Restrictions on the dynamic growth of navigation accuracy in groups of animals

Abstract

Many migratory animals regularly travel thousands of kilometers, exactly finding their destinations. It is assumed that migrants have both a compass sense to hold their course, and a map sense --- a kind of "biological" GPS --- to correct accumulated errors and determine right direction during navigation. Unlike the compass sense, the map sense is still not reliably explained. Therefore, an alternative way is discussed in literature to eliminate the errors --- the aggregation of animals in groups and their coordinated movement. Orientation accuracy of a group may be significantly higher because the errors caused by the action of a variety of casual factors are averaged. This idea, called the "many wrongs principle," has been confirmed both in behavioral experiments and in the results of computer simulations. However, until now there was no analytical model that considered this effect and its limitations. Such a model is presented in this article. The model is given in terms of the course deviation angle and its variance. It includes a few parameters: individual sensitivity of the animal compass, the power of the herd instinct, and the level of random noise. These parameters determine, among other factors, the size of the group that is optimal for precise navigation. It is shown that there is a range of the noise level, at which the aggregation of individuals into groups that do not exceed a certain size would be favorable.