Is the Primary Helper Always a Key Group for the Sustainability of Cooperative Birds? A Mathematical Study on Cooperative Breeding Blue-Tailed Bee-Eater.

Abstract

Cooperation is a fundamental requirement for the sustainability of group-living organisms. Despite the substantial research work in cooperative breeding birds, the dependence of the populations' sustainability young or adult helpers in migratory populations is unidentified. The mathematical models for predicting the birds' cooperative dynamics so far mostly ignore the migratory property. The cooperative breeding birds have three groups in their population, viz, immature or primary helpers, mature or secondary helpers, and breeders. We ask three questions to study migratory cooperative birds' sustainability through mathematical modeling under changing environments. Which group is the key to the sustainability of cooperative migratory birds? Does the maturate helper compensate young helpers' helping? Does the hierarchical structure of the population vary for variable migratory rates? We explore the answers based on the mathematical model's simulation experiment, a potential alternative to the game theory approach. This study estimates the parameters associated with the proposed model through the field survey and obtains the rest from existing literature. Although the study uses blue-tailed bee-eater as the test-bed species, the model is useful for analyzing other avian species' behavioral property. The model as a tool can determine whether the primary helpers of blue-tailed bee-eater are the key to sustainability. The model can also classify the adults' help as an addition or compensate to primary helpers' help. The model can predict any alteration in the cooperative breeding birds' hierarchy sizes for variable migration rates under changing climate.