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Biodiversity indicators: graphical techniques, smoothing and searching for what makes relationships work

Biodiversity indicators: graphical techniques, smoothing and searching for what makes... Knowledge of the distribution of biodiversity remains poor. This situation might more readily be resolved If the species richness of certain groups of organisms indicated the richness of other, less well known groups. A spatially explicit exploration of the pattern in the predictive power (hat one taxon (a potential 'indicator group') might have for the diversity of another has been performed previously. In this paper we respond to three important points that have been raised. First, we describe an additional graphical technique for visualising spatial aspects of indicator relationships. Second, we examine some of the consequences of smoothing species richness data on observed indicator relationships. Third, we consider some of the factors that may contribute to strong indicator relationships. Prendergast and Eversham (1997) present a stimulating description of empirical tests of biodiversity indicators (taxa for which spatial variation in the number of species is strongly correlated with spatial variation in the number of species of other taxa). This is a subject of much current interest because of the challenge of finding cost-effective approaches to measuring the distribution of wholesale biodiversity (e,g. Gaston and Williams 1993, Kremen et al. 1993, Prendergast et al, 1993a. Reid et ai. 1993, Pearson 1994. Williams and Gaston 1994, Samways et al. 1995, Gaston 1996a. b, Williams and Humphries 1996), In this paper, we discuss three important points raised by Prendergast and Eversham (1997). First, they recognised the need to investigate spatial pattern in deviations from strong positive indicator relationships. We describe an additional graphical technique for visualising spatial aspects of indicator relationships. Second, Prendergast and Eversham (1997) base their analyses on smoothed values of species richness. There are valid reasons for such an approach, and we examine some of the consequences of taking it. Third, Prendergast and Eversham (1997) consider some of the factors which may contribute to strong indicator relationships. We examine the extent to which their conclusions deECOGRAPHY 21:5(1998) pend on the form of data analysis, and therefore how readily they generalise. None of the observations that we make are at direct odds with those made by Prendergast and Eversham (1997). who explicitly acknowledge the uncertainty surrounding the possible generality of some of their findings, Prendergast and Eversham (1997) chose to use the fauna of Britain to investigate indicator relationships because the region is fortunate in having some of the best species-based distribution data of any country in the world (Prendergast et al. 1993b, Anon. 1994. Lawton et al, 1994). These data result in major part from information collected by volunteer recorders and painstakingly collated by the Biological Records Centre (BRC: Harding and Sheail 1992) and by the British Trust for Ornithology {BTO: Gibbons et al, 1993). To provide an empirical framework for the comments we make, we have compared the same groups of particularly well recorded organisms in Britain as used by Prendergast and Eversham (1997). Our study uses 10 x 10 km grid cell data published by the BRC and the BTO for: 1) breeding birds from Gibbons et al, (1993), collected between 1988 and 1991 for 218 species; 2) dragonflics (including damselflies) from Merritt et al. (1996), collected between 1975 and 1990 for 37 species; and 3) butterflies from Heath et al. (1984), collected between 1970 and 1982 for 60 species. These data are not identical to those used by Prendergast and Eversham (1997), but are very similar (for our purposes the differences are not of significance). Colour overlays The principal theme of Prendergast and Eversham's (1997) paper is that 'there has been no spatially explicit exploration of the pattem in the predictive power which one taxon might have for the diversity of another 551 across the full range of diversities for both taxa" (p. 210). To address this issue, using each 10 x 10 km grid cell in turn across Britain (excluding those that were coastal or did not contain records for both taxa), and for smoothed species richness scores, ihey calculated the correlation coefficient between the species numbers of each of two taxa in this core cell and the 24 surrounding cells (i.e. equivalent to a 50 x 50 km region), plotting the correlation coefficient within the core cell. They then used a combined grey-scale and spot technique to plot neighbourhood (regional) correlation coefficients. In other words, the two richness dimensions are reduced to a single correlation dimension at the scoring stage, before proceeding lo the plotting stage. This approach shows how the strength of the indicator relationship varies across Britain among 50 x 50 km regions (although these coefficients are not strictly independent, because a particular cell usually contributes to the calculation of more than one correlation coefficient). It assumes that the only relationships of interest are linear, and that a simple correlation coefficient can reasonably typify any such relationship for comparative purposes (although in principle the approach could be applied to other measures). We use an alternative approach for exploring local and regional deviations from any overall (national) indicator relationship (Williams 1996a). The geographical pattern of deviations from any positive linear relationship between two groups of organisms can be visualised by overlaying the richness maps in two separate colours. Therefore, in contrast to Prendergast and Eversham's (1997) approach, we maintain the two richness dimensions as separate throughout the scoring and plotting stages. This two-dimensional graphical technique can be applied to comparisons between two sets of grid-cell scores for any kind of measure. Similar colour techniques have been used before in other contexts (reviewed by Brewer 1994), and Williams (1992) provides an example of its application to a three-dimen- sional plot for comparing different aspects of diversity and rarity. We divided the species richness scores for each group of organisms into ten classes, arranged between the maximum and minimum observed (non-zero) scores. This procedure is designed to reduce the effects of differences in absolute richness between groups. The richness classes for each group are arranged to give an even frequency distribution of observed richness scores (at least within the constraints imposed by tied scores, Williams 1996a). Given that the underlying frequency distribution of species richness scores is seldom uniform, this acts as a general pui-pose transformation of these data. Other methods of arranging species richness scores into classes could be employed (see the discussion of regression techniques below), although at least when using the WORLDMAP software the transformation effect can be assessed by switching from equal-frequency to equal-interval grouping of scores. At the plotting stage, using colour may be an efficient way to communicate large amounts of information quickly, although only for people who are not colour blind. The principle followed here (after Tufte 1990) is to reserve the most saturated colours for drawing attention to the most extreme values, in this case to strong deviations from an overall relationship. In keeping with this, background colours of the map are given undistracting low-saturation, near-greys. The information they convey is less important, but is still needed to contrast with the area scores. It would be possible to use a white background and to reverse the colour scale, using black for high shared scores and white for low shared scores, but this would cause problems for distinguishing low shared scores from areas with no data without resorting to complicated additional symbols. To plot the two sets of score classes on the same map, increasing species richness of one group is shown by an increasing intensity of green (Fig, la), and in- Fig. 1. A two-colour technique for exploring local and regional deviations from the overall (national) relationship between species-richness scores for two groups of organisms. Data for this and the following figures are published distribution records for 10 X 10 km arid cells Trom some of the best-recorded British groups; 1) 218 species of breeding birds recorded 1988-199! from Gibbons et al. (1993): 2) 37 species of dragonflies (including damselflies) recorded 1975 1990 from Merritl et al. (1996); and 3) 60 species of butterliies recorded 1970 1982 from Heath et ul (1984). Species richness is taken to be the sum of the number of species recorded within a grid cell. Smoothing of species-rich ness scores was done using neighbourhood medians among neighbourhoods of 9 or 21 cells. To compare the richness distribuiions between two groups, the species-riehness scores for each are arranged in ten classes between the maximum and minimum observed (non-zero) scores, so as to give an even frequency distribution of observed richness scores. Then a) increasing species richness of one group (butterflies) is plotted in increasing intensity of green, and b) increasing speeies richness of the other group (birds) is plotted in inereasing iniensiiy of blue (a matching intensity of red is added on the diagonal io provide neutral greys). Consequently, c) blaek grid cells correspond to low richness for both; white correspond to high richness for both; and shades of grey sliow intermediate and eovarying richness for both, so that d) linearly eovarying scores (birds plotted against identical bird data) lie on the diagonal of the colour key. In contrast, e) areas with highly satur"ated green cells show a relative excess of richness of one group over the other (butterflies over birds), and e) areas with highly saturated blue show a relative excess in the reverse direction (birds over butterflies). On these maps, a low saturation brown is used for ihe land area, to contrast with the eolour scale for seores. so that areas with no scores may be distinguished. Shetland has been drawn eloser to Scotland. Also shown are different approaches to selecting indicator groups: e) butterflies and insectivorous birds (Paridae [tits] + Sylviidae [warblers]) (green x blue); 0 Pieridae ('white' butterflies) and other (non-pierid) butterflies (green x biue): g) Lycaenidae ("blue' butterflies) and other butterflies (green x blue); h) Hesperiidae (skippers) and other butterflies (green x blue); i) Nymphalidae (fritillaries etc.) and other butterflies (green x blue). See Tables 1 and 2 for numbers of grid cells and correlation eoeffteients. ECOGRAPHY 21:5 (1998) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Ecography Wiley

Biodiversity indicators: graphical techniques, smoothing and searching for what makes relationships work

Williams, p. H.
Ecography , Volume 21 (5) – Oct 1, 1998
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Publisher
Wiley
Copyright
Copyright © 1998 Wiley Subscription Services, Inc., A Wiley Company
ISSN
0906-7590
eISSN
1600-0587
DOI
10.1111/j.1600-0587.1998.tb00447.x
Publisher site
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Abstract

Knowledge of the distribution of biodiversity remains poor. This situation might more readily be resolved If the species richness of certain groups of organisms indicated the richness of other, less well known groups. A spatially explicit exploration of the pattern in the predictive power (hat one taxon (a potential 'indicator group') might have for the diversity of another has been performed previously. In this paper we respond to three important points that have been raised. First, we describe an additional graphical technique for visualising spatial aspects of indicator relationships. Second, we examine some of the consequences of smoothing species richness data on observed indicator relationships. Third, we consider some of the factors that may contribute to strong indicator relationships. Prendergast and Eversham (1997) present a stimulating description of empirical tests of biodiversity indicators (taxa for which spatial variation in the number of species is strongly correlated with spatial variation in the number of species of other taxa). This is a subject of much current interest because of the challenge of finding cost-effective approaches to measuring the distribution of wholesale biodiversity (e,g. Gaston and Williams 1993, Kremen et al. 1993, Prendergast et al, 1993a. Reid et ai. 1993, Pearson 1994. Williams and Gaston 1994, Samways et al. 1995, Gaston 1996a. b, Williams and Humphries 1996), In this paper, we discuss three important points raised by Prendergast and Eversham (1997). First, they recognised the need to investigate spatial pattern in deviations from strong positive indicator relationships. We describe an additional graphical technique for visualising spatial aspects of indicator relationships. Second, Prendergast and Eversham (1997) base their analyses on smoothed values of species richness. There are valid reasons for such an approach, and we examine some of the consequences of taking it. Third, Prendergast and Eversham (1997) consider some of the factors which may contribute to strong indicator relationships. We examine the extent to which their conclusions deECOGRAPHY 21:5(1998) pend on the form of data analysis, and therefore how readily they generalise. None of the observations that we make are at direct odds with those made by Prendergast and Eversham (1997). who explicitly acknowledge the uncertainty surrounding the possible generality of some of their findings, Prendergast and Eversham (1997) chose to use the fauna of Britain to investigate indicator relationships because the region is fortunate in having some of the best species-based distribution data of any country in the world (Prendergast et al. 1993b, Anon. 1994. Lawton et al, 1994). These data result in major part from information collected by volunteer recorders and painstakingly collated by the Biological Records Centre (BRC: Harding and Sheail 1992) and by the British Trust for Ornithology {BTO: Gibbons et al, 1993). To provide an empirical framework for the comments we make, we have compared the same groups of particularly well recorded organisms in Britain as used by Prendergast and Eversham (1997). Our study uses 10 x 10 km grid cell data published by the BRC and the BTO for: 1) breeding birds from Gibbons et al, (1993), collected between 1988 and 1991 for 218 species; 2) dragonflics (including damselflies) from Merritt et al. (1996), collected between 1975 and 1990 for 37 species; and 3) butterflies from Heath et al. (1984), collected between 1970 and 1982 for 60 species. These data are not identical to those used by Prendergast and Eversham (1997), but are very similar (for our purposes the differences are not of significance). Colour overlays The principal theme of Prendergast and Eversham's (1997) paper is that 'there has been no spatially explicit exploration of the pattem in the predictive power which one taxon might have for the diversity of another 551 across the full range of diversities for both taxa" (p. 210). To address this issue, using each 10 x 10 km grid cell in turn across Britain (excluding those that were coastal or did not contain records for both taxa), and for smoothed species richness scores, ihey calculated the correlation coefficient between the species numbers of each of two taxa in this core cell and the 24 surrounding cells (i.e. equivalent to a 50 x 50 km region), plotting the correlation coefficient within the core cell. They then used a combined grey-scale and spot technique to plot neighbourhood (regional) correlation coefficients. In other words, the two richness dimensions are reduced to a single correlation dimension at the scoring stage, before proceeding lo the plotting stage. This approach shows how the strength of the indicator relationship varies across Britain among 50 x 50 km regions (although these coefficients are not strictly independent, because a particular cell usually contributes to the calculation of more than one correlation coefficient). It assumes that the only relationships of interest are linear, and that a simple correlation coefficient can reasonably typify any such relationship for comparative purposes (although in principle the approach could be applied to other measures). We use an alternative approach for exploring local and regional deviations from any overall (national) indicator relationship (Williams 1996a). The geographical pattern of deviations from any positive linear relationship between two groups of organisms can be visualised by overlaying the richness maps in two separate colours. Therefore, in contrast to Prendergast and Eversham's (1997) approach, we maintain the two richness dimensions as separate throughout the scoring and plotting stages. This two-dimensional graphical technique can be applied to comparisons between two sets of grid-cell scores for any kind of measure. Similar colour techniques have been used before in other contexts (reviewed by Brewer 1994), and Williams (1992) provides an example of its application to a three-dimen- sional plot for comparing different aspects of diversity and rarity. We divided the species richness scores for each group of organisms into ten classes, arranged between the maximum and minimum observed (non-zero) scores. This procedure is designed to reduce the effects of differences in absolute richness between groups. The richness classes for each group are arranged to give an even frequency distribution of observed richness scores (at least within the constraints imposed by tied scores, Williams 1996a). Given that the underlying frequency distribution of species richness scores is seldom uniform, this acts as a general pui-pose transformation of these data. Other methods of arranging species richness scores into classes could be employed (see the discussion of regression techniques below), although at least when using the WORLDMAP software the transformation effect can be assessed by switching from equal-frequency to equal-interval grouping of scores. At the plotting stage, using colour may be an efficient way to communicate large amounts of information quickly, although only for people who are not colour blind. The principle followed here (after Tufte 1990) is to reserve the most saturated colours for drawing attention to the most extreme values, in this case to strong deviations from an overall relationship. In keeping with this, background colours of the map are given undistracting low-saturation, near-greys. The information they convey is less important, but is still needed to contrast with the area scores. It would be possible to use a white background and to reverse the colour scale, using black for high shared scores and white for low shared scores, but this would cause problems for distinguishing low shared scores from areas with no data without resorting to complicated additional symbols. To plot the two sets of score classes on the same map, increasing species richness of one group is shown by an increasing intensity of green (Fig, la), and in- Fig. 1. A two-colour technique for exploring local and regional deviations from the overall (national) relationship between species-richness scores for two groups of organisms. Data for this and the following figures are published distribution records for 10 X 10 km arid cells Trom some of the best-recorded British groups; 1) 218 species of breeding birds recorded 1988-199! from Gibbons et al. (1993): 2) 37 species of dragonflies (including damselflies) recorded 1975 1990 from Merritl et al. (1996); and 3) 60 species of butterliies recorded 1970 1982 from Heath et ul (1984). Species richness is taken to be the sum of the number of species recorded within a grid cell. Smoothing of species-rich ness scores was done using neighbourhood medians among neighbourhoods of 9 or 21 cells. To compare the richness distribuiions between two groups, the species-riehness scores for each are arranged in ten classes between the maximum and minimum observed (non-zero) scores, so as to give an even frequency distribution of observed richness scores. Then a) increasing species richness of one group (butterflies) is plotted in increasing intensity of green, and b) increasing speeies richness of the other group (birds) is plotted in inereasing iniensiiy of blue (a matching intensity of red is added on the diagonal io provide neutral greys). Consequently, c) blaek grid cells correspond to low richness for both; white correspond to high richness for both; and shades of grey sliow intermediate and eovarying richness for both, so that d) linearly eovarying scores (birds plotted against identical bird data) lie on the diagonal of the colour key. In contrast, e) areas with highly satur"ated green cells show a relative excess of richness of one group over the other (butterflies over birds), and e) areas with highly saturated blue show a relative excess in the reverse direction (birds over butterflies). On these maps, a low saturation brown is used for ihe land area, to contrast with the eolour scale for seores. so that areas with no scores may be distinguished. Shetland has been drawn eloser to Scotland. Also shown are different approaches to selecting indicator groups: e) butterflies and insectivorous birds (Paridae [tits] + Sylviidae [warblers]) (green x blue); 0 Pieridae ('white' butterflies) and other (non-pierid) butterflies (green x biue): g) Lycaenidae ("blue' butterflies) and other butterflies (green x blue); h) Hesperiidae (skippers) and other butterflies (green x blue); i) Nymphalidae (fritillaries etc.) and other butterflies (green x blue). See Tables 1 and 2 for numbers of grid cells and correlation eoeffteients. ECOGRAPHY 21:5 (1998)

Journal

Ecography – Wiley

Published: Oct 1, 1998

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