Groups of animals (including humans) may show flexible grouping patterns, in which temporary aggregations or subgroups come together and split, changing composition over short temporal scales, (i.e. fission and fusion). A high degree of fission–fusion dynamics may constrain the regulation of social relationships, introducing uncertainty in interactions between group members. Here we use Shannon's entropy to quantify the predictability of subgroup composition for three species known to differ in the way their subgroups come together and split over time: spider monkeys (Ateles geoffroyi), chimpanzees (Pan troglodytes) and geladas (Theropithecus gelada). We formulate a random expectation of entropy that considers subgroup size variation and sample size, against which the observed entropy in subgroup composition can be compared. Using the theory of set partitioning, we also develop a method to estimate the number of subgroups that the group is likely to be divided into, based on the composition and size of single focal subgroups. Our results indicate that Shannon's entropy and the estimated number of subgroups present at a given time provide quantitative metrics of uncertainty in the social environment (within which social relationships must be regulated) for groups with different degrees of fission–fusion dynamics. These metrics also represent an indirect quantification of the cognitive challenges posed by socially dynamic environments. Overall, our novel methodological approach provides new insight for understanding the evolution of social complexity and the mechanisms to cope with the uncertainty that results from fission–fusion dynamics.
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