Measuring up to reality : null models and analysis simulations to study parental coordination over provisioning offspring

Behavioral coordination when provisioning offspring, through alternation and synchrony, has been hypothesized to influence rearing success. However, studying coordination at the pair level presents two analytical difficulties. First, alternating or synchronous (i.e., simultaneous) feeding can occur randomly and be induced by a shared environment. Therefore, a null model must account for this apparent coordination that occurs by chance. Second, alternation and synchrony in provisioning are intrinsically linked to the rate of provisioning itself, and the effects of coordination and provisioning rate, for instance on fitness, need to be distinguished. In this paper, we explore several randomization procedures and simulation scenarios to tease apart true coordination from random alternation and synchrony, and to find an appropriate statistical model for analyzing coordination. First, to establish a baseline of alternated or synchronous visits expected by chance, we took data from a natural population of house sparrows and randomized inter-feeding intervals in various ways. Alternation and synchrony in the observed dataset were higher than expected by chance under any of our randomizations. However, it was impossible to exclude that alternation and synchrony patterns did not arise due to the pair's shared environment. Second, to identify a way of statistically modeling coordination without generating spurious effects due to intrinsic mathematical relationships between coordination and provisioning rates, we simulated data according to different scenarios. Only one out of five candidate models for analyzing alternation was deemed appropriate, and gave similarly appropriate results for analyzing synchrony. This work highlights the importance and difficulty of finding an adequate null model for studying behavioral coordination and other emergent behaviors. In addition, it demonstrates that analyzing simulated data, prior to analyzing empirical data, enables researchers to avoid spurious effects.