Problems to find maxima and minima (optimization) are common in biological modeling. We have already encountered them in the context of parameter estimation where we minimized the error between data and a function. Optimization also arises in models of the evolutionary process (e.g., optimal foraging) because a valuable working hypothesis when addressing questions of adaptations in organisms is that the observed traits maximize individual Darwinian fitness (i.e., reproductive contribution to future generations). A related application arises when modeling biological systems as control systems: systems that are able to adjust parameters in order to maintain system dynamics within some specified operating range. For example, in mammals, heart rate is increased when oxygen demand through physical exertion increases so that a constant amount of oxygen is delivered to vital organs. This can be considered to be an optimization problem since the system is “attempting” to minimize deviations of oxygen delivery rates from normal (acceptable) values. A third application arises when dynamic models must adjust flow rates of physical quantities between compartments so as to adhere to a physical law. For example, Caldwell et al. (1986, Chapter 16) modeled radiant heat absorption by leaves as part of a canopy-level photosynthesis model. Since there was no analytical solution for the heat flow into each layer of leaves in the canopy given only the input radiation, they used an iterative approximation that minimized the difference between the energy input at the top of the canopy and the total amount of energy absorbed based on a model of the effects of higher leaf levels on lower ones.
KeywordsRecombination Photosynthesis Sine Arena Rosen
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