To epigenetic regulation may either too weak to overcome

To estimate the model parameters, data from the metamorphosis assays were converted to percentage metamorphosis success and analyses were conducted using the R statistical platform. In this study we characterised the combined effect of copper and temperature on metamorphosis by fitting Equation 1 to metamorphosis versus Cu concentration data at different temperatures and then analysing how the fitted parameters of the equation changed with temperature. First, we used a nonlinear regression routine to fit Equation 1 to the metamorphosis versus copper data to quantify Mx, EC50 and w at each temperature. Uncertainty in parameter estimates was incorporated using Monte Carlo simulation. To do this we iterated the model 1000 times using parameters randomly drawn from multivariate normal distributions. These distributions were based on the variancecovariance matrices of the parameters describing the relationship between metamorphosis success and Cu concentration at each temperature. In summary, we randomly generated 1000 sets of parameter estimates for each metamorphosis versus Cu relationship, re-fit Equation 2 to each parameter set, and then re-evaluated the fitted model. The simulations were based on uncertainty in the Cu relationship, rather than uncertainty in the parameter temperature relationship, because the former is large relative to the latter. Two approaches were used to determine whether there effects of temperature and Cu concentration were additive, synergistic or antagonistic. First a two-way fixed effects analysis of variance was performed on the larval metamorphosis data. In this analysis, a non-significant interaction term would demonstrate that the effects of temperature and Cu were additive whereas a significant interaction indicates the presence of a synergistic or antagonistic effect. Where an significant interaction was identified, we used an isobologram approach to determine whether the effects were synergistic or antagonistic.