Extending Ellenberg's indicator values to a new area: an algorithmic approach


Mark O. Hill (fax + 44 1487 773467; e-mail m.hill@ite.ac.uk).


1. Ellenberg's indicator values scale the flora of a region along gradients reflecting light, temperature, continentality, moisture, soil pH, fertility and salinity. They can be used to monitor environmental change.

2. Ellenberg values can be extended from central Europe, for which they were defined, to nearby parts of Europe. Given a database of quadrat samples, they can be repredicted by a simple algorithm consisting of two-way weighted averaging, followed by local regression.

3. A database of British samples was assembled from two large surveys. Ellenberg values were repredicted.

4. Except for the indicator of continentality, the correlation of repredicted and original values was in the range 0·72 (light) to 0·91 (moisture). The continentality indicator could not be adequately repredicted by the algorithm, and is unusable in Britain.

5. Discrepancies between original and repredicted values can be attributed to various causes, including wrong original values, differing ecological requirements in Britain and central Europe, biased sampling of the British range of habitats, and the occurrence of small plants in shaded or basic microhabitats within well illuminated or predominantly acid quadrats.

6. The repredicted values were generally reliable, but a small proportion was clearly wrong. Wrong values were due to either inadequate sampling of species’ realized niches in Britain or sampling with quadrats that were too large and included species that were not close associates.


All field ecologists are aware of the differing habitat requirements of the organisms that they study. In one dimension, the requirements of a species can be specified as a response curve along an environmental gradient (ter Braak & Prentice 1988). Taking several gradients together, the requirements of a species can be described by its ecological niche, defined as the response surface of its abundance in an abstract environmental space (Hutchinson 1957). Species’ niches can be used to make inferences about the environment. Indeed, the bioindication of particular assemblages of organisms provides one of the standard methods of reconstructing the past from fossil assemblages. Diatoms can be used to reconstruct lake pH (ter Braak & van Dam 1989) and fossil beetle assemblages are used to reconstruct temperature on land (Atkinson, Briffa & Coope 1987).

Foresters and applied ecologists have long used ground vegetation to indicate site fertility in the boreal zone (Nieppola 1993). In this application, the interest is mainly in forest growth. In recent years, there has been increasing interest in the use of indicators to monitor change, including eutrophication and acidification of forests (Thimonier et al. 1994; Diekmann & Falkengren-Grerup 1998), succession on dunes (van der Maarel et al. 1985), the effect of past land use (Koerner et al. 1997) and the effects of clearcutting (Hannerz & Hånell 1997).

Numerous indicator scales have been proposed, for example the C, S and R scales of Grime (1979), a functional nitrogen index (Diekmann & Falkengren-Grerup 1998) and an index of human influence or ‘hemeroby’ (Kowarik 1990). Where the aim is to estimate the past value of a variable, such as temperature, special-purpose indices are necessary. Where, however, the aim is to determine overall differences and trends, a generally accepted comparative index may be more useful. Two general-purpose sets of indicator values have been elaborated for the flora of central Europe, that of Ellenberg (1979), updated by Ellenberg et al. (1991), and that of Landolt (1977). Both are included in the enumeration of Lindacher (1995).

Ellenberg's indicator values have been used widely outside central Europe, but many authors have expressed doubts about their appropriateness outside the region for which they were defined. There have been several attempts to adapt them to local conditions, for example in the Netherlands (ter Braak & Gremmen 1987; Ertsen, Alkemade & Wassen 1998) and Sweden (Diekmann 1995). Ertsen, Alkemade & Wassen (1998) related mean Ellenberg values for sites to environmental measurements of moisture, pH, nitrogen, standing crop and the concentration of chloride ion. They found that moisture measured by the Ellenberg bioindication corresponded to different groundwater regimes according to the type of soil. This raises the interesting possibility that the experience of wetness by plants may not correspond directly to a particular measured variable. Indeed, the Ellenberg bioindication may summarize the plants’ experience of moisture better. If so, then the indicator values can serve as a general reference system, to be calibrated against measured variables in specific contexts such as British woodland (Hawkes, Pyatt & White 1997).

Given that Ellenberg's indicators have numerous potential applications outside central Europe, the question of how to extend them to other geographical areas becomes important. Several species have differing ecological requirements across their range, so that some degree of alteration of the central European values to take account of local preferences is inevitable. To make the necessary changes, van der Maarel (1993) recommended that Ellenberg's values should be taken as more or less definite but corrected for a few misclassifications and regional deviations. Missing, indifferent or uncertain values should be supplied by using average values for sociological–ecological groups.

The need for a set of ecological indicator values for Britain has been apparent for some time and is reinforced by the observations of Thompson et al. (1993) and Hill & Carey (1997) that Ellenberg values are applicable in England. Indicator values are of particular interest to us because we wish to analyse trends of change in the British countryside recorded by repeated large-scale surveys, such as the Countryside Survey 1990 (Barr et al. 1993) and its successor, the Countryside Survey 2000, for which fieldwork was completed in 1999. We therefore set out to find a satisfactory means of extending and adapting Ellenberg's values for British use.

van der Maarel's (1993) technique requires that species should be classified into groups and then treated as members of those groups. Such groups are necessarily somewhat arbitrary. It is preferable, in principle, to treat species individually. We tried out the technique of ter Braak & Gremmen (1987), but found that it was unreliable with the less common species because random variation obscured the shape of the species’ response curves; optima were often not apparent. We therefore developed an algorithm that combines features of both these methods. For its input, it requires an extensive database of quadrat samples or association tables, together with the original Ellenberg values. As output, it produces a set of estimated Ellenberg values for all species recorded in the database.

Data and methods


Two data sets (Table 1) were combined to form a single large data matrix, with 14 602 rows (quadrats or plant associations) and 1398 columns, comprising 1293 species and 105 species aggregates.

Table 1.  Data used for reprediction of Ellenberg values. Data are envisaged as a matrix with rows representing quadrats or summarized plant communities and columns representing species
Data attributeCountryside Survey 1990British Plant Communities
Source of dataDatabase of quadratsPublished association table
Data itemPresence in quadratFrequency out of 5
Number of rows13 742860
Weight per item0·31
Total weight of data61 52265 440
Mean weight per row4·4876
Mean number of species per quadrat14·911·0

The Institute of Terrestrial Ecology's Countryside Survey 1990 (Barr et al. 1993) was based on a stratified random sample of 508 1-km squares throughout Britain. The quadrats varied in size, comprising standard plots 14·1 × 14·1 m (200 m2) as well as linear plots 10 × 1 m and targeted habitat plots 2 × 2 m. Each occurrence of a species in a plot was given weight 0·3, i.e. the corresponding matrix element was 0·3.

The other data set consisted of frequency values from the 860 plant communities whose composition is summarized as association tables in British Plant Communities (Rodwell 1991a, 1991b, 1992, 1995). In the association tables, species frequency was expressed on a five-point scale: 1 (1–20%), 2 (21–40%), 3 (41–60%), 4 (61–80%) and 5 (81–100%). These values were used directly in the data matrix for the present project. To derive the mean number of species per quadrat (Table 1), the estimated species probabilities were summed for each community, using the middle probability values in each frequency class, i.e. 1 (P = 0·1), 2 (P = 0·3), 3 (P = 0·5), 4 (P = 0·7) and 5 (P = 0·9). This estimate is a rather crude approximation, but it suffices to show that both the overall weight and the mean species richness of the two data sets are similar (Table 1).

When the data sets are combined in this way, the column totals are not directly interpretable as species frequencies. They are an index of frequency but not a direct measure. In Figs 1–4 they are signified by the phrase ‘weight in data’. The theoretical maximum weight for a species occurring in all quadrats was 8423. Of the 31 species whose weight exceeded 10% of the theoretical maximum, 15 were grasses. Of the seven species whose weight exceeded 20% of the theoretical maximum, six were grasses, the exception being Trifolium repens (nomenclature follows Stace 1991). Only the grass Holcus lanatus exceeded 30% of the theoretical maximum weight. Britain is a grassy country.

Figure 1.

Reprediction of the light value for Oxalis acetosella by regression of original against two-way averaged values. Abbreviated names are given for the more frequent species: Athyrium filix-femina, Conopodium majus, Deschampsia cespitosa, Digitalis purpurea, Dryopteris dilatata, Geum rivale, Hyacinthoides non-scripta, Primula vulgaris, Quercus robur, Pteridium aquilinum and Sorbus aucuparia. Species’ weights in the data are signified by black circles of differing size: small 1–9, medium 10–99, large 100–999.

Figure 2.

Reprediction of the moisture value for Caltha palustris by regression of original against two-way averaged values. Abbreviated names are given for the more frequent species: Angelica sylvestris, Cardamine pratensis, Epilobium palustre, Equisetum palustre, Hydrocotyle vulgaris, Juncus effusus, Lotus pedunculatus and Lychnis flos-cuculi. Species’ weights in the data are signified by black circles of differing size: small 1–9, medium 10–99, large 100–999.

Figure 3.

Reprediction of the reaction value for Nardus stricta by regression of original against two-way averaged values. Abbreviated names are given for the more frequent species: Carex binervis, C. pilulifera, C. pulicaris, Erica cinerea, E. tetralix, Juncus squarrosus, Luzula multiflora, Narthecium ossifragum, Pinguicula vulgaris, Polygala serpyllifolia, Selaginella selaginoides and Trichophorum cespitosum. Species’ weights in the data are signified by black circles of differing size: small 1–9, medium 10–99, large 100–999.

Figure 4.

Reprediction of the nitrogen value for Urtica dioica by regression of original against two-way averaged values. Abbreviated names are given for the more frequent species as well as for four relatively infrequent species that are mentioned in the text: Agrimonia procera, Agrostis gigantea, Alliaria petiolata, Anthriscus sylvestris, Arrhenatherum elatius, Fallopia japonica, Galium aparine, Glechoma hederacea, Heracleum sphondylium, Laburnum anagyroides, Lamium album, Rumex sanguineus, Stachys sylvatica and Torilis japonica. Species’ weights in the data are signified by black circles of differing size: small 1–9, medium 10–99, large 100–999.

Reprediction algorithm


A = [aij] (i = 1,,m; j = 1,,n)

be a data matrix specifying the occurrence of species (i = 1,,m) in samples (j = 1,,n). Let X be an ecological indicator variable, scaled for species. Define mXi to be the mean value of X in sample i, and mmXj to be the mean value of mXi for species j. In symbols:

mXi = ΣjaijXjjaij
mmXj = ΣiaijmXiiaij

If the matrix A is quantitative, these means are weighted means. If there are missing values, the averages are taken over those species or samples for which the value is not missing. The basic method of recalibration is based on simple principles.

1. The mean indicator value of a sample, mX, reflects an ecological variable, which can in principle be measured although this may present practical difficulties.

2. The mean indicator values, mmX, have an approximately monotonic relation to the original variable X.

3. Species with broadly similar requirements can be selected by choosing ones that have similar mean indicator values, mmX, on all indicator variables.

4. Given a variable mmX and a set of original values X, then a recalibrated variable X′ can be calculated by regressing X against mmX. This provides an extension of the variable X based on the data matrix A.

The essential requirement for rescaling to work is that the variable X is reflected in the data matrix A. For this to be the case, species with high or low values of X must have at least some tendency to occur together. If they do not occur together, then the values of mX will show little variation and the signal of X will be lost in the noise of A, so that mmX is not or is scarcely related to X.

This recalibration method has been put into practice by the following algorithm. The algorithm has been realized as computer program indext (INDicator EXTension), written in the fortran programming language.

Stage 1

For those species j that lack original values


, estimate missing values. A species may lack an original value either because it has broad amplitude for the variable (signified by the symbol × in the tabulation of Ellenberg et al. 1991; this also includes the case where the species has variable ecological requirements across its central European range) or because the species was not included in the original tabulation. The algorithm to calculate a missing value for species j is to calculate sample means mX based on those species that are already calibrated, then to calculate species’ means mmX. The process of calculating mmX is simply the first two stages of reciprocal averaging (Hill 1973) without any standardization. It is well known that with averaging techniques, there is shrinkage towards the mean value, especially near the ends of the scale (ter Braak 1995). Shrinkage is corrected by taking the S (= 20 in indext) calibrated species for which mmX is closest to mmXj, the two-way averaged value of j, and using them to calculate an offset. In symbols:

Oj = offset for species j = mean(S)(Xj - mmXj)

where mean(S) is the mean is taken over the S species’j′ for which abs(mmXj − mmXj) is smallest, subject to the proviso that Xj is not a missing value. The estimated value


of X for species j is then defined as:


where mmX(0) and O(0) are the mean and offset derived from the starting calibration X(0).

The process can be iterated to derive subsequent estimates X(2) and X(3). In the iterations, the original values X(0) are retained where these are defined. Thus, the second iteration uses


as starting values where these are available and


where values for


are lacking. It is theoretically possible that values for


might be lacking as well, because all the species co-occurring in quadrats with species j could themselves lack values for X(0). Provided that at least some of these species co-occur with species included in the initial calibration X(0), missing values will be eliminated after the second iteration.

After three iterations, the values X(3) define a recalibration based on a single variable. In stages 2 and 3, the calibration is modified to derive a new variable X(R), which takes account of similarity in the other variables as well as X. The question of whether X(R) is better or worse than X(3) is examined empirically.

Stage 2

Define a measure of similarity between species, based on their rescaled indicator scores. For this purpose, the species’ scores are rescaled by the non-linear rescaling algorithm used in detrended correspondence analysis (Hill & Gauch 1980) and canoco (ter Braak 1988). The purpose of the rescaling is mainly to ensure that the length of the original scale does not matter, i.e. the influence of the variable does not increase if, for example, its scale is multiplied by a factor of two. A secondary purpose is to expand or contract parts of the original scale according to the criterion of non-linear rescaling, namely that there is unit within-sample variance. Specifically, the range of mean sample scores mX(3) is divided into 20 segments and, in each segment, the spacing between species’ scores X(3) that lie there is expanded or contracted by dividing by the local mean within-sample standard deviation of the species’ scores. Local means are smoothed to achieve numerical stability. Species for which X(3) lies outside the range of mX(3) are assigned to the first or last segment as appropriate. An additional feature in indext is that the rescaled variables are multiplied by a factor intended to downgrade the influence of short gradients. Specifically, the rescaled variables are multiplied by the ratio of sample gradient length to species gradient length, i.e.:


where the operator r denotes rescaling by non-linear rescaling, and m is the averaging operator defined above. The difference between species is measured by ordinary multivariate Pythagorean distance in the space defined by the axes X(t), taking all variables into account.

Stage 3

This stage uses locally weighted regression (Cleveland & Devlin 1988), i.e. regression based on those species that are closest to species j in the multivariate space of variables X(t) defined at stage 2. For those S species’j′ that are closest to species j and for which X(0) is not undefined, the original values


are regressed on the two-way averaged values


, obtained at the third iteration. The regression excludes the target species j. The rescaled value of species j after this final regression step is denoted


. Note that


is defined for all species in the data matrix A, including those for which X(0) is undefined.


Goodness-of-fit of rescaled variables to the original variable was measured by the root-mean-square error (RMSE). The root-mean-square error of X(3) is defined as:

RMSE X(3) = √(average((X(3) - X(0))2))

where the average is taken over all those species for which both X(3) and X(0) are defined. Likewise, RMSE X(R) is defined as:

RMSE X(R) = √(average((X(R) - X(0))2))


Concordance between original and rescaled values

Rescaling by regression produced small gains over rescaling by a simple offset (Table 2). For salt tolerance, there was a distinct loss of accuracy. The RMSE were in the range 0·65–1·45 for rescaling by offset X(3) and in the range 0·75–1·33 for rescaling by local regression X(R). The RMSE for salt tolerance was lower than that for the other variables because the great majority of species have no salt tolerance and were not predicted to have any. Expressed as RMSE, predictions of R-values were generally the worst.

Table 2.  Errors and correlations between original (X(0)) and repredicted (X(3), X(R)) species indicator values. The scales are represented by their standard German abbreviations: L = light, T = temperature, K = Continentality (Kontinentalität), F = moisture (Feuchtigkeit), R = reaction, N = nitrogen, S = salt
Root-mean-square error
Repredicted by offset only (X(3))1·030·801·341·041·451·410·65
Repredicted by regression (X(R))1·010·751·271·031·331·320·75
Correlation with original values
Repredicted by offset only (X(3))0·710·750·390·910·680·770·88
Repredicted by regression (X(R))0·720·790·490·910·740·810·85

With the exception of continentality values, K, the correlations of X(3) and X(R) with the original variable X(0) were in the range 0·71–0·91. The best correlation was for moisture, F, which ranged from 1 to 12, and was a longer scale than the others. For continentality, K, the correlation between rescaled and original variables was much lower, 0·39 for K(3) and 0·49 for K(R).

Much of the RMSE for all variables could be attributed to systematic error in the correspondence between rescaled values and original values (Table 3). For example, the mean for K(R) only rose from 2·7 when K(0) = 1 to 4·1 when K(0) = 7. The origin of both systematic error and individual discrepancies can be illustrated by considering the following particular cases.

Table 3.  Numbers of species and their mean repredicted values in relation to original scale values X(0). The two repredictions are reprediction by offset only (X(3)) and reprediction by two-way averaging followed by local regression (X(R)). The standard abbreviations for the scales, L, T, K, F, R, N and S, are explained in Table 2. Note that the original scales are of differing length, the shortest being K and the longest F. The value * denotes a missing value, either × or ? in the original enumeration, or a species not included in the original list
Value on original scale X(0)
Numbers in category
Mean values, reprediction by offset X(3)
L6·9 4·84·44·75·25·96·57·07·57·9
Mean values, reprediction by regression X(R)


The largest discrepancy for light was in the values for Oxalis acetosella. For this species, L(0) was 1 and the repredicted values L(3) and L(R) were 4·8 and 5·2, respectively. Stage 3 of the analysis is illustrated in the regression shown in Fig. 1. The rescaled light values from stage 2 are the x-axis and the original light values L(0) are the y-axis. It is clear that O. acetosella had an exceptionally low L(0) value. Indeed, for no other species was the original light value 1. In Britain, O. acetosella is undoubtedly a shade plant (Packham 1978), but it is no more extreme in this respect than many ferns. Even Epipogium aphyllum and Neottia nidus-avis, orchids that completely lack chlorophyll and live in the darkest parts of woods, were rated L(0) = 2. Thus there appears to be some inconsistency in the original values.

It is fairly clear from Fig. 1 why the repredicted L-value should be about 5. Of the 20 most similar species, only the ferns Athyrium filix-femina, Dryopteris dilatata and Polystichum aculeatum and the woodland herb Viola reichenbachiana had L(0) < 5. Several of the species with higher light values were trees. It could well be argued that the trees are not similar to a small herb and that they ought to have been left out of the analysis. If trees are omitted from the regression then L(R) = 4·9, a slightly lower value but not greatly different.

Other species for which L(R)L(0) ≥ 3 were Brachypodium sylvaticum (L(0) = 3, L(R) = 6·0), Cardamine pratensis (4, 7·2) (using the same order, but with the names L(0) and L(R) omitted for brevity), Epipactis helleborine (3, 6·5), Huperzia selago (4, 7·5), Lysimachia nemorum (2, 5·0), Moneses uniflora (4, 8·0), Orthilia secunda (4, 7·3), Pyrola rotundifolia (4, 7·4) and Phegopteris connectilis (2, 5·2). Of these, B. sylvaticum is a plant of woodland margins, C. pratensis grows mainly in open pastures and marshes, and H. selago is a species of open moorland, while L. nemorum and P. connectilis are similar enough in their light requirements to O. acetosella. The high L(R) for P. rotundifolia reflects the fact that it often occurs on dunes, parasitizing the mycorrhiza of Salix repens (as does Monotropa hypopitys, which was not included in our quadrat samples). On the other hand, the original values for E. helleborine, M. uniflora and O. secunda did seem more appropriate than the recalculated values. These discrepancies were probably due to quadrat size. Quadrats of at least 200 m2 were used in woodland, and these may have included dark and light parts within them.

There were only three species for which L(R)L(0) ≤ −3, namely Juniperus communis (8, 4·7), Narcissus pseudonarcissus (8, 4·6) and Fallopia japonica (8, 5·0). Juniperus communis forms moderately dense scrub in a few localities in Scotland (McVean & Ratcliffe 1962) and these were perhaps disproportionately sampled. The low L-value was attributable to plants growing in its shade. The problem of layered communities with trees was noted in relation to O. acetosella; the phanerophytes Betula pendula (7, 5·1), B. pubescens (7, 5·3), Malus sylvestris (7, 4·2), Quercus robur (7, 5·2) and Rhamnus cathartica (7, 4·9) all showed the same phenomenon but in lesser degree. The situation is further complicated by the fact that the L-values for trees were intended to describe the requirements of juveniles rather than mature individuals. Narcissus pseudonarcissus frequently occurs in woodland in Britain, but it is also found in the open, and the value of L(R) = 4·6 is undoubtedly too low. Unintentional recording bias is the explanation; all but two of the records were from British Plant Communities (Rodwell 1991a, 1991b, 1992, 1995) woodland tables (ashwoods of type W8 and oakwoods of type W10). Fallopia japonica, familiar to city dwellers as a denizen of dark, squalid, derelict land, is also likely to have been sampled in a biased way. It is mainly a plant of half-shaded river banks and roadsides. A value of L = 6 would be more appropriate.

These discrepancies were notable but not especially numerous. Discrepancies greater than 2 in either direction amounted to 64 out of the 1060 species for which comparisons were possible. The majority of these discrepancies had an obvious explanation. Where they were adjusted to a value that was more suitable for Britain, they were an intended consequence of the reprediction.

Temperature and continentality

Preston & Hill (1997) discussed Ellenberg's values for temperature and continentality in relation to the wider geographical distribution of the British and Irish flora. They found a fairly good relation between Ellenberg T-values and the distribution of species in ‘major biomes’ (zonobiomes and orobiomes of Walter 1979). Several discrepancies could be attributed to differences in taxonomic circumscription. The relation between K-values and the eastern limit of European distributions, on the other hand, was poor. Britain, being in the Atlantic zone of Europe, ought in principle to have almost no species with high K-values. Unexpectedly, Lepidium latifolium had K = 8, and Quercus robur, one of the major woodland species of Atlantic Europe, had K = 6. The poor correlation between K(0) and K(R) (Table 2) was therefore very much to be expected. In the interests of brevity, T- and K-values are not considered further here.


Repredicted F-values were well correlated with original F-values F(0) (Table 2). Caltha palustris provides a second illustration of the use of regression for reprediction (Fig. 2). In this example, C. palustris occupies a rather extreme position on the x-axis, so that its repredicted value, F = 8·6, is appreciably larger than F = 7·4, the average moisture value of the 20 most similar species. The off-centre position of C. palustris reflects the fact that, although the species is always terrestrial, it is confined to localities close to the water table, while several similar species, such as Angelica sylvestris, Cardamine pratensis and Juncus effusus, occur in a wide range of other habitats, usually moist but not necessarily wet. The reprediction for C. palustris confirms the original Ellenberg value F = 9.

Of the 11 species for which F(R)F(0) ≥ 3·0, only the reprediction for Agrostis vinealis (F(0) = 2, F(R) = 6·1) was perhaps correct. In Britain, A. vinealis is one of the most common species of heaths and moors, including wet moorland on peaty gleys; it is certainly not confined to dry ground. Repredictions for Chenopodium murale (4, 8·5), Elatine hydropiper (5, 11·0) and Platanthera bifolia (5, 8·0) correctly raised the F-values, but raised them too much. Repredictions for Eleocharis parvula (10, 15·1), Filago lutescens (3, 7·1), Hesperis matronalis (7, 10·0), Juncus filiformis (9, 13·9), Moneses uniflora (5, 8·6), Ophrys insectifera (4, 9·1) and Zostera noltii (12, 15·8) were definitely unsatisfactory; indeed, three of these values were larger than the scale maximum of 12.

There were only six species for which F(R)F(0) ≤ −3·0. Brassica nigra (8, 4·9) and Carex vaginata (9, 5·6) were adequately repredicted; Carex divisa (9, 5·7), Ranunculus sardous (8, 4·6) and Sesleria caerulea (8, 4·1) were shifted in the right direction, but too far. Sesleria caerulea is abundant on limestone in northern England, but occurs in dry grassland as well as in mires. In any case, the discrepancy is basically taxonomic, because British authors unite S. caerulea (F = 8) and S. albicans (F = 4), which are distinguished in the list of Ellenberg et al. (1991). Crassula tillaea (7, 2·8) is a difficult case, growing where puddles form in winter but dry out in summer. It is often in close proximity to dry-ground therophytes, but at the scale of the individual puddle demands moisture.

As with the L-values, these discrepancies were very much the exception. Out of 1006 species for which a comparison was possible, only 65 had F(R) differing by 2 or more from F(0).


Repredicted R-values had the highest RMSE (Table 2). Even with this variable, most species were unproblematic. As an example, consider Nardus stricta (Fig. 3). Many of its typical associates in heathy grassland had R(0) = 1 or 2. However, it is also often associated with bryophytes and small herbs in closely grazed, base-enriched flushes and runnels. Its repredicted value R(R) = 3·0 was one unit larger than its original value, reflecting this additional range of habitats.

For 16 species, R(R)R(0) ≥ 3. For Centaurea nigra (3, 6·5), Epilobium lanceolatum (3, 6·5), Filago pyramidata (4, 7·3), Juncus ambiguus (4, 7·0), Minuartia stricta (2, 8·0), Poa chaixii (3, 6·3) and Subularia aquatica (2, 5·0), the repredicted values seemed appropriate enough. Indeed, the most common of these species, C. nigra, is not markedly calcifuge in Britain and is often found on basic soil. For Asplenium adiantum-nigrum (2, 6·9), Coeloglossum viride (4, 7·0), Elatine hydropiper (2, 6·6), Holcus mollis (2, 5·0), Oxyria digyna (3, 6·2), Teesdalia nudicaulis (1, 4·0), Trifolium arvense (2, 6·2) and T. striatum (2, 7·3), the repredicted values were arguably closer to the true values than the original values, although they were probably too large. For Radiola linoides (3, 6·4), however, R(R) did appear to be a clear overestimate.

For 15 species, R(R)R(0) ≤ −3. For Carex aquatilis (7, 3·8), Pinus nigra (9, 4·8), Utricularia intermedia (8, 4·3) and Viola lutea (8, 4·9), the repredicted values were credible. Pinus nigra is often planted on heathland in Britain and regenerates there from seed; V. lutea is characteristic of acid, but not heathy grassland. With Mentha spicata (9, 5·3), Schoenus nigricans (9, 5·4) and Silene acaulis (8, 4·5), the true value probably lies between the original and the repredicted one. Schoenus nigricans is a marked calcicole in eastern Britain, but extends to heathland with basic flushing in the south and west, and in western Ireland also to blanket bog (Sparling 1967a, b). Silene acaulis is commonly found on acid soils but is not a strong calcifuge. For the remaining eight species, namely Astragalus danicus (9, 5·5), Carex appropinquata (9, 5·5), C. montana (6, 1·0), Ornithogalum angustifolium (7, 3·9), Pinguicula vulgaris (7, 3·8), Salix purpurea (8, 4·8), S. reticulata (9, 5·8) and Veronica spicata (7, 3·8), the reprediction was unsatisfactory. Pinguicula vulgaris, like S. nigricans, often occurs in an acid matrix but in sites with at least slight basic flushing. The other species are all uncommon or rare, some extremely so. They were not (except for four records of S. reticulata) found by the Countryside Survey 1990. Carex montana was recorded by the British Plant Communities surveyors from Ulex gallii heath, O. angustifolium from a weed community, S. purpurea from swamp woodland and V. spicata from sandy Breckland grassland (no doubt with small-scale variation in pH). There were relatively numerous records of A. danicus, C. appropinquata and S. reticulata. Each of these species was recorded from several communities with a wide range of associates. The discrepancies were therefore almost all the result of calcicolous species occurring in a matrix of calcifuge or tolerant plants.

In spite of these discrepancies, the majority of the repredicted values gave a better indication of British pH preferences than the original ones. Examples of improvements are Hyacinthoides nonscripta (7, 5·3), Saxifraga aizoides (8, 6·1) and Tussilago farfara (8, 6·3). These are not strong calcicoles; indeed H. nonscripta is one of the most common species of woodland on acid brown earths. Likewise Carex arenaria (2, 4·9), Polygala vulgaris (3, 5·5) and Teucrium scorodonia (2, 4·5) can all occur on basic soils.

Only 854 species were originally scored for reaction. In 123 of these, R(R) differed by 2 or more from R(0).


Hill & Carey (1997) and Ertsen, Alkemade & Wassen (1998) have pointed out that Ellenberg N-values are, in effect, indicators of general fertility rather than nitrogen in particular. Urtica dioica, well known as an indicator of fertile conditions and of soil phosphorus as much as nitrogen (Pigott & Taylor 1964), can serve as an example here (Fig. 4). Most of the 20 similar species were common associates of U. dioica, occurring in fertile woods and fields and on waysides and waste ground; Galium aparine was the most similar species. Agrimonia procera, Agrostis gigantea, Fallopia japonica and Laburnum anagyroides were relatively uncommon species that occupied outlying positions in the diagram. None of these was particularly similar to U. dioica in its habitat requirements, although A. gigantea frequently occurs on fertile roadsides and F. japonica grows beside streams.

The small tree Laburnum anagyroides was the least similar to U. dioica of the selected species, and was by far the most aberrant in its N-value. In Britain, it is an introduced species, commonly grown as an ornamental in gardens. It is frequent as a garden escapee on waste ground but does not occur in semi-natural habitats. The Ellenberg value N = 3 is based on its natural occurrence in the Alps and is wildly unrealistic for Britain. This one species had a distinct effect on the repredicted value of N for U. dioica. If it was included, N(R) = 7·4; without it, N(R) = 7·7. This value, 1·3 less than the scale maximum of 9, is in fact appropriate; U. dioica occurs too widely in the British uplands, in localities that are fertile but not extremely so, to qualify for the scale maximum.

For 15 species, N(R)N(0) ≥ 3. For Bromus racemosus (5, 8·0), Euphrasia nemorosa (1, 4·5), Laburnum anagyroides (3, 6·7), Lathyrus japonicus (3, 6·3), Lepidium latifolium (5, 8·1) and Petasites albus (5, 8·0), the repredicted values were arguably correct. Lathyrus japonicus is a plant of maritime shingle that often grows with weedy species in a habitat with little soil, but the others undoubtedly grow on soils that are generally more fertile than the original values N(0) would suggest. Laburnum anagyroides and P. albus are introduced to Britain, where they occur mainly in gardens. For Artemisia campestris (2, 6·9), Epilobium lanceolatum (3, 7·5), Filago pyramidata (1, 4·3), Lactuca serriola (4, 7·7), Rosa mollis (1, 5·8) and Vulpia myuros (1, 5·0), the reprediction differed from N(0) in the right direction but exceeded the true value. In several cases, of which the most extreme was V. myuros, the reason was that the main associates are weeds, which tend to have high N-values but which can sometimes grow in low-fertility habitats such as bare sandy ground and railway sidings. These are analogous habitats to that of Lathyrus japonicus. For Allium carinatum (2, 6·3), Filago lutescens (2, 5·2) and Myosotis discolor (2, 5·0), the reprediction seemed to be unsatisfactory.

For 13 species, N(R)N(0) ≤ −3. For six of these, Adoxa moschatellina (8, 5·0), Athyrium distentifolium (7, 3·7), Atriplex littoralis (9, 5·9), Centaurium erythraea (6, 2·6), Huperzia selago (5, 2·0) and Leontodon hispidus (6, 2·7), the reprediction was credible. For Alopecurus aequalis (9, 3·8), Beta vulgaris (9, 5·7), Listera ovata (7, 3·3), Ornithogalum angustifolium (7, 1·7) and Rubus caesius (7, 3·7), the reprediction was in the right direction but overshot. Only for two species, Mentha spicata (7, 3·8) and Reseda luteola (6, 2·8) did the reprediction appear to be totally unsatisfactory.

The overall success of N repredictions was only moderate. In 131 out of 988 possible comparisons, N(R) differed by 2 or more from N(0).


Salt is a completely different variable from the others, because the great majority of vascular plants are not salt-tolerant. The indicator S is therefore of less general interest than L, F, R and N. For salt, the regression stage (stage 3 of indext) of reprediction was not a success (Table 2). There were so few salt-tolerant species that the requirement for the 20 most similar species to be similar with respect to all variables (stage 2 of indext) resulted in insufficient variation in the salt variable for good regression results. In other words, too many of the most similar species were not salt-tolerant. With the univariate methodology used at stage 1 this would not apply, because the 20 similar species used to calculate the offset have by definition to be similar only in mmS. The salt variable is not discussed further here.


Appropriateness of data

The data set was chosen to be broadly representative of British vegetation, including quadrats from all parts of the country. No effort was made to ensure that it was unbiased. Indeed, although it includes a set of quadrats chosen to be a systematic unbiased sample of the land cover of the country, it includes many more quadrats that were chosen deliberately to represent particular vegetation types and landscape features. The purpose of the data set was to provide a means of repredicting Ellenberg values. In principle, this requires that the realized niche of all species is adequately sampled. In practice, many interesting plants, such as Actaea spicata, Paris quadrifolia, Primula scotica and Spiranthes romanzoffiana, were not included. Others, such as Narcissus pseudonarcissus, were sampled mainly from one part of their total British habitat (woods rather than fields).

The two data sets were chosen carefully. One of them, the Countryside Survey (Barr et al. 1993) data set, was based on a statistical sample of the land area of Britain. Uncommon or rare species were seldom recorded. The other of them, the data set for British Plant Communities (Rodwell 1991a, 1991b, 1992, 1995), was highly skewed towards rare species and special habitats, especially those found in national nature reserves. Both data sets purport to be for the whole of Britain. Original quadrat data would have been preferable to published association tables, but were not available for British Plant Communities. Association tables with frequency values summarize the data but inevitably blur the precision with which the associates of the rarer species can be known. As explained in the methods section, there is also a slight discrepancy between the frequency classes 1, 2, 3, 4, 5 and frequency estimates based on middle values 0·1, 0·3, 0·5, 0·7, 0·9. The discrepancy would have a minimal effect on mean indicator values.

In the event, it is clear that the ecological profiles of most species were not obscured by the lumping of data in association tables. There were, however, a small number of rare species, such as Carex montana and Veronica spicata, that might have been better characterized if original quadrat data had been available. With rare species, some bias is hard to avoid unless they are confined to a single clearly defined habitat. This means that, however good the algorithm for repredicting Ellenberg values, the results must be scrutinized carefully. The reprediction provides a basis on which to build, but cannot be a final result.

Problems of scale

Several of the discrepancies discussed above are the result of sampling at scales that are very different from the size of an individual plant. For example, L-values for the ground flora may differ widely from those of the woody species. Likewise, repredicted R-values for plants such as Pinguicula vulgaris may reflect the acid moorland matrix in which the species grows rather than the basic flushing necessary for its occurrence.

Ellenberg values are by definition ‘plant-centred’. They refer to the immediate environment of a plant, i.e. the light falling on its leaves, the wetness of its roots and the reaction, fertility and salinity of its soil. Most quadrats were much bigger than an individual plant, with the result that the mean indicator values for the quadrat may not always have been appropriate to particular species within it.

There is no entirely satisfactory solution to problems of scale. On the one hand, quadrat indicator values ought to reflect mean conditions for a quadrat, while on the other, particular species may occupy special niches within it. Ellenberg values are most useful when information from several species is averaged. They then reflect overall site conditions, so that excessively plant-centred definitions may not be appropriate.

Suitability of the algorithm

The case studies suggest various ways in which the algorithm might be improved. For some variables, notably light, canopy architecture ought to be considered. Oxalis acetosella should not be compared with trees and ought to be compared with other members of the ground flora, preferably small ones.

The two-way averaging process used at stage 1 of the algorithm does not distinguish between species with a wide range of tolerance and those that are restricted to the middle part of the range. It is possible to take the profile of a species’ occurrence into account, either by means of logistic regression (ter Braak & Gremmen 1987) or simply by considering the frequency of species j in relation to variation in the sample means mXj. We have tried logistic regression (M. O. Hill et al., unpublished data) but did not find it to be superior, in spite of being more complicated and more computationally demanding.

Stage 2 of the algorithm, the measurement of similarity between species, is used only for selecting the 20 species to be used in the regression at stage 3. It therefore has in general a relatively small effect on the answers, X(R). However, it was clearly unsuccessful in the case of salt. That difficulty might be avoided by giving greater weight to the target variable, i.e. to the one to be repredicted. Fine-tuning at stage 2 could be achieved by trying out a range of weights for the target variable and for each target variable selecting the weight that minimizes the error measured by RMSE. Only the case where the target variable is given unit weight and the others no weight has been investigated. This produced repredicted values almost identical to those from stage 1 of the algorithm and made stages 2 and 3 worthless. The benefit from reweighing the target variable is probably small.

Another candidate for fine tuning is the number of species used in the regressions. There is no magic in the number 20 and the number of similar species could be varied in the same way as the weight to be given to the target variable. A further possibility is to use weighted regression based on a sliding scale of weights, from 1 for species that lie close to the target species to 0 for those that are far away. These variations have not been tried but could improve predictions for some variables.

Another weighting system for the regressions at stage 3 is to give greater weight to more common species. Regression weighted by the logarithm of species frequency was tried in earlier versions of indext, but did not markedly improve the quality of predictions as measured by RMSE. In the interests of simplicity, it was abandoned. A different possibility, suggested by the undesirable effect of Laburnum anagyroides on the repredicted N-value for Urtica dioica, is to ‘trim’ the regressions, i.e. systematically to remove or downweight (Cleveland 1979) those points that have particularly large residuals. This might make a small improvement but would certainly not make a large one, because such aberrant values are fortunately few.

It would in principle be possible to estimate the uncertainty of repredicted values by a Monte Carlo technique. Each value mmXj would be replaced by a normal variate with mean mmXj and standard deviation equal to the standard error calculated from the sample means mXi of those samples i that contained species j. Species with large standard errors could be omitted from the regression or at least given lower weight. In this way, the error associated with repredicted values could be partitioned into a part due to the stage 3 regressions and a part due to uncertainty about mXi values. Such precision would be slightly misleading, because of the unknown bias in sampling that has already been noted.

Finally, a counsel of perfection would be to bootstrap the estimates by setting the values


to ‘missing’ for each target species j in turn. In this way, the actual values


would not affect the repredicted values


. However, it is clear from the discrepancies described above that




can in practice be widely different. The influence of the original values on the repredicted values is real but is not, for the present purpose, excessive.

Adequacy of the original scaling

It is clear from the examples that the original scaling of several Ellenberg variables is either generally poor (continentality K) or has inconsistencies such as those noted for the L-values of species similar to Oxalis acetosella. In addition, there are numerous examples, considered above, where values may conceivably be correct for central Europe (Adoxa moschatellina N = 8, Carex arenaria R = 2, Coeloglossum viride R = 4, Huperzia selago L = 4, Laburnum anagyroides N = 3, Tussilago farfara R = 8) but are certainly wrong for Britain.

Provided that those values that are wrong (for whatever reason) are in a small minority, they will be largely corrected by the reprediction algorithm. If, however, they are relatively numerous (as with K), then the signal-to-noise ratio becomes small and the reprediction becomes ineffective. With most variables, there was a tendency towards compression of the overall scale. This was at least partly the result of the extreme values on the original scale not being reliable, e.g. the values of L(0) for plants of very dark places. The question of whether the repredicted values should indeed not be as extreme as the original ones must be addressed separately for each variable. There is no general answer.

In principle, the best way to achieve an adequate original scaling is to ensure that values correspond to physical or chemical variables that are measurable. Measurements are in principle easy to make for L, which corresponds to the relative illumination in July (although in some situations they could be complicated by sunflecks), for T, which can be measured by the annual temperature sum, and for R, which can be measured by the pH of soil at the mean depth of plant roots (although this too is subject to seasonal and small-scale spatial variation). They are much harder to make for F and S, which can be expected to show large seasonal fluctuations. The definition of the N scale given by Ellenberg (1988) is thoroughly vague; it could in principle be linked to annual mineralization of nitrogen (Diekmann & Falkengren-Grerup 1998) or even to annual productivity. Ellenberg's definition of the K scale seems quite clear but is not adhered to in practice; its weakness is that it is geographical rather than climatic.

In practice, the problems of linking indicator values to direct measurement are very great, particularly when large numbers of species and a wide range of habitats are to be considered. Even where good measurements are available, the problem of bias in selection of field sites is always present. For a truly plant-centred index, a random sample of all the sites at which each species is found should be taken. There would then even be the problem of whether to weight sites by the size of the population. Comprehensive species-centred samples were not available to us, with the result that some unintentional recording bias was unavoidable, for example the bias noted above for Narcissus pseudonarcissus and Veronica spicata.

Concluding remarks

There is merit in a general-purpose system that can be applied across a wide geographical range. With the exception of continentality, Ellenberg's indicator values correspond to environmental gradients that can be observed in many different types of habitat. Because of this, their significance in terms of what can actually be measured will differ from place to place. For example, the plants that are characteristic of upland flushes with base-enrichment will have similarities to those that grow on dry calcareous soils, even though the actual pH values may differ markedly. A general scale of R-values is still useful even if its calibration varies according to habitat.

The great advantage of the Ellenberg system is its universality. It permits comparisons of differing communities on scales that are ecologically meaningful.

In this study we have aimed to repredict Ellenberg values for the whole vascular-plant flora of Britain, taking account of all habitats present in the island. We have carefully scrutinized the output from indext, and have added values for L, F, R, N and S for those species that were not represented in the data set. The resulting table (Hill et al. 1999) of values for 1503 native species (including endemics and some microspecies), 33 possibly native species and 220 introduced species aims to be comprehensive. Reprediction by indext was an essential part of the reasoning required to reach these values. The extension of Ellenberg values to Britain is not only possible but desirable.


This paper is a contribution to ECOFACT, a project funded by the UK Department of the Environment, Transport and the Regions, contract CR0175. John Rodwell kindly let us have a copy of the association tables for weed communities in advance of their publication. We are grateful to the editors and three referees for valuable comments on an earlier draft.

Received 14 August 1998; revision received 9 July 1999