CHAPTER 4
Applications of Differentiation
4.4 Decisions and Optimization
Figure 4.1 A great tit is a species of bird whose foraging behavior was studied by biologist Richard Cowie and whose behavior can be predicted by optimal foraging models.
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“‘If one way be better than another, that you may be sure is nature's way.’ Aristotle clearly stated the basic premise of optimization in biology, yet it was almost 2,000 years before the power of this idea was appreciated. The essence of optimization is to calculate the most efficient solution to a given problem, and then to test the prediction. The concept has already revolutionized some aspects of biology, but it has the potential for much wider application.”
William Sutherland, on “The best solution” in Nature (2005) 435:569
One of the central ideas in physics, chemistry, and biology is that processes act to optimize some physically or biologically meaningful quantity. For example, from physics we know that light in a vacuum travels along a path that is the shortest distance between two points (taking into account that gravity “bends” space), and from biochemistry we know that proteins fold in a way that minimizes the energy of their constituent amino acid configuration.
Differential ...
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