Animal dance is composed of many behavioral elements. Then, what evolutionary factors decide complexity and length of animal dance? To answer this question, we made and analyzed a mathematical model of sexual selection.

In the model, each individual has three genetic elements. Each element prescribes a behavioral sequence of dance, a preference for behavioral sequences and general fitness (survival ability), respectively. We assume the following. First, each male performs a dance according to his gene, but the lower his fitness is, the more mistakes he commits in the dance (handicap principle). Therefore, a realized dance sequence is different from the genetically determined one. Second, each female chooses a mate by comparing male’s realized dances with her preference. Females are more likely to choose males whose dance is more similar to their preference. Reproduction in couple is subject to genetic recombination and mutation. Finally, these children survive in the next generation according to their own fitness.

As a result, although we assumed that mutation is more likely to shorten a behavioral sequence than to lengthen it, both dance and preference sequences became long and complex in the presence of sexual selection. The average fitness of the group increased. We'll present a simple explanation of the results by comparing the cases with and without sexual selection.