Spatial social dilemmas promote diversity

Cooperative investments in social dilemmas can spontaneously diversify into stably coexisting high and low contributors in well-mixed populations. Here we extend the analysis to emerging diversity in (spatially) structured populations. Using pair approximation, we derive analytical expressions for the invasion fitness of rare mutants in structured populations, which then yields a spatial adaptive dynamics framework. This allows us to predict changes arising from population structures in terms of existence and location of singular strategies, as well as their convergence and evolutionary stability as compared to well-mixed populations. Based on spatial adaptive dynamics and extensive individual-based simulations, we find that spatial structure has significant and varied impacts on evolutionary diversification in continuous social dilemmas. More specifically, spatial adaptive dynamics suggests that spontaneous diversification through evolutionary branching is suppressed, but simulations show that spatial dimensions offer new modes of diversification that are driven by an interplay of finite-size mutations and population structures. Even though spatial adaptive dynamics is unable to capture these new modes, they can still be understood based on an invasion analysis. In particular, population structures alter invasion fitness and can open up new regions in trait space where mutants can invade, but that may not be accessible to small mutational steps. Instead, stochastically appearing larger mutations or sequences of smaller mutations in a particular direction are required to bridge regions of unfavorable traits. The net effect is that spatial structure tends to promote diversification, especially when selection is strong.

Universality of evolutionary dynamics with arbitrary demography

The assumption of constant population size is central in population genetics. It led to a large body of results, which have proven successful to understand evolutionary dynamics. Part of this success is due to their robustness to modeling choices. On the other hand, allele frequencies and population size are both determined by the interaction between a population and the environment. Including explicitly the demographic factors and life-history traits that determine the eco-evolutionary dynamics makes the analysis difficult and the results dependent on model details. Here, we develop a framework that encompasses a great variety of systems with arbitrary population dynamics and competition between species. By using techniques based on scale separation for stochastic processes, we are able to compute evolutionary properties, such as the invasion probability. Remarkably, these properties assume a universal form with respect to our framework, which depends on only three life-history traits related to the exponential fitness, the invasion fitness, and the carrying capacity of the alleles. In other words, different systems, such as Lotka-Volterra or a chemostat model, share the same evolutionary outcomes after the correct remapping of the parameters of the models into three effective life-history traits. An important and surprising consequence of our results is that the direction of selection can be inverted, with a population evolving to reach lower values of fitness. This can happen because the obtained frequency-dependent noise (affected by the three life-history traits) can generate an effective force that counterbalance classical selection.

Origin of diversity in spatial social dilemmas

Cooperative investments in social dilemmas can spontaneously diversify into stably co-existing high and low contributors in well-mixed populations. Here we extend the analysis to emerging diversity in (spatially) structured populations. Using pair approximation we derive analytical expressions for the invasion fitness of rare mutants in structured populations, which then yields a spatial adaptive dynamics framework. This allows us to predict changes arising from population structures in terms of existence and location of singular strategies, as well as their convergence and evolutionary stability as compared to well-mixed populations. Based on spatial adaptive dynamics and extensive individual based simulations, we find that spatial structure has significant and varied impacts on evolutionary diversification in continuous social dilemmas. More specifically, spatial adaptive dynamics suggests that spontaneous diversification through evolutionary branching is suppressed, but simulations show that spatial dimensions offer new modes of diversification that are driven by an interplay of finite-size mutations and population structures. Even though spatial adaptive dynamics is unable to capture these new modes, they can still be under-stood based on an invasion analysis. In particular, population structures alter invasion fitness and can open up new regions in trait space where mutants can invade, but that may not be accessible to small mutational steps. Instead, stochastically appearing larger mutations or sequences of smaller mutations in a particular direction are required to bridge regions of unfavourable traits. The net effect is that spatial structure tends to promote diversification, especially when selection is strong.

Trait positions for elevated invasiveness in adaptive ecological networks

Our ability to predict the outcome of invasion declines rapidly as non-native species progress through intertwined ecological barriers to establish and spread in recipient ecosystems. This is largely due to the lack of systemic knowledge on key processes at play as species establish self-sustaining populations within the invaded range. To address this knowledge gap, we present a mathematical model that captures the eco-evolutionary dynamics of native and non-native species interacting within an ecological network. The model is derived from continuous-trait evolutionary game theory (i.e., Adaptive Dynamics) and its associated concept of invasion fitness which depicts dynamic demographic performance that is both trait mediated and density dependent. Our approach allows us to explore how multiple resident and non-native species coevolve to reshape invasion performance, or more precisely invasiveness, over trait space. The model clarifies the role of specific traits in enabling non-native species to occupy realised opportunistic niches. It also elucidates the direction and speed of both ecological and evolutionary dynamics of residing species (natives or non-natives) in the recipient network under different levels of propagule pressure. The versatility of the model is demonstrated using four examples that correspond to the invasion of (i) a horizontal competitive community; (ii) a bipartite mutualistic network; (iii) a bipartite antagonistic network; and (iv) a multi-trophic food web. We identified a cohesive trait strategy that enables the success and establishment of non-native species to possess high invasiveness. Specifically, we find that a non-native species can achieve high levels of invasiveness by possessing traits that overlap with those of its facilitators (and mutualists), which enhances the benefits accrued from positive interactions, and by possessing traits outside the range of those of antagonists, which mitigates the costs accrued from negative interactions. This ‘central-to-reap, edge-to-elude’ trait strategy therefore describes the strategic trait positions of non-native species to invade an ecological network. This model provides a theoretical platform for exploring invasion strategies in complex adaptive ecological networks.

Structured Populations and Games over Generations

The actions and state of an individual in one generation can affect the state of offspring in the next generation, and hence the ability of these offspring to leave offspring themselves. This chapter deals with games in this multigenerational setting. Projection matrices are used to keep track of the state and number of descendants in successive years and generations. Invasion fitness is then defined in terms of the leading eigenvalue of the projection matrix. Simple examples illustrate these concepts and show how to apply them. Reproductive value is a function that measures how the ability to leave descendants in future generations depends on the current state. The Nash equilibrium condition is reformulated in terms of reproductive value maximization. This new criterion is used to justify the fitness proxy used in the analysis of sex allocation earlier in the book. The analysis is extended to the case where offspring may inherit aspects of their mother’s quality, with a focus on the question of whether high-quality mothers should produce sons or daughters. As a second application of reproductive value maximization, the co-evolution of female preference for a particular male trait and the trait itself is analysed, with the evolution of tail length in the widowbird as an illustrative application. Mean lifetime reproductive success is used as a fitness proxy in much of the book. Its use is finally justified in this chapter, where the fitness proxy is used to analyse the evolutionarily stable age of first reproduction in a population.

Central Concepts

The chapter defines and discusses some of the central concepts in biological game theory. Strategies, which are rules for choosing actions as a function of state, play a pivotal role. It is explained how the theory operates at the level of strategies rather than attempting to follow the details of the underlying genetics that code for them. This is referred to as 'the phenotypic gambit', which is discussed and illustrated. The concept of the invasion fitness of a mutant strategy in a population that adopts another resident strategy is also central. This performance measure is used to give a necessary condition for evolutionary stability, formulated as the Nash equilibrium condition. It is explained how this stability condition can be reformulated in terms of simpler fitness proxies such as the mean lifetime number of offspring or the net rate of energy gain.

Effects of evolution on niche displacement and emergent population properties, a discussion on optimality

Understanding the effects of evolution on emergent population properties such as intrinsic growth rate, species abundance, or dynamical resilience is not only a key theoretical question, but has major empirical implications for conservation, agroecology, invasion ecology among others. In particular, could we classify evolutionary scenarios leading to optimisation of those properties, from the ones who do not. First, we uncover two classes of invasion fitness functions, only the first one allowing optimization of some (but typically not all) population properties. Second, we showed that our two classes are also strongly linked to niche displacement and emergence of polymorphism. Our results indicate that optimization is, in general, incompatible with niche differentiation and, therefore, with emergence of polymorphism through evolutionary branching. Actually, niche displacement between resident and mutant morphs, and potentially polymorphism, only arise when we do not expect optimality to hold. We extensively discuss which biological traits can fall into which class of invasion fitness. Although, it is possible to find traits for which optimality is expected, we argue that for the majority of the cases it does not hold. Finally, we provide practical applications of our results in conservation, agroecology, harvesting and invasion ecology.

Adaptation of Biotrophic Leaf Pathogens to Fertilization-Mediated Changes in Plant Traits: A Comparison of the Optimization Principle to Invasion Fitness

One of the conclusions of evolutionary ecology applied to agroecosystem management is that sustainable disease management strategies must be adaptive to overcome the immense adaptive potential of crop pathogens. In this context, knowledge of how pathogens adapt to changes in cultural practices is necessary. In this article we address the issue of the evolutionary response of biotrophic crop pathogens to changes in fertilization practices. For this purpose, we compare predictions of latent period evolution based on three empirical fitness measures (seasonal spore production, within-season exponential growth rate, and area under disease progress curves [AUDPCs]) with predictions based on the concept of invasion fitness from adaptive dynamics. We use pairwise invisibility plots to identify the evolutionarily stable strategies (ESSs) of the pathogen latent period. We find that the ESS latent period is in between the latent periods that maximize the seasonal spore production and the within-season exponential growth rate of the pathogen. The latent periods that maximize the AUDPC are similar to those of the ESS latent periods. The AUDPC may therefore be a critical variable to determine the issue of between-strain competition and shape pathogen evolution.

Evolution of Specialization in Dynamic Fluids

Previously we found mechanical factors involving diffusion and fluid shear promote evolution of social behavior in microbial populations Uppal and Vural (2018). Here, we extend this model to study the evolution of specialization using realistic physical simulations of bacteria that secrete two public goods in a dynamic fluid. Through this first principles approach, we find physical factors such as diffusion, flow patterns, and decay rates are as influential as fitness economics in governing the evolution of community structure, to the extent that when mechanical factors are taken into account, (1) Generalist communities can resist becoming specialists, despite the invasion fitness of specialization (2) Generalist and specialists can both resist cheaters despite the invasion fitness of free-riding. (3) Multiple community structures can coexist despite the opposing force of competitive exclusion. Our results emphasize the role of spatial assortment and physical forces on niche partitioning and the evolution of diverse community structures.

Fitness and community feedbacks: the two axes that drive long-term invasion impacts

Many facets of ecological theory rely on the analysis of invasion processes, and general approaches exist to understand the early stages of an invasion. However, predicting the long-term transformations of communities following an invasion remains a challenging endeavour. We propose an analytical method that uses community structure and invader dynamical features to predict when these impacts can be large, and show it to be applicable across a wide class of dynamical models. Our approach reveals that short-term invasion success and long-term consequences are two distinct axes of variation controlled by different properties of both invader and resident community. Whether a species can invade is controlled by its invasion fitness, which depends on environmental conditions and direct interactions with resident species. But whether this invasion will cause significant transformations, such as extinctions or a regime shift, depends on a specific measure of indirect feedbacks that may involve the entire resident community. Our approach applies to arbitrarily complex communities, from few competing phenotypes in adaptive dynamics to large nonlinear food webs. It hints at new questions to ask as part of any invasion analysis, and suggests that long-term indirect interactions are key determinants of invasion outcomes.