Competition between juveniles and adults in age-structured populations

The effect of competition between juveniles and adults is examined in a generalized, two-age-class, discrete-time model. Adult fecundity and juvenile survival are functions of both age-class densities. Possible configurations of the zero growth isoclines are examined, giving special attention to the isocline shapes, the number of equilibria, and the manner in which the population approaches these equilibria. It is found that small increases in the density of one age class may have either a positive or a negative effect on recruitment into the other class, depending upon the degree of density dependence in fecundity and survival. Closely allied to this, an increase in the resources for a given age class may result in either an increase or a decrease in its equilibrium density. Strong juvenile-adult competition generally has destabilizing effects on the population's equilibrium, with the system being more sensitive to juveniles competing with adults than to the reverse.     

Classical and resource-based competition: a unifying graphical approach

A graphical technique is given for determining the outcome of two species competition for two resources. This method is unifying in the sense that the graphical criterion leading to the various outcomes of competition are consistent across most of the spectrum of resource types (from those that fulfill the same growth needs to those that fulfill different needs) regardless of the classification method used, and the resulting graphs bear a striking resemblance to the well-known phase portraits for two species Lotka–Volterra competition. Our graphical method complements that of Tilman. Both include zero net growth isoclines. However, instead of using the consumption vectors at potential coexistence equilibria to determine input resource concentrations leading to specific competitive outcomes, we introduce curves bounding the feasible set (the set where the resource concentrations of any equilibrium solution must be located). The washout equilibrium (corresponding to the supply point) occurs at an intersection of curves defining the feasible set boundary. The resource concentrations of all other equilibria are found where zero net growth isoclines either intersect each other inside the feasible set or they intersect the feasible set boundary. A species has positive biomass at such an equilibrium only if its zero net growth isocline is involved in such an intersection. The competitive outcomes are then determined from the position of the single species equilibria, just as in the phase portrait analysis for classical competition (rather than from information at potential coexistence equilibria as in Tilman’s method).     

The behavioural final common path.

In this paper it is argued that any model of the motivational (i.e. reversible) processes governing the behaviour of an animal can be represented by means of isoclines in a multidimensional 'causal-factor space'. The argument is axiomatic, based upon the two prime assumptions: that (1) it is always possible to classify the behavioural repertoire of a species in such a way that the classes are mutually exclusive in the sense that the members of different classes cannot occur simultaneously, and (2) these incompatible actions are uniquely determined by a particular set of causal factors. The isoclines join all points in the space which present a given 'degree of competitiveness' of a particular 'candidate' for overt behavioural expression. The competition between candidates is an inevitable consequence of the fact that animals cannot 'do more than one thing at a time', and is envisaged as taking place in the behavioural final common path. An empirical method of determining the motivational state (i.e. point in causal-factor space) is outlined. This is a 'relative' method, independent of the arbitrary calibration of the axes of the causal-factor space. It is shown that an arbitrary scale of measurement along any two axes of the causal-factor space is all that is necessary for empirical determination of the shape of a motivational isocline. Experiments in which this method has been applied to the measurement of hunger and thirst in doves are outlined, and the results are discussed in terms of their implications for motivation theory in general.     

Multiple interactions: An empirically suggested model

A modified version of Schoener's non-linear competition model is presented. The model describes the competitive dynamics of two species competing for a common resource. A second resource made available by species 1 for the exclusive use of species 2 is also present. This second resource is generated in an undefined way from the common resource. The presence of the exclusive resource serves to prevent the extinction of species 2 even when that species is at a great competitive disadvantage in obtaining the common resource. A feedback loop is established, dependent on the exclusive resource, making possible an increase in numbers of species 2 as the numbers of species 1 increase. This is represented as a reversal in the slope of the species 2 isocline. The behavior of the isoclines of both species is examined as certain key parameters are varied. The model is related to the results obtained from experiments involving Tribolium and Drosophila.     

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.     

Competitive exclusion through reproductive interference

A simple differential equation model was developed to describe the competitive interaction that may occur between species through reproductive interference. The model has the form comparable to Volterra's competition equations, and the graphical analysis of the outcome of the two-species interaction based on its zero-growth isoclines proved that: (1) The possible outcome in this model, as in usual models of resource competition, is either stable coexistence of both species or gradual exclusion of one species by the other, depending critically upon the values of the activity overlapping coefficient c_ij; (2) but, for the same c_ij-values, competitive exclusion is much more ready to occur here than in resource competition; (3) and moreover, the final result of the competition is always dependent on the initial-condition due to its non-linear isoclines, i.e., even under the parameter condition that generally allows both species to coexist, an extreme bias in intial density to one species can readily cause subsequent complete exclusion of its counterparts. Thus, it may follow that the reproductive interference is likely to be working in nature as an efficient mechanism to bring about habitat partitioning in either time or space between some closely related species in insect communities, even though they inhabit heterogeneous habitats where resource competition rarely occurs so that they could otherwise attain steady coexistence.     

Effects of density-restricted food encounter on some single-level competition models

A family of two-species competition models in which density-restricted rates of food enounter are explicitly incorporated generates the following results:

1. 1. Sigmoidal growth. A new model for sigmoidal single-species growth is produced, but one whose inflection point always falls below half the carrying capacity.

2. 2. Comparison with simpler models. In models having shared and exclusive resources, the one or two stable nodes of simpler models may no longer occur in the first quadrant. Such models can simulate how one species by consuming enough overlapping resource can cause another species, unable to maintain itself on its exclusive resources, to go extinct. In models for interspecific interference competition (resource competition purely intraspecific), one or even two more intersections of the zero-isoclines may occur, or the isoclines may intersect once, but with different relative slopes than in the simpler models.

3. 3. Alternative communities. A new model is produced for alternative communities. Conditions for this situation, phrased in terms of parameters measuring feeding and competitive abilities, are rather narrow.

     

Parasite establishment in host communities

Many pathogens and parasites attack multiple host species, so their ability to invade a host community can depend on host community composition. We present a graphical isocline framework for studying disease establishment in systems with two host species, based on treating host species as resources. The isocline approach provides a natural generalization to multi‐host systems of two related concepts in disease ecology – the basic reproductive rate of a parasite, and threshold host density. Qualitative isocline shape characterizes the threshold community configurations that permit parasite establishment. In general, isocline shape reflects the relative forces of inter‐ and intraspecific transmission of shared parasites. We discuss the qualitative implications of parasite isocline shape for issues of mounting concern in conservation ecology.     

Is the shape of the density-growth relationship for stream salmonids evidence for exploitative rather than interference competition?

1. Empirical studies show that average growth of stream-dwelling salmon and trout often declines with increasing density in a characteristic concave relationship. However, the mechanisms that generate negative density-growth relationships in populations in natural streams are not certain. 2. In a recent study, Imre, Grant & Cunjak (2005; Journal of Animal Ecology, 74, 508-516) argue that density-dependent growth due to exploitative competition for prey causes the negative density-growth relationships for stream salmonids. They argue that the concave shape of empirical density-growth relationships is consistent with a simple model of exploitative competition and not consistent with interference competition for space. 3. We use a simple model to show that competition for space can yield concave density-growth relationships consistent with the empirical pattern when individuals compete for foraging sites that vary spatially in quality and lower-quality sites predominate. Thus, the predictions of the exploitative competition and spatial competition models overlap. 4. The shape of the density-growth relationship does not differentiate between candidate mechanisms underlying density-dependent growth for stream salmonids. Our results highlight the general problem with determining the mechanism driving an ecological process from patterns in observational data within the context of linking population demographics to habitat structure and animal behaviour.     

Multiple limit cycles for predator-prey models

We construct a Gause-type predator-prey model with concave prey isocline and (at least) two limit cycles. This serves as a counter-example to the global stability criterion of Hsu [Math. Biosci. 39:1-10 (1978)].     

The functional responses of adaptive consumers of two resources

This article investigates some aspects of the shape of the functional responses of consumers that utilize two resources. Adaptive variation in consumption behavior is shown to have a major effect on the relationship between amount of resource available and its rate of consumption by an average consumer individual. The effects of adaptive variation are dependent on the nutritional status of the two resources. If the resources are linearly substitutable, increases in the density of resource i will usually increase the quantity, functional response on i divided by density of i, and increases in the density of resource j will decrease this quantity. The result is that the functional response to resource i will generally decrease with the density of resource j, and will increase faster than it would otherwise have increased with the density of resource i. If resources are nonsubstitutable, an adaptive functional response to resource i will increase with the density of resource j, and it will increase more slowly with the density of resource i than it would have without adaptive change. If resources are both complementary and substitutable, the functional response will exhibit ranges of smooth change separated by rapid jumps between values, and different ranges of resource densities will result in a functional response with the characteristics of linearly substitutable or of non-substitutable resources. Adaptive functional response shape is dependent upon the tradeoff involved in raising each functional response. These results have implications for the types of indirect interactions that occur between resources as the result of a common consumer's functional response. They also suggest that the adaptive response of competing consumers to each other will differ depending on the nutritional status of the resources for which they are competing. Implications of these findings for consumer growth isocline shape and several other issues are explored.     

Density dependent selection incorporating intraspecific competition 1. A haploid model

A haploid model is introduced and analyzed in which intraspecific competition is incorporated within a density dependent framework. It is assumed that each genotype has a unique carrying capacity corresponding to the equilibrium population size when fixed for that type. Each genotypic fitness at a single multi-allelic locus is a function of a distinctive effective population size formed by adding the numbers of each genotype present, weighted by an intraspecific competition coefficient. As a result, the fitnesses depend upon the relative frequencies of the various genotypes as well as the total population size. Intergenotypic interactions can have a profound effect upon the outcome of the population. In particular, when the density effect of one individual upon another depends upon their respective genotypes, a unique stable interior equilibrium is possible in which all alleles are present. This stands in contrast to the purely density dependent haploid system in which the only possible stable state corresponds to fixation for the type with the highest carrying capacity. In the present model selective advantage is determined by a balance between carrying capacity and sensitivity to density pressures from other genotypes. Fixation for the genotype with the highest carrying capacity, for instance, will not be stable if it exerts a sufficiently weak competitive effect upon the other genotypes. In the diallelic case, maintenance of both alleles at a stable equilibrium requires that the net intragenotypic competition between individuals of like genotype be stronger than that between unlike types. As for purely density regulated systems, there may be no stable equilibria and/or regular and chaotic cycling may occur. The results may also be interpreted in terms of a discrete time model of interspecific competition with each haplotype representing a different species.     

Cartographic analysis of woodlice fauna of the former USSR

An inventory of the woodlice fauna of the former USSR yielded 190 species, 64 of them were recorded from the territory of Russia. According to the cartographic analysis, the limits of distribution of epigean terrestrial isopods over the area, excluding mountains, is explained by temperature. No woodlice records were found outside the isocline of 120 days a year with the mean daily air temperature >10°C. The highest species diversity was found between the isoclines of 180 and 210 days. These areas correspond to forest-steppe and steppe zones.     

Changes in Individual Allometry Can Lead to Species Coexistence without Niche Separation

The principle of competitive exclusion is a fundamental tenet of ecology. Commonly used competition models predict that at most only one species per limiting resource can coexist in the same environment at steady state; hence, the upper limit to species diversity depends only on the number of limiting resources and not on the rates of resource supply. We demonstrate that such model behavior is the result of both the growth and biomass turnover functions being proportional to the population biomass. We argue that at least the growth function should be a nonlinear, concave downward function of biomass. This form for the growth function should arise simply because of changes in the allometry of individuals in the population. With this change in model structure, we show that any number of species can coexist at an asymptotically stable steady state, even where there is only one limiting resource. Furthermore, if growth increases nonlinearly with biomass, the steady-state resource concentration and hence the potential for biodiversity increases as the resource supply rate increases. Received 31 August 2001; accepted 10 April 2002.     

An advantage for concavities in shape perception by chimpanzees (Pan troglodytes)

The significance of concavity in object shape perception by chimpanzees (Pan troglodytes) was investigated in a matching-to-sample procedure. For the task, chimpanzees were required to choose a polygon stimulus that was identical in shape to a sample. The incorrect alternative was defined by the addition or subtraction of a concave or convex apex. Chimpanzees were more sensitive to the concave deformation than to the convex deformation. This tendency conforms to the theories of human visual perception that have treated concave features as important factors in reconstructing three-dimensional structures from two-dimensional images. Our results suggest that shape representation in chimpanzees is similar to that in humans and that chimpanzees visually process two-dimensional images in the same manner as humans.     

Evidence and implications for multiplicative interactions among loci predisposing to human common disease

OBJECTIVE: The aim of this study was to utilize information on monozygotic twin concordance rates and linkage studies results for common diseases to predict the likely mode of interaction between susceptibility loci. METHODS: We calculated combinations of allele frequency and genotypic relative risk (GRR) that would generate linkage results typically observed in common human diseases. Given these single locus effects, we calculated the expected monozygotic twin concordance assuming different numbers of loci under different interaction models. RESULTS: We demonstrate that, for disorders like schizophrenia, a purely additive model of interaction among loci is not consistent with the available evidence. Instead there are likely significant multiplicative or stronger interactions. Given these interactions, we show that in a diagnostic test based on a subset of predisposing loci, the marginal increase of predictive value rises with each additional locus that is discovered. Our model was consistent with susceptibility alleles being common or rare. CONCLUSIONS: Evidence from monozygotic twin concordance rates and linkage results point to a significant degree of multiplicative interaction among loci.     

Which species will succesfully track climate change? The influence of intraspecific competition and density dependent dispersal on range shifting dynamics

Understanding the ability of species to shift their geographic range is of considerable importance given the current period of rapid climate change. Furthermore, a greater understanding of the spatial population dynamics underlying range shifting is required to complement the advances made in climate niche modelling. A simulation model is developed which incorporates three key features that have been largely overlooked in studies of range shifting dynamics: the form of intraspecific competition, density dependent dispersal and the transient dynamics of habitat patches. The results show that the exact shape of the response depends critically on both local and patch dynamics. Species whose intraspecific competition is contest based are more vulnerable than those whose competition is scramble based. Contesters are especially sensitive when combined with density dependent dispersal. Species living in patches whose carrying capacity grows slowly are also susceptible to rapid shifts of environmental conditions. A complementary analytic approach further highlights the importance of intraspecific competition.     

Biodiversity,habitat area,resource growth rate and interference competition

For the majority of species, per capita growth rate correlates negatively with population density. Although the popular logistic equation for the growth of a single species incorporates this intraspecific competition, multi-trophic models often ignore self-limitation of the consumers. Instead, these models often assume that the predator-prey interactions are purely exploitative, employing simple Lotka-Volterra forms in which consumer species lack intraspecific competition terms. Here we show that intraspecific interference competition can account for the stable coexistence of many consumer species on a single resource in a homogeneous environment. In addition, our work suggests a potential mechanism for field observations demonstrating that habitat area and resource productivity strongly positively correlate to biodiversity. In the special case of a modified Lotka-Volterra model describing multiple predators competing for a single resource, we present an ordering procedure that determines the deterministic fate of each specific consumer. Moreover, we find that the growth rate of a resource species is proportional to the maximum number of consumer species that resource can support. In the limiting case, when the resource growth rate is infinite, a model with intraspecific interference reduces to the conventional Lotka-Volterra competition model where there can be an unlimited number of coexisting consumers. This highlights the crucial role that resource growth rates may play in promoting coexistence of consumer species.