Table 1.
Summary of each model reviewed.
Fig 1.
Differences in the slope of the relationship between FID and approach speed indicate different escape rules species may.
Positive slopes are associated with the temporal margin of safety, a slope near zero is associated with a spatial margin of safety, and negative slopes are associated with the delayed margin of safety. If the slope is positive FID increases until it reaches AD, at which point FID is equal to AD. If the slope is negative FID decreases until it reaches 0, at which point FID is equal to 0. The minimum distance threshold is the last distance at which the animal will tolerate the approach of a threat whereafter if the threat continues to approach to where the animal will escape, regardless of the threats approach speed.
Fig 2.
Flowchart of methods used to evaluate sensitivity to speed for the FEAR hypothesis, Looming stimulus hypothesis, and the Bayesian optimal escape model.
Step 1: we reviewed the literature for studies which explored the effect of approach speed on FID in different avian taxa. The goal was to characterize the range of observed slopes of the FID vs. approach speed relationship when birds were exposed to human-related threats. Step 2: We established the distributions of AD, FID, then slope and intercept of the FID vs. approach speed relationship. Step 3: We simulated AD and FID based on the observed distributions from step 2 All three models required information on either FID, AD, or both to make quantitative predictions. Step 4: We generated model-specific FID predictions using additional parameters when needed. Step 5: We evaluated sensitivity to approach speed by estimating the average effect size of approach speed on model predicted FID at different slope values for each model.
Fig 3.
Illustration of the relationship between AD and FID according to the FEAR Hypothesis’s phi index.
The range of ϕ is between 0 and 1. A ϕ value of 0 occurs when animals do not escape at all even after detection and a ϕ value of 1 occurs when prey escape the moment it detects the predator. ϕ must be greater than 0.5 to support the FEAR hypothesis (Samia & Blumstein 2014) [44].
Fig 4.
Changes in approach speed’s effect size (i.e., the phi-index, or f 2) with different slopes for the FID and approach speed relationship for three different models potentially sensitive to vehicle approach speed.
a) The mean phi-index, the effect size metric for the FEAR hypothesis, across iterations for each slope. The figure suggest that model is most sensitive to vehicle approach speed when the slope is equal to or greater than zero. b) The mean f 2 across iterations for each slope according to the looming hypothesis when latency is 0.075 seconds, which suggest the model is sensitive to the delayed margin of safety. c) The mean f 2 across iterations for each slope according to the Bayesian optimal escape model when the body mass is 267.4 grams, which suggest the model is not sensitive to approach sped. d & e) The mean f 2 across iterations for each combination of slope and neuronal latency value for the looming stimulus hypothesis. d and e show the same graph but from two different viewpoints. Across neuronal latency values it seems the model is sensitive to the speed effect at slightly negative slopes. f) The mean f 2 across iterations for each combination of slope and body mass value for the Bayesian optimal escape model. The figure suggests that only at a size of larger then 1kg is the model FID predictions sensitive to vehicle approach speed.
Fig 5.
Illustrated differences in the detection assumptions for the five models capable of producing quantitative predictions.
FID refers to flight initiation distance, AD refers to alert distances, and DD refers to detection distance.