Abstract
Optimal escape theory states that animals should counterbalance the costs and benefits of flight when escaping from a potential predator. However, in apparent contradiction with this well-established optimality model, birds and mammals generally initiate escape soon after beginning to monitor an approaching threat, a phenomena codified as the “Flush Early and Avoid the Rush” (FEAR) hypothesis. Typically, the FEAR hypothesis is tested using correlational statistics and is supported when there is a strong relationship between the distance at which an individual first responds behaviorally to an approaching predator (alert distance, AD), and its flight initiation distance (the distance at which it flees the approaching predator, FID). However, such correlational statistics are both inadequate to analyze relationships constrained by an envelope (such as that in the AD-FID relationship) and are sensitive to outliers with high leverage, which can lead one to erroneous conclusions. To overcome these statistical concerns we develop the phi index (Φ), a distribution-free metric to evaluate the goodness of fit of a 1∶1 relationship in a constraint envelope (the prediction of the FEAR hypothesis). Using both simulation and empirical data, we conclude that Φ is superior to traditional correlational analyses because it explicitly tests the FEAR prediction, is robust to outliers, and it controls for the disproportionate influence of observations from large predictor values (caused by the constrained envelope in AD-FID relationship). Importantly, by analyzing the empirical data we corroborate the strong effect that alertness has on flight as stated by the FEAR hypothesis.
Highlights
Animals must escape predators because failure to do so can result in death and termination of any future contribution to fitness
We suggest that an ideal metric to test the Flush Early and Avoid the Rush’’ (FEAR) hypothesis must meet three criteria: (1) it must provide an intuitive measure of how close flight initiation distance (FID) are from alert distance (AD), (2) it must be robust to outliers in order to properly capture the strategy used by most individuals observed, and (3) it must not be biased by observations with large ADs that may have a larger range of FID values
By doing so we are calculating the deviance in a relative way. This approach aims to overcome the problems of potentially excessive influential observations in cases with large ADs that result from the envelope pattern seen in ADFID relationships
Summary
Animals must escape predators because failure to do so can result in death and termination of any future contribution to fitness. Optimal escape theory predicts that prey flee from predators at the point in which risk and cost are equal [1,2]. Because of the relative ease of studying flight initiation distance (FID, the predator-prey distance when escape begins), the theory has been widely supported by a number of studies since its publication. While there is a species-specific signal to FID [3], within species, it is affected by many different variables that may include both internal factors, such as age, sex, condition, and pregnancy, as well as external factors, such as temperature, season, degree of human impact, distance to cover, and relative exposure to predators (e.g., [4,5,6,7,8]). Understanding the distance at which an individual flees an approaching predator is of more than mere academic interest because animals may view humans as predators [9], and FID to humans has been used to develop set-back zones to reduce human disturbance on wildlife [10,11,12,13]
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