Three-way coexistence in obligate mutualist-exploiter interactions: the potential role of competition

Many mutualisms host "exploiter" species that consume the benefits provided by one or both mutualists without reciprocating. Exploiters have been widely assumed to destabilize mutualisms, yet they are common. We develop models to explore conditions for local coexistence of obligate plant/pollinating seed parasite mutualisms and nonpollinating exploiters. As the larvae of both pollinators and (at a later time) exploiters consume seeds, we examine the importance of intraspecific and (asymmetric) interspecific competition among and between pollinators and exploiters for achieving three-way coexistence. With weak intra- and interspecific competition, exploiters can invade the stable mutualism and coexist with the mutualists (either stably or with oscillations), provided the exploiters' intrinsic birthrate (b(E)) slightly exceeds that of the pollinators. At higher b(E), all three species go locally extinct. When facing strong interspecific competition, exploiters cannot invade and coexist with the mutualists if intraspecific competition in pollinators and exploiters is weak. However, strong intraspecific competition in pollinators and exploiters facilitates exploiter invasion and coexistence and greatly expands the range of b(E) over which stable coexistence occurs. Our results suggest that mutualist/exploiter coexistence may be more easily achieved than previously thought, thus highlighting the need for a better understanding of competition among and between mutualists and exploiters.     

On evolutionary stability of carrying capacity driven dispersal in competition with regularly diffusing populations

Two competing populations in spatially heterogeneous but temporarily constant environment are investigated: one is subject to regular movements to lower density areas (random diffusion) while the dispersal of the other is in the direction of the highest per capita available resources (carrying capacity driven diffusion). The growth of both species is subject to the same general growth law which involves Gilpin–Ayala, Gompertz and some other equations as particular cases. The growth rate, carrying capacity and dispersal rate are the same for both population types, the only difference is the dispersal strategy. The main result of the paper is that the two species cannot coexist (unless the environment is spatially homogeneous), and the carrying capacity driven diffusion strategy is evolutionarily stable in the sense that the species adopting this strategy cannot be invaded by randomly diffusing population. Moreover, once the invasive species inhabits some open nonempty domain, it would spread over any available area bringing the native species diffusing randomly to extinction. One of the important technical results used in the proofs can be interpreted in the form that the limit solution of the equation with a regular diffusion leads to lower total population fitness than the ideal free distribution.     

榕树–榕小蜂协同进化中的非对称性相互作用及其集合种群效应

在协同进化研究中,传统观点认为物种之间的相互作用是对称性的,在进化过程中将形成一个稳定的均衡状态或进化稳定策略。然而,近来的观测和实验数据表明,物种间的协同进化可能存在非对称性相互作用,而且这种非对称性可能造成集合种群效应(metapopulation effect)或形成非均衡状态(例如混沌,chaos)。本文利用"榕树–榕小蜂"这一经典的协同进化模式系统来介绍协同进化过程中的非对称性相互作用,以及这种非对称性如何产生集合种群效应。在榕–蜂共生系统中,栖身于榕果中的榕小蜂除了传粉小蜂之外,还有一些"投机"的非传粉小蜂。非传粉小蜂比传粉小蜂具有更强的竞争力,而榕树则可惩罚不合作的非传粉蜂,同时奖励合作的传粉小蜂,从而形成了复杂的非对称性种间相互作用。在某个斑块生境中,非传粉小蜂通过竞争作用排斥传粉小蜂,然而随着非传粉小蜂在蜂群中的比例不断升高,榕树惩罚作用(如落果等)常常会导致整个非传粉蜂群的数量急剧下降,甚至局域性灭绝。随后,其他斑块的传粉小蜂则迁移过来填补空白。然而,随着传粉小蜂种群的数量增长,该斑块又会集聚更多的投机性非传粉小蜂,进而诱发榕树再次进行惩罚。这样的非对称性相互作用导致了非传粉小蜂、传粉小蜂以及榕树种群的集合效应,其种群大小呈现周期性的"此消彼长"式的循环。     

Artificial neural networks in models of specialization, guild evolution and sympatric speciation

Sympatric speciation can arise as a result of disruptive selection with assortative mating as a pleiotropic by-product. Studies on host choice, employing artificial neural networks as models for the host recognition system in exploiters, illustrate how disruptive selection on host choice coupled with assortative mating can arise as a consequence of selection for specialization. Our studies demonstrate that a generalist exploiter population can evolve into a guild of specialists with an 'ideal free' frequency distribution across hosts. The ideal free distribution arises from variability in host suitability and density-dependent exploiter fitness on different host species. Specialists are less subject to inter-phenotypic competition than generalists and to harmful mutations that are common in generalists exploiting multiple hosts.When host signals used as cues by exploiters coevolve with exploiter recognition systems, our studies show that evolutionary changes may be continuous and cyclic. Selection changes back and forth between specialization and generalization in the exploiters, and weak and strong mimicry in the hosts, where non-defended hosts use the host investing in defence as a model. Thus, host signals and exploiter responses are engaged in a red-queen mimicry process that is ultimately cyclic rather then directional. In one phase, evolving signals of exploitable hosts mimic those of hosts less suitable for exploitation (i.e. the model). Signals in the model hosts also evolve through selection to escape the mimic and its exploiters. Response saturation constraints in the model hosts lead to the mimic hosts finally perfecting its mimicry, after which specialization in the exploiter guild is lost. This loss of exploiter specialization provides an opportunity for the model hosts to escape their mimics. Therefore, this cycle then repeats.We suggest that a species can readily evolve sympatrically when disruptive selection for specialization on hosts is the first step. In a sexual reproduction setting, partial reproductive isolation may first evolve by mate choice being confined to individuals on the same host. Secondly, this disruptive selection will favour assortative mate choice on genotype, thereby leading to increased reproductive isolation.     

The role of mobility for the emergence of diversity in victim-exploiter systems

Theoretical and empirical studies indicate that exploitation is a possible driver of exploiter and victim diversification. However, there are many factors which could promote and limit this diversification process. Using a spatially explicit individual-based model, where an exploiter's success depends on matching between its own and a victim's continuous trait, we simulate local communities of victims and exploiters. We investigate how exploiter mobility (searching ability and movement strategies) can influence diversification of victims. We find that if victim traits are under intermediate intensity of stabilizing selection, disruptive selection exerted by exploiters can indeed lead to diversification in victim population and the victim trait distribution can split into two or more groups. Searching ability and movement strategy of exploiters (local vs. global movement) play a role in determining the number of victim trait groups emerging. Moreover, they affect the proportion of infected victims and the formation of spatial patterns in the victim trait distribution. In addition, with a high searching ability, exploiters with global movement drive victims to be more diverse than exploiters with local movement.     

HOW TO PREVENT CHEATING: A DIGESTIVE SPECIALIZATION TIES MUTUALISTIC PLANT-ANTS TO THEIR ANT-PLANT PARTNERS

Mutualisms often involve reciprocal adaptations of both partners. Acacia ant-plants defended by symbiotic Pseudomyrmex ant mutualists secrete sucrose-free extrafloral nectar, which is unattractive to generalists. We aimed to investigate whether this extrafloral nectar can also exclude exploiters, that is nondefending ant species. Mutualist workers discriminated against sucrose whereas exploiters and generalists with no affinity toward Acacia myrmecophytes preferred sucrose, because mutualist workers lacked the sucrose-cleaving enzyme invertase, which is present in workers of the other two groups. Sucrose uptake induced invertase activity in workers of parasites and generalists, but not mutualists, and in larvae of all species: the mutualists loose invertase during their ontogeny. This reduced metabolic capacity ties the mutualists to their plant hosts, but it does not completely prevent the mutualism from exploitation. We therefore investigated whether the exploiters studied here are cheaters (i.e., have evolved from former mutualists) or parasites (exploiters with no mutualistic ancestor). A molecular phylogeny demonstrates that the exploiter species did not evolve from former mutualists, and no evidence for cheaters was found. We conclude that being specialized to their partner can prevent mutualists from becoming cheaters, whereas other mechanisms are required to stabilize a mutualism against the exploitation by parasites.     

Spreading speed, traveling waves, and minimal domain size in impulsive reaction-diffusion models

How growth, mortality, and dispersal in a species affect the species' spread and persistence constitutes a central problem in spatial ecology. We propose impulsive reaction-diffusion equation models for species with distinct reproductive and dispersal stages. These models can describe a seasonal birth pulse plus nonlinear mortality and dispersal throughout the year. Alternatively, they can describe seasonal harvesting, plus nonlinear birth and mortality as well as dispersal throughout the year. The population dynamics in the seasonal pulse is described by a discrete map that gives the density of the population at the end of a pulse as a possibly nonmonotone function of the density of the population at the beginning of the pulse. The dynamics in the dispersal stage is governed by a nonlinear reaction-diffusion equation in a bounded or unbounded domain. We develop a spatially explicit theoretical framework that links species vital rates (mortality or fecundity) and dispersal characteristics with species' spreading speeds, traveling wave speeds, as well as minimal domain size for species persistence. We provide an explicit formula for the spreading speed in terms of model parameters, and show that the spreading speed can be characterized as the slowest speed of a class of traveling wave solutions. We also give an explicit formula for the minimal domain size using model parameters. Our results show how the diffusion coefficient, and the combination of discrete- and continuous-time growth and mortality determine the spread and persistence dynamics of the population in a wide variety of ecological scenarios. Numerical simulations are presented to demonstrate the theoretical results.     

Effects of long-range taxis and population pressure on the range expansion of invasive species in heterogeneous environments

We consider a new model for biological invasions in periodic patchy environments, in which long-range taxis and population pressure are incorporated in the framework of reaction-diffusion-advection equations. We assume that long-range taxis is induced by a weighted integral of stimuli within a certain sensing range. Population pressure is incorporated in the diffusion coefficient that linearly increases with population density. We first analyze the model in the absence of population pressure and demonstrate how the sensing length of long-range taxis influences the range expansion pattern of invasive species and its rate of spread. The effects of population pressure are examined for both homogeneous and periodic patchy environments. For the homogeneous environment, an exact and explicit traveling wave solution and the spreading speed are obtained. For the periodic patchy environment, we find numerically that a population starting from any localized distribution evolves to a traveling periodic wave if the null solution of the RDA equation is locally unstable, and that the traveling wave speed significantly increases with increasing population pressure. Furthermore, the population pressure and taxis intensity synergistically enhance the spreading speed when they are increased together.     

Interference competition and species coexistence

Interference competition is ubiquitous in nature. Yet its effects on resource exploitation remain largely unexplored for species that compete for dynamic resources. Here, I present a model of exploitative and interference competition with explicit resource dynamics. The model incorporates both biotic and abiotic resources. It considers interference competition both in the classical sense (i.e. each species suffers a net reduction in per capita growth rate via interference from, and interference on, the other species) and in the broad sense (i.e. each species suffers a net reduction in per capita growth rate via interference from, but can experience an increase in growth rate via interference on, the other species). Coexistence cannot occur under classical interference competition even when the species inferior at resource exploitation is superior at interference. Such a trade-off can, however, change the mechanism of competitive exclusion from dominance by the superior resource exploiter to a priority effect. Now the inferior resource exploiter can exclude the superior resource exploiter provided it has a higher initial abundance. By contrast, when interference is beneficial to the interacting species, coexistence is possible via a trade-off between exploitation and interference. These results hold regardless of whether the resource is biotic or abiotic, indicating that the outcome of exploitative and interference competition does not depend on the exact nature of resource dynamics. The model makes two key predictions. First, species that engage in costly interference mechanisms (e.g. territoriality, overgrowth or undercutting, allelopathy and other forms of chemical competition) should not be able to coexist unless they also engage in beneficial interference mechanisms (e.g. predation or parasitism). Second, exotic invasive species that displace native biota should be superior resource exploiters that have strong interference effects on native species with little or negative cost. The first prediction provides a potential explanation for patterns observed in several natural systems, including plants, aquatic invertebrates and insects. The second prediction is supported by data on invasive plants and vertebrates.     

Neutral Genetic Patterns for Expanding Populations with Nonoverlapping Generations

We investigate the inside dynamics of solutions to integrodifference equations to understand the genetic consequences of a population with nonoverlapping generations undergoing range expansion. To obtain the inside dynamics, we decompose the solution into neutral genetic components. The inside dynamics are given by the spatiotemporal evolution of the neutral genetic components. We consider thin-tailed dispersal kernels and a variety of per capita growth rate functions to classify the traveling wave solutions as either pushed or pulled fronts. We find that pulled fronts are synonymous with the founder effect in population genetics. Adding overcompensation to the dynamics of these fronts has no impact on genetic diversity in the expanding population. However, growth functions with a strong Allee effect cause the traveling wave solution to be a pushed front preserving the genetic variation in the population. In this case, the contribution of each neutral fraction can be computed by a simple formula dependent on the initial distribution of the neutral fractions, the traveling wave solution, and the asymptotic spreading speed.     

Host discrimination in modular mutualisms: a theoretical framework for meta-populations of mutualists and exploiters

Plants in multiple symbioses are exploited by symbionts that consume their resources without providing services. Discriminating hosts are thought to stabilize mutualism by preferentially allocating resources into anatomical structures (modules) where services are generated, with examples of modules including the entire inflorescences of figs and the root nodules of legumes. Modules are often colonized by multiple symbiotic partners, such that exploiters that co-occur with mutualists within mixed modules can share rewards generated by their mutualist competitors. We developed a meta-population model to answer how the population dynamics of mutualists and exploiters change when they interact with hosts with different module occupancies (number of colonists per module) and functionally different patterns of allocation into mixed modules. We find that as module occupancy increases, hosts must increase the magnitude of preferentially allocated resources in order to sustain comparable populations of mutualists. Further, we find that mixed colonization can result in the coexistence of mutualist and exploiter partners, but only when preferential allocation follows a saturating function of the number of mutualists in a module. Finally, using published data from the fig–wasp mutualism as an illustrative example, we derive model predictions that approximate the proportion of exploiter, non-pollinating wasps observed in the field.     

The effect of spatial heterogeneity and parasites on the evolution of host diversity

Both spatial heterogeneity and exploiters (parasites and predators) have been implicated as key ecological factors driving population diversification. However, it is unclear how these factors interact. We addressed this question using the common plant-colonizing bacterium Pseudomonas fluorescens, which has been shown to diversify rapidly into spatial niche-specialist genotypes when propagated in laboratory microcosms. Replicate populations were evolved in spatially homogeneous and heterogeneous environments (shaken and static microcosms, respectively) with and without viral parasites (bacteriophage) for approximately 60 bacterial generations. Consistent with previous findings, exploiters reduced diversity in heterogeneous environments by relaxing the intensity of resource competition. By contrast, exploiters increased diversity in homogeneous environments where there was little diversification through resource competition. Competition experiments revealed this increase in diversity to be the result of fitness trade-offs between exploiter resistance and competitive ability. In both environments, exploiters increased allopatric diversity, presumably as a result of divergent selection for resistance between populations. Phage increased total diversity in homogeneous environments, but had no net effect in heterogeneous environments. Such interactions between key ecological variables need to be considered when addressing diversification and coexistence in future studies.     

Existence of traveling waves for integral recursions with nonmonotone growth functions

A class of integral recursion models for the growth and spread of a synchronized single-species population is studied. It is well known that if there is no overcompensation in the fecundity function, the recursion has an asymptotic spreading speed c*, and that this speed can be characterized as the speed of the slowest non-constant traveling wave solution. A class of integral recursions with overcompensation which still have asymptotic spreading speeds can be found by using the ideas introduced by Thieme (J Reine Angew Math 306:94–121, 1979) for the study of space-time integral equation models for epidemics. The present work gives a large subclass of these models with overcompensation for which the spreading speed can still be characterized as the slowest speed of a non-constant traveling wave. To illustrate our results, we numerically simulate a series of traveling waves. The simulations indicate that, depending on the properties of the fecundity function, the tails of the waves may approach the carrying capacity monotonically, may approach the carrying capacity in an oscillatory manner, or may oscillate continually about the carrying capacity, with its values bounded above and below by computable positive numbers. B. Li’s research was partially supported by the National Science Foundation under Grant DMS-616445. M. A. Lewis research was supported by “The Canada Research Chairs program,” and a grant from the Natural Sciences and Engineering Research Council of Canada.     

Evolution and persistence of obligate mutualists and exploiters: competition for partners and evolutionary immunization

Mutualisms are ubiquitous in nature, as is their exploitation by both conspecific and heterospecific cheaters. Yet, evolutionary theory predicts that cheating should be favoured by natural selection. Here, we show theoretically that asymmetrical competition for partners generally determines the evolutionary fate of obligate mutualisms facing exploitation by third-species invaders. When asymmetry in partner competition is relatively weak, mutualists may either exclude exploiters or coexist with them, in which case their co-evolutionary response to exploitation is usually benign. When asymmetry is strong, the mutualists evolve towards evolutionary attractors where they become extremely vulnerable to exploiter invasion. However, exploiter invasion at an early stage of the mutualism's history can deflect mutualists' co-evolutionary trajectories towards slightly different attractors that confer long-term stability against further exploitation. Thus, coexistence of mutualists and exploiters may often involve an historical effect whereby exploiters are co-opted early in mutualism history and provide lasting 'evolutionary immunization' against further invasion.     

Existence of Traveling Waves for the Generalized F–KPP Equation

Variation in genotypes may be responsible for differences in dispersal rates, directional biases, and growth rates of individuals. These traits may favor certain genotypes and enhance their spatiotemporal spreading into areas occupied by the less advantageous genotypes. We study how these factors influence the speed of spreading in the case of two competing genotypes under the assumption that spatial variation of the total population is small compared to the spatial variation of the frequencies of the genotypes in the population. In that case, the dynamics of the frequency of one of the genotypes is approximately described by a generalized Fisher–Kolmogorov–Petrovskii–Piskunov (F–KPP) equation. This generalized F–KPP equation with (nonlinear) frequency-dependent diffusion and advection terms admits traveling wave solutions that characterize the invasion of the dominant genotype. Our existence results generalize the classical theory for traveling waves for the F–KPP with constant coefficients. Moreover, in the particular case of the quadratic (monostable) nonlinear growth–decay rate in the generalized F–KPP we study in detail the influence of the variance in diffusion and mean displacement rates of the two genotypes on the minimal wave propagation speed.     

Bayesian Inference on the Effect of Density Dependence and Weather on a Guanaco Population from Chile

Understanding the mechanisms that drive population dynamics is fundamental for management of wild populations. The guanaco (Lama guanicoe) is one of two wild camelid species in South America. We evaluated the effects of density dependence and weather variables on population regulation based on a time series of 36 years of population sampling of guanacos in Tierra del Fuego, Chile. The population density varied between 2.7 and 30.7 guanaco/km², with an apparent monotonic growth during the first 25 years; however, in the last 10 years the population has shown large fluctuations, suggesting that it might have reached its carrying capacity. We used a Bayesian state-space framework and model selection to determine the effect of density and environmental variables on guanaco population dynamics. Our results show that the population is under density dependent regulation and that it is currently fluctuating around an average carrying capacity of 45,000 guanacos. We also found a significant positive effect of previous winter temperature while sheep density has a strong negative effect on the guanaco population growth. We conclude that there are significant density dependent processes and that climate as well as competition with domestic species have important effects determining the population size of guanacos, with important implications for management and conservation.     

Altruists Proliferate Even at a Selective Disadvantage within Their Own Niche

The evolutionary origin of altruism is a long-standing puzzle. Numerous explanations have been proposed, most prominently based on inclusive fitness or group selection. One possibility that has not yet been considered is that new niches will be created disproportionately often when altruism appears, perhaps by chance, causing altruists to be over-represented in such new niches. This effect is a novel variant of group selection in which altruistic groups benefit by discovering unoccupied niches instead of by competing for the limited resources within a single niche. Both an analytical population genetics model and computational simulations support that altruism systematically arises due to this side effect of increased carrying capacity even when it is strongly selected against within any given niche. In fact, even when selection is very strongly negative and altruism does not develop in most populations, it can still be expected to be observed in a consistent fraction of species. The ecological structure provided by niches thereby may be sufficient for altruists to proliferate even if they are always at a disadvantage within each niche considered individually.     

Instability of a hybrid module of antagonistic and mutualistic interactions

Mutualistic and antagonistic interactions coexist in nature. However, little is understood about their relative roles and interactive effects on multispecies coexistence. Here, using a three-species population dynamics model of a resource species, its exploiter, and a mutualist species, we show that a mixture of different interaction types may lead to dynamics that differ completely from those of the isolated interacting pairs. More specifically, a combination of globally stable antagonistic and mutualistic subsystems can lead to unstable population oscillations, suggesting the potential difficulty in the coexistence of antagonism and mutualism. Mutualism-induced instability arises from the indirect positive effect of mutualism on the exploiter. Furthermore, for a three-species system with a stronger mutualistic interaction to persist stably, a weaker antagonistic interaction is required. Network studies of communities composed of one type of interaction may not capture the dynamics of natural communities.     

Adding biotic complexity alters the metabolic benefits of mutualism

Mutualism is ubiquitous in nature and plays an integral role in most communities. To predict the eco‐evolutionary dynamics of mutualism it is critical to extend classic pair‐wise analysis to include additional species. We investigated the effect of adding a third species to a pair‐wise mutualism in a spatially structured environment. We tested the hypotheses that selection for costly excretions in a focal population (i) decreases when an exploiter is added (ii) increases when a third mutualist is added relative to the pair‐wise scenario. We assayed the selection acting on Salmonella enterica when it exchanges methionine for carbon in an obligate mutualism with an auxotrophic Escherichia coli. A third bacterium, Methylobacterium extorquens, was then added and acted either as an exploiter of the carbon or third obligate mutualist depending on the nitrogen source. In the tripartite mutualism M. extorquens provided nitrogen to the other species. Contrary to our expectations, adding an exploiter increased selection for methionine excretion in S. enterica. Conversely, selection for cooperation was lower in the tripartite mutualism relative to the pair‐wise system. Genome‐scale metabolic models helped identify the mechanisms underlying these changes in selection. Our results highlight the utility of connecting metabolic mechanisms and eco‐evolutionary dynamics.     

Repulsion Effect on Superinfecting Virions by Infected Cells

In this paper, the repulsion effect of superinfecting virion by infected cells is studied by a reaction diffusion equation model for virus infection dynamics. In this model, the diffusion of virus depends not only on its concentration gradient but also on the concentration of infected cells. The basic reproduction number, linear stability of steady states, spreading speed and existence of traveling wave solutions for the model are discussed. It is shown that viruses spread more rapidly with the repulsion effect of infected cells on superinfecting virions, than with random diffusion only. For our model, the spreading speed of free virus is not consistent with the minimal traveling wave speed. With our general model, numerical computations of the spreading speed show that the repulsion of superinfecting virion promotes the spread of virus, which confirms, not only qualitatively but also quantitatively, the experimental result of Doceul et al. (Science 327:873–876, 2010).