Models with indirect genetic effects depending on group sizes: a simulation study assessing the precision of the estimates of the dilution parameter.

Background: In settings with social interactions, the phenotype of an individual is affected by the direct genetic effect (DGE) of the individual itself and by indirect genetic effects (IGE) of its group mates. In the presence of IGE, heritable variance and response to selection depend on size of the interaction group (group size), which can be modelled via a 'dilution' parameter (d) that measures the magnitude of IGE as a function of group size. However, little is known about the estimability of d and the precision of its estimate. Our aim was to investigate how precisely d can be estimated and what determines this precision.

Methods: We simulated data with different group sizes and estimated d using a mixed model that included IGE and d. Schemes included various average group sizes (4, 6, and 8), variation in group size (coefficient of variation (CV) ranging from 0.125 to 1.010), and three values of d (0, 0.5, and 1). A design in which individuals were randomly allocated to groups was used for all schemes and a design with two families per group was used for some schemes. Parameters were estimated using restricted maximum likelihood (REML). Bias and precision of estimates were used to assess their statistical quality.

Results: The dilution parameter of IGE can be estimated for simulated data with variation in group size. For all schemes, the length of confidence intervals ranged from 0.114 to 0.927 for d, from 0.149 to 0.198 for variance of DGE, from 0.011 to 0.086 for variance of IGE, and from 0.310 to 0.557 for genetic correlation between DGE and IGE. To estimate d, schemes with groups composed of two families performed slightly better than schemes with randomly composed groups.

Conclusions: Dilution of IGE was estimable, and in general its estimation was more precise when CV of group size was larger. All estimated parameters were unbiased. Estimation of dilution of IGE allows the contribution of direct and indirect variance components to heritable variance to be quantified in relation to group size and, thus, it could improve prediction of the expected response to selection in environments with group sizes that differ from the average size.