Modelling growth patterns of bird species using non-linear mixed effects models

Master Thesis


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University of Cape Town

The analysis of growth data is important as it allows us to assess how fast things grow and determine various factors that have impact on their growth. In the current study, growth measurements on body features (body mass, wing length, head length, bill (culmen) length, foot length, and tarsus length) for Grey-headed Gulls populating Bonaero Park and Modderfontein Pan in Gauteng province, South Africa, and for Swift Terns on Robben Island were taken. Different methods such as polynomial regressions, non-parametric models and non-linear mixed effects models have been used to fit models to growth data. In recent years, non-linear mixed effects models have become an important tool for growth models. We have fitted univariate inverse exponential, Gompertz, logistic, and Richards non-linear mixed effects models to each of the six body features. We have modeled these six features simultaneously by adding a categorical covariate, which distinguishes between different features, to the model. This approach allows for straightforward comparison of growth between the different body features. In growth studies, the knowledge of the age of each individual is an essential information for growth analysis. For Swift Terns, the exact age of most chicks was unknown, but a small portion of the sample was followed from nestling up to the end of the study period. For chicks with unknown age, we estimated age by fitting the growth curve, obtained from birds with known age, to the mass measurements of the chick with unknown age. It was found that the logistic models were most appropriate to describe the growth of body mass and wing length while the Gompertz models provided best fits for bill, tarsus, head and foot for Grey-headed Gulls. For Swift Terns, the inverse exponential model provided the best univariate fit for four of six features. The logistic model, with a variance function increasing as a power of fitted values, with a different power for each feature and autoregressive correlation structure for within bird errors with errors from different features within the same subject assumed to be independent, gave the best model to describe the growth of all body features taken simultaneously for both Grey-headed Gull and Swift Tern data. It was shown that growth of Grey-headed Gull and Swift Tern chicks occurs in the following order (foot, body mass, tarsus)-(bill, head)-( wing) and (tarsus, foot)-(body mass, bill, head)-(wing) , respectively.

Includes bibliographical references.