The effect of the reproductive system on mutation load

J. B. S. Haldane (Amer. Nat. 71, 337–349, 1937) argued that, in equilibrium populations, the effect of deleterious mutation on average fitness depends primarily on the mutation rate and is independent of the severity of the mutations. Specifically, the equilibrium population fitness is e^−μH, where μ_H is the haploid genomic mutation rate. Here we extend Haldane's result to a variety of reproductive systems. Using an analysis based on the frequency of classes of individuals with a specified number of mutations, we show that Haldane's principle holds exactly for haploid sex, haploid apomixis, and facultative haploid sex. In the cases of diploid automixis with terminal fusion, diploid automixis with central fusion, and diploid selfing, Haldane's principle holds exactly for recessive mutations and approximately for mutations with some heterozygous effect. In the cases of K-ploid apomixis, diploid endomitosis, and haplodiploidy, we show that Haldane's principle holds exactly for recessive lethal mutations. In addition we extend Haldane's result to various mixtures of the above-mentioned reproductive systems. In the case of diploid out-crossing sexuals, we do not obtain an exact analytic result, but present arguments and computer simulations which show that Haldane's result extends to this case as well in the limit as the number of loci becomes large. Although diverse reproductive systems are equally fit at equilibrium, different reproductive systems harbor vastly different numbers of recessive genes at equilibrium and we provide estimates of these numbers. These different numbers of mutations may create transient selective pressures on individuals with reproductive systems different from that of the equilibrium population.     

THE EVOLUTION OF COSTLY MATE PREFERENCES I. FISHER AND BIASED MUTATION

Fisher's runaway process is the standard explanation of the evolution of exaggerated female preferences. But mathematical formulations of Fisher's process (haploid and additive diploid) show it cannot cause stable exaggeration if female preference carries a cost. At equilibrium female fitness must be maximized. Our analysis shows that evolutionary stable exaggeration of female preference can be achieved if mutation pressure on the male character is biased, that is, mutation has a directional effect. At this equilibrium female fitness is not maximized. We discuss the reasons and evidence for believing that mutation pressure is typically biased. Our analysis highlights the previously unacknowledged importance of biased mutation for sexual selection.     

On the interaction between stabilizing social factors and destabilizing trophic factors in small rodent populations

Mathematical models are developed in order to analyze whether or not social factors, such as, for example, the “social fence” (J. B. Hestbeck, 1982, Oikos 39, 157–163) will stabilize population density: the dynamic interaction between social factors and (dynamic) trophic factors is analyzed. It is concluded that social factors such as the “social fence” tend to stabilize population density; hence, if density cycles (as, e.g., seen in many microtine rodents) are observed in nature, it seems reasonable to conclude that density cycles are driven by, for example, trophic interactions and not by social factors. It is suggested that the “social fence” may explain why so many populations including several microtine populations have fairly stable densities despite the ever-existing destabilizing trophic interactions. Contrary to what is implied by J. B. Hestbeck (1983, “A Mathematical Model of Population Regulation in Cyclic Mammals,” Lecture notes in biomathematics, Vol. 52, Springer-Verlag, Berlin/New York), the analysis presented in this paper demonstrates that seasonal environmental changes are not essential for the generation of regular density cycles. Seasonal changes may, however, be necessary for generating a microtine-like density cycle. Empirical information on microtine rodents relating to the “social fence hypothesis” is discussed.     

The robustness of neutral models of geographical variation

The approximation of diploid migration by gametic dispersion is studied. The monoecious, diploid population is subdivided into panmictic colonies that exchange migrants. Generations are discrete and nonoverlapping; the analysis is restricted to a single locus in the absence of selection; every allele mutates to a new allele at the same rate u. Diploid-migration models without self-fertilization and with selfing at the “random” rate (equal to the reciprocal of the deme size in each deme) are investigated; in the gametic-dispersion models, selfing occurs at the random rate. It is shown for the unbounded stepping-stone model in one and two dimensions, the circular stepping-stone model, and the island model that the probabilitities of identity in state at equilibrium for diploid migration are close to those for gametic dispersion if the mutation rate is small or the deme size is large. Explicit error bounds are presented in all the above cases. It is also proved that if the number of demes is finite and the migration matrix is arbitrary but time independent and ergodic, then in the strong-migration approximation the equilibrium and the ultimate rate and pattern of convergence of both diploid-dispersion models are close to the corresponding gametic-dispersion formulae. For the strong-migration approximation at equilibrium, migration must dominate both mutation and random drift; for the convergence results, it suffices that migration dominate random drift. All the results apply to a dioecious population if the migration pattern and mutation rate are sex independent.     

Evolutionary limits to the frequency of aggression between related or unrelated conspecifics in diploid species with simple mendelian inheritance

Game theory has been used by some authors to analyse evolutionary limits to the expression of aggression in theoretical haploid parthenogenetic species. Others have examined frequency dependent selection, of which aggression may be a case, by applying population genetic models to diploid species. A model is presented which attempts to combine these two approaches. Game theory is used to determine evolutionarily stable strategies and corresponding stable polymorphisms for a two-strategy game played by members of a diploid sexual species, when choice of strategy is determined by two alleles at a single locus. Results are given for dominant, co-dominant and recessive determination of choice of the more aggressive of two strategies, for two levels of relationship: unrelated players and sibs. It is found that for a range of models of single locus inheritance the evolutionarily stable strategy (ESS) determined for haploid species remains the stable population strategy for diploid sexual species, when players are unrelated. In sibling contestants aggression is reduced. The mixed strategy haploid ESS underestimates, but the pure strategy haploid ESS provides a good indication of the degree to which relatedness lessens aggression in diploid species. For both haploid and diploid species there may be a considerable advantage to confining conflicts to kin.     

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.     

Multilocus dynamics under haploid selection

 A general haploid selection model with arbitrary number of multiallelic loci and arbitrary linkage distribution is considered. The population is supposed to be panmictic. A dynamically equivalent diploid selection model is introduced. There is a position effect in this model if the original haploid selection is not multiplicative. If haploid selection is additive then the fundamental theorem is established even with an estimate for the change in the mean fitness. On this basis exponential convergence to an equilibrium is proved. As rule, the limit states are single-gamete ones. If, moreover, linkage is tight, then the single-gamete state with maximal fitness attracts the population for almost all initial states. Received 27 November 1995; received in revised form 17 January 1996     

Mating-Type Functions for Meiosis and Sporulation in Yeast Act through Cytoplasm

Given a nutritional regime marked by a low nitrogen level and the absence of fermentable carbon sources, conventional a/α diploid cells of Saccharomyces cerevisiae exhibit a complex developmental sequence that includes a round of premeiotic DNA replication, commitment to meiosis and the elaboration of mature tetrads containing viable ascospores. Ordinarily, haploid cells and diploid cells of genotype a/a and α/α fail to display these reactions under comparable conditions. Here, we describe a simple technique for sporulation of α/α and a/a cells. Cells of genotype α/α are mated to haploid a cells carrying the kar1 (karyogamy defective) mutation to yield heterokaryons containing the corresponding diploid and haploid nuclei. The kar1 strains mate normally, but nuclei in the resultant zygotes do not fuse. When heterokaryotic cells are inoculated into sporulation media, they produce asci with six spores. Four spores carry genotypes derived from the diploid nucleus and the other two possess the markers originating from the haploid nucleus, i.e., the diploid nucleus divides meiotically while the haploid nucleus apparently divides mitotically. Similarly, the a/a genome is "helped" to sporulate as a consequence of mating with α kar1 strains. The results allow us to conclude that the mating-type functions essential for meiosis and sporulation are communicated and act through the cytoplasm and that sporulation can be dissociated from typical meiosis. This procedure will facilitate the genetic analysis of strains that are otherwise unable to sporulate.     

The evolution of payoff matrices: providing incentives to cooperate

Most of the work in evolutionary game theory starts with a model of a social situation that gives rise to a particular payoff matrix and analyses how behaviour evolves through natural selection. Here, we invert this approach and ask, given a model of how individuals behave, how the payoff matrix will evolve through natural selection. In particular, we ask whether a prisoner's dilemma game is stable against invasions by mutant genotypes that alter the payoffs. To answer this question, we develop a two-tiered framework with goal-oriented dynamics at the behavioural time scale and a diploid population genetic model at the evolutionary time scale. Our results are two-fold: first, we show that the prisoner's dilemma is subject to invasions by mutants that provide incentives for cooperation to their partners, and that the resulting game is a coordination game similar to the hawk-dove game. Second, we find that for a large class of mutants and symmetric games, a stable genetic polymorphism will exist in the locus determining the payoff matrix, resulting in a complex pattern of behavioural diversity in the population. Our results highlight the importance of considering the evolution of payoff matrices to understand the evolution of animal social systems.     

Evolution of dispersal in density regulated populations: A haploid model

The evolution of dispersal is explored in a density-dependent framework. Attention is restricted to haploid populations in which the genotypic fitnesses at a single diallelic locus are decreasing functions of the changing number of individuals in the population. It is shown that migration between two populations in which the genotypic response to density is reversed can maintain both alleles when the intermigration rates are constant or nondecreasing functions of the population densities. There is always a unique symmetric interior equilibrium with equal numbers but opposite gene frequencies in the two populations, provided the system is not degenerate. Numerical examples with exponential and hyperbolic fitnesses suggest that this is the only stable equilibrium state under constant positive migration rates (m) less than . Practically speaking, however, there is only convergence after a reasonable number of generations for relatively small migration rates ( ). A migration-modifying mutant at a second, neutral locus, can successfully enter two populations at a stable migration-selection balance if and only if it reduces the intermigration rates of its carriers at the original equilibrium population size. Moreover, migration modification will always result in a higher equilibrium population size, provided the system approaches another symmetric interior equilibrium. The new equilibrium migration rate will be lower than that at the original equilibrium, even when the modified migration rate is a nondecreasing function of the population sizes. Therefore, as in constant viability models, evolution will lead to reduced dispersal.     

Analysis of haploid mosaics in Drosophila

Adult chimeric epidermal structures were obtained following transplantation of haploid nuclei from haploid donor embryos of Drosophila into genetically marked diploid embryos. The haploid nuclei either remained haploid or became diploid. Where possible, physical measurements indicated that the haploid cells were smaller and produced smaller cuticular structures than did diploid cells. An increase in the number of pattern elements was observed in many patches which, by various criteria, were judged to be formed by haploid cells. The observation of altered pattern element spacing in haploid patches is in agreement with the conclusion, reached by L. I. Held (1979, Wilhelm Roux's Arch.187, 105–127) in triploid flies, that bristle spacing is a function of cell size.     

Learning in a game context: strategy choice by some keeps learning from evolving in others

Behavioural decisions in a social context commonly have frequency-dependent outcomes and so require analysis using evolutionary game theory. Learning provides a mechanism for tracking changing conditions and it has frequently been predicted to supplant fixed behaviour in shifting environments; yet few studies have examined the evolution of learning specifically in a game-theoretic context. We present a model that examines the evolution of learning in a frequency-dependent context created by a producer–scrounger game, where producers search for their own resources and scroungers usurp the discoveries of producers. We ask whether a learning mutant that can optimize its use of producer and scrounger to local conditions can invade a population of non-learning individuals that play producer and scrounger with fixed probabilities. We find that learning provides an initial advantage but never evolves to fixation. Once a stable equilibrium is attained, the population is always made up of a majority of fixed players and a minority of learning individuals. This result is robust to variation in the initial proportion of fixed individuals, the rate of within- and between-generation environmental change, and population size. Such learning polymorphisms will manifest themselves in a wide range of contexts, providing an important element leading to behavioural syndromes.     

Resource partitioning among competing species—A coevolutionary approach

A reasonably general theory for predicting the outcome of coevolution among interacting species is developed. It is applied to a model for resource partitioning among competing species.Current theory for resource partitioning is based on derivations of a “limiting similarity”—i.e., a limit to how similar competitors can be to one another consistent with coexistence. This theory presumes there is a mechanism, perhaps invasion and extinction, which causes competitors to attain the limiting similarity. The view taken in this paper is that partitioning is an evolutionary compromise between pressures for character displacement and disadvantages inherent in the shift to different resource types.A set of principles is offered for the evolution of the parameters in ecological models. (1) For single population models natural selection causes the parameters ultimately to assume those values which produce the highest equilibrium population size. (2) For models of interacting populations, but without interspecific frequency-dependence, natural selection causes the parameters to assume values which produce either the highest or lowest equilibrium population size for any species depending on the sign of the “feedback” in the community obtained by deleting that species. (3) For models of interacting populations with interspecific frequency dependence natural selection leads to parameter values which produce intermediate equilibrium population sizes. A function called the conditional equilibrium population size is introduced. Provided (a) the mean fitness is a maximum in each species at a stable coevolutionary equilibrium and (b) there is negative density-dependence in each species then natural selection causes the parameters to assume values which produce the highest conditional equilibrium population size for each species.These coevolutionary principles, applied to a model for resource partitioning, entail that the niche separation between species relative to given niche widths, increases with the variety of available resources and decreases with the number of competing populations. Also, the evolution of character displacement between two species does not proceed far enough to maximize the equilibrium population sizes of the species involved. These results imply that the relationship between the niche overlap (of nearest neighbors) and species diversity is qualitatively different depending on whether the variety of resources at any place covaries with the species diversity there. Without covariation niche overlap increases with species diversity; with covariation overlap may decrease with species diversity. This study provides the beginning of a theory for the convergent evolution of community structure.     

Oscillatory population growth in periodic environments

A general first-order nonlinear differential equation is derived for the dynamics of a population in such a way that the inherent growth rate r and the equilibrium “carrying capacity” K appear explicitly as parameters. By means of standard regular perturbation techniques, properties of the periodic asymptotic state of the population are studied under the assumption that r and K suffer periodic perturbations of small amplitude. Specific examples are studied analytically and numerically.     

Diploid Strains of the Pathogenic Basidiomycete Cryptococcus neoformans Are Thermally Dimorphic

Sia, R. A., Lengeler, K. B., and Heitman, J. 2000. Diploid strains of the pathogenic basidiomycete Cryptococcus neoformans are thermally dimorphic. Cryptococcus neoformans is an opportunistic human pathogenic fungus with a defined sexual cycle. Clinical and environmental isolates of C. neoformans are haploid, and the diploid stage of the lifecycle is thought to be transient and unstable. In contrast, we find that diploid strains are readily obtained following genetic crosses of congenic MATα and MATa strains. At 37°C, the diploid strains grow as yeast cells with a single nucleus that is larger than a haploid nucleus, contains a 2n content of DNA by FACS analysis, and is heterozygous for the MATα and MATa loci. At 24°C, these diploid self-fertile strains filament and sporulate, producing recombinant haploid progeny in which meiotic segregation has occurred. In contrast to dikaryotic filament cells that are typically linked by fused clamp connections during mating, self-fertile diploid strains produce monokaryotic filament cells with unfused clamp connections. We also show that these diploid strains can be transformed and sporulated and that an integrated selectable marker segregates in a mendelian fashion. The diploid state could play novel roles in the lifecycle and virulence of the organism and can be exploited for the analysis of essential genes. Finally, the observation that dimorphism is thermally regulated suggests similarities between the lifecycle of C. neoformans and other thermally dimorphic human pathogenic fungi, including Histoplasma capsulatum, Blastomyces dermatitidis, Coccidioides immitis, Paracoccidioides brasiliensis, and Sporothrix schenkii.     

The average frequency of private alleles in a partially isolated population

An analytic model is developed to explore the relationship between gene flow, selection, and genetic drift. We assume that a single copy of a mutant allele appears in a finite, partially isolated population and allow for the effects of immigration, genic selection, and mutation on the frequency of the mutant. Our concern is with the distribution of the mutant's frequency before it either is lost from the population or emigrates. Before either of these events, the allele will be a “private allele” and would be found in only one of several populations in a larger collection. Slatkin [(1985) Evolution 39, 53–65] found several simple properties of private alleles in his simulations. We use the method developed by Karlin and Tavaré [(1980) Genet. Res. 37, 33–46; (1981a), Theor. Pop. Biol. 19, 187–214; (1981b) Theor. Pop. Biol. 19, 215–229] for a model similar to ours to obtain a diffusion equation with a “killing term” and obtain the mean and variance of the mutant's frequency and its expected frequency in samples of a specified size. There is only fair agreement between the analytic results from this model and those from Slatkin's (loc. cit.) simulations. The rescaling method used to obtain the results indicates that if emigration is relatively frequent, the distribution of rare alleles is governed largely by the balance between genetic drift and emigration, with selection, mutation, and immigration playing a lesser role.     

Evolution and maintenance of haploid–diploid life cycles in natural populations: The case of the marine brown alga Ectocarpus

The evolutionary stability of haploid–diploid life cycles is still controversial. Mathematical models indicate that niche differences between ploidy phases may be a necessary condition for the evolution and maintenance of these life cycles. Nevertheless, experimental support for this prediction remains elusive. In the present work, we explored this hypothesis in natural populations of the brown alga Ectocarpus. Consistent with the life cycle described in culture, Ectocarpus crouaniorum in NW France and E. siliculosus in SW Italy exhibited an alternation between haploid gametophytes and diploid sporophytes. Our field data invalidated, however, the long‐standing view of an isomorphic alternation of generations. Gametophytes and sporophytes displayed marked differences in size and, conforming to theoretical predictions, occupied different spatiotemporal niches. Gametophytes were found almost exclusively on the alga Scytosiphon lomentaria during spring whereas sporophytes were present year‐round on abiotic substrata. Paradoxically, E. siliculosus in NW France exhibited similar habitat usage despite the absence of alternation of ploidy phases. Diploid sporophytes grew both epilithically and epiphytically, and this mainly asexual population gained the same ecological advantage postulated for haploid–diploid populations. Consequently, an ecological interpretation of the niche differences between haploid and diploid individuals does not seem to satisfactorily explain the evolution of the Ectocarpus life cycle.     

Selection and the Evolution of Genetic Life Cycles

The evolution of haploid and diploid phases of the life cycle is investigated theoretically, using a model where the relative length of haploid and diploid phases is under genetic control. The model assumes that selection occurs in both phases and that fitness in each phase is a function of the time spent in that phase. The equilibrium and stability conditions that allow for all-haploid, all-diploid, or polyphasic life cycles are considered for general survivorship functions. Types of stable life cycles possible depend on the form of the viability selection. If mortality rates are constant, either haploidy or diploidy is the only stable life cycle possible. Departures from constant mortality can give qualitatively different results. For example, when survivorship in each phase is a linear, decreasing function of the time spent in the phase, stable haploid, diploid or polyphasic life cycles are possible. The addition of genetic variation at a coevolving viability locus does not qualitatively affect the outcome with respect to the maintenance of polyphasic cycles but can lead to situations where more than one life cycle is concurrently stable. These results show that trade-offs between the advantages of being diploid and of being haploid may help explain the patterns of life cycles found in nature and that the type of selection may be critical to determining the results.     

The yield of experimental yeast populations declines during selection

The trade-off between growth rate and yield can limit population productivity. Here we tested for this life-history trade-off in replicate haploid and diploid populations of Saccharomyces cerevisiae propagated in glucose-limited medium in batch cultures for 5000 generations. The yield of single clones isolated from the haploid lineages, measured as both optical and population density at the end of a growth cycle, declined during selection and was negatively correlated with growth rate. Initially, diploid populations did not pay this cost of adaptation but haploidized after about 1000–3000 generations of selection, and this ploidy transition was associated with a decline in yield caused by reduced cell size. These results demonstrate the experimental evolution of a trade-off between growth rate and yield, caused by antagonistic pleiotropy, during adaptation in haploids and after an adaptive transition from diploidy to haploidy.