PHYSIOLOGICAL ECOLOGY - ORIGINAL PAPER Statistical analysis of structural compensatory growth: how can we reduce the rate of false detection? Alfredo G. Nicieza Æ David A ´ lvarez Received: 30 July 2008 / Accepted: 3 October 2008 / Published online: 31 October 2008 Ó Springer-Verlag 2008 Abstract Compensatory growth (CG) is a key issue in work aiming at a full understanding of the adaptive sig- nificance 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 com- parison 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 experi- mental 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. Keywords Asymptotic growth  Asynchronous control  Longitudinal data  Size dependence  Type I error Introduction Adaptive evolution is expected to have led to the optimi- zation of individual growth rates. This expectation is based on the common observation that there are both costs and benefits associated with rapid growth (Mangel and Munch 2005), and that their balance can determine the strength of selection on growth rates. The two-sided relationship between growth rate and fitness provides a conceptual basis for the idea of compensatory growth (CG) within the wider framework of the evolution of flexible growth strategies (Sibly et al. 1985). The term ‘‘compensatory growth’’ has been used to describe both the pattern and the process by Communicated by Marc Mangel. Electronic supplementary material The online version of this article (doi:10.1007/s00442-008-1194-8) contains supplementary material, which is available to authorized users. A. G. Nicieza (&)  D. A ´ lvarez Unidad de Ecologı ´a, Departamento de Biologı ´a de Organismos y Sistemas, Universidad de Oviedo, 33006 Oviedo, Spain e-mail: agnic@uniovi.es; nicieza@innova.uniovi.es A. G. Nicieza  D. A ´ lvarez Instituto Canta ´brico de Biodiversidad (ICAB), CSIC-Universidad de Oviedo-Principado de Asturias, 33006 Oviedo, Spain 123 Oecologia (2009) 159:27–39 DOI 10.1007/s00442-008-1194-8