Computer assisted vegetation analysis

A review of the ordination and classification methods is done in the light of the interpretation of the results. The iterative process of sampling and data analysis at different hierarchical levels is suggested as a necessary exercise to understand vegetation patterns. 1. The Medium: its spaces and description Vegetation is a complex system with states determined by all the interactions between living organisms (microscopic and macroscopic) and the chemical-physical environmental factors. Both are changing in time according to cyclic and/or non-cyclic trends, therefore the vegetation has to be seen under a dynamic system perspective. As suggested by Roberts (1987a) vegetation and environmental dynamics can be modelled as trajectories in the space defined by the vegetation variables (intrinsic) and in the space defined by chemical-physical variables (extrinsic). However, the system is unique and models should be developed within one space only. This space, which may be called ecological space, is defined by all the ecological factors. In this space every individual has its trajectory, so a population will have a set of trajectories, and a community existing in a specific area will have a set of the sets of trajectories of its populations. The community will endure in the site as long as the trajectories of its populations and the environmental components manage to stay within the hypervolume of its potential niche (Feoli, Ganis and Zerihun 1989). One of the main aims of plant ecology is to describe and to model the ecological space. It is a latent space of which only some aspects are illuminated by our traditional, mechanistic Galilean approach to science. However we must be conscious of this and we should develop methods of sampling and data analysis which will be able to reveal more fully the properties of this space and will allow interpretations in a way consistent with the nature of this space. In doing this we follow an approach that was defined by Goodall (1970) as descriptive. The 3 descriptive approach have a prominent role in being able to reach the level from which the planning of experiments and formulation of models may proceed. According to the descriptive approach vegetation is sampled and described as it appears in space and time. The observational unit is the releve. This is a vector or a matrix with elements which are records of the state of the vegetation and environment within a given area. The aims for which releves are taken may be many, however they can be categorized as concerned either with compositional comparisons of the vegetation in space and/or time on a floristic, structural, functional, biochemical, historical, geographic, evolutionary or reproductive basis, or with discovering spatial patterns and pattern connections inside or on the edges of community types. 2. Characters: states, types, measurement A character to be useful must have two or more states. There are many characters that may be used to describe a vegetation stand. The choice depends on the aim for which vegetation is studied. Intrinsic and extrinsic characters are recognized at the level of individual organism, population, and community. For example, height is a character that we record for an individual. Nutrients, pH, etc. can be sampled near individuals or randomly through the community. Cover, biomass, density (the number of individuals per unit area) or frequency (occupancy rate or count) are characters recorded for a population. Diversity, stratification (spatial or functional), spatial heterogeneity, evapotranspiration, etc. are community level characteristic. There is a fundamental uniqueness to E. Feoli and L. Orlaei (eds.), Computer Assisted Vegetation Analysis, 3-13. © 1991 Kluwer Academic Publishers. 4 The Properties and Interpretation of Observations in Vegetation Study / Part I population and community characteristics. By this we can delineate populations and communities based on the recognition of equivalence. This is typification, a key process in the study of vegetation. The type is a key concept without which science would collapse. The description of vegetation is accomplished by the measurement of its component organismal populations, individually or as a groups recognized according to their contribution to vegetation structure. Populations are normally typified as different species. The typification is mainly by conservative, reproductive characters which have little or no environment sensitivity. Adding weight to species as 'names' in a list is useful only if the interest is with the floristic aspects. If the aim is ecological, the vegetation description has to utilize environmentally sensitive characters, and the typification of plants have to be based on such characters. A set of characters chosen and character states specified, similar combinations of character states is the basis of the typification of plants as character set types (CST: Orl6ci and Orl6ci 1985). These mayor may not coincide with species. As a matter of fact species may be grouped into character set types on the basis of a selected number of characters and numerical methods (Feoli and Scimone 1984, Lausi and Nimis 1986, Lausi et al. 1989). Weight can be given to the character set types in a releve by estimation of the population quantities, such as cover, density, frequency, etc. (Orl6ci and Kenkel 1985). Only recently (Orl6ci and Orl6ci 1985, Orl6ci et al. 1986) has it been proposed that the releve record should be comprised of a score matrix: Character Character State Weight in set type 2 m releve j I Xljl Xlj2 Xljrn Xlj 2 X2jl X2j2 X2jrn X2j p Xpjl Xpj2 Xpjrn Xpj In a vector, such as the last column, the reieve elements describe only the weights of the character set types; this carries no information about relationships. In a score matrix, the releve elements specify the character states in addition to the weights of the character set types; these carry information about CST relationships. The character states may be nested to form a hierarchy (Feoli 1984, Orl6ci and Orl6ci 1985, Orl6ci and Kenkel 1985, Orl6ci et al. 1986) or left as independent data dimensions. The latter is typical in the sequential schemes (e.g. Knight and Louks 1969, Werger and Sprangers 1982) whose limitations were attributed to overlapping taxa and inadvertant weighting (see Orl6ci 1988a). There are implications of these for the type of information that data analysis can reveal. Clearly when the releve is a vector, the information which lies with the character states in imposing a unique order on the elements will not enter into the analysis and the relationships investigated are defined by the comparison of vectors. When the releve is a score matrix, the relationships between the characters and character set types is implicit and comparisons of reieves will have a richer information base to be utilized (Orl6ci 1988, 1990). For example, in the case of four binary characters, a reieve would be represented by the graph in Fig. 1. In this, the levels represent characters, the noda character states and the pathways, ++++, +++-, ++-+, etc., the character set types. The graph represents a multidimensional contingency table, since each nodum is a combination of character states to which corresponds a numerical value given by the sum of the values of the previous levels. When the characters are ordered in some hierarchical way a graph is automatically established, however, not all the branches of the graph may be realized in a releve. Each set of characters gives rise to a potential graph for each hierarchical order in which the characters may be arranged. Fig. 1 presents two score matrices and their graphs superimposed on the potential graph with origin in the hierarchical order A, B, C, D. This is a new way of conceiving releves and the methodology of the analysis has been developed. Orl6ci and Orl6ci (1985) and Orl6ci et al. (1986) propose to compare the score matrices according to the hierarchy chosen for the characters. In this case the order will matter (Orl6ci 1991). However, the graph originating in a hierarchical order of the characters in the score matrices, can be conceived as a variable that counts the realized branches of the graphs. In this case for computing the similarity between score matrices the hierarchical order is not important. The simple Gower (1971) index or the more complex measure of Goodall (1964) can have utility. The data for the comparisons are arranged as in Table 1. Also a set of releves may be described by a score matrix and by a hierarchical graph summarizing the information of the separate score matrices and hierarchical graphs. In this case to each segment joining the noda in the possible hierarchical graph, a frequency value, absolute or relative, can be assigned. The score matrix concept and the hierarchical analysis are relevant not only for the study of compositional variation of vegetation but also in studies directed to spatial pattern analysis where the spatial distribution of character set types would be of interest. An example of The Properties and Interpretation of Observations in Vegetation Study 5