Threshold models improve estimates of molt parameters in datasets with small sample sizes

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College of Forest Resources and Environmental Science


The timing of events in birds' annual cycles is important to understanding life history evolution and response to global climate change. Molt timing is often measured as an index of the sum of grown feather proportion or mass within the primary flight feathers. The distribution of these molt data over time has proven difficult to model with standard linear models. The parameters of interest are at change points in model fit over time, and so least-squares regression models that assume molt is linear violate the assumption of even variance. This has led to the introduction of other nonparametric models to estimate molt parameters. Hinge models directly estimate changes in model fit and have been used in many systems to find change points in data distributions. Here, we apply a hinge model to molt timing, through the introduction of a double-hinge (DH) threshold model. We then examine its performance in comparison to current models using simulated and empirical data. Our results suggest that the Underhill-Zucchini (UZ) and Pimm models perform well under many circumstances and appear to outperform the DH model in datasets with high variance. The DH model outperforms the UZ model at low sample sizes of birds in active molt and shorter molt durations and provides more realistic confidence intervals at smaller sample sizes. The DH model provides a novel addition to the toolkit for estimating molt phenology, expanding the conditions under which molt can accurately be estimated. LAY SUMMARY Modeling molt timing has been difficult for researchers, especially when sample sizes of birds in active molt are small. Many species of birds in museum and banding databases are represented by relatively small sample sizes of birds in active molt. We apply a threshold model approach by developing a novel double-hinge threshold model that estimates onset and termination of molt. We test this new model and existing models by comparing performance on simulated datasets and find that the threshold model performs well with small sample sizes of birds in active molt. We also demonstrate the threshold model on empirical datasets and make this model available in an update to the existing R package cnhgpt.

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