A theoretical model of flock formation to understand trade‐offs between cooperation and competition

Abstract Migratory birds often form flocks during spring migration and compete for territories once they arrive at breeding sites. Understanding the emergence and structure of these flocks has important implications for avian ecology and conservation, as flocking can influence migration success, resource distribution, and population resilience. In this study, we propose a sequential game model to examine if and when flocking behavior emerges and the types of flocks that form as a result of strategic decision‐making. Specifically, in the context of this study, we refer to migratory birds as “agents,” who make asynchronous decisions about their arrival time to breeding grounds. While earlier arrival can help individuals secure higher quality territories, traveling in a flock can improve foraging efficiency and lower flight energy consumption. Our model captures the competing dynamics between the benefits of arriving early (competition) and the benefits of flocking (cooperation). We study this model in the single‐species case and then extend it to a mixed‐species scenario. By analyzing the subgame perfect equilibrium (SPE) of these games, we find that when differences between territory quality are small relative to the benefits of flocking, agents tend to form larger flocks, favoring cooperation over competition. The opposite is also true—when the differences between territory quality are high, intense competition for high‐quality territories leads to smaller, less cohesive flocks, with stronger agents advancing their arrival time. Our model offers new theoretical insights on how flocking behaviors emerge that can help us understand the drivers of variation in migratory behavior observed in nature.