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.     

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.     

Strategy Diversity Stabilizes Mutualism through Investment Cycles,Phase Polymorphism,and Spatial Bubbles

There is continuing interest in understanding factors that facilitate the evolution and stability of cooperation within and between species. Such interactions will often involve plasticity in investment behavior, in response to the interacting partner''s investments. Our aim here is to investigate the evolution and stability of reciprocal investment behavior in interspecific interactions, a key phenomenon strongly supported by experimental observations. In particular, we present a comprehensive analysis of a continuous reciprocal investment game between mutualists, both in well-mixed and spatially structured populations, and we demonstrate a series of novel mechanisms for maintaining interspecific mutualism. We demonstrate that mutualistic partners invariably follow investment cycles, during which mutualism first increases, before both partners eventually reduce their investments to zero, so that these cycles always conclude with full defection. We show that the key mechanism for stabilizing mutualism is phase polymorphism along the investment cycle. Although mutualistic partners perpetually change their strategies, the community-level distribution of investment levels becomes stationary. In spatially structured populations, the maintenance of polymorphism is further facilitated by dynamic mosaic structures, in which mutualistic partners form expanding and collapsing spatial bubbles or clusters. Additionally, we reveal strategy-diversity thresholds, both for well-mixed and spatially structured mutualistic communities, and discuss factors for meeting these thresholds, and thus maintaining mutualism. Our results demonstrate that interspecific mutualism, when considered as plastic investment behavior, can be unstable, and, in agreement with empirical observations, may involve a polymorphism of investment levels, varying both in space and in time. Identifying the mechanisms maintaining such polymorphism, and hence mutualism in natural communities, provides a significant step towards understanding the coevolution and population dynamics of mutualistic interactions.     

Coevolution by different functional mechanisms modulates the structure and dynamics of antagonistic and mutualistic networks

A central problem in the study of species interactions is to understand the underlying ecological and evolutionary mechanisms that shape and are shaped by trait evolution in interacting assemblages. The patterns of interaction among species (i.e. network structure) provide the pathways for evolution and coevolution, which are modulated by how traits affect individual fitness (i.e. functional mechanisms). Functional mechanisms, in turn, also affect the likelihood of an ecological interaction, shaping the structure of interaction networks. Here, we build adaptive network models to explore the potential role of coevolution by two functional mechanisms, trait matching and exploitation barrier, in driving trait evolution and the structure of interaction networks. We use these models to explore how different scenarios of coevolution and functional mechanisms reproduce the empirical network patterns observed in antagonistic and mutualistic interactions and affect trait evolution. Scenarios assuming coevolutionary feedback with a strong effect of functional mechanism better reproduce the empirical structure of networks. Antagonistic and mutualistic networks, however, are better explained by different functional mechanisms and the structure of antagonisms is better reproduced than that of mutualisms. Scenarios assuming coevolution by strong trait matching between interacting partners better explain the structure of antagonistic networks, whereas those assuming strong barrier effects better reproduce the structure of mutualistic networks. The dynamics resulting from the feedback between strong functional mechanisms and coevolution favor the stability of antagonisms and mutualisms. Selection favoring trait matching reduces temporal trait fluctuation and the magnitude of arms races in antagonisms, whereas selection due to exploitation barriers reduces temporal trait fluctuations in mutualisms. Our results indicate that coevolutionary models better reproduce the network structure of antagonisms than those of mutualisms and that different functional mechanisms may favor the persistence of antagonistic and mutualistic interacting assemblages.     

Interaction intimacy affects structure and coevolutionary dynamics in mutualistic networks

The structure of mutualistic networks provides clues to processes shaping biodiversity [1-10]. Among them, interaction intimacy, the degree of biological association between partners, leads to differences in specialization patterns [4, 11] and might affect network organization [12]. Here, we investigated potential consequences of interaction intimacy for the structure and coevolution of mutualistic networks. From observed processes of selection on mutualistic interactions, it is expected that symbiotic interactions (high-interaction intimacy) will form species-poor networks characterized by compartmentalization [12, 13], whereas nonsymbiotic interactions (low intimacy) will lead to species-rich, nested networks in which there is a core of generalists and specialists often interact with generalists [3, 5, 7, 12, 14]. We demonstrated an association between interaction intimacy and structure in 19 ant-plant mutualistic networks. Through numerical simulations, we found that network structure of different forms of mutualism affects evolutionary change in distinct ways. Change in one species affects primarily one mutualistic partner in symbiotic interactions but might affect multiple partners in nonsymbiotic interactions. We hypothesize that coevolution in symbiotic interactions is characterized by frequent reciprocal changes between few partners, but coevolution in nonsymbiotic networks might show rare bursts of changes in which many species respond to evolutionary changes in a single species.     

Tolerance traits and the stability of mutualism

Identifying factors which allow the evolution and persistence of cooperative interactions between species is a fundamental issue in evolutionary ecology. Various hypotheses have been suggested which generally focus on mechanisms that allow cooperative genotypes in different species to maintain interactions over space and time. Here, we emphasise the fact that even within mutualisms (interactions with net positive fitness effects for both partners), there may still be inherent costs, such as the occasional predation by ants upon aphids. Individuals engaged in mutualisms benefit from minimising these costs as long as it is not at the expense of breaking the interspecific interaction, which offers a net positive benefit. The most common and obvious defence traits to minimise interspecific interaction costs are resistance traits, which act to reduce encounter rate between two organisms. Tolerance traits, in contrast, minimise fitness costs to the actor, but without reducing encounter rate. Given that, by definition, it is beneficial to remain in mutualistic interactions, the only viable traits to minimise costs are tolerance-based 'defence' strategies. Thus, we propose that tolerance traits are an important factor promoting stability in mutualisms. Furthermore, because resistance traits tend to propagate coevolutionary arms races between antagonists, whilst tolerance traits do not, we also suggest that tolerance-based defence strategies may be important in facilitating the transition from antagonistic interactions into mutualisms. For example, the mutualism between ants and aphids has been suggested to have evolved from parasitism. We describe how phenotypic plasticity in honeydew production may be a tolerance trait that has prevented escalation into an antagonistic arms race and instead led to mutualistic coevolution.     

Dynamical Transitions in a Pollination–Herbivory Interaction: A Conflict between Mutualism and Antagonism

Plant-pollinator associations are often seen as purely mutualistic, while in reality they can be more complex. Indeed they may also display a diverse array of antagonistic interactions, such as competition and victim–exploiter interactions. In some cases mutualistic and antagonistic interactions are carried-out by the same species but at different life-stages. As a consequence, population structure affects the balance of inter-specific associations, a topic that is receiving increased attention. In this paper, we developed a model that captures the basic features of the interaction between a flowering plant and an insect with a larval stage that feeds on the plant’s vegetative tissues (e.g. leaves) and an adult pollinator stage. Our model is able to display a rich set of dynamics, the most remarkable of which involves victim–exploiter oscillations that allow plants to attain abundances above their carrying capacities and the periodic alternation between states dominated by mutualism or antagonism. Our study indicates that changes in the insect’s life cycle can modify the balance between mutualism and antagonism, causing important qualitative changes in the interaction dynamics. These changes in the life cycle could be caused by a variety of external drivers, such as temperature, plant nutrients, pesticides and changes in the diet of adult pollinators.     

Evolution and coevolution in mutualistic networks

A major current challenge in evolutionary biology is to understand how networks of interacting species shape the coevolutionary process. We combined a model for trait evolution with data for twenty plant-animal assemblages to explore coevolution in mutualistic networks. The results revealed three fundamental aspects of coevolution in species-rich mutualisms. First, coevolution shapes species traits throughout mutualistic networks by speeding up the overall rate of evolution. Second, coevolution results in higher trait complementarity in interacting partners and trait convergence in species in the same trophic level. Third, convergence is higher in the presence of super-generalists, which are species that interact with multiple groups of species. We predict that worldwide shifts in the occurrence of super-generalists will alter how coevolution shapes webs of interacting species. Introduced species such as honeybees will favour trait convergence in invaded communities, whereas the loss of large frugivores will lead to increased trait dissimilarity in tropical ecosystems.     

Can the evolution of plant defense lead to plant-herbivore mutualism?

Moderate rates of herbivory can enhance primary production. This hypothesis has led to a controversy as to whether such positive effects can result in mutualistic interactions between plants and herbivores. We present a model for the ecology and evolution of plant-herbivore systems to address this question. In this model, herbivores have a positive indirect effect on plants through recycling of a limiting nutrient. Plants can evolve but are constrained by a trade-off between growth and antiherbivore defense. Although evolution generally does not lead to optimal plant performance, our evolutionary analysis shows that, under certain conditions, the plant-herbivore interaction can be considered mutualistic. This requires in particular that herbivores efficiently recycle nutrients and that plant reproduction be positively correlated with primary production. We emphasize that two different definitions of mutualism need to be distinguished. A first ecological definition of mutualism is based on the short-term response of plants to herbivore removal, whereas a second evolutionary definition rests on the long-term response of plants to herbivore removal, allowing plants to adapt to the absence of herbivores. The conditions for an evolutionary mutualism are more stringent than those for an ecological mutualism. A particularly counterintuitive result is that higher herbivore recycling efficiency results both in increased plant benefits and in the evolution of increased plant defense. Thus, antagonistic evolution occurs within a mutualistic interaction.     

Gene flow and geographically structured coevolution

Many of the dynamic properties of coevolution may occur at the level of interacting populations, with local adaptation acting as a force of diversification, as migration between populations homogenizes these isolated interactions. This interplay between local adaptation and migration may be particularly important in structuring interactions that vary from mutualism to antagonism across the range of an interacting set of species, such as those between some plants and their insect herbivores, mammals and trypanosome parasites, and bacteria and plasmids that confer antibiotic resistance. Here we present a simple geographically structured genetic model of a coevolutionary interaction that varies between mutualism and antagonism among communities linked by migration. Inclusion of geographic structure with gene flow alters the outcomes of local interactions and allows the maintenance of allelic polymorphism across all communities under a range of selection intensities and rates of migration. Furthermore, inclusion of geographic structure with gene flow allows fixed mutualisms to be evolutionarily stable within both communities, even when selection on the interaction is antagonistic within one community. Moreover, the model demonstrates that the inclusion of geographic structure with gene flow may lead to considerable local maladaptation and trait mismatching as predicted by the geographic mosaic theory of coevolution.     

The effects of space and diversity of interaction types on the stability of complex ecological networks

The relationship between structure and stability in ecological networks and the effect of spatial dynamics on natural communities have both been major foci of ecological research for decades. Network research has traditionally focused on a single interaction type at a time (e.g. food webs, mutualistic networks). Networks comprising different types of interactions have recently started to be empirically characterized. Patterns observed in these networks and their implications for stability demand for further theoretical investigations. Here, we employed a spatially explicit model to disentangle the effects of mutualism/antagonism ratios in food web dynamics and stability. We found that increasing levels of plant-animal mutualistic interactions generally resulted in more stable communities. More importantly, increasing the proportion of mutualistic vs. antagonistic interactions at the base of the food web affects different aspects of ecological stability in different directions, although never negatively. Stability is either not influenced by increasing mutualism—for the cases of population stability and species’ spatial distributions—or is positively influenced by it—for spatial aggregation of species. Additionally, we observe that the relative increase of mutualistic relationships decreases the strength of biotic interactions in general within the ecological network. Our work highlights the importance of considering several dimensions of stability simultaneously to understand the dynamics of communities comprising multiple interaction types.     

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.     

The origin of a mutualism: a morphological trait promoting the evolution of ant-aphid mutualisms

Mutualisms are mutually beneficial interactions between species and are fundamentally important at all levels of biological organization. It is not clear, however, why one species participates in a particular mutualism whereas another does not. Here we show that pre-existing traits can dispose particular species to evolve a mutualistic interaction. Combining morphological, ecological, and behavioral data in a comparative analysis, we show that resource use in Chaitophorus aphids (Hemiptera: Aphididae) modulates the origin of their mutualism with ants. We demonstrate that aphid species that feed on deeper phloem elements have longer mouthparts, that this inhibits their ability to withdraw their mouthparts and escape predators and that, consequently, this increases their need for protection by mutualist ants.     

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.     

Are flowers red in teeth and claw? Exploitation barriers and the antagonist nature of mutualisms

The romantic perception of plant–animal mutualisms as a cooperative endeavour has been shattered in the last decades. While the classic theory of plant–pollinator coevolution assumed that partner coevolution is largely mutualistic, an increasing appreciation of the inherent conflict of interests between such partners has led to the realization that genes that confer a reproductive advantage to plants may have negative effects on their pollinators (and vice versa), giving rise to an apparent paradox: that antagonistic processes may drive coevolution among mutualistic partners. Under this new paradigm, mutualistic partners are bound by mutual interest but shaped by “selfish” antagonistic processes. Exploitation barriers mediated by resource competition among pollinators are a key element of this paradigm. Exploitation barriers involve traits such as tubular corollas, red flowers, toxic or deterrent rewards, and attractants of floral predators. Exploitation barriers result in resource partitioning, increasing floral fidelity of favoured pollinators and therefore plant fitness; but they often entail a physiological, behavioural or developmental cost for such favoured pollinators. Resource partitioning mediated by exploitation barriers is a very powerful driver of floral diversification, robust to variation in pollinator assemblages; hence, it may contribute to elucidating the occurrence of co-evolutionary changes in multi-species contexts. Exploitation barriers provide also a mechanistic basis for trait-based modelling of interaction networks, and represent a reason for caution in assuming fixed interaction identity or strength when modelling such networks (e.g. in rarefaction procedures used to estimate secondary extinctions). We propose to replace the misleading metaphor that depicts flowers and pollinators as cooperative partners by a metaphor in which plants and pollinator are traders, seeking to obtain different services from each other in complete disregard for the benefit of their mutualistic partner.     

Inferring coevolution in a plant–pollinator network

Mutualistic interactions are at the core of community dynamics, determining dispersal, colonization and differential survival and reproduction among individuals and species. Mutualistic interactions therefore affect the fitness of interaction partners, hence modifying their respective evolutionary trajectories reciprocally, potentially leading to coevolution. Although mathematical models predict coevolution in mutualistic interaction networks, no empirical data are available. By taking into account the patterns of interactions and reconstructing evolutionary change in plant and pollinator traits, we tested the hypothesis that coevolution occurs between plants and insects that interact more frequently, or more symmetrically. To test this hypothesis, we built an interaction network with data from five flowering seasons, measured plant and insect morphology, mapped morphology on the plant and insect phylogenies, and reconstructed ancestral character changes based on maximum parsimony. We calculated an index, called the coevolutionary ratio, which represents the amount of correlated change in traits that mediate the interaction between plants and pollinators (i.e. proboscis versus corolla length, and body width and corolla aperture). Our results suggest that high frequency of interaction, i.e. the number of times two species interact, does not lead to coevolution. Instead, symmetry of interaction strength, i.e. the reciprocal similarity in the mutual effect of interaction partners, may lead to coevolution, in spite of a pervasive lack of reciprocal specialization and high interaction frequency. Although the statistical signal is quite weak, our results hold for three statistical tests of very different nature. The most specialized species, expected to be under directional selection, do not show more evolutionary change than do generalist species, expected to be under different, perhaps opposing, selective pressures. By dissecting the complexity of an interaction network we show that coevolution may partially shape functional morphology of interaction partners, thus providing the closest evidence to date of mutualistic adaptation of organisms within a community.     

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.     

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.     

Coevolution between parasite virulence and host life-history traits

Epidemiological models generally explore the evolution of parasite life-history traits, namely, virulence and transmission, against a background of constant host life-history traits. However, life-history models have predicted the evolution of host traits in response to parasitism. The coevolution of host and parasite life-history traits remains largely unexplored. We present an epidemiological model, based on resource allocation theory, that provides an analysis of the coevolution between host reproductive effort and parasite virulence. This model allows for hosts with either a fixed (i.e., genetic) or conditional (i.e., a phenotypically plastic) response to parasitism. It also considers superinfections. We show that parasitism always favors increased allocation to host reproduction, but because of epidemiological feedbacks, the evolutionarily stable host reproductive effort does not always increase with parasite virulence. Superinfection drives the evolution of parasite virulence and acts on the evolution of the host through parasite evolution, generally leading to higher host reproductive effort. Coevolution, as opposed to cases where only one of the antagonists evolves, may generate correlations between host and parasite life-history traits across environmental gradients affecting the fecundity or the survival of the host. Our results provide a theoretical framework against which experimental coevolution outcomes or field observations can be contrasted.