Operating parameters' effects on the outcome of pure and simple competition between two populations in configurations of two interconnected chemostats

It is known from the literature that two microbial populations competing purely and simply for a common substrate in a spatially inhomogeneous environment may under certain conditions coexist in a steady state. This paper studies pure and simple competition between two microbial species in three alternate configurations of two interconnected ideal chemostats and focuses on the effects of the operating parameters-dilution rate, substrate concentration in the feed to the vessels, recycle ratio, and volume ratio of the two vessels, splitting ratio of the external feed to the chemostats-on the coexistence of the two competitors. It is shown that the coexistence steady state is practically feasible in the sense that it occurs in a finite domain of the operating parameters space. Theoretical and numerical results are presented, some of them in the form of operating diagrams projected on the two-dimensional subspace. A comparison of the three possible configurations is offered.     

The growth of pure and simple microbial competitors in a moving distributed medium.

The dynamics of pure and simple competition between two microbial species are examined for the case of interaction arising in a distributed and nonstagnant environment. The environment is modeled as a tubular reactor. It is shown that for relatively small values of the dispersion coefficient (i.e., for small, but nonzero, backmixing of the medium), the two competing populations can coexist in a stable steady state. It has been assumed that the species grow uninhibited and that if there are maintenance requirements they are satisfied from endogenous sources. From numerical studies it has been found that a necessary condition for coexistence is that the net specific growth rate curves of the two competitors cross each other at a positive value of the concentration of the rate-limiting substrate. The model equations have been numerically solved by using the methods of orthogonal and spline collocation.     

Heteromyopia and the spatial coexistence of similar competitors

Most spatial models of competing species assume symmetries in the spatial scales of dispersal and interactions. This makes analysis tractable, and has led to the conclusion that segregation of species in space does not promote coexistence. However, these symmetries leave parts of the parameter space uninvestigated. Using a moment‐approximation method, we present a spatial version of the Lotka–Volterra competition equations to investigate effects of removing symmetries in the distances over which individuals disperse and interact. Some spatial segregation of the species always comes about due to competition, and such segregation does not necessarily lead to coexistence. But, if interspecific competition occurs over shorter distances than intraspecific competition (heteromyopia), spatial segregation becomes strong enough to promote coexistence. Such coexistence is most likely when the species have similar dynamics, in contrast to the competition–colonization trade‐off that requires large competitive differences between species.     

Preemption of space can lead to intransitive coexistence of competitors

Intransitive competition has the potential to be a powerful contributor to species coexistence, but there are few proposed biological mechanisms that could create intransitivities in natural communities. Using a three‐species model of competition for space, we demonstrate a mechanism for coexistence that combines a colonization–competition tradeoff between two species with the ability of a third species to preempt space from the other competitors. The combination of differential abilities to colonize, preempt, and overtake space creates a community where no single species can exclude both of its competitors. The dynamics of this kind of community are analogous to rock‐paper‐scissors competition, and the three‐species community can persist even though not all pairs of species can coexist in isolation. In distinction to prior results, this is a mechanism of intransitivity that does not require nonhierarchical local interference competition. We present parameter estimates from a subtidal marine community illustrating how documented competitive traits can lead to preemption‐based intransitivities in natural communities, and we describe methods for an empirical test of the occurrence of this mechanism.     

Patchiness, aggregation, and the coexistence of competitors for ephemeral resources

Abstract. 1. A laboratory experiment was conducted to determine the outcome of competition between two species of carrion-breeding Diptera for food at two levels of resource patchiness.
2. Adults of Fannia howardi Malloch (Muscidae) and Megaselia scalaris Loew (Phoridae) were released into a large population cage and were given access to three 2g sections of pork kidney in one treatment (low patchiness) and to twelve 0.5g sections in the other (high patchiness).
3. Increasing the patchiness of the resource resulted in reduced overlap in the distribution of the two species, and therefore less interspecific competition. However, this did not result in improved survival of the poorer competitor, F.howardi. Both species aggregated their eggs at high patchiness, and therefore suffered from increased levels of intraspecific competition.
4. The experiment shows that increasing patchiness in this way could lead to prolonged coexistence, as has been predicted in other studies.     

Aggregation, intraguild interactions and the coexistence of competitors on small ephemeral patches

It is well established that intraspecific aggregation has the potential to promote coexistence in communities of species competing for patchy ephemeral resources. We developed a simulation model to explore the influence of aggregation on coexistence in such communities when an important assumption of previous studies – that interspecific interactions have only negative effects on the species involved – is relaxed. The model describes a community of competing insect larvae in which an interaction that is equivalent to intraguild predation (IGP) can occur, and is unusual in that it considers species exploiting very small resource patches (carrying capacity=1). Model simulations show that, in the absence of any intraspecific aggregation, variation between species in the way that resource heterogeneity affects survival increases the likelihood of species coexistence. Simulations also show that intraspecific aggregation of the dominant competitor's eggs across resource patches can promote coexistence by reducing the importance of interspecific competition relative to that of intraspecific competition. Crucially, however, this effect is altered if one competitor indulges in IGP. In general, coexistence is only possible when the species that is capable of IGP is less effective at exploiting the shared resource than its competitor. Because it reduces the relative importance of interspecific interactions, intraspecific aggregation of the eggs of a species that is the victim of IGP actually reduces the likelihood of coexistence in parts of parameter space in which the persistence of the other species is dependent on its ability to exploit its competitor. Since resource heterogeneity, intraspecific aggregation and IGP are all common phenomena, these findings shed light on mechanisms that are likely to influence diversity in communities exploiting patchy resources.     

Hutchinson revisited: Patterns of density regulation and the coexistence of strong competitors

Ecologists have long been searching for mechanisms of species coexistence, particularly since G.E. Hutchinson raised the ‘paradox of the plankton’. A promising approach to solve this paradox and to explain the coexistence of many species with strong niche overlap is to consider over-compensatory density regulation with its ability to generate endogenous population fluctuations.Previous work has analysed the role of over-compensation in coexistence based on analytical approaches. Using a spatially explicit time-discrete simulation model, we systematically explore the dynamics and conditions for coexistence of two species. We go beyond the analytically accessible range of models by studying the whole range of density regulation from under- to very strong over-compensation and consider the impact of spatial structure and temporal disturbances. In particular, we investigate how coexistence can emerge in different types of population growth models.We show that two strong competitors are able to coexist if at least one species exhibits over-compensation. Analysing the time series of population dynamics reveals how the differential responses to density fluctuations of the two competitors lead to coexistence: The over-compensator generates density fluctuations but is the inferior competitor at strong amplitudes of those fluctuations; the competitor, therefore, becomes frequent and dampens the over-compensator's amplitudes, but it becomes inferior under dampened fluctuations.These species interactions cause a dynamic alternation of community states with long-term persistence of both species. We show that a variety of population growth models is able to reproduce this coexistence although the particular parameter ranges differ among the models. Spatial structure influences the probability of coexistence but coexistence is maintained for a broad range of dispersal parameters.The flexibility and robustness of coexistence through over-compensation emphasize the importance of nonlinear density dependence for species interactions, and they also highlight the potential of applying more flexible models than the classical Lotka-Volterra equations in community ecology.     

Predator selectivity alters the effect of dispersal on coexistence among apparent competitors

While the majority of studies on dispersal effects on patterns of coexistence among species in a metacommunity have focused on resource competitors, dispersal in systems with predator–prey interactions may provide very different results. Here, we use an analytical model to study the effect of dispersal rates on coexistence of two prey species sharing a predator (apparent competition), when the traits of that predator vary. Specifically, we explore the range in immigration rates where apparent competitors are able to coexist, and how that range changes with predator selectivity and efficiency. We find that if the inferior apparent competitor has a higher probability of being consumed, it will require less immigration to invade and to exclude the superior prey as the predator becomes more opportunistic. However, if the inferior apparent competitor has a lower probability of being consumed (and lower growth rates), higher immigration is required for the inferior prey to invade and exclude the superior prey as the predator becomes more opportunistic. We further find that the largest range of immigration rates where prey coexist occurs when predator selectivity is intermediate (i.e. they do not show much bias towards consuming one species or the other). Increasing predator efficiency generally reduces the immigration rates necessary for the inferior apparent competitor to invade and exclude the superior apparent competitor, but also reduces the range of immigration rates where the two apparent competitors can coexist. However, when the superior apparent competitor has a higher probability of being consumed, increased predator efficiency can increase the range of parameters where the species can coexist. Our results are consistent with some of the variation observed in the effect of dispersal on prey species richness in empirical systems with top predators.     

Evolutionary rescue and the coexistence of generalist and specialist competitors: an experimental test

Competition for resources is thought to play a critical role in both the origins and maintenance of biodiversity. Although numerous laboratory evolution experiments have confirmed that competition can be a key driver of adaptive diversification, few have demonstrated its role in the maintenance of the resulting diversity. We investigate the conditions that favour the origin and maintenance of alternative generalist and specialist resource-use phenotypes within the same population. Previously, we confirmed that competition for hosts among φ6 bacteriophage in a mixed novel (non-permissive) and ancestral (permissive) host microcosm triggered the evolution of a generalist phenotype capable of infecting both hosts. However, because the newly evolved generalists tended to competitively exclude the ancestral specialists, coexistence between the two phenotypes was rare. Here, we show that reducing the relative abundance of the novel host slowed the increase in frequency of the generalist phenotype, allowing sufficient time for the specialist to further adapt to the ancestral host. This adaptation resulted in ‘evolutionary rescue’ of the specialists, preventing their competitive exclusion by the generalists. Thus, our results suggest that competition promotes both the origin and maintenance of biodiversity when it is strong enough to favour a novel resource-use phenotype, but weak enough to allow adaptation of both the novel and ancestral phenotypes to their respective niches.     

The effect of density-independent mortality on the coexistence of exploitative competitors for renewing resources

Many ecologists believe that higher mortality imposed on competing species increases the probability that they will coexist. This belief has persisted in spite of many theoretical counterarguments. However, few of those counterarguments have been based on models having explicit representation of the resources for which competition is occurring. This article analyzes a series of consumer-resource models of competition for nutritionally substitutable renewable resources and determines the range of relative resource requirements that allow coexistence. In most cases, if consumers are initially efficient at reducing resource densities, increasing density-independent mortality widens the range of resource requirements of the consumers that allow coexistence, provided the increase in mortality is not too great. The coexistence-promoting effects of mortality occur because a very efficient consumer species usually reduces the diversity of the set of resources it consumes. This lessens the extent to which resource utilization differences between consumer species can be expressed. Mortality, in this case, increases the diversity of resource types, widening the conditions for coexistence. However, sufficiently high mortality will usually reduce the range of parameters allowing coexistence, in agreement with much previous theory. The results presented here also predict maximal diversity at intermediate levels of productivity. Previous empirical studies and theory are reviewed in light of the theory developed here.     

Mathematical model allowing the coexistence of closely related competitors at the initial stage of evolution

The mathematical model presented here aims to elucidate the essential mechanisms of coexistence of species, especially those of closely related forms, as a result of competition in the same environment. It describes a system where the fate of the competitors or mutants is observed at the initial stage of evolution. The model encompasses both the external variables and the internal state of the competitors, which differ only in one of the metabolic rate constants. Results of simulations, even with the simplified form of the model, show that stable coexistence of closely related forms in a uniform environment is possible. In addition, the model allows the analysis of the limitations on the level of differences and similarities among the competitors for achieving a state of coexistence. The essential mechanisms for the coexistence of closely related competitors are proposed to be the involvement of the metabolic network in allowing the same growth rate of competitors which have different internal states, and the interplay between the internal states of the competitors and the external variables of their environment.     

Integrating nested spatial scales: implications for the coexistence of competitors on a patchy resource

1. Intraspecific aggregation at a single spatial scale can promote the coexistence of competitors. This paper demonstrates how this same mechanism can be applied to the many systems that are patchy at two scales, with patches nested within 'superpatches'.
2. Data are presented from a field study showing that insects living in rotting fruits have aggregated distributions in the fruits under a single tree, and that the mean density and degree of aggregation varies significantly among trees. Observations in this system motivate the following models.
3. A model of competition has been developed between two species which explicitly represents spatial variation at two scales. By integrating the probability distributions for each scale, the marginal distributions of competitors over all patches can be found and used to calculate coexistence criteria. This model assumes global movement of the competitors.
4. Although spatial variation at a single scale may not be sufficient for coexistence, the total variation over all patches can allow coexistence. Variation in mean densities among superpatches and variation in the degree of aggregation among superpatches both promote coexistence, but act in different ways.
5. A second model of competition between two species is described which incorporates the effects of limited movement among superpatches. Limited movement among superpatches generally promotes coexistence, and also leads to correlations among aggregation and the mean densities of competitors.     

Enigmatic adult overwintering in damselflies: coexistence as weaker intraguild competitors due to niche separation in time

Odonata, like most freshwater invertebrates, tend to overwinter in water due to the thermal properties of a water environment. Winter damselflies (genus Sympecma), however, hibernate as adults in terrestrial habitats. The strategy of adult overwintering combined with high mortality is associated with several unique adaptations to semiarid conditions, but winter damselflies maintain this unique life history throughout almost the entire Palaearctic. We assume that the unique strategy of adult overwintering in temperate zones is indirectly maintained by niche separation in time. We used phenological data from the Czech Republic to compare the seasonal phenology of Sympecma spp. with other coexisting odonate species. Seasonal population growth patterns between S. fusca and other coexisting species representing different life histories were compared using GLMMs and LME. The models showed negative non-linear dependence between the population growth of S. fusca and the estimated abundance of compared species. We found that the specific strategy of adult overwintering makes it possible to avoid seasonal maxima of competition and predation in adult and larval stages. Adults may benefit from free niches during spring while larvae may benefit from size advantage among intraguild competitors and optimal conditions for development.     

Effects of growth rate and influent substrate concentration on effluent quality from chemostats containing bacteria in pure and mixed culture

Studies were performed using pure cultures of A. acrogenes and E. coli and a heterogeneous microbial population growing in carbon-limited chemostats with glucose as the sole carbon and energy source. A two-level factorial experimental design was employed to test the hypothesis that the concentration of growth-limiting substrate in a chemostat is controlled by the growth rate alone and is independent of the concentration of substrate entering the reactor. The pure culture experiments showed that the conclusions depend upon the measurement employed for growth-limiting substrate. When the concentration of glucose was measured directly, the hypothesis was found to be true within the limits of the study (500–1500 mg/liter). However, if the chemical oxygen demand (COD) test was used as the measure of growth-limiting substrate the hypothesis was found to be false. When heterogeneous cultures were employed the hypothesis was false regardless of the technique used to measure the concentration of growth-limiting substrate. Nevertheless, it was possible to generate regression equations which described the interactions among influent COD, growth rate, and effluent COD with a high level of correlation.     

Permanent coexistence in general models of three interacting species

We address the question of the long term coexistence of three interacting species whose dynamics are governed by the ordinary differential equations x _i = X _i f _i (i = 1, 2, 3). In order for any theory in this area to be useful in practice, it must utilize as little information as possible concerning the forms of the f _i , in view of the great difficulty of determining these experimentally. Here we obtain, under rather general conditions on the equations, a criterion for judging whether the species will coexist in a biologically realistic manner. This criterion depends only on the behaviour near the one or two species equilibria of the two dimensional subsystems, the behaviour there being relatively easy to examine experimentally. We show that with the exception of one class of cases, which is a generalization of a classical example of May and Leonard [21], invasibility at each such equilibrium suitably interpreted is both necessary and sufficient for a strong form of coexistence to hold. In the exceptional case, a single additional condition at the equilibria is enough to ensure coexistence.     

Genetic mapping of biomass yield in three interconnected Miscanthus populations

Improving biomass yield is a major goal of Miscanthus breeding. We conducted a study on one interspecific Miscanthus sinensis × Miscanthus sacchariflorus F₁ population and two intraspecific M. sinensis F₁ populations, each of which shared a common parent. A field trial was established at Urbana, IL during spring 2011, and phenotypic data were collected in 2012 and 2013 for fourteen yield traits. Six high‐density parental genetic maps, as well as a consensus genetic map integrating M. sinensis and M. sacchariflorus, were developed via the pseudotestcross strategy for noninbred parents with ≥1214 single‐nucleotide polymorphism markers generated from restriction site‐associated DNA sequencing. We confirmed for the first time a whole‐genome duplication in M. sacchariflorus relative to Sorghum bicolor, similar to that observed previously for M. sinensis. Four quantitative trait locus (QTL) analysis methods for detecting marker‐trait associations were compared: (1) individual parental map composite interval mapping analysis, (2) individual parental map stepwise analysis, (3) consensus map single‐population stepwise analysis and (4) consensus map joint‐population stepwise analysis. These four methods detected 288, 264, 133 and 109 total QTLs, which resolved into 157, 136, 106 and 86 meta‐QTLs based on QTL congruency, respectively, including a set of 59 meta‐QTLs common to all four analysis methods. Composite interval mapping and stepwise analysis co‐identified 118 meta‐QTLs across six parental maps, suggesting high reliability of stepwise regression in QTL detection. Joint‐population stepwise analysis yielded the highest resolution of QTLs compared to the other three methods across all meta‐QTLs. Strong, frequently advantageous transgressive segregation in the three populations indicated a promising future for breeding new higher‐yielding cultivars of Miscanthus.