﻿ Catching Prey

## Catching Prey

Vulnerabilty of Prey

• We implemented a model of killing rate similar to a classical formulation of attack rate × number of prey, with attack rate partitioned into an encounter rate (e) defined as the probability that a group of killer whales would encounter a particular individual prey, and vulnerability (v) equal to the probability of being killed by the group once encountered (i.e, expected kills per day equals e × v × number of prey). To make this dependent on group size (x), we used a simple logistic function with a user-defined maximum vulnerability and logistic parameters a and b: v = vmax * exp(a + b × x) / (1 + exp(a + b × x)). A sample vulnerabilty curve and resulting expected kills per whale by group size is shown below.
• Calf and juvenile killer whales are not as effective hunters as adults, so group size for this purpose was considered to be "adult equivalents", where juveniles began a linear increase in hunting effectiveness at age 3 (HuntAgeMin equivalent to 0 adults) and were considered fully effective hunters at age 12 (HuntAgeMax equivalent to a single adult). Thus, a group of killer whales comprised of animals aged 1.5, 7.5, 24.5, 36.5 and 60.5 years would have an effective group size of 3.5 for hunting purposes. We also linearly reduced the effectiveness of whales that become malnourished from full effectiveness to 0 effectiveness as metabolic rate declines (BeginStarve = 0.8 to EndStarve = 0.7, see section on Energetics). Thus, a group of two adult killer whales where one is at 0.95 of target mass and the other is at 0.75 of target mass would have an effective group size of 1.5.

Prey Capture

• In executing a daily time step, the model steps through all prey types, drawing a random variable from a Poisson distribution with expectation equal to e(i) × number (n(i)) of prey type i. Once all potential prey are selected, their order is randomized and each is subjected to a random trial to see if it is captured by comparing its vulnerability to a uniform random variable. The group kills prey in the list until the list is exhausted or enough prey are consumed to sate all the individuals in the group. The kills are shared proportional to the volume required for each to satisfy its maintenance metabolic requirements and reach satiation.