How to measure information carried by a modulated vocal signature?

Acoustic signaling systems that permit individual recognition are described in an increasing number of species. Evolutionary logic predicts that the efficiency of these signatures is related to the possibilities for confusion. To test this "signature adaptation" hypothesis, one needs a standardized method to estimate and compare the efficiency of different signatures. Beecher [Am. Zool. 22, 477-490 (1989)] developed such a method by comparing scalar parameters extracted from the signals. However, vocal signatures frequently consist in the evolution of one parameter against one other, which are not comparable through Beecher's method. Here we present a method to estimate the efficiency of modulated signatures. A signature's efficiency is given by its information capacity (Hm), derived from Shannon's information theory. The measure of Hm is based on an analysis of variance and uses the Euclidian distances between the signature's contours in the population. To validate our method, simulated datasets of modulated contours were used. The predicted efficiency of those signatures, estimated from Hm, was strongly correlated to its actual efficiency given by two classification methods: a discriminant analysis and a classification by human observers. Being also untied to sample size, Hm therefore allows comparing objectively vocal, but also visual and olfactory signatures.