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.     

PLOIDY AND EVOLUTION BY SEXUAL SELECTION: A COMPARISON OF HAPLOID AND DIPLOID FEMALE CHOICE MODELS NEAR FIXATION EQUILIBRIA

We compare the stability properties of haploid and diploid models of Fisherian sexual selection (with male contribution limited to sperm) by examining both models at equilibria for which a male trait is fixed or absent. Haploid and diploid two locus diallelic models share the property that the stability of such fixation equilibria is determined by the relationship between the harmonic mean of relative preference values for the common male trait, weighted by the frequency of the preferences, and the relative viability associated with the common male trait. When diploid females with heterozygotic-based preferences express preference strengths intermediate between homozygote-based preferences, then boundary equilibria of haploid and diploid models share many stability properties. However, even with intermediate heterozygote preferences, haploid and diploid models do differ: (1) for a particular frequency of the preference allele, both fixation boundaries can be stable for the diploid model, and (2) with over- or underdominance at the preference locus (a possibility precluded in the haploid model), a fixation boundary in the diploid model may show two switches in its stability state for increasing frequencies of one of the preference alleles. These differences are due not just to the impossibility of dominance in haploid models, but also to the larger number of diploid genotypes.     

DELETERIOUS MUTATION AND THE EVOLUTION OF GENETIC LIFE CYCLES

It is often proposed that the ability of diploids to mask deleterious mutations leads to an evolutionary advantage over haploidy. In this paper, we studied the evolution of the relative duration of haploid and diploid phases using a model of recurrent deleterious mutations across the entire genome. We found that a completely diploid life cycle is favored under biologically reasonable conditions, even when prolonging the diploid phase reduces a population's mean fitness. A haploid cycle is favored when there is complete linkage throughout the genome or when mutations are either highly deleterious or partially dominant. These results hold when loci interact multiplicatively and for synergistic epistasis. The strength of selection generated on the life cycle can be substantial because of the cumulative effect of selection against mutations across many loci. We did not find conditions that support cycles that retain both phases, such as those found in some plants and algae. Thus, selection against deleterious mutations may be an important force in the evolution of life cycles but may not be sufficient to explain all the patterns of life cycles seen in nature.     

Heterozygote Advantage and the Evolution of a Dominant Diploid Phase

The life cycle of eukaryotic, sexual species is divided into haploid and diploid phases. In multicellular animals and seed plants, the diploid phase is dominant, and the haploid phase is reduced to one, or a very few cells, which are dependent on the diploid form. In other eukaryotic species, however, the haploid phase may dominate or the phases may be equally developed. Even though an alternation between haploid and diploid forms is fundamental to sexual reproduction in eukaryotes, relatively little is known about the evolutionary forces that influence the dominance of haploidy or diploidy. An obvious genetic factor that might result in selection for a dominant diploid phase is heterozygote advantage, since only the diploid phase can be heterozygous. In this paper, I analyze a model designed to determine whether heterozygote advantage could lead to the evolution of a dominant diploid phase. The main result is that heterozygote advantage can lead to an increase in the dominance of the diploid phase, but only if the diploid phase is already sufficiently dominant. Because the diploid phase is unlikely to be increased in organisms that are primarily haploid, I conclude that heterozygote advantage is not a sufficient explanation of the dominance of the diploid phase in higher plants and animals.     

EVOLUTION BY FISHERIAN SEXUAL SELECTION IN DIPLOIDS

Most models of Fisherian sexual selection assume haploidy. However, analytical models that focus on dynamics near fixation boundaries and simulations show that the resulting behavior depends on ploidy. Here we model sexual selection in a diploid to characterize behaviour away from fixation boundaries. The model assumes two di-allelic loci, a male-limited trait locus subject to viability selection, and a preference locus that determines a female's tendency to mate with males based on their genotype at the trait locus. Using a quasi-linkage equilibrium (QLE) approach, we find a general equation for the curves of quasi-neutral equilibria, and the conditions under which they are attracting or repelling. Unlike in the haploid model, the system can move away from the internal curve of equilibria in the diploid model. We show that this is the case when the combined forces of natural and sexual selection induce underdominance at the trait locus.     

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.     

Selection in diplo-haplonts

A deterministic selection model is considered for diplohaplontic populations which reproduce in non-overlapping generations and form zygotes by random fusion of gametes. The model allows for vegetative propagation as well as for viability and fertility selection in both the haploid and diploid phases. Fertility selection in the haploid phases is permitted to differ according to sex, and all selection coefficients are assumed to be constant over the generations. The main result obtained is that this model, including all of the above selective forces, is formally and analytically equivalent to and thus shares all of the properties of the “classical” viability selection model. This result is essentially due to the fact that when haplogenotypic frequencies in the sporophytes are considered in consecutive generations, all of the different selection forces can be expressed with the help of a single selection coefficient for each diplogenotype. The benefits from this simplification are demonstrated with the help of two examples for a single, multiallelic locus. Restricting selection to the haplophases only, it is shown that fertility selection acting in opposing directions in the sexes can lead to stable multiallelic polymorphisms without assuming spatial heterogeneity of the environment. However, it is unlikely that the conditions for this will be realized in actual populations for more than two alleles. The second example is concerned with the problem of maintaining several sexual types (males, females and bisexuals) in a population, with special emphasis on the conditions for the establishment of dioecious or monoecious systems of sexuality or a mixture of these.     

Evolution of haploid–diploid life cycles when haploid and diploid fitnesses are not equal

Many organisms spend a significant portion of their life cycle as haploids and as diploids (a haploid–diploid life cycle). However, the evolutionary processes that could maintain this sort of life cycle are unclear. Most previous models of ploidy evolution have assumed that the fitness effects of new mutations are equal in haploids and homozygous diploids, however, this equivalency is not supported by empirical data. With different mutational effects, the overall (intrinsic) fitness of a haploid would not be equal to that of a diploid after a series of substitution events. Intrinsic fitness differences between haploids and diploids can also arise directly, for example because diploids tend to have larger cell sizes than haploids. Here, we incorporate intrinsic fitness differences into genetic models for the evolution of time spent in the haploid versus diploid phases, in which ploidy affects whether new mutations are masked. Life‐cycle evolution can be affected by intrinsic fitness differences between phases, the masking of mutations, or a combination of both. We find parameter ranges where these two selective forces act and show that the balance between them can favor convergence on a haploid–diploid life cycle, which is not observed in the absence of intrinsic fitness differences.     

FURTHER SIMULATION STUDIES ON EVOLUTION BY GENE DUPLICATION

In order to understand the origin of multigene families, Monte Carlo simulations were performed to see how a genetic system evolves under unequal crossing-over, mutation, random genetic drift and natural selection, starting from a single gene copy. Both haploid and diploid models were examined. Beneficial, neutral, and detrimental mutations were incorporated, and “positive” selection favors those chromosomes (haploid) or individuals (diploid) with more beneficial mutations than others. The same model for haploids was previously investigated with special reference to the evolution of gene organization, and the ratio of the numbers of beneficial genes to pseudogenes was found to be a rough indicator of the relative strengths of positive and negative (against deleterious alleles) natural selection (Ohta, 1987b). In the present paper, the evolution of gene organization and of sequence divergence among genes in the multigene family is examined. It is shown that positive selection accelerates the accumulation of arrays containing different beneficial mutations, but that total divergence including both neutral and beneficial mutations is not very sensitive to positive selection, under this model. The proportion of beneficial mutations in the total mutations accumulated is a better indicator of positive selection than is the total divergence. It is pointed out that various observed examples in which amino-acid substitutions are accelerated, as compared with synonymous substitutions in duplicated genes (Li, 1985), may reflect the effect of selection similar to the present scheme. The diploid model is shown to be more efficient for accumulating beneficial mutations in duplicated genes than the haploid one, and the relevance of this finding to the advantage of sexual reproduction is discussed.     

Ploidally antagonistic selection maintains stable genetic polymorphism

Understanding the maintenance of genetic variation in the face of selection remains a key issue in evolutionary biology. One potential mechanism for the maintenance of genetic variation is opposing selection during the diploid and haploid stages of biphasic life cycles universal among eukaryotic sexual organisms. If haploid and diploid gene expression both occur, selection can act in each phase, potentially in opposing directions. In addition, sex-specific selection during haploid phases is likely simply because male and female gametophytes/gametes tend to have contrasting life histories. We explored the potential for the maintenance of a stable polymorphism under ploidally antagonistic as well as sex-specific selection. Furthermore, we examined the role of the chromosomal location of alleles (autosomal or sex-linked). Our analyses show that the most permissible conditions for the maintenance of polymorphism occur under negative ploidy-by-sex interactions, where stronger selection for an allele in female than male diploids is coupled with weaker selection against the allele in female than male haploids. Such ploidy-by-sex interactions also promote allele frequency differences between the sexes. With constant fitness, ploidally antagonistic selection can maintain stable polymorphisms for autosomal and X-linked genes but not for Y-linked genes. We discuss the implications of our results and outline a number of biological settings where the scenarios modeled may apply.     

Bifurcations in haploid and diploid sequence space models

 Deterministic models of mutation and selection in the space of (binary) nucleotide-type sequences have been investigated for haploid populations during the past 25 years, and, recently, for diploid populations as well. These models, in particular their ‘error thresholds’, have mainly been analyzed by numerical methods and perturbation techniques. We consider them here by means of bifurcation theory, which improves our understanding of both equilibrium and dynamical properties. In a caricature obtained from the original model by neglecting back mutation to the favourable allele, the familiar error threshold of the haploid two-class model turns out to be a simple transcritical bifurcation, whereas its diploid counterpart exhibits an additional saddle node. This corresponds to a second error threshold. Three-class models with neutral spaces of unequal size introduce further features. Such are a global bifurcation in haploid populations, and simple examples of Hopf bifurcations (as predicted by Akin’s theorem) in the diploid case. Received 13 June 1995; received in revised form 26 July 1996     

Evolution of the alternation of haploid and diploid phases in life cycles. II. Maintenance of the haplo-diplontic cycle

The relative duration of the haploid and the diploid phases during the reproductive cycle varies greatly between organisms. This paper addresses the question of the evolution of haploid, diploid, and haplo-diplontic life cycles. When the life span of haploid and diploid individuals is constant whatever their cycle, we show that the haplo-diplontic cycle has an advantage, which depends on the sex-ratio in anisogamous species and on the probability of fertilization in isogamous species. This is because meiosis and fertilization occur half as often in the haplo-diplontic cycle as in haploid or diploid cycles, for the same number of generations of individuals. This argument is demonstrated using a model which considers a genetic determination of the cycle, and fixed haploid and diploid fitnesses. The relevance of measures of fitness of haploid and diploid individuals in predicting the evolution of life cycles is discussed. Measures obtained in algae are compared with theoretical predictions.     

On migration load of seeds and pollen grains in a local population

We have extended Wright's model of migration load to hermaphrodite plants showing variation at a single locus with two alleles. The model incorporates independent migration of seeds and pollen grains, the selection at both the haploid gametophyte and the diploid sporophyte stages, and a mixed mating system. The analytical relations between migration load and migration rate of seeds and pollen grains are explicitly formulated. The results show that under certain conditions, seed flow can have a more effect on migration load than pollen flow. Pollen selection at the gametophyte stage cannot substantially affect the migration load at the sporophyte stage. Selection at the diploid sporophyte stage is critical in determining the migration load of pollen grains. The relative migration loads of pollen versus seeds can be approximately estimated in predominantly outcrossing populations by the ratio of pollen flow to twice the seed flow, when the selection coefficient (s(T)) is greater than, or approximately equal to, the migration rate (m).     

DIFFERENCES BETWEEN SELECTION ON SEX VERSUS RECOMBINATION IN RED QUEEN MODELS WITH DIPLOID HOSTS

The Red Queen hypothesis argues that parasites generate selection for genetic mixing (sex and recombination) in their hosts. A number of recent papers have examined this hypothesis using models with haploid hosts. In these haploid models, sex and recombination are selectively equivalent. However, sex and recombination are not equivalent in diploids because selection on sex depends on the consequences of segregation as well as recombination. Here I compare how parasites select on modifiers of sexual reproduction and modifiers of recombination rate. Across a wide set of parameters, parasites tend to select against both sex and recombination, though recombination is favored more often than is sex. There is little correspondence between the conditions favoring sex and those favoring recombination, indicating that the direction of selection on sex is often determined by the effects of segregation, not recombination. Moreover, when sex was favored it is usually due to a long-term advantage whereas short-term effects are often responsible for selection favoring recombination. These results strongly indicate that Red Queen models focusing exclusively on the effects of recombination cannot be used to infer the type of selection on sex that is generated by parasites on diploid hosts.     

The population genetics of synthetic lethals.

Synthetic lethals are variants at different loci that have little or no effect on viability singly but cause lethality in combination. The importance of synthetic lethals and, more generally, of synthetic deleterious loci (SDL) has been controversial. Here, we derive the expected frequencies for SDL under a mutation-selection balance for the complete haploid model and selected cases of the diploid model. We have also obtained simple approximations that demonstrate good fit to exact solutions based on numerical iterations. In the haploid case, equilibrium frequencies of carrier haplotypes (individuals with only a single mutation) are comparable to analogous single-locus results, after allowing for the effects of linkage. Frequencies in the diploid case, however, are much higher and more comparable to the square root of the single-locus results. In particular, when selection operates only on the double-mutant homozygote and linkage is not too tight, the expected frequency of the carriers is approximately the quartic root of the ratio between the mutation rate and the selection coefficient of the synthetics. For a reasonably wide set of models, the frequencies of carriers can be on the order of a few percent. The equilibrium frequencies of these deleterious alleles can be relatively high because, with SDL, both dominance and epistasis act to shield carriers from exposure to selection. We also discuss the possible role of SDL in maintaining genetic variation and in hybrid breakdown.     

The interrelationship of cell growth and division in haploid and diploid cells of Saccharomyces cerevisiae

The coordination of cell growth and division has been examined in isogenic haploid and diploid strains of Saccharomyces cerevisiae. The average cell volume of the haploid and diploid cells was unaffected by a range of environmental conditions and generation times. For most environments and generation times the mean cell volume of diploid cells was between 1.52 and 1.83 of the haploid cell volume. Both haploid and diploid cell volumes were reduced drastically when the cells were grown in the chemostat with glucose as the limiting substrate. In this environment diploid cells have the same mean cell volume as haploid cells. Diploid cells are more elongated than haploid cells, and the characteristic shape (eccentricity) of the cells is unaffected by all environmental conditions and generation times tested. Mother cell volume increased during the cell cycle, although the pattern of this increase was affected by the environmental conditions. Under most growth conditions detectable mother cell volume increase occurred only during the budding phase, whereas under conditions of carbon limitation detectable increase only occurred during the unbudded phase. A consequence of this result is that the mean cell volume of haploids at bud initiation is relatively constant in all environments, including carbon limitation. This suggests that there is a critical size for bud initiation for haploids which is constant and independent of environmental conditions. The results for diploids are more complex. Coordination of growth and division in haploid cells can be explained by a simple model initially developed for prokaryotes by Donachie. A modification of this model is proposed to account for the results with diploids.     

The contribution of haploids, diploids and clones to fine-scale population structure in the seaweed Cladophoropsis membranacea (Chlorophyta)

Local populations of Cladophoropsis membranacea exist as mats of coalesced thalli composed of free-living haploid and diploid plants including clonally reproduced plants of either phase. None of the phases are morphologically distinguishable. We used eight microsatellite loci to explore clonality and fine-scale patch structure in C. membranacea at six sites on the Canary Islands. Mats were always composites of many individuals; not single, large clones. Haploids outnumbered diploids at all sites (from 2:1 to 10:1). In both haploid and diploid plants, genetic diversity was high and there was no significant difference in allele frequencies. Significant heterozygote deficiencies were found in the diploid plants at five out of six sites and linkage disequilibrium was associated with the haploid phase at all sites. Short dispersal distances of gametes/spores and small effective population sizes associated with clonality probably contribute to inbreeding. Spatial autocorrelation analysis revealed that most clones were found within a radius of approximately 60 cm and rarely further than 5 m. Dominance of the haploid phase may reflect seasonal shifts in the relative frequencies of haploids and diploids, but may alternatively reflect superiority of locally adapted and competitively dominant, haploid clones; a strategy that is theoretically favoured in disturbed environments. Although sexual reproduction may be infrequent in C. membranacea, it is sufficient to maintain both life history phases and supports theoretical modelling studies that show that haploid-diploid life histories are an evolutionarily stable strategy.     

Evolutionary dynamics in frequency-dependent two-phenotype models

General frequency-dependent selection models based on two phenotypic classes are analyzed with underlying one-locus multiallele phenotypic determination systems in diploid populations. It is proved that the mean phenotypic fitnesses tend to equality over discrete generations and genetic mutations if a phenotypic polymorphism is to be maintained. The exact conditions are examined. The present results are valid for a wide class of models whenever random groupings or assortative patterns based on phenotype and affecting fitness, linearly or not, are independent of sex, mating preferences, or kinship. They can also be applied to two-sex haploid models.     

Population Studies in Microorganisms I. Evolution of Diploidy in SACCHAROMYCES CEREVISIAE

The relative adaptation of isogenic haploid and diploid strains of yeast was investigated in different sets of physiological conditions. When all nutrients were present in excess, no difference in the reproductive rates of isogenic haploid and diploid strains of yeast was detected in both optimal and non-optimal growth conditions. Competition between haploid and diploid strains of yeast was observed when growth was limited by the concentration of a single nutrilite. Under certain conditions when fitness (reproductive rate) is determined by transport of an essential nutrilite that exists in very low concentrations, diploid cells were selected against. These environmental conditions are similar to those found in offshore marine environments where nutrients are often present in extremely low concentrations. The fitness of diploid cells was estimated to be.93 +/-.02 (haploid fitness = 1). The reduced fitness of diploid cells in this environment can be explained by the reduced surface area/volume ratio possessed by diploid cells in comparison to haploid cells. The fitnesses of haploid and diploid cells in these environments are closely correlated with geometric variations in these strains. These results are consistent with the hypothesis that diploid cells are simply double haploids, and diploidy per se does not confer any direct adaptive advantage. The mechanism of the evolution of diploidy as a dominant phase in the life cycle of higher plants and animals remains obscure.     

The evolution of life cycles with haploid and diploid phases

Sexual eukaryotic organisms are characterized by an alternation between haploid and diploid phases. In vascular plants and animals, somatic growth and development occur primarily in the diploid phase, with the haploid phase reduced to the gametic cells. In many other eukaryotes, however, growth and development occur in both phases, with substantial variability among organisms in the length of each phase of the life cycle. A number of theoretical models and experimental studies have shed light on factors that may influence life cycle evolution, yet we remain far from a complete understanding of the diversity of life cycles observed in nature. In this paper we review the current state of knowledge in this field, and touch upon the many questions that remain unanswered. BioEssays 20 :453–462, 1998. © 1998 John Wiley & Sons, Inc.