Modelling nutritional mutualisms: challenges and opportunities for data integration

Nutritional mutualisms are ancient, widespread, and profoundly influential in biological communities and ecosystems. Although much is known about these interactions, comprehensive answers to fundamental questions, such as how resource availability and structured interactions influence mutualism persistence, are still lacking. Mathematical modelling of nutritional mutualisms has great potential to facilitate the search for comprehensive answers to these and other fundamental questions by connecting the physiological and genomic underpinnings of mutualisms with ecological and evolutionary processes. In particular, when integrated with empirical data, models enable understanding of underlying mechanisms and generalisation of principles beyond the particulars of a given system. Here, we demonstrate how mathematical models can be integrated with data to address questions of mutualism persistence at four biological scales: cell, individual, population, and community. We highlight select studies where data has been or could be integrated with models to either inform model structure or test model predictions. We also point out opportunities to increase model rigour through tighter integration with data, and describe areas in which data is urgently needed. We focus on plant‐microbe systems, for which a wealth of empirical data is available, but the principles and approaches can be generally applied to any nutritional mutualism.     

Influence of evolution on the stability of ecological communities

In randomly assembled communities, diversity is known to have a destabilizing effect. Evolution may affect this result, but our theoretical knowledge of its role is mostly limited to models of small food webs. In the present article, I introduce evolution in a two-species Lotka-Volterra model in which I vary the interaction type and the cost constraining evolution. Regardless of the cost type, evolution tends to stabilize the dynamics more often in trophic interactions than for mutualism or competition. I then use simulations to study the effect of evolution in larger communities that contain all interaction types. Results suggest that evolution usually stabilizes the dynamics. This stabilizing effect is stronger when evolution affects trophic interactions, but happens for all interaction types. Stabilization decreases with diversity and evolution becomes destabilizing in very diverse communities. This suggests that evolution may not counteract the destabilizing effect of diversity observed in random communities.     

Ecological theory of mutualism: Robust patterns of stability and thresholds in two‐species population models

Mutualisms are ubiquitous in nature, provide important ecosystem services, and involve many species of interest for conservation. Theoretical progress on the population dynamics of mutualistic interactions, however, comparatively lagged behind that of trophic and competitive interactions, leading to the impression that ecologists still lack a generalized framework to investigate the population dynamics of mutualisms. Yet, over the last 90 years, abundant theoretical work has accumulated, ranging from abstract to detailed. Here, we review and synthesize historical models of two‐species mutualisms. We find that population dynamics of mutualisms are qualitatively robust across derivations, including levels of detail, types of benefit, and inspiring systems. Specifically, mutualisms tend to exhibit stable coexistence at high density and destabilizing thresholds at low density. These dynamics emerge when benefits of mutualism saturate, whether due to intrinsic or extrinsic density dependence in intraspecific processes, interspecific processes, or both. We distinguish between thresholds resulting from Allee effects, low partner density, and high partner density, and their mathematical and conceptual causes. Our synthesis suggests that there exists a robust population dynamic theory of mutualism that can make general predictions.     

The Benefits of Mutualism: A Conceptual Framework

There are three general mechanisms by which phenotypic benefits are transferred between unrelated organisms. First, one organism may purloin benefits from another by preying on or parasitizing the other organism. Second, one organism may enjoy benefits that are incidental to or a by-product of the self-serving traits of another organism. Third, an organism may invest in another organism if that investment produces return benefits which outweigh the cost of the investment. Interactions in which both parties gain a net benefit are mutualistic. The three mechanisms by which benefits are transferred between organisms can be combined in pairs to produce six possible kinds of original or 'basal' mutualisms that can arise from an amutualistic state. A review of the literature suggests that most or all interspecific mutualism have origins in three of the six possible kinds of basal mutualism. Each of these three basal mutualisms have byproduct benefits flowing in at least one direction. The transfer of by-product benefits and investment are common to both intra- and interspecific mutualisms, so that some interspecific mutualisms have intraspecific analogs. A basal mutualism may evolve to the point where each party invests in the other, sometimes obscuring the nature of the original interaction along the way. Two prominent models for the evolution of mutualism do not include by-product benefits: Roughgarden's model for the evolution of the damsel-fish anemone mutualism and the 'Tit-for-Tat' model of reciprocity. Using the conceptual framework presented here, including in particular by-product benefits, I have shown how it is possible to construct more parsimonious alternatives to both models.     

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.     

Anthropogenic effects on interaction outcomes: examples from insect-microbial symbioses in forest and savanna ecosystems

The influence of humans on ecosystem dynamics has been, and continues to be, profound. Anthropogenic effects are expected to amplify as human populations continue to increase. Concern over these effects has given rise to a large number of studies focusing on impacts of human activities on individual species or on biotic community structure and composition. Lacking are studies on interactions, particularly mutualisms. Because of the role of mutualisms in ecosystem stability, such studies are critically needed if we are to begin to better understand and predict the responses of ecosystems to anthropogenic change. Most organisms are involved in at least one mutualism, and many in several. Mutualisms facilitate the ability of partners to exploit particular habitats and resources, and play a large role in determining ecological boundaries. When change disrupts, enhances, or introduces new organisms into a mutualism, the outcome and stability of the original partnership(s) is altered as are effects of the symbiosis on the community and ecosystem as a whole. In this paper, using examples from six microbe-insect mutualisms in forest and savanna settings, we showcase how varied and complex the responses of mutualisms can be to an equally varied set of anthropogenic influences. We also show how alterations of mutualisms may ramify throughout affected systems. We stress that researchers must be cognizant that many observed changes in the behaviors, abundances, and distributions of organisms due to human activities are likely to be mediated by mutualists which may alter predictions and actual outcomes in significant ways.     

Phenological shifts and the fate of mutualisms

Climate change is altering the timing of life history events in a wide array of species, many of which are involved in mutualistic interactions. Because many mutualisms can form only if partner species are able to locate each other in time, differential phenological shifts are likely to influence their strength, duration and outcome. At the extreme, climate change‐driven shifts in phenology may result in phenological mismatch: the partial or complete loss of temporal overlap of mutualistic species. We have a growing understanding of how, when, and why phenological change can alter one type of mutualism–pollination. However, as we show here, there has been a surprising lack of attention to other types of mutualism. We generate a set of predictions about the characteristics that may predispose mutualisms in general to phenological mismatches. We focus not on the consequences of such mismatches but rather on the likelihood that mismatches will develop. We explore the influence of three key characteristics of mutualism: 1) intimacy, 2) seasonality and duration, and 3) obligacy and specificity. We predict that the following characteristics of mutualism may increase the likelihood of phenological mismatch: 1) a non‐symbiotic life history in which co‐dispersal is absent; 2) brief, seasonal interactions; and 3) facultative, generalized interactions. We then review the limited available data in light of our a priori predictions and point to mutualisms that are more and less likely to be at risk of becoming phenologically mismatched, emphasizing the need for research on mutualisms other than plant–pollinator interactions. Future studies should explicitly focus on mutualism characteristics to determine whether and how changing phenologies will affect mutualistic interactions.     

Dynamics within mutualism and the maintenance of diversity: inference from a model of interguild frequency dependence

Numerical models have suggested that the dynamics within mutualisms are not important for the maintenance of diversity. In this study it is demonstrated that the dynamics within mutualism can contribute to the maintenance of diversity within its participants, using a general model of frequency dependence between two mutualistically interacting guilds. Specifically, it is demonstrated that while mutualisms may exhibit positive feedback in density, there may be a negative feedback within a mutualism as a result of the change in composition within the interacting guild. Such a negative feedback results from an asymmetry in the delivery of benefit between participants of the mutualism that generates a negative interguild frequency dependence. This dynamic contributes to the maintenance of diversity within the interacting guilds. Conditions are identified for the maintenance of diversity and the maximization of benefit from mutualism within the context of the model. The utility of these conditions for testing hypotheses using data from the mutualistic interaction between plants and mycorrhizal fungi is then demonstrated.     

The exploitation of mutualisms

Mutualisms (interspecific cooperative interactions) are ubiquitously exploited by organisms that obtain the benefits mutualists offer, while delivering no benefits in return. The natural history of these exploiters is well-described, but relatively little effort has yet been devoted to analysing their ecological or evolutionary significance for mutualism. Exploitation is not a unitary phenomenon, but a set of loosely related phenomena: exploiters may follow mixed strategies or pure strategies at either the species or individual level, may or may not be derived from mutualists, and may or may not inflict significant costs on mutualisms. The evolutionary implications of these different forms of exploitation, especially the threats they pose to the stability of mutualism, have as yet been minimally explored. Studies of this issue are usually framed in terms of a "temptation to defect" that generates a destabilizing conflict of interest between partners. I argue that this idea is in fact rather inappropriate for interpreting most observed forms of exploitation in mutualisms. I suggest several alternative and testable ideas for how mutualism can persist in the face of exploitation.     

Parasites of mutualisms

Cooperation invites cheating, and nowhere is this more apparent than when different species cooperate, known as mutualism. In almost all mutualisms studied, specialist parasites have been identified that purloin the benefits that one mutualist provides another. Explaining how parasites are kept from driving mutualisms extinct remains an unsolved problem because existing theories explaining the maintenance of cooperation do not apply to parasites of mutualisms. Nonetheless, these theories can be summarized in such a way as to suggest how mutualisms can persist in the face of parasites. (1) For cooperation to occur, the recipient of a benefit must reciprocate, and the recriprocated benefit must be captured by the initial giver or its offspring. (2) For cooperation to persist, the mutualism must be re-assembled each generation. Because most mutualisms are of the "by-product' type, broadly defined, the first condition is normally always fulfilled. Thus, the maintenance of mutualism usually requires enforcement of the second condition: reliable re-assembly. Hence, I argue that the persistence of mutualism is best understood by using theories of species coexistence, because each mutualist can be considered a resource for the other, and species coexistence theory explains how multiple taxa (e.g. parasites and mutualists) can stably partition a resource over multiple generations. This approach connects the study of mutualism to theories of population regulation and helps to identify key factors that have promoted the evolution, maintenance and breakdown of mutualism. I discuss how these ideas might apply to and be tested in ant-plant, fig-wasp and yucca-moth mutualisms.     

The role of plant–mycorrhizal mutualisms in deterring plant invasions: Insights from an individual‐based model

Understanding the factors that determine invasion success for non‐native plants is crucial for maintaining global biodiversity and ecosystem functioning. One hypothesized mechanism by which many exotic plants can become invasive is through the disruption of key plant–mycorrhizal mutualisms, yet few studies have investigated how these disruptions can lead to invader success. We present an individual‐based model to examine how mutualism strengths between a native plant (Impatiens capensis) and mycorrhizal fungus can influence invasion success for a widespread plant invader, Alliaria petiolata (garlic mustard). Two questions were investigated as follows: (a) How does the strength of the mutualism between the native I. capensis and a mycorrhizal fungus affect resistance (i.e., native plant maintaining >60% of final equilibrium plant density) to garlic mustard invasion? (b) Is there a non‐linear relationship between initial garlic mustard density and invasiveness (i.e., garlic mustard representing >60% of final equilibrium plant density)? Our findings indicate that either low (i.e., facultative) or high (i.e., obligate) mutualism strengths between the native plant and mycorrhizal fungus were more likely to lead to garlic mustard invasiveness than intermediate levels, which resulted in higher resistance to garlic mustard invasion. Intermediate mutualism strengths allowed I. capensis to take advantage of increased fitness when the fungus was present but remained competitive enough to sustain high numbers without the fungus. Though strong mutualisms had the highest fitness without the invader, they proved most susceptible to invasion because the loss of the mycorrhizal fungus resulted in a reproductive output too low to compete with garlic mustard. Weak mutualisms were more competitive than strong mutualisms but still led to garlic mustard invasion. Furthermore, we found that under intermediate mutualism strengths, the initial density of garlic mustard (as a proxy for different levels of plant invasion) did not influence its invasion success, as high initial densities of garlic mustard did not lead to it becoming dominant. Our results indicate that plants that form weak or strong mutualisms with mycorrhizal fungi are most vulnerable to invasion, whereas intermediate mutualisms provide the highest resistance to an allelopathic invader.     

Persistence of mutualisms with bidirectional interactions in a two-species system

In Lotka–Volterra equations (LVEs) of mutualisms, population densities of mutualists will increase infinitely if the mutualisms between them are strong, which is called the divergence problem. In order to avoid the problem, a mutualism system of two species is analyzed in this work. The model is derived from reactions on lattice and has a form similar to that of LVEs. Population densities of species will not increase infinitely because of spatial limitation on the lattice. Stability analysis of the model demonstrates basic mechanisms by which the mutualisms lead to coexistence/extinction of the species. When in coexistence, intermediate mutualistic effect is shown to lead to the maximal density in certain parameter ranges, while a strong or weak mutualistic effect is not so good. Furthermore, the stability analysis exhibits that extremely strong/weak mutualisms will result in extinction of one/both species.     

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.     

Mutualisms in a changing world: an evolutionary perspective

Ecology Letters (2010) 13: 1459-1474 ABSTRACT: There is growing concern that rapid environmental degradation threatens mutualistic interactions. Because mutualisms can bind species to a common fate, mutualism breakdown has the potential to expand and accelerate effects of global change on biodiversity loss and ecosystem disruption. The current focus on the ecological dynamics of mutualism under global change has skirted fundamental evolutionary issues. Here, we develop an evolutionary perspective on mutualism breakdown to complement the ecological perspective, by focusing on three processes: (1) shifts from mutualism to antagonism, (2) switches to novel partners and (3) mutualism abandonment. We then identify the evolutionary factors that may make particular classes of mutualisms especially susceptible or resistant to breakdown and discuss how communities harbouring mutualisms may be affected by these evolutionary responses. We propose a template for evolutionary research on mutualism resilience and identify conservation approaches that may help conserve targeted mutualisms in the face of environmental change.     

Facultative mutualisms: A double‐edged sword for foundation species in the face of anthropogenic global change

Ecosystems worldwide depend on habitat‐forming foundation species that often facilitate themselves with increasing density and patch size, while also engaging in facultative mutualisms. Anthropogenic global change (e.g., climate change, eutrophication, overharvest, land‐use change), however, is causing rapid declines of foundation species‐structured ecosystems, often typified by sudden collapse. Although disruption of obligate mutualisms involving foundation species is known to precipitate collapse (e.g., coral bleaching), how facultative mutualisms (i.e., context‐dependent, nonbinding reciprocal interactions) affect ecosystem resilience is uncertain. Here, we synthesize recent advancements and combine these with model analyses supported by real‐world examples, to propose that facultative mutualisms may pose a double‐edged sword for foundation species. We suggest that by amplifying self‐facilitative feedbacks by foundation species, facultative mutualisms can increase foundation species’ resistance to stress from anthropogenic impact. Simultaneously, however, mutualism dependency can generate or exacerbate bistability, implying a potential for sudden collapse when the mutualism's buffering capacity is exceeded, while recovery requires conditions to improve beyond the initial collapse point (hysteresis). Thus, our work emphasizes the importance of acknowledging facultative mutualisms for conservation and restoration of foundation species‐structured ecosystems, but highlights the potential risk of relying on mutualisms in the face of global change. We argue that significant caveats remain regarding the determination of these feedbacks, and suggest empirical manipulation across stress gradients as a way forward to identify related nonlinear responses.     

A general model for the evolution of mutualisms

The evolution of mutualisms presents a puzzle. Why does selection favour cooperation among species rather than cheaters that accept benefits but provide nothing in return? Here we present a general model that predicts three key factors will be important in mutualism evolution: (i) high benefit to cost ratio, (ii) high within‐species relatedness and (iii) high between‐species fidelity. These factors operate by moderating three types of feedback benefit from mutualism: cooperator association, partner‐fidelity feedback and partner choice. In defining the relationship between these processes, our model also allows an assessment of their relative importance. Importantly, the model suggests that phenotypic feedbacks (partner‐fidelity feedback, partner choice) are a more important explanation for between‐species cooperation than the development of genetic correlations among species (cooperator association). We explain the relationship of our model to existing theories and discuss the empirical evidence for our predictions.     

EXPLAINING MUTUALISM VARIATION: A NEW EVOLUTIONARY PARADOX?

The paradox of mutualism is typically framed as the persistence of interspecific cooperation, despite the potential advantages of cheating. Thus, mutualism research has tended to focus on stabilizing mechanisms that prevent the invasion of low‐quality partners. These mechanisms alone cannot explain the persistence of variation for partner quality observed in nature, leaving a large gap in our understanding of how mutualisms evolve. Studying partner quality variation is necessary for applying genetically explicit models to predict evolution in natural populations, a necessary step for understanding the origins of mutualisms as well as their ongoing dynamics. An evolutionary genetic approach, which is focused on naturally occurring mutualist variation, can potentially synthesize the currently disconnected fields of mutualism evolution and coevolutionary genetics. We outline explanations for the maintenance of genetic variation for mutualism and suggest approaches necessary to address them.     

Mutualistic networks: moving closer to a predictive theory

Plant–animal mutualistic networks sustain terrestrial biodiversity and human food security. Global environmental changes threaten these networks, underscoring the urgency for developing a predictive theory on how networks respond to perturbations. Here, I synthesise theoretical advances towards predicting network structure, dynamics, interaction strengths and responses to perturbations. I find that mathematical models incorporating biological mechanisms of mutualistic interactions provide better predictions of network dynamics. Those mechanisms include trait matching, adaptive foraging, and the dynamic consumption and production of both resources and services provided by mutualisms. Models incorporating species traits better predict the potential structure of networks (fundamental niche), while theory based on the dynamics of species abundances, rewards, foraging preferences and reproductive services can predict the extremely dynamic realised structures of networks, and may successfully predict network responses to perturbations. From a theoretician's standpoint, model development must more realistically represent empirical data on interaction strengths, population dynamics and how these vary with perturbations from global change. From an empiricist's standpoint, theory needs to make specific predictions that can be tested by observation or experiments. Developing models using short‐term empirical data allows models to make longer term predictions of community dynamics. As more longer term data become available, rigorous tests of model predictions will improve.     

Nutrient loading alters the performance of key nutrient exchange mutualisms

Nutrient exchange mutualisms between phototrophs and heterotrophs, such as plants and mycorrhizal fungi or symbiotic algae and corals, underpin the functioning of many ecosystems. These relationships structure communities, promote biodiversity and help maintain food security. Nutrient loading may destabilise these mutualisms by altering the costs and benefits each partner incurs from interacting. Using meta‐analyses, we show a near ubiquitous decoupling in mutualism performance across terrestrial and marine environments in which phototrophs benefit from enrichment at the expense of their heterotrophic partners. Importantly, heterotroph identity, their dependence on phototroph‐derived C and the type of nutrient enrichment (e.g. nitrogen vs. phosphorus) mediated the responses of different mutualisms to enrichment. Nutrient‐driven changes in mutualism performance may alter community organisation and ecosystem processes and increase costs of food production. Consequently, the decoupling of nutrient exchange mutualisms via alterations of the world's nitrogen and phosphorus cycles may represent an emerging threat of global change.     

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.