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.

     

Competitive exclusion and coexistence of pathogens in a homosexually-transmitted disease model

A sexually-transmitted disease model for two strains of pathogen in a one-sex, heterogeneously-mixing population has been studied completely by Jiang and Chai in (J Math Biol 56:373-390, 2008). In this paper, we give a analysis for a SIS STD with two competing strains, where populations are divided into three differential groups based on their susceptibility to two distinct pathogenic strains. We investigate the existence and stability of the boundary equilibria that characterizes competitive exclusion of the two competing strains; we also investigate the existence and stability of the positive coexistence equilibrium, which characterizes the possibility of coexistence of the two strains. We obtain sufficient and necessary conditions for the existence and global stability about these equilibria under some assumptions. We verify that there is a strong connection between the stability of the boundary equilibria and the existence of the coexistence equilibrium, that is, there exists a unique coexistence equilibrium if and only if the boundary equilibria both exist and have the same stability, the coexistence equilibrium is globally stable or unstable if and only if the two boundary equilibria are both unstable or both stable.     

The impact of habitat loss and fragmentation on genetic drift and fixation time

In this study, a simple genetic model is integrated with an established method from landscape ecology to investigate the effect of habitat geometry and availability on genetic drift. Previous ecological modelling has identified a sharp threshold in habitat availability for species' persistence, beyond which the species rapidly becomes extinct. This study demonstrates the existence of a similar threshold for fixation time of selectively neutral genotypes by genetic drift, the location of which is determined by habitat shape and spatial correlation of habitat loss. Time to fixation is greater for habitats if they are long and thin rather than square. Despite reductions in population size due to habitat loss, fixation time remains relatively constant until a pre-threshold value, beyond which there is often a substantial increase in time to fixation. Further habitat loss results in the percolation threshold being reached and beyond this point the time to fixation decreases very rapidly. This study reveals a complex relationship between habitat availability, habitat geometry and the process of genetic drift. Possible implications of our results for conservation are discussed. Further work is required to improve our understanding of the interaction between evolutionary, ecological and landscape processes.     

Conditions for the Existence of Clines

A very general partial differential equation in space and time satisfied by the gene frequency in a monoecious population distributed continuously over an arbitrary habitat is derived. The treatment is restricted to a single diallelic locus in the absence of mutation and random drift, and it is supposed that time is continuous, births and deaths occur at random, and migration is independent of genotype. With the further assumptions that migration is isotropic and homogeneous, the population density is constant and uniform (as permitted by the population regulation mechanism included in the formulation), and Hardy-Weinberg proportions obtain locally, this partial differential equation reduces to the simplest multidimensional generalization of the classical Fisher-Haldane cline model. The efficacy of migration and selection in maintaining genetic variability at equilibrium in this model is investigated by deducing conditions for the existence of clines under various circumstances. The effects of the degree of dominance, a neutral belt between the regions where a particular allele is advantageous and deleterious, finiteness of the habitat, and habitat dimensionality are evaluated. Provided at least one of the alleles is favored only in a finite region, excluding the special case in which its total effective selective coefficient is zero, if conditions for supporting a cline are too unfavorable because migration is too strong, selection is too weak, or both, a cline cannot exist at all. Thus, unless there is overdominance, the population must be monomorphic. It is possible for a cline which can barely exist under the prevailing ecological circumstances to show a large amount of variation in gene frequency.     

Theoretical aspects of extinction by inbreeding depression

Populational extinction due to inbreeding depression is analyzed with simple population genetic and population ecological models. Two alternative genetic mechanisms of inbreeding depression, i.e. recessive deleterious genes and overdominant genes, are assumed in separate analyses in order to examine their relative importance. With both mechanisms the population size and the coefficient of inbreeding are maintained at stable equilibria if there is no non-genetic demographic disturbance or stress. With a certain amount of demographic disturbance the population declines rapidly due to interaction between the decrease of population size and the increase of inbreeding coefficient. Such rapid extinction occurs with both genetic mechanisms. However, in the case of overdominant genes extinction happens only if the equilibrium population size is small and the selection coefficient is large such that segregation load is large. In nature, extinction due to overdominant genes is considered to be much less likely than extinction due to recessive deleterious genes.     

Evolutionary principles for general frequency-dependent two-phenotype models in sexual populations

The evolutionary dynamics in general two-sex two-phenotype frequency-dependent selection models are studied with respect to underlying multi-allele one-locus genetic systems. Two classes of equilibria come into play: genotypic equilibria, with equilibrium allelic frequencies independent of the phenotype, and phenotypic equilibria, which are characterized by equal mean phenotypic fitnesses. The exact conditions for genotypic equilibria to exist and be stable and for phenotypic equilibria to exist and be evolutionarily attractive are examined. Using adequate definitions of mean fitnesses in general contexts of frequency-dependent selection in dioecious populations, we show that two phenotypes, when they can coexist in the population, tend to balance their fitnesses as far as is allowed by the genetic system as more alleles responsible for phenotype determination are introduced into the population.     

Signalling among relatives. I. Is costly signalling too costly?

Zahavi''s handicap principle,originally proposed as an explanation for sexual selection ofelaborate male traits, suggests that a sufficient cost to dishonest signals can outweigh the rewards of deception and allow individuals to communicate honestly. Maynard Smith (1991) and Johnstone and Grafen (1992) introduce the Sir Philip Sidney game in order to extend the handicap principle to interactions among related individuals, and to demonstrate that stable costly signalling systems can exist among relatives.In this paper we demonstrate that despite the benefits associated with honest information transfer, the costs incurred in a stable costly signalling system may leave all participants worse off than they would be in a system with no signalling at all. In both the discrete and continuous forms of the Sir Philip Sidney game, there exist conditions under which costly signalling among relatives, while stable, is so costly that it is disadvantageous compared with no signalling at all. We determine the factors which dictate signal cost and signal benefit in a generalized version of this game, and explain how signal cost can exceed signal value. Such results raise concerns about theevolutionary pathways which could have led to the existence of signalling equilibria in nature. The paper stresses the importance of comparing signalling equilibria with other possible strategies, beforedrawing conclusions regarding the optimality of signalling.     

Nonlinear frequency-dependent selection at a single locus with two alleles and two phenotypes

 The paper investigates the discrete frequency dynamics of two phenotype diploid models where genotypic fitness is an exponential function of the expected payoff in the matrix game. Phenotypic and genotypic equilibria are defined and their stability compared to frequency-dependent selection models based on linear fitness when there are two possible phenotypes in the population. In particular, it is shown that stable equilibria of both types can exist in the same nonlinear model. It is also shown that period-doubling bifurcations emerge when there is sufficient selection in favor of interactions between different phenotypes. Received: 22 October 1998     

Geometric criteria for the non-existence of cycles in predator-prey systems with group defense

In this paper, we study the existence of cycles in a predator-prey system in which the prey species is equipped with the group defense capability. Some geometric criteria are developed, relating the location of the two positive equilibria on the prey isocline and the non-existence of cycles. We show that under a general geometric condition, if both positive equilibria lie on a downslope or both lie on an upslope of the prey isocline, cycles do not exist.     

Habitat selection reduces extinction of populations subject to Allee effects

Theoretical studies indicate that a single population under an Allee effect will decline to extinction if reduced below a particular threshold, but the existence of multiple local populations connected by random dispersal improves persistence of the global population. An additional process that can facilitate persistence is the existence of habitat selection by dispersers. Using analytic and simulation models of population change, I found that when habitat patches exhibiting Allee effects are connected by dispersing individuals, habitat selection by these dispersers increases the likelihood that patches persist at high densities, relative to results expected by random settlement. Populations exhibiting habitat selection also attain equilibrium more quickly than randomly dispersing populations. These effects are particularly important when Allee effects are large and more than two patches exist. Integrating habitat selection into population dynamics may help address why some studies have failed to find extinction thresholds in populations, despite well-known Allee effects in many species.     

Balancing selection, random genetic drift, and genetic variation at the major histocompatibility complex in two wild populations of guppies (Poecilia reticulata)

Our understanding of the evolution of genes of the major histocompatibility complex (MHC) is rapidly increasing, but there are still enigmatic questions remaining, particularly regarding the maintenance of high levels of MHC polymorphisms in small, isolated populations. Here, we analyze the genetic variation at eight microsatellite loci and sequence variation at exon 2 of the MHC class IIB (DAB) genes in two wild populations of the Trinidadian guppy, Poecilia reticulata. We compare the genetic variation of a small (Ne, 100) and relatively isolated upland population to that of its much larger (Ne approximately 2400) downstream counterpart. As predicted, microsatellite diversity in the upland population is significantly lower and highly differentiated from the population further downstream. Surprisingly, however, these guppy populations are not differentiated by MHC genetic variation and show very similar levels of allelic richness. Computer simulations indicate that the observed level of genetic variation can be maintained with overdominant selection acting at three DAB loci. The selection coefficients differ dramatically between the upland (s > or = 0.2) and lowland (s < or = 0.01) populations. Parasitological analysis on wild-caught fish shows that parasite load is significantly higher on upland than on lowland fish, which suggests that large differences in selection intensity may indeed exist between populations. Based on the infection intensity, a substantial proportion of the upland fish would have suffered direct or indirect fitness consequences as a result of their high parasite loads. Selection by parasites plays a particularly important role in the evolution of guppies in the upland habitat, which has resulted in high levels of MHC diversity being maintained in this population despite considerable genetic drift.     

Phylogeography and population genetics of pine butterflies: Sky islands increase genetic divergence

The sky islands of southeastern Arizona (AZ) mark a major transition zone between tropical and temperate biota and are considered a neglected biodiversity hotspot. Dispersal ability and host plant specificity are thought to impact the history and diversity of insect populations across the sky islands. We aimed to investigate the population structure and phylogeography of two pine‐feeding pierid butterflies, the pine white (Neophasia menapia) and the Mexican pine white (Neophasia terlooii), restricted to these “islands” at this transition zone. Given their dependence on pines as the larval hosts, we hypothesized that habitat connectivity affects population structure and is at least in part responsible for their allopatry. We sampled DNA from freshly collected butterflies from 17 sites in the sky islands and adjacent high‐elevation habitats and sequenced these samples using ddRADSeq. Up to 15,399 SNPs were discovered and analyzed in population genetic and phylogenetic contexts with Stacks and pyRAD pipelines. Low genetic differentiation in N. menapia suggests that it is panmictic. Conversely, there is strong evidence for population structure within N. terlooii. Each sky island likely contains a population of N. terlooii, and clustering is hierarchical, with populations on proximal mountains being more related to each other. The N. menapia habitat, which is largely contiguous, facilitates panmixia, while the N. terlooii habitat, restricted to the higher elevations on each sky island, creates distinct population structure. Phylogenetic results corroborate those from population genetic analyses. The historical climate‐driven fluxes in forest habitat connectivity have implications for understanding the biodiversity of fragmented habitats.     

The maintenance (or not) of polygenic variation by soft selection in heterogeneous environments

On the basis of single-locus models, spatial heterogeneity of the environment coupled with strong population regulation within each habitat (soft selection) is considered an important mechanism maintaining genetic variation. We studied the capacity of soft selection to maintain polygenic variation for a trait determined by several additive loci, selected in opposite directions in two habitats connected by dispersal. We found three main types of stable equilibria. Extreme equilibria are characterized by extreme specialization to one habitat and loss of polymorphism. They are analogous to monomorphic equilibria in singe-locus models and are favored by similar factors: high dispersal, weak selection, and low marginal average fitness of intermediate genotypes. At the remaining two types of equilibria the population mean is intermediate but variance is very different. At fully polymorphic equilibria all loci are polymorphic, whereas at low-variance equilibria at most one locus remains polymorphic. For most parameters only one type of equilibrium is stable; the transition between the domains of fully polymorphic and low-variance equilibria is typically sharp. Low-variance equilibria are favored by high marginal average fitness of intermediate genotypes, in contrast to single-locus models, in which marginal overdominance is particularly favorable for maintenance of polymorphism. The capacity of soft selection to maintain polygenic variation is thus more limited than extrapolation from single-locus models would suggest, in particular if dispersal is high and selection weak. This is because in a polygenic model, variance can evolve independently of the mean, whereas in the single-locus two-allele case, selection for an intermediate mean automatically leads to maintenance of polymorphism.     

Interactions between Caenorhabditis elegans individuals during chemotactic response

The chemotactic response of the nematode Caenorhabditis elegans is known to be affected by the population density on an assay plate, suggesting the existence of interactions between individual animals. To clarify the interactions between individuals during chemotaxis, we investigated the effect of population density at an attractant area on the chemotactic response to water-soluble sodium acetate and odorant diacetyl using wild-type N2 animals and daf-22 (m130) mutants, which have defective pheromone secretion but can sense pheromone. The chemotaxis index of N2 animals at 90 min of the assay negatively correlated with the number of animals on the assay plate regardless of the type of attractant used (p<0.01). On the other hand, there was no significant difference in the chemotaxis indices of daf-22 (m130) mutants for either of the attractants between the low-and high-population groups. When daf-22 (m130) mutants of a high population density were placed at the attractant location in advance, the chemotaxis index of N2 animals was almost the same as that in the control assay in which no animals were placed at the attractant location in advance. When N2 animals of a high population density were placed at the attractant location in advance, the chemotaxis indices of N2 animals and daf-22 (m130) mutants were significantly smaller than those obtained in the control assay (p<0.05). In the absence of an attractant, we observed a decline in the fraction of animals in the neighborhood of N2 animals of a high population density, although the nematodes were not influenced by daf-22 (m130) mutants of a high population density. These results suggest that the attraction of nematodes to chemicals is inhibited by an increase in the concentration of the pheromone generated by N2 animals at the attractant location.     

Natural Selection with Nuclear and Cytoplasmic Transmission. I. a Deterministic Model

A deterministic model allowing variation at a nuclear genetic locus in a population segregating two cytoplasmic types is formulated. Additive, multiplicative and symmetric viability matrices are analyzed for existence and stability of equilibria. The protectedness of polymorphisms in both nuclear genes and cytoplasmic types is also investigated in the general model. In no case is a complete polymorphism protected with this deterministic model. Results are discussed in light of the extensive variation in mtDNA that has recently been reported.     

Spatial genetic structuring in a vagile species, the European wood mouse

We examined the genetic structure of natural populations of the European wood mouse Apodemus sylvaticus at the microgeographic (<3 km) and macrogeographic (>30 km) scales. Ecological and behavioural studies indicate that this species exhibits considerable dispersal relative to its home-range size. Thus, there is potential for high gene flow over larger geographic areas. As levels of population genetic structure are related to gene flow, we hypothesized that population genetic structuring at the microgeographic level should be negligible, increasing only with geographic distance. To test this, four sites were sampled within a microgeographic scale with two additional samples at the macrogeographic level. Individuals ( n =415) were screened and analysed for seven polymorphic microsatellite loci. Contrary to our hypothesis, significant levels of population structuring were detected at both scales. Comparing genetic differentiation with geographic distance suggests increasing genetic isolation with distance. However, this distance effect was non-significant being confounded by surprisingly high levels of differentiation among microgeographic samples. We attribute this pattern of genetic differentiation to the effect of habitat fragmentation, splitting large populations into components with small effective population sizes resulting in enhanced genetic drift. Our results indicate that it is incorrect to assume genetic homogeneity among populations even where there is no evidence of physical barriers and dispersal can occur freely. In the case of A. sylvaticus , it is not clear whether dispersal does not occur across habitat barriers or behavioural dispersal occurs without consequent gene flow.     

EFFECTIVENESS OF SELECTION IN REDUCING THE GENETIC LOAD IN POPULATIONS OF PEROMYSCUS POLIONOTUS DURING GENERATIONS OF INBREEDING

It has been hypothesized that natural selection reduces the “genetic load” of deleterious alleles from populations that inbreed during bottlenecks, thereby ameliorating impacts of future inbreeding. We tested the efficiency with which natural selection purges deleterious alleles from three subspecies of Peromyscus polionotus during 10 generations of laboratory inbreeding by monitoring pairing success, litter size, viability, and growth in 3604 litters produced from 3058 pairs. In P. p. subgriseus, there was no reduction across generations in inbreeding depression in any of the fitness components. Strongly deleterious recessive alleles may have been removed previously during episodes of local inbreeding in the wild, and the residual genetic load in this population was not further reduced by selection in the lab. In P. p. rhoadsi, four of seven fitness components did show a reduction of the genetic load with continued inbreeding. The average reduction in the genetic load was as expected if inbreeding depression in this population is caused by highly deleterious recessive alleles that are efficiently removed by selection. For P. p. leucocephalus a population that experiences periodic bottlenecks in the wild, the effect of further inbreeding in the laboratory was to exacerbate rather than reduce the genetic load. Recessive deleterious alleles may have been removed from this population during repeated bottlenecks in the wild; the population may be close to a threshold level of heterozygosity below which fitness declines rapidly. Thus, the effects of selection on inbreeding depression varied substantially among populations, perhaps due to different histories of inbreeding and selection.     

General analysis of frequency-dependent sexual selection at a multi-allelic locus

A general model is analyzed in which arbitrarily frequency-dependent selection acts on one sex of a diploid population with several alleles at one locus, as a result of viability or mating-success differences. The existence of boundary and polymorphic equilibria is examined, and conditions for local stability, internal and external, are obtained. The status of Hardy-Weinberg approximations in studying stability and approach to equilibria is also considered. The general principles are then applied to two specific models: one where genotypes fall into two phenotypic classes; and one with a hierarchy of dominance where viability and sexual selection are opposed. In the latter case it is found that, of all the equilibria present, there is one and only one which could possibly be stable: the existence of a unique globally stable equilibrium might then be inferred.     

Evolution at a multiallelic locus under migration and uniform selection

The semilinear parabolic system that describes the evolution of the gene frequencies in the diffusion approximation for migration and selection at a multiallelic locus is investigated. The population occupies a finite habitat of arbitrary dimensionality and shape. The drift and diffusion coefficients may depend on position, but the selection coefficients do not. It is established that if p is a uniform equilibrium point under pure selection, then p is a migration-selection equilibrium, and that generically the introduction of migration does not change the stability of p. It is also proved that if p is a uniform, globally asymptotically stable, internal equilibrium point under pure selection, then the gene frequencies converge to p when both migration and selection are present. Thus, in this case, after a sufficiently long time, there is no genetic indication of the spatial distribution of the population.     

Examples of the effect of genetic variation on competing species

An ordinary differential equation model for two competing populations with genetic variation in one population is presented. The degree of frequency dependence needed to produce various configurations of stable equilibria is discussed. For example, if the fitnesses are frequency independent then there may exist stable polymorphism although the genetically varying population becomes extinct in each fixation plane. Stable polymorphism where the genetically invariant population becomes extinct in each fixation plane requires frequency dependence in the fitness of the genetically invariant population.