In evolutionary game theory, a behavior is Evolutionarily Stable if it cannot be invaded by another alternative behavior. In Broom and Ruxton’s journal article, they talk about the evolutionarily stability of stealing food. Specifically, they discuss an individual-based model where each animal can either obtain undiscovered food on their own or steal food from other animals, which is called kleptoparasitism. Broom and Ruxton focus on how intraspecific kleptoparasitism affects the food uptake rates of individuals.

An individual’s food uptake rate is generally a function of food availability and competition from other foragers. In Ruxton and Moody’s model, they assume that when individuals search and discover a food, they spend a finite amount of time to process the item before eating it, which will be called the handling time. If another individual encounters the handler (the individual processing the item), both individuals compete for the item, where there will always be a defined winner. However, during this competition, both individuals sacrifice time leading to an interference effect, where the average uptake rates decline with forager density (Holmgren, 1995; Ruxton and Moody, 1997). Hence, stealing may not always be the most time-efficient strategy since time spent challenging another individual may have been used to search for undiscovered food. In the article, Broom and Ruxton try to explain when opportunities of stealing should be given up. Without working out all the calculations done by Broom and Ruxton, consider a set value p, which is an individual’s natural tendency to take up opportunities to steal and τ, which is the average time a searcher encounters a handler and then begins handling a food item itself. The most optimal value of p is to minimize τ because an individual will want to accept opportunities to steal if it will take a little time to do so.

Another assumption Ruxton and Moody’s model made is that the search for undiscovered food and the search for handlers are different activities that can vary independently. However, it seems like the ability to enhance at one of the activities will come at the expense of the other activity. (Ruxton and Moody, 1997) Broom and Ruxton suggest that searching has a finite capacity between searching for food and searching for handlers to steal from. In their research, Ruxton and Broom find that either individuals should always or never challenge others to maximize uptake rate. The decision is dependent upon the availability of food and duration of fight. If the duration of fighting is long or food is easy to find, then it will be optimal for opportunities of kleptoparasitism to be passed up. It can be predicted that there will be no aggressive behavior between individuals. As the food density decreases, the uptake rate declines. After the food density falls below a certain critical value, an individual’s decision to pass up an opportunity to steal changes. When food becomes hard to find or fights are of short duration, individuals should accept all opportunities for kleptoparasitism. With the change in an individual’s behavior, there will be a sudden drop in uptake rate, and then further reduction in the food supply and decline in uptake rate. As described above, changes in ecological conditions can cause a dramatic change in aggressive behavior of individuals. Given certain ecological conditions, individuals should behave a certain way that will be evolutionarily stable. By using game theory, Broom and Ruxton have found the evolutionarily stable strategy for investing in searching for food or searching for handlers in terms of the ecological parameters of the model.

http://beheco.oxfordjournals.org/cgi/reprint/9/4/397

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