Optimal Allocation of Energy to Growth of the Alimentary Tract in Birds

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Abstract
One hypothesis concerning the growth rates of birds is that weight (size) of alimentary tract limits the availability of energy to growing chicks. To test this, the optimal allocation of energy to the growth of the alimentary tract compared to the rest of the body is considered, under the assumption that the duration of postnatal development in birds is to be minimized. The model starts from bioenergetic equations, and the optimal solution is found by means of the Pontryagin Maximum Principle, assuming that growth is constrained by physiological limitations and not by availability of food. Depending on the initial and final proportion of the alimentary tract to body weight, the predicted optimal relationship between body weight and alimentary tract weight can be described by a single straight line, or two- or three-segmented straight lines. Predictions from the model are compared with data on the growth of a small altricial species - the tree sparrow (Passer montanus Linnaeus) - and support is found for the model.

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