A Comparison of Variability in Two Cassin’s Auklet <i>(Ptychoramphus aleuticus)</i> Colonies Using Spline-based Nonparametric Models

Abstract

While variability in the reproductive performance of a population over time is a familiar and useful concept to ecologists, it can be difficult to capture mathematically. Commonly used ecological variability statistics, such as the standard deviation of the logarithm and coefficient of variation, discard the time-ordering of observations and consider only the unordered response variable values. We used a relatively new methodology, the cubic regression spline (a flexible curve fitted to a scatterplot of data), both to illustrate trends in reproductive performance over time and to explore the utility of the cubic regression spline roughness penalty (J) as a statistic for measuring variability while retaining time-ordering information. We concluded that although J measures variability in a mathematical sense, it can be inappropriate in a population ecology context because of sensitivity to small-scale fluctuations. To illustrate our methodology, we used the CRS approach in an analysis of historical data from two Cassin’s Auklet colonies located on Frederick and Triangle Islands in coastal BC, developing a model for the annual mean nestling growth rate on each island over seven contiguous years. Model selection indicated a complex (nonlinear) trend in growth rate on both islands. We report higher variability in the resident bird population of Triangle Island than Frederick Island, based on a comparison of the fitted curves, and the values of the coefficient of variation and population variability summary statistics.