The reward system is one of the fundamental drivers of animal behaviors and is critical for survival and reproduction. Despite its importance, the problem of how the reward system has evolved is underexplored. In this paper, we try to replicate the evolution of biologically plausible reward functions and investigate how environmental conditions affect evolved rewards' shape. For this purpose, we developed a population-based decentralized evolutionary simulation framework, where agents maintain their energy level to live longer and produce more children. Each agent inherits its reward function from its parent subject to mutation and learns to get rewards via reinforcement learning throughout its lifetime. Our results show that biologically reasonable positive rewards for food acquisition and negative rewards for motor action can evolve from randomly initialized ones. However, we also find that the rewards for motor action diverge into two modes: largely positive and slightly negative. The emergence of positive motor action rewards is surprising because it can make agents too active and inefficient in foraging. In environments with poor and poisonous foods, the evolution of rewards for less important foods tends to be unstable, while rewards for normal foods are still stable. These results demonstrate the usefulness of our simulation environment and energy-dependent birth and death model for further studies of the origin of reward systems.

Animals in social foraging not only present the ordered and aggregated group movement but also the individual movement patterns of Lévy walks that are characterized as the power-law frequency distribution of flight lengths. The environment and the conspecific effects between group members are two fundamental inducements to the collective behavior. However, most previous models emphasize one of the two inducements probably because of the great difficulty to solve the behavior conflict caused by two inducements. Here, we propose an environment-driven social force model to simulate overall foraging process of an agent group. The social force concept is adopted to quantify the conspecific effects and the interactions between individuals and the environment. The cohesion-first rule is implemented to solve the conflict, which means that individuals preferentially guarantee the collective cohesion under the environmental effect. The obtained results efficiently comply with the empirical reports that mean the Lévy walk pattern of individual movement paths and the high consistency and cohesion of the entity group. By extensive simulations, we also validate the impact of two inducements for individual behaviors in comparison with several classic models