Studying Natural Optimization

One of the valuable uses of calculus is the ability to find the critical points, the local maxima and minima, of a function. For example, if we can find a function for energy expended, then, using calculus, we can find the minimum energy expended. This is what is known in math as optimization, which refers to any process by which the best solution is found amongst many less desirable alternatives. Scientists and mathematicians have found that, in many examples, optimization occurs naturally. That is, the decision-making of plants or animals verifies what our scientific knowledge suggests would be the optimal behaviour.

The particular example we will discuss is an example of what is called optimal foraging, which refers to obtaining the greatest amount of food as easily as possible. The basis of our project is a study performed by Reto Zach carried out to discover the habits of Northwestern crows in finding and eating whelks, which are large marine snails.