Effects of density dependent sex allocation on the dynamics of a simultaneous hermaphroditic population: Modelling and analysis

In this work we present a mathematical model describing the dynamics of a population where sex allocation remains flexible throughout adult life and so can be adjusted to current environmental conditions. We consider that the fractions of immature individuals acquiring male and female sexual roles are density dependent through nonlinear functions of a weighted total population size. The main goal of this work is to understand the role of life-history parameters on the stabilization or destabilization of the population dynamics.The model turns out to be a nonlinear discrete model which is analysed by studying the existence of fixed points as well as their stability conditions in terms of model parameters. The existence of more complex asymptotic behaviours of system solutions is shown by means of numerical simulations.Females have larger fertility rate than males. On the other hand, increasing population density favours immature individuals adopting the male role. A positive equilibrium of the system exists whenever fertility and survival rates of one of the sexual roles, if shared by all adults, allow population growing while the opposite happens with the other sexual role. In terms of the female inherent net reproductive number, η_F, it is shown that the positive equilibria are stable when η_F is larger and closed to 1 while for larger values of η_F a certain asymptotic assumption on the investment rate in the female function implies that the population density is permanent. Depending on the other parameters values, the asymptotic behaviour of solutions becomes more complex, even chaotic. In this setting the stabilization/destabilization effects of the abruptness rate in density dependence, of the survival rates and of the competition coefficients are analysed.     

Evolutionary sex allocation theory explains sex ratios in natural Plasmodium falciparum infections

Malaria transmission is achieved by sexual stages, called gametocytes, and the proportion of gametocytes that are male versus female (sex ratio) influences transmission success. In malaria model systems, variation in gametocyte sex ratios can be explained by the predictions of evolutionary sex allocation theory. We test these predictions using natural Plasmodium falciparum infections. The predicted negative correlation between sex ratio and gametocyte density holds: the sex ratio increases when gametocyte densities decrease, and this is most apparent in single genotype infections and in the dry season. We do not observe higher gametocyte sex ratios in mixed compared with single genotype infections.     

Profound Effects of Population Density on Fitness-Related Traits in an Invasive Freshwater Snail

Population density can profoundly influence fitness-related traits and population dynamics, and density dependence plays a key role in many prominent ecological and evolutionary hypotheses. Here, we evaluated how individual-level changes in population density affect growth rate and embryo production early in reproductive maturity in two different asexual lineages of Potamopyrgus antipodarum, a New Zealand freshwater snail that is an important model system for ecotoxicology and the evolution of sexual reproduction as well as a potentially destructive worldwide invader. We showed that population density had a major influence on individual growth rate and early-maturity embryo production, effects that were often apparent even when comparing treatments that differed in population density by only one individual. While individual growth rate generally decreased as population density increased, we detected a hump-shaped relationship between embryo production and density, with females from intermediate-density treatments producing the most embryos and females from low- and high-density treatments producing the fewest embryos. The two lineages responded similarly to the treatments, indicating that these effects of population density might apply more broadly across P. antipodarum. These results indicate that there are profound and complex relationships between population density, growth rate, and early-maturity embryo production in at least two lineages of this important model system, with potential implications for the study of invasive populations, research on the maintenance of sex, and approaches used in ecotoxicology.     

Carry-over effects,sequential density dependence and the dynamics of populations in a seasonal environment

Most animal populations have distinct breeding and non-breeding periods, yet the implications of seasonality on population dynamics are not well understood. Here, we introduce an experimental model system to study the population dynamics of two important consequences of seasonality: sequential density dependence and carry-over effects (COEs). Using a replicated seasonal population of Drosophila, we placed individuals at four densities in the non-breeding season and then, among those that survived, placed them to breed at three different densities. We show that COEs arising from variation in non-breeding density negatively impacts individual performance by reducing per capita breeding output by 29–77%, implying that non-lethal COEs can have a strong influence on population abundance. We then parametrized a bi-seasonal population model from the experimental results, and show that both sequential density dependence and COEs can stabilize long-term population dynamics and that COEs can reduce population size at low intrinsic rates of growth. Our results have important implications for predicting the successful colonization of new habitats, and for understanding the long-term persistence of seasonal populations in a wide range of taxa, including migratory organisms.     

Complex consequences of increased density for reproductive output in an invasive freshwater snail

Population density can have profound, often negative effects on fitness-related traits and population dynamics, and density dependence is of central importance to many prominent ecological and evolutionary hypotheses. Here, we used experimental manipulations of food, population density, and water conditioning to characterize the mechanisms underlying reproductive density-dependence in Potamopyrgus antipodarum. This New Zealand freshwater snail is a prominent model system for invasion biology, ecotoxicology, and the maintenance of sexual reproduction. We demonstrated that a primary source of negative density-dependence is food limitation, but surprisingly, we found that P. antipodarum reproductive output was much higher in high density versus low-density conditions when food was adequate. We then used manipulations of water environment to demonstrate that these positive effects of high density are likely caused by a waterborne substance produced by P. antipodarum. Altogether, these results indicate that there are strong and complex connections between food availability, density, and reproductive output in this important model system that could influence the dynamics of invasive populations, the costs and benefits of sex, and the approaches used for ecotoxicology studies.     

Negative or positive density‐dependence in movements depends on climatic seasons: The case of a Neotropical marsupial

One of the major challenges in animal ecology is to understand the factors and processes driving movement behaviour. Although density may influence movement patterns, the occurrence and nature of density‐dependence in animal movements are still unclear, particularly whether it may vary among populations of a species, or across time within a population. Here, we evaluate the occurrence and nature of density‐dependence in the movements of a Neotropical marsupial, the Grey four‐eyed opossum Philander frenatus (Didelphidae, Didelphimorphia). We quantified fine‐scale path tortuosity of individuals inhabiting continuous forest areas and forest fragments, in different climatic seasons (humid vs. super‐humid). We also determined the relative importance of population size compared to sex and body mass on movements, using a model‐selection approach. In forest fragments, path tortuosity increased with population size in the super‐humid season, but decreased in the humid season. In the continuous forest, path tortuosity was affected only by sex and body mass, being slightly higher in males and negatively related to body mass. The occurrence of density‐dependence on movements only in forest fragments is likely to reflect the higher overall density of P. frenatus in small forest fragments. The variation in the nature of density‐dependence between climatic seasons is likely to reflect a trade off between foraging over large areas (humid season, low resource availability) versus avoiding agonistic encounters (super‐humid season, high resource availability). Our results show that (i) density‐dependence in movements may be context‐dependent occurring only in areas of relatively high overall population density; and (ii) density may affect movements in different ways at different climatic seasons.     

Influence of density dependence on the detection of trends in unobserved life-history stages

In many species, certain life-history stages are difficult or impossible to observe directly, hampering management. Often more easily observed stages are monitored instead, but the extent to which various forms of uncertainty cloud our ability to discern trends in one critical life-history stage by observing another is poorly studied. We develop a stochastic simulation model for threatened California coho salmon Oncorhynchus kisutch to examine how well trends in one stage can be detected from observations of another. In particular, we use the model to examine the effect density dependence has on our ability to detect trends. We present a structural form for the transition between life-history stages that encompasses the common functional forms: density independence, Beverton–Holt compensatory density dependence and Ricker-type over-compensation. In small populations, such density dependence is often ignored. However, it may in fact be extremely important, for example if population decline was caused by a decrease in carrying capacity. Our results show that density dependence in any life-history transition significantly reduces the ability to detect trends in abundance; critical but inaccessible stages cannot generally be studied by monitoring more easily observed stages, especially if density dependence is present for any life-cycle transition.     

Daphnia females adjust sex allocation in response to current sex ratio and density

Cyclical parthenogenesis presents an interesting challenge for the study of sex allocation, as individuals’ allocation decisions involve both the choice between sexual and asexual reproduction, and the choice between sons and daughters. Male production is therefore expected to depend on ecological and evolutionary drivers of overall investment in sex, and those influencing male reproductive value during sexual periods. We manipulated experimental populations, and made repeated observations of natural populations over their growing season, to disentangle effects of population density and the timing of sex from effects of adult sex ratio on sex allocation in cyclically parthenogenetic Daphnia magna. Male production increased with population density, the major ecological driver of sexual reproduction; however, this response was dampened when the population sex ratio was more male‐biased. Thus, in line with sex ratio theory, we show that D. magna adjust offspring sex allocation in response to the current population sex ratio.     

Phenotypic plasticity in sex allocation and body size leads to trade-offs between male function and growth in a simultaneously hermaphroditic fish

Phenotypic plasticity in sex allocation enables organisms to maximize reproductive success in variable environments, and thus may generate different sex allocation patterns among populations that experience different mating opportunities. In this experiment, I test whether sex allocation is phenotypically plastic in Serranus tortugarum, a simultaneously hermaphroditic fish, by using reciprocal transplants among four reef study sites with populations at high and low densities and significant differences in sex allocation. Fish transplanted across different densities were predicted to alter sex allocation and body size through trade-offs in investments to somatic growth and male and/or female reproduction. As a control for effects of transplanting, I also transplanted fish across study sites with the same densities and marked and returned fish to their original study sites. As predicted, sex allocation and body size shifted significantly for fish transplanted across different densities but not for those transplanted across the same densities. Separate analyses revealed that the treatment effect on sex allocation was driven strongly by a reduction in male investment by fish transplanted from high to low density, and this reduction in male investment was accompanied by an increase in body size. Fish transplanted from low to high density did not appear to change either male or female investments, but they were smaller than transplants from low to low density. A trade-off between male and female function was not evident, but phenotypic plasticity in body size suggested a trade-off between growth and male function when sex allocation is adjusted. Large-scale empirical tests of sex allocation in the field are relatively rare, and the results of this experiment give novel insights into how animals respond to a change in mating opportunities under natural conditions. The effects of logistical problems associated with fieldwork, such as mortality of experimental animals, are considered in the discussion.     

Production of male flowers does not decrease with plant size in insect‐pollinated Sagittaria trifolia,contrary to predictions of size‐dependent sex allocation

Abstract It has been proposed that relative allocation to female function increases with plant size in animal‐pollinated species. Previous investigations in several monoecious Sagittaria species seem to run contrary to the prediction of size‐dependent sex allocation (SDS), throwing doubt on the generalization of SDS. Plant size, phenotypic gender, and flower production were measured in experimental populations of an aquatic, insect‐pollinated herb Sagittaria trifolia (Alismataceae) under highly different densities. The comparison of ramets produced clonally can reduce confounding effects from genetic and environmental factors. In the high‐density population, 48% of ramets were male without female flowers, but in the low‐density population all ramets were monoecious. We observed allometric growth in reproductive allocation with ramet size, as evident in biomass of reproductive structures and number of flowers. However, within both populations female and male flower production were isometric with ramet size, in contrast to an allometric growth in femaleness as predicted by SDS. Phenotypic gender was not related to ramet size in either population. The results indicated that large plants may increase both female and male function even in animal‐pollinated plants, pointing towards further studies to test the hypothesis of size‐dependent sex allocation using different allocation currencies.     

Root morphological responses to population density vary with soil conditions and growth stages: The complexity of density effects

AimHow plants cope with increases in population density via root plasticity is not well documented, although abiotic environments and plant ontogeny may have important roles in determining root response to density. To investigate how plant root plasticity in response to density varies with soil conditions and growth stages, we conducted a field experiment with an annual herbaceous species (Abutilon theophrasti).MethodsPlants were grown at low, medium, and high densities (13.4, 36.0, and 121.0 plants m⁻², respectively), under fertile and infertile soil conditions, and a series of root traits were measured after 30, 50, and 70 days.ResultsRoot allocation increased, decreased, or canalized in response to density, depending on soil conditions and stages of plant growth, indicating the complex effects of population density, including both competitive and facilitative effects.Main conclusionsRoot allocation was promoted by neighbor roots at early stages and in abundant resource availability, due to low‐to‐moderate belowground interactions among smaller plants, leading to facilitation. As plants grew, competition intensified and infertile soil aggravated belowground competition, leading to decreased root allocation in response to density. Root growth may be more likely restricted horizontally rather than vertically by the presence of neighbor, suggesting a spatial orientation effect in their responses to density. We emphasized the importance of considering effects of abiotic conditions and plant growth stages in elucidating the complexity of density effects on root traits.     

Loss of animal seed dispersal increases extinction risk in a tropical tree species due to pervasive negative density dependence across life stages

Overhunting in tropical forests reduces populations of vertebrate seed dispersers. If reduced seed dispersal has a negative impact on tree population viability, overhunting could lead to altered forest structure and dynamics, including decreased biodiversity. However, empirical data showing decreased animal-dispersed tree abundance in overhunted forests contradict demographic models which predict minimal sensitivity of tree population growth rate to early life stages. One resolution to this discrepancy is that seed dispersal determines spatial aggregation, which could have demographic consequences for all life stages. We tested the impact of dispersal loss on population viability of a tropical tree species, Miliusa horsfieldii, currently dispersed by an intact community of large mammals in a Thai forest. We evaluated the effect of spatial aggregation for all tree life stages, from seeds to adult trees, and constructed simulation models to compare population viability with and without animal-mediated seed dispersal. In simulated populations, disperser loss increased spatial aggregation by fourfold, leading to increased negative density dependence across the life cycle and a 10-fold increase in the probability of extinction. Given that the majority of tree species in tropical forests are animal-dispersed, overhunting will potentially result in forests that are fundamentally different from those existing now.     

Condition Dependent Effects on Sex Allocation and Reproductive Effort in Sequential Hermaphrodites

Theory predicts the optimal timing of sex change will be the age or size at which half of an individual''s expected fitness comes through reproduction as a male and half through reproduction as a female. In this way, sex allocation across the lifetime of a sequential hermaphrodite parallels the sex allocation of an outbreeding species exhibiting a 1∶1 ratio of sons to daughters. However, the expectation of a 1∶1 sex ratio is sensitive to variation in individual condition. If individuals within a population vary in condition, high-condition individuals are predicted to make increased allocations to the sex with the higher variance in reproductive success. An oft-cited example of this effect is seen in red deer, Cervus elaphus, in which mothers of high condition are more likely to produce sons, while those in low condition are more likely to produce daughters. Here, we show that individual condition is predicted to similarly affect the pattern of sex allocation, and thus the allocation of reproductive effort, in sequential hermaphrodites. High-condition sex-changers are expected to obtain more than half of their fitness in the high-payoff second sex and, as a result, are expected to reduce the allocation of reproductive effort in the initial sex. While the sex ratio in populations of sequential hermaphrodites is always skewed towards an excess of the initial sex, condition dependence is predicted to increase this effect.     

Single‐ or multistage regulation in complex life cycles: does it make a difference?

Data on the different stages of complex life cycles are often rather unbalanced, especially those concerning the effects of density. How does this affect our understanding of a species’ population dynamics? Two discrete three‐stage models with overlapping generations and delayed maturation are constructed to address this question. They assume that survival or emigration in any life stage and/or reproduction can be density dependent. A typical pond‐breeding amphibian species with a well‐studied larval stage serves as an example. Numerical results show that the population dynamics resulting from density dependence at a single (e.g. the larval) stage can be decisively and unpredictably modified by density dependence in additional stages. Superposition of density‐dependent processes could thus be one reason for the difficulties in identifying density dependence in the field. Moreover, in a simulated source‐refuge system with habitat‐specific density‐dependent dispersal of juveniles density dependence in multiple stages can stabilize or destabilize the dynamics and produce misleading age structures. From an applied perspective this model shows that excluding multistage regulation prematurely clearly affects our ability to predict consequences of human impacts.     

Evidence for an even sex allocation in haplodiploid cyclical parthenogens

Recent theoretical work has shown that haplodiploid cyclical parthenogens, such as rotifers, are expected to have an equal frequency of male‐producing and resting‐egg producing females during their sexual phase. We tested this prediction by following sexual reproduction dynamics in two laboratory populations and one field population of the rotifer Brachionus plicatilis through two growing seasons. We recorded population density, proportion of sexual females, and sex allocation (the proportion of male‐producing sexual females as a fraction of total sexual females). We found this sex allocation ratio to vary from 0.3 to 1.0 in single sampling events. However, when we computed sex allocation by using the integrated densities of both male‐producing sexual females and resting‐egg producing sexual females over time, the two laboratory populations and one of the two field growing seasons showed sex allocation ratios that did not significantly differ from the expected value of 0.5.     

Density-dependent dispersal promotes female-biased sex allocation in viscous populations

A surprising result emerging from the theory of sex allocation is that the optimal sex ratio is predicted to be completely independent of the rate of dispersal. This striking invariance result has stimulated a huge amount of theoretical and empirical attention in the social evolution literature. However, this sex-allocation invariant has been derived under the assumption that an individual''s dispersal behaviour is not modulated by population density. Here, we investigate how density-dependent dispersal shapes patterns of sex allocation in a viscous-population setting. Specifically, we find that if individuals are able to adjust their dispersal behaviour according to local population density, then they are favoured to do so, and this drives the evolution of female-biased sex allocation. This result obtains because, whereas under density-independent dispersal, population viscosity is associated not only with higher relatedness—which promotes female bias—but also with higher kin competition—which inhibits female bias—under density-dependent dispersal, the kin-competition consequences of a female-biased sex ratio are entirely abolished. We derive analytical results for the full range of group sizes and costs of dispersal, under haploid, diploid and haplodiploid modes of inheritance. These results show that population viscosity promotes female-biased sex ratios in the context of density-dependent dispersal.     

Scale-specific determinants of a mixed beech and oak seedling–sapling bank under different environmental and biotic conditions

Based on the hypothesis that both plant size and local conspecific density influence allocation to female/male functions, we explored the relationship between plant height, local conspecific density, sexual expression, and fruit production in the andromonoecious shrub Caesalpinia gilliesii. We quantified the total number of perfect and staminate flowers, the pollen received and fruits produced per plant in two populations, and estimated phenotypic gender and fruit set. Local density failed to explain phenotypic gender, nevertheless, plant height and fruit set increased with local density in one population where, in addition, the slopes for the size-dependent sex allocation curve were steeper. As observed for other plant species, this suggests that between population differences in resource availability is the main underlying factor for the observed population differences in the size-dependent allocation pattern to flowers and fruits. On the other hand, the number of staminate and perfect flowers per plant increased with plant height and the fastest increase of staminate flowers resulted in a male-biased size-dependent sex allocation strategy in both populations. Since pollination intensity was not correlated with plant height in any population, the observed allocation strategy cannot be attributed to differences in pollen availability between different sized individuals, but to differences in plant size. Finally, because fruit set and total fruit number increased with plant height in one population, the obtained results provide further evidence that animal-pollinated, andromonoecious species may exhibit a male-biased size-dependent sex allocation strategy, which may favor female fecundity.     

Mischaracterising density dependence biases estimated effects of coloured covariates on population dynamics

Environmental effects on population growth are often quantified by coupling environmental covariates with population time series, using statistical models that make particular assumptions about the shape of density dependence. We hypothesized that faulty assumptions about the shape of density dependence can bias estimated effect sizes of temporally autocorrelated covariates. We investigated the presence of bias using Monte Carlo simulations based on three common per capita growth functions with distinct density dependent forms (θ-Ricker, Ricker and Gompertz), autocorrelated (coloured) ‘known’ environmental covariates and uncorrelated (white) ‘unknown’ noise. Faulty assumptions about the shape of density dependence, combined with overcompensatory intrinsic population dynamics, can lead to strongly biased estimated effects of coloured covariates, associated with lower confidence interval coverage. Effects of negatively autocorrelated (blue) environmental covariates are overestimated, while those of positively autocorrelated (red) covariates can be underestimated, generally to a lesser extent. Prewhitening the focal environmental covariate effectively reduces the bias, at the expense of the estimate precision. Fitting models with flexible shapes of density dependence can also reduce bias, but increases model complexity and potentially introduces other problems of parameter identifiability. Model selection is a good option if an appropriate model is included in the set of candidate models. Under the specific and identifiable circumstances with high risk of bias, we recommend prewhitening or careful modelling of the shape of density dependence.     

Male Aggregation Pheromones Inhibit Ideal Free Habitat Selection in Red Flour Beetles (<Emphasis Type="Italic">Tribolium castaneum</Emphasis>)

The ideal free distribution (IFD) predicts that individuals should be distributed between habitats in proportion to habitat suitability such that mean fitness is equal in each habitat. The IFD is useful in studies examining habitat selection, yet its key assumptions are often violated and the expected IFDs are not consistently detected. While the use of aggregation pheromones by insects is expected to evolve in systems that experience positive density dependence (Allee effect), through a series of experiments we test the hypothesis that aggregation pheromones may limit the ability of individuals to achieve an IFD. Using red flour beetles (Tribolium castaneum), we specifically test the prediction that beetles in groups with an equal sex ratio or in the presence of an artificial aggregation pheromone will deviate from an IFD, whereas female-only groups will achieve an IFD. We also test the hypothesis that aggregation pheromones evolved to promote Allee effects by testing the prediction that beetle fitness will show positive density dependence at low densities. Consistent with our first hypothesis, female groups achieved an IFD, while mixed sex groups and females in the presence of an aggregation pheromone in the low food habitat under-matched the IFD. We found no evidence of Allee effects at low density, but we did find evidence of strong negative density dependence. We demonstrate that the use of aggregation pheromones may negatively impact a population’s ability to achieve an IFD and cast doubt on the hypothesis that male aggregation pheromones evolve to promote Allee effects.     

Sex Allocation in a Colobine Monkey

In polygynous, sexual dimorphic species with higher variance in male reproductive success compared with females, females are expected to invest more heavily in sons than daughters within the constraints imposed by their physical condition (Science 1973; 179:90). Mothers in good condition, usually those of high rank, should produce more sons than females in poor condition or of low rank. We investigated sex allocation and sex‐biased maternal investment in a population of wild Hanuman langurs using rank and group size as approximations of female physical condition. Our results show that reproductive costs of sons were higher with both significantly longer interbirth intervals following male births and longer lactational periods for sons. Not in all groups did analyses of rank‐dependent sex allocation reveal the expected pattern of high‐ranking mothers producing more sons. However, sex ratio was significantly influenced by group size, with females from larger groups, i.e., in worse physical condition, producing a daughter‐biased sex ratio. In fact, only females of population‐wide superior physical condition can be expected to produce sons, because in Hanuman langurs males disperse and compete population‐wide. Thus, our results support the Trivers–Willard model and may explain the mixed evidence accruing from studies of single groups. We present a graphical model of how group size and dominance‐related differences in energy gain may influence sex allocation under different competitive regimes relative to overall resource availability. Tests of adaptive sex allocation models should consider whether reproductive competition of the preferred sex takes place primarily within a group or within the population.