Are parametric models suitable for estimating avian growth rates?

Abstract

For many bird species, growth is negative or equivocal during development. Traditional, parametric growth curves assume growth follows a sigmoidal form with prescribed inflection points and is positive until asymptotic size. Accordingly, these curves will not accurately capture the variable, sometimes considerable, fluctuations in avian growth over the course of the trajectory. We evaluated the fit of three traditional growth curves (logistic, Gompertz, and von Bertalanffy) and a nonparametric spline estimator to simulated growth data of six different specified forms over a range of sample sizes. For all sample sizes, the spline best fit the simulated model that exhibited negative growth during a portion of the trajectory. The Gompertz curve was the most flexible for fitting simulated models that were strictly sigmoidal in form, yet the fit of the spline was comparable to that of the Gompertz curve as sample size increased. Importantly, confidence intervals for all of the fitted, traditional growth curves were wholly inaccurate, negating the apparent robustness of the Gompertz curve, while confidence intervals of the spline were acceptable. We further evaluated the fit of traditional growth curves and the spline to a large data set of wood thrush Hylocichla mustelina mass and wing chord observations. The spline fit the wood thrush data better than the traditional growth curves, produced estimates that did not differ from known observations, and described negative growth rates at relevant life history stages that were not detected by the growth curves. The common rationale for using parametric growth curves, which compress growth information into a few parameters, is to predict an expected size or growth rate at some age or to compare estimated growth with other published estimates. The suitability of these traditional growth curves may be compromised by several factors, however, including variability in the true growth trajectory. Nonparametric methods, such as the spline, provide a precise description of empirical growth yet do not produce such parameter estimates. Selection of a growth descriptor is best determined by the question being asked but may be constrained by inherent patterns in the growth data.

Advantages of nonlinear mixed models for fitting avian growth curves

“…Previous methodological suggestions for studies of avian growth have largely focused on the appropriateness of different nonlinear functions (e.g. logistic, Gompertz, von Bertalanffy, and Richards functions; Starck and Ricklefs 1998, Brown et al 2007, Tjorve and Tjorve 2010), but have not discussed how these functions may be altered to test specific hypotheses. Our study illustrates how to incorporate parameters that estimate the difference between two groups in the growth rate constant, asymptotic mass, or inflection point.…”

Modelling avian growth with the Unified‐Richards: as exemplified by wader‐chick growth

“…Fitting such regression models to growth data yields a number of parameter values and derived measurements used to discuss this type of growth. Regression models fitted to avian growth data have traditionally been the three‐parameter logistic, Gompertz and von Bertalanffy models (Ricklefs , , Brown et al , Tjørve and Tjørve ), which all belong to the Richards‐model family, meaning that they are all special cases of the four‐parameter Richards model. This is so because any of the three‐parameter models can be achieved by fixing the exponent in a Richards model to a specific value (see Tjørve and Tjørve and for specifics).…”

“…Because this method relies on strict assumptions about the data, and growth data tend to violate these test assumptions, Jacknifed standard errors are sometimes calculated instead of the usual standard errors (Schekkerman et al 1998a, b, Pearce-Higgens and Yalden 2002, Ross et al 2012. Alternative curve-fitting methods used in bird-growth analysis include mixed models (Sofaer et al 2013, Aldredge 2015, nonparametric spline estimators (Aggrey 2002, Brown et al 2007, and robust regression (Tjørve et al 2007b(Tjørve et al , 2009b, which relax some of the assumptions about the data.…”

Trophic structure of arthropods in Starling nests matter to blood parasites and thereby to nestling development

“…Bauchau (1997) found that mite densities did not directly influence body mass in Pied Flycatchers (Ficedula hypoleuca) and suggested that parental quality may have been influencing nestling growth. Second, mite densities were estimated at day 23, and finding no correlation between day 10 nestling (Brown et al 2007). After reaching a maximum body mass, parents often reduce nestling provisioning to induce fledging, resulting in a decrease of body mass (Lemel 1989).…”