Splitting behavior by social category

At the conclusion of the last committee meeting, it was decided that I should redo my analyses of rhesus macaque behavior while splitting social behaviors according to the relationships of the interacting animals. The logic was that, given that we know that relationships are a critical determinant of macaque behavior, distinguishing between social categories of interaction partners would “carve nature at its joints” so to speak and could yield richer behavioral variability.

Accordingly I decided to split social behaviors according to two highly salient social categories: kin, and relative status. I didn’t do these splits at the same time, however, since that lead to a prohibitively large number of behaviors and behavioral categories that were too sparse to do much with. Moreover, as rank is inheritted matrilineally among females, these two categories are pretty closely intertwined.

These four behaviors were the same across all splittings:

The following behaviors differed across behavior splittings:

Under the none splitting, these behaviors included all interactions with adult conspecifics and were not subdivided based the interaction partner, giving a total of seven behaviors.

Under the kin splitting, the behaviors were subdivided according to whether the interaction partner was a close kin of the focal animal, for a total of ten behaviors. I considered a pair to be kin if their kinship coefficient was at least 0.25.

Finally, under the rank splitting, grooming and approaches were subdivided based on whether the interaction parter was of higher rank versus similar or lower rank than the focal animal. Aggression was not subdivided because aggression directed at higher-ranked animals was, by definition, exceedingly rare. This yielded a total of nine behaviors. Only interactions with adult conspecifics of the same sexs were counted under this splitting, as the rankings of males and females are not commensurate.

Rank was measured on an ordinal scale: low-ranking animals outranked less than 50% of their social group, medium-ranking animals outranked between 50% and 80%; and high-ranking animals outranked greater than 80%. For high-ranking animals, interacting with higher-ranking animals than themselves is not possible, so for them behaviors were subdivided into interactions with similarly high-ranking animals versus interactions with those of low and medium rank.

Models

This is a brief refresher. No new material here.

Our aim is to compare models that impose different restrictions on the ways in which animals within a population can differ from each other. The standard treatment of behavioral data in a population is to consider the rates of each behavior in isolation. Under this treatment, an animal’s unique behavioral phenotype is restricted to the difference in their rates of behaviors from the population means. Here, we consider two models that relax the assumption that animals differ only in their rates, and also allow animals to differ in the patterns in which their behaviors co-occur.

We use two models, the quadratic exponential binary mixed-effects model (QEBmm) and the behavioral state model (BS), which differ in how they structure the dependencies between different behaviors. QEBmm describes the joint distribution of behaviors in terms of main effects of and pair-wise interactions between behaviors, which are analogous to means and correlations in a multivariate normal distribution, and here we will refer to them as rates and correlations between behaviors. Crucially, under the QEBmm animals can differ in both of these components.

The BS model describes the joint distribution of behaviors using a mixture model where each mixture component corresponds to a set of co-occurring behavioral rates, with each focal observation belonging to one mixture component. We refer to these mixture components as behavioral states, in that they capture tendencies for behaviors to co-occur (or not) in ways that change over time. For example, an animal might have a high energy state, in which many behaviors have high rates, and a low energy state, in which all non-active behaviors have low rates. Animals share the same states, but they differ in their probabilities of engaging in each state.

Results

Our first question is whether the data contains evidence that animals differ in their patterns of behaviors rather than only their rates of behaviors. We will answer this by comparing the QEBmm and BS models to submodels in which animals are constrained to vary only in their rates of behavior. The models and submodels are fit separately to each of the data splittings described above, and for BS with a range of number of behavioral states permitted in the model.

The figures above show the in the Widely-Applicable Information Criterion (WAIC) between the full models (Variability in rates and correlations for QEBmm, Varibility in rates and states for BS) and the restricted submodels (Variability in rates only), using a model where all animals are assumed to be identical as the baseline. Note that WAIC is an approximation of the predictive likelihood for unobserved data.

The picture is similar across both models and all data splittings. The difference between the full models and “rate only” models is nominally significant, but the improvement from allowing animals to differ in patterns as well as rates is marignal relative to the improvement from allowing animals to differ in their rates versus constraining all animals to be the same.

It’s worth noting that, for the BS model, it appears that the predictive accuracy would improve more with the addition of more behavioral states. Right now I’m running the model with up to 16 states to try to rectify this.

The above figures show the repeatability of behavior – the within-animal variability in behavior compared to the total behavioral variability in the population – for the models and submodels. Repeatability is consistently estimated to be between 3% and 5%.

We can estimate the proportion of repeatability that is uniquely contributed by variability in patterns of behavior co-occurrence (correlations for QEBmm, states in BS) by comparing the repeatability of the full models to the submodels that allow only variability in behavior rates. Under QEBmm this proportion is about 10% across behavior splittings, with the largest value achieved by the “none” splitting with 14%. The story is a bit more complicated under the BS model, with the proportion of repeatability depending on the number of states. With intermediate numbers of states, both the none and rank splittings reach proportions of 20%. However, this proportion collapses at larger numbers of states (which are also better fitting), across all splittings. The final interpretation will have to wait on the results of the models with even more behavioral states.

Conclusion?

There’s no particular evidence that splitting behaviors by social relation meaningfully impacts the repeatability of behaviors, or the proportion of those behaviors accounted for by variability in rates alone. I don’t think there is anything contradictory or counter-intuitive here. Social categories like kin and rank relations impact behavior, but it doesn’t necessarily follow that animals vary in impacts of those categories. It could even be that because these social categories are so important, they constrain rather than permit variability; animals have no choice but to respect dominance rank and affiliate with kin, or they don’t survive long enough to get picked up in our behavioral data.