Species diversity
R.A. Kempton Volume 4, pp 2086–2092
in
Encyclopedia of Environmetrics (ISBN 0471 899976)
Edited by
Abdel H. El-Shaarawi and Walter W. Piegorsch
John Wiley & Sons, Ltd, Chichester, 2002 Species diversity 40 )
n (
Species diversity, the taxonomic variety of living S organisms, is one of the three principal levels of 30 biological diversity which include genetic diver- sity within species, species diversity and ecosystem or community (see Community, ecological) diver- sity [8]. In much environmental assessment, however, 20 biodiversity is identified as synonymous with species diversity and measured by the number of species in an area – the species richness. 10 While the species is often seen as the fundamental unit in ecology, using the number of species to of species, number Cumulative measure diversity requires the resolution of a number of issues [5]. First, there is the choice of taxonomic group, since differences in the species concept and 0 50 100 150 the levels of discrimination applied in different taxa Number of samples pooled, n mean that species counts cannot automatically be Figure 1 Species accumulation curve for seedlings ger- combined across groups. Measuring species richness minating from 121 soil samples. The points and error bars at the global or large regional scale often runs into represent the means and standard deviations of species problems of synonymy, the same species being given numbers Sn for 100 random combinations of n samples different names in different regions [28]. A simple n D 5, 10,...,120. The fitted curve is the inverse lin- species count also gives all species equal value, ear function, Sn D STn/c C n with ST D 35. Redrawn which may be inappropriate from a conservation from Colwell and Coddington [2] standpoint. Furthermore, with more mobile taxa such as birds, the total count can be substantially inflated is commonly modeled by a negative exponential or by transient vagrants that may be better omitted from inverse linear function [2], but least squares meth- environmental comparisons. These issues will vary in ods of fitting often ignore the variance structure of importance, and their resolution will depend on the species counts and the interdependence of combined objective of the diversity assessment. An even more samples. pervasive problem arises in the estimation of species When n equal samples are drawn from the popula- richness from samples. tion, an alternative estimator that does not depend on a particular model is based on first-order jackknife resampling, S C a1n 1/n,whereS is the total Assessing Species Richness from Samples number of species observed across all samples and a is the number of species that occur in only one A complete census of species in an area is rarely 1 sample [9]. The second-order jackknife estimator, feasible, except for highly visible and closely studied taxa such as birds and plants. Assessment is therefore 2 a12n 3 a2n 2 usually based on samples from the population, but the S C C n nn 1 species count then depends on sampling effort. Plotting species count against sampling effort pro- where a2 is the number of species that occur in just duces a species accumulation curve with decreasing two samples, has smaller bias but larger variance [2]. slope, as shown in Figure 1. Sampling effort may be Total species counts can also be estimated from defined by the number of samples, the time or area a single random sample by utilizing the distribu- sampled, or the number of individuals examined. If tion of species abundances in the sample to esti- the samples represent a small and random proportion mate the number of missing species. Preston [23] of individuals from the study population, the total suggested that the abundances of species in the popu- species count ST may be equated with the asymp- lation will follow a lognormal distribution, whence tote of the species accumulation curve. This curve the distribution in a random sample is a Poisson 2 Species diversity
60 Number of species
40 (b)
20 Number of species Number of species 116+ 256+ 4096+ 1 16+ 256+ (a)Individuals per species (c) Individuals per species
Figure 2 Lognormal fits to three abundance distributions (using logarithmic intervals) of moth species from annual light-trap samples with decreasing proportions of the species assemblage sampled. (a) Cumulative distribution from 225 UK sites: N D 656 943 moths, S D 585 species. (b) Distribution for stable (woodland) site: N D 10 705, S D 205. (c) Distribution for impoverished (urban) site: N D 153, S D 38. Redrawn from Taylor [29] lognormal with missing zero cell [1]. Fitting the 400 zero-truncated Poisson lognormal to the sample dis- A tribution (Figure 2) gives an estimate of the num- 350 B ber of missing species a0 and total species count 300 S D S C a . C T 0 250 Both approaches to estimating the total species count suffer from the usual problems of extrapo- S 200 lation, particularly when a substantial proportion of 150 the total species is not sampled. For example, in sam- pling insects from the canopy of tropical forests by 100 using knock-down insecticides over 50% of species 50 may be represented by only a single individual, sug- 0 gesting a vast hidden reservoir of species [28]. Taylor 1.5 3 6 12 24 48 96 et al. [30] found that the species accumulation curves Trapping months from eight years of sampling moth species by light Figure 3 Species accumulation curves for eight years of traps were often linear on log n [7] and showed no sampling by light trap at three stable woodland sites in evidence of approaching an asymptote (Figure 3). southern Britain. Individual nightly samples are pooled and Kempton and Taylor [12] also found that estimates then subsampled at 2-, 4-, 8-, 16-, 32- and 64-day inter- of ST from fitting the Poisson lognormal to the vals to simulate samples obtained with different sampling abundance distributions of moth species from annual intensity. Note that if diversity is identified with the sample light-trap samples had large variances and were poor species count, S, the ordering of sites changes with sam- pling effort. This can be explained by the fact that the same discriminators for sites. sampling effort produced more than twice the number of An alternative approach to comparing species rich- individual moths in site C compared with site B. Drawn ness that avoids the need for extrapolation is based on from data in Taylor et al. [30] Species diversity 3 standardizing sample species counts to a fixed sam- measures. A standard measure of variability is the ple size by using a rarefaction technique. Suppose standard deviation of the species abundances or, we collect a random sample of size N consisting of given their observed approximation to a lognormal S species with abundances Ni,iD 1,...,S.Thenan distribution, their log abundances. The diversity of unbiased estimator of the expected number of species a multispecies population might then be character- in a smaller sample of size m is ized by both the total number of species and the evenness or equitability of their abundances [21]. An 1 CN N ,m Sm D i 1 alternative development has been to define compound CN, m i diversity measures that are functions of the species proportional abundances i D 1,...,S . Hill [10] where Cu, v is equal to u!/[v!u v!] for u ½ v i T proposed a family of such measures: and is zero otherwise [26]. In 1979 I compared the annual totals of moth species trapped at two stable 1/1r p D r 2 woodland sites over 10 years and found that stan- r i dardizing all samples to the minimum sample size where r is any real number. When r D 0, all species substantially reduced the annual variation in S and have equal weighting and 0 D ST, but for positive increased site discrimination [11]. When differences r, r gives greater weight to the more abundant in sample size between sites are due to sampling species. In particular, 1 D exp H,whereH D artifacts standardization can easily be justified, but i log i is the Shannon information index, and 2 D when they reflect real differences in population den- 2 1/ i , the reciprocal of Simpson’s index [25]. sity the use of standardized comparisons is more Both these long-standing indices have been given debatable [5]. Nevertheless, the alternative of stan- theoretical interpretations as diversity measures but dardizing for sample effort is more likely to produce convincing evidence of their suitability needs to the inconsistencies in site comparisons observed in come from empirical studies of the performance of Figure 3. their sample estimators (Table 1). Since 2 and, to a lesser extent, 1 are relatively insensitive to Compound Diversity Measures the rarer species, these measures are less affected by sample size than is the species count S, but The total species count provides a very limited char- they were found to be poorer discriminators in a acterization of population variability, and substan- study that compared between-site variation of dif- tial effort has been directed to investigating other ferent diversity indices with year-to-year variation
Table 1 Estimators of some diversity measures for a sample of S species with ordered abundances Ni,iD 1,...,S, Ni D N, with an assessment of their discriminant ability and sensitivity to sample size under a typical species abundance model [17, Table 4.5]. The discriminant ability of an index is measured by the ratio of its variance between sites to that within sites [11, Figure 2]. For the Q index, an alternative estimator for small samples is given in [15] Sensitivity to Discriminant Index Estimator sample size ability Species richness S High Moderate Interquartile, QS/[2 logN0.25S/N0.75S] Moderate Good Shannon H log N N log N /N Moderate Moderate i i Simpson NiNi 1 NN 1 Low Poor Berger–Parker N1/N Low Poor Shannon evenness H/ log S Moderate Poor Log-series ˛ Low Good Lognormal ST Low Poor Lognormal Low Poor Lognormal ST/ Low Good 4 Species diversity within sites [11]. In general, indices that are sen- diversity to examine whether an absolute ordering sitive to the rarer species are severely affected by can be applied to two populations P and P0 based on differences in sample size, while indices that are sen- their species proportional abundances. P0 is defined sitive to the most abundant species are often poor site to be intrinsically more diverse than P if it can be discriminators because of their high variability across derived from P by a sequence of two operations: years. This led Kempton and Taylor [13] to propose an index Q based on the middle-ranking species in 1. introducing a new species to share the abundance the population and defined by the interquartile slope with a species already present; of the cumulative distribution of species log abun- 2. transferring abundance between two species to make them more equivalent. dance, Q D ST/[2 log0.25ST /0.75ST ], where q is the proportional abundance of the qth most abundant Intuitively, both operations raise the diversity, the species. The need to compromise between discrimi- first by increasing species richness, the second by nant ability and sensitivity to sample size in choice of increasing evenness. A necessary and sufficient con- diversity measure was highlighted by Magurran [16]. dition for P0 ½ P is The performance of diversity measures on these two criteria will depend on the form of the distri- 0 0 i ½ i , 8j D 1,...,maxST,ST bution of species abundances and the nature of their iÄj iÄj individual variability, but some guidance is given in 0 0 Table 1. where ST is the species total for population P ,i and 0 An alternative, parametric approach to measuring i are the proportional abundances of the ith com- diversity comes from empirically modeling the vari- monest species in populations P and P0, respectively, ability of species abundances. The parameters of the and the vectors p and p0 are filled out with zeros if fitted distribution are then used as diversity measures. necessary so that they are of equal length [27]. Hence, If the underlying population distribution is assumed two populations have an intrinsic diversity ordering if to be lognormal, sample estimates may be derived their curves of cumulative species proportional abun- for both ST and the standard deviation of log abun- dance do not intersect. dances . Kempton and Taylor [12] found that these A minimum requirement of any proposed measure two estimates are usually highly positively correlated of diversity is that it orders sites according to the and, taken individually, are poor site discriminators; intrinsic diversity ordering of their local populations, but their ratio, D ST/, is well defined and may whenever such an ordering exists. A necessary and be equated with a constant multiple of the Q statis- sufficient condition for a function fp to be an tic. Similar results hold for the gamma distribution, a intrinsic diversity measure is that common alternative to the lognormal. In this case, if ∂f ∂f S and are large, the sample distribution approxi- Ä 0, 8i, j T ∂ ∂ i j mates to a log series with single diversity parameter i j ˛. Each of the diversity measures in Table 1 can that is, that f is Schur concave [27]. It is easy to show be expressed as a function of the parameters of that all commonly used diversity indices, including the chosen species abundance distribution, leading the rarefraction index (1) and Hill’s family (2), are to estimates that are more efficient and less depen- Schur concave and so will give identical orderings dent on sample size under the model assumptions. of a set of sites whose populations have an intrinsic An important characteristic of a diversity measure diversity ordering. If the population abundance dis- is, then, the robustness of its estimate to the model tributions at all sites follow a log-series distribution, assumptions, particularly when the abundance distri- the sites have an intrinsic diversity ordering given bution is not well defined by the sample (see Robust by the parameter ˛. However, if populations P and inference). P0 follow a lognormal distribution then P0 is intrin- 0 Interpreting diversity assessments is particularly sically more diverse than P if and only if ST ½ ST difficult when different diversity measures give dif- and 0 Ä ,i.e.P0 exceeds P in both species richness 0 0 ferent orderings of environmental sites, even after and evenness. If, however, ST >ST and >,the allowing for differences in sample size. Patil and diversity ordering will depend on choice of measure. Taillie [19, 20] introduced the concept of intrinsic For example, with Hill’s family r, the populations Species diversity 5 will be ordered on species richness for r close to zero, groups; indirect assessment from specialization to whereas for large r ordering is based on evenness plant species; and estimates inferred from empiri- 1/. Likewise, Kempton and Taylor [14] explained cal patterns in species-size relations or community the inconsistencies in site ordering for moth diversity, food web structures. These lead to a range of species for different rarefraction indices Sm, by the devia- estimates from 3 million to 30 million, although the tions of species abundance distributions of some sites breakdown of the traditional species concept for very from the log-series model. small organisms makes any assessment here particu- larly questionable. Up to 2 million species are cur- rently named but, allowing for synonyms, the total Patterns of Diversity number of species so far identified is estimated at between 1.4 million and 1.6 million [28], perhaps lit- Despite extensive research into diversity measures, tle more than 10% of the total. The proportion of mainly concentrated in the 1970s, most biodiversity species identified varies substantially between taxo- assessment is still based on species richness. This nomic groups (Figure 4): for birds, Diamond [4] notes may be explained by the general lack of information that of the 9000 or so species recorded up to 1975, on the distribution of species abundances and the ease only 134 had been discovered in the previous 42 years, of interpretation of species counts. suggesting that the current inventory is well over 90% One rich source of study has been the assess- complete; for many insect groups, however, fewer ment of global biodiversity for different species than 10% of species may yet have been recorded. groups. May [18] describes various methods of infer- The largest taxon, in terms of both identified and pro- ence: extrapolation of trends in species identifica- jected numbers, is that of beetles, which is estimated tion since the first classification by Linaeus in 1758; to include more than 25% of all living species. direct assessment based on the overall fraction of Much interest has focused on global and regional species previously recorded among newly studied patterns of diversity [6]. The most widely cited
Coleoptera Lepidoptera Hymenoptera Diptera Other insects Arachnids Crustaceans Other arthropods Other invertebrates Molluscs Nematodes Vertebrates Plants (Embryophytes) Algae Fungi Protozoans Bacteria Viruses
01234 Number of species (millions)
Figure 4 Global totals of species for different taxa: open bars are projected totals based on overall global estimate of 12.5 million species, shaded areas are numbers identified to date. Reproduced from Stork [28] by permission of the National Academy of Sciences 6 Species diversity example of a direct gradient in overall taxonomic [8] Harper, J.L. & Hawksworth, D.L. (1995). Preface, diversity relates to latitude. Overall taxonomic diver- in Biodiversity: Measurement and Estimation,D.L. sity is high towards the tropics and low towards Hawksworth, ed., Chapman & Hall, London, pp. 5–12. [9] Heltsche, J. & Forrester, N.E. (1984). Estimating the poles. A frequently cited explanation for this is species richness using the jackknife procedure, Biomet- the increase in climatic energy (measured, e.g., by rics 39, 1–11. potential evapotranspiration) as one moves towards [10] Hill, M.O. (1973). Diversity and evenness: a unifying the tropics, though at the regional level the effect of notation and its consequences, Ecology 54, 427–432. latitudinal trends may be masked by local factors, [11] Kempton, R.A. (1979). The structure of species abun- including habitat heterogeneity [16]. dance and measurement of diversity, Biometrics 35, Diversity is also generally observed to be higher 307–321. [12] Kempton, R.A. & Taylor, L.R. (1974). Log-series and in low to middle elevations and in forests and to be log-normal parameters as diversity discriminants for the lower at higher altitudes and in arid regions. Nev- Lepidoptera, Journal of Animal Ecology 43, 381–399. ertheless, there are many examples of regions and [13] Kempton, R.A. & Taylor, L.R. (1976). Models and taxonomic groups where these general observations statistics for species diversity, Nature 262, 818–820. do not hold and spatial correlations among groups [14] Kempton, R.A. & Taylor, L.R. (1979). Some observa- are often found to be weak or nonexistent [6]. Where tions on the yearly variability of species abundance at correlations in species richness do exist, for example a site and the consistency of measures of diversity, in Contemporary Quantitative Ecology and Related Econo- in numbers of butterflies and birds among states of metrics, G.P. Patil & M.L. Rosenzweig, eds, Inter- the US [24], they may be partly attributable to dif- national Co-operative Publishing House, Burtonsville, ferences in habitat area. Studies of hotspots of high pp. 3–22. diversity within regions also show poor coincidence [15] Kempton, R.A. & Wedderburn, R.W.M. (1978). A among taxonomic groups [6, 22]. Moreover, diversity comparison of three measures of species diversity, hotspots do not appear to contain a higher proportion Biometrics 34, 25–37. [16] Kerr, J.T. & Packer, L. (1997). Habitat heterogeneity of the rarer species in a region [3, 22], which has as a determinant of mammal species richness in high- important implications for conservation and the plan- energy regions, Nature 385, 252–254. ning of nature reserves. [17] Magurran, A.E. (1996). Ecological Diversity and Its Measurement, Chapman & Hall, London. [18] May, R.M. (1990). How many species?, Philosophi- References cal Transactions of the Royal Society of London 330, 293–304. [1] Bulmer, M.G. (1974). On fitting the Poisson lognormal [19] Patil, G.P. & Taillie, C. (1979). An overview of distribution to species-abundance data, Biometrics 30, diversity, in Ecological Diversity in Theory and Prac- pp. 101–110. tice, J.F. Grassle, G.P. Patil, W. Smith & C. Taillie, [2] Colwell, R.K. & Coddington, J.A. (1995). Esti- eds, International Co-operative Publishing House, Bur- mating terrestrial biodiversity through extrapola- tonsville, pp. 3–27. tion, in Biodiversity: Measurement and Estimation, [20] Patil, G.P. & Taillie, C. (1982). Diversity as a concept D.L. Hawksworth, ed., Chapman & Hall, London, and its measurement (with discussion), Journal of the pp. 101–118. American Statistical Association 77, 548–567. [3] Curnutt, J., Lockwood, J., Luh, H.-K., Nott, P. & [21] Pielou, E.C. (1975). Ecological Diversity, Wiley, New Russell, G. (1994). Hotspots and species diversity, York. Nature 367, 326–7. [22] Prendergast, J.R., Quinn, R.M., Lawton, J.H., Ever- [4] Diamond, J.M. (1985). How many unknown species are sham, B.C. & Gibbons, D.W. (1993). Rare species, yet to be discovered?, Nature 315, 538–539. the coincidence of diversity hotspots and conservation [5] Gaston, K.J. (1996). Species richness: measure and strategies, Nature 365, 335–337. measurement, in Biodiversity: A Biology of Numbers [23] Preston, F.W. (1948). The commonness and rarity of and Difference, K.J. Gaston, ed., Blackwell, Oxford, species, Ecology 29, 254–283. pp. 77–113. [24] Robbins, R.K. & Opler, P.A. (1997). Butterfly diversity [6] Gaston, K.J. & Williams, P.H. (1996). Spatial patterns in and a preliminary comparison with bird and mam- species diversity, in Biodiversity: A Biology of Numbers mal diversity, in Biodiversity II, M.L. Reaka-Kudla, and Difference, K.J. Gaston, ed., Blackwell, Oxford, D.E. Wilson & E.O. Wilson, eds, Joseph Henry Press, pp. 202–229. Washington, pp. 69–82. [7] Gleason, H.A. (1922). On the relation between species [25] Simpson, E.H. (1949). The measurement of diversity, and area, Ecology 3, 158–162. Nature 163, 688. Species diversity 7
[26] Smith, W. & Grassle, J.F. (1977). Sampling proper- [29] Taylor, L.R. (1978). Bates, Williams, Hutchinson – a ties of a family of diversity indices, Biometrics 33, variety of diversities, in Diversity of Insect Faunas, 283–292. L.A. Mound & N. Waloff, eds, Blackwell, Oxford, [27] Solomon, D.L. (1979). A comparative approach to pp. 1–18. species diversity, in Ecological Diversity in Theory [30] Taylor, L.R., Kempton, R.A. & Woiwod, I.P. (1976). and Practice, J.F. Grassle et al., eds, International Diversity statistics and the log-series model, Journal of Co-operative Publishing House, Burtonsville, Animal Ecology 45, 255–271. pp. 29–35. [28] Stork, N.E. (1997). Burtonsville, Measuring global bio- diversity and its decline, in Biodiversity II, M.L. Reaka- (See also Diversity profiles; Population ecology) Kudla, D.E. Wilson & E.O. Wilson, eds, Joseph Henry Press, Washington, pp. 41–68. R.A. KEMPTON