The identification of patterns is a first step in finding rules governing systems. Patterns can be found in biotic space, but also in environmental, spatial and temporal (Section 2.3.2). As a next step in the investigation of ecosystems, spaces are compared in search of common patterns. Clarke (1993), introducing this strategy to analysis of benthic communities, puts it as follows: 'Having allowed the community data to "tell its own story", its relationship to matching environmental data is examined by superimposing the values of each abiotic variable separately onto the biotic ordination.' Hence, when talking of 'joining' in this chapter I address various methods of comparison, such as superimposing, correlating, variance partitioning and so on. The simplest case of comparison is the univariate, where a vector expressing performance of a species is correlated with an environmental factor such as precipitation. However, even if a strong correlation is found, this will not allow straightforward conclusions, because plant species interact and the change in performance may not be directly related to an environmental factor, but caused by competition or facilitation from another species. The same holds among environmental factors: water uptake of plants, for example, depends on temperature, and an ecologically sound interpretation requires a simultaneous view of these two factors. Hence, rather than just pairwise correlating variables, the focus of this chapter is on the analysis of relationships between spaces - the biological, the ecological, the physical and the temporal (according to Section 2.3.2). There are methods relating single variables of one space to another space, and others correlating two or more entire spaces. An example for the comparison of two multivariate spaces is the analysis of contingency, where data from different spaces are classified and the resulting frequencies are compared in contingency tables. These are further analysed, agreement measured, tested and interpreted. And then there is constrained ordination, where variance is partitioned and that shared by two spaces is used for joint ordination, of vegetation and environmental data, for example. The spaces are usually vegetation and site data. Examples are shown in Section 7.5.
What does it mean if one finds common properties in patterns? It is a good reason to hypothesize that there exists a response in either direction; that is, an interaction. Typically, vegetation responds to environmental conditions, which play the role of independent - and vegetation the dependent - variables. In the ecological reality, the opposite can happen too. In a ruderal environment species composition can be a result of the seed bank and not so much of present site conditions. As time progresses, it is expected that a correlation between species composition and site factors will start to emerge, not only developing dependence, but also generating a temporal pattern. Although time processes are treated separately in Chapter 9, much of what is presented here applies to these as well.
Often occurring in spatio-temporal systems is autocorrelation. This is the phenomenon that any two observational vectors are more similar than expected if they occur in close neighbourhood, be it spatial or temporal. Thus, autocorrelation is the phenomenon of dependence across small distances. In vegetation data spatial autocorrelation is often a result of plant dispersal and for this reason it is of great ecological significance. As will be seen in the sequel, there are methods to identify true autocorrelation, whilst most other methods of correlation are hampered by this.
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