A case for quantile regression in behavioral ecology: getting more out of flight initiation distance data

A central goal of behavioral ecology is to quantify and explain variation in behavior. While much previous work has focused on the differences in mean behavior across groups or treatments, we present a complementary approach studying changes in the distribution of the response variable. This is important because changes in the edges of a distribution may be more informative than changes in the mean if behavior at the edges of a distribution better reflects behavioral constraints. Quantile regression estimates the rate of change of conditional quantiles of a response variable and thus allows the study of changes in any part of its distribution. Although quantile regression is gaining popularity in the ecological literature, it is strikingly unused in behavioral ecology. Here, we demonstrate the usefulness of this method by analyzing the relationship between the starting distance (SD) at which an observer approach a focal animal and its flight initiation distance (FID, the distance between the observer and the animal when it decides to flee). In particular, we used a simple model of flight initiation distance to show that in most situations ordinary least-square regression cannot be used to analyse the SD-FID relationship. Quantile regression conducted on the lowest quantiles appears more robust and we applied this approach to data from four bird species. Overall, changes in the lowest FID values appeared to be the most informative to determine if a species displays a flush early strategy, a strategy which has been hypothesized to be a general rule. We hope this example will bring quantile regression to the attention of behavioral ecologists as a valuable tool to add to their statistical toolbox.