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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
[41
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).