Question

1. How does distance of a prey item affect the net energy gain of the predator?

2. How does prey size affect the optimal distance at which to pursue prey?

3. How does abundance of prey affect the optimal distance?

4. What is the relationship between net energy gain and distance to the prey item for small prey?

Answer 1

1. There are two general categories of predators: sit-and-wait and active. The main objective of this example is to study and analyze the behaviour of a sit-and-wait predator whose optimal foraging strategy is to maximize the energy that it gains during each foraging course. A sit-and-wait predator usually waits for prey to come within striking distance. It waits in one place for long periods of time and makes decisions regarding when to hunt or when not to hunt the prey that it sees. A major part of this decision depends on how far the prey is from its predator.

To study the behaviour of such a predator, I am making use of the foraging strategy of a kingfisher. The Common Kingfisher hunts from a perch above the water, on a branch, beak pointing down as it seeks for prey. When food is detected, it dives steeply down to grab its prey. For example, consider a kingfisher waiting on a perch on a branch, looking down at a river and choosing which fish to go for. For the sake of understanding, let us assume that the pattern of the foraging area as a semicircle around it and the size and behaviour of all the fishes are same. When a kingfisher takes the decision to grab a particular fish, it dives from its perch, seizes the fish, and come back to its perch.

The energy spent in waiting and pursuit of the prey depends on the size of the foraging area. Increasing the size of the foraging area decreases the time and energy spent in waiting for a fish to come into sight as there is a chance of choosing more fishes. Also, increasing the size of the foraging area increases the average time and energy spent in capturing the prey, because the kingfisher has to fly longer distance to catch its prey.

As explained above, the abundance of the fish increases as the size of the foraging area (semicircle) increases. We need to know how the abundance of the prey increases as it is helpful to find the optimal size of the foraging area. It is known that the area of the semicircle is1/2 πr ². The rate at which area changes with radius is the derivative of the area with respect to the radius, and that is πr. Therefore, on integrating the abundance per unit area will help to obtain the total abundance of the prey within that foraging area (in this case it is semicircle).