THE EFFECTS OF SELECTION IN THE GAMETOPHYTE STAGE ON MUTATIONAL LOAD

We have studied a multilocus selection model of a plant population in which mutations to deleterious alleles occur that may affect not only the diploid sporophyte stage, but also the haploid pollen stage before zygote formation. We investigated the reduction in inbreeding depression (as measured in the sporophyte) caused by the lowering of mutant allele frequencies due to selection in the pollen. This is important for a full understanding of the role of inbreeding depression in the maintenance of outcrossing in seed plants. We also studied the theoretically expected relationship between the pollen fitnesses of different pollen donor genotypes and the fitnesses of the diploid progeny that they sire. This relationship can be compared with the results of experiments in which pollen was subjected to selection, and improved progeny quality was observed. We found that on the mutational load model there is, as expected intuitively, a positive covariance between the pollen and zygote fitnesses, but that it is likely to be small. Subjecting pollen to an episode of strong selection is usually expected to increase sporophyte fitness only slightly.     

Selfishness and altruism can coexist when help is subject to diminishing returns

Altruism and selfishness are 30-50% heritable in man in both Western and non-Western populations. This genetically based variation in altruism and selfishness requires explanation. In non-human animals, altruism is generally directed towards relatives, and satisfies the condition known as Hamilton's rule. This nepotistic altruism evolves under natural selection only if the ratio of the benefit of receiving help to the cost of giving it exceeds a value that depends on the relatedness of the individuals involved. Standard analyses assume that the benefit provided by each individual is the same but it is plausible in some cases that as more individuals contribute, help is subject to diminishing returns. We analyse this situation using a single-locus two-allele model of selection in a diploid population with the altruistic allele dominant to the selfish allele. The analysis requires calculation of the relationship between the fitnesses of the genotypes and the frequencies of the genes. The fitnesses vary not only with the genotype of the individual but also with the distribution of phenotypes amongst the sibs of the individual and this depends on the genotypes of his parents. These calculations are not possible by direct fitness or ESS methods but are possible using population genetics. Our analysis shows that diminishing returns change the operation of natural selection and the outcome can now be a stable equilibrium between altruistic and selfish alleles rather than the elimination of one allele or the other. We thus provide a plausible genetic model of kin selection that leads to the stable coexistence in the same population of both altruistic and selfish individuals. This may explain reported genetic variation in altruism in man.     

Demography of source—sink populations and the evolution of ecological niches

Summary The demography of populations living in variable environments is an important factor molding the evolution of ecological niches, for it determines the relative strength of selection pressures on adaptations to different habitats. Here I consider a coarse-grained environment consisting of two habitat types and investigate how the selection pressure on reproductive success in different habitats depends on their quality and frequency and the dispersal pattern. The results suggest that selection on adaptations to optimal habitats will usually be stronger than on adaptations to poor habitats and the ecological niche will thus tend to be an evolutionarily conservative character. It is because under the habitat choice or limited dispersal that seem to prevail in natural populations, more individuals encounter the better habitat than would be expected solely on the basis of its relative area. This bias results in reduced selection pressure on reproductive success in the poorer habitat. With habitat choice or limited dispersal, selection pressure on reproductive success in the poorer habitat may exceed that on reproductive success in the better habitat only if the poorer habitat is much more frequent in the environment than the better habitat and the difference in their quality is not large.     

Stochastic selection in large and small populations

We describe two models of stochastic variation in selection intensity. In both models the arithmetic mean fitness of all genotypes is equal; in both models the geometric mean fitness of the heterozygous genotype is greater than that of both homozygous genotypes. In one model the correlation between the fitnesses of the homozygous genotypes is +1; in the other it is −1. We show that the expected time to absorption of an allele in a finite population is significantly retarded for all initial gene frequencies in the former model. The expected time to absorption of an allele in the latter model is retarded only at extreme initial gene frequencies; at intermediate initial gene frequencies the expected time to absorption is accelerated. We conclude that the criterion for polymorphism based on the geometric mean of the heterozygote being greater than that of both homozygotes provides only limited information about the fate of gene frequency.     

Frequency and fitness cost of resistance to Bacillus thuringiensis in Chrysomela tremulae (Coleoptera: Chrysomelidae)

The "high dose-refuge" (HDR) strategy is commonly recommended and currently used for delaying or preventing pest adaptation to transgenic plants producing Bacillus thuringiensis (Bt) toxins. The efficiency of this strategy depends, among other factors, on the initial frequency of Bt resistance alleles and on the fitness costs associated with these alleles. Two years ago, an allele conferring resistance to Bt poplar was detected in a French population of the poplar pest Chrysomela tremulae F. Although this pest had never been subjected to Bt selection pressure due to human activities, the frequency of this allele was estimated at 0.0037, with a 95% credible (CI) interval of 0.00045-0.0080. We investigated the frequency of this allele in a second sample of C. tremulae collected more than 500 km from the site of the initial population. The estimated frequency in this sample was 0.0113 (95% CI 0.0031-0.0247), reinforcing the conclusion that resistance to Bt plants may be present at detectable frequencies in pest populations before selection resulting from pest management by humans. The frequency of the Bt resistance allele over the two samples was 0.0049 (95% CI 0.0020-0.0091). We also followed five laboratory lines in which the frequency of this allele was initially fixed at 0.500. After five generations maintained on non-Bt poplar leaves, the frequency of this allele decreased in all lines, whereas allelic frequencies at a neutral locus were unaffected. Thus, the Bt resistance allele detected in French populations of C. tremulae is probably associated with a fitness cost.     

A macroscopic approach to population genetics

Conventional population genetics uses as primitive variables the frequencies and fitnesses of individual genes. This paper develops a formalism whose primitive variables are the frequencies and fitnesses of genotypes and environmental histories in a population. From the mathematical relation that describes genetic variation and selection of genotypes and environmental histories we derive a sequence of more specialized equations, including those of the conventional theory. Some familiar formulas of the conventional theory (including Fisher's fundamental theorem, the formula relating the rate of change of a metric character to selection pressure, and the definitions of broad and narrow heritability) are shown to be special cases of simpler and more general formulas. It is shown that the “genotypic value” of a trait, together with its heritability, may depend strongly on genotype-environment correlations.A generalization of Fisher's fundamental theorem shows that the rate of evolution of a trait depends on the skewness of its fitness distribution. An equation relating the second derivative of the mean fitness to the skewness is derived.Finally, the formalism is applied in a preliminary way to a recent theory of genetic variation (Layzer,1978a), according to which the genetic variability of a trait is selected along with the trait itself. It is shown that there is positive feedback between the two kinds of selection.     

The Maintenance of Single-Locus Polymorphism. IV. Models with Mutation from Existing Alleles

The ability of viability selection to maintain allelic polymorphism is investigated using a constructionist approach. In extensions to the models we have previously proposed, a population is bombarded with a series of mutations whose fitnesses in conjunction with other alleles are functions of the corresponding fitnesses with a particular allele, the parent allele, already in the population. Allele frequencies are iterated simultaneously, thus allowing alleles to be driven to extinction by selection. Such models allow very high levels of polymorphism to evolve: up to 38 alleles in one case. Alleles that are lethal as homozygotes can evolve to surprisingly high frequencies. The joint evolution of allele frequencies and viabilities highlights the necessity to consider more than the current morphology of a population. Comparisons are made with the neutral theory of evolution and it is suggested that failure to reject neutrality using the Ewens-Watterson test cannot be regarded as evidence for the neutral theory.     

Climate‐driven habitat change causes evolution in Threespine Stickleback

Climate change can shape evolution directly by altering abiotic conditions or indirectly by modifying habitats, yet few studies have investigated the effects of climate‐driven habitat change on contemporary evolution. We resampled populations of Threespine Stickleback (Gasterosteus aculeatus) along a latitudinal gradient in California bar‐built estuaries to examine their evolution in response to changing climate and habitat. We took advantage of the strong association between stickleback lateral plate phenotypes and Ectodysplasin A (Eda) genotypes to infer changes in allele frequencies over time. Our results show that over time the frequency of low‐plated alleles has generally increased and heterozygosity has decreased. Latitudinal patterns in stickleback plate phenotypes suggest that evolution at Eda is a response to climate‐driven habitat transformation rather than a direct consequence of climate. As climate change has reduced precipitation and increased temperature and drought, bar‐built estuaries have transitioned from lotic (flowing‐water) to lentic (still‐water) habitats, where the low‐plated allele is favoured. The low‐plated allele has achieved fixation at the driest, hottest southernmost sites, a trend that is progressing northward with climate change. Climate‐driven habitat change is therefore causing a reduction in genetic variation that may hinder future adaptation for populations facing multiple threats.     

The ecology and genetics of fitness in Chlamydomonas. X. The relationship between genetic correlation and genetic distance

Abstract.— A necessary condition for the maintenance of genetic variation in heterogenous environments is that the relative fitnesses of a collection of genotypes vary as conditions of growth change. This can be detected by estimating the amount of gene-by-environment interaction (G X E) when a range of types are tested across a range of conditions. However it is the sign and magnitude of the genetic correlation, which is a component of G X E, that governs the ultimate fate of variation. Whether genetic variation will be preserved, then, depends on how the genetic correlation changes as a function of the ecological differences among environments and the genetic differences among genotypes. To evaluate this, we assayed the performance of 15 chlorophyte species of known genetic relation in 20 environments. We found that the quantity of G X E increased as both the environmental variance across environments and the genetic distance increased. Moreover the genetic correlation declined as the environmental variance between pairs of environments and the genetic distance between pairs of genotypes increased. These results suggest that divergent selection will be more likely to maintain genetic variation when environments are strongly contrasted and genotypes widely divergent.     

PHYSIOLOGICAL AND BEHAVIORAL ADAPTATION TO VARYING ENVIRONMENTS: A MATHEMATICAL MODEL

We develop a mathematical model to explore the evolution of habitat selection and physiological adaptation in a heterogeneous environment. The model assumes the following conditions: 1) a panmictic population of infinite size; 2) prereproductive individuals mobile enough to move between patches; 3) alleles at one locus code for absence or presence of adaptation to detrimental patches; 4) alleles at a second locus code for absence or presence of behavior(s) that cause avoidance of the detrimental patches; 5) additive effects of alleles controlling physiology and behavior; 6) frequency-independent fitness. Results of the model indicate that nontrivial, polymorphic equilibria do not exist. The pattern of genotypic fitnesses and the initial allelic frequencies can influence whether the population adapts by physiological or behavioral mechanisms, or by both. Linkage between the two loci can alter the outcome of evolution, given specified genotypic fitness values and initial allelic frequencies.     

Estimation of relative fitnesses from relative risk data and the predicted future of haemoglobin alleles S and C

Epidemiological studies of genetic differences in disease susceptibility often estimate the relative risks (RR) of different genotypes. Here I provide an approach to calculate the relative fitnesses of different genotypes based on RR data so that population genetic approaches may be utilized with these data. Using recent RR data on human haemoglobin beta genotypes from Burkina Faso, this approach is used to predict changes in the frequency of the haemoglobin sickle-cell S and C alleles. Overall, it generally appears that allele C will quickly replace the S allele in malarial environments. Explicit population genetic predictions suggest that this replacement may occur within the next 50 generations in Burkina Faso.     

Coevolutionary clines across selection mosaics

Abstract. Much of the dynamics of coevolution may be driven by the interplay between geographic variation in reciprocal selection (selection mosaics) and the homogenizing action of gene flow. We develop a genetic model of geographically structured coevolution in which gene flow links coevolving communities that may differ in both the direction and magnitude of reciprocal selection. The results show that geographically structured coevolution may lead to allele-frequency clines within both interacting species when fitnesses are spatially uniform or spatially heterogeneous. Furthermore, the results show that the behavior and shape of clines differ dramatically among different types of coevolutionary interaction. Antagonistic interactions produce dynamic clines that change shape rapidly through time, producing shifting patterns of local adaptation and maladaptation. Unlike antagonistic interactions, mutualisms generate stable equilibrium patterns that lead to fixed spatial patterns of adaptation. Interactions that vary between mutualism and antagonism produce both equilibrium and dynamic clines. Furthermore, the results demonstrate that these interactions may allow mutualisms to persist throughout the geographic range of an interaction, despite pockets of locally antagonistic selection. In all cases, the coevolved spatial patterns of allele frequencies are sensitive to the relative contributions of gene flow, selection, and overall habitat size, indicating that the appropriate scale for studies of geographically structured coevolution depends on the relative contributions of each of these factors.     

Population dynamics of the additive polygenic system under truncation selection]

Common features of the equations describing dynamics of the additive polygenic system under truncation selection are summarized. A combination of parameters playing the role of the effective selective pressure on the ith polygenic locus was revealed. The product of mean relative fitnesses of the individual polygenic loci, [formula: see text], was shown to play the role of relative mean fitness of the polygenic population. This value depends on the measurable parameters of the character distribution in the population: [formula: see text]. It was shown that under the constant population number during truncation selection, the characteristic of the best genotype increases, [formula: see text]; which is also a product of the frequencies of preferable genotypes at individual polygenic loci. This value plays the role of the proportion of the number of the best ("champion") genotype in the population. In fact, this is the champion genotype polygene consensus pattern frequency, which a priori indicates the possibility of the champion pattern fixation. The analogue of Haldane's dilemma for the polygenic system which restrict the number of polygenes simultaneously subjected to adaptive evolution [formula: see text] was obtained for the case of constant effective population number (Ne = const).     

Urban noise and the cultural evolution of bird songs

In urban environments, anthropogenic noise can interfere with animal communication. Here we study the influence of urban noise on the cultural evolution of bird songs. We studied three adjacent dialects of white-crowned sparrow songs over a 30-year time span. Urban noise, which is louder at low frequencies, increased during our study period and therefore should have created a selection pressure for songs with higher frequencies. We found that the minimum frequency of songs increased both within and between dialects during the 30-year time span. For example, the dialect with the highest minimum frequency is in the process of replacing another dialect that has lower frequency songs. Songs with the highest minimum frequency were favoured in this environment and should have the most effective transmission properties. We suggest that one mechanism that influences how dialects, and cultural traits in general, are selected and transmitted from one generation to the next is the dialect''s ability to be effectively communicated in the local environment.     

A Monte Carlo simulation model for studying evolution in age-structured populations

This model provides for any number of genotypes defined by age-specific survival and fecundity rates in a population with completely overlapping generations and growing under the control of density-governing functions affecting survival or fecundity. It is tested in situations involving two alleles at one locus. Nonselection populations at Hardy–Weinberg equilibrium obey the ecogenetic law; i.e., each genotype follows Lotka's law regarding rate of increase and stable age distribution as if it were an independent true-breeding population. Populations experiencing age- and density-independent selection approximate this situation, and the changes in gene frequency are predicted by relative fitnesses bases on λ, the finite rate of increase of the genotypes. Polymorphic gene equilibria occurring at steady-state population sizes are determined by fitnesses based on R, the net reproductive rate. In examples involving differences in generation time produced by age-dependent differences in fecundity, the allele associated with longer generation time may be favored or opposed by selection, depending on whether the density-governing factor controlling population size affects survival or fecundity. If such genotypes have similar R's, a genetic equilibrium may be established if the population is governed by a density function acting upon fecundity. Received: August 23, 1999 / Accepted: July 13, 2000     

Temporally varying selection on multiple alleles: A diffusion analysis

A generalization of Gillespie's SAS-CFF model for natural selection acting on multiple alleles in a randomly fluctuating environment is presented that relaxes symmetry assumptions concerning the variances and covariances of allelic effects. The stationary density for a multidimensional diffusion approximation of the model is obtained and provides approximate necessary and sufficient conditions for the existence of stable polymorphisms. These conditions have exactly the same form as those derived by Kimura and Mandel for polymorphism under multiple allele selection in a constant environment, except that the time-invariant fitnesses are replaced by the approximate geometric mean fitnesses of the genotypes over time. An example illustrates that this simple relationship between random environment and constant environment conditions for polymorphism does not hold for more general selection schemes. The implications of these results for the maintenance of multiple alleles by balancing selection are discussed.     

Growth form evolution and shifting habitat specialization in annual plants

Optimal plant growth form should vary across environments. We examined the potential for mutations causing large changes in growth form to produce new optimal phenotypes across light environments. We predicted that the upright growth form would be favoured in a light limiting environment as leaves were in a position to maximize light interception, while a rosette (leaves in a basal position) growth form would be favoured in a high light environment. Growth form genotypes of Brassica rapa (upright wild-type and rosette mutants) and Arabidopsis thaliana (large rosette wild-type and increasingly upright growth form mutants) were grown in a greenhouse in control (ambient) and filtered (low) light treatments. Compared to upright genotypes, rosette genotypes had relatively high fitness in control light but had a relatively large fitness reduction in filtered light. Our results demonstrate the potential importance of rapid growth form evolution in plant adaptation to new or changing environments.     

Escaping an evolutionary lobster trap: drug resistance and compensatory mutation in a fluctuating environment

The fitness landscape concept aids intuition on adaptive evolution through low fitness genotypes. Evolutionary processes become complex when environments and therefore fitnesses fluctuate. Antibiotic resistance evolution in bacteria is an important example of such dynamics. Resistance bears a cost in the drug-free environment, but compensatory mutation can lower this cost, creating a fitness valley. With the drug present, the valley becomes a hill that is easily climbed. Once a population is dominated by resistant-compensated genotypes, reversion to sensitivity is difficult: this phenomenon has been described as an evolutionary lobster trap. With increasing frequencies of drug resistance among pathogenic bacteria, it is critical to understand how this trap can be escaped. Here, we develop stochastic models to investigate these dynamics. The residual fitness cost (the cost remaining after compensatory mutation has occurred) is a key parameter. Reversion to sensitivity is favored when the time spent in the absence of the drug relative to its presence is high compared to the residual fitness cost. Population sizes are also important: in large populations, resistant-compensated mutants appear in resistant-uncompensated or sensitive-compensated genotypes without fixation of these intermediates. This stochastic tunneling effect occurs when sufficient time is allowed by the rates of environmental fluctuation.     

Nuclear–mitochondrial epistasis: a gene's eye view of genomic conflict

We use population genetic models to investigate the cooperative and conflicting synergistic fitness effects between genes from the nucleus and the mitochondrion. By varying fitness parameters, we examine the scope for conflict relative to cooperation among genomes and the utility of the “gene's eye view” analytical approach, which is based on the marginal average fitness of specific alleles. Because sexual conflict can maintain polymorphism of mitochondrial haplotypes, we can explore two types of evolutionary conflict (genomic and sexual) with one epistatic model. We find that the nuclear genetic architecture (autosomal, X‐linked, or Z‐linked) and the mating system change the regions of parameter space corresponding to the evolution by sexual and genomic conflict. For all models, regardless of conflict or cooperation, we find that population mean fitness increases monotonically as evolution proceeds. Moreover, we find that the process of gene frequency change with positive, synergistic fitnesses is self‐accelerating, as the success of an allele in one genome or in one sex increases the frequency of the interacting allele upon which its success depends. This results in runaway evolutionary dynamics caused by the positive intergenomic associations generated by selection. An inbreeding mating system tends to further accelerate these runaway dynamics because it maintains favorable host–symbiont or male–female gene combinations. In contrast, where conflict predominates, the success of an allele in one genome or in one sex diminishes the frequency of the corresponding allele in the other, resulting in considerably slower evolutionary dynamics. The rate of change of mean fitness is also much faster with positive, synergistic fitnesses and much slower where conflict is predominant. Consequently, selection rapidly fixes cooperative gene combinations, while leaving behind a slowing evolving residue of conflicting gene combinations at mutation–selection balance. We discuss how an emphasis on marginal fitness averages may obscure the interdependence of allelic fitness across genomes, making the evolutionary trajectories appear independent of one another when they are not.     

Simulating the impact of cross resistance between Bt toxins in transformed clover and apples in New Zealand

Simulation were conducted to guide development of resistance management strategies aimed at prolonging the usable life of B. thuringiensis (Bt) endotoxins in multiple cropping situations, where different crops expressing Bt endotoxins are host plants for a common pest. We used the New Zealand apple and clover model ecosystem to explore the relative impact on the rate of resistance development of varying levels of cross-resistance between different toxins expressed in these 2 potentially Bt-transformed crops. These 2 crops are hosts for a complex of leaf-rollers in New Zealand, including the light-brown apple moth, used here as the model pest. Cross-resistance was varied between 0.0 and 0.5 (zero to partial cross-resistance) to allow for the case in which selection by one plant has a potential effect on resistance to the toxin in another plant. The largest factor affecting the evolution of resistance was the total habitat area occupied by transgenic orchards. The proportion of the clover habitat that was transformed was also an important factor, even in the absence of cross-resistance. The effect of increasing the proportion of the second transformed crop (clover) acted on resistance evolution mainly by reducing the external refuge of susceptibility for the transgenic orchards. Hence, the ecological implications of reducing the available source of susceptible insects from clover, which can help to slow resistance development in the orchard ecosystem, had a more significant impact than the presence of cross-resistance. Partial cross-resistance between different toxins in the separate crops was overall of relatively minor importance. These simulations have implications for deployment decisions for individual transformed crops in multiple cropping systems, where there is the potential for the crops to serve as refugees for each other. These decisions may need to focus less on cross-resistance between toxins, than on economic trade-offs between the relative roles of individual crops as refugia maintaining susceptibility in the system as a whole.