The population genetics of anisogamy

This paper analyses the population genetics of anisogamy controlled by a single locus, in both the haploid and diploid cases. The conclusions of Parker et al. (1972), based on computer calculations, are confirmed analytically. The effects of the existence of two mating types on the evolution of anisogamy are examined. Close linkage between a mating type locus and the gamete size locus may produce non-random associations of alleles, leading to disassortative fusion with respect to gamete size. With loose linkage, there is random association of alleles, but selection favours closer linkage.     

Selection on non-random fusion of gametes during the evolution of anisogamy

Correction of an error in earlier simulations which show how anisogamy could evolve by selection on individuals (Parker et al., 1971) now indicates that anisogamy can evolve when the range of gamete size is very much smaller than previously thought. These models assumed random fusion of gametes, external fertilization, and that zygote viability is dependent on the volume of provisioning it receives from one or both gametes.The present analysis concerns the success of strategies for selective fusion of gametes arising in a randomly-fusing parental population. On a priori grounds selection is expected to favour assortative fusion in ova but disassortative fusion in sperm; anisogamy can persist only if genes for assortative fusion of ova will not spread, and “perfect” anisogamy where genes for disassortative fusion fixate. Mutant strategies for assortatively-fusing ova may not be successful if such ova must compete with sperm for fusions with the randomly-fusing ova. Particularly at high levels of anisogamy, very few of the mutant ova will be fused by the time all other ova have become zygotes; hence their spread may be checked by the enhanced chances of death before fusion, or by problems associated with selfing if they do manage to fuse. In contrast, disassortatively-fusing sperm generally have an advantage when anisogamy would be favoured under random fusion. Genetic simulations (involving two loci, one with alleles for fusion behaviour and the other with alleles for gamete size) were used to confirm these conclusions. Where there is some degree of asynchrony of spawning, disassortative fusion alleles do even better than with perfect synchrony.Simulations with various sex-limited fusion strategies show that non-limited disassortative fusion, i.e. for both ova and sperm, is likely to be an ESS at high anisogamy against all strategies but the one which plays random fusion in ova, disassortative fusion in sperm. This is the ultimate ESS and it does not disrupt anisogamy, but at high anisogamy it has an extremely small advantage over non-limited disassortative fusion. The reasons for the establishment of non-limited disassortative fusion are probably related to avoiding selfing, and to the cost of maintaining random-fusion in ova (in terms of motility, etc.) outweighing the benefits of becoming obligatorily disassortative (non-motile).     

A comparative test of a theory for the evolution of anisogamy

Why are sperm small and eggs large? The dominant explanation for the evolution of gamete size dimorphism envisages two opposing selection pressures acting on gamete size: small gametes are favoured because many can be produced, whereas large gametes contribute to a large zygote with consequently increased survival chances. This model predicts disruptive selection on gamete size (i.e. selection for anisogamy) if increases in zygote size confer disproportional increases in fitness (at least over part of its size range). It therefore predicts that increases in adult size should be accompanied by stronger selection for anisogamy. Using data from the green algal order Volvocales, we provide the first phylogenetically controlled test of the model''s predictions using a published phylogeny and a new phylogeny derived by a different method. The predictions that larger organisms should (i) have a greater degree of gamete dimorphism and (ii) have larger eggs are broadly upheld. However, the results are highly sensitive to the phylogeny and the mode of analysis used.     

The evolution of anisogamy: a game-theoretic approach

A popular theory has proposed that anisogamy originated through disruptive selection acting on an ancestral isogamous population, though recent work has emphasized the importance of other factors in its evolution. We re-examine the disruptive selection theory, starting from an isogamous population with two mating types and taking into account the functional relationship, g(m), between the fitness of a gamete and its size, m, as well as the relationship, f(S), between the fitness of a zygote and its size, S. Evolutionary game theory is used to determine the existence and continuous stability of isogamous and anisogamous strategies for the two mating types under various models for the two functions g(m) and f(S). In the ancestral unicellular state, these two functions are likely to have been similar; this leads to isogamy whether they are sigmoidal or concave, though in the latter case allowance must be made for a minimal gamete size. The development of multicellularity may leave g(m) relatively unchanged while f(S) moves to the right, leading to the evolution of anisogamy. Thus, the disruptive selection theory provides a powerful explanation of the origin of anisogamy, though other selective forces may have been involved in the subsequent specialization of micro- and macrogametes.     

Gametic conflict versus contact in the evolution of anisogamy

Anisogamy refers to gametes that differ in size, and characterizes the difference between males and females. The evolution of aniosgamy is widely interpreted as involving conflict between gamete producers with small sperm parasitizing on the investment made by the eggs. Using a population genetic model for evolution at a locus that codes jointly for sperm and egg sizes of a hermaphrodite, we show that the origin of anisogamy in an externally spawning population need not involve conflict between gamete producers. Gamete size dimorphism may be an adaptation that increases gamete encounter rates when large zygotes are selected, and we show this in a mechanistically general individual selection model. We use the Vance survival function without specific allometric assumptions to model the zygote fitness dependence on its size, and hence obtain ecological and life-history correlates of isogamy and anisogamy, which we successfully compare with data from Volvocales.     

Letter: Notes on "heat loss from a Newtonian animal"

Parker, Baker &; Smith (1972) have demonstrated mathematically that given the evolution of sexual reproduction, disruptive selection for the production of either many small gametes or a few large gametes may occur, resulting in a stable polymorphism of “sperm” and “egg” producers. Their model for the evolution of anisogamy requires only that zygote fitness (F) increase steeply with increases in zygote volume (V) (for Foc∝ V^x, x must be greater than 1·5) and that a sufficiently broad range of zygote productivity-size variants exist in the population (the higher the value of x, the broader the range needed). They suggest that anisogamy is almost universal in multicellular organisms but relatively rare in unicellular organisms because only for the former is an investment in extra gametic reserves at the expense of the number of gametes produced likely to be worthwhile in terms of increasing the survival probability of the zygote. In this note a graphical analysis and evidence from the anisogamous Protista will be presented concerning this hypothesis.     

Why do organisms produce gametes of only two different sizes? Some theoretical aspects of the evolution of anisogamy

This paper extends the population genetic model of (the evolution of) anisogamy of Charlesworth (1978), which is based on the model of Parker, Baker & Smith (1972). The effect of parthenogenesis on the evolution of anisogamy is examined; this effect turns out to be only quantitative. Furthermore, the problem of the occurrence of only two different gamete sizes is considered. It is shown that a stable polymorphism with three different gamete sizes cannot exist. This result is robust to changes in the mating structure (random or disassortative gamete fusion) and to changes in the mode of reproduction (only sexual or partially parthenogenetic).     

Evolution of gamete size in primitive taxa without mating types

An ESS model to better understand the evolutionary dynamics of a primitive non-mating type gamete size was developed with reference to the PBS (Parker, Baker and Smith’s) theory, which was based on total numbers of zygotes formed and the zygote survival rates. We did not include mating types since it has been suggested that primitive mating systems did not have mating types. As input parameters, we used experimental data on gamete motility of marine green algae. Based on hard sphere collision mechanics, we detailed the fertilization kinetics of gametes that swim in water prior to fusing with their partners through a set of coupled, non-linear differential equations. These equations were integrated numerically using typical values of the constant parameters. To estimate the relative zygote survival rate, we used a function that is sigmoid in shape and examined some evolutionarily stable strategies in mating systems that depend on optimizing values of the invasion success ratio.     

Positive size–speed relationships in gametes and vegetative cells of Chlamydomonas reinhardtii; implications for the evolution of sperm

It is commonly held that differences in gametes of the two sexes (anisogamy) evolved from ancestors whose gametes were similar in size and behavior (isogamy). Underlying many hypotheses explaining anisogamy are assumed relationships between cell size and speed in the ancestral isogamous population. Using the isogamous alga Chlamydomonas reinhardtii, we explored size–speed distributions in vegetative and gamete cells of 10 cell lines, and clonal data from within two cell lines. We applied an independent speed selection approach to gamete populations of C. reinhardtii, monitoring correlated responses in size following selection for high speed. We demonstrate positive size–speed relationships in clones, cell lines, and artificially selected speed selection lines. We found different size–speed relationships in the two cell types of C. reinhardtii even though they overlap in size, suggesting that cell composition and/or programs of gene expression are capable of altering this relationship, and that the relationship is evolvable. The positive genetic size‐speed correlation means that the division of parent vegetative cells into numerous gametes trades off against not only size, but also speed, a trade‐off that has not received previous attention. Our results support reevaluating the role of speed selection in the evolution of anisogamy.     

Phototaxis and the evolution of isogamy and 'slight anisogamy' in marine green algae: insights from laboratory observations and numerical experiments

The evolution of anisogamy in marine algae was studied through numerical simulations of gamete mating behaviour in three dimensions, using observed traits of marine green algae as input parameters. The importance of phototaxis became apparent from the numerical experiments: all gametes with phototactic systems are favoured over those without, but this advantage is reduced with increasing tank depth or shorter search times. Phototactic gametes were advantaged over non-phototactic gametes if the water was shallower than about 30–40 mm when the time available for gamete encounter was 1000 time steps (5.55 min). If gametes of both sexes are positively phototactic, slightly anisogamous species are at a disadvantage to isogamous species, which invalidates the sperm-limitation theory as a driver for the evolution of slight anisogamy. Conflicting selection forces of search efficiency and zygote fitness may be needed.  © 2004 The Linnean Society of London, Botanical Journal of the Linnean Society , 2004, 144 , 321–327.     

Selection for high gamete encounter rates explains the evolution of anisogamy using plausible assumptions about size relationships of swimming speed and duration

A previous general model describing physical constraints on gamete encounter rates was modified to incorporate assumptions that increased size causes decreased swimming speed and increased fertile period (or other proportional enhancement to gamete fertility). The analysis indicates that with moderately strong size dependence of fertile period and a range of speed dependencies, selection for high encounter rates pressures mating systems that develop any heritable difference in size between the gametes of different mating types to exaggerate the difference and evolve from isogamy to anisogamy. The smaller gamete has an optimal size, but the larger faces continuing selection for increased size. This continues to a size that is estimated to be sufficient to make pheromone production of sperm attractants practical. This mechanism then bridges the missing link between isogametes and oogamy in a previous analysis of the effectiveness of pheromones in explaining the success of male-female mating systems. The evolution and success of anisogamy and oogamy can be explained solely on the basis of physical effects on the encounter process.     

Covariances between Arbitrary Relatives in Autotetraploids with Panmictic Disequilibrium

In random mating autopolyploid populations which have not reached equilibrium, two alleles may be interdependent as a result of the phenomenon of gametic recombination, i.e. the maintenance through successive gamete generations of an association of two alleles from the same gamete in a source reference generation. Any two alleles are dependent by this relationship if they derive by descent from the same ancestral gamete in the source population. Applied with the classical notion of identity by descent, the concept thus defined identifies new coefficients of dependence between arbitrary relatives. Coefficients of dependence are probabilities attached to the drawing of genes from two zygotes such that there are certain relationships amongst them. Applying the concept to autotetraploids, consideration of the states of dependence between the genes of a zygote or of a pair of zygotes leads to the definition of new parameters bearing on population means, variances and covariances, for arbitrary inbreeding. The absence of epistasis is supposed. Some applications of interest in artificial selection are briefly envisaged, with simplifying restrictions on genetic effects. The particular case of diallelism is also considered.     

Having sex,yes, but with whom? Inferences from fungi on the evolution of anisogamy and mating types

The advantage of sex has been among the most debated issues in biology. Surprisingly, the question of why sexual reproduction generally requires the combination of distinct gamete classes, such as small and large gametes, or gametes with different mating types, has been much less investigated. Why do systems with alternative gamete classes (i.e. systems with either anisogamy or mating types or both) appear even though they restrict the probability of finding a compatible mating partner? Why does the number of gamete classes vary from zero to thousands, with most often only two classes? We review here the hypotheses proposed to explain the origin, maintenance, number, and loss of gamete classes. We argue that fungi represent highly suitable models to help resolve issues related to the evolution of distinct gamete classes, because the number of mating types vary from zero to thousands across taxa, anisogamy is present or not, and because there are frequent transitions between these conditions. We review the nature and number of gamete classes in fungi, and we attempt to draw inferences from these data on the evolutionary forces responsible for their appearance, loss or maintenance, and number.     

Ecological models explaining the success of distinctive sperm and eggs (oogamy)

Several lineages have independently evolved from isogamy (all sexes producing similar gametes) through anisogamy (dissimilar gametes) to the familiar male (producing sperm) and female (producing eggs) condition of most large, multicellular organisms (oogamy). A variety of hypotheses explaining the selective mechanisms causing such evolution and the success of these lineages have been proposed, but little evidence and some confusion persists. Here, a few simplifying assumptions are used to extract and compare the essential features of the various ecological hypotheses. The comparisons reveal that the critical need is to identify a selective advantage of large, immobile gametes (eggs). Assumptions about the effect of sperm size on swimming speed are not important. The classic assumption of increasing zygote success with large size requires a relationship even stronger than survival proportional to volume, which seems unlikely and lacks empirical support. An assumption that eggs produce a pheromone sperm attractant leads, by established physical principles, to a more than sufficient advantage of large egg size. Without pheromones, combinations of increased target size and weaker increased zygote fitness or increased gamete longevity also provide sufficient selection.     

Evolution of hierarchical cytoplasmic inheritance in the plasmodial slime mold Physarum polycephalum

A striking linear dominance relationship for uniparental mitochondrial transmission is known between many mating types of plasmodial slime mold Physarum polycephalum. We herein examine how such hierarchical cytoplasmic inheritance evolves in isogamous organisms with many self-incompatible mating types. We assume that a nuclear locus determines the mating type of gametes and that another nuclear locus controls the digestion of mitochondria DNAs (mtDNAs) of the recipient gamete after fusion. We then examine the coupled genetic dynamics for the evolution of self-incompatible mating types and biased mitochondrial transmission between them. In Physarum, a multiallelic nuclear locus matA controls both the mating type of the gametes and the selective elimination of the mtDNA in the zygotes. We theoretically examine two potential mechanisms that might be responsible for the preferential digestion of mitochondria in the zygote. In the first model, the preferential digestion of mitochondria is assumed to be the outcome of differential expression levels of a suppressor gene carried by each gamete (suppression-power model). In the second model (site-specific nuclease model), the digestion of mtDNAs is assumed to be due to their cleavage by a site-specific nuclease that cuts the mtDNA at unmethylated recognition sites. Also assumed is that the mtDNAs are methylated at the same recognition site prior to the fusion, thereby being protected against the nuclease of the same gamete, and that the suppressor alleles convey information for the recognition sequences of nuclease and methylase. In both models, we found that a linear dominance hierarchy evolves as a consequence of the buildup of a strong linkage disequilibrium between the mating-type locus and the suppressor locus, though it fails to evolve if the recombination rate between the two loci is larger than a threshold. This threshold recombination rate depends on the number of mating types and the degree of fitness reduction in the heteroplasmic zygotes. If the recombination rate is above the threshold, suppressor alleles are equally distributed in each mating type at evolutionary equilibrium. Based on the theoretical results of the site-specific nuclease model, we propose that a nested subsequence structure in the recognition sequence should underlie the linear dominance hierarchy of mitochondrial transmission.     

Population genetic aspects of deleterious cytoplasmic genomes and their effect on the evolution of sexual reproduction.

A conflict of interest may arise between intra-cellular genomes and their host cell. The example explicitly investigated is that of a 'selfish' mitochondrion which increases its own rate of replication at the cost of reduced metabolic activity which is deleterious to the host cell. The results apply to deleterious cytoplasmic agents in general, such as intracellular parasites. Numerical simulation suggests that selfish mitochondria are able to invade an isogamous sexual population and are capable of reducing its fitness to below 5% of that prior to their invasion. Their spread is enhanced by decreasing the number of mitotic divisions between meioses, and this may constitute a significant constraint on the evolution of lifecycles. The presence of such deleterious cytoplasmic agents favours a nuclear mutation whose expression prevents cytoplasm from the other gamete entering the zygote at fertilization, resulting in uniparental inheritance of cytoplasm. Such a mutation appears physiologically plausible and can increase in frequency despite its deleterious effect in halving the amount of cytoplasm in the zygote. It is suggested that these were the conditions under which anisogamy evolved. These results have implications for the evolution of sexual reproduction. Standard theory suggests there is no immediate cost of sex, a twofold cost being incurred later as anisogamy evolves. The analysis described here predicts a large, rapid reduction in fitness associated with isogamous sexual reproduction, due to the spread of deleterious cytoplasmic agents with fitness only subsequently rising to a maximum twofold cost as uniparental inheritance of cytoplasm and anisogamy evolve.     

Gamete evolution and sperm numbers: sperm competition versus sperm limitation

Both gamete competition and gamete limitation can generate anisogamy from ancestral isogamy, and both sperm competition (SC) and sperm limitation (SL) can increase sperm numbers. Here, we compare the marginal benefits due to these two components at any given population level of sperm production using the risk and intensity models in sperm economics. We show quite generally for the intensity model (where N males compete for each set of eggs) that however severe the degree of SL, if there is at least one competitor for fertilization (N − 1 ≥ 1), the marginal gains through SC exceed those for SL, provided that the relationship between the probability of fertilization (F) and increasing sperm numbers (x) is a concave function. In the risk model, as fertility F increases from 0 to 1.0, the threshold SC risk (the probability q that two males compete for fertilization) for SC to be the dominant force drops from 1.0 to 0. The gamete competition and gamete limitation theories for the evolution of anisogamy rely on very similar considerations: our results imply that gamete limitation could dominate only if ancestral reproduction took place in highly isolated, small spawning groups.     

Small sperm,uniparental inheritance and selfish cytoplasmic elements: a comparison of two models

It has previously been suggested that small sperm size may be an adaptation to achieve uniparental inheritance of organelles, and hence to prevent the spread of selfish cytoplasmic elements. Such an explanation for anisogamy implies a mechanism whereby the male gamete eliminates its own cytoplasm prior to fusion with the egg. A model has been presented demonstrating the invasion and persistence of a modifier that acts gametically to kill its own organelles. Here we show, however, that this model is far from robust; indeed, if any cost is associated with the modifier it cannot persist. We also show that despite an empirically demonstrated association between anisogamy and multicellularity, this result also applies if the analysis is applied in the multicellular case. This class of model contrasts with the majority of analyses in which the modifier kills off the incoming gamete’s organelles. We show that these models are highly robust, even if uniparental inheritance is imperfect.     

Cytoplasmic inheritance of organelles in brown algae

Brown algae, together with diatoms and chrysophytes, are a member of the heterokonts. They have either a characteristic life cycle of diplohaplontic alternation of gametophytic and sporophytic generations that are isomorphic or heteromorphic, or a diplontic life cycle. Isogamy, anisogamy and oogamy have been recognized as the mode of sexual reproduction. Brown algae are the characteristic group having elaborated multicellular organization within the heterokonts. In this study, cytoplasmic inheritance of chloroplasts, mitochondria and centrioles was examined, with special focus on sexual reproduction and subsequent zygote development. In oogamy, chloroplasts and mitochondria are inherited maternally. In isogamy, chloroplasts in sporophyte cells are inherited biparentally (maternal or paternal); however, mitochondria (or mitochondrial DNA) derived from the female gamete only remained during zygote development after fertilization. Centrioles in zygotes are definitely derived from the male gamete, irrespective of the sexual reproduction pattern. Female centrioles in zygotes are selectively broken down within 1–2 h after fertilization. The remaining male centrioles play a crucial role as a part of the centrosome for microtubule organization, mitosis, determination of the cytokinetic plane and cytokinesis, as well as for maintaining multicellularity and regular morphogenesis in brown algae.