Stability properties of 2-species models of mutualism: Simulation studies

Summary Most previous analyses of the stability properties of models of mutualism have emphasized the destabilizing effects of mutualism. However, these analyses can be shown to be based upon inappropriate assumptions, or to be applicable only for special cases of mutualism. In this paper three basic 2-species models of mutualism are presented and their six combinations are analyzed by computer simulation for their return time stability and persistence stability. Four out of six models show greater return time stability than an appropriate model without mutualism, and all models show higher persistence stability than the model without mutualism. It is argued that real biological systems can be related to the qualitative structure of each of the basic models of mutualism, and that therefore none of the basic models or their stability properties can be eliminated a priori as being inappropriate. The conclusion follows that while some kinds of mutualistic interactions may be relatively unstable, other mutualisms, probably representing the majority of cases, can be considered to be relatively stable. The limitations of these models and analyses are considered.     

On the structure and stability of mutualistic systems: Analysis of predator-prey and competition models as modified by the action of a slow-growing mutualist

Two basic models of mutualism are presented in which interactions among three species lead to mutualism between two of them. The models represent 2-species predator-prey or competition systems in which a third species acts as a mutualist with either the predator, the prey, or one of the competitors. The models include the assumptions that there is a cost of associating with the mutualist and that the mutualist population grows much more slowly than the other two populations. Special cases of these two models correspond to six qualitatively different types of mutualistic benefit, all of which are known to occur in nature: deterring predation, increasing prey availability, feeding on (or competing with) a predator, increasing competitive interactions, decreasing competitive interactions, and feeding on (or competing with) a competitor. These models and their special cases are subjected to a local stability analysis. The results show that mutualism based upon deterring predation, competing with a predator, or decreasing competitive interactions enhances local stability, while mutualism based upon increasing prey availability or increasing competitive interactions reduces local stability. These results clearly reject the idea that mutualism is an inherently unstable process, and reinforces the idea that each different kind of mutualism will have to be considered separately. Compared to 2-species models of mutualism, the 3-species models provide a more realistic representation of the structure of many mutualistic systems, the mechanisms by which one species benefits another, and the regulation of the interaction.     

Analysis of three species models of mutualism in predator-prey and competitive systems

Mutualism arises in many qualitatively different ways, but previous 2-species models of mutualism correspond to only a few of these. Following Addicott and Freedman (1983), we present two models of mutualism in which interactions among three species lead to mutualism between two of them. One model involves interactions among a predator, a mutualist-prey, and a mutualist, while the other involves interactions among a competitor, a mutualist-competitor, and a mutualist. Given biologically reasonable constraints upon the functions in the model, we present (1) the conditions for boundedness of solutions, (2) the equilibria and their local stability, and (3) the conditions for the existence of small amplitude periodic solutions, a behavior not predicted by 2-species models of mutualism. The models include costs to the mutualist-prey or mutualist-competitor of associating with the mutualist. Analysis of special cases shows that mutualism can cause the extinction of the predator, or the reversal of competitive outcomes.     

Global stability of obligate mutualism in community modules with facultative mutualists

Mutualism is a fundamental building block of ecological communities and an important driver of biotic evolution. Classic theory suggests that a pairwise two‐species obligate mutualism is fragile, with a large perturbation potentially driving both mutualist populations into extinction. In nature, however, there are many cases of pairwise obligate mutualism. Such pairwise obligate mutualisms are occasionally associated with additional interactions with facultative mutualists. Here, we use a mathematical model to show that when a two‐species obligate mutualism has a single additional link to a third facultative mutualist, the obligate mutualism can become permanently persistent. In the model, a facultative mutualist interacts with one of two inter‐dependent obligate mutualists, and the facultative mutualist enhances the persistence not only of its directly interacting obligate mutualist, but also that of the other obligate mutualist indirectly, enabling the permanent coexistence of the three mutualist species. The effect of the facultative mutualist is strong; it can allow a three‐species permanent coexistence even when two obligate mutualists by themselves are not sustainable (i.e. not locally stable). These results suggest that facultative mutualists can play a pivotal role for the persistence of obligate mutualisms, and contribute to a better understanding on the mechanisms maintaining more complex mutualistic networks of multiple species.     

Dual lattice model of the evolution of facultative symbiosis with continuous Prisoner's Dilemma game

Mutualism is ubiquitous in nature and is thought to have played a key role in the history of life. However, how mutualism could evolve despite being prone to unilateral exploitation is a puzzling question in evolutionary ecology. Some theoretical studies have shown that spatial structure of habitat can facilitate the emergence and maintenance of mutualism. However, they are based on the simple assumption that the trait in question is discrete: each individual is either a mutualist or a non-mutualist. In this article I develop a simple simulation model of coevolution of facultative symbiosis using a one-shot continuous Prisoner's Dilemma game to investigate the evolutionary dynamics of mutualism between two species. In this model I assume continuous traits for both species from -1 (fully deceptive) to 1 (fully cooperative). The habitat has a dual-lattice structure, each layer is inhabited by one species. Interspecific interaction is restricted between two corresponding sites of the two layers. Without limitation on the magnitude of a single mutation, I find that mutualism can arise and persist when the intrinsic reproduction rate is low (but is above a threshold) and the benefit/cost ratio of the cooperative strategy is large, which is consistent with Yamamura et al. [2004. Evolution of mutualism through spatial effects. J. Theor. Biol. 226, 421-428]. In these cases, extreme antagonism often evolves starting from a neutral population that seems nearly stable, but once mutualism arises, the cooperative individuals quickly increase and both the populations eventually become mutualistic on average, although they are polymorphic. However, when the effect of a single mutation was limited to be small, extreme antagonism is much likely to dominate unless the intrinsic reproduction rate is low. When only one species is allowed to evolve, mutualism arises when the initial strategy of the other species is cooperative. Otherwise, excessive deception evolves in the former, and the latter often becomes driven to extinction.     

Diversification of transmission modes and the evolution of mutualism

In order for mutualism to evolve, some force must align the interests of the two interacting partners. Vertical transmission can fill this role, but it is still unknown whether mutualism can be stable when vertically transmitted symbionts can evolve toward horizontal transmission. In this article, we investigate how symbionts' transmission mode and virulence should evolve, depending on the relationship between these two traits. We show that pathogens that reduce their host's fecundity can have more complex evolutionary dynamics than those that increase mortality. In some cases, runaway evolution of virulence can drive the host population extinct. In most cases, evolutionary branching results in the differentiation of avirulent, vertically transmitted symbionts from virulent, contagious pathogens. The population of symbionts then becomes polymorphic, and because the least virulent symbionts are the most frequent, the average virulence of symbionts is much lower than it would be in a monomorphic population. When the link between transmission and virulence results from correlated mutational changes and not from fixed constraints, vertically transmitted symbionts do not simply lose virulence; they evolve toward mutualism. We show that the force that stabilizes mutualism in such situations is the competition for transmission between symbionts.     

Functional traits determine formation of mutualism and predation interactions in seed-rodent dispersal system of a subtropical forest

Network structure in plant-animal systems has been widely investigated but the roles of functional traits of plants and animals in formation of mutualism and predation interactions and community structure are still not fully understood. In this study, we quantitatively assessed interaction strength of mutualism and predation between 5 tree species and 7 rodent species by using semi-natural enclosures in a subtropical forest in southwest China. Seeds with high handling-time and nutrition traits (for both rat and mouse species) or high tannin trait (for mouse species) show high mutualism but low predation with rodents; while seeds with low handling-time and low nutrition traits show high predation but low mutualism with rodents. Large-sized rat species are more linked to seeds with high handling-time and high nutrition traits, while small-sized mouse species are more connected with seeds with low handling-time, low nutrition value and high tannin traits. Anti-predation seed traits tend to increase chance of mutualism instead of reducing predation by rodents, suggesting formation of mutualism may be connected with that of predation. Our study demonstrates that seed and animal traits play significant roles in the formation of mutualism and predation and network structure of the seed-rodent dispersal system.     

传粉细蛾与大戟科植物专性授粉的互惠共生体系

在已知的昆虫与植物所形成的专性授粉互惠共生体系中,榕树—榕小蜂、丝兰—丝兰蛾体系是经典实例,国内外学者已经从不同角度进行了大量的研究,为我们理解植物—传粉者互惠共生体系协同进化的机理和历史积累了宝贵的资料。近些年的研究发现鳞翅目细蛾科头细蛾属昆虫与大戟科植物之间也存在相似的协同进化关系。文章对国内外学者有关传粉细蛾与大戟科植物互惠共生协同进化的研究进行了整理。     

The ecological effects of the ant–hemipteran mutualism: A meta-analysis

Ant–hemipteran mutualism has a variety of ecological effects on the host plants, but the magnitude and moderators of those effects are poorly known. We evaluated this issue by conducting a meta-analysis based on 49 published studies. Results showed that the mutualism had significant protective effects on the host plans, although those effects did not lead to enhanced plant growth or reproductive performance. Both herbivores and predators on plants were strongly suppressed by the mutualism; a similar pattern was also detected for fruit removal. The ecological effects of the mutualism tended to be more consistent and stronger in tropical and subtropical regions, whereas in temperate regions, none of the tested variables was significantly affected by the mutualism. The protective effects of the mutualism on plants were independent of plant life form and the invasiveness of ants. The effect of the mutualism on predators varied with plant life form. The study confirmed that the ant–hemipteran mutualism has a wide range of ecological influences on plants and highlights the significance of a common and wide-spread mutualism.     

Negotiation, sanctions, and context dependency in the legume-Rhizobium mutualism

Two important questions about mutualisms are how the fitness costs and benefits to the mutualist partners are determined and how these mechanisms affect the evolutionary dynamics of the mutualism. We tackle these questions with a model of the legume-rhizobium symbiosis that regards the mutualism outcome as a result of biochemical negotiations between the plant and its nodules. We explore the fitness consequences of this mechanism to the plant and rhizobia and obtain four main results. First, negotiations permit the plant to differentially reward more-cooperative rhizobia--a phenomenon termed "plant sanctions"--but only when more-cooperative rhizobia also provide the plant with good outside options during negotiations with other nodules. Second, negotiations may result in seemingly paradoxical cases where the plant is worse off when it has a "choice" between two strains of rhizobia than when infected by either strain alone. Third, even when sanctions are effective, they are by themselves not sufficient to maintain cooperative rhizobia in a population: less cooperative strains always have an advantage at the population level. Finally, partner fidelity feedback, together with genetic correlations between a rhizobium strain's cooperativeness and the outside options it provides, can maintain cooperative rhizobia. Our results show how joint control over the outcome of a mutualism through the proximate mechanism of negotiation can affect the evolutionary dynamics of interspecific cooperation.     

Evolution of obligate pollination mutualism in the tribe Phyllantheae (Phyllanthaceae)

The landmark discovery of obligate pollination mutualism between Glochidion plants and Epicephala moths has sparked increased interest in the pollination systems of Phyllantheae plants. In this paper I review current information on the natural history and evolutionary history of obligate pollination mutualism in Phyllantheae. Currently, an estimated >500 species are mutualistic with Epicephala moths that actively pollinate flowers and whose progeny feed on the resulting seeds. The Phyllantheae also includes species that are not mutualistic with Epicephala moths and are instead pollinated by bees and/or flies or ants. Phylogenetic analyses indicate that the mutualism evolved independently five times within Phyllantheae, whereas active pollination behavior, a key innovation in this mutualism, evolved once in Epicephala . Reversal of mutualism has occurred at least once in both partner lineages, involving a Breynia species that evolved an alternative pollination system and a derived clade of Epicephala that colonized ant-pollinated Phyllantheae hosts and thereby lost the pollinating habit. The plant–moth association is highly species specific, although a strict one-to-one assumption is not perfectly met. A comparison of plant and moth phylogenies suggests signs of parallel speciation, but partner switches have occurred repeatedly at a range of taxonomic levels. Overall, the remarkable species diversity and multiple originations of the mutualism provide excellent opportunities to address many important questions on mutualism and the coevolutionary process. Although research on the biology of the mutualism is still in its infancy, the Phyllantheae– Epicephala association holds promise as a new model system in ecology and evolutionary biology.     

Emergence of mutualism: Application of a differential model to endosymbiosis

A population dynamics approach based on a system of differential equations allows us to establish conditions for the emergence of mutualism for cases such as coelenterates-algae symbionts. A central assumption of the model is that a host organism is able to discriminate, via some molecular recognition mechanisms, among different invading organisms and preferentially rejectparasites rather thanbona fide symbionts. Large differential rejection rates allow the emergence of mutualism. Different attractors of the population dynamics correspond to the emergence of mutualism, predominance of “selfish” species, or coexistence of many species.     

Construction of bacteria–eukaryote synthetic mutualism

Mutualism is ubiquitous in nature but is known to be intrinsically vulnerable with regard to both population dynamics and evolution. Synthetic ecology has indicated that it is feasible for organisms to establish novel mutualism merely through encountering each other by showing that it is feasible to construct synthetic mutualism between organisms. However, bacteria–eukaryote mutualism, which is ecologically important, has not yet been constructed. In this study, we synthetically constructed mutualism between a bacterium and a eukaryote by using two model organisms. We mixed a bacterium, Escherichia coli (a genetically engineered glutamine auxotroph), and an amoeba, Dictyostelium discoideum, in 14 sets of conditions in which each species could not grow in monoculture but potentially could grow in coculture. Under a single condition in which the bacterium and amoeba mutually compensated for the lack of required nutrients (lipoic acid and glutamine, respectively), both species grew continuously through several subcultures, essentially establishing mutualism. Our results shed light on the establishment of bacteria–eukaryote mutualism and indicate that a bacterium and eukaryote pair in nature also has a non-negligible possibility of establishing novel mutualism if the organisms are potentially mutualistic.     

Joint evolution of interspecific mutualism and regulation of variation of interaction under directional selection in trait space

The present study theoretically examines the process by which interspecific mutualism is established with trait matching. The mathematical model includes joint evolution of the mutualistic relationship between two species and regulation of variation of interaction in one-dimensional trait space, assuming abiotic directional selection. The model considers three types of regulation: homeostasis against environmental variation, developmental stability, and acceptability of dissimilar mutualism partners (mutualism kernel). Mainly focusing on the developmental stability, the analysis indicates that the mutualism can evolve when (1) higher levels of developmental stability are more intensively degenerated by deleterious mutations, (2) the basal rate of deleterious mutation is low, (3) trait expression is less influenced by environmental factors, and (4) the specificity of mutualism is high. It also shows that the evolution of developmental stability can promote the evolution of mutualism with trait matching when the deleterious mutation bias disappears at a certain level of developmental instability. Evolution of homeostasis and mutualism kernel can be discussed in the similar way because of formal similarities in the model. In plant–pollinator interactions, it has recently been proposed that evolutionary increments of developmental stability in mutualistic traits might promote plant diversification. The present results partly support this hypothesis with respect to the evolutionary relationship between mutualism and developmental stability.     

Coevolutionary dynamics in one-to-many mutualistic systems

“One-to-many” mutualisms are often observed in nature. In this type of mutualism, each host individual can interact with many symbionts, whereas each individual symbiont can interact with only one host individual. Partner choice by the host is a potentially critical mechanism for maintaining such systems; however, its long-term effects on the coevolution between the hosts and symbionts have not been completely explored. In this study, I developed a simple mathematical model to describe the coevolutionary dynamics between hosts and symbionts in a one-to-many mutualism. I assumed that each host chooses a constant number of symbionts from a potential symbiont population, a fraction of which are chosen through preferential choice on the basis of the cooperativeness of the symbionts and the rest are chosen randomly. Using numerical calculations, I found that mutualism is maintained when the preferential choice is not very costly and the mutation rate of symbionts is large. I also found that symbionts that receive benefits from hosts without a return (cheater symbionts) and hosts that do not engage in preferential partner choice (indiscriminator hosts) can coexist with mutualist symbionts and discriminator hosts, respectively. The parameter domain of pure mutualism, i.e., free from cheater symbionts and indiscriminator hosts, can be narrower than the whole domain where the mutualism persists.     

An invasive plant-fungal mutualism reduces arthropod diversity

Ecological theory holds that competition and predation are the most important biotic forces affecting the composition of communities. Here, we expand this framework by demonstrating that mutualism can fundamentally alter community and food web structure. In large, replicated field plots, we manipulated the mutualism between a dominant plant ( Lolium arundinaceum ) and symbiotic fungal endophyte ( Neotyphodium coenophialum ). The presence of the mutualism reduced arthropod abundance up to 70%, reduced arthropod diversity nearly 20%, shifted arthropod species composition relative to endophyte-free plots and suppressed the biomass and richness of other plant species in the community. Herbivorous arthropods were more strongly affected than carnivores, and for both herbivores and carnivores, effects of the mutualism appeared to propagate indirectly via organisms occurring more basally in the food web. The influence of the mutualism was as great or greater than previously documented effects of competition and predation on arthropod communities. Our work demonstrates that a keystone mutualism can significantly reduce arthropod biodiversity at a broad community scale.     

Bet hedging based cooperation can limit kin selection and form a basis for mutualism

Mutualism is a mechanism of cooperation in which partners that differ help each other. As such, mutualism opposes mechanisms of kin selection and tag-based selection (for example the green beard mechanism), which are based on giving exclusive help to partners that are related or carry the same tag. In contrast to kin selection, which is a basis for parochialism and intergroup warfare, mutualism can therefore be regarded as a mechanism that drives peaceful coexistence between different groups and individuals. Here the competition between mutualism and kin (tag) selection is studied. In a model where kin selection and tag-based selection are dominant, mutualism is promoted by introducing environmental fluctuations. These fluctuations cause reduction in reproductive success by the mechanism of variance discount. The best strategy to counter variance discount is to share with agents who experience the most anticorrelated fluctuations, a strategy called bet hedging. In this way, bet hedging stimulates cooperation with the most unrelated partners, which is a basis for mutualism. Analytic results and simulations reveal that, if this effect is large enough, mutualistic strategies can dominate kin selective strategies. In addition, mutants of these mutualistic strategies that experience fluctuations that are more anticorrelated to their partner, can outcompete wild type, which can lead to the evolution of specialization. In this way, the evolutionary success of mutualistic strategies can be explained by bet hedging-based cooperation.     

Stability analysis of commensal and mutual relations with competitive assimilation in continuous mixed culture

The population dynamics of continuous mixed cultures with pure commensalism, commensalism plus competitive assimilation, pure mutualism, and mutualism plus competitive assimilation was disused. The population does not display oscillatory phenomena where there is a single interaction of commensalism or mutualism. Damped oscillations take place when two interactions (such commensalism and competitive assimilation or mutualism and competitive assimilation) coexist in the continuous mixed culture. The stability of these systems was discussed in detail.     

Symbiotic complexity: discovery of a fifth symbiont in the attine ant-microbe symbiosis

The fungus-growing ant-microbe mutualism is a classic example of organismal complexity generated through symbiotic association. The ants have an ancient obligate mutualism with fungi they cultivate for food. The success of the mutualism is threatened by specialized fungal parasites (Escovopsis) that consume the cultivated fungus. To defend their nutrient-rich garden against infection, the ants have a second mutualism with bacteria (Pseudonocardia), which produce antibiotics that inhibit the garden parasite Escovopsis. Here we reveal the presence of a fourth microbial symbiont associated with fungus-growing ants: black yeasts (Ascomycota; Phialophora). We show that black yeasts are commonly associated with fungus-growing ants, occurring throughout their geographical distribution. Black yeasts grow on the ants' cuticle, specifically localized to where the mutualistic bacteria are cultured. Molecular phylogenetic analyses reveal that the black yeasts form a derived monophyletic lineage associated with the phylogenetic diversity of fungus growers. The prevalence, distribution, localization and monophyly indicate that the black yeast is a fifth symbiont within the attine ant-microbe association, further exemplifying the complexity of symbiotic associations.