Nonequilibrium coexistence in a competition model with nutrient storage

Resource competition theory predicts that, in equilibrium, the number of coexisting species cannot exceed the number of limiting resources. In some competition models, however, competitive interactions may result in nonequilibrium dynamics, allowing the coexistence of many species on few resources. The relevance of these findings is still unclear, since some assumptions of the underlying models are unrealistic. Most importantly, these models assume that individual growth directly reflects the availability of external resources, whereas real organisms can store resources, thereby decoupling their growth from external fluctuations. Here we study the effects of resource storage by extending the well-known Droop model to the context of multiple species and multiple resources. We demonstrate that the extended Droop model shows virtually the same complex dynamics as models without storage. Depending on the model parameters, one may obtain competitive exclusion, stable equilibrium coexistence, periodic and non-periodic oscillations, and chaos. Again, nonequilibrium dynamics allows for the coexistence of many species on few resources. We discuss our findings in the light of earlier work on resource competition, highlighting the role of luxury consumption, trade-offs in competitive abilities, and ecological stoichiometry.     

Coexistence of three specialist aphids on common milkweed, Asclepias syriaca

Coexistence of host-specific herbivores on plants is believed to be governed by interspecific interactions, but few empirical studies have systematically unraveled these dynamics. We investigated the role of several factors in promoting coexistence among the aphids Aphis nerii, Aphis asclepiadis, and Myzocallis asclepiadis that all specialize on common milkweed (Asclepias syriaca). Competitive exclusion is thought to occur when interspecific competition is stronger than intraspecific competition. Consequently, we investigated whether predators, mutualists, or resource quality affected the strength of intra- vs. interspecific competition among aphids in factorial manipulations of competition with exposure to predation, ants, and variable plant genotypes in three separate experiments. In the predation x competition experiment, predators reduced aphid per capita growth by 66%, but the strength of intra- and interspecific competition did not depend on predators. In the ants x competition experiment, ants reduced per capita growth of A. nerii and M. asclepiadis (neither of which were mutualists with ants) by approximately one-half. In so doing, ants ameliorated the negative effects of these competitors on ant-tended A. asclepiadis by two-thirds, representing a novel benefit of ant-aphid mutualism. Nevertheless, ants alone did not explain the persistence of competitively inferior A. asclepiadis as, even in the presence of ants, interspecific competition remained stronger than intraspecific competition. In the plant genotype x competition experiment, both A. asclepiadis and M. asclepiadis were competitively inferior to A. nerii, with the strength of interspecific competition exceeding that of intraspecific competition by 83% and 23%, respectively. Yet these effects differed among milkweed genotypes, and there were one or more plant genotypes for each aphid species where coexistence was predicted. A synthesis of our results shows that predators play little or no role in preferentially suppressing competitively dominant A. nerii. Nonetheless, A. asclepiadis benefits from ants, and A. asclepiadis and M. asclepiadis may escape competitive exclusion by A. nerii on select milkweed genotypes. Taken as a whole, the coexistence of three host-specific aphid species sharing the same resource was promoted by the dual action of ants as antagonists and mutualists and by genetic diversity in the plant population itself.     

Coexistence of intraguild predators and prey in resource-rich environments

The prevalence of intraguild predation (IGP) in productive environments has long puzzled ecologists. Theory predicts the exclusion of intraguild prey from such environments, but data consistently defy this expectation. This suggests that coexistence mechanisms at high resource productivity may differ from those at lower productivity. Here I present a mathematical model that investigates multiple coexistence mechanisms. I incorporate two biological features widely observed in IGP communities: intraspecific interference via cannibalism or superparasitism, and temporal refuges arising from differential sensitivities to abiotic variation. I develop predictions based on three aspects of the IG prey-IG predator interaction: mutual invasibility, transient dynamics, and long-term abundances. These predictions specify the conditions under which coexistence mechanisms reinforce vs. deter one another: when a competition-IGP trade-off allows coexistence at intermediate productivity a temporal refuge for the intraguild prey always allows coexistence at high productivity, but intraspecific interference does so only at a net fitness cost to the intraguild predator. Intraspecific interference that benefits the intraguild predator not only reduces tradeoff-mediated coexistence at intermediate productivity, but also undermines the refuge's coexistence-enhancing effect at high productivity. Different mechanism combinations yield characteristic signatures in time series data during transient dynamics. By judicious measurement of parameters and examining time series for critical signatures, one can elucidate the mechanisms that allow IGP to prevail in resource-rich environments.     

Exploring community assembly through an individual-based model for trophic interactions

Traditionally, the dynamics of community assembly has been analyzed by means of deterministic models of differential equations. Despite the theoretical advances provided by such models, they are restricted to questions about community-wide features. The individual-based modeling offers an opportunity to link bionomic features to patterns at the community scale, allowing us to understand how trait-based assembly rules can arise by dynamical processes. The present paper introduces an individual-based model of community assembly, and discusses some of the major advantages and drawbacks of this approach. The model was framed to deal with predation among size-structured populations, incorporating allometric constraints to energetic requirements, movement, life-history features and interaction relationships among individuals. A protocol of assembly procedure is proposed, in which a period of intense species introductions is followed by a period without introductions. The resultant communities did not present any pattern of trait over-dispersion, meaning that the multivariate distances of bionomic features among co-occurring species were neither larger nor more regular than expected in a random collection of species. It suggests a weak influence of interspecific interactions in the model environment and individualistic rules of coexistence, driven mainly by the spatial structure. This highlights that trait over-dispersion and resource partitioning should not be considered a necessary condition for coexistence, even in communities entirely structured by internal processes like predation and competition.     

A simple population theory for mutualism by the use of lattice gas model

The population dynamics of species interactions provides valuable information for life sciences. Lotka-Volterra equations (LVEs) are known to be the most popular model, and they are mainly applied to the systems of predation and competition. However, LVEs often fail to catch the population dynamics of mutualism; the population sizes of species increase infinitely under certain condition (divergence problem). Furthermore, LVEs never predicts the Allee effect in the systems of obligate mutualism. Instead of LVEs, several models have been presented for mutualism; unfortunately, they are rather complicated. It is, therefore, necessary to introduce a simpler theory for mutualism. In the present paper, we apply the lattice gas model which corresponds to the mean-field theory of the usual lattice model. The derived equations are cubic and contain only essential features for mutualism. In the case of obligate mutualism, the dynamics exhibits the Allee effect, and it is almost the same as in the male-female systems. In our model, the population sizes never increase infinitely, because our model contains not only intra- but also interspecific competitions. If the density of one species increases disproportionately in respect of its mutual partners, then this might imply downward pressure on the population abundance of the mutual partner species and such feedback would eventually act as a controlling influence on the population abundance of either species. We discuss several assumptions in our model; in particular, if both species can occupy in each cell simultaneously, then the interspecific competition disappears.     

Reconciling empirical ecology with neutral community models

Neutral community models embody the idea that individuals are ecologically equivalent, having equal fitness over all environmental conditions, and describe how the spatial dynamics and speciation of such individuals can produce a wide range of patterns of distribution, diversity, and abundance. Neutral models have been controversial, provoking a rush of tests and comments. The debate has been spurred by the suggestion that we should test mechanisms. However, the mechanisms and the spatial scales of interest have never clearly been described, and consequently, the tests have often been only peripherally relevant. At least two mechanisms are present in spatially structured neutral models. Dispersal limitation causes clumping of a species, which increases the strength of intraspecific competition and reduces the strength of interspecific competition. This may prolong coexistence and enhance local and regional diversity. Speciation is present in some neutral models and gives a donor-controlled input of new species, many of which remain rare or are short lived, but which directly add to species diversity. Spatial scale is an important consideration in neutral models. Ecological equivalence and equal fitness have implicit spatial scales because dispersal limitation and its emergent effects operate at population levels, and populations and communities are defined at a chosen spatial scale in recent neutral models; equality is measured relative to a metacommunity, and this necessitates defining the spatial scale of that metacommunity. Furthermore, dispersal has its own scales. Thorough empirical tests of neutral models will require both tests of mechanisms and pattern-producing ability, and will involve coupling theoretical models and experiments.     

Local Population Dynamics in Metapopulation Models: Implications for Conservation

Abstract: Habitat fragmentation and the division of populations into spatially separated units have led to the increasing use of metapopulation models to characterize these populations. One prominent model that has served as a heuristic tool was introduced by Levins and is based on a collection of simplifying assumptions that exclude information on the dynamics and spatial distribution of local populations. Levins's and similar models predict the proportion of occupied habitat patches at equilibrium and the conditions needed to avoid total extinction. There are many obvious concerns about using such models, including how realistic alterations might change the predictions and whether occupancy has any relationship to population-level processes. Although many of the assumptions of these simple models are known to be unrealistic, we do not know how the assumptions affect model predictions. We simulated a metapopulation, and our results show that assumptions such as homogeneity of habitat patches, random migration among patches, equivalent extinction probabilities in all patches, and a large number of patches can lead to large overestimations of habitat occupancy. But when we explicitly modeled the underlying population dynamics within each patch, we found (1) that there was a strong correlation between proportion of occupied patches and total metapopulation size and (2) that the distribution of individuals among patches was relatively insensitive to model assumptions. Thus, our results show that although realistic modifications will change model predictions for occupancy, occupancy and population trends will be correlated. These correlations between occupancy and population size suggest that occupancy models may have some utility in conservation applications.     

Social foraging and dominance relationships: the effects of socially mediated interference

In socially foraging animals, it is widely acknowledged that the position of an individual within the dominance hierarchy of the group has a large effect upon its foraging behaviour and energetic intake, where the intake of subordinates can be reduced through socially mediated interference. In this paper, we explore the effects of interference upon group dynamics and individual behaviour, using a spatially explicit individual-based model. Each individual follows a simple behavioural rule based upon its energetic reserves and the actions of its neighbours (where the rule is derived from game theory models). We show that dominant individuals should have larger energetic reserves than their subordinates, and the size of this difference increases when either food is scarce, the intensity of interference suffered by the subordinates increases, or the distance over which dominant individuals affect subordinates increases. Unlike previous models, the results presented in this paper about differences in reserves are not based upon prior assumptions of the effects of social hierarchy and energetic reserves upon predation risk, and emerge through nothing more than a reduction in energetic intake by the subordinates when dominants are present. Furthermore, we show that increasing interference intensity, food availability or the distance over which dominants have an effect also causes the difference in movement between ranks to increase (where subordinates move more than dominants), and the distance over which dominants have an effect changes the size of the groups that the different ranks are found in. These results are discussed in relation to previous studies of intra- and interspecific dominance hierarchies.     

Adaptive significance of phytoplankton stickiness with emphasis on the diatom Skeletonema costatum

Diatom aggregate formation was analyzed using coagulation theory. Population dynamics models show that coagulation has an important impact on species succession during diatom blooms. When different species collide and form mixed aggregates this process causes interspecific interference competition within the diatom community. The outcome can be predicted by a set of simple differential equations. For a twospecies system the equations reduce to the Lotka-Volterra two-species competition model. The outcome of this interference competition depends on species-specific growth rates, cell sizes, stickiness and on the species composition of the seeding populations of a bloom. Due to mutual flocculation some species may disappear from the environment. Small and fast growing diatoms are favoured by high stickiness coefficients. The impact of stickiness on species succession was found to be most pronounced in eutrophic and hydrographically isolated environments. The sticking properties of the diatom Skeletonema costatum are discussed in an evolutionary context; we suggest that mutual coagulation increases the abundance of S. costatum relative to other diatom species in coastal areas. The model was tested on field data, and the predicted dynamics of a spring bloom was very similar to that observed.     

Modulation of predator-prey interactions by the Allee effect

An Allee effect arising from density-dependent mating success can have significant impacts at the ecosystem level when considered in the context of predator-prey interactions. These are captured by a mathematical model for the exchange of biomass between a structured predator population (continuous weight distribution) and a resource. Because the predator’s mating success affects the amount of resources required for the production of offsprings and their future growth into mature organisms, it influences the flux of biomass between trophic levels. Under simple assumptions, the equations can be reduced to an equivalent unstructured predator-prey model in which the Allee effect modulates the predation rate: the mating probability multiplies the rate of predator growth as well as the rate of resource depletion. Implications of the Allee effect for the bifurcation structure and equilibrium densities are examined. The model is compared to a modified version in which the Allee effect instead modulates the assimilation efficiency, hence the mating probability does not appear in the dynamical equation for the resource density. Both models exhibit qualitatively similar dynamics. However, compared to the model in which the Allee effect modulates predation, the model in which the Allee effect modulates assimilation efficiency predicts (i) unrealistically inefficient resource assimilation when predator density is low, (ii) a higher risk of catastrophic extinction resulting from a change in the parameter controlling the strength of the Allee effect, and (iii) no possibility of an increase in population size when the density dependence is enhanced.     

Evaluation of discrete host–parasitoid models for diamondback moth and Diadegma semiclausum field time population density series

The performance of discrete mathematical models to describe the population dynamics of diamondback moth (DBM) (Plutella xylostella L.) and its parasitoid Diadegma semiclausum was investigated. The parameter values for several well-known models (Nicholson–Bailey, Hassell and Varley, Beddington, Free and Lawton, May, Holling type 2, 3 and Getz and Mills functional responses) were estimated. The models were tested on 20 consecutive sets of time series data collected at 14 days interval for pest and parasitoid populations obtained from a highland cabbage growing area in eastern Kenya. Model parameters were estimated from minimized squared difference between the numerical solution of the model equations and the empirical data using Powell's method. Maximum calculated DBM growth rates varied between 0.02 and 0.07. The carrying capacity determined at 16.5 DBM/plant by the Beddington et al. model was within the range of field data. However, all the estimated parameter values relating to the parasitoid, including the instantaneous searching rate (0.07–0.28), per capita searching efficiency (0.20–0.27), search time (5.20–5.33), handling time (0.77–0.90), and parasitism aggregation index (0.33), were well outside the range encountered empirically. All models evaluated for DBM under Durbin–Watson criteria, except the May model, were not autocorrelated with respect to residuals. In contrast, the criteria applied to the parasitoid residuals showed strong autocorrelations. Thus, these models failed to estimate parasitoid dynamics. We conclude that the interactions of the DBM with its parasitoid cannot be explained by any of the models tested. Two factors may be associated with this failure. First, the parasitoid in this integrated biological control system may not be playing a major role in regulating DBM population. Second, and perhaps more likely, poor correlations reflect gross inadequacies in the theoretical assumptions that underlie the existing models.     

Population feedback after successful invasion leads to ecological suicide in seasonal environments

For most consumer species, winter represents a period of harsh food conditions in addition to the physiological strain that results from the low ambient temperatures. In size-structured populations, larger-bodied individuals do better during winter as they have larger energy reserves to buffer starvation periods. In contrast, smaller-bodied individuals do better under growing conditions, as they have lower maintenance costs. We study how the interplay between size-dependent life-history processes and seasonal changes in temperature and food availability shape the long-term dynamics of a size-structured consumer population and its unstructured resource. We show that the size dependence of maintenance requirements translates into a minimum body size that is needed for surviving starvation when consumers can adapt only to a limited extent to the low food densities in winter. This size threshold can lead to population extinction because adult individuals suffer only a little during winter and hence produce large numbers of offspring. Due to population feedback on the resource and intense intra-cohort competition, newborn consumers then fail to reach the size threshold for survival. Under these conditions, small numbers of individuals can survive, increase in density, and build up a population, which will subsequently go extinct due to its feedback on the resource. High juvenile mortality may prevent this ecological suicide from occurring, as it releases resource competition among newborns and speeds up their growth. In size-structured populations, annual fluctuations in temperature and food availability may thus lead to a conflict between individual fitness and population persistence.     

Modeling the Persistence of Small Populations of Strongly Interdependent Species: Figs and Fig Wasps

Conservation problems are usually studied at the population or ecosystem levels. Formulating predictive theory for the domain in between has been difficult. Fig trees and their pollinating wasps, principally tropical groups of organisms, form pairs of obligate mutualists that provide unique opportunities for studying the influence of species interactions on the survival of small populations. Survival of each partner depends on that of the associated species. The pollinator population can be maintained only if figs are produced year-round. Because fig trees flower synchronously at the individual level, wasps have to locate a new individual host tree at each generation. We describe results of simulation models estimating the minimum number of trees required to maintain a wasp population using two levels of the criteria: (1) different probability of survival (50% and 99%) and (2) different time of survival (5 or 1000 years). We also examined how these different estimates are sensitive to differences in the seasonality of flowering period and in the length of the period of female receptivity in figs. Such estimates can be used to understand the potential effects of the reduction of fig population size via fragmentation. Unlike most studies on the effect of low population size on population viability, our paper focuses on maintenance of a biotic interaction, rather than on single-species dynamics. The biotic interaction on which we focus is important because figs in many tropical ecosystems may be keystone resources for frugivores that are in turn essential seed dispersal agents for other plants.     

A dynamic programming implemented resource competition game theoretic model

Resource competition is commonly occurred in animal populations and studied intensively by researchers. Previous studies have applied game theoretic model by finding Nash equilibrium to investigate this phenomenon. However computation of the Nash equilibrium requires an understanding of the payoff matrix that allocates the rewards received by players when they adopt each of the strategies in the game. In our study we present a dynamic programming implemented framework to compute 2 × 2 intraspecific finite resource allocation game's payoff matrix explicitly. We assume that two distinct types of individuals, aggressive and non-aggressive, are in the population. Then we divide the entire animal development period into three different stages: initialization, quasilinear growth and termination. Each stage for each type of players is specified with their own development coefficient, which determines how resource consumption could convert into strength as reward. Each player has equal and finite resource at the beginning of their development and fights against other players in the population to maximize its own potential reward. Based on these assumptions it is reasonable to use backward induction dynamic programming to compute payoff matrix. We present numerical examples for three different types of aggressive individuals and compute the payoff matrices correspondingly. Then we use the derived payoff matrices to determine the Nash equilibrium and Evolutionary Stable Strategy. Our research provide a framework for future quantitative studies on animal resource competition problems and could be expanded to n-players interspecific stochastic asymmetric resource allocation problem by changing some settings of dynamic programming formulation.     

Population dynamics of Müllerian mimicry under interspecific competition

We ask what the effects of mutualism on population dynamics of two competitive species are. We model the population dynamics of mutualistic interactions with positive density- and frequency-dependences. We specifically assume the dynamics of Müllerian mimicry in butterflies, where the mortality of both species is reduced depending on the relative frequency of the other species. We assume that the two species are under Lotka–Volterra density-dependent competition. The equilibria are compared with the cases of competition alone. Unlike the traditional model of positive density-dependence, population explosion does not appear in the current dynamics, but the new equilibrium is simply achieved. It is because the effects of positive density- or frequency-dependence are restricted to parts of mortality. Both positive density- and frequency-dependences do promote coexistence of the mimetic species. However, the two models show a distinctive difference for coexistence. The effects of positive density-dependence are rather limited. In contrast, positive frequency-dependence always promotes coexistence, irrespective of environmental conditions. The results may imply that the evolutionary origin of Müllerian mimicry may depend on frequency-dependence (and density-dependence), but that its current population dynamics may depend solely on density-dependence. The role of frequency- and density-dependences on evolutionary dynamics is an open question.     

Intraspecific Chromosome Number Variation: a Neglected Threat to the Conservation of Rare Plants

Abstract: The effectiveness of rare plant conservation will increase when life history, demographic, and genetic data are considered simultaneously. Inbreeding depression is a widely recognized genetic concern in rare plant conservation, and the mixing of genetically diverse populations in restoration efforts is a common remedy. Nevertheless, if populations with unrecognized intraspecific chromosome variation are crossed, progeny fitness losses will range from partial to complete sterility, and reintroductions and population augmentation of rare plants may fail. To assess the current state of cytological knowledge of threatened and endangered plants in the continental United States, we searched available resources for chromosome counts. We also reviewed recovery plans to discern whether recovery criteria potentially place listed species at risk by requiring reintroductions or population augmentation in the absence of cytological information. Over half the plants lacked a chromosome count, and when a taxon did have a count it generally originated from a sampling intensity too limited to detect intraspecific chromosome variation. Despite limited past cytological sampling, we found 11 plants with documented intraspecific cytological variation, while 8 others were ambiguous for intraspecific chromosome variation. Nevertheless, only one recovery plan addressed the chromosome differences. Inadequate within‐species cytological characterization, incomplete sampling among listed taxa, and the prevalence of interspecific and intraspecific chromosome variation in listed genera, suggests that other rare plants are likely to have intraspecific chromosome variation. Nearly 90% of all recovery plans called for reintroductions or population augmentation as part of recovery criteria despite the dearth of cytological knowledge. We recommend screening rare plants for intraspecific chromosome variation before reintroductions or population augmentation projects are undertaken to safeguard against inadvertent mixtures of incompatible cytotypes.     

Predation affects the susceptibility of hard clam Meretrix lusoria to Hg-stressed birnavirus

Predator–prey interaction in aquatic ecosystem is one of the simplest drivers affecting the species population dynamics. Predation controls are recognized as important aspects of ecosystem husbandry and management. In this paper we investigated how predation control cause an increase in host growth in the abundance of hard clam (Meretrix lusoria) populations subject to mercury (Hg)-stressed birnavirus. Here we linked predator–prey relationships with a bioenergetic matrix population model (MPM) associated with a susceptible–infectious–mortality (SIM) model based on a host–pathogen–predator framework to quantify the predator effects on population dynamics of disease in hard clam populations. Our results indicated that relative high predation rates could promote the hard clam abundances in relation to predators that selectively captured the infected hard clam, by which the disease transmission was suppressed. The results also demonstrated that predator-induced modifications in host behavior could have potential negative or positive effects on host growth depending on relative species density and resource dynamics. The most immediate implication of this study for the management of aquatic ecosystem is that, beyond the potential for causing a growth in abundance, predation might provoke greater predictability in aquatic ecosystem species populations and thereby increase the safety of ecosystem production from stochastic environmental events.     

A methodological approach to develop “contaminant migration–population effects” models

The main aim of the present work is to discuss the methodological approaches that underpin the “contaminant migration–population effects” models for the evaluation of the detriment to populations of moving organisms in environmental systems with spatial and time dependent pollution levels. A technique to couple the equations controlling the population dynamics and the pollutant dispersion is described and discussed. The domain of application and the limitations of the methodology are analysed and illustrated by some examples. Possible alternative approaches are briefly presented.     

Size- and food-dependent growth drives patterns of competitive dominance along productivity gradients

Patterns of coexistence among competing species exhibiting size- and food-dependent growth remain largely unexplored. Here we studied mechanisms behind coexistence and shifts in competitive dominance in a size-structured fish guild, representing sprat and herring stocks in the Baltic Sea, using a physiologically structured model of competing populations. The influence of degree of resource overlap and the possibility of undergoing ontogenetic diet shifts were studied as functions of zooplankton and zoobenthos productivity. By imposing different size-dependent mortalities, we could study the outcome of competition under contrasting environmental regimes representing poor and favorable growth conditions. We found that the identity of the dominant species shifted between low and high productivity. Adding a herring-exclusive benthos resource only provided a competitive advantage over sprat when size-dependent mortality was high enough to allow for rapid growth in the zooplankton niche. Hence, the importance of a bottom-up effect of varying productivity was dependent on a strong top-down effect. Although herring could depress shared resources to lower levels than could sprat and also could access an exclusive resource, the smaller size at maturation of sprat allowed it to coexist with herring and, in some cases, exclude it. Our model system, characterized by interactions among size cohorts, allowed for consumer coexistence even at full resource overlap at intermediate productivities when size-dependent mortality was low. Observed shifts in community patterns were crucially dependent on the explicit consideration of size- and food-dependent growth. Accordingly, we argue that accounting for food-dependent growth and size-dependent interactions is necessary to better predict changes in community structure and dynamics following changes in major ecosystem drivers such as resource productivity and mortality, which are fundamental for our ability to manage exploitation of living resources in, e.g., fisheries.