Performance of basic strategies for following gradients in two dimensions

Computer models for following stimulus gradients in two-dimensional space were evaluated to determine the relative advantages of different strategies and to identify the issues that must be addressed in making such a comparison. The simulations were implemented with emphasis on making them as general and free of specific assumptions as possible. Performance was defined as progress along the gradient divided by the cost of the movements and time taken. Plausible values of costs were taken from data on animal energetics. The models also included various kinds of noise that limit performance. These included unintended variations and biases in motor outputs as well as sensory inputs. An initial guess at appropriate noise levels led to performance worse than that observed in experiments with leukocytes. Reduced noise levels gave good agreement. Under these, more appropriate, conditions, peak performance for the various models varied from 24 to 99% of the maximum possible. The threshold gradient required to provide performance equal to 1% of the maximum possible varied from 800 to 5000 searcher diameters per gradient decay length. Some models performed well only over a narrow range of gradients. There was no indication of a tradeoff between sensitivity to shallow gradients and high performance in steep gradients. The model of tropotaxis (simultaneous, spatial comparison) with movement in any direction was superior in having the lowest threshold, the highest maximum performance, requiring the fewest parameters to fit, and performed well over the widest range of gradients. This result suggests that amoeboid cells and echinoderms might be particularly well suited to following gradients. The modeling demonstrates the need to obtain quantitative estimates for a number of parameters (relating costs and noise levels) for a more rigorous understanding of the relative advantages of these different strategies.