The Contingency Periodogram: A Method of Identifying Rhythms in Series of Nonmetric Ecological Data

(1) Analysis of series, in time or space is a subject of growing interest in ecology, but the methods hitherto available (correlogram, periodogram, spectral analysis) were restricted to the analysis of metric (quantitative) data. Many ecological series, however, are of (or contain) essential variables which are qualitative (categorical), and many quantitative variables are more efficiently sampled as rank-ordered (ordinal) variables. There are no numerical methods to analyse series of nonmetric data. (2) In this paper, the periodogram of Whittaker & Robinson is generalized to qualitative data series, using information theoretic measures. Algorithms are also described to partition rank-ordered variables into classes, in order to analyse them using the contingency periodogram. (3) The validity of the contingency periodogram is assessed by comparing its results with those of the periodogram of Schuster, using two series of metric data. Both methods identify the same periods for a series of artificial data, and also for serial measurements of the photosynthetic capacity of estuarine phytoplankton, even when these metric data are reduced to a small number of states prior to contingency periodogram analysis. (4) The contingency periodogram is also used to analyse a multivariate (multi-species) phytoplankton series. The multivariate data are reduced to a single multi-state qualitative variate by clustering the samples. At least one of the periods revealed is surprising, but can be explained.