidly evolve in response to changed environmental conditions. We argue that degeneracy, the ability of diverse population elements to function similarly, can satisfy both the current need to maximize fitness and the future need for diversity. Degenerate ensembles appear functionally redundant in certain environmental contexts and functionally diverse in others. We propose that genetic variation not contributing to the observed range of phenotypes in a current population, also known as cryptic genetic variation (CGV), is a specific case of degeneracy. We argue that CGV, which gradually accumulates in static populations in stable environments, reveals hidden trait differences when environments change. By allowing CGV accumulation, static populations prepare themselves for future rapid adaptations to environmental novelty. A greater appreciation of degeneracy's role in resolving the inherent tension between current stabilizing selection and future directional selection has implications in conservation biology and may be applied in social and technological systems to maximize current performance while strengthening the potential for future changes.     

Heterogeneous selection on trichome production in Alaskan Arabidopsis kamchatica (Brassicaceae)

? Premise of the study: Environmental heterogeneity is thought to be one of the primary factors in the evolutionary maintenance of morphological variation. Here, we explore the role of environmental heterogeneity in the maintenance of variation in leaf hair (trichome) production in Arabidopsis kamchatica. ? Methods: We investigate abiotic correlates of trichome production in A. kamchatica via surveys of both herbarium specimens and wild populations. In addition, we examine patterns of phenotypic selection on trichome production among populations that differ in environmental characteristics. ? Key results: Trichome-producing herbarium specimens were more likely to occur at lower latitudes and in locations with lower mean annual precipitation and less annual variation in temperature than glabrous specimens. In surveys of wild populations, frequencies of trichome-producing plants were higher in drier habitats than in wetter environments. Using phenotypic selection analysis, we found divergent selection through female fitness (fruit production) on trichome number in populations that differ in environmental characteristics; there was selection for reduced trichome number in one population and selection for increased trichome number in another population. In a population containing both glabrous and trichome-producing plants, glabrous plants produced significantly more fruits than trichome-producing individuals, which indicates selection against the trichome morph. ? Conclusions: Our results demonstrate that there is heterogeneity in selection among populations, which could be responsible for the maintenance of trichome variation in Alaskan populations of A. kamchatica.     

Evolution of a single niche specialist in variable environments

The pattern (space versus time) and scale (relative to the lifetime of individuals) of environmental variation is thought to play a central role in governing the evolution of the ecological niche and the maintenance of genetic variance in fitness. To evaluate this idea, we serially propagated an initially genetically uniform population of the bacterium Pseudomonas fluorescens for a few hundred generations in environments that differed in both the pattern and scale at which two highly contrasted carbon substrates were experienced. We found that, contrary to expectations, populations often evolved into a single niche specialist adapted to the less-productive substrate in variable environments and that the genetic variance in fitness across different components of the environment was not generally higher in variable environments when compared with constant environments. We provide evidence to suggest that our results reflect a novel constraint on niche evolution imposed by the supply of beneficial mutations available to selection in variable environments.     

Quantitative genetics of ovariole number in Drosophila melanogaster. II. Mutational variation and genotype-environment interaction.

The rare alleles model of mutation-selection balance (MSB) hypothesis for the maintenance of genetic variation was evaluated for two quantitative traits, ovariole number and body size. Mutational variances (VM) for these traits, estimated from mutation accumulation lines, were 4.75 and 1.97 x 10(-4) times the environmental variance (VE), respectively. The mutation accumulation lines were studied in three environments to test for genotype x environment interaction (GEI) of new mutations; significant mutational GEI was found for both traits. Mutations for ovariole number have a quadratic relationship with competitive fitness, suggesting stabilizing selection for the trait; there is no significant correlation between mutations for body size and competitive fitness. Under MSB, the ratio of segregating genetic variance, VG, to mutational variance, VM, estimates the inverse of the selection coefficient against a heterozygote for a new mutation. Estimates of VG/VM for ovariole number and body size were both approximately 1.1 x 10(4). Thus, MSB can explain the level of variation, if mutations affecting these traits are under very weak selection, which is inconsistent with the empirical observation of stabilizing selection, or if the estimate of VM is biased downward by two orders of magnitude. GEI is a possible alternative explanation.     

Coexistence of trichome variation in a natural plant population: a combined study using ecological and candidate gene approaches

The coexistence of distinct phenotypes within populations has long been investigated in evolutionary ecology. Recent studies have identified the genetic basis of distinct phenotypes, but it is poorly understood how the variation in candidate loci is maintained in natural environments. In this study, we examined fitness consequences and genetic basis of variation in trichome production in a natural population of Arabidopsis halleri subsp. gemmifera. Half of the individuals in the study population produced trichomes while the other half were glabrous, and the leaf beetle Phaedon brassicae imposed intensive damage to both phenotypes. The fitness of hairy and glabrous plants showed no significant differences in the field during two years. A similar result was obtained when sibling hairy and glabrous plants were transplanted at the same field site, whereas a fitness cost of trichome production was detected under a weak herbivory condition. Thus, equivalent fitness of hairy and glabrous plants under natural herbivory allows their coexistence in the contemporary population. The pattern of polymorphism of the candidate trichome gene GLABROUS1 (GL1) showed no evidence of long-term maintenance of trichome variation within the population. Although balancing selection under fluctuating biotic environments is often proposed to explain the maintenance of defense variation, the lack of clear evidence of balancing selection in the study population suggests that other factors such as gene flow and neutral process may have played relatively large roles in shaping trichome variation at least for the single population level.     

Learning, climate and the evolution of cultural capacity

Patterns of environmental variation influence the utility, and thus evolution, of different learning strategies. I use stochastic, individual-based evolutionary models to assess the relative advantages of 15 different learning strategies (genetic determination, individual learning, vertical social learning, horizontal/oblique social learning, and contingent combinations of these) when competing in variable environments described by 1/f noise. When environmental variation has little effect on fitness, then genetic determinism persists. When environmental variation is large and equal over all time-scales ("white noise") then individual learning is adaptive. Social learning is advantageous in "red noise" environments when variation over long time-scales is large. Climatic variability increases with time-scale, so that short-lived organisms should be able to rely largely on genetic determination. Thermal climates usually are insufficiently red for social learning to be advantageous for species whose fitness is very determined by temperature. In contrast, population trajectories of many species, especially large mammals and aquatic carnivores, are sufficiently red to promote social learning in their predators. The ocean environment is generally redder than that on land. Thus, while individual learning should be adaptive for many longer-lived organisms, social learning will often be found in those dependent on the populations of other species, especially if they are marine. This provides a potential explanation for the evolution of a prevalence of social learning, and culture, in humans and cetaceans.     

Resource-dependent selection.

This paper presents a resource-dependent viability selection differential equation model of continuously reproducing diploid population with two alleles at one locus for a single limiting resource. This model assumes that the genotypic fitness is only a function of the limiting resource. The conditions that the interior equilibrium point of the system exists are that the heterozygote fitness is positive and the homozygote fitness is negative, or the heterozygote fitness is negative and the homozygote fitness is positive at the point. The sufficient and necessary conditions of locally asymptotical stability of the interior equilibrium point are that the heterozygote fitness is positive at the point, or the locally asymptotically stable equilibrium corresponds to the point at which the level of the limiting resource is locally minimized on the zero mean fitness curve, f = 0.     

Predicting population genetic change in an autocorrelated random environment: Insights from a large automated experiment

Most natural environments exhibit a substantial component of random variation, with a degree of temporal autocorrelation that defines the color of environmental noise. Such environmental fluctuations cause random fluctuations in natural selection, affecting the predictability of evolution. But despite long-standing theoretical interest in population genetics in stochastic environments, there is a dearth of empirical estimation of underlying parameters of this theory. More importantly, it is still an open question whether evolution in fluctuating environments can be predicted indirectly using simpler measures, which combine environmental time series with population estimates in constant environments. Here we address these questions by using an automated experimental evolution approach. We used a liquid-handling robot to expose over a hundred lines of the micro-alga Dunaliella salina to randomly fluctuating salinity over a continuous range, with controlled mean, variance, and autocorrelation. We then tracked the frequencies of two competing strains through amplicon sequencing of nuclear and choloroplastic barcode sequences. We show that the magnitude of environmental fluctuations (determined by their variance), but also their predictability (determined by their autocorrelation), had large impacts on the average selection coefficient. The variance in frequency change, which quantifies randomness in population genetics, was substantially higher in a fluctuating environment. The reaction norm of selection coefficients against constant salinity yielded accurate predictions for the mean selection coefficient in a fluctuating environment. This selection reaction norm was in turn well predicted by environmental tolerance curves, with population growth rate against salinity. However, both the selection reaction norm and tolerance curves underestimated the variance in selection caused by random environmental fluctuations. Overall, our results provide exceptional insights into the prospects for understanding and predicting genetic evolution in randomly fluctuating environments.     

Uniqueness of polymorphic equilibria under soft selection

Any two allele polymorphic equilibrium of a subdivided haploid population subject to soft selection is stable. This provides that for a two allele system in a subdivided haploid population there is a globally attracting equilibrium which is polymorphic if a polymorphic equilibrium exists, otherwise monomorphic. These results extend to diploid populations if within each habitat the heterozygote viability is greater than or equal to the geometric mean of the homozygote viabilities.     

Adaptive maintenance of genetic polymorphism in an intertidal barnacle: habitat- and life-stage-specific survivorship of Mpi genotypes

In the northern acorn barnacle, Semibalanus balanoides, genotype frequencies of three genetic markers were tracked over time in four types of intertidal habitats. These habitats were selected to represent natural variation in several environmental parameters, specifically the degree of physical stress experienced by barnacles. Frequencies for one allozyme locus (Gpi) and a presumably neutral mtDNA marker were homogeneous among habitats in each temporal sample. Similarly, no temporal stratification in genotype frequencies was evident across the five sampling intervals: from planktonic larvae sampled in March to juveniles collected at the end of June. In contrast to the Gpi and mtDNA loci, Mpi genotypes significantly changed in frequency in two habitats in the high intertidal zone. On exposed substrate, the Mpi-FF homozygote increased in frequency, whereas the alternative homozygote, Mpi-SS, significantly decreased in frequency. Barnacles that were protected from environmental stress at high intertidal heights by the Ascophyllum nodosum algal canopy demonstrated the opposite pattern. In both habitats, the change in frequency of the heterozygote was intermediate to that of the homozygous genotypes. Furthermore, these patterns of genotype-by-environment association reflected a pulse of genotype-specific mortality that occurred over a two-week interval subsequent to metamorphosis from the larval to the adult form. These data indicate that each Mpi homozygote is the highest fitness genotype in some portion of the intertidal environment. Using the Levene (1953) model to evaluate the spatial variation in genotypic fitness, the stable maintenance of the Mpi polymorphism is predicted under certain subsets of conditions. Environmental heterogeneity in the intertidal zone translates to spatial variation in selection pressures, which may result in the active maintenance of the Mpi polymorphism in this species.