山口 幸

Marine animals show diverse and flexible sexual systems. Here, we review several advancements of theoretical studies made in the last decade. (i) Sex change in coral fishes is often accompanied by a long break in reproductive activity. The delay can be shortened by retaining the inactive gonad for the opposite sex. (ii) Barnacles adopt diverse sexual patterns. The game model was analysed assuming that newly settled larvae choose either growth or immediate reproduction and large individuals adjust male–female investments. (iii) Some parasitic barnacles produce larvae with sexual size dimorphism and others produce larvae with the sex determined after settlement on hosts. (iv) In some fish and many reptiles, sex is determined by the temperature experienced as eggs. The dynamics of sex hormones were studied when the enzymatic reaction rates were followed by the Arrhenius equation. The FMF pattern (male at intermediates temperature; female both at high and low temperatures) required some reactions with enhanced temperature dependence at higher temperatures. The game model provides a useful framework for understanding diverse sexual patterns if we incorporate various constraints, such as unpredictability, cost of trait change and social situations. For further developments, we need to consider constraints imposed by physiological and molecular mechanisms.

In some species of separate sexes, males present a nuptial gift containing nutrition to their mate. Producing a large nuptial gift is a considerable cost to the male, but it may improve his siring success if the female reduces the likelihood to accept another male after receiving a large gift. The female may receive a direct benefit by accepting another male who provides an additional nuptial gift. Additionally, the female may receive an indirect fitness benefit via laying offspring sired by a male who is able to produce a large nuptial gift. We formalized the multivariate quantitative genetics model describing the coevolution of the size of nuptial gift produced by the male (x) and the female's propensity to engage in remating (y). We analyzed the model focusing two cases: [1] remating females receive no indirect fitness benefit, but enjoy direct benefit of nutrition; and [2] remating females receive no direct benefit, but enjoy an indirect fitness benefit due to a positive genetic correlation of x and y, which is possible if random mutations tend to make males produce small nuptial gifts. In both cases, the stable evolutionary equilibrium with neither nuptial gift nor remating (x-=y-=0) always exists. Another stable equilibrium may exist in which male produces nuptial gifts (x->0) and female engage in multiple mating (y->0). We discussed implications to the sexual conflict.

Many marine invertebrates have a benthic adult life with planktonic long feeding larval stages (planktotrophy). In other species, planktonic larvae do not eat, and after a rather short period, they settle and initiate their benthic stages (lecithotrophy). Still other species skip planktonic larval stages altogether, and adults produce benthic offspring (direct development). In this paper, we develop an evolutionary game among different life-cycle types and examine the conditions for each life-cycle type to win in a seasonal environment. The growth rate and mortality of benthic individuals are the same among all three life-cycle types, the local habitat (patches) for benthic individuals have a finite longevity, and adults may engage in a limited dispersal just before breeding. Planktotrophy evolves if the planktonic stages are more efficient in terms of biomass gain than benthic life. Otherwise, lecithotrophy or direct development should evolve. Among them, direct development is more advantageous than lecithotrophy if the cost of having planktonic larvae is large, the habitat for benthic individuals is stable, and adults engage in some dispersal.

Fish live in water with a different osmotic pressure from that in the body. Their gills have chloride cells that transport ions to maintain an appropriate level of osmotic pressure in the body. The direction of ion transport is different between seawater and freshwater. There are two types of chloride cells that specialize in unidirectional transport and generalist cells that can switch their function quickly in response to environmental salinity. In species that experience salinity changes throughout life (euryhaline species), individuals may replace some chloride cells with cells of different types upon a sudden change in environmental salinity. In this paper, we develop a dynamic optimization model for the chloride cell composition of an individual living in an environment with randomly fluctuating salinity. The optimal solution is to minimize the sum of the workload of chloride cells in coping with the difference in osmotic pressure, the maintenance cost, and the temporal cost due to environmental change. The optimal fraction of generalist chloride cells increases with the frequency of salinity changes and the time needed for new cells to be fully functional but decreases with excess maintenance cost.

Androdioecy, the coexistence of hermaphrodites and males, is very rare in vertebrates but occurs in mangrove killifish living in ephemeral or unstable habitats. Hermaphrodites reproduce both by outcrossing with males and by selling. Outbreeding is advantageous because of inbreeding depression, but it requires encounters with males. The advantages of a propensity for outcrossing among hermaphrodites and the production of males affect each other very strongly. To study the evolutionary coupling of these two aspects, we here analyze a simple evolutionary game for a population composed of three phenotypes: outcrossing-oriented hermaphrodites, selling-oriented hermaphrodites, and males. Outcrossing-oriented hermaphrodites first attempt to search for males and perform outcrossing if they encounter males. If they fail to encounter males, they reproduce via selling. Selling-oriented hermaphrodites simply reproduce by selling. The replicator dynamics may show bistability, in which both the androdioecious population (with outcrossing-oriented hermaphrodites and males) and the pure hermaphroditic population are locally stable. The model shows the fraction of males is either zero or relatively high (more than 25%), which is not consistent with the observed low fraction of males (less than 5%). To explain this discrepancy, we studied several models including immigration and enforced copulation. We concluded that the observed pattern can be most likely explained by a population dominated by selling-oriented hermaphrodites receiving immigration of males. (C) 2021 The Author(s). Published by Elsevier Ltd.

Legumes produce root nodules containing symbiotic rhizobial bacteria that convert atmospheric molecular nitrogen into ammonia or related nitrogenous compounds. The host plant supplies photosynthetic products to root nodules forming a mutualistic system. Legumes have physiological mechanisms for regulating nodule production with chemical signals produced in leaves, called the autoregulation of nodulation. In this paper, we discuss the optimal number of root nodules that maximizes the performance of the host plant. Here, we study two models. In the stationary plant model, the acquired photosynthetic products minus cost and loss are used for reproduction. In the growing plant model, the excess material is invested to produce leaves, roots, and root nodules, resulting in the exponential growth of the whole plant. The analysis shows that having root nodules is beneficial to the plant for a high leaf nitrogen content, faster plant growth rate, a short leaf longevity, a low root/shoot ratio, and low soil nutrient concentration. We discuss the long-distance control of nodulation-autoregulation and dependence on the environmental conditions of terrestrial plants considering these results. (C) 2020 The Authors. Published by Elsevier Ltd.

This chapter reviews sex determination and sex allocation strategies among crustaceans with different sexual systems (gonochorism, sequential and simultaneous hermaphroditism, and androdioecy), from the perspective of evolutionary ecology. The discussion includes genetic, environmental, and cytoplasmic sex determination in free-living and parasitic crustaceans, timing and frequency of sex change especially in partial protandry, the effects of mating group size on resource allocation by simultaneous hermaphrodites, and sex ratio and determination in androdioecious crustaceans. The fascinating diversity of crustacean reproduction stimulated theoretical biologists to construct models to explain them, and empirical biologists attempted to test hypotheses derived from those models. This review clearly shows that the interaction between theoretical and empirical studies has facilitated understanding of the evolutionary conditions of diverse sexual strategies among crustaceans. Since sexual strategies often interact with other aspects of adaptive strategies such as life history, integrating different aspects into both theoretical and empirical studies will provide further understandings into crustacean sexual systems. In addition, the authors point out the potential of phylogenetic comparative analyses using natural history data as a tool to understand the tempo and mode of evolution of sex allocation strategies.

Cancer is caused by the lifetime accumulation of multiple somatic deformations of the genome and epigenome. At a very low rate, mistakes occur during genomic replication (e.g., mutations or modified epigenetic marks). Long-lived species, such as elephants, are suggested to have evolved mechanisms to slow down the cancer progression. Recently, the life span of companion dogs has increased considerably than before, owing to the improvement of their environment, which has led to an increase in the fraction of companion dogs developing cancer. These findings suggest that short-term responses of cancer risk to longevity differ from long-term responses. In this study, to clarify the situation, we used a simple multi-step model for cancer. The rates of events leading to malignant cancer are assumed to be proportional to those of genomic replication error. Perfect removal of replication error requires a large cost, resulting in the evolution of a positive rate of genomic replication error. The analysis of the model revealed: that, when the environment suddenly becomes benign, the relative importance of cancer enhances, although the age-dependent cancer risk remains unchanged. However, in the long run, the genomic error rate evolves to become smaller and mitigates the cancer risk.

The male larvae of many parasitic barnacles are planktonic and are seasonally released. To achieve reproductive success, a male must be accepted by a receptive female that has successfully infected a host. To understand the seasonality of the breeding biology of parasitic barnacles, we developed an evolutionary game theoretical model for the seasonal pattern in the production of male larvae. Assumptions are that female parasitic barnacles become receptive following a given seasonal pattern. The parental females (mothers) choose the timing of producing their own male larvae to achieve maximum reproductive success. In the evolutionarily stable seasonal pattern, the production of male larvae often shows a sharp peak on a single day, indicating strongly synchronized production of male larvae, even when the supply of receptive females is distributed over the breeding season. When the total number of male larvae is large, the evolutionarily stable male production pattern may include multiple peaks, but it never shows a continuous distribution. This is very different from the game model previously developed for the emergence pattern of butterflies, where evolutionarily stable male emergence is always continuously distributed over a fraction of the mating season. As planktonic larvae, male parasitic barnacles have a naturally limited ability to find receptive females, and females may stay receptive for many days, whereas in butterflies, newly emerged females are mated within a day of their emergence.

Wise decision-making for coping with infectious diseases is a key to the success of farming, agriculture, as well as public health. Mastitis of dairy cows causes large economic burden to dairy farmers. Here, we study the optimal operation for a dairy farmer to manage cows infected by mastitis. In the simple model, we considered cows with different number of breasts (quarters) infected by mastitis. In the detailed model, we considered additional complexities: a cow produces milk only after the first birth of a calf, old cows are culled, milking is not practiced for 10 weeks prior to expected calf-birth, and a newborn calf provides an economic benefit. By fitting the parameters to the Japanese dairy farming situation, the dynamic programming analysis reveals whether an infected cow should receive medical treatment depends on the number of breasts infected, age, and season. Cows should be culled if many breasts are infected, they are old, and it is not close to the next calf-birth. The optimal management policy depends critically on milk price, maintenance cost, and recovery rate from mastitis infection, but not on infection rate. (C) 2020 The Author(s). Published by Elsevier Ltd.

Temperature-dependent sex determination (TSD) is adopted by many animal taxa, including reptiles and fishes. In some species, the eggs develop into females under a low hatching temperature, whereas they will develop into males under a high hatching temperature (called the FM-pattern). In other species, the eggs develop into males (or females) under a low (or high) hatching temperature (MF-pattern). Still, in other species, the eggs develop into females, males, or females, respectively, when under a low, intermediate, or high hatching temperature (FMF-pattern). In this paper, we study a mechanism for realizing TSD. Specifically, we explore a hypothesis that the temperature dependence of enzymatic reaction rates causes a clear switching of sex hormone levels with gradual change of temperature. Herein, we analyze a simple hormonal-dynamics with temperature-sensitive rates of enzymatic reactions included in the sex-determining gene-protein regulatory network. We first examined the cases in which the enzymatic reactions followed Arrhenius equation. The MF-pattern appeared when the rates of aromatase production and/or estradiol production depend more strongly on temperature than do the rates of their decay. By contrast, the FM-pattern appeared when the temperature dependence is stronger for the decay rates of aromatase and/or estradiol than their production rates. However, the FMF-pattern appeared only when some enzymatic reactions follow Berthelot–Hood equation, which exhibits a stronger temperature dependence under higher temperatures than Arrhenius equation. We discuss the possible mechanisms for TSD of FMF-pattern, including alternative splicing and post-translational modification.

Among animals living in groups with reproductive skew associated with a dominance hierarchy, subordinates may do best by using various alternative tactics. Sequential hermaphrodites or sex changers adopt a unique solution, that is, being the sex with weaker skew when they are small and subordinate, and changing sex when they become larger. In bi-directionally sex-changing fishes, although most are haremic and basically protogynous, subordinate males can change sex to being females. We study a mathematical model to examine when and why such reversed sex change is more adaptive than dispersal to take over another harem. We attempt to examine previously proposed hypotheses that the risk of dispersal and low density favor reversed sex change, and to specify an optimal decision-making strategy for subordinates. As a result, while the size-dependent conditional strategy in which smaller males tend to change sex is predicted, even large males are predicted to change sex under low density and/or high risk of dispersal, supporting both previous hypotheses. The importance of spatiotemporal variation of social and ecological conditions is also suggested. We discuss a unified framework to understand hermaphroditic and gonochoristic societies. (C) 2017 Elsevier Ltd. All rights reserved.

Many species of teleost fish live in coral reefs and change sex depending on their social status; some even demonstrate sex change in both directions. Typically, in the absence of a more dominant competitive individual, the fish functions as a male; however, when a more competitively superior individual arrives, the focal fish becomes a female. Among these bidirectional sex changers, there are species that retain the gonads of the currently nonfunctional sex, i.e., a male retains female reproductive tissues or a female retains male reproductive tissues. We construct a game-theoretic model and examine the conditions under which gonads of both the functional and the nonfunctional sex would be kept. We observe that a focal fish always retains both gonads when the social conditions change frequently in either direction, while it retains only the gonads of the currently functional sex when there is an infrequent change of social conditions. However, in order to explain the observed patterns of a monogamous goby Paragobiodon echinocephalus that undergoes a complete reconstruction of the entire gonad during sex change and a polygynous goby Trimma okinawae that retains the gonad of the nonfunctional sex, we need to assume that the cost of a male retaining the female gonad is much less than that of a female retaining a male gonad. We argue that this assumption is plausible given structural differences in male and female fitness payoffs. Significance Statement Among coral fish that exhibit bidirectional sex change, some retain the gonad of the nonfunctional sex as well as the current sex, while others exhibit the gonad of the current sex only. A game-theoretic model was developed to investigate under what conditions we might expect a bidirectional sex changer should keep the gonad of the nonfunctional sex. The frequency of sex change opportunity, the time required to reconstruct the gonad, and the maintenance cost all affect the evolution of gonad retention. A quantitative parameterization of the model for well-studied species concluded that the cost for a male to keep a female gonad must be much smaller than the cost for a female to retain a male gonad. The results demonstrated the importance of combining physiological and morphological aspects in the evolutionary ecology of sex changing fish.

Bidirectional sex change is observed in many teleost fish. When social conditions change, the sex transition may take place over a period of several days to a few months. To understand temporal differences for sex change in either direction, I propose a simple mathematical model for the hormone enzyme dynamics. Aromatase (P450arom) catalyses the synthesis of estradiol from testosterone. I assume that a change in social conditions for individuals affects the rates of production and degradation of P450arom. I then consider the evolution of parameters in the dynamics. Optimal parameter values are those that minimize total fitness cost, defined as the sum of fitness losses due to delay in being a functional male or female, and the cost of accelerated degradation of P450arom in changing from female to male sex. The model predicts that, in haremic species, sex change promotes a faster degradation of P450arom, resulting in a faster female-to-male transition than male-to-female transition. In contrast, in monogamous species, or with a small number of females, there is no benefit in a faster degradation of P450arom when changing to male, resulting in approximately equal timespans for sex change in either direction. (C) 2016 Elsevier Ltd. All rights reserved.

Descriptions of the diversity of sexual systems in animal taxa such as the thoracican barnacles are needed to study the evolution of sexual systems. Androdioecious systems (coexistence of hermaphrodites and males) are particularly important due to their possible role as evolutionary intermediates in transitions between hermaphroditism and dioecy. In this study, we used histology to examine the sexual system of the crab-epizoic barnacle Octolasmis unguisiformis to determine if dwarf males were present or not; a previous study reported the existence of conspecific-attached individuals, but did not investigate their sexuality. All conspecific-attached individuals were dwarf males, irrespective of their attachment site. However, crab-attached individuals never acted as dwarf males even if they were small and lived together with large individuals. The result emphasizes the importance of attachment to conspecifics, but not to specific sites on conspecifics, in the evolution of dwarf males. Other individuals were hermaphroditic, indicating androdioecy in this species. However, their functional sexuality (that is, whether they actually do act as males) requires further study. The presence of dwarf males in this species supports theoretical predictions that small group size, short-lived habitats, or spatial limitation favor the evolution of dwarf males.

Organisms may adjust their phenotypes in response to social and physical environments. Such phenotypic plasticity is known to help or retard adaptive evolution. Here, we study the evolutionary outcomes of adaptive phenotypic plasticity in an evolutionary game involving two players who have no conflicts of interest. A possible example is the growth and sex allocation of a lifelong pair of shrimps entrapped in the body of a sponge. We consider random pair forrnation, the limitation of total resources for growth, and the needs of male investment to fertilize eggs laid by the partner. We compare the following three different evolutionary dynamics: (1) No adjustment: each individual develops a phenotype specified by its own genotype; (2) One-player adjustment: the phenotype of the first player is specified by its own genotype, and the second player chooses the phenotype that maximizes its own fitness; (3) Two-player adjustment: the first player exhibits an initial phenotype specified by its own genotype, the second player chooses a phenotype given that of the first player, and finally, the first player readjusts its phenotype given that of the second player. We demonstrate that both one-player and two-player adjustments evolve to achieve maximum fitness. In contrast, the dynamics without adjustment fails in some cases to evolve outcomes with the highest fitness. For an intermediate range of male cost, the evolution of no adjustment realizes two hermaphrodites with equal size, whereas the one-player and two-player adjustments realize a small male and a large female. (C) 2015 Elsevier Inc. All rights reserved.

The parasitic (rhizocephalan) barnacles include species of which larval sex is determined by the mother (genetic sex determination, GSD), male larvae are larger than female larvae, and a female accepts only two dwarf males who sire all the eggs laid by her. In contrast, other species of parasitic barnacles exhibit monomorphic larvae that choose to become male or female depending on the condition of the host they settle (environmental sex determination, or ESD), and a female accepts numerous dwarf males. Here, we ask why these set of traits are observed together, by examining the evolution of sex determination and the larval size. ESD has an advantage over GSD because each larva has a higher chance of encountering a suitable host. On the other hand, GSD has two advantages over ESD: the larval size can be chosen differently between sexes, and their larvae can avoid spending time for sex determination on the host. We conclude that, in species whose female accepts only two males, the male larvae engage in intense contest competition for reproductive opportunities, and male's success-size relation is very different from female's. Then, larvae with predetermined sex (GSD) with sexually dimorphic larvae is more advantageous than ESD. In contrast, in species whose females accept many dwarf males, the competition among males is less intense, and producing larvae with undetermined sex should evolve. We also discuss the condition for females to evolve receptacles to limit the number of males she accepts. (C) 2014 Elsevier Ltd. All rights reserved.

The specimens of Paralepas maculata on a sea urchin, Prionocidaris sp. were collected in Okinawa, southern Japan. This species has not been reported since its original description. This represents the first observation of this species from Okinawa and the first instance found on this sea urchin species. In this paper, the morphology of the new P. maculata specimens is reported, and compared with the type series of this species. Small individuals were found on the holotype. The probable androdioecious sexual system of the species, which includes dwarf-male like individuals and hermaphrodites, is discussed. This study was facilitated by the collaboration of scientists and aquarium staff, suggesting the potential of such collaborations in biodiversity studies. © Marine Biological Association of the United Kingdom, 2014.

In many marine sedentary species, dwarf males coexist with large individuals who are either hermaphrodites or females. Simple models of the evolutionary game of sex allocation and life history choice predict that stable coexistence of dwarf males and hermaphrodites is rather difficult. In many of these models, however, newly settled larvae are assumed to choose freely between becoming a dwarf male or an immature fast growing individual. In this paper, we consider a new model in which the opportunity for a newly settled individual to become a dwarf male is limited, for example by the scarcity of large individuals near its settlement site. In the evolutionarily stable strategy, the stationary population is either (1) dominated by hermaphrodites, with dwarf males scarce or absent, if immature individuals are fast-growing, (2) a mixture of dwarf males and large females, if larval growth is slow and the opportunity to become dwarf males is high, (3) a mixture of dwarf males and hermaphrodites, if larval growth is slow and the opportunity to become dwarf males is limited. We also examine the case in which the opportunity to be a growing individual is spatially limited. (C) 2013 Elsevier Ltd. All rights reserved.

Barnacles (Crustacea: Thoracica) show diverse sexual systems, including simultaneous hermaphroditism, androdioecy (hermaphrodites + males), and dioecy (females + males). When males occur, they are always much smaller (called dwarf males) than conspecific hermaphrodites or females. Ever since Darwin made this discovery, many scientists have been fascinated by such diversity. In this study, we provide an overview of (1) the diversity of sexual systems in barnacles, (2) the continuity between different sexual systems in some genera or species, and (3) the plasticity in sexual expression in several species. First, although most barnacles are hermaphroditic, both theoretical and empirical studies suggest that females and dwarf males tend to occur in species with small mating groups. Low sperm competition among hermaphrodites and little chance to act as a male are both associated with small group sizes and identified as the forces promoting the evolution of dwarf males and pure females, respectively. Second, in some groups of barnacles, the distinction between hermaphrodites and dwarf males is unclear because of the potential of dwarf males to become hermaphrodites. As many barnacle species tend toward protandric simultaneous hermaphroditism (develop male function first and then add female function without discarding male function), the dwarf males in such cases are best described as potential hermaphrodites that arrest growth and emphasize male function much earlier because of attachment to conspecifics. This is presumably advantageous in fertilizing the eggs of the host individuals. The distinction between hermaphrodites and females may also be obscured in some species. Third, sex allocation and penial morphology are plastic in some species. We also report the results of a transplanting experiment on small individuals of the pedunculate barnacle Octolasmis angulata, which suggests that individuals transplanted onto conspecifics developed longer and broader penises than did control individuals. Overall, the diversity, continuity, and plasticity in the sexual systems of barnacles are sources of important insights into the evolution and maintenance of the diversity of sexual systems.

In this study, we investigate the evolutionarily stable schedule of growth and sex allocation for marine benthic species that contain dwarf males. We consider a population in an ephemeral microhabitat that receives a constant supply of larvae. Small individuals can immediately reproduce as a dwarf male or remain immature and grow. Large individuals allocate reproductive resources between male and female functions. The fraction c of newly settled individuals who remain immature and the sex allocation of large individuals m are quantities to evolve. In the stationary ESS, if the relative reproductive success of dwarf males is greater than the survivorship of immature individuals until they reach a mature size, then the population is a mixture of females and dwarf males. If the opposite inequality holds, the population is dominated by hermaphrodites and lacks dwarf males. There is no case in which a mixture of hermaphrodites and dwarf males to be the ESS in the stationary solution. The ESS can be solved by dynamic programming when the strategies depend on the age of the microhabitat (c (t) and m (t)). Typically, the ESS schedule begins with a population composed only of hermaphrodites, which is replaced by a mixture of dwarf males and hermaphrodites and then by a mixture of dwarf males and pure females. The relative importance of these three phases depends on multiple parameters. (c) 2013 Elsevier Inc. All rights reserved.

Barnacles, which are sedentary marine crustaceans, have diverse sexual systems that include simultaneous hermaphroditism, androdioecy (coexistence of hermaphrodites and males) and dioecy (females and males). In dioecious and androdioecious species, the males are very small and are thus called dwarf males. These sexual systems are defined by two factors: sex allocation of non-dwarf individuals and the presence or absence of dwarf males. We constructed an ESS model treating sex allocation and life history simultaneously to explain sexual systems in barnacles. We analyzed the evolutionarily stable size-dependent resource allocation strategy to male reproductive function, female reproductive function and growth in non-dwarf barnacles, and the ESS proportion of dwarf males, under conditions of varying mortality and food availability. Sex allocation in non-dwarf individuals (hermaphrodites or females) is affected by mate availability and the proportion of dwarf males. When hermaphrodites appear, all hermaphrodites become protandric simultaneous hermaphrodites. Furthermore, high mortality and poor resource availability favor dwarf males because of their early maturation and weakened sperm competition. In conclusion, we showed that combining sex allocation and life history theories is a useful way to understand various sexual systems in barnacles and perhaps in other organisms as well. (c) 2012 Elsevier Ltd. All rights reserved.

Sex change is known from various fish species. In many polygynous species, the largest female usually changes sex to male when the dominant male disappeared, as predicted by the classical size-advantage model. However, in some fishes, the disappearance of male often induces sex change by a smaller female, instead of the largest one. The halfmoon triggerfish Sufflamen chrysopterum is one of such species. We conducted both field investigation and theoretical analysis to test the hypothesis that variation in female fecundity causes the sex change by less-fertile females, even if they are not the largest. We estimated the effect of body length and residual body width (an indicator of nutrition status) on clutch size based on field data. Sex-specific growth rates were also estimated from our investigation and a previous study. We incorporated these estimated value into an evolutionarily stable strategy model for status-dependent size at sex change. As a result, we predict that rich females change sex at a larger size than poor ones, since a rich fish can achieve high reproductive success as a female. In some situations, richer females no longer change sex (i.e. lifelong females), and poorer fish changes sex just after maturation (i.e. primary males). We also analyzed the effect of size-specific growth and mortality. © 2012 Elsevier Ltd.

Thoracican barnacles show one of the most diverse sexual systems in animals: hermaphroditism, dioecy (males and females), and androdioecy (males and hermaphrodites). In addition, when present, male barnacles are very small and are called "dwarf males". The diverse sexual systems and male dwarfism in this taxon have attracted both theoretical and empirical biologists. In this article, we review the theoretical studies on barnacles' sexual systems in the context of sex allocation and life history theories. We first introduce the sex allocation models by Charnov, especially in relation to the mating group size, and a new expansion of his models is also proposed. We then explain three studies by Yamaguchi et al., who have studied the interaction between sex allocation and life history in barnacles. These studies consistently showed that limited mating opportunity favors androdioecy and dioecy over hermaphroditism. In addition, other factors, such as rates of survival and availability of food, are also important. We discuss the importance of empirical studies testing these predictions and how empirical studies interact with theoretical constructs.

Some simultaneously hermaphroditic animals are known to digest received sperm. To investigate the effect of sperm digestion on the sex allocation of simultaneous hermaphrodites, we constructed models about evolutionarily stable resource allocation between male and female functions. We assumed that resource obtained from sperm digestion is used for gametogenesis (sperm and/or egg production). As a result, we found that sperm digestion increases the evolutionarily stable allocation to male function under finite number of matings. This is because excess sperm function as nuptial gift or paternal investment when at least a fraction of digested sperm is translated into eggs. Therefore, some factors which affect the assurance of paternity for sperm donors, such as cryptic female choice and/or sperm displacement, may change the result. In addition, this result implies that sperm digestion does not necessarily make male role less preferred. Further studies on the usage of donated sperm are required to test the validity of our models.

We analyze the online learning of a Perceptron (student) from signals produced by a single Perceptron (teacher) in which both the student and the teacher suffer from external noise. We adopt three typical learning rules and treat the input and output noises. In order to improve learning when it fails in the sense that the student vector does not converge to the teacher vector, we use a method based on the optimal learning rate. Furthermore, in order to control learning, we propose a concrete method for the Perceptron rule in the output noise model. Finally, we analyze time domain ensemble online learning. The theoretical results agree quite well with the numerical simulation results.

Questions: Why do barnacles have many modes of sexuality, including hermaphroditism, androdioecy (large hermaphrodites with dwarf males), and dioecy (large females with dwarf males)? Can mating group size, relative body size, competitive advantage or survival rate of dwarf male individuals explain which type of sexuality is favoured by natural selection? Mathematical methods: We developed an ESS model to investigate factors affecting the optimal proportion of larvae that become dwarf males (q*). Allocation to male function of large hermaphrodites is calculated according to Charnov's sex allocation theory, although sperm competition with dwarf males is taken into account. Our model is based on a life history of androdioecious barnacles, which includes hermaphroditism (q* = 0) and dioecy (q* > 0 and the male allocation of large hermaphrodites = 0) as special cases. We incorporate average mating group size (m) into the model, together with body size, competitive advantage, and survival rate of dwarf males relative to large hermaphrodites. Results: The proportion of dwarf males, q*, increases from 0 (hermaphroditism) as mating group size decreases, and approaches 0.5 when group size, m, nears 0. At the latter extreme, large individuals should become females instead of hermaphrodites. Thus mating group size can explain the major trend of sexuality in barnacles: hermaphroditism in relatively large mating groups, androdioecy in smaller groups, and dioecy in even smaller groups. Relative body size, competitive advantage, and survival rate of dwarf males all have positive effects on the evolutionarily stable proportion of males. If there is a simple trade-off between body size and survival rate, survival rate will have the greater influence on sexuality.

Barnacles, marine crustaceans, have various patterns of sexuality depending on species including simultaneous hermaphroditism, androdioecy (hermaphrodites and dwarf males), and dioecy (females and dwarf males). We develop a model that predicts the pattern of sexuality in barnacles by two key environmental factors: (i) food availability and (ii) the fraction of larvae that settle on the sea floor. Populations in the model consist of small individuals and large ones. We calculate the optimal resource allocation toward male function, female function and growth for small and large barnacles that maximizes each barnacle's lifetime reproductive success using dynamic programming. The pattern of sexuality is defined by the combination of the optimal resource allocations. In our model, the mating group size is a dependent variable and we found that sexuality pattern changes with the food availability through the mating group size: simultaneous hermaphroditism appears in food-rich environments, where the mating group size is large, protandric simultaneous hermaphroditism appears in intermediate food environments, where the mating group size also takes intermediate value, the other sexuality patterns, androdioecy, dioecy, and sex change are observed in food-poor environments, where the mating group size is small. Our model is the first one where small males can control their growth to large individuals, and hence has ability to explain a rich spectrum of sexual patterns found in barnacles. (c) 2008 Elsevier Ltd. All rights reserved.

Barnacles, marine crustaceans, have three sexual patterns: simultaneous hermaphroditism, dioecy and androdioecy. In dioecy and androdioecy, large individuals (females and hermaphrodites, respectively) are attached by dwarf males. Depending on species, some dwarf males grow up, others do not in their life time. To investigate which environmental conditions affect growth patterns of dwarf males of barnacles, we investigate the evolutionarily stable life history strategy of dwarf males using Pontryagin's maximum principle. Sperm competition among dwarf males and that among dwarf males and large hermaphrodites is taken into account. Dwarf males grow up in food-rich environments, while they do not grow at all in food-poor environments. ESS of the resource allocation schedule between reproduction and growth follows an "intermediate growth strategy" (simultaneous growth and reproduction) for dioecious species, in which sperm competition is not severe. On the other hand, it approaches "bang-bang control" (switching from allocating all resources toward growth then to reproduction), as sperm competition against surrounding large hermaphrodites becomes severe in androdioccious species. (c) 2006 Elsevier Ltd. All rights reserved.

We analyze the on-line learning of a Perceptron from signals produced by a single Perceptron suffering from external noise or by two independent Perceptrons without noise. We adopt typical three learning rules in both single-teacher and two-teacher cases. For the single-teacher case, we treat the input and output noises and for the two-teacher case, we assume that signals are given by two teachers with a definite probability. In the single-teacher case, in order to improve the learning when it does not succeed in the sense that the student vector does not converge to the teacher vector, we use two methods: a method based on the optimal learning rate and an averaging method. Furthermore, we obtain an asymptotic form of the generalization error using an optimal learning rate for the three learning rules, and we estimate noise parameters using the simulation data by the averaging method. In the two-teacher case, for the Hebbian rule, we give analytical solutions of order parameters. Furthermore, we estimate noise parameters using the Perceptron rule by the averaging method. The theoretical results agree quite well with the numerical simulations.