**1. Introduction**

146 The Dynamical Processes of Biodiversity – Case Studies of Evolution and Spatial Distribution

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Patterns in vegetation can be expressed through the variation in species composition between plots, which has been termed 'beta-diversity' by Whittaker (1960, 1972). The general importance of beta-diversity has been emphasized in recent years (e.g. Gering et al., 2003; Olden et al., 2006; Sax and Gaines 2003; Srivastava 2002). However, even though Legendre et al., (2005) postulate that "beta diversity is a key concept for understanding the functioning of ecosystems, for the conservation of biodiversity, and for ecosystem management", implementation is still scarce compared to measures of species richness, alpha-diversity and its derivates (but see e.g. Condit et al., 2002; Kluth and Bruelheide, 2004; Pitkänen 2000).

However, the term 'beta-diversity' is not very clear and has multiple meanings (e.g. Jurasinski and Retzer, 2009; Lande, 1996; Qian et al., 2005). Most often 'beta-diversity' is defined as the compositional similarity between vegetation samples (sites, habitats, plots) expressed through (dis)similarity or distance measures. Generally, compositional similarity decreases with distance between plots. This phenomenon is called 'distance decay' of similarity (Tobler, 1970) and can be seen as a characteristic of all geographic systems. Nekola and White (1999) investigated species compositional similarity between fir and spruce stands across North America (Qian et al., 1998, 2005) and concluded that distance decay of similarity might be useful as a descriptor of diversity distribution as well as for the study of factors influencing the spatial structures of communities. The few comparative studies investigating distance decay for more than one group of organisms show that it heavily depends on organism groups as well as on the region under study (Ferrier et al., 1999; Oliver et al., 2004).

Although it is far from being well covered, the spatial change in species composition has received some more attention in recent years (Jurasinski and Retzer 2009). The phenomenon

Spatial Patterns of Phytodiversity - Assessing Vegetation Using (Dis) Similarity Measures 149

shall therefore be discussed in some detail in this chapter. Data on species composition is generally of multivariate character. Thus, hypothesis testing regarding the relation between species composition and its drivers can hardly be achieved with normal statistics. This led to a specific set of methods for vegetation ecologists (Jongman et al., 1987; Legendre & Legendre, 1998; Leyer and Wesche 2007; Sokal and Rohlf, 1981). The majority of this method is based on the calculation of biological resemblance and ecological distance in data space. Resemblance can be calculated with a wide range of coefficients and indices, measuring similarity, dissimilarity, proximity, distance, association or correlation (Orlóci 1978; Tamas

Compositional similarity measures differentiation diversity (Jurasinski and Retzer, 2009) and can be calculated with resemblance measures. These are available in two primary groups (Legendre and Legendre 1998): (1) Quantitative or distance indices are used to calculate the proximity of two samples in data space from quantitative measurements or abundance data. (2) Similarity/Dissimilarity measures can handle binary data as it is typically found in presence/absence data sets. There are a large number of different indices and coefficients available and comparative reviews can be found in Cheetham and Hazel (1969), Hubalek (1982), Janson and Vegelius (1981), Koleff et al., (2003), Shi (1993) and Wolda (1981). All binary similarity/dissimilarity measures are based on the same set of variables. Whether a coefficient measures similarity or dissimilarity depends on the implementation of the formula. However, most of them can easily be transformed from a similarity to a dissimilarity measure by calculating 1-S (with S being similarity, Legendre and Legendre, 1998; Shi, 1993). From some similarity coefficients a dissimilarity measure following the Euclidean metric can be obtained by calculating sqrt 1 − S instead (for details

Indices incorporating the species not present in both of the compared samples (d, see Fig. 1) are controversially discussed (e.g. Simple Matching by Sokal & Michener (1958) or the coefficient of Russel and Rao (1940)). Legendre and Legendre (1998) call these symmetrical (see Janson and Vegelius, 1981 for another definition of symmetry) and discuss the "doublezero problem" at the beginning of their chapter on similarity indices, because it "is so fundamental with ecological data" (Legendre and Legendre, 1998, p. 253): Species are supposed to have unimodal distributions along environmental gradients. If a species is absent from two compared sampling units (which is expressed by zeros in the species matrix), it is not discernable on which end of the gradient the both sites are with respect to a certain environmental parameter (Field, 1969). Both might be above the optimal niche value for that species, or both below, or on opposite tails of the gradient. Thus, the incorporation of unshared species (d) might lead to wrong conclusions when the relation between environment and species composition is under study (Legendre and Legendre, 1998). Additionally, Shi (1993) states that the status of d in similarity coefficients for paleoecological studies is not clear and cannot be assessed directly because of its great dependence on the less common taxa absent from both sites: "In palaeontology, absence of a taxon, particularly a rare one, may have been derived from differential preservation and/or sampling errors rather than some ecological factors". Finally, Field (1969) shall be cited as he found a very well fitting metaphor: "No marine ecologist would say that the intertidal and abyssal faunas were similar because both lacked the species found on the continental shelf".

et al., 2001).

**1.1.2 Measuring similarity** 

see Legendre and Legendre, 1998).

was utilized to evaluate the validity of the dispersal theory (Hubbell 2001) against niche concepts in the Neotropic: Chust et al., (2006), Condit et al., (2002), Duivenvoorden et al., (2002) and Ruokolainen et al., (2002), investigated distance decay in terra firme forests in Panama, Ecuador, and Peru, whereas Duivenvoorden et al., (1995), Ruokolainen et al., (1997), and Tuomisto et al., (2003) concentrated on rain forests in the Amazon basin. However, there are no studies in this regard in the Paleotropic. This hinders the overall generalization of the findings. The data set of the Eastern Ghats provides a unique opportunity as we can calculate distance decay rates in paleotropic ecosystems. Unfortunately there were only few environmental variables recorded. Furthermore these are categorical and assign relatively coarse classes to the plots.

Our aim is to develop a spatially explicit, widely applicable method to assess phytodiversity encompassing species richness, spatial and temporal heterogeneity, and functional diversity and to relate it to environmental conditions (including site conditions, disturbance regime and biological richness value). There is an urgent need for standardized and comparable data in order to detect changes of biodiversity. Such methods are required to be representative as well as pragmatic due to the simple fact that there is insufficient time to obtain complete data sets relating to temporal trends. If biodiversity is lost rapidly at the landscape level, frequent re-investigations have to be done in order to detect and analyze such changes. Thus, our objective was to provide a method that allows for the tracking of changes in biodiversity at the landscape scale. Here, we investigate the distance decay of compositional similarity whilst accounting for the change of the relationship between compositional similarity and its drivers with geographical distance between plots.

Steinitz et al., (2006) highlight that the studies are limited to which extent patterns of distance decay depend on the position along environmental gradients. Accordingly Jones et al., (2006) emphasize that explanatory power of variables might increase with the length of the gradient covered. Based on this, we hypothesize for the present study (Eastern Ghats part of Andhra Pradesh, India) as:

