Advantages of nonlinear mixed models for fitting avian growth curves

Abstract

Our understanding of avian growth rates can benefit from the use of two statistical approaches that explicitly model the sources of intraspecific variation. First, random effects can evaluate whether there are consistent differences between individuals and groups of siblings within a population, and also account for any lack of statistical independence among data points. Second, nonlinear fixed‐effect functions can be extended to test specific biological hypotheses of interest, such as for differences between groups or populations. We illustrate the advantages of these methods by using nonlinear mixed models to study variation in the growth trajectories of nestling orange‐crowned warblers Oreothylpis celata. Specifically, we quantify the sources of variation within populations, analyze the effects of asynchronous hatching, and test for a difference in the growth rates of populations in Alaska and California, which are at the northern and southern limits of the species’ breeding distribution. We found that growth rates did not consistently vary between nests and individuals within populations and were not affected by asynchronous hatching, but were higher in Alaska than in California. Our extensions of traditional methods allowed us to accurately quantify this difference between populations, which is consistent with life history theory but has rarely been demonstrated in previous comparisons of intraspecific passerine populations. The methods we present can be applied to any taxonomic group and adjusted to fit any nonlinear function, and we provide code and implementation advice to facilitate the use of this analytical framework in future studies.

Geographical and temporal variation in environmental conditions affects nestling growth but not immune function in a year-round breeding equatorial lark

“…These random factors accounted for the lack of independence between nest mates due to shared genetic background and parental care [57] and repeated measurements on individual nestlings. We used residuals of absolute nestling size (i.e., absolute mass, wing length, or tarsus length) and residuals of relative nestling size (i.e., % of adult mass, wing length, or adult tarsus length) in this comparison.…”

Sex roles, parental care and offspring growth in two contrasting coucal species

“…We used a nonlinear mixed model approach (function nlme in R package nlme, [31]) following Sofaer et al . [36]. Nestling ID was included as a random effect to model repeated measurements of individuals.…”

“…Nestling ID was included as a random effect to model repeated measurements of individuals. The nestling ID was nested within nest ID as another random effect to control for non-independence of nest-mates due to a common nest environment, genetic background, maternal effects and parental care [36]. As the starting values for the estimation of growth parameters, we used the parameter values for A , I and K (for each sex separately) from a previous study on black coucals [24].…”

Weather‐mediated decline in prey delivery rates causes food‐limitation in a top avian predator

“…The equation above shows only the fixed‐effects, but we also included random‐effects to account for repeated observations from the same nest and nestling. We tested for nest‐ and nestling‐level random‐effects on A, K and I and used AIC c to determine the most parsimonious random‐effects structure (Sofaer et al ). We evaluated the parameter estimates and statistical significance of Aw, Kw and Iw to determine whether nestling growth trajectories were significantly different across weather treatments.…”