Interspecific Competition Models Derived from Competition Among Individuals

This paper demonstrates how discrete-time models describing population dynamics of two competing species can be derived in a bottom-up manner by considering competition for resources among individuals and the spatial distribution of individuals. The competition type of each species is assumed to be either scramble, contest, or an intermediate between them. Individuals of two species are distributed over resource sites or patches following one of three distribution functions. According to the combination of competition types of the two species and the distribution of individuals, various interspecific competition models are derived. Furthermore, a general interspecific competition model that includes various competition models as special cases is derived for each distribution of individuals. Finally, this paper examines dynamics of some of the derived competition models and shows that the likelihood of coexistence of the two species varies greatly, depending on the type of spatial distribution of individuals.     

The mechanistic basis of discrete-time population models: The role of resource partitioning and spatial aggregation

The purpose of this paper is to present a unified view to understand mechanistic basis of various discrete-time population models from the viewpoints of resource partitioning and spatial aggregation of individuals. A first-principles derivation is presented of a new population model which incorporates both scramble and contest competition using a site-based framework in which individuals are distributed over discrete resource sites. The derived model has parameters relating to the way of resource partitioning and the degree of spatial aggregation of individuals, respectively. The model becomes various population models in various limits in these parameters. This model thus provides a unified view to understand how various population models are interrelated. The dependence of the stability of the model on the parameters is also examined.     

Hierarchical models of intra-specific competition: scramble versus contest

Hierarchical structured models for scramble and contest intraspecific competition are derived. The dynamical consequences of the two modes of competition are studied under the assumption that both populations divide up the same amount of a limiting resource at equal population levels. A comparison of equilibrium levels and their resiliences is made in order to determine which mode of competition is more advantageous. It is found that the concavity of the resource uptake rate is an important determining factor. Under certain circumstances contest competition is more advantageous for a population while under other circumstances scramble competition is more advantageous.Supported by NSF grant DMS-9306271     

Larval competition causes the difference in male ejaculate expenditure in Callosobruchus maculatus

The seed beetle Callosobruchus maculatus larvae exhibit two types of resource competition: scramble, in which a resource is shared, and contest, in which the resource is monopolized. This difference in larval behavior results in different adult densities. Under contest competition, adult density remains constant regardless of larval density, but under scramble competition, adult density increases with larval density. This in turn affects mating frequency during adulthood, and thus, the intensity of sexual selection operating on males. In this study, we examined the relationship between larval competition types and male reproductive investment in mating. We assessed the male ejaculate expenditure per mating across geographic strains of C. maculatus. The male investment (ejaculate expenditure) increased with the degree of scramble competition and decreased with the degree of contest competition. We therefore suggest that males experience different selective pressures depending on the type of larval competition: scramble type males are selected for increased reproductive investment.     

Individual-Based Competition Between Species with Spatial Correlation and Aggregation

In order to clarify the theoretical relationship between individual behavior and population-level competition between two species with spatial correlation, this paper describes how discrete-time competition equations for the two species can be derived from local resource competition among individuals. Competition type of each species is either scramble, contest, or modified contest, and for various combinations of two competition types, different competition models are derived. Simple competition models that can approximate the above models when competition is weak are also derived. Furthermore, the derived models are used to investigate how coexistence conditions and coexistence probability depend on spatial correlation and aggregation of individuals. For the weak competition models, spatial aggregation and non-correlation, in terms of measures adopted here, play exactly symmetric roles in promoting coexistence. In contrast, for the fully developed models, spatial aggregation generally exerts stronger effects than non-correlation on coexistence. Coexistence probability also depends greatly on competition types. For example, two species are generally more likely to coexist when they are of the same competition type than of different competition types. Coexistence probabilities from the mathematical analysis are in good agreement with those from individual-based simulations.     

Polymorphism of competition type and its genetics in Callosobruchus maculatus (Coleoptera: Bruchidae)

Callosobruchus maculatus has both contest and scramble competition strategies. The currently existing theoretical models using game theory suggest that the contest strategy should be selected for. However, most geographic strains of C. maculatus show scramble competition. We experimentally crossed the representative strains of contest and scramble. We expressed the degree of contest competition by a continuous value named the C-value, which ranges from zero (pure scramble) to unity (pure contest). The competition types expressed in the C-value were genetically additive. Their larval developmental rates were negatively correlated with C-values. Multiple-generation experiments of the mixed strains confirmed that there were no overwhelming advantages of contest over scramble type. Most of the mixed strains remained in the intermediate states. We discuss the results in terms of the resource size necessary for developmental success and developmental speed. Received: April 19, 2001 / Accepted: November 2, 2001     

Contest‐type competition between age classes in scramble‐type Callosobruchus maculatus (Coleoptera: Bruchidae)

We examined the effect of age differences on competition type in individuals of a scramble‐type strain of Callosobruchus maculatus (F.). When oviposition of two individuals on a bean was manipulated to introduce time intervals using two lines with different adult body colors, the frequency of two‐adult emergence decreased with the introduction of sequential oviposition. This result indicates that an age difference between two individuals induces contest competition. The frequency of adult emergence in older individuals decreased, whereas in younger individuals it increased with the introduction of sequential oviposition. Using a dissecting microscope, we observed that bodies of older individuals that died in the bean during the 4‐day oviposition interval were crushed at the pupal stage under the pupal chambers of younger individuals. These results show that an age difference between two larvae in a bean causes contest competition due to one‐sided interference by a younger individual during pupation of an older individual. Based on these experimental results, we discuss the ecological cause of contest competition and the population‐level consequences of identified interactions in scramble‐type C. maculatus.     

Wall-making behavior as a proximate mechanism to generate variation in larval competition in Callosobruchus maculatus (Coleoptera: Bruchidae)

Variation from contest to scramble in larval competition types was observed among laboratory lines derived from a geographic strain of Callosobruchus maculatus. In contest competition, only one adult can emerge from a small bean because the successful larva monopolizes resources. In scramble competition, however, multiple adults can emerge from the bean because larvae share resources. To explain the variation in competition types, we used six lines of the geographic strain to test the hypothesis that the larval competition type is determined by the larval behavior of building walls, which prevent larvae from interfering with each other, allowing multiple adults to emerge from a single bean. We also investigated the proportions of wall-making in contest-scramble hybrid lines to test whether the formation of a wall structure was genetically determined. Results support our hypothesis that wall-making behavior determines the type of larval competition within a geographic strain, and that the behavior is genetically determined. Scramble-type lines exhibited higher frequencies of wall-making than contest-type lines when two larvae of the same line infested a bean. Larval competition type and the tendency towards wall formation in contest-scramble hybrid lines ranged intermediate of parental lines. We concluded that the variation in larval competition type is determined by the variation in larval wall-making behavior among laboratory lines derived from the geographic strain. We will discuss the evolution of scramble-type larvae in C. maculatus based on our results.     

Two-species asymmetric competition: effects of age structure on intra- and interspecific interactions

1. The patterns of density-dependent resource competition and the mechanisms leading to competitive exclusion in an experimental two-species insect age-structured interaction were investigated. 2. The modes of competition (scramble or contest) and strength of competition (under- to overcompensatory) operating within and between the stages of the two species was found to be influenced by total competitor density, the age structure of the competitor community and whether competition is between stages of single or two species. 3. The effect of imposed resource limitation on survival was found to be asymmetric between stages and species. Environments supporting both dominant and subordinate competitors were found to increase survival of subordinate competitors at lower total competitor densities. Competitive environments during development within individual stage cohorts (i.e. small or large larvae), differed from the competitive environment in lumped age classes (i.e. development from egg-->pupae). 4. Competition within mixed-age, stage or species cohorts, when compared with uniform-aged or species cohorts, altered the position of a competitive environment on the scramble-contest spectrum. In some cases the competitive environment switched from undercompensatory contest to overcompensatory scramble competition. 5. Such switching modes of competition suggest that the relative importance of the mechanisms regulating single-species population dynamics (i.e. resource competition) may change when organisms are embedded within a wider community.     

From individual interactions to population dynamics: individual resource partitioning simulation exposes the causes of nonlinear intra-specific competition

Intra-specific competition defines the relationship between population density and the performance of individual organisms (R-function). Observation of this relationship in nature shows it to be frequently nonlinear, and it has been argued, on intuitive grounds, that this nonlinearity is due to the type of competition (scramble or contest) being expressed. Here, we use an individual-based simulation model to investigate the effects of three resource partitioning schemes, representing different types of competition, on the form of the R-function. Results indicate that all resource partitioning schemes can give rise to concave or convex functions depending on the balance between maximum individual birth rate, maintenance cost, and demand for resources. Given high growth rates and maintenance costs, contest competitors tend to exhibit less concavity than scramblers. Therefore, population stability can be strongly affected by the strategy of resource partitioning. Life histories and environmental conditions that encourage the homogeneous distribution of resources among individuals lead to complex and unstable dynamics. Stable dynamics is fostered by heterogeneous resource distribution, which could result from such things as social hierarchies, individual and environmental variability, and large, indivisible resource packets.     

Modeling density dependence in heterogeneous landscapes: Dispersal as a case study

Population models often pose density-dependent rates as relations between current population size on a habitat patch, n, and some threshold size defined by limiting resources, r. In fourteen recent modeling studies incorporating density-dependent dispersal, formulations of the density-dependent rate (or probability) fall into two distinct groups, expressing the rate as a function of n-r or n/r. These two depictions of the same process differ fundamentally: they can cause strikingly different dynamics in otherwise identical systems and they have different scaling properties in heterogeneous landscapes. Here I consider the implications of the two formulations under two broad ecological scenarios: scramble competition for an equally divided resource (e.g. food) and contest competition for an unequally divided resource (e.g. nest sites). In both cases, simple arguments show that the n/r form is preferable when density dependence is driven by individual access to resources. Other circumstances may require different formulations, but modelers must ensure that these have appropriate scaling and non-equilibrium behavior.     

Contest and scramble competitions in two bruchid species,Callosobruchus analis andC. phaseoli (Coleoptera: Bruchidae)

Larval competition between contest and scramble strategists was investigated using the two bruchid species, C. analis (contest species) and C. phaseoli (scramble species) with two different sized mung beans (large and small beans). In both sized beans, the adult emergences of each species dependen on total density of the initial larval densities of the two species and the ratio of the two densities. The emergence of one species was suppressed by the existence of the other species when the initial larval density per bean of the former species was less than that of the latter one. There were many cases in which both C. analis and C. phaseoli emerged from one bean in large beans, but such cases were quite rare in small beans. C. analis performed interference behavior only at late larval stages, whereas C. phaseoli was superior in exploitative competition all through their larval stages. These, combined with the niche segregation inside a bean, are throught to be the major factors of observed density- and frequency-dependent competition results. Based on the above experimental results, long-term competition results between the contest and scramble species were predicted.     

Larval competition within seeds: From the behaviour process to the ecological outcome in the seed beetle Callosobruchus maculatus

Abstract Environmental conditions experienced by organisms during development can have profound impacts on adult fitness and behaviour. Internally feeding larvae unable to leave the seed selected by their mother face limitations of resource suitability and competition. The host seed may guide the larval behaviour within the seed leading to differential intensity of competition and determining its process and outcome, which varies in strains of the legume seed beetle Callosobruchus maculatus (Coleoptera: Bruchidae). However, the intensity, process and outcome of larval competition in different hosts have yet to be simultaneously considered, the objective of the present study. Here we assessed the intensity, process and outcome of intrastrain larval competition as related to host type, and how they are interrelated. Larval competition was faced with two distinct strategies – scramble and contest competition depending on the insect strain and host seed species. The intensity of competition did not show any straight link with the process and outcome of competition. Only a single strain showed a contest competition process with likely interference between larvae, while the four other strains studied showed the process of scramble competition. The process of scramble competition, however, led to variable outcomes in mung beans based on larval competition curves. Such differences were not apparent on cowpea seeds and either the plateau or the peak expected on the larval fitness curves were not reached preventing the distinction of the competition outcome, a likely consequence of the egg laying behaviour of these strains limiting the maximum number of eggs laid per seed. Seed host species rather than seed size are the likely cause of the differences observed from the initial expectation. The strain showing the process of contest competition increased larval fitness with density of larvae emerged per seed regardless of the host species, an unexpected outcome based on theoretical models. In this case the egg laying behaviour of the adult female is probably the main fitness determinant of its progeny.     

From local interactions to population dynamics in site-based models of ecology

A central problem in ecology is relating the interactions of individuals-described in terms of competition, predation, interference, etc.-to the dynamics of the populations of these individuals-in terms of change in numbers of individuals over time. Here, we address this problem for a class of site-based ecological models, where local interactions between individuals take place at a finite number of discrete resource sites over non-overlapping generations and, between generations, individuals move randomly between sites over the entire system. Such site-based models have previously been applied to a wide range of ecological systems: from those involving contest or scramble competition for resources to host-parasite interactions and meta-populations. We show how the population dynamics of site-based models can be accurately approximated by and understood through deterministic and stochastic difference equations. Conversely, we use the inverse of this approximation to show what implicit assumptions are made about individual interactions by modelling of population dynamics in terms of difference equations. To this end, we prove a useful and general theorem: that any model in our class of site-based models has a corresponding stochastic difference equation population model, by which it can be approximated. This theorem allows us to calculate long-term population dynamics, evolutionary stable strategies and, by extending our theory to account for large deviations, extinction probabilities for a wide range of site-based systems. Our methodology is then illustrated to various examples of between species competition, predator-prey interactions and co-operation.     

Contest and scramble competitions inCallosobruchus maculatus (Coleoptera: Bruchidae)

Larval competition curves and resource sharing patterns of 5 strains of Callosobruchus maculatus (iQ, yQ, aaQ, wQ, and tQ) were examined. Offspring emergences as a function of the initial larval density were recorded to construct competition curves. Elytron length of emerged adults was used as the indicator of resource sharing patterns among competing larvae inside a bean. In the large beans, strain iQ showed a saturated competition curve and tQ strain showed a humped curve. Competition curves of the other 3 strains (yQ, aaQ, and wQ) were between those two extremes. In the small beans, strains iQ and tQ also showed a saturated and a humped competition curves, respectively, whereas the competition curves of the 3 intermediate scramble strains could not be distinguished from that of the iQ strain. Thus, the classification based on competition curves was sensitive to the resource condition (bean size). In both the large and the small beans, the elytron lengths of iQ strain remained constant irrespective of initial larval density. On the contrary, the elytron lengths of the 4 other strains decreased monotonically with higher initial larval density. Thus, the judgment based on the resource sharing pattern was shown to be robust. Only iQ strain should be designated as a contest type, and the remaining strains as scaramble types. Contest and scramble types in C. maculatus were also compared with those observed in C. analis and C. phaseoli using competition curves, resource sharing patterns, and other physiological characters.     

Evolution of contest competition and its effect on host–parasitoid dynamics

In experimental populations of the cowpea bean weevil Callosobruchus maculatus (Coleoptera: Bruchidae) and a parasitic wasp Heterospilus prosopidis (Hymenoptera: Braconidae), large changes in the abundances and the fluctuations of both species occurred after approximately 20 generations. In this paper, we examine the hypothesis that this observed change in the dynamics may have been caused by an evolutionary shift in the mode of competition among the bean weevils. A Nicholson-Bailey type model is developed using parameters measured from the experiments. The host larvae can differ in the type of competitive behaviour that they exhibit, which can be either of a contest type or of a scramble type. If a bean contains one or more larvae of the contest type, only one of these will survive and any scramble-type larvae in the bean will be killed. If no contest-type larvae are present within a bean, multiple individuals of the scramble type can emerge from a single bea n. The model assumes many genotypes, differing in the fraction of offspring of the two types. If a high per capita resource availability is maintained, then the scramble type is selected for, but if resources are limited, then the contest type is selected for. The host population at the start of the experiment, taken from a stock culture, was composed mostly of the scramble type. The model is successful in explaining the initial quick increase in the host's abundance, followed by the evolutionary increase in the fraction of the contest type among hosts, resulting in the more stable population dynamics of the host–parasitoid system, as observed in the experiments. However, it predicts a parasitoid abundance much higher than that observed. We discuss alternative hypotheses to explain the observed evolutionary shift in the population dynamics. We also examine the effect of the difference in size of the beans in the stock culture and those used in the experiments.     

Competition strategies and correlated selection on responses to polyandry in the seed beetle Callosobruchus maculatus

Abstract Polyandry reflected in multiple mating with different mates is regarded as favoured by natural selection in males but not necessarily in females, where conflicting effects on fitness components can occur. The present study aims to provide empirical evidence to predict which fitness components may be affected in this sexual conflict using a species that demonstrates potential between‐population variation in their resolution: the cowpea weevil Callosobruchus maculatus. Two strains showing contrasting competition outcomes (scramble × contest) and contrasting life‐history strategies based on trade‐offs between longevity and fecundity are crossed for subsequent selection based on larval‐competition strategy, expecting the production of a correlated response to multiple (polyandrous) mating. Such a response is expected because the scramble strain shows high fecundity (and lower longevity) and would benefit from multiple mating, in contrast with the contest strain, which shows high juvenile mortality. The scramble‐selected lines would evolve a response of increased fecundity and reduced longevity under multiple and potentially polyandrous mating but the contest‐selected lines would not respond to multiple (polyandrous) mating. Instead, both scramble‐ and contest‐selected lines show increased fecundity and reduced longevity with multiple (polyandrous) matings, which did not affect egg weight. Indirect benefits of multiple (polyandrous) mating appear to be relevant for lines showing contest competition among juveniles.     

Scramble in behaviour and ecology

Nicholson's distinction between 'scramble' and 'contest' modes of competition has received widespread attention in ecology and in behaviour, though the emphasis has been different between the two disciplines. In ecology the focus has been on the effects on population; in behavioural ecology the focus has been on the consequences at the individual level. This paper reviews and develops a theory of scramble competition at the individual level, deriving a general evolutionarily stable strategy (ESS) for individual scramble expenditure in a patchy habitat in which individuals compete in local groups for available resources, and examines two population consequences. The critical parameter determining the relationship between individual scramble expenditure and the number of competitors in a patch is the expected resource per capita. If resource input, R, to a patch is constant and independent of the number of competitors, n, then as the number of competitors increases, the per-capita resources declines as R/n, and the ESS scramble level declines (in proportion to (n-1)/n2). However, if the resource input to a patch is positively related to the number of competitors in the patch, scramble expenditure may increase with the number of competitors. In the case where the per-capita resource input stays constant (i.e. R(n) = Rn), the scramble level increases with competitor number (in proportion to (n-1) /n). There are plausible ecological reasons why either of these extreme limits may be approached in nature, making it important to ascertain the relationship between R and n before predicting individual scramble expenditure. For example, resource input may be constant when groups of competitors are constrained to remain together in given patches, and constant per-capita resources may be approached when ideal-free foraging rules apply. However, in the latter case, scramble expenditure must be accounted for in determining the ideal-free distribution. An analysis shows that this leads to 'undermatching', i.e. the ratio of numbers of competitors for good/bad patches becomes progressively less than the ratio of input rates for good/bad patches as the difference between the good and bad patches increases. A second population consequence of the scramble ESS relates to the fact that scrambles may dramatically affect fitness. The per-capita gain in energy can be reduced by a factor of up to 1/n as a result of scramble expenditure, potentially reducing realized population size to as little as the square root of the maximum potential carrying capacity, though reasons are given why such large reductions are unlikely.     

Population structure inhibits evolutionary diversification under competition for resources

A model is presented that explores how population structure affects the evolutionary outcome of ecological competition for resources. The model assumes that competition for resources occurs within groups of a finite number of individuals (interaction groups), and that limited dispersal of individuals between groups (according to Wright's island model of population structure) results in genetic structuring of the population. It is found that both finite-sized interaction groups and limited dispersal can have substantial effects on the evolution of resource exploitation strategies as compared to models with a single, infinitely large, well-mixed interaction group. Both effects, in general, tend to select for less aggressive competitive strategies. Moreover, both effects also tend to reduce the likelihood of the evolutionary diversification of resource exploitation strategies that often occurs in models of resource competition with infinite populations. The results are discussed in the context of theories of the evolutionary diversification of resource exploitation strategies and speciation.