1 Introduction
The study of mutualistic relationships—interspecific interactions that benefit both species—is a rich field of theoretical and experimental study [
3,
6,
10,
11,
38,
49,
70]. Intuition arising from the short-sighted nature of selection, combined with simple game-theoretic models, calls into question the enduring nature of mutualisms: selection stands to reward species that exploit partner-provided resources, even though exploitation risks the destruction of among-partner interactions [
77]. Theoretical models—particularly those that assume extremes of actions, for example, agents that either cooperate, defect, provide or withhold resources—lead to similar conclusions [
5,
6].
However, the expectation that mutualisms are short-lived and prone to failure is out of kilter with experimental studies that draw attention to the durability of mutualisms [
16,
51,
84]. Important in recent work has been the realisation that mutualisms are sometimes stabilised by interactions with a third species [
67]. For example, the mutualism between fungus-growing ants and the fungus they cultivate is stabilised by a third species that parasitises the fungus [
55]. Similarly, the mutualistic interaction between figs and fig wasps is stabilised by a third parasitic wasp species that competes directly with pollinators [
20]. On occasion, one mutualistic partner is the environment of the other. This is particularly so in the case of interactions between animals and associated microbiomes [
47] with the recognition that microbial communities encompass a diversity of interacting types and effects [
44,
53]. These examples highlight higher-order interactions within and between species, making studying isolated interactions between species an exceptional case.
Advances in biological understanding have fuelled the development of new theoretical frameworks [
24,
62]. Of particular note have been models that change simple game theoretic dynamics by inclusion of higher-order factors such as sanctions and rewards [
4,
25,
29]. Unfortunately, these models are often specific to particular systems and lack generality when considering the varied ecologies of the different systems. General models that do exist do take into account interspecific and intraspecific interactions but so far neglected external environmental factors such as phenology [
4,
23,
25]. Desirable are general models that take into account the dynamic nature of interactions, and especially models that embrace feedback between ecological factors and ensuing evolutionary responses at both population and community levels [
2,
42,
48].
Here we examine the effect of within-species interactions on the maintenance of mutualisms. While a multispecies community factor would be a welcome addition to the analysis via evolutionary games, we focus on two species and devote our attention to realistic intricacies even in this simple system. Using a multi-player evolutionary game theoretic approach [
34,
69], we show that within-species interactions exert a powerful effect on the dynamics of between-species interactions and can prevent precariously balanced mutualisms from descending into parasitism. We then use our framework to explore two particular ecological factors in mutualistic scenarios—seasonality of interactions and density-dependence.
Typically, the ever-changing nature of environments constantly challenges the stability of mutualistic relationships. While mutualisms elevate the collective productivity of the involved partners, they are not without risks, as their destinies become intricately intertwined [
51]. The dynamics of these interactions remain highly responsive to environmental and ecological shifts, whether stemming from natural processes or human-induced activities [
1,
13,
32,
46]. In the case of seasonal or episodic mutualisms, there is a significant potential for phenological partner mismatch due to various environmental factors [
72]. Specifically focusing on the domain of mutualism-pollination and the associated phenological mismatch, recent investigations have explored social dilemmas and the impact of seasonal fluctuations of the game parameters within isolated populations [
33].
Population sizes are inherently dynamic and subject to fluctuations over time. In scenarios where ecological changes occur rapidly enough to be averaged, their influence on evolutionary dynamics is often disregarded. However, the occurrence of evolution unfolding at remarkably rapid timescales, comparable to those of ecological dynamics, is well documented [
8,
37,
71,
79]. Consequently, it becomes imperative to embrace eco-evolutionary dynamics, intertwining ecological and evolutionary processes also for mutualisms [
17,
59].
Considering the above two ecological factors, we show that mutualisms can be robust to the destabilising effects of seasonality and density-dependence. Our findings indicate that mutualisms, while often prone to failure at the level of individual interactors, can remain stable due to dynamic feedback between ecological and evolutionary dynamics.
3 Discussion
The traditional view of mutualism is one in which there exists a harmonious relationship between species, each providing benefits to the other. However, classical theory on the evolution of cooperation demonstrates that such relationships are prone to exploitation. Such a situation can lead to ecological arms races, in which species play exploiter and exploited. While such reciprocal antagonistic interactions may persist in the short term, failure in the long term results in the loss of one or both species. Despite this fact, mutualisms appear to be remarkably common in nature. One possibility is that many putative mutualisms have been wrongly identified [
28]; the other is that mutualisms are indeed common, but our understanding of the ecological and evolutionary factors shaping them is incomplete. A further possibility lies somewhere in between: mutualisms are common and persist over evolutionary time but are prone to failure over ecological time scales at any given locale.
Our investigation aligns with the latter possibilities and an expanding body of research that underscores the delicate equilibrium characterizing mutualistic relationships, where the balance between success and failure teeters precariously. It has become increasingly evident that secondary and even tertiary level interactions play a pivotal role in the long-term persistence of such associations [
2,
37,
71,
79]. Our study and previous investigations highlight the limitations of models that depict mutualisms with linear species interactions. Understanding the mechanisms driving their maintenance becomes significantly challenging within such reductionist frameworks [
19,
29]. However, models that incorporate even a modest degree of ecological and evolutionary realism, particularly nonlinear interactions within and between species, offer a more comprehensive perspective and demonstrate the potential for the persistence of mutualistic associations [
2,
22]. As previously indicated in [
50] and [
77], it is reasonable to surmise that such intricate interactions extend to numerous other instances, further emphasizing their widespread prevalence and significance.
Incorporating intra- and inter-species interactions represents a significant stride in comprehending the intricate dynamics of eco-evolutionary processes. Nevertheless, it is essential to acknowledge that these factors alone might fall short of fully capturing the immense complexity inherent in such phenomena. The role of intraspecific interactions was already highlighted in [
68]. Interspecific competition between two species of carrion flies could be alleviated by intraspecific aggression brought about by aggregation [
45]. In contrast to competition, herein we focus of mutualistic interaction structures while making a similar argument about connecting intra and interspecific dynamics. We delve deeper into mutualistic associations and recognize the profound influence exerted by ecological fluctuations, capable of fundamentally reshaping the nature of species interactions [
41]. To illustrate this point, we focus on an exemplary case study involving the hawk moth species
Manduca sexta and the agave plant species
Agave palmeri. Empirical investigations have illuminated the detailed intricacies of their mutualistic relationship, revealing the necessity of coordinated spatial and temporal behaviours. Intriguingly, these interactions exhibit density-dependent effects, hinting at underlying eco-evolutionary feedback mechanisms. Remarkably, the triadic involvement of a third species,
Datura wrightii, further amplifies the complexity of this ecological interplay [
73], a fact that we do not consider in our current model. Nevertheless, temporal coordination emerges as a critical factor, particularly in the context of pollination-related mutualisms [
72]. Our findings, visually depicted in Fig.
3, underscore the paramount importance of seasonality in shaping the dynamics of these intricate interactions. However, it is imperative to recognize that the sensitivity of mutualistic associations to environmental conditions extends far beyond what might seem a mere exaggeration. As the weather systems of the globe shift due to anthropogenic activities, the phenological mismatch in pollination mutualisms are not the only ones reaching criticality. The ongoing climate change phenomenon has triggered a fundamental transformation in the coral-dinoflagellate symbiosis, steering it towards a precarious path of parasitism [
7]. The repercussions of such mutualism breakdown are far-reaching and can potentially lead to catastrophic ecological meltdowns [
18,
60,
92].
Similarly, the mutualism between
Vibrio fischeri and the bobtailed squid appears to depend on a wide range of host and symbiont factors, although their specific contributions to the persistence of the mutualism are unclear. The squid provides a protected niche for
V. fischeri, which in return provides light that the squid uses as a form of counter-illumination. A well studied ‘winnowing’ mechanism has been attributed [
65,
82] to the separation of
Vibrio from the rest of the microbiome and specially grown to high densities. Nevertheless, a closer analysis quickly leads to questions about how the interaction between the two species can be maintained in such a seemingly benign state. After all,
V. fischeri colonises squid mucosal surfaces, which can be readily exploited even if the initial coloniser is a mutualist due to the rapid growth within the light organ. In addition, infections are typically established by a mixture of genotypes and the bacterium is horizontally transmitted [
76]. These factors alone should drive
V. fischeri to become virulent unless some checks are established [
29,
52,
54]. Just how the squid avoids outright exploitation by the bacterium is not known, but the daily expulsion of bacteria by the squid results in diel changes in bacterial population density that may have more to do with limiting opportunity for within-host evolution than allowing the bacterial population to reach some optimal light-emitting status. What of population ecology? It is hard to imagine that
V. fischeri mutants that take unfairly of host resources do not arise. Perhaps an opportunity for these types to persist is limited because of host density and limited opportunity for transmission. Thus inclusion of density-dependent dynamics are crucial when exploring the interactions between species Fig.
5.
As is evident throughout, our approach is implicitly multilevel. This allows community dynamics to be understood as a set of interactions between levels of selection [
58,
87], and for within-species interactions to be understood in light of between-species interactions and vice versa. Such an approach shines light on a higher dimensional ecological space that is often overlooked: it facilitates predictions as to the range of parameters over which mutualisms can be maintained and allows exploration of the effects of community structure on the emergence of mutualisms in the absence of “game-changing" factors. This does not mean that game-changers, such as host sanctioning, are not important, but it shows that mutualisms can sometimes be understood simply in terms of community dynamics. From such an ecology-first perspective it becomes possible to understand how selective processes consequently shape the evolution of host sanctioning and various “lock and key" mechanisms that likely contribute to the long term persistence and refinement of mutualisms [
88].
Finally, although we have included complex intra- and interspecies interactions along with density-dependence and phenology, the implementation outlined here has made several simplifying assumptions. For example, interaction terms used to define each player’s fitness are identical, and the threshold at which benefits are generated to each species are also identical, as are the number of players of each species. For simplicity, we have kept within-species strategies the same as that of between species. If there is no linkage between the traits of individuals when acting between or within species, then several interactions are possible. In a separate study, we have relaxed this assumption [
91]. Assuming no linkage between strategies, we would have a two-population model with multiple strategies playing multiple games. Our previous work has shown that as long as the number of strategies is not more than two, the complex dynamics of multiple multiplayer games can be captured by a linear combination of the games. However, for multistrategy games, a dynamical inconsistency emerges [
14,
15]. Thus the dynamics of the system can no longer be captured by a simple combination of the constituent interactions and demonstrates emergent phenomena.
We have explored all combinations of simple games in Appendix
B and Fig.
6. With the theory developed, more complex scenarios can be readily analysed, including those involving addition of parameters to accommodate policing or sanctioning [
16], and extension to finite populations [
90]. Our framework is extensible to include a multi-species community context as discussed in the Introduction. That it is not necessary to invoke such complexity to explain the maintenance of mutualisms is an affirmation of the generality of our framework, but it also emphasises the role of the feedback between external ecological factors and evolutionary change. Since introduction of game theory in biology by [
57], the primary focus of evolutionary game theory has been on antagonistic interactions and the resolution of conflicting interests to explain observations such as cooperation and mutualism. Numerous solutions have been proposed over the decades. Still, the explicit inclusion of ecological processes is emerging to be a necessity when aiming to provide a broader context [
58,
86,
90]. Combining the dynamical nature of ecological processes with evolutionary games is thus the logical next step.
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