Evolutionary dynamics of collective action in spatially structured populations

Abstract

Many models proposed to study the evolution of collective action rely on a formalism that represents social interactions as n-player games between individuals adopting discrete actions such as cooperate and defect. Despite the importance of spatial structure in biological collective action, the analysis of n-player games games in spatially structured populations has so far proved elusive.We address this problem by considering mixed strategies and by integrating discrete-action n-player games into the direct fitness approach of social evolution theory. This allows to conveniently identify convergence stable strategies and to capture the effect of population structure by a single structure coefficient, namely, the pairwise (scaled) relatedness among interacting individuals. As an application, we use our mathematical framework to investigate collective action problems associated with the provision of three different kinds of collective goods, paradigmatic of a vast array of helping traits in nature: "public goods" (both providers and shirkers can use the good, e.g., alarm calls), "club goods" (only providers can use the good, e.g., participation in collective hunting), and "charity goods" (only shirkers can use the good, e.g., altruistic sacrifice). We show that relatedness promotes the evolution of collective action in different ways depending on the kind of collective good and its economies of scale. Our findings highlight the importance of explicitly accounting for relatedness, the kind of collective good, and the economies of scale in theoretical and empirical studies of the evolution of collective action.

Evolutionary multiplayer games on graphs with edge diversity

“…Our framework are also able to address the more realistic situation where individuals concurrently face diverse social dilemmas. This is in stark contrast with the ideal assumption in most previous studies where all interactions are described by a unified game metaphor [19][20][21][22][30][31][32]. In the real word, an individual may be caught in a volunteer's dilemma with its colleagues and meanwhile engage in public goods games with its neighbors.…”

Evolutionary multiplayer games on graphs with edge diversity

“…Our framework are also able to address the more realistic situation where individuals concurrently face diverse social dilemmas. This is in stark contrast with the ideal assumption in most previous studies where all interactions are described by a unified game metaphor [19][20][21][22][30][31][32]. In the real word, an individual may be caught in a volunteer's dilemma with its colleagues and meanwhile engage in public goods games with its neighbors.…”

Cooperative dilemmas with binary actions and multiple players

“…These properties have proved useful in applications ranging from approximation theory (DeVore and Lorentz, 1993) to computer-aided geometric design (Farouki, 2012). More recently, they have also been applied to game theory (Sah, 1991;Motro, 1991;Carlsson and van Damme, 1993;Menezes and Pitchford, 2006;Peña et al, 2014Peña et al, , 2015Nöldeke and Peña, 2016;De Jaegher, 2019). For instance, they can be used to analyze group-size and group-size variability effects in many of the cooperative dilemmas we used to illustrate our results, and in other binary-action multi-player games (Peña and Nöldeke, 2016;Peña and Nöldeke, 2018).…”

The evolution of environmentally mediated social interactions and posthumous spite under isolation by distance

“…With this in mind, the coefficient κ k , t ( Eq 19 ) can be thought of as a measure of relatedness scaled to competition (or scaled relatedness for short, e.g. [ 7 , 52 , 53 ]; with Eq 19 extending to isolation by distance the formalization of this concept found in [ 54 ]). To see this, suppose that the evolving trait helps current patch neighbours (i.e.…”

Evolutionary multiplayer games on graphs with edge diversity

“…Our framework are also able to address the more realistic situation where individuals concurrently face diverse social dilemmas. This is in stark contrast with the ideal assumption in most previous studies where all interactions are described by a unified game metaphor [19][20][21][22][30][31][32]. In the real word, an individual may be caught in a volunteer's dilemma with its colleagues and meanwhile engage in public goods games with its neighbors.…”

Cooperative dilemmas with binary actions and multiple players

“…These properties have proved useful in applications ranging from approximation theory (DeVore and Lorentz, 1993) to computer-aided geometric design (Farouki, 2012). More recently, they have also been applied to game theory (Sah, 1991;Motro, 1991;Carlsson and van Damme, 1993;Menezes and Pitchford, 2006;Peña et al, 2014Peña et al, , 2015Nöldeke and Peña, 2016;De Jaegher, 2019). For instance, they can be used to analyze group-size and group-size variability effects in many of the cooperative dilemmas we used to illustrate our results, and in other binary-action multi-player games (Peña and Nöldeke, 2016;Peña and Nöldeke, 2018).…”

The evolution of environmentally mediated social interactions and posthumous spite under isolation by distance

“…With this in mind, the coefficient κ k , t ( Eq 19 ) can be thought of as a measure of relatedness scaled to competition (or scaled relatedness for short, e.g. [ 7 , 52 , 53 ]; with Eq 19 extending to isolation by distance the formalization of this concept found in [ 54 ]). To see this, suppose that the evolving trait helps current patch neighbours (i.e.…”

Evolutionary multiplayer games on graphs with edge diversity

“…Our framework are also able to address the more realistic situation where individuals concurrently face diverse social dilemmas. This is in stark contrast with the ideal assumption in most previous studies where all interactions are described by a unified game metaphor [19][20][21][22][30][31][32]. In the real word, an individual may be caught in a volunteer's dilemma with its colleagues and meanwhile engage in public goods games with its neighbors.…”

Cooperative dilemmas with binary actions and multiple players

“…These properties have proved useful in applications ranging from approximation theory (DeVore and Lorentz, 1993) to computer-aided geometric design (Farouki, 2012). More recently, they have also been applied to game theory (Sah, 1991;Motro, 1991;Carlsson and van Damme, 1993;Menezes and Pitchford, 2006;Peña et al, 2014Peña et al, , 2015Nöldeke and Peña, 2016;De Jaegher, 2019). For instance, they can be used to analyze group-size and group-size variability effects in many of the cooperative dilemmas we used to illustrate our results, and in other binary-action multi-player games (Peña and Nöldeke, 2016;Peña and Nöldeke, 2018).…”

The evolution of environmentally mediated social interactions and posthumous spite under isolation by distance

“…With this in mind, the coefficient κ k , t ( Eq 19 ) can be thought of as a measure of relatedness scaled to competition (or scaled relatedness for short, e.g. [ 7 , 52 , 53 ]; with Eq 19 extending to isolation by distance the formalization of this concept found in [ 54 ]). To see this, suppose that the evolving trait helps current patch neighbours (i.e.…”