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Ecological Entomology (1988) 13, 25-37 Species number, species abundance and body length relationships of arboreal beetles in Bornean lowland rain forest trees D. R. MORSE, N. E. STORK* and J. H. LAWTON? The Computing Laboratory, The University, Canterbury, *Department of Entomology, British Museum (Natural History), and ?Department of Biology, University of York ABSTRACT. 1. The relationships between number of species, abundance per species, and body length are examined for 859 species of beetles in samples of arthropods collected from ten Bornean lowland forest trees by insecticide fogging. Similar relationships are examined for different feeding guilds of these beetles, and for those beetles from different species of trees. 2. The data are used to construct four interrelated graphs, namely species:abundance, species :body length, population abundance:body length and total number of individuals:body length distributions. 3. In contrast to a number of previous studies, no consistent linear relationship between population density and body length was found for the Bornean beetles and it is suggested that, as in birds, the added dispersal ability of flight reduces critical population densities necessary for persistence in small species. Previous relationships between body weight and population abundance may also be artefacts of the way in which data were gathered. 4. Despite large samples, we failed to locate the mode in plots of the number of species in each abundance category (species: abundance distribution). 5. Species:body length and total number of individuals:body length plots were similar to those found in previous studies, although using data for Coleoptera alone may have produced a steeper decline in the total number of individuals as body size increases than is apparent in samples of all arthropods. 6. We present the first three-dimensional graph relating numbers of species, body lengths and population abundances. The surface of this three-dimensional relationship is relatively simple. Key words. Species abundance, body length, beetles, Borneo, tree canopy, rain forest, insecticide fogging. Correspondence: Mr D. R. Morse, The Computing Laboratory, The University, Canterbury, Kent CT2 7NF. 25 26 D.R. Morse, N . E. Stork utidJ. H . Lawtoti Introduction The structure of animal communities can be described in a number of ways; the simplest is the number of coexisting species. More subtle descriptions of samples of organisms from a community include: the number of species in each abundance category (the so-called species: abundance distribution. or species : frequency distribution. e.g. Preston. 1938; Williams. 1953; May, 1Y75: Southwood. 1978: Sugihara. 1980); the number of species of different body sizes (species: body-size distribution) (e.g. Hemmingsen. 103.1; Hutchinson & MacArthur. 1959: May. 1978. 1986; Griffiths. 1986); and the abundance of each species versus body size (population abundance; body size relationship) (e.g. Damuth. 1981; Peters. 1983: Peters & Raelson, 1984: Peters & Wassenberg. 'T\ 1983; Brown & Maurer, 1986). Summing individuals for all species of one body size yields a fourth pattern. the total number of individuals of a particular size, irrespective of species (total number of individuals: body size, or if biomass rather than number is used. total biomass:body size relationship, e.g. Janzen & Schoener, 1968; Janzen, 1973; Morse eral., 1985; Griffiths, 1986; Rodriguez & Mullin. 1986; Strayer. 1986). Each of these relationships has its own literature, and theoretical explanations for particular patterns (loc. cit.). But, as Fig. 1 makes plain, they are interrelated. For example. fixing any two of the basic relationships in Fig. 1 (i) (species:abundance, species:body size. or population abundance :body size) automatically defines the limits of the third (Harvey & Lawton, 1Y86). A growing number of papers consider relationships between two of the dis- NUMBER OF SPECIES LOG ABUNDANCE PER SPECIES TOTAL INDIVIDUALS Y SPECIES FIG. 1 . Generalized relationship between community variables. The upper (3-D) figure (i) illustrates relationships between three distributions. In the Y X , plane is the species:abundance distribution, here illustrated for convenience as a log-normal distribution (Preston. 1967). The YZ plane defines the species: body size distribution. and the ZX, plane the population abundance:body size relationship. Summing individuals for all species of one body size gives the projected ZX? plane in (ii). Focusing on (i), the question is. what does the full. three-dimensional surface (iii) look like in real communities'? Species nbundnncelsize in canopy beetles tributions (e.g. Janzen, 1973; Griffiths, 1986; Strayer, 1986; Harvey & Godfrey, 1987). but because data are almost always presented in two dimensions (for example species: abundance distributions are presented by summing across individuals of all body sizes), development of a unifying theory is hampered by ignorance about the shape of the full three-dimensional surface depicted in Fig. 1. May (1978) is one of the few to have realized that all these community patterns are interrelated. The surface defined by Fig. 1 will not necessarily be simple, and may differ from community to community. For example, attempts to predict observed numbers of insect species (S) in different body size classes, knowing only the total number of individuals of each body size (N), using the empirical relationship S a p 2 5 , derived from Preston’s log-normal distribution of species abundances (May, 1978), fail (Lawton, 1986). One possible explanation is that different species abundance distributions hold for species of different body size classes. The present work is the first to establish empirical relationships between the variables depicted in Fig. 1, for an assemblage of species collected at one place and time, namely adult, arboreal beetles sampled from the canopy of rain forest trees using knockdown insecticides (Stork, 1987a, b; and unpublished). Our purpose is to establish what the patterns look like, not to develop theories to explain the patterns; the end result is the three-dimensional surface depicted in Fig. 7. As will become apparent, the data are not ideal, but they are the best currently available, based on samples of 23,000 individuals and approximately 3000 species of arthropods. Although full information on body lengths, numbers of species and numbers of individuals are only available for the Coleoptera in these samples, the data nevertheless consist of 859 species and nearly 4000 individuals. We are, however, aware that the Coleoptera may represent a biased sample of the relationships displayed by the entire arthropod assemblage of the canopy. We have attempted to discover whether this bias might be serious by reanalysing Janzen’s (1973) sweep net samples from the understorey of tropical forest, for total arthropods and the Coleoptera alone. We return to the problem of taxonomic and other sampling biases in the Discussion. Finally, as a first step in understanding the biological basis underpinning the patterns revealed by the data, we have 27 analysed not only the total collection of Coleoptera, but also different feeding guilds, and the species associated with different species of trees. Methods Samples of arthropods were collected by fogging the canopy of trees with a synthetic pyrethroid insecticide in an area of lowland rain forest near Bukit Sulang, Brunei (Borneo) in September 1982. Full details of the techniques used will be given elsewhere (Stork, unpublished). Ten trees were chosen for sampling; trees 1-4, Shorea johorensis Foxwood; trees 5-6, S.macrophylla (De Vriese) [Dipterocarpaceae]; trees 7-8, Pentaspadon motleyi Hook [Anacardiaceae]; tree 9, Number of individuals 1000. 100 10 1 1000 100 10 1 4 8 12 16 20 24 Body length 28 3 2 36 4 0 44 mm FIG. 2. Histograms of the number of individuals of all arthropods in different 1 mm size classes (i.e. graphs in the Z X , plane of Fig. l(ii) for sweep samples of understorey vegetation from (a) Taboga primary riparian vegetation and (b) Osa secondary vegetation, Costa Rica (from Janzen, 1973). The shaded bars represent the number of beetles of different body lengths. 28 D . R . Morse, N . E . Stork and J . H . Lawton Casranopsis sp. [Fagaceae]; and tree 10. unidentified species and family. The insect samples were sorted to orders and for most groups, to morpho-species (for simplicity, referred to as species from here on). The 859 species (3919 individuals) of adult Coleoptera were assigned to four guilds, herbivores (384 species), predators (200). scavengers (120) and fungivores (141) (guild assignments as in Stork (1987a), but with the fungivores separated from the scavengers); a further fourteen species could not be confidently assigned to guilds. We used body length as a measure of the size of each species since length is considerably easier to measure than weight, and for arthropods the two measures are highly correlated (Rogers el a l . , 1976,1977; Schoener, 1980). Measurements of the body lengths of species were taken from the hind-most tip of the abdomen or the elytra to the most forward part of the head (excluding the antennae) using a dissecting microscope with an eyepiece graticule. For most species of beetle in the samples. body length varies little. the smallest individual usually not being more than 10% shorter than the longest. Mean body lengths. therefore, were estimated Number of species from a maximum sample of ten specimens per species (or all available specimens of species represented by less than ten individuals) and grouped into a series of length classes arranged on a logarithmic scale. Results Analysis of'Janzen's Costa Rican datu In Figs. 2(a-b) total numbers of individuals are plotted against log body length classes, for the arthropods in sweep samples from two tropical lowland sites in Costa Rica. In both samples the Coleoptera comprise a major part of the smaller arthropods but are almost totally lacking in the larger size classes; hence the rate of decline from the mode in number of individuals is much steeper for the Coleoptera than for all arthropods combined. Species :abundance distribution The species: abundance distribution for all individuals combined is shown in Fig. 3(a). The most striking feature of the graph is the number t -- i. =I3 21 lo, 8-0 0&3;4 0 62 0 133 496 1 I I 0 (a) Number of Indlviduals per species (b) 100 200 300 400 500 600 700 800 Species ranked in order 01 abundance FIG. 3. (a) Species:abundance distributions for all the beetles in ten Bornean tree samples (1.e. the YX, plane of Fig. 1 ) . (b) The same data as (a), plotted as abundance (on a log scale) versus species rank. Numbers are given where data points in each block are too numerous to illustrate. Species abundancelsize in canopy beetles 29 TABLE 1. Equations of regression lines fitted through the species rankabundance plots of Fig. 3(b) for the beetles collected from three different species of tree. The regression lines were fitted by ordinary least squares techniques through the data after it had been logarithmically transformed. All regression lines are significant at the 0.1% level. Also shown are the mean numbers of species and individual beetles found on each tree. Tree species Slope SE Intercept SE Shorea johorensis Shorea macrophylla Pentaspadon motleyi -0.2810 -0.2747 -0.1780 0.0031 0.0058 0.0069 2.1546 1.8313 1.0176 0.0215 0.0352 0.0362 Tree species Mean no. per tree Shorea johorensis Shorea macrophylla Pentaspadon motleyi Species Individuals 175.5 143.0 72.0 466.0 513.0 112.0 of rare species, 58% of the species in the samples being represented by single individuals. We have not attempted to fit a log-normal distribution to the data, because it is clear that we have not yet discovered the mode of the distribution (parameters estimated for log-normal distributions without a mode are probably meaningless (Hughes, 1986)). Instead, in order to compare samples from the different tree species, we replotted the data (Fig. 3b) as a rank-abundance graph (e.g. Williamson, 1973). The equation of the line fitted to the data in Fig. 3(b) is: abundance=470 * rank-0.96(P<O.OOl) Similar plots for samples taken from the different species of tree show a linear relationship between species-rank and species-abundance on a double logarithmic plot, but their slopes are different (Table 1) (the data from trees 9 and 10 were not sufficient to justify separate analyses). The slopes of the lines through the rank abundance data for beetles from Shorea johorensis and S. macrophylla are very similar. However, that for Pentaspadon motleyi is approximately half the value of the slopes for either Shorea species, and the intercept for P. motleyi is lower. Species:body length distributions In Fig. 4(a) the number of species is plotted against body length class. The maximum number of species occurs in size class 3 (a body length of about 2 mm). The upper tail of the distribution from size class 5 (a body length of about 3 mm) shows a near linear decline, indicating a power-law relationship between number of species and body length. May (1978) provides a theoretical argument for the expected shape of the upper tail of this distribution (quantitative theoretical predictions about the shape of the full distribution have not been made). Following May (1978) we have therefore fitted a regression line to the upper (right-hand) part of the distribution (taking the mid-point of each size class on the abscissa); the fitted line has a slope of -2.64 (k0.38). Equivalent data for the different guilds of beetles are in Figs. 4(b-e). It is clear that each guild contributes differentially to the overall picture in Fig. 4(a). The most speciesrich size classes are in different positions for each guild and the shapes of the distributions appear to be quite different. Population abundance:body length distributions In Fig. S(a) the number of individuals per species is plotted against the body length of each species on double logarithmic axes. The resulting scatter-plot has two peaks the lower of which (corresponding to body lengths of 0.7-1.4 mm and population abundances of up to fifty individuals) is comprised mainly of fungivores (Fig. 5d) and the upper (corresponding to body lengths of 3-5 mm and population abundances of up to 200 individuals) mainly of herbivores (Fig. 5b). There are no consistent relationships between size and population abundances in Figs. 5(a-e) of the form proposed by Peters (1983) and Peters & Wassenberg (1983). Significant but 30 D.R . Morse. N . E . Stork and J . H. Lawton a 100 I - m .-0u a . a c 15 a 10- 5 2 : . n - 1, 0 -2 -2 i! 0 loo3 b 0 1 1 1 1 I 1 1 4 ~ I 1 8 2 8 10 12 14 16 Body length c l a s s 16 14 I I 1 1 I 1 1 12 1 16 1 I 1 1 1 20 I 24 1 1 1 28 B o d y length mm C k Herbivores - Fungivores - Scavengers -1 r- - 4 Body length classes FIG. 4. Histograms of number of species in different length classes (i.e. the Y Z plane of Fig. 1) for (a) all beetles in the Bornean samples. and for the following guilds of beetles: (b) herbivores, (c) predators, (d) fungivors. (e) scavengers. ( N . B . In order to display the dataeconomically, the Y axisof the Y Z plane of Fig. 1 is here logarithmically transformed. The scale converting length classes to actual length is displayed below Fig. 4 (a). For cxample. beetles in length class 14 are hetween 16.4 and 20 mm long; classes are in groups of 5*10& length.) Species abundancelsize in canopy beetles a 0. 100 .. ... ... . ... ... .. ... ....... . .. . . ..... .... ..... ...... . ........ ........ . * I - - * 10 * . 0 . .:..A. w.. . w . .w No-..... ..m..-- . n o . . . 7 . . 7 " 1 10 a .. ..... ... . . .... . ............ 0 100 . ...-... -.'.. . . ... . . . . .... ..-. .. . d 10 ' e .. . . ... ...... ...... .- .. . ........- ... .........--.-. . ". 10. .. ..... . .......... ...-... . . . . ..... ..-. ... 7- 31 32 D . R . Morse, N . E . Stork and J . H . Lawton Total number 01 individuals 01 a11 species Total number of individuals: body length distributions 1 2 0 2 8 10 12 14 16 Body length class FIG.6. Histogram or the total number of individuals in different length classes (i.e. the Z X z plane of Fig. 1 (ii)). The scale converting length classes to actual length is displayed below Fig. 4(a). very weak relationships were found in the predators (which have a positive. rather than negative slope, as expected; log length=0.100 log abundance+0.325, P<O.OOl). and the fungivores (log length= -0.129 log abundance+0.229, P<O.Ol) but were not found in the other guilds, nor for all of the species when pooled. In both the predator and fungivore guilds the relationships are weak; only 4% and 0.7% of the variance is explained, respectively. The total number of individuals in the different body length classes are shown in Fig. 6. The upper tail of the distribution from modal length class 6 (a body size of c . 3 . 5 4 mm) shows an almost linear decline in the number of individuals with increasing body length. Similar, but less clear-cut, patterns are evident in the individuals: body lengths graphs for each guild and in the samples taken from the different species of tree (not illustrated). The distributions for individual guilds tend to be skewed relative to the total distribution, with modes in different body length classes (Table 2). Least squares regressions fitted through the upper tails of the total individuals: length distributions (when the data have been logarithmically transformed) are in Table 2. After excluding the scavengers from the analysis, because the residual variance after regression was not homogeneous with that of other guilds (Bartlett’s test for homogeneity of variances, ,yz (with 3 df)=20.54, P<O.OOl), the slopes for the other guilds were found to differ significantly from one P<O.OOl). The another (ANOVA, F’2,18=21.85, slopes for the individual species of tree also differed significantly from one another (ANOVA, F2,y=30.91, P t O . O O 1 ) . The slope for Penfaspadon motleyi is lower by a factor of more than 2.5 than the slopes of the lines through the data for either of the two Shorea species (again, data for trees 9 and 10 were too sparse to justify separate analyses). TABLE 2. Equations of regression lines fitted through the upper parts of the total individua1s:body length graphs for different subsets of the data (i.e. slopes to the right of the mode in Fig. 6). The regressions were fitted by ordinary leastsquares techniques after the data had been logarithmically transformed. All data from and to the right of the mode of the distribution were included. The geometric mean of the limits on each size class was used for the abscissa. All regressions are significant at the 0.5% level. Data set SE Slope ~ Intercept’ SE All species Herbivores Predators Fungivores Scavengers Shorea johorensis S . macrophylla Pentaspadon motleyi -4.14 -4.63 -3.70 -2.27 -2.54 -4.32 -4.55 -1.56 Modal size-class __-_ ~~ 0.369 0.213 0.238 0.248 0.376 0.379 0.455 0.208 5.20 5.28 4.28 2.13 3.01 4.70 4.92 2.18 0.352 0.190 0.199 0.132 0.552 0.324 0.371 0.162 6 6 6 0 4 5 6 3 * log,, number of individuals at a body-size of 1 mm (based on extrapolation). Species ahundancelsize in canopy beetles 33 e FIG. 7. (a) A three-dimensional graph plotting number of species against each log body length class and against total log abundance class for all beetles, and for each guild: (b) herbivores, (c) predators, (d) fungivores, and (e) scavengers. The height of each intersection is proportional to the number of species having a particular combination of body length in each length class (see Fig. 4(a) for the conversion scale) and abundance in each octave on the conventional logz scale of species abundances (Preston, 1962). Combining the variables The three-dimensiuna1 plots for the beetles, and for individual guilds, are in Figs. 7(a-e). Note that, unlike Fig. 4, the y-axis in Fig. 7 is not logarithmic. The full surface is reasonably smooth, although careful inspection shows three ‘ridges’ running roughly parallel to the X,-axis in the YX, plane (Fig. 7a). These ‘ridges’are due to the main and two subsidiary modes in the number of species in different body length classes, with different guilds contributing differentially to (Figs. 7b-e). each Discussion Confining the scope of this study to the Coleoptera has both advantages and disadvantages. 34 D.R . Morse, N . E. Stork and J . H.Larvton The chief disadvantage is lack of generality. It is difficult to extrapolate from beetles to complete arthropod communities. Examination of total number of individuals: body length distributions for arthropods in sweep net samples from two sites in Costa Rica (Fig. 2) reveals that the Coleoptera comprise the major part of the lower body length classes although sweep netting captures a biased sample of arthropods (e.g. Hespenheide, 1979). The beetles make up only 18.0% of the species and 16.5% of the individuals in the complete arthropod samples from the Bornean trees (Stork, unpublished). However, they represent major proportions of four of the guilds of arthropods most closely associated with trees. For instance. the beetles account for a mean of 79.2% of the species and 66.8% of the individual chewing herbivores. For predators the equivalent figures are 50.4% and 45.6%. and for scavengers and fungivores combined, 40.7% and 37.9% respectively (Stork. 1987a). The Coleoptera clearly represent an important cross-section, in terms of feeding habits, of the arthropod fauna in the Brunei rain forest canopy. We are also aware that insecticide fogging as a method of collecting is not without problems but these are considerably less than for other methods of sampling from the canopy. and beetles appear to be particularly well sampled (Stork, 1987a, and unpublished). Confining attention to adult Coleoptera also has other advantages. One of the problems of examining body length relationships is that species in some groups have individuals with a wide range of body lengths. This is particularly true of Hemiptera and the orthopteroid orders where the adults and nymphs often occur together, are similar in appearance, and have similar feeding habits. For instance, 95% of the Blattodea in the samples were nymphs of a range of instars and hence sizes. Even the adults of some species can vary considerably in size. These problems are of only minor relevance to this study for several reasons. First, most of the adult beetles varied little in size within species. Second. beetle larvae are usually very different in appearance from the adults and, in some groups, are found in different habitats. Third, beetle larvae represented less than 5% of all Coleoptera in the Bornean samples (and were excluded from our analyses). Taxonomic restrictions aside, there is one other important way in which Fig. 7, and its component parts (Figs. 3, 4 and 5) may give a distorted or indeed totally false impression of the relationships that exist between these variables in more natural and taxonomically diverse faunal assemblages. Our analyses are based on samples of selected trees (see Methods), and are not stratified according to tree abundance, and as we have indicated, different species of tree have rather different patterns (e.g. Tables 1 and 2). Only further studies, designed to overcome taxonomic and sampling biases, can reveal whether the patterns in our total data are serious distortions of patterns in real communities. At the present time we can do no more than present the data to illustrate the nature of the problem, as a spur to others to gather more and better data. The interpretations that follow must be viewed in the light of these major caveats. It is unclear which of the many available models (see Southwood. 1978. for summary) would be the most appropriate to fit the species: abundance distribution (Fig. 3). Taylor (1978) and Hughes (1986) point out that in small samples both the logarithmic series and the upper section of the log-normal distribution fit equally well, which is also true of the data in Fig. 3(a). Since there is no mode or suggestion of a mode. the true number of beetle species in the Bornean lowland trees must be much greater than the 859 species found, if they have a lognormal distribution. Because there is no mode in Fig. 3(a), it isdifficult (e.g. Hughes, 1986) to test the notion (see Introduction; Lawton, 1986) that species of different sizes may have different species:abundance distributions with modes in different abundance classes. Fig. 7(a) simply shows monotonic declines in the numbers of species in each abundance category for beetles of all sizes (i.e. ‘slices’ in the Y X , plane look qualitatively similar at all points along the Z axis). The species: body length distributions for beetles in Bornean rain forest (Figs. 4a-e) are similar to those found by other authors (e.g. Hemmingsen, 1934; Schoener & Janzen, 1968) in that they approximately conform to a lognormal distribution. The slope of -2.64 (k0.38) 17132.6x46.9for the upper tail of the distribution for the combined data when plotted on doublelogarithmic axes shows a reasonable fit to May’s (1978) predicted value of approximately -2. More recent calculations (May, 1986) based on Species abundancelsize in canopy beetles the fractal nature of plant surfaces (Morse et al., 1985) imply slopes lying between -1.5 and -3.0. Data from independent studies of tropical canopy beetles (Erwin & Scott, 1980; Erwin, 1983) and other insect communities (Terakawa & Ohsawa, 1981) also conform reasonably closely to May’s (1978) prediction that the number of species scales as body length-’, above some critical minimum body size (see Lawton, 1986). It is unclear whether the total number of arthropod species declines below the modal size class 3 in Fig. 4(a), or whether very small species in groups other than Coleoptera would markedly increase the total number of arthropod species, below a length of about 2 mm (see also May, 1978, 1986). Several studies (Damuth, 1981; Peters, 1983; Peters & Raelson, 1984; Peters & Wassenberg, 1983; Brown & Maurer. 1986) have found a simple linear relationship between the population densities of individual species and body weight. The graphs presented by these authors are noticeably lacking in data for small, rare species equivalent to a complete lack of points close to the Y-axis on the Z X , plane of Fig. 1 (i.e. there is a ‘hole’ in the data on the ‘floor’ of Fig. l(i), furthest from the reader). Then, by definition, a Fig. 1style three-dimensional plot of their data would result in an incomplete surface, with two implications for the other faces of Fig. 1. First, rare species in a species:frequency distribution (the Y X 1plane) would tend mainly to be large individuals; secondly, only more abundant species would contribute to the shape of the Y Z plane for small values of Z (small body size). In marked contrast to these authors, we found a considerable number of small rare species in the Z X , plane (Fig. 5 ) and the three-dimensional surface was complete (Fig. 7). There was no consistent relationship between the average abundance and body size of species (Fig. 5). There are three possible reasons why the data in Fig. S differ from that of earlier studies, two biological, the other an artefact of the way in which earlier data have been assembled. Both biological reasons centre on species mobilities. For example, it is interesting to observe that both Peters & Wassenberg (1983) and Juanes (1986) found only weak and inconsistent relationships between population density and body size for birds. Perhaps the feature that sets both birds and beetles apart from the other groups analysed is that most of their species are winged, 35 highly mobile, and therefore able to encounter one another and to mate at very low population densities (see also Juanes (1986) for alternative biological arguments). Second, high mobility will tend to yield many ‘tourists’ (sensu Moran & Southwood, 1982) in the samples, possibly boosting the number of very rare species. It is also possible that the clear correlations that exist in earlier studies between population density and body size are sampling artefacts; many of these data were gathered from published studies on the autecology of individual species. Such species may tend to be both commoner and larger than average (few biologists choose to work with small, rare species). Hence data for smaller, rarer species may be under represented in many earlier studies (but see Brown & Maurer, 1986). Summing individual population abundances for species of a particular size in Fig. 5(a). yields the data in Fig. 6 (see also Fig. 1, showing how the Z X , plane gives rise to the Z X 2graph). Fig. 6 is again roughly log-normally distributed, with a mode at size class 6. Although there is considerable variation in the rate of decline in the total number of individuals with body length to the right of this mode for various beetle guilds (Table 2), the majority of those plots have slopes much greater, sometimes by an order of magnitude, than has been found in other studies of insect communities (Hijii, 1984; Kikuzawa & Shidei, 1967; Terakawa & Ohsawa, 1981; Lawton, 1986; Morse et al., 198s). On average, the Bornean beetle data show that for an order of magnitude decrease in body length, the total number of individual beetles, summed over all species, increases by a factor of approximately 10,000. However, analysis of Janzen’s (1973) data (Fig. 2) indicates that restricting our study to the Coleoptera may have had the effect of greatly increasing the slope above the mode, compared with similar slopes for entire arthropod assemblages. Data for rain forest beetles may not therefore be at variance with the model proposed by Morse ef al. (1985) and Lawton (1986), which predicts a slope of -3.25 to the right of the mode for data of the type displayed in Fig. 6 and Table 2. The end point of our analyses is the threedimensional surface displayed in Fig. 7(a). Small ridges run across it, roughly parallel to the YX, plane, for species in the smallest body length classes; however, the bulk of the surface is 36 D.R . Morse, N . E . Stork arid J . H . Lawton relatively smooth. Each guild (Fig. 7b-e) contributes to the shape of the overall surface in a different way but we have no theoretical basis for interpreting these patterns. It is possible that they are artefacts produced by taking subsamples. Further progress is impossible without even larger samples. which might also be required to carry out separate analyses for each species of tree. It is unclear whether widening the taxonomic base of our samples, or collecting at different seasons, will alter the shape of the surface. Future empirical and theoretical studies will have to address both points. Because there are no similar data in the literature, we cannot say whether they are typical or unusual. There are hints in the literature (e.g. Griffiths, 1086: Strayer, 1986). that surfaces for other communities may be both more complex and more irregular. Acknowledgments We are particularly grateful to colleagues at the BM(NH), who will be fully acknowledged in a later publication, for assisting Nigel Stork in sortingthe Coleoptera to species. We thank Paul Harvey, Bob May, Stuart Pimm and Mark Wetton for valuable discussion. Nigel Stork acknowledges the permission of the Sultan of Brunei to study in Brunei, assistance from Jaya bin Sahat of the Brunei Museum, and fieldwork support from members of the Leeds University Expedition to Brunei. David Morse was supported by an NERC studentship. The insecticide was provided by Wellcome Research Laboratories through Peter Chadwick. Peter Hammond. Cliff Moran, Joe Perry and an anonymous referee made helpful comments o n the manuscript. References Brown. J.H. & Maurer. B.A. (1986) Body size. ecological dominance and Cope’s rule. Nature. 324, 248-250. Damuth, J . (1981) Population density and body size in mammals. Narure, 230, 699-700. Erwin. T.L. (1983) Beetles and other insects of tropical forest canopies at Manaus. Brazil, sampled by insecticidal fogging. Tropical Rain Foresit Ecology and management (ed. by S . L. Sutton. T. C. Whitmore and A. C. Chadwick), pp. 59-75. Special publication no. 2 of the British Ecological Society. Blackwell Scientific Publications. 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