Competitive exclusion and limiting similarity: A unified theory

Spatial aspects of prebiotic replicator coexistence and community stability in a surface-bound RNA world model

Background

The coexistence of macromolecular replicators and thus the stability of presumed prebiotic replicator communities have been shown to critically depend on spatially constrained catalytic cooperation among RNA-like modular replicators. The necessary spatial constraints might have been supplied by mineral surfaces initially, preceding the more effective compartmentalization in membrane vesicles which must have been a later development of chemical evolution.

Results

Using our surface-bound RNA world model – the Metabolic Replicator Model (MRM) platform – we show that the mobilities on the mineral substrate surface of both the macromolecular replicators and the small molecules of metabolites they produce catalytically are the key factors determining the stable persistence of an evolvable metabolic replicator community.

Conclusion

The effects of replicator mobility and metabolite diffusion on different aspects of replicator coexistence in MRM are determined, including the maximum attainable size of the metabolic replicator system and its resistance to the invasion of parasitic replicators. We suggest a chemically plausible hypothetical scenario for the evolution of the first protocell starting from the surface-bound MRM system.

Self-extinction through optimizing selection

Evolutionary suicide is a process in which selection drives a viable population to extinction. So far, such selection-driven self-extinction has been demonstrated in models with frequency-dependent selection. This is not surprising, since frequency-dependent selection can disconnect individual-level and population-level interests through environmental feedback. Hence it can lead to situations akin to the tragedy of the commons, with adaptations that serve the selfish interests of individuals ultimately ruining a population. For frequency-dependent selection to play such a role, it must not be optimizing. Together, all published studies of evolutionary suicide have created the impression that evolutionary suicide is not possible with optimizing selection. Here we disprove this misconception by presenting and analyzing an example in which optimizing selection causes self-extinction. We then take this line of argument one step further by showing, in a further example, that selection-driven self-extinction can occur even under frequency-independent selection.

Limiting similarity, species packing, and the shape of competition kernels

A traditional question in community ecology is whether species' traits are distributed as more-or-less regularly spaced clusters. Interspecific competition has been suggested to play a role in such structuring of communities. The seminal theoretical work on limiting similarity and species packing, presented four decades ago by Robert MacArthur, Richard Levins and Robert May, has recently been extended. There is now a deeper understanding of how competitive interactions influence community structure, for instance, how the shape of competition kernels can determine the clustering of species' traits. Competition is typically weaker for greater phenotypic difference, and the shape of the dependence defines a competition kernel. The clustering tendencies of kernels interact with other effects, such as variation in resource availability along a niche axis, but the kernel shape can have a decisive influence on community structure. Here we review and further extend the recent developments and evaluate their importance.

How specialised must natural enemies be to facilitate coexistence among plants?

The Janzen-Connell hypothesis proposes that plant interactions with host-specific antagonists can impair the fitness of locally abundant species and thereby facilitate coexistence. However, insects and pathogens that associate with multiple hosts may mediate exclusion rather than coexistence. We employ a simulation model to examine the effect of enemy host breadth on plant species richness and defence community structure, and to assess expected diversity maintenance in example systems. Only models in which plant enemy similarity declines rapidly with defence similarity support greater species richness than models of neutral drift. In contrast, a wide range of enemy host breadths result in spatial dispersion of defence traits, at both landscape and local scales, indicating that enemy-mediated competition may increase defence-trait diversity without enhancing species richness. Nevertheless, insect and pathogen host associations in Panama and Papua New Guinea demonstrate a potential to enhance plant species richness and defence-trait diversity comparable to strictly specialised enemies.

Revising the tolerance-fecundity trade-off; or, on the consequences of discontinuous resource use for limiting similarity, species diversity, and trait dispersion

The recently proposed tolerance-fecundity trade-off model represents a step forward in the study of seed size diversity in plant communities. However, it uses an oversimplified picture of seed tolerance, with an infinitely sharp threshold: the probability that a seed tolerate a given stress level is either 1 or 0. This invites a revision of the model, presented here. We demonstrate that this simplification has large impacts on model behavior, including altering predictions regarding limiting similarity, raising expected diversity levels, and lessening expected spacing between species along the trait axis. Such dramatic impacts ultimately stem from the fact that a discontinuity in the probability of tolerating a site drastically reduces competition between similar species. This is one example of a class of models with a nondifferentiable peak in the competition kernel, which we recently showed is produced by resource use unrealistically modeled as discontinuous and affects fundamental predictions regarding limiting similarity. This article illustrates those general results and offers a revised model of the tolerance-fecundity trade-off.

A construction method to study the role of incidence in the adaptive dynamics of pathogens with direct and environmental transmission

We study the adaptive dynamics of virulence of a pathogen transmitted both via direct contacts between hosts and via free pathogens that survive in the environment. The model is very flexible with a number of trade-off functions linking virulence to other pathogen-related parameters and with two incidence functions that describe the contact rates between hosts and between a host and free pathogens. Instead of making a priori particular assumptions about the shapes of these functions, we introduce a construction method to create specific pairs of incidence functions such that the model becomes an optimization model. Unfolding the optimization model leads to coexistence of pathogen strains and evolutionary branching of virulence. The construction method is applicable to a wide range of eco-evolutionary models.

Quantifying the likelihood of co-existence for communities with asymmetric competition

Trade-offs in performance of different ecological functions within a species are commonly offered as an explanation for co-existence in natural communities. Single trade-offs between competitive ability and other life history traits have been shown to support a large number of species, as a result of strong competitive asymmetry. We consider a single competition-fecundity trade-off in a homogeneous environment, and examine the effect of the form of asymmetry on the likelihood of species co-existing. We find conditions that allow co-existence of two species for a general competition function, and show that (1) two species can only co-exist if the competition function is sufficiently steep when the species are similar; (2) when competition is determined by a linear function, no more than two species can co-exist; (3) when the competition between two individuals is determined by a discontinuous step function, this single trade-off can support an arbitrarily large number of species. Further, we show analytically that as the degree of asymmetry in competition increases, the probability of a given number of species co-existing also increases, but note that even in the most favourable conditions, large numbers of species co-existing along a single trade-off is highly unlikely. On this basis, we suggest it is unlikely that single trade-offs are able to support high levels of bio-diversity without interacting other processes.

A rigorous model study of the adaptive dynamics of Mendelian diploids

Adaptive dynamics (AD) so far has been put on a rigorous footing only for clonal inheritance. We extend this to sexually reproducing diploids, although admittedly still under the restriction of an unstructured population with Lotka-Volterra-like dynamics and single locus genetics (as in Kimura's in Proc Natl Acad Sci USA 54: 731-736, 1965 infinite allele model). We prove under the usual smoothness assumptions, starting from a stochastic birth and death process model, that, when advantageous mutations are rare and mutational steps are not too large, the population behaves on the mutational time scale (the 'long' time scale of the literature on the genetical foundations of ESS theory) as a jump process moving between homozygous states (the trait substitution sequence of the adaptive dynamics literature). Essential technical ingredients are a rigorous estimate for the probability of invasion in a dynamic diploid population, a rigorous, geometric singular perturbation theory based, invasion implies substitution theorem, and the use of the Skorohod M 1 topology to arrive at a functional convergence result. In the small mutational steps limit this process in turn gives rise to a differential equation in allele or in phenotype space of a type referred to in the adaptive dynamics literature as 'canonical equation'.

What life cycle graphs can tell about the evolution of life histories

We analyze long-term evolutionary dynamics in a large class of life history models. The model family is characterized by discrete-time population dynamics and a finite number of individual states such that the life cycle can be described in terms of a population projection matrix. We allow an arbitrary number of demographic parameters to be subject to density-dependent population regulation and two or more demographic parameters to be subject to evolutionary change. Our aim is to identify structural features of life cycles and modes of population regulation that correspond to specific evolutionary dynamics. Our derivations are based on a fitness proxy that is an algebraically simple function of loops within the life cycle. This allows us to phrase the results in terms of properties of such loops which are readily interpreted biologically. The following results could be obtained. First, we give sufficient conditions for the existence of optimisation principles in models with an arbitrary number of evolving traits. These models are then classified with respect to their appropriate optimisation principle. Second, under the assumption of just two evolving traits we identify structural features of the life cycle that determine whether equilibria of the monomorphic adaptive dynamics (evolutionarily singular points) correspond to fitness minima or maxima. Third, for one class of frequency-dependent models, where optimisation is not possible, we present sufficient conditions that allow classifying singular points in terms of the curvature of the trade-off curve. Throughout the article we illustrate the utility of our framework with a variety of examples.

Niche and fitness differences relate the maintenance of diversity to ecosystem function

The frequently observed positive correlation between species diversity and community biomass is thought to depend on both the degree of resource partitioning and on competitive dominance between consumers, two properties that are also central to theories of species coexistence. To make an explicit link between theory on the causes and consequences of biodiversity, we define in a precise way two kinds of differences among species: niche differences, which promote coexistence, and relative fitness differences, which promote competitive exclusion. In a classic model of exploitative competition, promoting coexistence by increasing niche differences typically, although not universally, increases the "relative yield total", a measure of diversity's effect on the biomass of competitors. In addition, however, we show that promoting coexistence by decreasing relative fitness differences also increases the relative yield total. Thus, two fundamentally different mechanisms of species coexistence both strengthen the influence of diversity on biomass yield. The model and our analysis also yield insight on the interpretation of experimental diversity manipulations. Specifically, the frequently reported "complementarity effect" appears to give a largely skewed estimate of resource partitioning. Likewise, the "selection effect" does not seem to isolate biomass changes attributable to species composition rather than species richness, as is commonly presumed. We conclude that past inferences about the cause of observed diversity-function relationships may be unreliable, and that new empirical estimates of niche and relative fitness differences are necessary to uncover the ecological mechanisms responsible for diversity-function relationships.

Rapid exploiter-victim coevolution: the race is not always to the swift

The modeling of coevolutionary races has traditionally been dominated by methods invoking a timescale separation between ecological and evolutionary dynamics, the latter assumed to be much slower than the former. Yet it is becoming increasingly clear that in many cases the two processes occur on similar timescales and that such "rapid" evolution can have profound implications for the dynamics of communities and ecosystems. After briefly reviewing the timescale separations most common in coevolution theory, we use a general model of exploiter-victim coevolution to confront predictions from slow-evolution analysis with Monte Carlo simulations. We show how rapid evolution radically alters the dynamics and outcome of coevolutionary arms races. In particular, a fast-evolving exploiter can enable victim diversification and thereby lose a race it is expected to win. We explain simulation results, using mathematical analysis with relaxed timescale separations. Unusual mutation parameters are not required, since rapid evolution naturally emerges from slow competitive exclusion. Our results point to interesting consequences of exploiter rapid evolution and experimentally testable patterns, while indicating that more attention should be paid to rapid evolution in evolutionary theory.

Coexistence in a fluctuating environment by the effect of relative nonlinearity: a minimal model

The minimal model of the "relative nonlinearity" type fluctuation-maintained coexistence is investigated. The competing populations are affected by an environmental white noise. With quadratic density dependence, the long-term growth rates of the populations are determined by the average and the variance of the (fluctuating) total density. At most two species can coexist on these two "regulating" variables; competitive exclusion would ensue in a constant environment. A numerical study of the expected time until extinction of any of the two species reveals that the criterion of mutual invasibility predicts the parameter range of long-term coexistence correctly in the limit of zero extinction threshold. However, any extinction threshold consistent with a realistic population size will allow only short-term coexistence. Therefore, our simulations question the biological relevance of mutual invasibility, as a sufficient condition of coexistence, for large density fluctuations. We calculate the average and the variance of the fluctuating density of the coexisting populations analytically via the moment-closure approximation; the results are reasonably close to the simulated behavior. Based on this treatment, robustness of coexistence is studied in the limit of infinite population size. We interpret the results of this analysis in the context of necessity of niche segregation with respect to the regulating variables using a framework theory published earlier.

Plant competition and exclusion with optimizing individuals

Most models of plant competition represent competition as taking place between species when realistically competition takes place between individuals. We model individual plants as optimally choosing biomass in order to maximize net energy that is directed into reproduction. Competition is for access to light and a plant that grows more biomass adds to the leaf area index, creating negative feedback in the form of more self shading and shading of its neighbors. In each period and for given species densities, simultaneous maximization by all plants yields an equilibrium characterized by optimum biomasses. Between periods the net energies plants obtain are used to update the densities, and if densities change the equilibrium changes in the subsequent period. A steady state is attained when all plants have net energies that just allow for replacement. Four main predictions of the resource-ratio theory of competition are obtained, providing behavioral underpinnings for species level models. However, if individual plant parameters are not identical across species, then the predictions do not follow. The optimization framework yields many other predictions, including how specific leaf areas and resource stress impact biomass and leaf area indices.

Species competition: coexistence, exclusion and clustering

We present properties of Lotka-Volterra equations describing ecological competition among a large number of interacting species. First we extend previous stability conditions to the case of a non-homogeneous niche space, i.e. that of a carrying capacity depending on the species trait. Second, we discuss mechanisms leading to species clustering and obtain an analytical solution for a state with a lumped species distribution for a specific instance of the system. We also discuss how realistic ecological interactions may result in different types of competition coefficients.

Evolution of specialization in resource utilization in structured metapopulations

We study the evolution of resource utilization in a structured discrete-time metapopulation model with an infinite number of patches, prone to local catastrophes. The consumer faces a trade-off in the abilities to consume two resources available in different amounts in each patch. We analyse how the evolution of specialization in the utilization of the resources is affected by different ecological factors: migration, local growth, local catastrophes, forms of the trade-off and distribution of the resources in the patches. Our modelling approach offers a natural way to include more than two patch types into the models. This has not been usually possible in the previous spatially heterogeneous models focusing on the evolution of specialization.

Reproductive isolation and ecological niche partition among larvae of the morphologically cryptic sister species Chironomus riparius and C. piger

BACKGROUND

One of the central issues in ecology is the question what allows sympatric occurrence of closely related species in the same general area? The non-biting midges Chironomus riparius and C. piger, interbreeding in the laboratory, have been shown to coexist frequently despite of their close relatedness, similar ecology and high morphological similarity.

METHODOLOGY/PRINCIPAL FINDINGS

In order to investigate factors shaping niche partitioning of these cryptic sister species, we explored the actual degree of reproductive isolation in the field. Congruent results from nuclear microsatellite and mitochondrial haplotype analyses indicated complete absence of interspecific gene-flow. Autocorrelation analysis showed a non-random spatial distribution of the two species. Though not dispersal limited at the scale of the study area, the sister species occurred less often than expected at the same site, indicating past or present competition. Correlation and multiple regression analyses suggested the repartition of the available habitat along water chemistry gradients (nitrite, conductivity, CaCO(3)), ultimately governed by differences in summer precipitation regime.

CONCLUSIONS

We show that these morphologically cryptic sister species partition their niches due to a certain degree of ecological distinctness and total reproductive isolation in the field. The coexistence of these species provides a suitable model system for the investigation of factors shaping the distribution of closely related, cryptic species.

Grinnellian and Eltonian niches and geographic distributions of species

In the recent past, availability of large data sets of species presences has increased by orders of magnitude. This, together with developments in geographical information systems and statistical methods, has enabled scientists to calculate, for thousands of species, the environmental conditions of their distributional areas. The profiles thus obtained are obviously related to niche concepts in the Grinnell tradition, and separated from those in Elton's tradition. I argue that it is useful to define Grinnellian and Eltonian niches on the basis of the types of variables used to calculate them, the natural spatial scale at which they can be measured, and the dispersal of the individuals over the environment. I use set theory notation and analogies derived from population ecology theory to obtain formal definitions of areas of distribution and several types of niches. This brings clarity to several practical and fundamental questions in macroecology and biogeography.

Adaptive dynamics for physiologically structured population models

We develop a systematic toolbox for analyzing the adaptive dynamics of multidimensional traits in physiologically structured population models with point equilibria (sensu Dieckmann et al. in Theor. Popul. Biol. 63:309-338, 2003). Firstly, we show how the canonical equation of adaptive dynamics (Dieckmann and Law in J. Math. Biol. 34:579-612, 1996), an approximation for the rate of evolutionary change in characters under directional selection, can be extended so as to apply to general physiologically structured population models with multiple birth states. Secondly, we show that the invasion fitness function (up to and including second order terms, in the distances of the trait vectors to the singularity) for a community of N coexisting types near an evolutionarily singular point has a rational form, which is model-independent in the following sense: the form depends on the strategies of the residents and the invader, and on the second order partial derivatives of the one-resident fitness function at the singular point. This normal form holds for Lotka-Volterra models as well as for physiologically structured population models with multiple birth states, in discrete as well as continuous time and can thus be considered universal for the evolutionary dynamics in the neighbourhood of singular points. Only in the case of one-dimensional trait spaces or when N = 1 can the normal form be reduced to a Taylor polynomial. Lastly we show, in the form of a stylized recipe, how these results can be combined into a systematic approach for the analysis of the (large) class of evolutionary models that satisfy the above restrictions.

Quasi-local competition in stage-structured metapopulations: a new mechanism of pattern formation

A central question of ecology is what determines the presence and abundance of species at different locations. In cases of ecological pattern formation, population sizes are largely determined by spatially distributed interactions and may have very little to do with the habitat template. We find pattern formation in a single-species metapopulation model with quasi-local competition, but only if the populations have (at least) two age or stage classes. Quasi-local competition is modeled using an explicit resource competition model with fast resource dynamics, and assuming that adults, but not juveniles, spend a fraction of their foraging time in habitat patches adjacent to their home patch. Pattern formation occurs if one stage class depletes the common resource but the shortage of resource affects mostly the other stage. When the two stages are spatially separated due to quasi-local competition, this results in competitive exclusion between the populations. We find deep similarity between spatial pattern formation and population cycles due to competitive exclusion between cohorts of biennial species, and discuss the differences between the present mechanism and established ways of pattern formation such as diffusive instability and distributed competition with local Allee-effects.

Diversity as a product of inter-specific interactions

We demonstrate diversification rather than optimization for highly interacting organisms in a well-mixed biological system by means of a simple model of coevolution. We find the cause to be the complex network of interactions formed, allowing species that are less well adapted to an environment to succeed, instead of the 'best' species. This diversification can be considered as the construction of many coevolutionary niches by the network of interactions between species. The model predictions are discussed in relation to experimental work on dense communities of the bacteria Escherichia coli, which may coexist with their own mutants under certain conditions. We find that diversification only occurs above a certain threshold interaction strength, below which competitive exclusion occurs.

Coexistence in a metacommunity: the competition-colonization trade-off is not dead

The competition-colonization trade-off model is often used to explain the coexistence of species. Yet its applicability has been severely criticized, mainly because the original model assumed a strict competitive hierarchy of species and did not allow for any preemptive effect. We considered the impact of relaxing both of these limitations on coexistence. Relaxing trade-off intensity makes coexistence less likely and introduces a minimum colonization rate below which any coexistence is impossible. Allowing for preemption introduces a limit to dissimilarity between species. Surprisingly, preemption does not impede coexistence as one could presume from previous studies, but can actually increase the likelihood of coexistence. Its effect on coexistence depends on whether or not species in the regional pool are strongly limited in their colonization ability. Preemption is predicted to favour coexistence when: (i) species are not strongly limited in their colonization ability; and (ii) the competitive trade-off is not infinitely intense.