Estimating heritability of social phenotypes from social networks

For understanding how social behaviour evolves and responds to selection, we need to be able to accurately estimate heritability with quantitative genetic models. More recently, this has moved into using node-specific statistics from social networks as social phenotypes. However, parameter estimation can be problematic because social phenotypes are not independent observations and standard models tend to ignore the uncertainties around their estimates. Here I present a framework using latent variable modelling to account for these dependencies and uncertainties. I use edge weights, rather than node-specific network statistics, as dependent variables. From these edge weights, two types of latent (i.e. unobserved) phenotypes are estimated: the individual tendency to be social (i.e. social tendency) and the relative contribution to associations (i.e. social governance). Effects of the social environment and indirect genetic effects are accounted for in the model and can be estimated post hoc. If edge weights are a proportion (e.g. simple ratio index) their uncertainty can be accounted for by a binomial sampling process. I illustrate this method in Stan, a flexible Bayesian inference library, using a publicly available dataset on bottlenose dolphin networks. This method not only accounts for dependencies and uncertainties, it also illuminates aspects of social evolution which are not observed with standard quantitative genetic models. For instance, indirect genetic effects models predict heritable variation in sociality (21.9%), while latent variable modelling shows heritability of social tendency (28.7%), but not for social governance (0.0%). Covariates at different levels in the model (edge and node level) highlight differences in sociality between different foraging strategies and the sexes. This example shows that not properly accounting for the assumptions underlying the use of social network statistics can have misleading effects on conclusions. Although some model assumption violations are less common, others are inherit to the study of (semi)wild populations. The presented framework offers solutions for some critical assumptions and is a flexible tool to further develop and tailor to the needs of specific studies, to ensure the proper fit to the study system.