“Hidden Markov models reveal tactical adjustment of temporally-clustered courtship displays in response to the behaviors of a robotic female”

Posted on

Anna C. Perry, Alan H. Krakauer, Richard McElreath, David J. Harris, and Gail L. Patricelli (July 2019)

The DOI will be https://dx.doi.org/10.1086/703518

Understanding courtship tactics using a robotic female bird and advanced statistical tools

A male greater sage-grouse (Centrocercus urophasianus), left, performs a ‘strut display’ to court a female, right. The authors studied how sage-grouse males tactically adjust the timing of these temporally-clustered displays during interactions with a robotic female grouse.
(Credit: Anna C. Perry)

To convince females to mate, males in many species spend a great deal of energy producing vocal and dance displays during courtship. In order to put on a good show for females that are likely to mate with them, males may have to be tactical in how they spend that energy. One way they may do this is by responding to female behaviors that indicate interest (or lack of interest) in mating. Investigators at the University of California, Davis studied whether male greater sage-grouse (Centrocercus urophasianus) adjust their display effort in response to female behaviors. To do so, they tested males on their display grounds in Wyoming with a robotic female, which either imitated the behaviors of real females uninterested in mating (pecking at the ground) or females becoming interested in mating (standing upright and looking toward the male). To determine whether males adjusted their display effort in response to these female behaviors, they analyzed the timing of males’ displays using a hidden Markov model (or HMM). HMMs are a versatile statistical tool that can be adapted to accommodate different types of time series data.

The robotic female grouse, shown above, was used to manipulate sage-grouse males’ courtship displays via remote control.
(Credit: Alan H. Krakauer)

Like many species of birds, frogs, and insects, male sage-grouse display in bouts separated by intervals of inactivity. The HMM enabled the researchers to determine that male sage-grouse primarily respond to female behaviors by adjusting their display persistence (rather than their display rate). They also found that these adjustments were directly related to males’ success in convincing real females to mate. Males with more matings were more persistent regardless of robot behavior, while males with fewer matings tended to reserve their display effort for when the robotic female already looked interested. Two simpler statistical techniques that are commonly used to quantify animals’ display effort were much less effective at analyzing the same data set. This study demonstrates that HMMs can be very useful for quantifying changes in animals’ display bout behavior, which will benefit researchers interested in broad questions about the evolution of animal sexual displays.


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 also 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 female presence versus absence. We conclude with suggestions for adapting our HMM approach for use in other animal systems.