Growth curve analysis of birds: the Richards model and procedural problems

Abstract

Four sigmoid growth curve models for birds were compared using the daily body masses and primary-feather lengths of 35 nestling tree swallows (Tachycineta bicolor). The Richards model was superior to the von Bertalanffy, Gompertz, and logistic models for body mass, but not for primary-feather length. The latter models have fixed growth forms and are special cases of the flexible Richards model. Owing to parameter correlations, the Richards model was very sensitive to the starting parameter values for the numerical computer fitting routines. The lack of data leading up to the asymptote made it difficult to calculate good starting values for primary-feather length. None of the models tested was completely satisfactory for primary-feather length, as indicated by nonrandomly distributed residuals over time. The log transformation was appropriate for body mass. It homogenized the residual variances and increased the explained percentage of variation. The explained percentage of variation was a useful selection criterion for the best-fitting model, especially since it was directly related to randomness in the distribution of the residuals and homogeneity of residual variances. However, even percentages of variation exceeding 99.5%, did not necessarily indicate an excellent fit. The Richards model did not yield more model parameters for growth curve analysis, because the shape parameter and the growth rate constant were almost perfectly correlated.