Association indices for quantifying social relationships: how to deal with missing observations of individuals or groups

Social network analysis has provided important insight into many population processes in wild animals. Constructing social networks requires quantifying the relationship between each pair of individuals in the population. Researchers often use association indices to convert observations into a measure of propensity for individuals to be seen together. At its simplest, this measure is just the probability of observing both individuals together given that one has been seen (the simple ratio index). However, this probability becomes more challenging to calculate if the detection rate for individuals is imperfect. We first evaluate the performance of existing association indices at estimating true association rates under scenarios where (1) only a proportion of all groups are observed (group location errors), (2) not all individuals are observed despite being present (individual location errors), and (3) a combination of the two. Commonly used methods aimed at dealing with incomplete observations perform poorly because they are based on arbitrary observation probabilities. We therefore derive complete indices that can be calibrated for the different types of incomplete observations to generate accurate estimates of association rates. These are provided in an R package that readily interfaces with existing routines. We conclude that using calibration data is an important step when constructing animal social networks, and that in their absence, researchers should use a simple estimator and explicitly consider the impact of this on their findings.