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.     

A reaction-diffusion system of a predator-prey-mutualist model

Mutualism is part of many significant processes in nature. Mutualistic benefits arising from modification of predator-prey interactions involve interactions of at least three species. In this paper we investigate the Homogeneous Neumann problem and Dirichlet problem for a reaction-diffusion system of three species—a predator, a mutualist-prey, and a mutualist. The existence, uniqueness, and boundedness of the solution are established by means of the comparison principle and the monotonicity method. For the Neumann problem, we analyze the constant equilibrium solutions and their stability. For the Dirichlet problem, we prove the global asymptotic stability of the trivial equilibrium solution. Specifically, we study the existence and the asymptotic behavior of two nonconstant equilibrium solutions. The main method used in studying of the stability is the spectral analysis to the linearized operators. The O.D.E. problem for the same model was proposed and studied in [13]. Through our results, we can see the influences of the diffusion mechanism and the different boundary value conditions upon the asymptotic behavior of the populations.     

Obligate mutualism with a predator: Stability and persistence of three-species models

We present a general model for three interacting populations, where one population, called a mutualist, benefits a predator in its interaction with the prey. Biologically, there are four different ways in which the mutualist could benefit the predator: by enhancing prey growth rate, by enhancing the rate of prey capture, by providing an alternative food supply for the predator, and by enhancing the efficiency of utilization of prey, once they are ingested. We discuss examples of each type of interaction. We restrict our model to those situations in which the predator cannot survive on the prey in the absence of the mutualist. Therefore, if mutualism exists, it is obligate for the predator. Other conditions of the model include the dynamics of the prey and the mutualist alone and together in the absence of the predator. Given additional reasonable restrictions on the model, we determine the conditions for persistence, where persistence is defined as the continued existence of all three populations without any of them going extinct. There are two ways in which survival may arise in these models. Under one set of conditions, which is equivalent to the predator being able to invade a prey-mutualist system when rare, persistence will occur for any set of positive critical population sizes. Alternatively, survival will occur if there is an asymptotically stable interior equilibrium. However, the conditions for this are complex, and survival may occur only for initial populations in a limited region around the equilibrium.     

Global stability of the coexistence equilibrium for a general class of models of facultative mutualism

Many models of mutualism have been proposed and studied individually. In this paper, we develop a general class of models of facultative mutualism that covers many of such published models. Using mild assumptions on the growth and self-limiting functions, we establish necessary and sufficient conditions on the boundedness of model solutions and prove the global stability of a unique coexistence equilibrium whenever it exists. These results allow for a greater flexibility in the way each mutualist species can be modelled and avoid the need to analyse any single model of mutualism in isolation. Our generalization also allows each of the mutualists to be subject to a weak Allee effect. Moreover, we find that if one of the interacting species is subject to a strong Allee effect, then the mutualism can overcome it and cause a unique coexistence equilibrium to be globally stable.     

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.     

Adaptation in a hybrid world with multiple interaction types: a new mechanism for species coexistence

In ecological communities, numerous species coexist and affect each others’ population levels via various types of interspecific interactions. Previous ecological theory explaining multispecies coexistence tended to focus on a single interaction type, such as antagonism, competition, or mutualism, and its consequences on population dynamics. Hence, it remains unclear what, if any, contribution multiple coexisting interaction types have on the multispecies coexistence. Here, we show that the coexistence of multiple interaction types can be essential for multispecies coexistence. We present a simple model in which the exploiter and mutualist adaptively switch between two competing resource species. An adaptive mutualist, which favors the more abundant species, provides a mechanism of majority-advantage and, thus, potentially inhibits the coexistence of resource species. In the absence of an exploiter, an adaptive mutualist leads to competitive exclusion at the resource species level. However, the coexistence of an adaptive exploiter and a mutualist allows the coexistence of all species in the community, because the mutualist-mediated “winner” tends to be suppressed by the adaptive exploiter. The mutualist indirectly increases the abundance of the exploiter through mutualistic interactions, thereby indirectly supporting this coexistence mechanism. In fact, coexistence may occur even if the exploiter or mutualist alone cannot mediate the coexistence of two resources. We conclude that the coexistence of mutualism and antagonism may be the key to the persistence of the four-species module in the presence of adaptive switching.     

Pollination and seed predation by moths on Silene and allied Caryophyllaceae: evaluating a model system to study the evolution of mutualisms

Nursery pollinators, and the plants they use as hosts for offspring development, function as exemplary models of coevolutionary mutualism. The two pre-eminent examples--fig wasps and yucca moths--show little variation in the interaction: the primary pollinator is an obligate mutualist. By contrast, nursery pollination of certain Caryophyllaceae, including Silene spp., by two nocturnal moth genera, Hadena and Perizoma, ranges from antagonistic to potentially mutualistic, offering an opportunity to test hypotheses about the factors that promote or discourage the evolution of mutualism. Here, we review nursery pollination and host-plant interactions in over 30 caryophyllaceous plants, based on published studies and a survey of researchers investigating pollination, seed predation, and moth morphology and behavior. We detected little direct evidence of mutualism in these moth-plant interactions, but found traits and patterns in both that are nonetheless consistent with the evolution of mutualism and merit further attention.     

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.     

Dynamics of mutualist populations that are demographically open

1. Few theoretical studies have examined the impact of immigration and emigration on mutualist population dynamics, but a recent empirical study (A.R. Thompson Oecologia, 143, 61-69) on mutualistic fish and shrimp showed that immigration can prevent population collapse, and that intraspecific competition for a mutualistic partner can curb population expansion. To understand in a theoretical context the implications of these results, and to assess their generality, we present a two-species model that accounts explicitly for immigration and emigration, as well as distinguishing the impacts of mutualism on birth rates, death rates and habitat acquisition. 2. The model confirms that immigration can stabilize mutualistic populations, and predicts that high immigration, along with enhanced reproduction and/or reduced mortality through mutualism, can cause population sizes to increase until habitat availability curbs further expansion. 3. We explore in detail the effects of different forms of habitat limitation on mutualistic populations. Habitat availability commonly limits the density of both populations if mutualists acquire shelter independently. If a mutualist depends on a partner for habitat, densities of that mutualist are capped by the amount of space provided by that partner. The density of the shelter-provider is limited by the environment. 4. If a mutualism solely augments reproduction, and most locally produced individuals leave the focal patch, then the mutualism will have a minimal effect on local dynamics. If the mutualism operates by reducing rates of death or enhancing habitat availability, and there is at least some immigration, then mutualism will affect local dynamics. This finding may be particularly relevant in marine systems, where there is high variability (among species and locations) in the extent to which progeny disperse from natal locations. 5. Overall, our results demonstrate that the consequences of immigration and emigration for the dynamics of mutualists depend strongly on which demographic rate is influenced by mutualism. 6. By relating our model to a variety of terrestrial and aquatic systems, we provide a general framework to guide future empirical studies of the dynamics of mutualistic populations.     

Coevolution in temporally variable environments

Many potentially mutualistic interactions are conditional, with selection that varies between mutualism and antagonism over space and time. We develop a genetic model of temporally variable coevolution that incorporates stochastic fluctuations between mutualism and antagonism. We use this model to determine conditions necessary for the coevolution of matching traits between a host and a conditional mutualist. Using an analytical approximation, we show that matching traits will coevolve when the geometric mean interaction is mutualistic. When this condition does not hold, polymorphism and trait mismatching are maintained, and coevolutionary cycles may result. Numerical simulations verify this prediction and suggest that it remains robust in the presence of temporal autocorrelation. These results are compared with those from spatial models with unrestricted movement. The comparisons demonstrate that gene flow is unnecessary for generating empirical patterns predicted by the geographic mosaic theory of coevolution.     

Interactions between seed predators/pollinators and their host plants: a first step towards mutualism?

The mutualisms between fig trees and their pollinator fig wasps and between yucca plants and yucca moths are spectacular examples of coevolution. The characteristics of these independently evolved mutualisms have resulted from long‐term processes, the first stages of which are unknown. A fundamental question in the study of mutualism is how these interactions evolve. Seed predator/pollinator and host plant interactions, which may initially be considered as mainly antagonistic, have the potential to provide good model systems for the study of the first stages of evolution towards mutualism. We present here theoretical models assessing the consequences of interactions between specialized seed predator insects and their host plants. These models describe the parameters that affect the fitness of an individual female seed predator and her influence on the fitness of the host plant. In an optimal strategy for the seed predator, the number of eggs laid in each flower depends on the interaction between the adult and larva survival. Along with a growing predation pressure on adults and larvae several eggs must be laid in each flower by the female seed predator to enhance her fitness. However, in a situation where the host plant selectively aborts flowers with a high number of eggs the fitness of the seed predator will seriously decrease. If the cost of selective abortion is less than the cost of seed predation the host plant will maintain fitness. In a mutualistic relationship a balance between the cost and the benefit of the parameters in the fitness models of the seed predator and the host plant has to occur so that the net seed output is larger than zero (0). Any unselfish behaviour or quality of the seed predator that would benefit the host plant in such a way that the net seed output increases might be a first stage in an interaction becoming mutualistic. The models presented here will not only provide a platform for empirical studies on interactions that may swing from parasitism to mutualism, but also for seed predator/pollinator and host plant interactions in general.     

Evolution of mutualism through spatial effects

Mutualism among species is ubiquitous in natural ecosystems but its evolution is not well understood. We provided a simple lattice model to clarify the importance of spatial structure for the evolution of mutualism. We assumed reproductive rates of two species are modified through interaction between species and examine conditions where mutualists of both species, that give some benefit to the other species with their own cost, invade non-mutualists populations. When dispersal of offspring is unlimited, we verified the evolution of mutualism is impossible under any condition. On the other hand, when the dispersal is limited to neighboring lattice sites, mutualists can invade if the ratio of cost to benefit is low and the intrinsic reproductive rate is low in case where the parameter values are symmetric between species. Under the same conditions, non-mutualists cannot invade mutualist populations, that is, the latter are evolutionarily stable. In case of asymmetric parameters, mutualists tend to invade if the average value of costs to two species is low or that of benefits is high, and if the intrinsic reproductive rate is low for one of the two species. A mechanistic explanation of why mutualists increase when the dispersal is limited is given by showing that mutualist pairs of the two species at the same lattice site rapidly increase at the initial phase of the invasion.     

Defaunation leads to interaction deficits,not interaction compensation,in an island seed dispersal network

Following defaunation, the loss of interactions with mutualists such as pollinators or seed dispersers may be compensated through increased interactions with remaining mutualists, ameliorating the negative cascading impacts on biodiversity. Alternatively, remaining mutualists may respond to altered competition by reducing the breadth or intensity of their interactions, exacerbating negative impacts on biodiversity. Despite the importance of these responses for our understanding of the dynamics of mutualistic networks and their response to global change, the mechanism and magnitude of interaction compensation within real mutualistic networks remains largely unknown. We examined differences in mutualistic interactions between frugivores and fruiting plants in two island ecosystems possessing an intact or disrupted seed dispersal network. We determined how changes in the abundance and behavior of remaining seed dispersers either increased mutualistic interactions (contributing to “interaction compensation”) or decreased interactions (causing an “interaction deficit”) in the disrupted network. We found a “rich‐get‐richer” response in the disrupted network, where remaining frugivores favored the plant species with highest interaction frequency, a dynamic that worsened the interaction deficit among plant species with low interaction frequency. Only one of five plant species experienced compensation and the other four had significant interaction deficits, with interaction frequencies 56–95% lower in the disrupted network. These results do not provide support for the strong compensating mechanisms assumed in theoretical network models, suggesting that existing network models underestimate the prevalence of cascading mutualism disruption after defaunation. This work supports a mutualist biodiversity‐ecosystem functioning relationship, highlighting the importance of mutualist diversity for sustaining diverse and resilient ecosystems.     

Prey temporarily escape from predation in the presence of a second prey species

1. Indirect interactions between populations of different prey species mediated by a shared predator population are known to affect prey dynamics. 2. Depending on the temporal and spatial scale, these indirect interactions may result in positive (apparent mutualism), neutral or negative effects (apparent competition) of the prey on each other's densities. Although there is ample evidence for the latter, evidence for apparent mutualism is scarce. 3. The effectiveness of using one species of predator for biological control of more than one pest species depends on the occurrence of such positive or negative effects. 4. We used an experimental system consisting of the two prey species Western flower thrips (Franklineilla occidentalis Pergande) and greenhouse whitefly (Trialeurodes vaporariorum Westwood) and a shared predator, the phytoseiid mite Amblyseius swirskii Athias‐Henriot. We released all three species on the same plant and studied their dynamics and distribution along rows of plants. 5. We expected that the more mobile prey species (thrips) would escape temporarily in the presence of the other prey species (whitefly) by dispersing from plants with the predator. The predator was expected to disperse slower in the presence of two prey species because of the higher availability of food. 6. Evidence was found for slower dispersal of predators and short‐term escape of thrips from predation when whiteflies were present, thus confirming the occurrence of short‐term apparent mutualism. 7. The apparent mutualism resulted in a cascade to the first trophic level: a higher proportion of fruits was damaged by thrips in the presence of whiteflies. 8. We conclude that apparent mutualism can be an important phenomenon in population dynamics, and can significantly affect biological control of pest species that share a natural enemy.     

Evolutionary stability of mutualism: interspecific population regulation as an evolutionarily stable strategy

Interspecific mutualisms are often vulnerable to instability because low benefit : cost ratios can rapidly lead to extinction or to the conversion of mutualism to parasite-host or predator-prey interactions. We hypothesize that the evolutionary stability of mutualism can depend on how benefits and costs to one mutualist vary with the population density of its partner, and that stability can be maintained if a mutualist can influence demographic rates and regulate the population density of its partner. We test this hypothesis in a model of mutualism with key features of senita cactus (Pachycereus schottii)-senita moth (Upiga virescens) interactions, in which benefits of pollination and costs of larval seed consumption to plant fitness depend on pollinator density. We show that plants can maximize their fitness by allocating resources to the production of excess flowers at the expense of fruit. Fruit abortion resulting from excess flower production reduces pre-adult survival of the pollinating seed-consumer, and maintains its density beneath a threshold that would destabilize the mutualism. Such a strategy of excess flower production and fruit abortion is convergent and evolutionarily stable against invasion by cheater plants that produce few flowers and abort few to no fruit. This novel mechanism of achieving evolutionarily stable mutualism, namely interspecific population regulation, is qualitatively different from other mechanisms invoking partner choice or selective rewards, and may be a general process that helps to preserve mutualistic interactions in nature.     

Acoustic alarm signalling facilitates predator protection of treehoppers by mutualist ant bodyguards

Mutualism is a net positive interaction that includes varying degrees of both costs and benefits. Because tension between the costs and benefits of mutualism can lead to evolutionary instability, identifying mechanisms that regulate investment between partners is critical to understanding the evolution and maintenance of mutualism. Recently, studies have highlighted the importance of interspecific signalling as one mechanism for regulating investment between mutualist partners. Here, we provide evidence for interspecific alarm signalling in an insect protection mutualism and we demonstrate a functional link between this acoustic signalling and efficacy of protection. The treehopper Publilia concava Say (Hemiptera: Membracidae) is an insect that provides ants with a carbohydrate-rich excretion called honeydew in return for protection from predators. Adults of this species produce distinct vibrational signals in the context of predator encounters. In laboratory trials, putative alarm signal production significantly increased following initial contact with ladybeetle predators (primarily Harmonia axyridis Pallas, Coleoptera: Coccinellidae), but not following initial contact with ants. In field trials, playback of a recorded treehopper alarm signal resulted in a significant increase in both ant activity and the probability of ladybeetle discovery by ants relative to both silence and treehopper courtship signal controls. Our results show that P. concava treehoppers produce alarm signals in response to predator threat and that this signalling can increase effectiveness of predator protection by ants.     

Natural selection on extrafloral nectar production in Chamaecrista fasciculata: the costs and benefits of a mutualism trait

Cost-benefit models of the evolution of mutualism predict that the current state of mutualism results from trade-offs between fitness costs of mutualist traits and the fitness benefits of association. We test the assumptions of such models by measuring patterns of natural selection on a mutualist trait, extrafloral nectar production in Chamaecrista fasciculata. Selection was measured on plants from which ants had been excluded (removing the mutualist benefit of the trait), from which all insects had been excluded (removing costs of herbivory in addition to mutualist benefits), and unmanipulated plants (where both costs and benefits were present). Selection analysis based on half-sibling-mean regressions of fitness on the trait revealed no evidence of costs of extrafloral nectar production in the absence of all insects or in the absence of ants. However, examination of the selective surfaces for these treatments suggest that costs of nectar production may exist and are exacerbated by the presence of herbivory. In the presence of ants, natural selection favors high extrafloral nectar production, consistent with a fitness benefit to this mutualist trait in the presence of the mutualist partner. In this study, the interaction of costs and benefits did not produce an evolutionary optimum for the trait within the range of variation observed, suggesting that application of a cost-benefit framework to this trait will benefit from considering the influence of temporal and spatial variation on the quality of costs and benefits.     

Context dependence in the coevolution of plant and rhizobial mutualists

Several mechanisms are expected to rapidly rid mutualisms of genetic variation in partner quality. Variation for mutualist quality, however, appears to be widespread. We used a model legume-rhizobium mutualism to test for evidence that context-dependent selection may maintain variation in partner quality. In a greenhouse experiment using 10 natural populations of Medicago truncatula and two strains of Sinorhizobium medicae, we detected significant genotype x genotype (G x G) interactions for plant fitness, indicating that the most beneficial rhizobium strain depends on the host genotype. In a second experiment using a subset of the plant populations used in the first experiment, we detected significant G x G interactions for both plant and rhizobium fitness. Moreover, the plant population with which rhizobium strains gained the greatest benefit depended on the nitrogen environment. Finally, we found that in a high nitrogen environment, all plant populations had lower fitness when inoculated with a 1:1 mixture of strains than with the worse single strain alone, suggesting that nitrogen shifts the exchange of benefits in favour of rhizobia. Our data suggest that genotype, nitrogen and biotic dependency might contribute to the maintenance of genetic variation in mutualist quality when coupled with spatial or temporal heterogeneity in the environment.     

Contrasting exotic Solenopsis invicta and native Forelius pruinosus ants as mutualists with Catalpa bignonioides, a native plant

Abstract. 1. The suitability of the red imported fire ant Solenopsis invicta Buren and a native ant Forelius pruinosus (Roger) as participants in a food-for-protection mutualism with a native nectaried tree Catalpa bignonioides Walter was compared.
2. The mean mortality of folivore larvae of Ceratomia catalpae Boisduval was similar for S. invicta and F. pruinosus although S. invicta attacked fewer caterpillar aggregations and was a devastating pupal predator. Solenopsis invicta also differed from the native ant in that it attacked the parasitoid Cotesia congregata Say, another plant mutualist, and visited extrafloral nectaries less frequently.
3. Habitats invaded by S. invicta are characterised by a scarcity of both herbivores and of beneficial insects that visit extrafloral nectaries. The plants do not require protection, and extrafloral nectaries are visited rarely. Although plants are defended incidentally by S. invicta , the insect-plant mutualism therein is greatly simplified or defunct.