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Methods to Analyse the Spatial Structure of Plant Communities Paul Braun, Heiko Balzter and Wolfgang Kohlerl Abstract. - Though many methodsfor analysing the spatial structure of plant communities are available, few of them deal with the problem of clonal plant growth or spatio-temporal dynamics. This paper shows two possibilities for quantifying the spatio-temporal dynamics of a plant population and a vegetation. It turns out, that fine shifts in plant populations or plant community structure can be discovered, if spatial and temporal dynamics are analysed simultaneously. Still there remains the need for improved or new methods.

INTRODUCTION Any knowledge about the spatial distribution of a plant population allows to draw conclusions on predominant biotic or abiotic factors. This in turn enables us to better predict the population dynamics of a specific plant population or even a vegetation. If discrete objects/individual plants are identifiable, common methods of quantitative ecology are used to further process the data (Greig-Smith 1983, Elliott 1971, Kershaw 1978, Upton and Fingleton 1990, Vandermeer 1981). These methods can be grouped as either aggregation or distance methods. While aggregation methods count individuals (e.g. Variance to Mean Ratio, Morisita Index), distance methods (e.g. Nearest Neighbour Index, L-Plot) utilize inter-plant distances to conclude, whether plants are randomly, clustered or regularly dispersed. When plants no longer can be assigned to one point, as is the case with clonal plants or vegetations, the above mentioned methods are less useful to describe spatial dynamics of populations. In vegetation science different procedures are used to quantify the proportions of species in a plant community, where discrete objects cannot be counted, e.g. Braun-Blanquet-, Quadrat-, Point-Quadrat-Method. Depending on the type of data, various methods can be applied to detect spatial structures. The Point-QuadratMethod provides a good base to apply a Moving Window Algorithm (Balzter et al. 1995). l~ustus-~iebig-~niversity, Dep. of Biometry and Population Genetics, Ludwigstr. 27, 0-35390 Giessen, Federal Republic of Germany; email gh80@agrar. uni-giessen.de

THE SPATIO-TEMPORAL DYNAMICS OF A THISTLE-POPULATION (CZRSZUMARVENSE (L.) SCOPOLI). After mapping plant populations on a recultivated area close to Giessen in 1991, we used these data to examine the usefulness of various aggregation and distance methods to quantify the spatial distribution of plant populations (Braun and Lachnit 1993, Braun and Lachnit 1994). We found the Nearest Neighbour Index (R) to be a suitable statistic for describing spatial and temporal changes in plant populations of discrete objects. R depends on data about the distance of each plant to its nearest neighbour. As under field conditions this information may not easily be obtained, we mapped the whole plant population (C. arvense) in a 2x2 m plot. With these coordinates the average distance, rM,of all individual plants to its nearest neighbour had been calculated and normalized by the expected nearest neighbour distance, r,. This is expressed formally by

where R is the ratio between the measured average nearest neighbour distance r~ and the expected nearest neighbour distance r~ (i.e. random distribution of individual plants in the population). The value of rMis obtained by

where ri is the distance of plant i to its nearest neighbour and N is the population size. The expected value r~ is defined as with u = N / A Here A stands for the area of the mapped plot. R close to 1 indicates randomness, R < 1 indicates a clustered and R > 1 indicates a regularly dispersed plant population. To test the significance of R, Clark and Evans (1954) proposed the following test statistic: CE=R/oE,

where

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CE is standardnormally distributed and can be tested by z-values. For six different sampling dates in 1991 we calculated R. In Figure 1 the dynamics of the R values for the thistle-population plot is shown.

days after 1.I.I991 Figure 1. - Spatial (Nearest Neighbour Index) and temporal (population size) dynamics of a thistle-population in 1991. Sampling dates were: 25.3., 17.4., 8 . 5 , 5.6., 15.7. and 19.9.1991.

The population size (measured by N) stays steady except for a temporary seasonal increase. This population dynamics is quite usual for natural populations in central Europe. Our data suggest a decrease in clustering of the thistle-population during the year. It seems that the thistle-population spreads, although it does not increase in number. This could be due to competition, because grouped thistle plants experienced stronger competition than single plants. The observed loss in aggregation would not have been detected by only looking at the population dynamics.

THE SPATIO-TEMPORAL DYNAMICS OF' A MEADOW VEGETATION (Lolio-Cynosureturn). In the continuous case, i.e. when plants are not viewed as single points, aggregation and distance methods are not efficient. We therefore recorded an area by the Point-Quadrat-Method (PQM) and processed these raw data with a Moving Window Algorithm (MWA). Our investigation was conducted on a meadow in Giessen. Except for the centre, which remained unrnown all the time, the meadow was cut up to ten times a year.

This led to an association of L o 1i o - Cynosure t u m on the outer part of the meadow (Figure 2). Whereas in the unmown centre only a class of Molinio-Arr h e n a t h e r e tea could be observed (Oberdorfer 1990).

Orchard

Beech Hedge Figure 2. - Investigated meadow in Giessen (630 m2). The whole area is divided in 120 subplots, which were sampled every three months. The central part remained unmown (72 m2). The scientific name for thuja is Thuja occidentalis and for beech Carpinus betulus.

As shown in Figure 2 the whole area was divided into 120 subplots. Inside of each subplot a vegetation sample was taken with a point quadrat frame (three needles, 0 1 mrn, each 30 cm apart). A vegetation sample means, that all contacts of plant species with any of the three needles in one frame were recorded. Four subplots or one window half yielded a multivariate vector, where each variable contained the mean number of contacts that one plant species had with any of the needles. To compare two successive years, the vegetation data of the same window half, but for two successive years were used. These two window halfs - a window - represented two multivariate vectors for which the Squared Euclidian Distance (SED) was calculated:

Variables n and w denote the number and size of the window, respectively. The total species number is s. Index A is the window half of the first year and B the window half of the second year. An SED value of zero would mean that no vegetation change has occured. High SED values indicate large vegetation change between the years. In our example we moved the window stepwise, that means one subplot, from left to right (Fig. 2). Thus the window stretched over two years but was moved in space. For one row this gave 11 values. After finishing one row the procedure continued with the next row. Thus the vegetation change between years is described by 11x9 points, where each value represents a window comparing two years. Figure 3 shows the vegetation change from 1993 to 1994.

Figure 3. - Plot of the SED's between the vegetation from 14.5.1993 and 20.6.1994. In the background the orchard is located, on the left hand stretches the lane, etc. (see Fig. 2).

There are fluctuations in the vegetation composition, but there is no obvious change in vegetation. To get an idea on the importance of peaks, we compared the SED values of 1993194 (Fig. 3) with the corresponding values for 1994195. (Figure 4).