Non-linear mixed effects models of leafminer growth

In this paper, the effects of two factors, leaf size and group size, on the performance of a leaf-mining insect, Antispila nysaefoliella (Lepidoptera: Heliozelidae) were examined by fitting non-linear mixed effects (nlme) models to mine expansion data. One of the benefits of using nlme models is that they allow for simultaneous fitting of both fixed and random effects of the factors of interest. The rate of mine expansion served as a proxy for larval performance because of its correlation with both feeding activity and growth rate – where the more quickly that a larva feeds or grows, the more it is expected to consume per unit time, and thus, the more quickly its mine will expand. Leaf quality is expected to increase both feeding and growth rates; and group size (number of larvae per leaf) is expected to influence competitive interactions by increasing the feeding rates of some larvae (i.e. the better competitors) or reduce the total consumption of others (i.e. the weaker competitors). To investigate these interactions, the Gompertz and von Bertalanffy growth equations were fitted to data on the sizes of individual leaf mines measured throughout the mining (larval) stage. Linear and non-linear associations of each factor with model parameters were then evaluated using a hierarchical testing procedure to determine: (1) whether inclusion of the factor produced a better-fit model, and (2) if it did, the form of the relationship (e.g. linear or nonlinear). The analyses showed that leaf size had a significant linear and positive relationship and group size had a significant quadratic relationship (positive, then gradual negative) with larval performance.