Complexity in Animal Communication: Estimating the Size of N-Gram Structures

In this paper, new techniques that allow conditional entropy to estimate the 1 combinatorics of symbols are applied to animal communication studies to estimate the 2 communication’s repertoire size. By using the conditional entropy estimates at multiple 3 orders, the paper estimates the total repertoire sizes for animal communication across 4 bottlenose dolphins, humpback whales, and several species of birds for N-grams length 5 one to three. In addition to discussing the impact of this method on studies of animal 6 communication complexity, the reliability of these estimates is compared to other methods 7 through simulation. While entropy does undercount the total repertoire size due to rare 8 N-grams, it gives a more accurate picture of the most frequently used repertoire than just 9 repertoire size alone. 10