Optimal foraging theory

A central concern of ecology has traditionally been foraging behavior. In its most basic form, optimal foraging theory states that organisms focus on consuming the most energy while expending the least amount of energy. The understanding of many ecological concepts such as adaptation, energyflow and competition hinges on the ability to comprehend what, and why, animals select certain food items.

History of OFT

MacArthur and Pianka (1966) developed a theoretical and empirical construct, the optimal foraging theory (OFT), which lead to a better understanding of foraging behavior. Emlen (1966) published a paper on foraging behavior at the same approximate time. Although it was different in detail, it demonstrated the need for a model where food item selection of animals could be understood as an evolutionary construct which maximizes the net energy gained per unit feeding time. Since its original conception, there have been many papers and books published mentioning OFT which have made important contributions to a number of disciplines including ecology, psychology and anthropology. Some of these additions include papers from ^* (1972, 1978, 1985), Smith (1966, 1974), Ricklefs (1973), Schoener (1974, 1983), Pyke (1984), Krebs, Stephens & Sutherland (1983) and Stephens & Krebs (1986). The following is an outline of MacArthur and Pianka’s model.

The functional classes of predators

The OFT uses predators as the object of analysis. There are four functional classes of predators:

True predators attack large numbers of their prey throughout their life. They kill their prey immediately, or shortly after the attack. They may eat all or only part of their ^*. True predators include tigers, lions, plankton eating whales, seed eating birds & ants and humans.
Grazers attack large numbers of their prey throughout their lifetime and eat only a portion of their prey. They harm the prey, but rarely kill it. Grazers include cows, sheep, leeches and mosquitoes.
Parasites, like grazers, eat only a part of the prey (host) but rarely eat the entire organism. This much more intimate relationship is typical of tapeworms, liver flukes and plant parasites such as the potato blight.
Parasitoids are mainly typical of wasps (order Hymenoptera) and some flies (order Diptera). Eggs are laid inside the larvae of other arthropods which hatch and consume the host from the inside, killing it. This intimate predator-host relationship is typical of about 10% of all insects.

Basic variables of OFT

The OFT attempts to explain predator behavior since no predator eats everything available. This is typically due to habitat and size constraints, but even within habitats, predators eat only a proportion of what is available.

E is the amount of energy (calories) from a prey item. h is the handling time which includes capture, killing, eating and digesting. h starts once the prey has been spotted. E/h is therefore the profitability of the prey item.

Animals typically eat the most profitable prey types more than would be expected by chance since it will appear in the diet more often than it is encountered in the environment. Predators do not, however, eat only the most profitable prey types. Other prey types may be easier to find, and E is not the only nutritional requirement. Toxins may be present in many prey types, therefore variability of diet prevents any one toxin from reaching dangerous levels.

Optimal foraging and diet breadth

The predator attempts to maximize E/(h+s), where s is the search time involved. For a range of prey, the predators average intake rate is Eaverage/(haverage+saverage). Where Eaverage is the average E of all prey items in the diet, haverage is the average handling time and saverage is the average search time.

When the predator has found an item it doesn’t currently eat, it has two choices. It can eat the new item, in which case the profitability is Enew/hnew or it can leave it and search for an item already in its diet, in which case we use Eaverage/(haverage+saverage). The predator should eat this new item when Enew/hnew ≥ Eaverage/(haverage+saverage) because the new item increases Eaverage/(haverage+saverage).

This leads to new insights:

Predators with short haverage and long saverage should be generalists and include a wide range of items.
Specialists have a longer haverage and saverage , they are choosy. Lions, for example, have a very low saverage but a high haverage , which can be prohibitively large for some prey individuals. They therefore pick out the sick and old.
Predators should be generalists in unproductive environments and specialists in productive environments.
Predator-prey co-evolution often makes it non-profitable for a prey item to be included in the diet, 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.

Since there is a search time for each item, when predator density increases the search time depends on the density of the prey. There is also a handling time which is species specific. This is best understood with a response curve:

At low prey densities the predator is searching most of the time and eating every prey item it finds
At high prey densities, each new prey item is caught almost immediately. The predator spends almost all of its time catching, eating or digesting the prey. It chooses only those individuals with the highest E/h.

Handling time may not be the only reason why the slope levels off:

Confusion effects at very high prey densities occur.
Handling time may vary between individual prey items.

With a Type II functional response curve:

At low prey densities, intake rate increases linearly with prey density, there is no handling time.
At high prey densities, the predator has simply eaten enough.

With a Type III functional response curve:

At high prey densities, each new prey item is caught almost immediately. The predator spends almost all of its time catching, eating or digesting the prey. It chooses only those individuals with the highest E/h.
At low prey densities the intake rate increases faster than linearly. The predator will start to switch to this prey type as it becomes more abundant. This implies the existence of a search image.

Most predators can probably only hold a few search images at one time. Hunter-gatherers, however, may hold numerous search images, yet focus on the most profitable prey types. As the prey density increases, they become less limited by search time and more limited by handling time.

Conclusion

Predators obviously do not solve OFT equations, and most animals will deviate from the aforementioned models. Application of this model to hunter-gatherer systems has helped ecological anthropologists empirically quantify predator-prey relationships.

References

MacArthur, R. H. and Pianka, E. R. (1966). On the optimal use of a patchy environment. American Naturalist, 100
Kamil, Alan C., John R. Krebs and H. Ronald Pulliam. (1987). Foraging Behavior, Plenum Press, New York and London

Ecology