Individual behavioral type captured by a Bayesian model comparison of cap making by sponge crabs.

'Animal personality' is considered to be developed through complex interactions of an individual with its surrounding environment. How can we quantify the 'personality' of an individual? Quantifying intra- and inter-individual variability of behavior, or individual behavioral type, appears to be a prerequisite in the study of animal personality. We propose a statistical method from a predictive point of view to measure the appropriateness of our assumption of 'individual' behavior in repeatedly measured behavioral data from several individuals. For a model case, we studied the sponge crab known to make and carry a 'cap' from a natural sponge for camouflage. Because a cap is most likely to be rebuilt and replaced repeatedly, we hypothesized that each individual crab would grow a unique behavioral type and it would be observed under an experimentally controlled environmental condition. To test the hypothesis, we conducted behavioral experiments and employed a new Bayesian model-based comparison method to examine whether crabs have individual behavioral types in the cap making behavior. Crabs were given behavioral choices by using artificial sponges of three different sizes. We modeled the choice of sponges, size of the trimmed part of a cap, size of the cavity of a cap, and the latency to produce a cap, as random variables in 26 models, including hierarchical models specifying the behavioral types. In addition, we calculated the marginal-level widely applicable information criterion (mWAIC) values for hierarchical models to evaluate and compared them with the non-hierarchical models from the predictive point of view. As a result, the crabs of less than about 9 cm in size were found to make caps from the sponges. The body size explained the behavioral variables namely, choice, trimmed cap characteristics, and cavity size, but not latency. Furthermore, we captured the behavioral type as a probabilistic distribution structure of the behavioral data by comparing WAIC. Our statistical approach is not limited to behavioral data but is also applicable to physiological or morphological data when examining whether some group structure exists behind fluctuating empirical data.