A frequent goal in ecology is to understand the relationships among biological organisms and their environment. Most field data are collected as scalar measurements, such that observations are recorded as a collection of datums. The observations are typically analyzed using classical univariate or multivariate statistical techniques. However, sensor technology makes available data that are comprised of continuous, or near continuous, series of observations taken across time or space. Such series of observations can be characterized as a mathematical function. Generalized additive models (GAMS) have been used to incorporate such series as a response variable in ecological analyses. In the GAMS approach, the series is incorporated as a non-parametric regression fit to the series. This presentation describes the use of functional data analysis, within which the GAMS analysis can be considered a subset.
Results/Conclusions
Functional data analysis allows considering one or more ecological response variables as functions, extending the GAMS viewpoint where one explanatory variable is a function. In functional data analysis the functions do not have to be “well behaved”, that is the analysis can accommodate abrupt changes in the data. Explanatory and/or response functional variables can be analyzed jointly with scalar values. Additionally, the first and higher derivatives of the functions can be calculated. Examination of the derivatives allows the consideration of the rate of change of the data series, which is an important aspect of the data that biological organisms may be responding to. Plotting derivatives against one another (a phase plane plot) allows detection of linear relationships between functions. Counterparts to well-known statistical approaches, such as the analysis of variance, principal component analysis, canonical correlation, and discriminant function analysis, are available for use in functional data analysis. In particular, functional principal component analysis yields components that themselves are functions. Such functions provide a baseline, so that significant departures from expected conditions can be detected. Examples of functional data analysis of water quality observations are presented to demonstrate the utility of this approach.