Statistical analysis of structural compensatory growth: how can we reduce the rate of false detection?

Compensatory growth (CG) is a key issue in work aiming at a full understanding of the adaptive significance of growth plasticity and its carryover effects on life-history. The number of studies addressing evolutionary explanations for CG has increased rapidly during the last few years, but there has not been a parallel gain in our understanding of the methodological difficulties associated with the analysis of CG. We point out two features of growth that can have serious consequences for detecting CG: (1) size dependence of growth rates, which causes nonlinearity of growth trajectories, and; (2) temporal overlapping of structural growth and replenishment of energy reserves after a period of famine. We show that the currently used methods can be prone to spurious detection of CG (Type I error) under conditions of nonlinear growth, and therefore lead to the accumulation of a significant amount of false "empirical support." True and simulated growth data provided consistent results suggesting that a substantial fraction of the existing evidence for CG may be spurious. A small curvature in the growth trajectory can lead to spurious "detection" of CG when control and manipulated trajectories are compared over the same time interval (the "simultaneous" approach). We present a novel, robust method (the "asynchronous" approach) based on the accurate selection of control trajectories and comparison of control and treatment growth rates at different times. This method enables a reliable test to be performed for compensation under asymptotic growth. While the general results of our simulations do not support the application of conventional methods to the general case of nonlinear growth trajectories under the simultaneous approach, simple methods may prove valid if the experimental design allows for asynchronous comparisons. We advocate an alternative approach to deal with "safe" detection of CG that overcomes the problems associated with the occurrence of nonlinear and asymptotic growth, and provide recommendations for improving CG study designs.