The concept of evolution implies that fitness traits of an organism tend toward some constrained optimality. Here, the fitness trait we consider is the distribution of photoreceptors on an organism's retina. We postulate that an organism's photoreceptor distribution optimizes some balance between two quantities, a benefit and a cost. The benefit is defined as the area of the field of vision. The cost is defined as the amount of time spent saccading to some target in the visual field; during this time we assume nothing is seen. Three constraints are identified. First, we assume proportional noise exists in the motor command. Second, we assume saccades are a noisy process. Third, we constrain the number of total photoreceptors. This simplified model fails to predict the human retinal photoreceptor distribution in full detail. Encouragingly, the photoreceptor distribution it predicts gets us closer to that goal. We discuss possible reasons for its current failure, and we suggest future research directions.
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