Coevolution of cooperation and language

As a cooperative act decreases an individual's fitness for others to benefit, it is expected to be selected against by natural selection. That, how contrary to this naive expectation cooperation has evolved, is a fundamental problem in evolutionary biology and social sciences. Here, by introducing a mathematical model, we show that coevolution of cooperation and language can provide an avenue through which both cooperation and language evolve. In this model, individuals in a population play a prisoner's dilemma game and at the same time try to communicate a set of representations by producing signals. For this purpose, individuals try to build a common language, which is composed of a set of signal-representation associations. Individuals decide in language learning based on their payoff from the prisoner's dilemma game and decide about their strategy in the prisoner's dilemma game based on their success in conveying symbolic information. The model shows cooperators are able to build a common language and protect it against defectors' attempt to decode it. The language channels the benefit of cooperation toward cooperators, and defectors, being banished from the language, are unable to exploit cooperators, and are doomed to extinction.

Figure 1

Time dependence of the model. (a), (b) The population fraction of conditional cooperators $m$ (blue solid line), and the population consistency of the language $PC$ (red dashed line), a measure of how well individuals understand each other. In panel (a) a well-mixed population is considered and in panel (b) the population resides on a first-nearest-neighbor square lattice with periodic boundaries. Cooperation, and a common language evolve in a correlated fashion indicated by bursts where both take a high value, and periods when both drop. (c), (d) Color plot of the time-dependent population consistency, a measure of how well individuals at different generations understand each other, in a well-mixed population (c) and for a population on a lattice (d). While in a well-mixed population, population consistency of language remains small, for a structured population, language reaches a high level of population consistency and historical similarity.

Figure 2

Dependence on the model parameters. The time average cooperation level, ${\langle m\rangle }_t$ (blue), and the population consistency of the language (red), ${\langle PC\rangle }_t$, as a function of model parameters, for two different population structures. Cooperation evolves in a broad range of parameter values. The level of cooperation (blue solid line) and population consistency of language (red dashed line), are much higher for a structured population (squares) compared to a well-mixed population (circles). $l_t$ is the number of correct communications necessary for a conditional cooperator to cooperate, $l$ is the number of communications before a game, $\eta$ the amount of noise in parental learning, and $N$ the population size. The network used here is a first-nearest-neighbor lattice with periodic boundaries. The simulations are performed for ${10}^5$ time steps and time averages and standard deviations (error bars) are calculated after discarding the first ${10}^4$ time steps.

Figure 3

Dependence on the model parameters. The time average cooperation level, ${\langle m\rangle }_t$ (blue), and the population consistency of the language (red), ${\langle PC\rangle }_t$, as a function of the model parameters, for two different population structures. Cooperation evolves in a broad range of parameter values. The level of cooperation (blue solid line) and population consistency of language (red dashed line), are much higher for a structured population (squares) compared to a well mixed population (circles). $\nu$ is the mutation rate in strategies, $n$ is the number of representations (equal to the number of signals), $d$ is the learning rate, $T$ the temptation, and $P$ the punishment. The network used here is a first-nearest-neighbor square lattice with periodic boundaries. The simulations are performed for ${10}^5$ time steps and time averages and standard deviations (error bars) are calculated after discarding the first ${10}^4$ time steps.

Figure 4

Existence of an optimal population size for the evolution of cooperation in a mixed population. The average cooperation level is maximized in an intermediate population size for different parameter values. Here, the base parameter values are used. In each panel, one of the parameters is changed as specified in the figure and the time average cooperation level is plotted as a function of population size. In panels (a)–(c), the simulations is run for $T=4*{10}^5$ time steps, and in panels (d)–(h) it is run for ${10}^6$ time steps. In all the cases, the average is taken after discarding the first ${10}^4$ time steps. Error bars show standard deviation calculated based on the same sample.

Figure 5

Dependence on model parameters in the model with birth-death update rule. The time average cooperation level, ${\langle m\rangle }_t$ (blue), and the population consistency of the language (red), ${\langle PC\rangle }_t$, as a function of model parameters, for a structured population. Cooperation and a common language evolve and are maintained in a broad range of parameter values. $l_t$ is the number of correct communications necessary for a conditional cooperator to cooperate, $l$ is the number of coordination before a prisoner's dilemma game, $\eta$ is the amount of noise in parental learning, $N$ is the population size, $\nu$ is the mutation rate in the strategies, $n$ is the number of representations (equal to the number of signals), $d$ is the learning rate, $T$ the temptation, and $P$ the punishment. The simulations are performed for ${10}^5$ time steps and time averages and standard deviations (error bars) are calculated after discarding the first ${10}^4$ time steps.

Figure 6

Time dependence of the model for a population of unconditional cooperators on a first-nearest-neighbor square lattice. (a) The population fraction of cooperators $m$ (blue solid line) and the population consistency of the language $PC$ (red dashed line). Cooperation, and a common language evolve in a correlated fashion indicated by bursts where both take a high value, and periods when both drop. (b) Color plot of the time depended population consistency, a measure of how well individuals at different generations understand each other. Cooperators are under constant pressure to change their language to keep it incomprehensible for the defectors. Languages evolved in different times show historical similarity. Which means the same language is preserved by small modifications to purge the defectors away.

Figure 7

Dependence on the model parameters in the model with unconditional cooperators on a first-nearest-neighbor square lattice. The time average cooperation level, ${\langle m\rangle }_t$ (blue), and the population consistency of the language (red), ${\langle PC\rangle }_t$, as a function of model parameters. Cooperation and a common language evolve and are maintained in a broad range of parameter values. $l_t$ is the number of correct communications necessary for a cooperator to play the game, $l$ is the number of coordination before a prisoner's dilemma game, $\eta$ is the amount of noise in parental learning. $N$ is the population size. $\nu$ is the mutation rate for the strategies, $n$ number of representations (equal to the number of signals), $d$ is the learning rate, $T$ the temptation, and $P$ the punishment. The simulations are performed for ${10}^5$ time steps and time averages and standard deviations (error bars) are calculated after discarding the first ${10}^4$ time steps.