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Effects of taxonomic uncertainty on species diversity indices
Marine Environmental
Research
6 (1982) 215-225
EFFECTS OF TAXONOMIC UNCERTAINTY ON SPECIES DIVERSITY INDICES
R.S.S. Wu
Fisheries Research Station, IOOA Shek Pal Wan Road, Aberdeen, Hong Kong (Received: 6 May, 1981)
ABSTRACT
As a result of taxonomic uncertainty, generic and higher taxonomic ranks (family, order, class or phylum) are often treated as units in calculating diversity indices, instead of species. In this paper, the errors introduced by such practices are examined for rarious dirersity indices (Shannon-Wiener Index, Maximum Information Index, Evenness, Margalef's Species Richness Index and Hurlbert's Probability of lnterspec([ic Encounter). The use of higher taxonomic ranks may invalidate comparison of diversity indices. In a single stud)', substantial error and erroneous conclusion mal' arise, even if consistent practices are adopted.
INTRODUCTION
Species diversity has been related to community stability, evolution and competition (Margalef, 1963; Connell & Orias, 1964; MacArthur, 1965; Odum, 1971) and is an important parameter in current ecological theory (Heip & Engels, 1974). Various diversity indices are available and provide mathematical means to describe and compare community structure(s) between habitats, or temporally within a habitat. As a consequence, diversity indices have been extensively used in marine environmental research, especially in studies of benthic communities and pollution (e.g. Wade, 1972: Harger et al., 1974: Littler & Murray, 1975; Taslakian & Hardy, 1976; Moore, 1978; Nybakken, 1978: Rosenberg & M611er, 1979). Some authors have discussed the theoretical basis of diversity indices: Peet (1974) has reviewed the criteria in the selection of an appropriate index and Heip & Engels (1974) have compared the statistical nature of different indices. However, little attention has been paid to the accuracy and validity of diversity indices when taxonomic ranks higher than species are employed. This is a common practice when 215 Marine Era'iron. Res. 0141 - I 136/82/0006-0215/$02.75 c~ Applied Science Publishers Ltd, England, 1982 Printed in Great Britain
216
R.S.S. WV
difficult taxonomic groups (e.g. nematodes) are included in the sample, since it is impossible or impractical to identify every organism in the collection to species level. As a result, it is not uncommon in the literature to find that some of the organisms in the sample have been identified to species, but others have been assigned to generic or higher taxonomic levels only and are treated as individual units in calculating diversity indices. Some examples of using a mixture of species and genus in calculating diversity indices are found in Borowitzka (1972) (Enteromorpha spp. and Ceramium spp.); Harger & Nassichuk (1974) (Nitzchia spp., Naricula spp. and many other genera) and Rosenberg & M611er (1979) (Hydrobia spp. and Nephtys spp.). Others used phylum (e.g. Blue-green algae; in Littler & Murray, 1975) or a combination of various taxonomic levels in their calculation (for example: Cumacea and Cirripedia (Wade, 1972): Cyanophyta, pennate diatoms, Cvlindrotheca spp. and Nm'icula spp. (Taslakian & Hardy. 1976): Clupeidae, Menidia spp. and Fundulus spp. (Hillman et al., 1977) and unidentified flagellates, cyclops and nematodes (Reed, 1978)). Such a practice may, however, elicit errors in the comparison of diversity indices. Illustrated with two examples, this paper examines the possible effects of taxonomic uncertainty on the calculation of five commonly used diversity indices.
MATERIALS AND METHODS
Two examples are used to illustrate the assertion of the present paper.
Example A The purpose of this example is to illustrate the effect of various levels of taxonomic lumping on the accuracy of diversity indices calculation. A collection of macrobenthos obtained by trawling for 15 min (with an Agassiz trawl) near South Lamma Island, Hong Kong (114°8 ' E, 2209 ' N) was used in this example. Assuming the following cases: Case A 1: All the animals in the collection were identified to species and treated as units. Case A2: All the animals in the collection were identified to species, except Babylonia (occurring in small numbers, n = 18) to genus and treated as a unit. Case A3: All the animals in the collection were identified to species, except Anadara (occurring in large numbers, n = 149) to genus and treated as a unit. Case A4." All the animals in the collection were identified to genus and treated as units. Case A5: All the animals in the collection were identified to species, except the bivalves which were not so differentiated and were treated as a unit.
EFFECTS OF T A X O N O M I C U N C E R T A I N T Y O N SPECIES DIVERSITY INDICES
217
Case A6." All the animals in the collection were identified to a higher taxonomic category (e.g. shrimps, crabs, fish, gastropods, bivalves, etc.) and treated as units. The following five diversity indices were then calculated for each of the above cases:
(1) Shannon-Wiener index (H') (Shannon & Weaver, 1963): S
H'=
VNiln(Ni~
\NJ i=1
(2) Maximum information index (Hmax) (Pielou, 1966): Hma x =
In S
(3) Evenness (E) (Pielou, 1966):
E = H'/Hma x (4) Margalef's species richness index (D) (Margalef, 1969): D = (S - 1)/ln N (5) Hurlbert's probability of interspec(/ic encounter (PIE) (Hurlbert, 1971): S
V(Ni)(N-Ni) eI E = / ~ \ ~ / \ - ~ - - - ~ - j where: S = Total number of units (species) in the collection. N = Total number of individuals in the collection. Ni = Number of individuals in the ith species (i = I to S). These five indices were chosen for comparison and illustration because they are most commonly used in community ecology and pollution studies. (See, for example, Bechtel & Copeland, 1970; McErlan et al., 1973; Help & Engels, 1974; Peet, 1974; Moore, 1978.)
Example B In order to examine whether erroneous conclusions will be derived when higher taxonomic levels are used consistently in a single study, the following levels of taxonomic lumping were applied consistently in the calculation and comparison of the Shannon-Wiener index (H') for three trawl samples obtained from south of Lamma Island (114°8 ' E, 22o9 ' N), Tolo Channel (114 ° 17' E, 22 °29' N) and north of Lantau Island (114°2 ' E, 22020 ' N): Case BI: All the animals in the collections were identified to species and treated as units.
218
R. S. S. WU
Case B2: All the animals in the collections were identified to genus. Case B3: All the animals in the collections were identified to species, except the bivalves which were treated as a unit. Case B4: All the animals in the collections were identified to species except the bivalves, gastropods and crabs, which were treated as units. Case B5: As B1, but assuming a highly skewed distribution of bivalves, with one individual per species and all remaining individuals in one species. Case B6: As B1, but assuming an equal number of individuals in each bivalve species, so far as whole numbers permit.
RESULTS
Example A The five diversity indices calculated for each of the six cases (A1 to A6) are shown in Table 1. The value of each diversity index obtained from Cases A2 to A6 is then compared with the same from Case A1 (all individuals identified to species). The error involved is expressed in terms of the percentage deviation from the value obtained in Case 1 and is shown in brackets below each value. Only a small error is introduced when a genus with a small number of individuals is treated as a unit in calculation (Case A2). A large error is associated in calculating diversity indices when a genus/group with a large number of individuals is not differentiated into species and treated as a single unit (Cases A3 and A5). Generally, the less precise the identification, the lower the values of diversity indices obtained and the larger the error incurred (Cases A4, A5 and A6). Shannon-Wiener (H') and Margalef's species richness index (D) are particularly sensitive to the grouping of species (the errors in calculating H' and D in C a s e A 6 = 4 5 . 8 and 73.7°0, respectively) whereas Evenness (E) is relatively insensitive. Example B The number of individuals in each species for the three samples are shown in Table 2. The value of H' calculated for each sample at various taxonomic levels (Cases B I to B6) are shown in Table 3. The rank orders of H' for the three samples, resulting from each level of identical taxonomic treatment, are also shown. In Case B1 (all individuals identified to species), the highest value of H' is found for Sample 1, followed by Samples 2 and 3. The rank order of H' becomes: Sample 2 > Sample 1 > Sample 3, when all the species in the same genera were lumped in the same way consistently for the three samples; and changes into: S a m p l e 2 > Sample 3 > Sample I when all the bivalves, gastropods and crabs were lumped, or when all the bivalves only were lumped. When comparing the H' values derived from Case B5 (skewed distribution of
EFFECTS OF TAXONOMIC UNCERTAINTY ON SPECIES DIVERSITY INDICES <
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EFFECTS OF TAXONOMIC UNCERTAINTY ON SPECIES DIVERSITY INDICES
221
TABLE 2 NUMBER OF INDIVIDUALS IN EACH SPECIES FOR THE THREE TRAWL SAMPLES USED IN EXAMPLE B
Sample 1 (South o f Lamina)
Sample 2 (Tolo Channel)
Sample 3 (North o f Lantau)
4
4 3
l
11
18
2
12 6 2
4 3
I
Anemones
Carcinactis ichikawai Cerianthus filiformis
13
8
Sea Pens
Pteroeides esperi P. sparmanni Sclerobelemnon burgeri Gastropods
Babylonia areolata B. formosae Bursa rana Clypeomorus traillis Murex trapa Notocochlis hilaris N. zebra Philine orientalis Turritella terebra
12
5
8
4 2 6 4 6
1
7 42 74 26 10
25
4
22
2
Bivalves
Anadara granosa A. nipponensis A. subcrenata A. tricenicosta Atrina kuioshitae A. pectinata Callianaitis hiraseana Pinctada fucata P. margaritifera P. martensii Paphia undulata
5 8
11 46 24
5
Cephalopods
Eupryma morsel Octopus aeginea
6 1
1
4
25
2
Stomatopods
Oratosquilla oratoria Shrimps
Metapenaeopsis barbara Metapenaeus ]oyneri Trach)penaeus fuh'us
12 8 6
Crabs
Ceratoplax sagamiensis Charybdis t,adorum C. varwgatus Doripe granulata Portunus hastatoides P. pelagicus P. sanquinolentus Thalamita picta
1 29
2
1
8 12
4
1
42
64
2
2 8 16
4
1
TABLE 2--contd.
Sample 1 (South of Lamina)
Sample 2 (Tolo Channel)
7
20
4
1I
Sample 3 (North of Lantau)
Heart Urchins
Lorenia subcarinata Schizaster lacunosus Urchins
Temnopleurus toreumatleus Starfish
Luidia hardwickii
11
Brittle star
Ophiura kinbergii
24
26
52
22 34
Sea cucumber
Paracaudina chilensis Fish
Callionymus richardsonii Leiognathus brerirostris Siganus oramin Syngnathus acus Tr)'pauchen vagina Vespicula bottae
6 47
25
8
TABLE 3 VALUES OF SHANNON-WIENER DIVERSITY INDEX ( H ' ) CALCULATED FOR THREE TRAWL SAMPLES AT DIFFERENT LEVELS OF TAXONOMICUNCERTAINTIES
Taxonomic lumping
Sample 1 Sample 2 Sample 3 Rank orders of (South of Lamina) (Tolo Channel) (North of Lantau)diversity index (H')
Case B1 No lumping, all individuals identified to species
3.229
2-868
2.645
1> 2 > 3
2.715
2.829
2.645
2 > 1> 3
2.425
2.734
2.539
2> 3> 1
2.057
2.409
2.124
2> 3> 1
2-519
2.761
2.614
2> 3> 1
3.363
2.890
2.655
1> 2 > 3
Case B Lumping of all species in the same genera
Case B3 Lumping of all bivalve species
Case B4 Lumping of all crab, gastropod and bivalve species
Case B5 Highly skewed distribution of bivalve species
Case B6 Highly even distribution of bivalve species
EFFECTS OF TAXONOMIC UNCERTAINTY ON SPECIES DIVERSITY INDICES
223
bivalve species) and Case B6 (even distribution of bivalve species) for each sample, the deviation is 33.5 ~o, 4.7 ~ and 1.6 ~ for Samples 1, 2, 3, respectively.
DISCUSSION
It is clear from a comparison of the diversity indices calculated for Cases A 1, A4, A5, A6 and BI to B4, that the value of the indices decreases, whereas the error involved increases, as identification becomes less specific. This applies to all the five diversity indices under current consideration. In Cases A2 to A3, a genus is not differentiated into species and is treated as a unit in calculating diversity indices. Such a grouping potentially introduces an error in calculation, which is directly related to the number of individuals within the genus/ group. The error incurred also depends on the distribution of individuals between the unidentified species within the genus/group and would be large if the number of individuals in each unidentified species within the genus/group is relatively even. Conversely, for example, if99 % of the individuals within the genus/group belong to a single species, the error incurred would be small and negligible. It is also clear that a large error is incurred when higher taxonomic groups (genus and upward) are treated as units in calculating diversity indices (Cases A5 and A6). This suggests that the calculation of diversity indices based on gross identification (to the level of genus and higher) is not likely to be accurate. In Case B2, lumping of species of the same genus changes the rank orders of H'. This occurs mainly because Sample I contains many individuals spread between four species of Anadara, three species of Pinctada and three species of Portunus. Samples 2 and 3 are much less affected, because generally they have fewer or only one species per genus. In Cases B3 (grouping of all bivalves together) and B4 (grouping of bivalves, gastropods and crabs), the rank order of H' changes to: Sample 2 > Sample 3 > Sample 1. The reduction in H' in Sample i is particularly marked because this sample contains large numbers of bivalves, gastropods and crabs. Wilhm & Dorris (1968) and Wilhm (1972) have demonstrated that diversity contributed by rare species is small whereas the maximum contribution to total diversity will be made by a species that comprises 37 ~o of the sample. It is clear from Example B that rank order of H' for the three samples varies with different types of taxonomic lumping. This indicates that even when taxonomic groupings are consistently used in a single study, erroneous conclusions may be reached in the calculation and comparison of diversity indices, because an unknown and varying error is incurred in each calculation. For example, the difference between the values of H' derived from Cases B5 (skewed distribution of bivalve species) and B6 (even distribution of bivalve species) may be as high as 33.5 o~ for
224
R.S.S. wU
Sample 1, although the total number of individuals and the total number of species remains unchanged. An error will be introduced in comparing diversity indices unless both the number and distribution of individuals and species within the unidentified group are the same in both sets of data. Obviously, this can be established if all the individuals within the unidentified group have been identified to species level. A good diversity index should be sensitive to change in species composition and/or abundance (Peet, 1974). Of the five diversity indices considered, the Shannon-Wiener Index (H') and Margalef's Species Richness Index (D) seem to be particularly sensitive to the grouping of species, because the value of these two indices are directly dependent on S (the number of taxonomic unit). Evenness (E) is, on the other hand, relatively insensitive because only the distribution of the relative abundance is important for this index, and also because it is the ratio of two indices (H' and H~a~) which contain the same bias. Reish & Unzicker (1975) demonstrated that it is dangerous to use genus or higher taxonomic levels to serve as indicators of water quality, and emphasised the need for species level identification in establishing biological indicators. Similarly, the results derived from the two examples here presented suggest that a substantial error may be involved in using taxonomic levels higher than species (i.e. genus and upward) in calculating diversity indices. (One of the referees has commented that 'Jacknife' techniques would probably effectively detect this type of bias by providing higher variance estimates.) Care should be taken in the interpretation of data if part of the collection has not been identified to species and the following rules may be useful: (1)
(2) (3)
If accurate identification of species is impossible, differentiation into unidentified species 1,2,3 . . . . . etc., based on obvious morphological differences, should be made as far as possible before diversity indices are calculated or compared. If only a small number of individuals is involved within the unidentified taxa, the error may probably be small and negligible. If a large number of individuals is involved within the unidentified taxa, a large error is likely to occur. Calculating and comparing diversity indices may be meaningless in this case, and more detailed identification is necessary if diversity indices are to be used.
ACKNOWLEDGEMENTS
I thank Dr G. B. Thompson for reading and criticising this manuscript. Thanks are also due to Mr E. H. Nichols, Director of Agriculture and Fisheries, Hong Kong Government, for his permission to publish.
EFFECTS OF TAXONOMIC UNCERTAINTY ON SPECIES DIVERSITY INDICES
225
REFERENCES ALLAN, J. D. (1975). The distributional ecology and diversity of benthic insects in Cement Creek, Colorado. Ecology, 56, 1040-53. BECHTEL, T.J. & COPELAND, B.J. (1970). Fish species diversity indices as indicators of pollution in Galveston Bay, Texas. Contr. Mar. Sci. Univ. Texas, 15, 103-32. BOROWITZKA, M.A. (1972). Intertidal algal species diversity and the effect of pollution. Aust. J. Mar. Freshwat. Res., 23, 73-84. CONNELL,J. C. • ORIAS,E. (1964). The ecological regulation of species diversity. Am. Nat., 98, 399-414. HARGER, J. R. E. & NAmlCHUK, M. D. (1974). Marine intertidal community responses of kraft pulp mill effluent. Wat. Air and Soil Pollut., 3, 107-22. HEIP, C. & ENGELS, P. (1974). Comparing species diversity and evenness indices. J. Mar. Biol. Assoc. UK, 54, 559-63. HIELMAN, R. E., DAVIS, N. W. &. WENNEMER,J. (1977). Abundance, diversity and stability in shore-zone fish communities in an area of Long Island Sound affected by the thermal discharge of nuclear power station. Estuar. Cstl. mar. Sci., 5, 355-81. HURLBERT, S. H. (1971). The nonconcept of species diversity: A critique and alternative parameters. Ecology, 52, 577-86. LITTLER, M. M. & MURRAY, S. N. (1975). Impact of sewage on the distribution, abundance and community structure of rocky intertidal macroorganism. Mar. Biol., 30, 277-92. MCERLEAN, A. J., O'CoNNER, S. G., Mmul~stV, J. A. & GIBSON,C. I. (1973). Abundance, diversity and seasonal patterns of estuarine fish populations. Estuar. cstl. mar. Sci., 1, 19-36. MACARTHUR, R. H. (1965). Pattern of species diversity. Biol. Rev., 40. 510-33. MARGALEF, R. (1963). On certain unifying principles in ecology. Am. Nat., 97, 357-74. MARGALEF, R. (1969). Diversity and stability: A practical proposal and a model of interdependence. Brookhaven Syrup. Biol., 22, 25-37. MOORE. R. H. (1978). Variations in the diversity of summer estuarine fish populations in Aransas Bay, Texas, 1966-1973. Estuar. and cstl. mar. Sci., 6, 495-501. NYBAKKEN, J. (1978). Abundance, diversity and temporal variability in a Californian intertidal nudibranch assemblage. Mar. Biol., 45, 129-46, ODUM, E. P. (1971). Fundamentals o f ecology. (3rd edn.), W.B. Saunders, Philadelphia, 574 pp. PEET, R, K. (1974). The measurement of species diversity. Annual Rev. Ecol. Syst., $, 285-307. PIELOU, E. C. (1966). Shannon's formula as a measure of species diversity: Its use and misuse. Am. Nat., !00, 463-5. REED, C. (1978). Species diversity in aquatic microecosystems. Ecology, 59, 481-8. REISH, D. J. & UNZlCrd~R,T. C. (1975). Water quality monitoring and aquatic organisms: Importance of species identification. J. War. Pollut. Cont. Fed., 47, 9-19. ROSENBERG,R. & M6LLER, R. (1979). Salinity stratified benthic macrofaunal communities and long term monitoring along the west coast of Sweden. J. exp. mar. Biol. Ecol., 37, 175-203. SHANNON, C. E. & WEAVER, W. (1963). The mathematical theory of communication. Univ. Ill. Press, ll7pp. TASLAKIAN,M. J. & HARDY, J. T. (1976). Sewage nutrient enrichment and phytoplankton ecology along the central coast of Lebanon. Mar. Biol., 38, 315-25. WADE, B. A. (1972). A description of a highly diverse soft-bottom community in Kingston Harbour, Jamaica, Mar. Biol., 13, 57-69. WIEHM. J. L (1972). Graphic and mathematical analysis of biotic communities in polluted streams. Annual Rev. Emomol., 17, 223-52. WILHM. J. L. and DORRIS, T. C. (1968). Biological parameters for water quality criteria. Biosci., 18, 477-81
Research
6 (1982) 215-225
EFFECTS OF TAXONOMIC UNCERTAINTY ON SPECIES DIVERSITY INDICES
R.S.S. Wu
Fisheries Research Station, IOOA Shek Pal Wan Road, Aberdeen, Hong Kong (Received: 6 May, 1981)
ABSTRACT
As a result of taxonomic uncertainty, generic and higher taxonomic ranks (family, order, class or phylum) are often treated as units in calculating diversity indices, instead of species. In this paper, the errors introduced by such practices are examined for rarious dirersity indices (Shannon-Wiener Index, Maximum Information Index, Evenness, Margalef's Species Richness Index and Hurlbert's Probability of lnterspec([ic Encounter). The use of higher taxonomic ranks may invalidate comparison of diversity indices. In a single stud)', substantial error and erroneous conclusion mal' arise, even if consistent practices are adopted.
INTRODUCTION
Species diversity has been related to community stability, evolution and competition (Margalef, 1963; Connell & Orias, 1964; MacArthur, 1965; Odum, 1971) and is an important parameter in current ecological theory (Heip & Engels, 1974). Various diversity indices are available and provide mathematical means to describe and compare community structure(s) between habitats, or temporally within a habitat. As a consequence, diversity indices have been extensively used in marine environmental research, especially in studies of benthic communities and pollution (e.g. Wade, 1972: Harger et al., 1974: Littler & Murray, 1975; Taslakian & Hardy, 1976; Moore, 1978; Nybakken, 1978: Rosenberg & M611er, 1979). Some authors have discussed the theoretical basis of diversity indices: Peet (1974) has reviewed the criteria in the selection of an appropriate index and Heip & Engels (1974) have compared the statistical nature of different indices. However, little attention has been paid to the accuracy and validity of diversity indices when taxonomic ranks higher than species are employed. This is a common practice when 215 Marine Era'iron. Res. 0141 - I 136/82/0006-0215/$02.75 c~ Applied Science Publishers Ltd, England, 1982 Printed in Great Britain
216
R.S.S. WV
difficult taxonomic groups (e.g. nematodes) are included in the sample, since it is impossible or impractical to identify every organism in the collection to species level. As a result, it is not uncommon in the literature to find that some of the organisms in the sample have been identified to species, but others have been assigned to generic or higher taxonomic levels only and are treated as individual units in calculating diversity indices. Some examples of using a mixture of species and genus in calculating diversity indices are found in Borowitzka (1972) (Enteromorpha spp. and Ceramium spp.); Harger & Nassichuk (1974) (Nitzchia spp., Naricula spp. and many other genera) and Rosenberg & M611er (1979) (Hydrobia spp. and Nephtys spp.). Others used phylum (e.g. Blue-green algae; in Littler & Murray, 1975) or a combination of various taxonomic levels in their calculation (for example: Cumacea and Cirripedia (Wade, 1972): Cyanophyta, pennate diatoms, Cvlindrotheca spp. and Nm'icula spp. (Taslakian & Hardy. 1976): Clupeidae, Menidia spp. and Fundulus spp. (Hillman et al., 1977) and unidentified flagellates, cyclops and nematodes (Reed, 1978)). Such a practice may, however, elicit errors in the comparison of diversity indices. Illustrated with two examples, this paper examines the possible effects of taxonomic uncertainty on the calculation of five commonly used diversity indices.
MATERIALS AND METHODS
Two examples are used to illustrate the assertion of the present paper.
Example A The purpose of this example is to illustrate the effect of various levels of taxonomic lumping on the accuracy of diversity indices calculation. A collection of macrobenthos obtained by trawling for 15 min (with an Agassiz trawl) near South Lamma Island, Hong Kong (114°8 ' E, 2209 ' N) was used in this example. Assuming the following cases: Case A 1: All the animals in the collection were identified to species and treated as units. Case A2: All the animals in the collection were identified to species, except Babylonia (occurring in small numbers, n = 18) to genus and treated as a unit. Case A3: All the animals in the collection were identified to species, except Anadara (occurring in large numbers, n = 149) to genus and treated as a unit. Case A4." All the animals in the collection were identified to genus and treated as units. Case A5: All the animals in the collection were identified to species, except the bivalves which were not so differentiated and were treated as a unit.
EFFECTS OF T A X O N O M I C U N C E R T A I N T Y O N SPECIES DIVERSITY INDICES
217
Case A6." All the animals in the collection were identified to a higher taxonomic category (e.g. shrimps, crabs, fish, gastropods, bivalves, etc.) and treated as units. The following five diversity indices were then calculated for each of the above cases:
(1) Shannon-Wiener index (H') (Shannon & Weaver, 1963): S
H'=
VNiln(Ni~
\NJ i=1
(2) Maximum information index (Hmax) (Pielou, 1966): Hma x =
In S
(3) Evenness (E) (Pielou, 1966):
E = H'/Hma x (4) Margalef's species richness index (D) (Margalef, 1969): D = (S - 1)/ln N (5) Hurlbert's probability of interspec(/ic encounter (PIE) (Hurlbert, 1971): S
V(Ni)(N-Ni) eI E = / ~ \ ~ / \ - ~ - - - ~ - j where: S = Total number of units (species) in the collection. N = Total number of individuals in the collection. Ni = Number of individuals in the ith species (i = I to S). These five indices were chosen for comparison and illustration because they are most commonly used in community ecology and pollution studies. (See, for example, Bechtel & Copeland, 1970; McErlan et al., 1973; Help & Engels, 1974; Peet, 1974; Moore, 1978.)
Example B In order to examine whether erroneous conclusions will be derived when higher taxonomic levels are used consistently in a single study, the following levels of taxonomic lumping were applied consistently in the calculation and comparison of the Shannon-Wiener index (H') for three trawl samples obtained from south of Lamma Island (114°8 ' E, 22o9 ' N), Tolo Channel (114 ° 17' E, 22 °29' N) and north of Lantau Island (114°2 ' E, 22020 ' N): Case BI: All the animals in the collections were identified to species and treated as units.
218
R. S. S. WU
Case B2: All the animals in the collections were identified to genus. Case B3: All the animals in the collections were identified to species, except the bivalves which were treated as a unit. Case B4: All the animals in the collections were identified to species except the bivalves, gastropods and crabs, which were treated as units. Case B5: As B1, but assuming a highly skewed distribution of bivalves, with one individual per species and all remaining individuals in one species. Case B6: As B1, but assuming an equal number of individuals in each bivalve species, so far as whole numbers permit.
RESULTS
Example A The five diversity indices calculated for each of the six cases (A1 to A6) are shown in Table 1. The value of each diversity index obtained from Cases A2 to A6 is then compared with the same from Case A1 (all individuals identified to species). The error involved is expressed in terms of the percentage deviation from the value obtained in Case 1 and is shown in brackets below each value. Only a small error is introduced when a genus with a small number of individuals is treated as a unit in calculation (Case A2). A large error is associated in calculating diversity indices when a genus/group with a large number of individuals is not differentiated into species and treated as a single unit (Cases A3 and A5). Generally, the less precise the identification, the lower the values of diversity indices obtained and the larger the error incurred (Cases A4, A5 and A6). Shannon-Wiener (H') and Margalef's species richness index (D) are particularly sensitive to the grouping of species (the errors in calculating H' and D in C a s e A 6 = 4 5 . 8 and 73.7°0, respectively) whereas Evenness (E) is relatively insensitive. Example B The number of individuals in each species for the three samples are shown in Table 2. The value of H' calculated for each sample at various taxonomic levels (Cases B I to B6) are shown in Table 3. The rank orders of H' for the three samples, resulting from each level of identical taxonomic treatment, are also shown. In Case B1 (all individuals identified to species), the highest value of H' is found for Sample 1, followed by Samples 2 and 3. The rank order of H' becomes: Sample 2 > Sample 1 > Sample 3, when all the species in the same genera were lumped in the same way consistently for the three samples; and changes into: S a m p l e 2 > Sample 3 > Sample I when all the bivalves, gastropods and crabs were lumped, or when all the bivalves only were lumped. When comparing the H' values derived from Case B5 (skewed distribution of
EFFECTS OF TAXONOMIC UNCERTAINTY ON SPECIES DIVERSITY INDICES <
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E
E
EFFECTS OF TAXONOMIC UNCERTAINTY ON SPECIES DIVERSITY INDICES
221
TABLE 2 NUMBER OF INDIVIDUALS IN EACH SPECIES FOR THE THREE TRAWL SAMPLES USED IN EXAMPLE B
Sample 1 (South o f Lamina)
Sample 2 (Tolo Channel)
Sample 3 (North o f Lantau)
4
4 3
l
11
18
2
12 6 2
4 3
I
Anemones
Carcinactis ichikawai Cerianthus filiformis
13
8
Sea Pens
Pteroeides esperi P. sparmanni Sclerobelemnon burgeri Gastropods
Babylonia areolata B. formosae Bursa rana Clypeomorus traillis Murex trapa Notocochlis hilaris N. zebra Philine orientalis Turritella terebra
12
5
8
4 2 6 4 6
1
7 42 74 26 10
25
4
22
2
Bivalves
Anadara granosa A. nipponensis A. subcrenata A. tricenicosta Atrina kuioshitae A. pectinata Callianaitis hiraseana Pinctada fucata P. margaritifera P. martensii Paphia undulata
5 8
11 46 24
5
Cephalopods
Eupryma morsel Octopus aeginea
6 1
1
4
25
2
Stomatopods
Oratosquilla oratoria Shrimps
Metapenaeopsis barbara Metapenaeus ]oyneri Trach)penaeus fuh'us
12 8 6
Crabs
Ceratoplax sagamiensis Charybdis t,adorum C. varwgatus Doripe granulata Portunus hastatoides P. pelagicus P. sanquinolentus Thalamita picta
1 29
2
1
8 12
4
1
42
64
2
2 8 16
4
1
TABLE 2--contd.
Sample 1 (South of Lamina)
Sample 2 (Tolo Channel)
7
20
4
1I
Sample 3 (North of Lantau)
Heart Urchins
Lorenia subcarinata Schizaster lacunosus Urchins
Temnopleurus toreumatleus Starfish
Luidia hardwickii
11
Brittle star
Ophiura kinbergii
24
26
52
22 34
Sea cucumber
Paracaudina chilensis Fish
Callionymus richardsonii Leiognathus brerirostris Siganus oramin Syngnathus acus Tr)'pauchen vagina Vespicula bottae
6 47
25
8
TABLE 3 VALUES OF SHANNON-WIENER DIVERSITY INDEX ( H ' ) CALCULATED FOR THREE TRAWL SAMPLES AT DIFFERENT LEVELS OF TAXONOMICUNCERTAINTIES
Taxonomic lumping
Sample 1 Sample 2 Sample 3 Rank orders of (South of Lamina) (Tolo Channel) (North of Lantau)diversity index (H')
Case B1 No lumping, all individuals identified to species
3.229
2-868
2.645
1> 2 > 3
2.715
2.829
2.645
2 > 1> 3
2.425
2.734
2.539
2> 3> 1
2.057
2.409
2.124
2> 3> 1
2-519
2.761
2.614
2> 3> 1
3.363
2.890
2.655
1> 2 > 3
Case B Lumping of all species in the same genera
Case B3 Lumping of all bivalve species
Case B4 Lumping of all crab, gastropod and bivalve species
Case B5 Highly skewed distribution of bivalve species
Case B6 Highly even distribution of bivalve species
EFFECTS OF TAXONOMIC UNCERTAINTY ON SPECIES DIVERSITY INDICES
223
bivalve species) and Case B6 (even distribution of bivalve species) for each sample, the deviation is 33.5 ~o, 4.7 ~ and 1.6 ~ for Samples 1, 2, 3, respectively.
DISCUSSION
It is clear from a comparison of the diversity indices calculated for Cases A 1, A4, A5, A6 and BI to B4, that the value of the indices decreases, whereas the error involved increases, as identification becomes less specific. This applies to all the five diversity indices under current consideration. In Cases A2 to A3, a genus is not differentiated into species and is treated as a unit in calculating diversity indices. Such a grouping potentially introduces an error in calculation, which is directly related to the number of individuals within the genus/ group. The error incurred also depends on the distribution of individuals between the unidentified species within the genus/group and would be large if the number of individuals in each unidentified species within the genus/group is relatively even. Conversely, for example, if99 % of the individuals within the genus/group belong to a single species, the error incurred would be small and negligible. It is also clear that a large error is incurred when higher taxonomic groups (genus and upward) are treated as units in calculating diversity indices (Cases A5 and A6). This suggests that the calculation of diversity indices based on gross identification (to the level of genus and higher) is not likely to be accurate. In Case B2, lumping of species of the same genus changes the rank orders of H'. This occurs mainly because Sample I contains many individuals spread between four species of Anadara, three species of Pinctada and three species of Portunus. Samples 2 and 3 are much less affected, because generally they have fewer or only one species per genus. In Cases B3 (grouping of all bivalves together) and B4 (grouping of bivalves, gastropods and crabs), the rank order of H' changes to: Sample 2 > Sample 3 > Sample 1. The reduction in H' in Sample i is particularly marked because this sample contains large numbers of bivalves, gastropods and crabs. Wilhm & Dorris (1968) and Wilhm (1972) have demonstrated that diversity contributed by rare species is small whereas the maximum contribution to total diversity will be made by a species that comprises 37 ~o of the sample. It is clear from Example B that rank order of H' for the three samples varies with different types of taxonomic lumping. This indicates that even when taxonomic groupings are consistently used in a single study, erroneous conclusions may be reached in the calculation and comparison of diversity indices, because an unknown and varying error is incurred in each calculation. For example, the difference between the values of H' derived from Cases B5 (skewed distribution of bivalve species) and B6 (even distribution of bivalve species) may be as high as 33.5 o~ for
224
R.S.S. wU
Sample 1, although the total number of individuals and the total number of species remains unchanged. An error will be introduced in comparing diversity indices unless both the number and distribution of individuals and species within the unidentified group are the same in both sets of data. Obviously, this can be established if all the individuals within the unidentified group have been identified to species level. A good diversity index should be sensitive to change in species composition and/or abundance (Peet, 1974). Of the five diversity indices considered, the Shannon-Wiener Index (H') and Margalef's Species Richness Index (D) seem to be particularly sensitive to the grouping of species, because the value of these two indices are directly dependent on S (the number of taxonomic unit). Evenness (E) is, on the other hand, relatively insensitive because only the distribution of the relative abundance is important for this index, and also because it is the ratio of two indices (H' and H~a~) which contain the same bias. Reish & Unzicker (1975) demonstrated that it is dangerous to use genus or higher taxonomic levels to serve as indicators of water quality, and emphasised the need for species level identification in establishing biological indicators. Similarly, the results derived from the two examples here presented suggest that a substantial error may be involved in using taxonomic levels higher than species (i.e. genus and upward) in calculating diversity indices. (One of the referees has commented that 'Jacknife' techniques would probably effectively detect this type of bias by providing higher variance estimates.) Care should be taken in the interpretation of data if part of the collection has not been identified to species and the following rules may be useful: (1)
(2) (3)
If accurate identification of species is impossible, differentiation into unidentified species 1,2,3 . . . . . etc., based on obvious morphological differences, should be made as far as possible before diversity indices are calculated or compared. If only a small number of individuals is involved within the unidentified taxa, the error may probably be small and negligible. If a large number of individuals is involved within the unidentified taxa, a large error is likely to occur. Calculating and comparing diversity indices may be meaningless in this case, and more detailed identification is necessary if diversity indices are to be used.
ACKNOWLEDGEMENTS
I thank Dr G. B. Thompson for reading and criticising this manuscript. Thanks are also due to Mr E. H. Nichols, Director of Agriculture and Fisheries, Hong Kong Government, for his permission to publish.
EFFECTS OF TAXONOMIC UNCERTAINTY ON SPECIES DIVERSITY INDICES
225
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