The Optimal Diet Model: Key Variables

• E₁, h₁, S₁: Energy value, handling time, and search time for big prey (prey 1)

• E₂, h₂, S₂: Energy value, handling time, and search time for small prey (prey 2)

Profitability of a prey item is typically defined as the energy obtained per unit of handling time (E/h). However, when considering the opportunity cost of searching for more profitable prey, search time becomes a crucial factor.

The Decision Rule for Prey Choice

According to the optimal diet model, a predator should always take the more profitable prey (with higher E/h) when it encounters it. But when it encounters the less profitable prey, the decision depends on whether the energy gained per handling time from the smaller prey exceeds the average rate of energy gain possible by searching for and handling the larger prey.

The predator will preferentially select prey 2 (the smaller prey) when:

E2h2>E1h1+S1h2E2>h1+S1E1

• E₂/h₂: Profitability of the small prey (energy per handling time)

• E₁/(h₁ + S₁): Average rate of energy gain from the big prey, factoring in both handling and search time

This means that if the rate of energy gain from the small prey exceeds the average rate from searching for and handling the big prey, the predator should include the small prey in its diet12.

Why Search Time Matters

When big prey becomes scarce, the search time (S₁) increases, reducing its overall profitability. At a certain point, even if the big prey offers more energy per handling time, the time spent searching for it makes the smaller, more easily found prey a better choice. This dynamic ensures predators adapt their diets based on prey availability and environmental conditions.

Evaluating the Options

• Option 1: When E₂/h₂ > E₁/(h₁ + S₁)
  This is the correct condition for the predator to select the smaller prey, according to optimal foraging theory.

• Option 2: When the abundance of prey 1 is very high
  If prey 1 is abundant, search time S₁ is low, making prey 1 more profitable; the predator would not prefer prey 2.

• Option 3: When the abundance of prey 1 and prey 2 are equal
  Abundance alone does not determine choice; profitability per unit time is the key.

• Option 4: When E₂/h₂ = E₁/h₁
  This ignores search time, which is essential for accurate decision-making.

Conclusion

According to optimal foraging (diet) theory, a predator will preferentially select the smaller prey (prey 2) when:

(1) E₂/h₂ > E₁/(h₁ + S₁)