Coexistence of competing species by the oscillation of polymorphisms

Scale-eating cichlids in Lake Tanganyika exhibit genetically determined lateral asymmetry, especially in their mouth-opening. Frequencies of the morphs oscillate due to strong frequency-dependent selection caused by the switching of prey's attention, and its delayed effect by their growth period. Two scale-eaters coexist in similar densities at south shore of the lake, with their morph frequencies oscillating in phase. We investigated the effect of the oscillation in morph frequencies to the coexistence of competing species. If the difference of two species' growth period is large, the oscillation facilitates the coexistence of the two species, while small difference of growth periods hinders their coexistence. In the latter case, the species with shorter growth period drives the other species to the extinction.     

Periodic coexistence of four species competing for three essential resources

We show the existence of a periodic solution in which four species coexist in competition for three essential resources in the standard model of resource competition. By assuming that species i is limited by resource i for each i near the positive equilibrium, and that the matrix of contents of resources in species is a combination of cyclic matrix and a symmetric matrix, we obtain an asymptotically stable periodic solution of three species on three resources via Hopf bifurcation. A simple bifurcation argument is then employed which allows us to add a fourth species. In principle, the argument can be continued to obtain a periodic solution adding one new species at a time so long as asymptotic stability can be assured at each step. Numerical simulations are provided to illustrate our analytical results. The results of this paper suggest that competition can generate coexistence of species in the form of periodic cycles, and that the number of coexisting species can exceed the number of resources in a constant and homogeneous environment.     

Coexistence and displacement in consumer-resource systems with local and shared resources

Competition for local and shared resources is widespread. For example, colonial waterbirds consume local prey in the immediate vicinity of their colony, as well as shared prey across multiple colonies. However, there is little understanding of conditions facilitating coexistence vs. displacement in such systems. Extending traditional models based on type I and type II functional responses, we simulate consumer-resource systems in which resources are “substitutable,” “essential,” or “complementary.” It is shown that when resources are complementary or essential, a small increase in carrying capacity or decrease in handling time of a local resource may displace a spatially separate consumer species, even when the effect on shared resources is small. This work underscores the importance of determining both the nature of resource competition (substitutable, essential, or complementary) and appropriate scale-dependencies when studying metacommunities. We discuss model applicability to complex systems, e.g., urban wildlife that consume natural and anthropogenic resources which may displace rural competitors by depleting shared prey.     

Coexistence of competing species of seaweed flies: the role of temperature

Abstract.

• 1 Competition is shown to be occurring within and between the congeners Coelopa frigida and C.pilipes; it is noted that the two species frequently coexist despite ongoing competition.
• 2 Observations on natural wrack-beds indicate that there is a marked difference in the distributions of the larvae: C.frigida larvae aggregate in cooler parts of the bed, C.pilipes in warmer parts. This difference in microdistribution reflects a broader-scale difference in the geographical distributions of the species - C.pilipes being the more southerly of the two.
• 3 The larval distributions are shown to be caused primarily by the behaviour of the larvae themselves - not by choices made by ovipositing females, nor (at least to any great extent) by differential survival.
• 4 The different micro-distributions within beds constitute a form of niche difference which will cause competitive abilities to be frequency-dependent and hence have a stabilizing effect. It is possible that this effect may be supplemented by others; and, in particular, effects operating at the level of the‘linear meta-population’may be worthy of further investigation both in Coelopa and in other coastal species.

     

Coexistence of competing juvenile-adult structured populations

The Leslie-Gower model is a discrete time analog of the competition Lotka-Volterra model and is known to possess the same dynamic scenarios of that famous model. The Leslie-Gower model played a historically significant role in the history of competition theory in its application to classic laboratory experiments of two competing species of flour beetles (carried out by Park in the 1940s-1960s). While these experiments generally supported what became the Competitive Exclusion Principle, Park observed an anomalous coexistence case. Recent literature has discussed Park's 'coexistence case' by means of non-Lotka-Volterra, non-equilibrium dynamics that occur in a high dimensional model with life cycle stages. We study this dynamic possibility in the lowest possible dimension, that is to say, by means of a model involving only two species each with two life cycle stages. We do this by extending the Leslie-Gower model so as to describe the competitive interaction of two species with juvenile and adult classes. We give a complete account of the global dynamics of the resulting model and show that it allows for non-equilibrium competitive coexistence as competition coefficients are increased. We also show that this phenomenon occurs in a general class of models for competing populations structured by juvenile and adult life cycle stages.     

Behaviour and resource use of two competing vole species under shared predation risk

Indirect interaction between two competing species via a shared predator may be an important determinant of population and community dynamics. We studied the effect of predation risk imposed by the least weasel Mustela nivalis nivalis on space use, foraging and activity of two competing vole species, the grey-sided vole Myodes rufocanus, and the bank vole Myodes glareolus. The experiment was conducted in a large indoor arena, consisting of microhabitat structures providing food, shelter, trees for refuge and separated areas with high and low predation risk. Voles were followed for 5 days: 2 days before, 1 day during and 2 days after the presence of weasel. Our results suggest an effect of weasel presence on the vole community. Voles of both species shifted their activity from risky to less risky areas, climbed trees more often and were less active. Seed consumption was not affected by weasel presence. The time spent in the risky and less risky area did not differ between species, but bank voles spent more time in trees than grey-sided voles. Males of both species were more exposed to predation risk than females, i.e. generally spent more time in the risky area. Proportion of time spent in the risky area, the use of area, trees and food stations were sex dependent. Activity and use of trees were species dependent. We found no evidence for despotic distribution between our two species, although bank voles seemed to be more affected by coexistence, since they lost weight during the experiment. Based on our results we conclude that predator response was largely similar between species, while the sex-specific responses dominated. Besides a stronger escape response in the bank vole, the strongest individual differences were sex specific, i.e. males were more prone to take risks in space use and activity.     

Coexistence of competing microbial species in a chemostat where one population feeds on another

In this paper, we consider a model for a chemostat in which two microbial species compete for a single rate-limiting nutrient, while one of the species feeds on another. Under certain simplifying hypotheses, such a chemostat can be described by a system of three nonlinear ordinary differential equations. A theoretical study is conducted to characterize the possible types of solutions. A limit cycle solution was obtained for some parametric values of the system indicating that coexistence of the two species is possible in a significant range of the operating parameters.     

Periodic coexistence in the chemostat with three species competing for three essential resources

A chemostat model of three species of microorganisms competing for three essential, growth-limiting nutrients is considered. J. Husiman and F.J. Weissing [Nature 402 (1999) 407] show numerically that this model can generate periodic oscillations. The present contribution is concerned with rigorous analysis regarding the existence of periodic oscillations in this model. Our analysis is based on the following observation made by Huisman and Weissing: there is a cyclic replacement of species, if each species becomes limited by the resource for which it is the intermediate competitor. Using a permanence theory, an index theory, and a Poincaré-Bendixson theory for three-dimensional competitive systems, we analytically succeed to give sufficient conditions for the existence of periodic orbits in the limit sets in this model. The results in this paper suggest that with a wide range of parameter values, sustained periodic oscillations of species abundances for the model are possible, without involving external disturbances. Our results also suggest that competition is not necessarily destructive, i.e., in the case of existence of sustained periodic oscillations, if one of three competitors is absent, one of the other two rivals cannot survive.     

Coexistence of competing predators in a chemostat

An analysis is given of a mathematical model of two predators feeding on a single prey growing in the chemostat. In the case that one of the predators goes extinct, a global stability result is obtained. Under appropriate circumstances, a bifurcation theorem can be used to show that coexistence of the predators occurs in the form of a limit cycle.     

Fast food in ant communities: how competing species find resources

An understanding of foraging behavior is crucial to understanding higher level community dynamics; in particular, there is a lack of information about how different species discover food resources. We examined the effect of forager number and forager discovery capacity on food discovery in two disparate temperate ant communities, located in Texas and Arizona. We defined forager discovery capacity as the per capita rate of resource discovery, or how quickly individual ants arrived at resources. In general, resources were discovered more quickly when more foragers were present; this was true both within communities, where species identity was ignored, as well as within species. This pattern suggests that resource discovery is a matter of random processes, with ants essentially bumping into resources at a rate mediated by their abundance. In contrast, species that were better discoverers, as defined by the proportion of resources discovered first, did not have higher numbers of mean foragers. Instead, both mean forager number and mean forager discovery capacity determined discovery success. The Texas species used both forager number and capacity, whereas the Arizona species used only forager capacity. There was a negative correlation between a species’ prevalence in the environment and the discovery capacity of its foragers, suggesting that a given species cannot exploit both high numbers and high discovery capacity as a strategy. These results highlight that while forager number is crucial to determining time to discovery at the community level and within species, individual forager characteristics influence the outcome of exploitative competition in ant communities.     

Coexistence of two competing corixid species (Heteroptera) in an archipelago of temporary rock pools

Summary Coexistence of Callicorixa producta and Arctocorisa carinata in an archipelago of rock pools appears to be facilitated by division of the environment on the time axis. To test this, a hypothesis is built on r-K theory. As A. carinata is twice the size of C. producta it is expected that the former species is more K-selected living in more permanent pools where food resources are limiting and competition strong. The smaller C. producta is expected to prefer newly refilled pools with abundant food, and thus to be more r-selected. Gathered test data on 17 life history and population ecological features agree with the prediction. It is also shown that the both rock-pool corixids are more r-selected than other species of the family.     

Coexistence of insect species competing for a pulsed resource: toward a unified theory of biodiversity in fluctuating environments

Background

One major challenge in understanding how biodiversity is organized is finding out whether communities of competing species are shaped exclusively by species-level differences in ecological traits (niche theory), exclusively by random processes (neutral theory of biodiversity), or by both processes simultaneously. Communities of species competing for a pulsed resource are a suitable system for testing these theories: due to marked fluctuations in resource availability, the theories yield very different predictions about the timing of resource use and the synchronization of the population dynamics between the competing species. Accordingly, we explored mechanisms that might promote the local coexistence of phytophagous insects (four sister species of the genus Curculio) competing for oak acorns, a pulsed resource.

Methodology/Principal Findings

We analyzed the time partitioning of the exploitation of oak acorns by the four weevil species in two independent communities, and we assessed the level of synchronization in their population dynamics. In accordance with the niche theory, overall these species exhibited marked time partitioning of resource use, both within a given year and between different years owing to different dormancy strategies between species, as well as distinct demographic patterns. Two of the four weevil species, however, consistently exploited the resource during the same period of the year, exhibited a similar dormancy pattern, and did not show any significant difference in their population dynamics.

Conclusions/Significance

The marked time partitioning of the resource use appears as a keystone of the coexistence of these competing insect species, except for two of them which are demographically nearly equivalent. Communities of consumers of pulsed resources thus seem to offer a promising avenue for developing a unifying theory of biodiversity in fluctuating environments which might predict the co-occurrence, within the same community, of species that are ecologically either very similar, or very different.     

Testing competing measures of profitability for mobile resources

Optimal diet theory often fails to predict a forager’s diet choice when prey are mobile. Because they escape or defend themselves, mobile prey are likely to increase the forager’s handling time, thereby decreasing its fitness gain rate. Many animals have been shown to select their prey so as to maximize either their fitness gain or their fitness gain rate. However, no study has yet compared directly these two measures of profitability by generating testable predictions about the choice of the forager. Under laboratory conditions, we compared these two measures of profitability, using the aphid parasitoid Aphidius colemani and its host, Myzus persicae. Fitness gain was calculated for parasitoids developing in each host instar by measuring life-history traits such as developmental time, sex ratio and fecundity. Fitness gain rate was estimated by dividing fitness gain by handling time, the time required to subdue the host. Fourth instar aphids provided the best fitness gain to parasitoids, whereas second instar aphids were the most profitable in terms of fitness gain rate. Host choice tests showed that A. colemani females preferred second instar hosts, suggesting that their decision maximizes fitness gain rate over fitness gain. Our results indicate that fitness gain rate is a reliable predictor of animal’s choice for foragers exploiting resources that impose additional time cost due to their mobility. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Coexistence of cryptic species

Recent discovery of cryptic species in fig‐pollinating wasps creates a puzzle for the ecological competition theory: how do two or more apparently identical species coexist? Conventional theory predicts that they should not. Chesson (Trends Ecol. Evol., 1991, 6 , 26–28) identified one exception which he considered unlikely to occur in reality: coexistence might be possible if appropriate social behaviour was discriminately directed towards conspecifics and heterospecifics. Here we present an example of the exception by showing that two identical species with local mate competition and population size‐dependent sex ratio adjustment may coexist. The new findings about fig‐pollinating wasps provide a putative example of unexpected coexistence of identical competitors via this mechanism.     

Coexistence of nearly neutral species

Aims The neutral theory of biodiversity provides a powerful framework for modeling macroecological patterns and interpreting species assemblages. However, there remain several unsolved problems, including the effect of relaxing the assumption of strict neutrality to allow for empirically observed variation in vital rates and the 'problem of time'—empirically measured coexistence times are much shorter than the prediction of the strictly neutral drift model. Here, we develop a nearly neutral model that allows for differential birth and death rates of species. This model provides an approach to study species coexistence away from strict neutrality.Methods Based on Moran's neutral model, which assumes all species in a community have the same competitive ability and have identical birth and death rates, we developed a model that includes birth–death trade-off but excludes speciation. This model describes a wide range of asymmetry from strictly neutral to nearly neutral to far from neutral and is useful for analyzing the effect of drift on species coexistence. Specifically, we analyzed the effects of the birth–death trade-off on the time and probability of species coexistence and quantified the loss of biodiversity (as measured by Simpson's diversity) due to drift by varying species birth and death rates.Important findings We found (i) a birth–death trade-off operating as an equalizing force driven by demographic stochasticity promotes the coexistence of nearly neutral species. Species near demographic trade-offs (i.e. fitness equivalence) can coexist even longer than that predicted by the strictly neutral model; (ii) the effect of birth rates on species coexistence is very similar to that of death rates, but their compensatory effects are not completely symmetric; (iii) ecological drift over time produces a march to fixation. Trade-off-based neutral communities lose diversity more slowly than the strictly neutral community, while non-neutral communities lose diversity much more rapidly; and (iv) nearly neutral systems have substantially shorter time of coexistence than that of neutral systems. This reduced time provides a promising solution to the problem of time.     

Costs of jasmonate-induced responses in plants competing for limited resources

We present a design to quantify fitness consequences of jasmonate-induced responses in plants that are competing for limited resources with a conspecific. Under both high and low nitrogen supply rates, uninduced (control) Nicotiana attenuata plants growing next to a plant induced with 250 μg methyl jasmonate (MJ) yielded more seed capsules than control plants competing with another control plant. We conclude that there is a opportunity benefit for control plants growing next to an induced plant. Initially, MJ-induced plants grew more slowly, but by senescence they had produced the same number of seed capsules as control plants that had competed with another control plant. Replacement series showed that the fitness of MJ-induced plants is not influenced by the competitive status of their neighbour plant. We argue that competitive designs are useful tools for evaluating the phenotypic costs of ecologically important traits.     

Coexistence of two microbial populations competing for a renewable resource in a non-predator-prey system

If two microbial populations compete for a single resource in a homogeneous environment with time invariant inputs they cannot coexist indefinitely if the resource competed for is not renewed by biological activity within the system. Mathematical studies have shown that in a predator-prey system, where the resource (prey) is self-renewing, the two competitors (predators) can coexist in a limit cycle. This suggests that if the resource competed for is renewed by biological activity within the system coexistence can occur in any microbial system provided that it exhibits the same features as, but without being, a predator-prey one. A food chain involving commensalism, competition and amensalism is presented here. Two subcases are considered. It is only when maintenance effects are taken into account that coexistence, in limit cycles, can occur for this system. Limit cycle solutions for the system are demonstrated with the help of computer simulations. Some necessary conditions for coexistence are presented, as are some speculations regarding the possible physical explanations of the results.     

About the theory of competing species

We review some typical features of the dynamics of systems of competing species, described by the Lotka-Volterra equations and give some new results concerning the coexistence of many species and the linear stability of equilibrium states. We also commenton some types of asymptotic behaviors for three-dimensional systems.     

Herbivore-induced coexistence of competing plant species

We study a series of spatially implicit lottery models in which two competing plant species, with and without defensive traits, are grazed by a herbivore in a homogeneous habitat. One species (palatable) has no defensive traits, while the other (defended) has defensive traits but suffers reduced reproduction as the result of an assumed trade-off. Not surprisingly, coexistence of these plants cannot occur when the herbivore density is very low (the palatable plant always wins) or very high (the defended plant wins). At intermediate densities, however, herbivory can mediate plant coexistence, even in a homogeneous environment. If the herbivore eats several plants per bite, and its forage-selection depends on the average palatability of the plants it eats, then palatable species in the immediate neighbourhood of defended plants may be more likely to persist (associational resistance) even at higher grazing pressure. If the herbivore shows a positive numerical response to the average palatability of the habitat as a whole, then both plant populations are stabilized and coexistence is promoted, because both species obtain a minority advantage through the negative feedback caused by herbivory. If the herbivore exhibits both of these traits, the system may have at most two non-trivial equilibria, one of which is stable and the other unstable. This means that coexistence in such a system is vulnerable to large fluctuations in herbivore density and identity, and this has implications for conservation in systems where large herbivores are managed to promote plant diversity.     

Disturbances allow coexistence of competing species

We give the first mathematically rigorous proof that disturbances allow competing species to coexist. This work provides a mathematical framework to explain the existence of fugitive species and the role played by disturbances in increasing or decreasing the biodiversity of ecosystems. We study modifications of the metapopulation model for patchy environments proposed by Caswell and Cohen (1990, 1991). For the one- and two-species models we give necessary and sufficient conditions on the parameters for the existence of a non-trivial equilibrium solution, which is shown to be always globally stable.