Gause's Principle and the Effect of Resource Partitioning on the Dynamical Coexistence of Replicating Templates

Models of competitive template replication, although basic for replicator dynamics and primordial evolution, have not yet taken different sequences explicitly into account, neither have they analyzed the effect of resource partitioning (feeding on different resources) on coexistence. Here we show by analytical and numerical calculations that Gause''s principle of competitive exclusion holds for template replicators if resources (nucleotides) affect growth linearly and coexistence is at fixed point attractors. Cases of complementary or homologous pairing between building blocks with parallel or antiparallel strands show no deviation from the rule that the nucleotide compositions of stably coexisting species must be different and there cannot be more coexisting replicator species than nucleotide types. Besides this overlooked mechanism of template coexistence we show also that interesting sequence effects prevail as parts of sequences that are copied earlier affect coexistence more strongly due to the higher concentration of the corresponding replication intermediates. Template and copy always count as one species due their constraint of strict stoichiometric coupling. Stability of fixed-point coexistence tends to decrease with the length of sequences, although this effect is unlikely to be detrimental for sequences below 100 nucleotides. In sum, resource partitioning (niche differentiation) is the default form of competitive coexistence for replicating templates feeding on a cocktail of different nucleotides, as it may have been the case in the RNA world. Our analysis of different pairing and strand orientation schemes is relevant for artificial and potentially astrobiological genetics.     

Survival of replicators with parabolic growth tendency and exponential decay

The claim that the competition of parabolically growing self-replicators leads to dynamically stable coexistence was challenged by Lifson & Lifson [(1999). J. theor. Biol.199, 425-433]. They have shown that, if single- and double-strands are treated separately, and only single-strands undergo spontaneous decay, then there is natural selection rather than survival of everybody. We use their models to show that if double-strand decay is not neglected, then dynamical coexistence is still possible under a wide range of parameter values, in agreement with the chromatographized replicator model of von Kiedrowski & Szathmáry [(2000). Selection 1-3, 173-179]. Coexistence is always ensured above a critical resource (monomer) inflow rate. Recycling of decayed replicators into monomers further favours dynamical coexistence. The claim that parabolic growth invariably results in coexistence remains valid for the model for which it was meant to apply, namely for parabolic growth without template decay. Exponential decay acting on single- and double-strands, combined with parabolic growth, may or may not result in a dynamical coexistence of self-replicators.     

Coexistence and error propagation in pre-biotic vesicle models: a group selection approach

Compartmentalization of unlinked, competing templates is widely accepted as a necessary step towards the evolution of complex organisms. However, preservation of information by templates confined to isolated vesicles of finite size faces much harder obstacles than by free templates: random drift allied to mutation pressure wipe out any template that does not replicate perfectly, no matter how small the error probability might be. In addition, drift alone hinders the coexistence of distinct templates in a same compartment. Here, we investigate the conditions for group selection to prevail over drift and mutation and hence to guarantee the maintenance and coexistence of distinct templates in a vesicle. Group selection is implemented through a vesicle survival probability that depends on the template composition. By considering the limit case of an infinite number of vesicles, each one carrying a finite number of templates, we were able to derive a set of recursion equations for the frequencies of vesicles with different template compositions. Numerical iteration of these recursions allows the exact characterization of the steady state of the vesicle population-a quasispecies of vesicles-thus revealing the values of the mutation and group selection intensities for which template coexistence is possible. Within the main assumption of the model-a fixed, finite or infinite, number of vesicles-we find no fundamental impediment to the coexistence of an arbitrary number of template types with the same replication rate inside a vesicle, except of course for the vesicle capacity. Group selection in the form of vesicle selection is a must for compartmentalized primordial genetic systems even in the absence of intra-genomic competition of different templates.     

物种对资源竞争的动力机制及数值模拟

建立了集合种群物种在两个斑块中对资源竞争的数学模型,并进行了数值模拟实验,结果表明：（1）通过R^＊来预测竞争物种的结局,存在几种可能性：一是具有低R^＊值的物种竞争取代高R^＊值的物种;二是具有不同R^＊值的物种,甚至是具有相同R^＊值的物种也存在共存的可能性;三是具有高R^＊值的物种也可以竞争排斥低R^＊值的物种,结论存在不确定性。（2）竞争物种的随机迁移形成了源一汇结构,对物种竞争共存具有促进作用,但弱的资源利用者（较高的R^＊）的迁移率不宜过高。（3）在种群统计率相同的条件下,资源增长率差异越大,越不利于消费者物种的共存;若种群统计率不相同,在资源增长率相同的情况下,物种共存又是不可能的,在自然界中,物种共存需要资源增长率的差异。（4）不同类型的资源增长对竞争物种的稳定性的影响是不同的。     

Building modern coexistence theory from the ground up: The role of community assembly

Modern coexistence theory (MCT) is one of the leading methods to understand species coexistence. It uses invasion growth rates—the average, per-capita growth rate of a rare species—to identify when and why species coexist. Despite significant advances in dissecting coexistence mechanisms when coexistence occurs, MCT relies on a ‘mutual invasibility’ condition designed for two-species communities but poorly defined for species-rich communities. Here, we review well-known issues with this component of MCT and propose a solution based on recent mathematical advances. We propose a clear framework for expanding MCT to species-rich communities and for understanding invasion resistance as well as coexistence, especially for communities that could not be analysed with MCT so far. Using two data-driven community models from the literature, we illustrate the utility of our framework and highlight the opportunities for bridging the fields of community assembly and species coexistence.     

A shared limiting resource leads to competitive exclusion in a cross-feeding system

Species interactions and coexistence are often dependent upon environmental conditions. When two cross-feeding bacteria exchange essential nutrients, the addition of a cross-fed nutrient to the environment can release one species from its dependence on the other. Previous studies suggest that continued coexistence depends on relative growth rates: coexistence is maintained if the slower-growing species is released from its dependence on the other, but if the faster-growing species is released, the slower-growing species will be lost (a hypothesis that we call ‘feed the faster grower’ or FFG). Using invasion-from-rare experiments with two reciprocally cross-feeding bacteria, genome-scale metabolic modelling and classical ecological models, we explored the potential for coexistence when one cross-feeder became independent. We found that whether nutrient addition shifted an interaction from mutualism to commensalism or parasitism depended on whether the nutrient that limited total growth was required by one or both species. Parasitism resulted when both species required the growth-limiting resource. Importantly, coexistence was only lost when the interaction became parasitism, and the obligate species had a slower growth rate. Under these restricted conditions, the FFG hypothesis applied. Our results contribute to a mechanistic understanding of how resources can be manipulated to alter interactions and coexistence in microbial communities.     

Rainfall variability maintains grass‐forb species coexistence

Environmental variability can structure species coexistence by enhancing niche partitioning. Modern coexistence theory highlights two fluctuation‐dependent temporal coexistence mechanisms —the storage effect and relative nonlinearity – but empirical tests are rare. Here, we experimentally test if environmental fluctuations enhance coexistence in a California annual grassland. We manipulate rainfall timing and relative densities of the grass Avena barbata and forb Erodium botrys, parameterise a demographic model, and partition coexistence mechanisms. Rainfall variability was integral to grass–forb coexistence. Variability enhanced growth rates of both species, and early‐season drought was essential for Erodium persistence. While theoretical developments have focused on the storage effect, it was not critical for coexistence. In comparison, relative nonlinearity strongly stabilised coexistence, where Erodium experienced disproportionately high growth under early‐season drought due to competitive release from Avena. Our results underscore the importance of environmental variability and suggest that relative nonlinearity is a critical if underappreciated coexistence mechanism.     

Proto-Organism Kinetics: Evolutionary Dynamics of Lipid Aggregates with Genes and Metabolism

A synthetic proto-organism could be self-assembled by integrating a lipid proto-container with a proto-metabolic subsystem and a proto-genetic subsystem. This three-component system can use energy and nutrients by means of either redox or photo-chemical reactions, evolve its protogenome by means of template directed replication, and ultimately die. The evolutionary dynamics of the proto-organism depends crucially on the chemical kinetics of its sub-systems and on their interplay. In this work the template replication kinetics is investigated and it is found that the product inhibition inherent in the ligation-like replication process allows for coexistence of unrelated self-replicating proto-genes in the lipid surface layer. The combined catalytic effects from the proto-genes on the metabolic production rates determine the fate of the strain protocell.     

Interspecific competition between Sitophilus zeamais and Sitotroga cerealella in a patchy environment

The maize weevil, Sitophilus zeamais (Motchulsky) (Coleoptera: Curculionidae), and the Angoumois grain moth, Sitotroga cerealella (Olivier) (Lepidoptera: Gelechiidae), are important insect pests of stored products. The coexistence in nature of the two species on maize has been difficult to explain from laboratory set‐ups, as the moth is inevitably eliminated by S. zeamais. However, early laboratory experiments ignored the spatial dimension, while several studies have lately revealed that two competing species may coexist in a spatially divided environment even though one of the species is competitively superior in a simpler universe. Two hypotheses for coexistence were examined by studying the interactions in a system where the resources were spatially divided. It was found that spatial subdivision in the current experiment was insufficient to ensure coexistence between the two species, so neither of the hypotheses could be confirmed. A simple model describing the population dynamics of S. zeamais was fitted to the data. Its parameters provide important information about how resource depletion influences the per capita growth rate. Finally, the study indicates that the mechanism responsible for S. zeamais's rapid elimination of S. cerealella is the superiority of the former species to colonize and monopolize new patches. The design of this study may serve as a template for further laboratory experiments revealing the effect of a spatially divided environment on competitive interactions. However, the present study also indicates that choosing the appropriate spatial scale may be critical for relating the results to natural environments.     

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.     

Package models and the information crisis of prebiotic evolution

The coexistence between different types of templates has been the choice solution to the information crisis of prebiotic evolution, triggered by the finding that a single RNA-like template cannot carry enough information to code for any useful replicase. In principle, confining d distinct templates of length L in a package or protocell, whose survival depends on the coexistence of the templates it holds in, could resolve this crisis provided that d is made sufficiently large. Here we review the prototypical package model of Niesert et al. [1981. Origin of life between Scylla and Charybdis. J. Mol. Evol. 17, 348-353] which guarantees the greatest possible region of viability of the protocell population, and show that this model, and hence the entire package approach, does not resolve the information crisis. In particular, we show that the total information stored in a viable protocell (Ld) tends to a constant value that depends only on the spontaneous error rate per nucleotide of the template replication mechanism. As a result, an increase of d must be followed by a decrease of L, so that the net information gain is null.     

Species coexistence in a variable world

The contribution of deterministic and stochastic processes to species coexistence is widely debated. With the introduction of powerful statistical techniques, we can now better characterise different sources of uncertainty when quantifying niche differentiation. The theoretical literature on the effect of stochasticity on coexistence, however, is often ignored by field ecologists because of its technical nature and difficulties in its application. In this review, we examine how different sources of variability in population dynamics contribute to coexistence. Unfortunately, few general rules emerge among the different models that have been studied to date. Nonetheless, we believe that a greater understanding is possible, based on the integration of coexistence and population extinction risk theories. There are two conditions for coexistence in the presence of environmental and demographic variability: (1) the average per capita growth rates of all coexisting species must be positive when at low densities, and (2) these growth rates must be strong enough to overcome negative random events potentially pushing densities to extinction. We propose that critical tests for species coexistence must account for niche differentiation arising from this variability and should be based explicitly on notions of stability and ecological drift.     

Relatedness among arbuscular mycorrhizal fungi drives plant growth and intraspecific fungal coexistence

Arbuscular mycorrhizal fungi (AMF) form symbioses with most plant species. They are ecologically important determinants of plant growth and diversity. Considerable genetic variation occurs in AMF populations. Thus, plants are exposed to AMF of varying relatedness to each other. Very little is known about either the effects of coexisting AMF on plant growth or which factors influence intraspecific AMF coexistence within roots. No studies have addressed whether the genetics of coexisting AMF, and more specifically their relatedness, influences plant growth and AMF coexistence. Relatedness is expected to influence coexistence between individuals, and it has been suggested that decreasing ability of symbionts to coexist can have negative effects on the growth of the host. We tested the effect of a gradient of AMF genetic relatedness on the growth of two plant species. Increasing relatedness between AMFs lead to markedly greater plant growth (27% biomass increase with closely related compared to distantly related AMF). In one plant species, closely related AMF coexisted in fairly equal proportions but decreasing relatedness lead to a very strong disequilibrium between AMF in roots, indicating much stronger competition. Given the strength of the effects with such a shallow relatedness gradient and the fact that in the field plants are exposed to a steeper gradient, we consider that AMF relatedness can have a strong role in plant growth and the ability of AMF to coexist. We conclude that AMF relatedness is a driver of plant growth and that relatedness is also a strong driver of intraspecific coexistence of these ecologically important symbionts.     

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.     

Shade tolerance,canopy gaps and mechanisms of coexistence of forest trees

The belief that canopy gaps are important for the maintenance of tree species diversity appears to be widespread, but there have been no formal theoretical models to assess under what conditions gap phase processes allow coexistence. Much of the empirical research on niche differentiation in response to gaps has focused on evidence for an interspecific tradeoff between low light survival and high light growth. The objectives of this study are first to distinguish the possible mechanisms allowing coexistence based on this tradeoff, and second, to explore their limitations. We present a theory of forest dynamics driven by small‐scale disturbances as a special case of the theory of coexistence in variable environments. We demonstrate that temporal and spatial heterogeneity in light conditions that results from canopy gaps can allow stable coexistence as a result of three previously documented general mechanisms: ‘relative non‐linearity’, ‘the successional niche’ and the ‘storage effect’. We find that temporal fluctuations in light availability alone allow the stable coexistence of only two species. Spatial variation in disturbance synchronicity and intensity allows three species to coexist in a narrow parameter space. The rate of extinction is, however, extremely slow and there is transient coexistence of a larger number of species for a long period of time. We conclude that while the low light survival/high light growth tradeoff may be ubiquitous in forest tree species, it is unlikely to function as an important mechanism for the stable coexistence of several tree species.     

Drastic growth effect may explain sympatric cannibalistic polymorphism

Cannibalistic polyphenism is observed in many fishes and amphibians. In the case of amphibian larvae, cannibal morph and typical morph coexist. Benefits and costs of the cannibal morph have been studied empirically but the mechanism of the maintenance of polymorphism is not well known. Here, we construct a game model of typical and cannibal morph strategies to obtain the condition of stable coexistence. Generally, once an individual succeeds in cannibalism, it grows very quickly, which facilitates the next cannibalism. In a model without this 'drastic growth effect', stable coexistence cannot occur. To represent drastic growth effect, it is assumed that cannibal/typical morph stage is followed by giant/normal stage. A cannibal morph that performs cannibalism in the first stage can become a 'giant' in the next stage. This model allows stable coexistence of cannibal and typical morphs. The condition for coexistence is that payoff of a giant is two times larger than normal individuals. As long as direct consumption of victim's body is considered as reward for successful cannibalism, coexistence cannot be explained. When the reward is considered as social standing of being outstanding size in a population, sympatric cannibalistic polymorphism is possible, without regard to the initial size variation or resource shortage.     

Mixed-mode oscillations in a self-replicating dimerization mechanism

Recently, self-replicating molecules have been synthesized in the laboratory by Rebek. Given the importance of such molecules, we proposed a simple model of a self-replicating dimer, which works as a template for its own formation. Here we consider a three variable model. For the model, we obtain mixed-mode and chaotic oscillations. Also, we find coexistence between two periodic attractors as well as a periodic and a chaotic attractor.     

Variation between individuals fosters regional species coexistence

Although individual‐level variation (IV) is ubiquitous in nature, it is not clear how it influences species coexistence. Theory predicts that IV will hinder coexistence but empirical studies have shown that it can facilitate, inhibit, or have a neutral effect. We use a theoretical model to explore the consequences of IV on local and regional species coexistence in the context of spatial environmental structure. Our results show that individual variation can have a positive effect on species coexistence and that this effect will critically depend on the spatial structure of such variation. IV facilitates coexistence when a negative, concave‐up relationship between individuals’ competitive response and population growth rates propagates to a disproportionate advantage for the inferior competitor, provided that each species specialises in a habitat. While greater variation in the preferred habitat generally fosters coexistence, the opposite is true for non‐preferred habitats. Our results reconcile theory with empirical findings.     

The impact of consumer-resource cycles on the coexistence of competing consumers

This article seeks to determine the extent to which endogenous consumer-resource cycles can contribute to the coexistence of competing consumer species. It begins with a numerical analysis of a simple model proposed by Armstrong and McGehee. This model has a single resource and two consumers, one with a linear functional response and one with a saturating response. Coexistence of the two consumer species can occur when the species with a saturating response generates population cycles of the resource, and also has a lower resource requirement for zero population growth. Coexistence can be achieved over a wide range of relative efficiencies of the two consumers provided that the functional response of the saturating consumer reaches its half-saturation value when the resource population is a small fraction of its carrying capacity. In this case, the range of efficiencies allowing coexistence is comparable to that when two competitors have stable dynamics and a high degree of resource partitioning. A variety of modifications of this basic model are analyzed to investigate the consequences for coexistence of different resource growth equations, different functional and numerical response shapes, and other factors. Large differences in functional response shape appear to be the most important factor in producing robust coexistence via resource cycles. If the unstable species has a concave numerical response, this greatly expands the conditions allowing coexistence. If the stable consumer species has a convex (accelerating) functional and/or numerical response, the range of conditions allowing coexistence is also expanded. We argue that large between-species differences in functional response form can often be produced by between-consumer differences in the adaptive adjustments of foraging effort to food density. Consumer-resource cycles can also expand the conditions allowing coexistence when there is resource partitioning, but do so primarily when resource partitioning is relatively slight; this makes the ease of coexistence relatively independent of consumer similarity.     

The presence of generalist plant pathogens might not explain the long-term coexistence of plant species

Pathogens have been shown to contribute to the possibility of coexistence of competing plant species by creating ecological distinction between the coexisting species. This coexistence promoting mechanism resembles intra-specific density dependence as found in Lotka-Volterra models. However, plant species adapt in their level of resistance against pathogen infection and this adaptation has been shown to be traded-off by a reduction in growth rate. A model is developed to show that taking into account the possible adaptation of plant species to increase their resistance against pathogen infection by generalist pathogens has consequences for the coexistence of the plant species. The results show that in systems where plants adapt to the pathogen infection, coexistence becomes impossible. The implication of this finding is that plant pathogens might contribute less to the coexistence of plant species than is commonly thought.