Revisiting the Böcher-modified Raunkiær method for estimating the frequency of plant species

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Highlights

  • A framework for analyzing data sampled by the Böcher-modified Raunkiær method

  • Absence–presence data in increasingly large circles, centered on the same point

  • The original data sampled by Böcher in 1935 is reanalyzed.

Abstract

The frequency of plant species in a plot of a certain area was introduced as a species abundance measure by Raunkiær in 1910. One drawback of the method is that plots with a relatively small area are useful for estimating the frequency of dominant plants, whereas plots with a relatively large area are more useful for estimating the frequency of infrequently observed plant species. Consequently, Böcher suggested modifying the method by using a set of increasingly large circles, centered on the same point, and recording the smallest circle where the species is observed. The aim of this study is to provide a statistical framework for analyzing data sampled by the Böcher-modified Raunkiær method in such a way that the results are comparable to the results obtained when using a grid frame with many subplots. In order to demonstrate the suggested statistical framework, the original data sampled by Böcher in 1935 is reanalyzed. Finally, it is argued that the Böcher-modified Raunkiær method in some ways is a superior method for measuring plant occurrence probabilities compared to the typically used grid frame.

Introduction

Generally, it is an important and often performed task in basic and applied plant ecological research to describe and compare plant abundance among different plant communities, among different treatments, through time, or along environmental gradients. A classic and often used measure of plant abundance is the probability of occurrence or the frequency with which the plant is observed within randomly positioned plots (Raunkiær, 1910). Raunkiær (1910) examined the effect of varying the area of the plots and found that the area of the plot had an important effect on the estimated frequencies, but also that this area effect depended on the species. Generally, plots with a relatively small area were useful for estimating the frequency of dominant plants, whereas plots with a relatively large area were more useful for estimating the frequency of infrequently observed plant species. Consequently, Böcher (1935) suggested modifying the method by using a set of increasingly large circles, centered on the same point, and recording the smallest circle where the species is observed (Fig. 1a). For example, if a set of three circles is used and the species is absent from the smallest circle, but present in the second-smallest circle, then this second circle is recorded. Naturally, the species will also be present in the largest circles and there is no need to record this.

Böcher, who was an outstanding empirical plant ecologist, had an important insight that the use of several circles with different areas would lead to a better description of the plant community than the traditionally used method with a single circle (Raunkiær, 1910), since the frequency of both dominant and infrequently observed plant species would be measured effectively. However, it was a problem that the obtained data were only ordinal, i.e. there was no method of comparing an observation in the smallest circle with an observation in the second-smallest circle in a quantitative sense. This means that you cannot calculate e.g. the mean or variance of the frequency data, and consequently, Böcher (1935) summarized his results by the number of plants he observed in the different circles and a rather lengthy verbal account.

Another important aspect of measuring plant abundance in natural communities is that many plant species have an aggregated spatial pattern due to e.g. the size of the plant, clonal growth, or limited seed dispersal (Chen et al., 2006, Chen et al., 2008, Herben et al., 2000, Pacala and Levin, 1997, Stoll and Weiner, 2000), and as noted by both Raunkiær (1910) and Böcher (1935), such spatial aggregation of the plants has a profound influence on the estimated frequencies, but neither author had the mathematical tools to address the problem in a general and quantitative way.

The Böcher-modified Raunkiær method has been used in Arctic research. For example, in permanently positioned vegetation plots along a transect from the sea level to the peak of Aucellabjerg at 1040 m in Zackenberg, Greenland (Fredskild and Mogensen, 1979), and in permanently positioned plots with herbivore exclosures in sheep farming districts in South Greenland (Feilberg, 1997). However, probably because the method only generated ordinal data and the original description of the method was written in Danish (Böcher, 1935), the method, as far as I know, has not been widely employed. Instead plant ecologists typically have used a grid frame (Fig. 1b) made of metal and recorded presence data in each of the small subplots. The advantage of using a grid frame with many subplots is that it is possible to summarize the obtained count data with e.g. the mean frequency of occurrence and make statistical inferences.

In this study, I will show how to analyze the data of the Böcher modified method and get the same type of results as when using a grid frame (Fig. 1). Furthermore, I will argue that the Böcher modified method i) is more effective than the typically used grid frame, ii) allows for the measurement of the spatial aggregation of plant species at the site level, and iii) is much easier to use in remote areas, since the only needed equipment is a rod and a string (Böcher, 1935). More specifically, the aim of the study is to provide a statistical framework for analyzing data sampled by the Böcher-modified Raunkiær method. The chosen strategy is to use the frequency data of the differently-sized circles to get information on the probability of observing the species in a subplot with an area equal to the smallest circle (Fig. 1). The effect of the within-site spatial aggregation on the frequency data will be modeled using the beta-distribution that previously has been used for modeling plant cover data (e.g. Chen et al., 2006, Chen et al., 2008, Damgaard, 2012). In order to demonstrate the suggested statistical framework, the original data sampled by Böcher in 1935 is reanalyzed.

Section snippets

Böcher's data

Böcher (1935) used the modified Raunkiær method in 20 plots of a short willow shrub community near Angmagssalik in Eastern Greenland using four circles with areas 0.01 m2, 0.03 m2, 0.06 m2, and 0.10 m2. Böcher (1935) denoted the presence in the smallest circle by four, the presence in the second-smallest circle by three, etc. (Table 1).

The distribution of frequency data in the Böcher-modified Raunkiær method

In order to generalize the described method to any number of circles of any size, the set of circles used in the specific Böcher-modified Raunkiær method that need

Results and discussion

The measurement of interest, i.e. the probability of observing the species in a subplot with an area equal to the smallest circle, ν, depends on both the mean probability p and the intra-plot correlation parameter δ at the site, and these two parameters are assumed to be sufficient statistics for modeling the species frequency at a site according to the beta distribution (Eq. (1)). This assumption is corroborated by the circumstance that the same beta distribution successfully has been used to

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