Maternal effects on offspring size and number in mosquitofish,Gambusia holbrooki

Given a trade-off between offspring size and number, all mothers are predicted to produce the same optimal-sized offspring in a given environment. In many species, however, larger and/or older mothers produce bigger offspring. There are several hypotheses to explain this but they lack strong empirical support. In organisms with indeterminate growth, there is the additional problem that maternal size and age are positively correlated, so what are their relative roles in determining offspring size? To investigate this, we measured the natural relationship between maternal and offspring size in a wild population of Gambusia holbrooki (eastern mosquitofish), and experimentally disentangled the effects of maternal age and size on offspring size in the laboratory. In combination, our data indicate that the relationship between maternal and offspring size is nonlinear. Small mothers seem to produce larger than average offspring due to integer effects associated with very small broods. For extremely large mothers, which were only sampled in our wild data, these larger than average offspring may result from greater maternal resources or age effects. However, maternal age had no effect on offspring size or number in the laboratory experiment. Our results highlight the importance of sampling the full size–range of mothers when investigating maternal effects on offspring size. They also point to the difficulty of experimentally manipulating maternal size, because any change in size is invariably associated with a change in at least one factor affecting growth (be it temperature, food availability, or density) that might also have an indirect effect on offspring size.     

Evolution in heterogeneous populations: From migration models to fixation probabilities

Although dispersal is recognized as a key issue in several fields of population biology (such as behavioral ecology, population genetics, metapopulation dynamics or evolutionary modeling), these disciplines focus on different aspects of the concept and often make different implicit assumptions regarding migration models. Using simulations, we investigate how such assumptions translate into effective gene flow and fixation probability of selected alleles. Assumptions regarding migration type (e.g. source-sink, resident pre-emption, or balanced dispersal) and patterns (e.g. stepping-stone versus island dispersal) have large impacts when demes differ in sizes or selective pressures. The effects of fragmentation, as well as the spatial localization of newly arising mutations, also strongly depend on migration type and patterns. Migration rate also matters: depending on the migration type, fixation probabilities at an intermediate migration rate may lie outside the range defined by the low- and high-migration limits when demes differ in sizes. Given the extreme sensitivity of fixation probability to characteristics of dispersal, we underline the importance of making explicit (and documenting empirically) the crucial ecological/ behavioral assumptions underlying migration models.     

Females allocate differentially to offspring size and number in response to male effects on female and offspring fitness

Female investment in offspring size and number has been observed to vary with the phenotype of their mate across diverse taxa. Recent theory motivated by these intriguing empirical patterns predicted both positive (differential allocation) and negative (reproductive compensation) effects of mating with a preferred male on female investment. These predictions, however, focused on total reproductive effort and did not distinguish between a response in offspring size and clutch size. Here, we model how specific paternal effects on fitness affect maternal allocation to offspring size and number. The specific mechanism by which males affect the fitness of females or their offspring determines whether and how females allocated differentially. Offspring size is predicted to increase when males benefit offspring survival, but decrease when males increase offspring growth rate. Clutch size is predicted to increase when males contribute to female resources (e.g. with a nuptial gift) and when males increase offspring growth rate. The predicted direction and magnitude of female responses vary with female age, but only when per-offspring paternal benefits decline with clutch size. We conclude that considering specific paternal effects on fitness in the context of maternal life-history trade-offs can help explain mixed empirical patterns of differential allocation and reproductive compensation.     

Assessing the roles of population density and predation risk in the evolution of offspring size in populations of a placental fish

Population density is an ecological variable that is hypothesized to be a major agent of selection on offspring size. In high-density populations, high levels of intraspecific competition are expected to favor the production of larger offspring. In contrast, lower levels of intraspecific competition and selection for large offspring should be weaker and more easily overridden by direct selection for increased fecundity in low-density populations. Some studies have found associations between population density and offspring size consistent with this hypothesis. However, their interpretations are often clouded by a number of issues. Here, we use data from a 10-year study of nine populations of the least killifish, Heterandria formosa, to describe the associations of offspring size with habitat type, population density, and predation risk. We found that females from spring populations generally produced larger offspring than females from ponds; however, the magnitude of this difference varied among years. Across all populations, larger offspring were associated with higher densities and lower risks of predation. Interestingly, the associations between the two ecological variables (density and predation risk) and offspring size were largely independent of one another. Our results suggest that previously described genetic differences in offspring size are due to density-dependent natural selection.     

The trade-off between number and size of offspring in humans and other primates

Life-history theory posits a fundamental trade-off between number and size of offspring that structures the variability in parental investment across and within species. We investigate this 'quantity-quality' trade-off across primates and present evidence that a similar trade-off is also found across natural-fertility human societies. Restating the classic Smith-Fretwell model in terms of allometric scaling of resource supply and offspring investment predicts an inverse scaling relation between birth rate and offspring size and a (-1/4) power scaling between birth rate and body size. We show that these theoretically predicted relationships, in particular the inverse scaling between number and size of offspring, tend to hold across increasingly finer scales of analyses (i.e. from mammals to primates to apes to humans). The advantage of this approach is that the quantity-quality trade-off in humans is placed into a general framework of parental investment that follows directly from first principles of energetic allocation.     

Indeterminate growth is selected by a trade-off between high fecundity and risk avoidance in stochastic environments

 We developed a stage-structured model to describe optimal energy allocation among growth, reproduction, and survival. Our model includes stochastic fluctuations in survival rate at age 0 but constant survival rate at older ages. Many mammals and birds cease to grow after maturity (i.e., determinate growth), whereas organisms in a number of other taxa grow beyond maturation (i.e., indeterminate growth). We discuss the conditions under which each of the following strategies is optimal: (I) semelparity, (II) iteroparity with determinate growth, and (III) iteroparity with indeterminate growth. Our model demonstrates that iteroparity with indeterminate growth is selected for when a nonlinear relationship exists between weight and energy production; this strategy is also often selected for in stochastic environments, even with a linear relationship between weight and energy production. The optimal strategy in stochastic environments is to maximize the long-term population growth rate, which does not correspond with maximization of total fecundity. The optimal life history is determined by a balance between spreading a risk and increasing the number of offspring. Our model suggests that optimal life history strategy depends on the magnitude of environmental fluctuations, the advantage of investing in growth, the cost of survival, and the nonlinearity between weight and energy production. Received: February 20, 2002 / Accepted: September 20, 2002 Acknowledgments We thank Drs. Y. Matsumiya, K. Morita, K. Shirakihara, and Y. Watanabe for encouragement and helpful advice. We also thank the responsible editor and anonymous reviewers for helpful comments. This work was supported by a Japan Society for the Promotion of Science grant to H.M. Correspondence to:Y. Katsukawa     

Cross-cultural analysis of migration rates: effects of geographic distance and population size.

A model is developed that treats migration rates among populations as a function of the geographic distance between them and the size of both sources and recipient population. Specifically, mij/mjj = a(Ni/Nj)pe-bd, where mij/mjj is the relative migration rate into population j from population i, Ni is the size of the source population, Nj is the size of the recipient population, d is the geographic distance between populations i and j, p is a measure of differential density-dependence, b is a measure of distance decay, and a is an adjustment parameter with little demographic meaning. Methods of parameter estimation and hypothesis testing using maximum likelihood are outlined. These methods are applied to migration matrix data from 13 samples obtained from the literature representing a wide range of ecological settings. All samples show a significant effect of geographic distance on migration, and all but one show a significant effect of differential population size. All but one sample show an overall tendency for migration to be negative density-dependent; that is, the relative migration rate is greater from larger populations to smaller populations than the reverse.     

Optimal size and number of propagules: allowance for discrete stages and effects of maternal size on reproductive output and offspring fitness

Existing optimality models of propagule size and number are not appropriate for many organisms. First, existing models assume a monotonically increasing offspring fitness/propagule size relationship. However, offspring survival during certain stages may decrease with increasing propagule size, generating a peaked offspring fitness/propagule size function (e.g., egg size in oxygen-limited aquatic environments). Second, existing models typically do not consider maternal effects on total reproductive output and the expression of offspring survival/propagule size relationships. However, larger females often have greater total egg production and may provide better habitats for their offspring. We develop a specific optimality model that incorporates these effects and test its predictions using data from salmonid fishes. We then outline a general model without assuming specific functional forms and test its predictions using data from freshwater fishes. Our theoretical and empirical results illustrate that, when offspring survival is negatively correlated with propagule size, optimal propagule size is larger in better habitats. When larger females provide better habitats, their optimal propagule size is larger. Nevertheless, propagule number should increase more rapidly than propagule size for a given increase in maternal size. In the absence of density dependence, females with greater relative reproductive output (i.e., for a given body size) should produce more but not larger propagules.     

Maternal effects on offspring size in a natural population of the viviparous tsetse fly

1. Theory predicts that mothers should adaptively adjust reproductive investment depending on current reserves and future reproductive opportunities. Females in better intrinsic state, or with more resources, should invest more in current reproduction than those with fewer resources. Across the lifespan, investment may increase as future reproductive opportunities decline, yet may also decline with reductions in intrinsic state. 2. Across many species, larger mothers produce larger offspring, but there is no theoretical consensus on why this is so. This pattern may be driven by variation in maternal state such as nutrition, yet few studies measure both size and nutritional state or attempt to tease apart confounding effects of size and age. 3. Viviparous tsetse flies (Glossina species) offer an excellent system to explore patterns of reproductive investment: females produce large, single offspring sequentially over the course of their relatively long life. Thus, per‐brood reproductive effort can be quantified by offspring size. 4. While most tsetse reproduction research has been conducted on laboratory colonies, maternal investment was investigated in this study using a unique field method where mothers were collected as they deposited larvae, allowing simultaneous mother‐offspring measurements under natural conditions. 5. It was found that larger mothers and those with a higher fat content produced larger offspring, and there was a trend for older mothers to produce slightly larger offspring. 6. The present results highlight the importance of measuring maternal nutritional state, rather than size alone, when considering maternal investment in offspring. Implications for understanding vector population dynamics are also discussed.     

The estimation of population size,migration rates and survival in a stratified population

Summary Estimates of survival, migration rates, and population size are developed for a triple catch marking experiment onn (n>-2) areas with migration among all areas and death in all areas occurring, but no recruitment (birth). This repressents the extension to three sampling times of the method ofChapman andJunge (1956) for estimates in a stratified population. The method is further extented to allow for ‘losses on capture’.     

The influence of maternal age and mating frequency on egg size and offspring performance in Callosobruchus maculatus (Coleoptera: Bruchidae)

Maternal age influences offspring quality of many species of insects. This observed maternal age influence on offspring performance may be mediated through maternal age effects on egg size, which in turn may be directly influenced by the female's nutritional state. Thus, behaviors that influence a female's nutritional status will indirectly influence egg size, and possibly offspring life histories. Because males provide nutrients to females in their ejaculate, female mating frequency is one behavior which may influence her nutritional status, and thus the size of her eggs and the performance of her offspring. In this paper, I first quantify the influences of maternal age on egg size and offspring performance of the bruchid beetle, Callosobruchus maculatus. I then examine whether nutrients transferred during copulation reduce the magnitude of maternal age effects on egg size and larval performance when mothers are nutrient-stressed. Egg size and egg hatchability decreased, and development time increased, with increasing maternal age. Multiple mating and adult feeding by females both resulted in increased egg size. This increase in egg size of females mated multiply did not translate into reduced development time or increased body size and egg hatchability, but did correlate with improved survivorship of offspring produced by old mothers. Thus, it appears that because the influence of mating frequency on egg size is small relative to the influence of maternal age, the influence of nutrients derived from multiple mating on offspring life history is almost undetectable (detected only as a small influence on survivorship). For C. maculatus, female multiple mating has been demonstrated to increase adult female survivorship (Fox 1993a), egg production (Credland and Wright 1989; Fox 1993a), egg size, and larval survivorship, but, contrary to the suggestion of Wasserman and Asami (1985), multiple mating had no detectable influence on offspring development time or body size.     

Body mass, population density, and offspring number in mammals

The negative relationship between population density and body mass with the body mass exponent of -0.75 implies that the energy flow through populations of small- and large-bodied species is the same, for individual metabolism scales to body mass raised to the power of +0.75. This relationship called the energetic equivalence rule, has often been observed for mammal species assemblages studied at regional scales. Here we suggest a demography-based mechanism that may generate it. Having analyzed about 130 literature sources, mostly in Russian, we collected demography and body-mass data for 88 mammalian species from the territory and coastal waters of the former Soviet Union. The data were used to construct a number of interspecific relationships. It is shown that (1) the number of offspring per lifetime is approximately inversely proportional to the relative mass at birth (the exponent is not significantly different from -1), (2) the average lifespan is proportional to body mass to the 0.25 power, (3) body mass at birth is proportional to the adult body mass. We develop a simple theory to demonstrate that relations (1) to (3) entail the energetic equivalence rule. The theory also allows us to explain violation of this rule (in non-flying birds, for example), namely, to predict the exponent of relation (1) for any given exponent of the relation between population density and body mass. This is possible because relations (2) and (3) are likely to more universally hold than relation (1). Finally, since natural selection acts on individual traits rather than on population-level ones such as population density, the theory opens up the way to an evolutionary explanation for the energetic equivalence rule.     

Scaling of offspring number and mass to plant and animal size: model and meta-analysis

The scaling of reproductive parameters to body size is important for understanding ecological and evolutionary patterns. Here, we derived allometric relationships for the number and mass of seeds, eggs and neonates from an existing model on population production. In a separate meta-analysis, we collected 79 empirical regressions on offspring mass and number covering different taxa and various habitats. The literature review served as a validation of the model, whereas, vice versa, consistency of isolated regressions with each other and related ecological quantities was checked with the model. The total offspring mass delivered in a reproductive event scaled to adult size with slopes in the range of about 3/4 to 1. Exponents for individual seed, egg and neonate mass varied around 1/2 for most heterotherms and between 3/4 and 1 for most homeotherms. The scaling of the progeny number released in a sowing, clutch or litter was opposite to that of their size. The linear regressions fitted into a triangular envelope where maximum offspring mass is limited by the size of the adult. Minimum seed and egg size scaled with weight exponents of approximately 0 up to 1/4. These patterns can be explained by the influence of parents on the fate of their offspring, covering the continuum of r-strategists (pelagic–aquatic, arial, most invertebrates, heterotherms) and K-strategists (littoral–terrestrial, some invertebrates, homeotherms).     

Evolution of polyandry by reduction in progeny number variance in structured populations

When there is a variation in the quality of males in a population, multiple mating can lead to an increase in the genetic fitness of a female by reducing the variance of the progeny number. The extent of selective advantage obtainable by this process is investigated for a population subdivided into structured demes. It is seen that for a wide range of model parameters (deme size, distribution of male quality, local resource level), multiple mating leads to a considerable increase in the fitness. Frequency-dependent selection or a stable coexistence between polyandry and monandry can also result when the possible costs involved in multiple mating are taken into account.     

Multiple resources and the optimal balance between size and number of offspring

Summary We extend the classical Smith-Fretwell model for the optimal size of an offspring to the case of allocation of two or more fitness enhancing resources. Unlike the results of the single-resource model, the new model predicts that the optimal allocations will depend on the resource pool sizes. We apply this new model to the problem of carbon and nitrogen allocation to seeds and conclude (1) that the optimal seed size (carbon allocation) should be positively correlated with the ratio of the size of the carbon and nitrogen pools available for investment to offspring (C/N ratio) and (2) that there should be a negative correlation between seed size and absolute seed nitrogen content. These results may account for some of the within- and between-plant variation in resource allocation to seeds.     

The evolution of offspring size and number: a test of the Smith-Fretwell model in three species of crickets

Most models of parental investment in offspring assume a trade-off between propagule size and number, and an increasing concave down function relating offspring fitness to propagule size. In this study, we test these two fundamental assumptions, using three closely related species of crickets, Gryllus firmus, G. veletis, and G. pennsylvanicus. Egg weight, 35-day fecundity and 35-day egg biomass were estimated in a population of each species, and the relationships between these reproductive traits and date of egg laying and body size were estimated. The relationships between egg weight and offspring survival were also sought for eggs buried at different depths, soil moistures, and soil types (G. firmus and G. veletis), as well as in the field (G. pennsylvanicus). A trade-off between egg weight and 35-day fecundity was revealed in a multivariate analysis taking into account among-species variation in egg weight and body size. Independent of the environmental conditions affecting the eggs, a positive correlation existed between the number of larvae that emerged from the soil and propagule weight in each species. Therefore, these findings provide partial support for the assumptions considered in the models mentioned above. A single optimal egg size was favored in two out of the three sets of conditions in which the functions relating egg weight to larval survival could be derived. The conditions encountered by the eggs, however, influenced the average survival of the larvae, as well as the shape of the relationship between egg weight and offspring survival. This suggests that cricket eggs frequently face heterogeneous environments with respect to egg and hatchling survival; the implication of habitat heterogeneity on the evolution of an optimal egg size is considered. The relationships between the reproductive components and female age and size, as well as between egg size and variation in cricket life-history, are discussed in an ecological and evolutionary context.     

Smaller amphipod mothers show stronger trade-offs between offspring size and number

Trade-offs between embryo mass and number were studied in 10 populations of the freshwater amphipod Gammarus minus . Trade-offs were stronger in populations with small brooding females than in those with larger brooding females. Relationships between embryo mass and maternal body mass were also stronger in populations dominated by small versus large brooding females. These patterns are likely the result of morphological constraints, at least in part. Embryo size is more affected by brood size and maternal size in small mothers, probably because of offspring-packaging constraints associated with small brood pouches. Energy constraints appear to be less important. These results suggest that body size may not only affect the magnitude of individual life-history traits, as is well known, but also the covariance between traits.     

The inbreeding effective number and the effective number of alleles in a population that varies in size

Consider a population that does not change in size. If it is assumed that there are an infinite number of possible neutral alleles at a locus and u is the probability that a particular gene mutates to some other gene in one generation, the effective number of alleles n_e is computed to be 4N_eu + 1, where N_e is the inbreeding effective population number. It is assumed in this paper that the number of individuals in a monoecious population, or the numbers of males and females in a dioecious population, are states in a finite irreducible Markov chain. In general it is impossible to obtain a single value of n_e. In some cases where the computation of n_e is possible, the results are as follows. When the population is monoecious, N_e is the reciprocal of the asymptotic average, over population sizes, of the probabilities that two gametes uniting to form an individual came from the same individual one generation earlier. In dioecious populations, N_e is the reciprocal of the long-run average of the probabilities that two homologous genes in separate individuals of one generation came from the same individual one generation earlier. Special cases are discussed.