Hidden Markov Models Reveal Tactical Adjustment of Temporally Clustered Courtship Displays in Response to the Behaviors of a Robotic Female.

We present a statistical approach-a custom-built hidden Markov model (HMM)-that is broadly applicable to the analysis of temporally clustered display events, as found in many animals, including birds, orthopterans, and anurans. This HMM can simultaneously estimate both the expected lengths of each animal's display bouts and their within-bout display rates. We highlight the HMM's ability to estimate changes in animals' display effort over time and across different social contexts, using data from male greater sage grouse (Centrocercus urophasianus). Male display effort was modeled across three sites in two experimental treatments (robotic female simulating interested or uninterested behavior) and in the presence or absence of live females. Across contexts, we show that sage grouse males primarily adjust their bout lengths rather than their within-bout display rates. Males' responses to female behavior were correlated with male mating success: males with more matings showed high display persistence regardless of female behavior, while males with fewer matings tended to invest selectively in females that were already showing interest in mating. Additionally, males with higher mating success responded more to the presence of a female than males with fewer matings did. We conclude with suggestions for adapting our HMM approach for use in other animal systems.