Enzyme Polymorphism and Cyclic Parthenogenesis in DAPHNIA MAGNA. II. Heterosis following Sexual Reproduction

Cyclical parthenogenesis exaggerates the force of selection relative to recombination and will therefore enhance interlocus effects. Observations of electrophoretic variation in a natural population of Daphnia magna Straus (Crustacea: Cladocera) are interpreted in this light. Sexual reproduction led to Hardy-Weinberg equilibrium, but heterozygote excesses rapidly developed at each of three observed loci during subsequent parthenogenesis. Homozygote fecundity was often lower than that of heterozygotes; this may have been the cause of some of the observed frequency changes. The superior fitness of the enzyme heterozygotes does not imply that selection was necessarily acting on the enzyme loci themselves, since apparent heterosis is the expected result of linkage disequilibrium.     

The significance of over- and underdominance for the maintenance of genetic polymorphisms. I. Underdominance and stability

It is pointed out that the standard selection models in population genetics all require some form of heterozygote advantage in fitness in order to guarantee the maintenance or stability of genetic polymorphisms. Even more recent results demonstrating the existence of stable two-locus polymorphisms with marginal underdominance at both loci are based on certain epistatically acting heterosis assumptions. This raises the question as to whether heterozygote advantage in fitness is indeed a generally valid principle of maintaining polymorphisms. To avoid ambiguity in definition of heterozygote advantage (overdominance) as it appears in multiallele or multilocus systems, a one-locus-two-allele model is considered. This model allows for sexually asymmetric selection and random mating. It is shown that the model produces globally stable polymorphisms exhibiting underdominance in fitness for a considerable and biologically reasonable range of selection values. Having thus properly refuted the general validity of the common overdominance principle, a modified version is suggested which covers the classical viability selection model and its extension to arbitrary, sexually asymmetric viability and fertility selection. This modified overdominance principle is based on the notion of fractional fitnesses and relates protectedness of biallelic polymorphisms to the extent to which each genotype reproduces its own type. The fact that the model treated displays frequency dependent fitnesses which may change in ranking while approaching equilibrium is discussed in relation to problems of the evolution of overdominance and underdominance.     

Son preference among Filipino Muslims: A causal analysis

Abstract

A social selection model for deleterious genes has been studied by considering two alleles at one locus. The model allows for the fitness of an individual to be determined by parental phenotypes as well as by his/her own phenotype. We show that the equilibrium gene frequency depends on the loss of fitness of an individual due to the trait (γ) and due to affected parents (P), and the probability that the heterozygote develops the trait (h). We show that whenever an interior equilibrium point exists for given values of γ and β, it is unique and that the sufficient condition for the existence of the equilibrium point is given by     

Preferential mating in symmetric multilocus systems: limits for multiallelism and for many Loci

Models in which general forms of preferential mating have been superimposed on the framework of the symmetric heterozygosity selection regime have been examined previously with respect to the existence and local stability of a central polymorphic equilibrium. The results are now extended to produce the limiting form of the stability conditions in two cases: First, where the number of alleles per locus is assumed to be very large; second, where the number of loci affecting the character is very large. It is argued that some type of frequency dependence in the mating pattern must be included, and a particular case is examined in detail. It is shown that multiallelism is ambiguous in its effect on stability, while an increasing number of loci, at least under zero linkage, leads to a simple stability condition which is analogous to the one-locus heterosis principle. Assortative mating appears to be more likely to produce a stable central polymorphism under high levels of allelism than is sexual selection, but is relatively very much weaker than sexual or viability selection if the number of loci involved is large.     

Frequency-Dependent Selection at the PGM-1 Locus of DROSOPHILA PSEUDOOBSCURA

Frequency-dependent fitness was studied at the Pgm-1 locus of Drosophila pseudoobscura with respect to two fitness components: rate of development and larva-to-adult survival. The Pgm-1 locus is very polymorphic with only two alleles, Pgm-1¹⁰⁰ and Pgm-1¹⁰⁴, occurring at high frequencies. For each of these two alleles, 20 homozygous strains were obtained from a sample of 1,140 wild-inseminated females. First-instar larvae of the two genotypes were combined in a set of eight different frequencies: 0.0, 0.10, 0.25, 0.40, 0.60, 0.75, 0.90, and 1.0. Frequency-dependent fitness effects were observed for the two survival-related fitness components examined: larvae of the less common genotype develop faster and have a higher probability of survival than larvae of the more common genotype. The rate of survival at intermediate genotypic frequencies is similar to that in pure cultures. If selection acted solely as frequency-dependent effects on survival-related components of fitness, the equilibrium frequency of the Pgm-1¹⁰⁰ allele would be 0.615 for a two-genotype system, which fits an observed frequency range for this allele in nature between 0.55 and 0.71. Experimentally created linkage disequilibrium was excluded from the experiment by using a large number of independent strains. It is nevertheless possible that the frequency-dependent selection may not affect the Pgm-1 locus per se, but may reflect a linkage disequilibrium present in the natural population. Even if this were the case, the frequency-dependent selection could affect the frequency of the Pgm-1 alleles in nature.     

An inclusive fitness analysis of synergistic interactions in structured populations

We study the evolution of a pair of competing behavioural alleles in a structured population when there are non-additive or ‘synergistic’ fitness effects. Under a form of weak selection and with a simple symmetry condition between a pair of competing alleles, Tarnita et al. provide a surprisingly simple condition for one allele to dominate the other. Their condition can be obtained from an analysis of a corresponding simpler model in which fitness effects are additive. Their result uses an average measure of selective advantage where the average is taken over the long-term—that is, over all possible allele frequencies—and this precludes consideration of any frequency dependence the allelic fitness might exhibit. However, in a considerable body of work with non-additive fitness effects—for example, hawk–dove and prisoner''s dilemma games—frequency dependence plays an essential role in the establishment of conditions for a stable allele-frequency equilibrium. Here, we present a frequency-dependent generalization of their result that provides an expression for allelic fitness at any given allele frequency p. We use an inclusive fitness approach and provide two examples for an infinite structured population. We illustrate our results with an analysis of the hawk–dove game.     

Analysis of Homothallic Saccharomyces cerevisiae Strain Mating during Must Fermentation

Genetic instability and genome renewal may cause loss of heterozygosity (LOH) in homothallic wine yeasts (Saccharomyces cerevisiae), leading to the elimination of the recessive lethal or deleterious alleles that decrease yeast fitness. LOH was not detected in genetically stable wine yeasts during must fermentation. However, after sporulation, the heterozygosity of the new yeast population decreased during must fermentation. The frequency of mating between just-germinated haploid cells from different tetrads was very low, and the mating of haploid cells from the same ascus was favored because of the physical proximity. Also, mating restriction between haploid cells from the same ascus was found, leading to a very low frequency of self spore clone mating. This mating restriction slowed down the LOH process of the yeast population, maintaining the heterozygote frequency higher than would be expected assuming a fully random mating of the haploid yeasts or according to the Mortimer genome renewal proposal. The observed LOH occurs because of the linkage of the locus MAT to the chromosome III centromere, without the necessity for self spore clone mating or the high frequency of gene conversion and rapid asymmetric LOH observed in genetically unstable yeasts. This phenomenon is enough in itself to explain the high level of homozygosis found in natural populations of wine yeasts. The LOH process for centromere-linked markers would be slower than that for the nonlinked markers, because the linkage decreases the frequency of newly originated heterozygous yeasts after each round of sporulation and mating. This phenomenon is interesting in yeast evolution and may cause important sudden phenotype changes in genetically stable wine yeasts.     

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.     

Dynamics of genetic rescue in inbred Drosophila melanogaster populations

Genetic rescue has been proposed as a management strategy to improve the fitness of genetically eroded populations by alleviating inbreeding depression. We studied the dynamics of genetic rescue in inbred populations of Drosophila. Using balancer chromosomes, we show that the force of heterosis that accompanies genetic rescue is large and allows even a recessive lethal to increase substantially in frequency in the rescued populations, particularly at stress temperatures. This indicates that deleterious alleles present in the immigrants can increase significantly in frequency in the recipient population when they are in linkage disequilibrium with genes responsible for the heterosis. In a second experiment we rescued eight inbred Drosophila populations with immigrants from two other inbred populations and observe: (i) there is a significant increase in viability both 5 and 10 generations after the rescue event, showing that the increase in fitness is not transient but persists long-term. (ii) The lower the fitness of the recipient population the larger the fitness increase. (iii) The increase in fitness depends significantly on the origin of the rescuers. The immigrants used were fixed for a conditional lethal that was mildly deleterious at 25°C but lethal at 29°C. By comparing fitness at 25°C (the temperature during the rescue experiment) and 29°C, we show that the lethal allele reached significant frequencies in most rescued populations, which upon renewed inbreeding became fixed in part of the inbred lines. In conclusion, in addition to the fitness increase genetic rescue can easily result in a substantial increase in the frequency of mildly deleterious alleles carried by the immigrants. This can endanger the rescued population greatly when it undergoes recurrent inbreeding. However, using a sufficient number of immigrants and to accompany the rescue event with the right demographic measures will overcome this problem. As such, genetic rescue still is a viable option to manage genetically eroded populations.     

Stable Equilibria at Two Loci in Populations with Large Selfing Rates

The equilibrium structure of two-locus, two-allele models with very large selfing rates is found using perturbation techniques. For free recombination, r = 1/2, the following results hold. If the heterozygotes do not have at least an approximate 30% advantage in fitness relative to homozygotes, a stable equilibrium with all alleles present is possible only if all of the homozygote fitnesses differ at most by approximately the outcrossing rate, t, and all stable polymorphic equilibria have disequilibrium values, D, that are at most on the order of the outcrossing rate. Once the heterozygote fitnesses are above the threshold, there are stable equilibria possible with D near its maximum possible value. The results show that the observed disequilibria in highly selfed plant populations are not likely to result from selection leading to an equilibrium.     

Loss of genetic variation in declining populations of Aricia artaxerxes in Northern Hungary

Rapid decline of population size often gives rise to loss of genetic variation and may result in a reduction in fitness. It is, therefore, essential to detect past demographic changes in populations of endangered species. Aricia artaxerxes occurs in two regions of Northern Hungary: Bükk Mts. and the Aggtelek Karst region. The species prefers short-grass habitats, which are subject to succession. Due to climatic differences between the two regions succession is more rapid in the Bükk plateau resulting in the decline and isolation of A. artaxerxes populations there. In contrast, most populations have remained rather large and stable in the Karst region. This situation provides an excellent possibility to compare the genetic composition of stable and declining populations. A. artaxerxes was collected in four populations of the Bükk Mountains and in ten in the Aggtelek Karst region in 2002 and 2005. We analysed 19 polymorphic allozyme loci in all samples. The results revealed an extremely high level of enzyme polymorphism in A. artaxerxes. Most parameters of polymorphism proved to be significantly higher in the Karst region compared to the Bükk. The shape of the distribution of alleles among the frequency classes indicated the effect of bottleneck in three Bükk and one Karst population. Though heterozygote excess was only significant in one Bükk population a tendency was observed for higher values of standardised heterozygote excess in those populations that had a typical bottleneck distribution of alleles. Our results clearly demonstrated that those populations/subpopulations that compose a network with intense migration are able to maintain their genetic diversity in a long run, while the isolated small populations of the Bükk plateau have lost a sizeable part of their variation.     

A criterion for the establishment of a stable polymorphism of higher order with an application to the evolution of polymorphism

This note gives some further useful properties of the constant fitness selection model for multiple alleles which pertain to the effects of adding a new allele to n preexisting alleles in stable equilibrium. In particular the conditions are derived for the establishment of a stable equilibrium involving all n + 1 alleles. For 3 alleles (i.e. n = 2) I give a complete qualitative solution, including the case of the replacement of one diallelic polymorphism by another. As an application I discuss a possible mechanism for the evolution of polymorphism using Monte Carlo methods similar to Lewontin, Ginzburg and Tuljapurkar (1978).     

Heterosis or Neutrality?

Various statistics have been proposed on an ad hoc basis to test whether alleles at a locus are selectively neutral. By considering population models in which selection operates, this paper shows that the population homozygosity is a powerful test statistic for testing departures from neutrality, in the direction of heterozygote advantage or disadvantage. The sample homozygosity plays a similar role when only sample data are available. Some numerical examples are included, showing the application of the test.—An analysis is made of the effect of heterosis on such quantities as the expected number of alleles in the population or sample, the effective number of alleles, the expected homozygosity, and on the population and sample allele frequency distributions generally.     

Single-locus polymorphism in a heterogeneous two-deme model

Environmental heterogeneity has long been considered a likely explanation for the high levels of genetic variation found in most natural populations: selection in a spatially heterogeneous environment can maintain more variation. While this theoretical result has been extensively studied in models with limited parameters (e.g., two alleles, fixed gene flow, and particular selection schemes), the effect of spatial heterogeneity is poorly understood for models with a wider range of parameters (e.g., multiple alleles, different levels of gene flow, and more general selection schemes). We have compared the volume of fitness space that maintains variation in a single-deme model to the volume in a two-deme model for multiple alleles, random selection schemes, and various levels of migration. Furthermore, equilibrium allele-frequency vectors were examined to see if particular patterns of variation are more prevalent than first expected. The two-deme model maintains variation for substantially larger volumes of fitness space with lower heterozygote fitness than the single-deme model. This result implies that selection schemes in the two-deme model can have a wider range of fitness patterns while still maintaining variation. The equilibrium allele-frequency patterns emerging from the two-deme model are more variable and strongly influenced by gene flow.     

Density- and Frequency-Dependent Selection at the Mdh-2 Locus in DROSOPHILA PSEUDOOBSCURA

We have studied differences in the number of Drosophila pseudoobscura produced in a culture when the flies differ with respect to two alleles (F and S) at the Mdh-2 locus, which codes for a malate dehydrogenase enzyme. The studies were done at low and at high density in two- and three-genotype combinations (S/S, F/F and S/F), with one-genotype cultures as controls.——Density affects the fitness of the Mdh-2 genotypes. Different genotypes are differently affected, and the genotype of the competitors also makes a difference on the fitness of a given genotype. When three genotypes are present in a culture, particularly at high density, intergenotypic competition is less intense than intragenotypic competition at several frequency combinations. That is, there is "overcompensation": the three genotypes together exploit the environmental resources better than one genotype alone.—The fitness of the genotypes is frequency dependent in both two-genotype and three-genotype combinations. An inverse relationship between frequency and fitness is observed at high density. This may lead to a stable polymorphism, because the fitness of a genotype increases as its frequency decreases.—Forty independent strains, sampled from a natural population, were used in the experiments. This ensures that more than 95% of the variation present in the genome in the natural population is also present is the experimental cultures. It also ensures that the genetic background of the Mdh-2 alleles is randomized in the same way as it is in nature. However, the possibility remains that Mdh-2 alleles in nature are nonrandomly associated with alleles at closely linked loci. If linkage disequilibrium is present in the experiments because it exists in nature, then the observed effects (such as frequency-dependent selection) would affect the Mdh-2 locus in nature as well.     

Adaptive nature of chromosomal rearrangement: differential fitness in pocket gophers

A chromosomal centric fusion polymorphism in populations of the plains pocket gopher, Geomys bursarius, was studied to determine the relative fitness associated with the karyotypic phenotypes. There was a greater number of heterozygous individuals than expected χ₁ ²=8.58, P=0.001. Calculations indicate that the viabilities of the two chromosomal homozygotes were only 35 and 76 percent or that of the heterozygote. Differences in fitness values for the chromosomal morphs for Geomys strongly emphasize the possible adaptive nature of the karyotype and provides a primary mechanism for chromosomal evolution, even in species composed of demes of relatively large size. This is the first case of positive chromosomal heterosis in vertebrates. The plains pocket gopher can now be added to the few empirically documented samples of balanced polymorphism.     

Heterosis increases the effective migration rate

Individuals coming from the same subpopulation are more likely to share deleterious mutations at any given locus than hybrids formed between parents from different populations. Offspring of migrants therefore may experience heterosis and have higher fitness than resident individuals. This will, in turn, result in the immigrant alleles being present in higher frequencies than predicted from neutral expectations and thus a higher effective migration rate. In this paper we derive a formula to calculate the effective migration rate in the presence of heterosis. It is shown that the effect of heterosis on the migration rate can be substantial when fitness reduction within local populations is severe. The effect will be more pronounced in species with relatively short map lengths. Furthermore the heterosis effect will be highly variable throughout the genome, with the largest effect seen near selected genes and in regions of high gene density.     

Adaptation at Specific Loci. I. Natural Selection on Phosphoglucose Isomerase of Colias Butterflies: Biochemical and Population Aspects

Electrophoretic variants of phosphoglucose isomerase (PGI) in Colias butterflies have been studied from field and laboratory viewpoints. The transmission pattern is that of a dimeric enzyme controlled by one structural gene locus. Populations usually harbor four to six allelic mobility classes. These mobility classes are shared among species complexes, though their frequencies differ widely. Preliminary Ferguson plot analysis of the variants has been carried out. Purified preparations of Colias PGI alleles are more effective in standardizing Ferguson plots than heterologous proteins, such as ferritin. Variation of Ferguson plot parameters is not an infallible guide to electrophoretically "cryptic alleles," as one putative case proved to be due to nonallele-specific effects. S, M, and F mobility classes in two Colias semispecies show the same retardation coefficients in Ferguson plots. Adults early in the flight periods of their nonoverlapping generations show genotype frequencies in Hardy-Weinberg equilibrium, but heterozygote excess develops as the insects age. Simple directional selection and large-scale population mixing are unlikely to be causes of this, although several other selection modes remain possible. Identical-by-descent lines of the four frequent-to-common alleles in C. eurytheme have been set up in culture, and enzyme has been purified from these for study of functional properties. Major differenecs in heat stability and in various kinetic parameters are found among the ten possible genotypes. In some cases, heterosis for kinetic parameters is seen; in other cases, opposing trends in kinetic function and heat stability create potential for net heterosis in function. Possible interpretations of these results in an adaptive metabolic context are discussed, and directions for further work are stated.     

The multiple-locus symmetric fertility model

Selection due to variation in the fecundity among matings of genotypes with respect to many loci each with two alleles is studied. The fitness of a mating depends only on the genotypic distinction between homozygote and heterozygote at each locus in the two individuals, and differences among loci are allowed. This symmetric fertility model is therefore a generalization of the multiple-locus symmetric viability model. The phenomena seen in the two-locus symmetric fertility model generalize—e.g., the possibility of joint stability of equilibria with linkage equilibrium and with linkage disequilibrium, and the existence of different types of totally polymorphic equilibria with the gametic proportions in linkage equilibrium. The central equilibrium with genotypic frequencies in Hardy-Weinberg proportions and gametic frequencies in Robbins proportions exists for all symmetric fertility models. For some symmetric fertility regimes additional equilibria exist with gametic frequencies in linkage equilibrium and with genotypic frequencies in Hardy-Weinberg proportions at all except one locus. These equilibria may exist in the dioecious symmetric viability model, and then they will be locally stable. For free recombination the stable equilibria show linkage equilibrium, but several of these with different numbers of polymorphic loci may be stable simultaneously.     

The Effects of Overdominance on Linkage in a Multilocus System

Computer simulations were performed with overdominant multiple alleles among tightly linked multiple loci under a multiplicative fitness model. The quantity X²/N(n — 1) was introduced as a new measure of linkage disequilibrium which, unlike previously available measures, can be applied to multiple allele models, where N is the sample size, and n is the number of alleles at the locus possessing fewest alleles. Simulations showed that (1) With multiple (three or four) alleles, the approach to stable disequilibrium is slower and the amount of disequilibrium established is weaker than in a two allele system. (2) The number of complementary chromosomes is a function of number of alleles and of population size. (3) As population size increases, the rate of the approach to stable disequilibrium is slower. (4) There is an optimum selection coefficient which minimizes the transient fixation probability of alleles when linkage is present. (5) The absence of linkage disequilibrium is in most cases not a practical method of testing the hypothesis of balancing selection of genetic polymorphisms because it depends strongly on population size in determining linkage disequilibria.