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Food: Optimal Foraging Models

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Theories of optimality involve a mathematical model of cost and benefit analysis that can give quantitative predictions about an animal's behavior. These hypotheses can be tested experimentally or through comparative phylogeny. By no means are these models fully accurate; each comes with certain assumptions and variations that are not included in these simple models. But we can often use the models to predict behavior to a reasonably certain degree.

To some degree, animals display the ability to modify their behavior so that they receive an optimal balance of benefits and costs. Costs can include danger, loss of valuable time, and wasted energy. Benefits are usually counted in terms of net energy intake (consumed calories) per unit time or number of offspring produced. In this section, we will focus on optimal foraging methods to achieve the highest net energy intake. We will discuss reproductive fitness and the production of offspring in the next section.

Contingency Theory

Contingency Theory, also called the prey choice model, predicts what an animal will do when it encounters a particular food. Should the animal eat what he has, or search for a more profitable food item? We do not often imagine animals refusing to eat the food in front of them to search for other items, but this does occur. Shorecrabs, for instance, eat muscles that become increasingly difficult to crack open as their size increases. Crabs will pass up large muscles, which would take too much time and energy to crack, to search for smaller muscles. This way, the crab can spend less time and energy handling their food, and, even though they pass up the massive meals, will increase their net food intake.

Models similar to that just described for the Shorecrab can include several food choices, though the math involved can quickly complicated; we will focus on the simpler version with two food types.

PARARAPH For the purpose of the model, we will define the following terms:

  • energy (E) is the net number of calories obtained by consuming the food item.
  • Handling time (h) is the amount of time required to handle the food between the time it is encountered to the time it is consumed. Handling time can include cracking a shell, digging it out of the ground, or manipulating the item.
  • Search time (s) is the mean expected time between encounters of items of the same food type. Search time depends on the abundance of the item and the ease of locating it.
  • total time foraging (T) is the sum of searching and handling times.
The model we are building is concerned with profitability, the energy gained divided by the time spent handling it (E/h) for a single food source, and the maximum energy gained per total time foraging (E/T) when there are multiple food sources.

Using the Model

Food choice 1 is scarce, but is highly profitable, meaning it will yield a high amount of energy with a low handling time. E/h for food 1 is therefore quite high. However, because we are trying to maximize both E/h and E/t, we must also take into account the time it takes to find the very scarce food choice 1.