less time searching for prey and more and more time handling the prey. The rate of prey capture increases less and less, until it finally plateaus. The high number of prey basically "swamps" the predator. A Type III functional response curve is a sigmoid curve. The rate of prey capture increases at first with prey density at a positively accelerated rate, but then at high densities changes to the negatively accelerated form, similar to that of the Type II curve. At high prey densities (the top of the curve), each new prey item is caught almost immediately. The predator is able to be choosy and doesn't eat every item it finds. So, assuming that there are two prey types with different profitabilities that are both at high abundance, the predator will choose the item with the higher E/h. However, at low prey densities (the bottom of the curve) the rate of prey capture increases faster than linearly. This means that as the predator feeds and the prey type with the higher E/h becomes less abundant, the predator will start to switch its preference to the prey type with the lower E/h, because that type will be relatively more abundant. This phenomenon is known as prey switching. Predator–prey interaction Predator–prey coevolution often makes it unfavorable for a predator to consume certain prey items, since many anti-predator defenses increase handling time. Examples include porcupine quills, the palatability and digestibility of the poison dart frog, crypsis, and other predator avoidance behaviors. In addition, because toxins may be present in many prey types, predators include a lot of variability in their diets to prevent any one toxin from reaching dangerous levels. Thus, it is possible that an approach focusing only on energy intake may not fully explain an animal's foraging behavior in these situations. The marginal value theorem and optimal foraging The marginal value theorem is a type of optimality model that is often applied to optimal foraging. This theorem is used to describe a situation in which an organism searching for food in a patch must decide when it is economically favorable to leave. While the animal is within a patch, it experiences the law of diminishing returns, where it becomes harder and harder to find prey as time goes on. This may be because the prey is being depleted, the prey begins to take evasive action and becomes harder to catch, or