  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.
