Parental control of primary sex ratio has been reported in a mammal (red deer), some birds, and a snake. However, it remains uncertain whether other vertebrates including Amphibia can control sex ratio. In this paper, we examined the possibility in a wild population of the Japanese frog Rana rugosa which has female heterogamety. Sex ratios of their eggs were determined using DNA markers. The eggs were sampled in the field from May to August in 1998. Each egg was then sexed by polymerase chain reaction-restriction fragment length polymorphism (PCR-RFLP) using a sex-specific DNA marker. The result showed a male bias early in the season which changed to a female bias later, suggesting that females of R. rugosa can control the primary sex ratio.

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.

The chemostat theory on two species competition has shown that the dilution rate where transition of dominance occurs-transision-dilution rate-is independent of limiting-nutrient concentration. However, we obtained the experimental data indicating that the transition-dilution rate changed with variations in limiting-ammonium concentrations, using the chemostat mixed-culture of the cyanobacterium Microcystis novacekii and the green alga Scenedesmus quadricauda. The transition-dilution rate was dependent on the concentration of limiting ammonium in the influx culture medium. We tried to simulate the experimental results. Though the dilution rate has been considered independent of nutrient concentration, we introduce the effective dilution rate that depends on nutrient concentration (ammonium concentration in this study). A hyperbolic Monodtype function is used to represent the effective dilution rate for each species. The maximum dilution rate of the function is set to be the mechanical dilution rate (nominal dilution rate) of the chemostat culture. The calculation shows that the nominal transitiondilution rate where transition of dominance occur decreases with increased concentration. This simulation is well consistent with our experimental data. These results may suggest that the species-specificity of limiting nutrients, here nitrogen. Or they may imply that the depreciation of nitrogen becomes critical when both dilution rate and concentration are very low, especially for the green algae. In the latter case, spatial effects are induced internally in the ecosystem.

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