Figure 1.

Effect of Foxo^RNAi on the highly nutrition-sensitive, sigmoidal scaling relationship between body size and horn length. Foxo^RNAi induced horn growth in low nutrition, normally hornless males (a,b), while modestly reducing horn growth in some high nutrition, normally fully horned males (b,c). Comparing control-injected (grey) and knockdown individuals (red) using independently fitted four-parameter Hill equations followed by Welch's t-tests to compare parameter estimates revealed a significant difference in amplitude, inflection point, y-intercept, but not slope. Comparing AIC and R² values between sigmoidal and linear models for both treatment groups revealed a major difference in fit for control-injected individuals, indicating that a sigmoid model most accurately captures the scaling relationship between body size and horn length. By contrast, fitting a sigmoid model to Foxo^RNAi individuals only modestly improves fit compared with a simple linear regression, suggesting that Foxo^RNAi partly transforms body size–horn length allometry from strongly sigmoidal towards a more linear relationship. (Online version in colour.)