Shared spatial effects on quantitative genetic parameters

http://onlinelibrary.wiley.com/doi/10.1111/j.1558-5646.2012.01620.x/full

Linear mixed-effects models (LMMs) were conducted in ASReml3 (VSN International, Hemel Hempsted, UK; Gilmore et al. 2009). We used two techniques to incorporate spatial information into the models. First, we fitted average lifetime spatial coordinates as ordered row and column effects, fitted as additional random effects, with a covariance structure that assumed a first-order separable autoregressive processto account for spatial dependence (AR1 × AR1, Gilmour et al. 1997). Second, we incorporated information on home range overlap between individuals into the animal model by fitting a vector of shared home range effects as an additional random effect, with the corresponding covariance matrix , where S is the home range overlap matrix (the “S matrix”). For full details of how we incorporated spatial information into linear mixed models, please see File 2 in supporting information.