Stable demographic ratios of haploid gametophyte to diploid sporophyte abundance in macroalgal populations.

Macroalgal populations often consist of free-living haploid (gametophyte) and diploid (sporophyte) stages. Various ecological studies have been conducted to examine the demographic diversity of haploid-diploid populations with regard to the dominant stage. Here, I relaxed the assumption of classical research that the life history parameters of haploids and diploids are identical and developed a generalized haploid-diploid model that explicitly accounts for population density dependence and asexual reproduction. Analysis of this model yielded an exact solution for the abundance ratio of haploids to diploids in a population in which the ratio is determined by the balance of four demographic forces: sexual reproduction by haploids, sexual reproduction by diploids, asexual reproduction by haploids, and asexual reproduction by diploids. Furthermore, the persistence of a haploid-diploid population and its total biomass are shown to be determined by the basic reproductive number (R0), which is shown to be a function of these four demographic forces. When R0 is greater than one, the haploid-diploid population stably persists, and the ploidy ratio obtained by the analytical solution is realized.

Evolution of parental care in haploid-diploid plants.

In bryophytes that alternate between haploid gametophytes and diploid sporophytes through sexual reproduction, sporophytes are often attached to and nurtured on the female gametophyte. A similar phenomenon is seen in Florideophyceae (a group of red algae). These systems in which a gametophyte (mother) invests nutrients in sporophytes (offspring) are ideal for studying the evolution of 'parental care' in non-animal organisms. Here, we propose a model of a haploid-diploid life cycle and examine the evolution of maternal investment in sporophytes focusing on two effects: the degree of paternal or maternal control of investment and the number of sporophytes. We find that when the female dominantly controls the investment, the evolutionarily stable level of investment is that which maximizes the expected reproductive success of the female gametophyte. The genomic conflict between maternal and paternal alleles complicates the evolutionary outcome; however, a greater male allelic effect and a higher number of sporophytes favour a higher energy investment, which may lead to evolutionary branching or run-away escalation of the investment level. This suggests that the selfishness of the paternal gene is the evolutionary driver of parental care and that complex structures such as fusion cells in red algae may have evolved to suppress it.

Fixation and effective size in a haploid-diploid population with asexual reproduction.

The majority of population genetic theory assumes fully haploid or diploid organisms with obligate sexuality, despite complex life cycles with alternating generations being commonly observed. To reveal how natural selection and genetic drift shape the evolution of haploid-diploid populations, we analyze a stochastic genetic model for populations that consist of a mixture of haploid and diploid individuals, allowing for asexual reproduction and niche separation between haploid and diploid stages. Applying a diffusion approximation, we derive the fixation probability and describe its dependence on the reproductive values of haploid and diploid stages, which depend strongly on the extent of asexual reproduction in each phase and on the ecological differences between them.

Spatially explicit modeling of metapopulation dynamics of broadcast spawners and stabilizing/destabilizing effects of heterogeneity of quality across local habitats.

Many coastal invertebrate species are broadcast spawners. These species have a highly sedentary adult stage and disperse by oceanic transport of planktonic larvae. One commercially important group of broadcast spawners is abalones, which live in suitable habitat patches of rock reefs that are discretely distributed. Because of these life-history and habitat characteristics, abalones tend to exhibit a metapopulation structure. Despite fisheries management and the release of juveniles, wild populations of broadcast spawners have undergone dramatic reductions in density due to overexploitation, which has been partly attributed to a failure to account for spatial structure. To clarify the relationship between the persistence of a metapopulation and the bottleneck that occurs during reproduction and dispersal processes caused by spatial structure, we developed a spatially explicit metapopulation model accounting for the effects of both life history and fishery pressure. By analyzing the model, we derived a metric to evaluate metapopulation quality as the leading eigenvalue of a non-negative matrix (the landscape matrix). Using this measure, we clarified that the effect of spatial structure on metapopulation stability is explained well by the mean and variance of parameter values across patches under the condition in which the heterogeneity of the metapopulation network is weak. In particular, the presence of both a higher average and higher variance of quality in the landscape could indicate stable fishery stocks under certain conditions. For example, when the decline in the mean longevity of local patch due to the fishery pressures gradually diminishes, the rescue effects by good patches would work more effectively than the negative effect of bad patches and then the stabilizing effect of spatial heterogeneity could be observed in a metapopulation. Furthermore, optimal patch characteristics for the improvement of quality strongly depend on specific parameter values. For example, when adult fertility is improved, a patch with higher "source" ability is more suitable. In contrast, when the settlement success of planktonic larvae is improved or fishery pressure is reduced, a patch with higher "buffer" ability is more suitable for the improvement of fishery management.

Fixation Probability in a Haploid-Diploid Population.

Classical population genetic theory generally assumes either a fully haploid or fully diploid life cycle. However, many organisms exhibit more complex life cycles, with both free-living haploid and diploid stages. Here we ask what the probability of fixation is for selected alleles in organisms with haploid-diploid life cycles. We develop a genetic model that considers the population dynamics using both the Moran model and Wright-Fisher model. Applying a branching process approximation, we obtain an accurate fixation probability assuming that the population is large and the net effect of the mutation is beneficial. We also find the diffusion approximation for the fixation probability, which is accurate even in small populations and for deleterious alleles, as long as selection is weak. These fixation probabilities from branching process and diffusion approximations are similar when selection is weak for beneficial mutations that are not fully recessive. In many cases, particularly when one phase predominates, the fixation probability differs substantially for haploid-diploid organisms compared to either fully haploid or diploid species.

The evolutionary advantage of haploid versus diploid microbes in nutrient-poor environments.

Sexual eukaryotic organisms are characterized by haploid and diploid nuclear phases. In many organisms, growth and development occur in both haploid and diploid phases, and the relative length of these phases exhibits considerable diversity. A number of hypotheses have been put forward to explain the maintenance of this diversity of life cycles and the advantage of being haploid versus that of being diploid. The nutrient-limitation hypothesis postulates that haploid cells, because they are small and thus have a higher surface area to volume ratio, are advantageous in nutrient-poor environments. In this paper, we examine this hypothesis theoretically and determine the conditions under which it holds. On the basis of our analysis, we make the following predictions. First, the relative advantages of different ploidy levels strongly depend on the ploidy-dependent energy conversion efficiency and the scaling of mortality with cell size. Specifically, haploids enjoy a higher intrinsic population growth rate than diploids do under nutrient-poor conditions, but under nutrient-rich conditions the intrinsic population growth rate of diploids is higher, provided that the energy conversion efficiency of diploids is higher than that of haploids and the scaling of mortality with cell size is weak. Second, differences in nutrient concentration in the inflowing medium have almost no effect on the relative advantage of ploidy levels at population equilibrium. Our study illustrates the importance of explicit modeling of microbial life history and population dynamics to understand the evolution of ploidy levels.

Variability in the evolutionarily stable seasonal timing of germination and maturation of annuals and the mode of competition.

Here, we present a study examining the evolutionarily stable patterns of a seasonal schedule for an annual plant. We consider an evolutionary game in which the dates for germination and maturation are x and y, respectively. An individual increases its mass during the growing stage (from day x to y) and reproduces on y with a number of seeds proportional to its size. The seeds remain dormant from day y to day x in the following year. The daily mortality in the growing stage varies seasonally, whilst the mortality in the dormant stage is constant and small. Due to competition among individuals, the growth rate, mortality, and recruitment rate may depend on the total biomass of individuals in the growing stage. The evolutionarily stable population contains a mixture of phenotypes differing in germination date and maturation date if either the growth rate decreases or the mortality increases with the total biomass. If competition occurs through a lowered growth rate, the variance in the maturation date is greater than that in the germination date. However, these two variances are not very different if competition results mainly in enhanced mortality. If instead the competition results in lower recruitment success of the growing stage, the evolutionarily stable strategy (ESS) is composed of individuals with very early germination and maturation dates with small variability among individuals.

Increasing costs due to ocean acidification drives phytoplankton to be more heavily calcified: optimal growth strategy of coccolithophores.

Ocean acidification is potentially one of the greatest threats to marine ecosystems and global carbon cycling. Amongst calcifying organisms, coccolithophores have received special attention because their calcite precipitation plays a significant role in alkalinity flux to the deep ocean (i.e., inorganic carbon pump). Currently, empirical effort is devoted to evaluating the plastic responses to acidification, but evolutionary considerations are missing from this approach. We thus constructed an optimality model to evaluate the evolutionary response of coccolithophorid life history, assuming that their exoskeleton (coccolith) serves to reduce the instantaneous mortality rates. Our model predicted that natural selection favors constructing more heavily calcified exoskeleton in response to increased acidification-driven costs. This counter-intuitive response occurs because the fitness benefit of choosing a better-defended, slower growth strategy in more acidic conditions, outweighs that of accelerating the cell cycle, as this occurs by producing less calcified exoskeleton. Contrary to the widely held belief, the evolutionarily optimized population can precipitate larger amounts of CaCO(3) during the bloom in more acidified seawater, depending on parameter values. These findings suggest that ocean acidification may enhance the calcification rates of marine organisms as an adaptive response, possibly accompanied by higher carbon fixation ability. Our theory also provides a compelling explanation for the multispecific fossil time-series record from ∼200 years ago to present, in which mean coccolith size has increased along with rising atmospheric CO(2) concentration.

Optimal seasonal schedules and the relative dominance of heteromorphic and isomorphic life cycles in macroalgae.

Marine macroalgae (seaweed) show diverse life cycles. Species with a heteromorphic life cycle have a large multicellular algal body in one generation but have a very small body in the second generation of the same year. In contrast, the diploid and haploid life forms of isomorphic species have similar morphology, and these species often have more than two generations in a year. Here, we first study the optimal life cycle schedule of marine macroalgae when daily mortality changes seasonally, and then we discuss the conditions for coexistence and relative dominance of different life cycles. According to the optimal life cycle schedule, heteromorphic species tend to have a generation with a large algal body when mortality is low, and a microscopic-sized generation when mortality is high. In contrast, isomorphic species tend to mature when body size reaches a threshold value that is the same for different generations. We then examine the coexistence of the two life cycles when growth rate decreases with biomass. The model predicts that (1) at high latitudes (i.e., in strongly seasonal environments), heteromorphic species are likely to dominate over isomorphic species, and (2) species with a heteromorphic life cycle should dominate in the supratidal and upper intertidal zones where macroalgae tend to suffer high mortality, and also in the subtidal zone, where mortality is low, whereas isomorphic species are likely to be more successful when mortality is intermediate. These predictions are consistent with the observed distribution patterns of the two life cycles in macroalgae.