Altruism and energy flow in dynamic beehive models

This work explores the relationship between altruism and the genetic system of arrhenotoky through an evolutionary game theory (EGT)-inspired lens, using a dynamic model of beehive populations consisting of three castes: workers, drones, and the queen. Arrhenotoky is a form of asexual reproduction in which unfertilized eggs become males while fertilized eggs develop into females, leading to unusual patterns of genetic relatedness between family members. This mode of reproduction occurs in insects such as the Hymenoptera, including bees. In the hive environment, bees often display altruistic behavior, or actions taken by an organism that reduce its own fitness to increase the fitness of others. Eusociality, an elaborate form of social organization characterized by complex and altruistic social behaviors, is also observed in the Hymenoptera. To explore the interplay between altruism and the reproductive patterns of arrhenotoky, we employ a population dynamics model to simulate beehive populations over a range of parameters, controlling for altruism in workers and the queen. Our results show that altruistic behaviors are essential for beehive success, with optimal worker altruism corresponding to the division of labor observed in eusocial species. Furthermore, we find that modest altruism from the queen is also vital for hive survival, emphasizing the delicate balance that can exist in these complex social systems. Overall, our findings shed light on the co-evolution of altruism, arrhenotoky, and eusociality in the natural world.