Detection of discontinuities in multivariate series

Detection of discontinuities in multivariate data series is a problem familiar to ecologists (Objective 4 in Section 12.2 and Table 12.2). For example, studies on Succession changes in species assemblages over time often refer to the concept of succession.

According to Margalef (1968), the theory of species succession within ecosystems plays the same role in ecology as does evolutionary theory in general biology.

The simplest way to approach the identification of discontinuities in multivariate series is by visual inspection of the curves depicting changes with time (or along a spatial direction) in the abundance of the various taxa or/and in the values of the environmental variables. For example, in Ecological application 8.9c, inspection of Fig. 8.21 was sufficient to determine that a succession, from diatoms to dinoflagellates, took place after the spring bloom. In most instances, however, simple visual examination of a set of curves does not allow one to unambiguously identify discontinuities in multivariate series. Numerical techniques must be used.

Methods of series analysis described in Sections 12.3 to 12.5 are not appropriate for detecting discontinuities in multivariate series, because the presence of discontinuities is not the same as periodicity in the data. Four types of methods are summarized here.

Instead of dividing multivariate series into subsets, Orloci (1981) proposed a multivariate method for identifying successional trends and separating them into monotonic and cyclic components. This method may be viewed as complementary to those described below.

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