EvoGamesPlus - Evolutionary Game Theory and Population Dynamics: From Theory to Applications

Evolutionary game theory has proved to be a powerful tool to probe the self-organization of collective behaviour by considering frequency-dependent fitness in evolutionary processes. It has shown that the stability of a strategy depends not only on the payoffs received after each encounter but also on the population’s size. Here, we study 2 × 2 games in well-mixed finite populations by analyzing the fixation probabilities of single mutants as functions of population size. We proved that nine of the 24 possible games always lead to monotonically decreasing functions, similarly to fixed fitness scenarios. However, fixation functions showed increasing regions under 12 distinct anti-coordination, coordination and dominance games. Perhaps counter-intuitively, this establishes that single-mutant strategies often benefit from being in larger populations. Fixation functions that increase from a global minimum to a positive asymptotic value are pervasive but may have been easily concealed by the weak selection limit. We obtained sufficient conditions to observe fixation increasing for small populations and three distinct ways this can occur. Finally, we describe fixation functions with the increasing regions bounded by two extremes under intermediate population sizes. We associate their occurrence with transitions from having one global extreme to other shapes.

The origin of eukaryotes and organellogenesis have been recognized as a major evolutionary transition and subject to in-depth studies. Acknowledging the fact that the initial interactions and conditions of cooperative behaviour between free-living single-celled organisms are widely debated, we narrow our scope to a single mechanism that could possibly have set-off multi-species associations. We hypothesize that the very first step in the evolution of such cooperative behaviour could be a single mutation in an ancestral symbiont genome that results in the formation of an ecto-commensalism with its obligate ancestral host. We investigate the ecological and evolutionary stability of inter-species microbial interactions with vertical transmissions as an association based on syntrophy (cross-feeding). To the best of our knowledge, this is the first time that a commensalistic model based on the syntrophy hypothesis is considered in the framework of coevolutionary dynamics and invadability by mutant phenotype into a monomorphic resident system.

The coevolution of hosts and symbionts based on virulence and mode of transmission is a complex and diverse biological phenomenon. We introduce a conceptual model to study the stable coexistence of an obligate symbiont (mutualist or parasite) with mixed-mode transmission and its host. The existence of evolutionarily and ecologically stable coexistence is analyzed in the framework of coevolutionary dynamics. Using an age-structured Leslie model for the host, we demonstrate how the obligate symbiont can modify the host's life history parameters (survival and fecundity) and the long-term growth rate of the infected lineage. The evolutionary success of the symbionts is given by the long-term growth rate of the infected population (multi-level selection). When the symbiont is vertically transmitted, we find that the host and its symbiont can maximize the long-term growth rate of the infected lineage. Moreover, we provide conditions for the ecological and evolutionary stability of the resident host-symbiont pair in the coevolutionary model, which does not allow invasion by any rare mutants (each mutant dies out by ecological selection). We observed that ecological competition, clearing of infection, and density-dependent interactions could play a role in determining the criteria for evolutionary stability.

Here we analyze Darwinian dynamics of cancer introduced in [1], extended by including a competition matrix, and evaluate (i) when the eco-evolutionary equilibrium is positive and (ii) when the eco-evolutionary equilibrium is asymptotically stable.

Rapid evolution is ubiquitous in nature. We briefly review some of this quite broadly, particularly in the context of response to anthropogenic disturbances. Nowhere is this more evident, replicated and accessible to study than in cancer. Curiously cancer has been late - relative to fisheries, antibiotic resistance, pest management and evolution in human dominated landscapes - in recognizing the need for evolutionarily informed management strategies. The speed of evolution matters. Here, we employ game-theoretic modeling to compare time to progression with continuous maximum tolerable dose to that of adaptive therapy where treatment is discontinued when the population of cancer cells gets below half of its initial size and re-administered when the cancer cells recover, forming cycles with and without treatment. We show that the success of adaptive therapy relative to continuous maximum tolerable dose therapy is much higher if the population of cancer cells is defined by two cell types (sensitive vs. resistant in a polymorphic population). Additionally, the relative increase in time to progression increases with the speed of evolution. These results hold with and without a cost of resistance in cancer cells. On the other hand, treatment-induced resistance can be modeled as a quantitative trait in a monomorphic population of cancer cells. In that case, when evolution is rapid, there is no advantage to adaptive therapy. Initial responses to therapy are blunted by the cancer cells evolving too quickly. Our study emphasizes how cancer provides a unique system for studying rapid evolutionary changes within tumor ecosystems in response to human interventions; and allows us to contrast and compare this system to other human managed or dominated systems in nature.

Evolutionary game theory mathematically conceptualizes and analyzes biological interactions where one’s fitness not only depends on one’s own traits, but also on the traits of others. Typically, the individuals are not overtly rational and do not select, but rather inherit their traits. Cancer can be framed as such an evolutionary game, as it is composed of cells of heterogeneous types undergoing frequency-dependent selection. In this article, we first summarize existing works where evolutionary game theory has been employed in modeling cancer and improving its treatment. Some of these game-theoretic models suggest how one could anticipate and steer cancer’s eco-evolutionary dynamics into states more desirable for the patient via evolutionary therapies. Such therapies offer great promise for increasing patient survival and decreasing drug toxicity, as demonstrated by some recent studies and clinical trials. We discuss clinical relevance of the existing game-theoretic models of cancer and its treatment, and opportunities for future applications. Moreover, we discuss the developments in cancer biology that are needed to better utilize the full potential of game-theoretic models. Ultimately, we demonstrate that viewing tumors with evolutionary game theory has medically useful implications that can inform and create a lockstep between empirical findings and mathematical modeling. We suggest that cancer progression is an evolutionary competition between different cell types and therefore needs to be viewed as an evolutionary game.