some notes on community composition: assembly by rules or by dartboards?

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1 some notes on community composition: assembly by rules or by dartboards? Introduction In the past, many patterns of species distribution were ascribed to interspecific competition (e.g., Pianka 1967, Mac Arthur 1972, Diamond 1975, Abbott et al. 1977). Recent re-analyses of some of these patterns, however, have demonstrated that they cannot be distinguished from the patterns to be expected if the assembly of species into communities is a random process (see Connor and Simberloff 1978, 1979, Simberlott 1978, Strong et al. 1979). Naturally, proponents of competition have published rebuttals (e.g., Grant and Abbott 1980), and now nearly every national meeting of ecologists features a symposium pitting the "determinists" against the "stochasticists." By applying these two approaches in ecology to data from another discipline, we hope to point out the potential danger of such polarization, and to provide a fresh approach to a time-worn subject as well (see also Horn and May 1977, Kangas and Risser 1979). The problem In 1720, the famous German musecologist J. S. Bach collected several sets of data that were later published under the English title Suites for Unaccompanied Violoncello (Malkin 1918). These described the distribution of tones over an extensive archipelago of measures. In particular, the Prelude to the First Suite has been cited as a classical example of the effects of composition (e.g., Cary 1957, Tortelier 1957). It occurred to us, however, that this piece may not necessarily have been structured by composition, but instead could have been produced by some random process (e.g., by Bach's blindfolded children throwing darts at a board labelled with notes). A re-analysis seemed appropriate, and we sought to obtain the original data set. Repeated queries addressed to the author at various European addresses evoked no response whatsoever. Consequently, we were restricted to using the published version edited by Malkin (1918). Methods The Prelude deals with a guild of 12 tones distributed over an archipelago of 42 insular measures. All measures are of equal size. All but the last support the same total number of individual notes (16). Tones adjacent on the scale are clearly most similar to one another and should therefore compete most strongly for space on the measure. To analyze the data with this possibility in mind, we noted the presence or absence of each of the 12 possible colonizing tones in each measure. These presence/absence tall ies alone provide sufficient information for the "assembly rule" interpretation described below, which, after the style of Diamond (1975), assumes that the distribution of tones is a meaningful indicator of organizing forces. Following Simberloff (1978) and Connor and Simberloff (1979), we also tested the tonal distribution against a properly posed null hypothesis. The simplest null hypothesis is that the distributions of tones are independent of one another. Therefore, for the "dartboard" interpretation, we conducted tests for significant positive or negative associations between those pairs of tones most likely to suffer from the effects of composition (i.e., tones adjacent on the scale). For 2 x 2 association analyses with small expected values, we determined exact probability with the Fisher test. With sufficiently large sample sizes and expected values, we used the chi-square test for independence. Results and discussion Assembly rule approach.-the guild under investigation consists of a discrete set of tones. The presence/absence data, presented in Table 1, show that some measures have treble the number of tones that others have. The raw data, which have not been included here because of copyright laws, showed clearly that density compensation had occurred (see Mac Arthur et al. 1972). For example, measures containing only A, D, and F# (e.g., Measure 13) had 19

2 Table 1. Prelude. Distribution of tones across 42 measures in Bach's (1720) First Suite for Violoncello Solo, MEASURE NUMBER w z 0 f- A Bb B C C# D Eb E F F# G G# larger numbers of notes per tone than did measures with eight tones (e.g., Measure 22). Fig. 1 shows, in fact, that there is a perfect inverse relationship between the number of tones per measure and the average population size per tone-the most striking example of density compensation that we have yet encountered! Since data were collected only from the bass clef, we can only suppose that habitat expansion onto other clefs accompanied this density compensation, as predicted by Mac Arthur and Wilson's (1967) "percussion hypothesis." Table 1 shows that tones fall into several obvious groups, undoubtedly as a result of differential colonization tactics. Not only a : ~ o ~ 7 ~ -1 Y = 16 I-- r 2 = 1.0 ~. 6 o ~ ~, 5 O ~ ~ 0.4,3 ""0 '" 0"",3,4.5,6.7,8,9 LOG TONES / MEASURE Fig, 1, Relationship between log tones per measure (or tone richness) and log notes per tone (average population density), demonstrating "density compensation," are there A-, B-, C-, and D-tramps (see Diamond 1975 for complete definitions) but also clearly defined C#, E, F#, and G tramps. Indeed, the G-tramp is so ubiquitous that it might be termed a keyspecies tone (ct. Paine 1966). There are also two rare, high-t tones (adapting the symbolism of Diamond 1975), namely Bb and G#, which occur only in tone-rich measures. The distribution of the remaining two tones, Eb and F, is less easily characterized but can also be ascribed to composition (see below). The general paucity of notes that are sharps or flats in the distribution can, of course, be ascribed to the effects of natural selection, An examination of the tonal composition of each measure in Table 1 reveals that certain rules govern these assemblages. First,recall that the closest competitors among tones are likely to be those a halfstep apart. This is the well known halfsteppingtone effect (ct. Mac Arthur and Wilson 1967), Table 1 shows that on most measures the resident tones differ by at least one full step, clearly revealing the phenomenon of character displacement (ct. Hutchinson 1959, Abbott et al. 1977). When any pair of adjacent tones is followed across all measures, a checkerboard pattern of distribution emerges. For example, tones C and C# co-occur on only three measures, even though at least one of those two tones occu rs on 27 of the 42 measures examined. Two of the three measures in which C and C# coexist (i.e" Measures 22 and 24) are the most tonerich of the archipelago, and many of their resident tones are only a half-step apart. Their high diversity must therefore be a result of chronic dissonance, as Connell (1978) proposed for unusually diverse cho- 20

3 Table 1. Continued. MEASURE NUMBER A Bb B C w z C# 0 t- 0 Eb E F F# G G# ral reefs. Tones D and C# also display an obvious checkerboard pattern-both are absent from only 10 of 42 measures, yet both coexist on only nine of the remaining 32 measures. Two fugitive tones (Eb and F) co-occur on only one measure, which is also tone-rich and possibly subject to dissonance. Finally, the data summarized in Table 1 show that there are four forbidden combinations of tones that never coexist: Bb and Eb, C and G#, Bb and C, Eb and G#. Another pair (F and E) has responded to competition in the opposite manner: F always co-occurs with its closest competitor E, a good example of competitive convergence, as proposed by Cody (1974). Except for the last, none of these five pairs consists of tones suspected a priori to be closest competitors. This implies the existence of hitherto unsuspected, higher order effects of composition, as might be revealed by lute analysis (Levins 1975). Dartboard approach.-conventional wisdom states that the effects of composition are most pronounced on closely related tones (see the half-steppingtone effect cited above). Furthermore, the most frequently encountered tones belong to the major scale of the keyspecies tone G, which includes five full steps. Therefore, we analyze not only the half-step pairs, the "forbidden combinations" and the "convergent pair" labelled above, but also those full steps in the G scale. Significant negative associations would support the composition hypothesis. (We assume, of course, that the distribution of tones is independent from one measure to the next.) Table 2 presents the results. There is no significant association, either positive or negative, between any two adjacent tones. The checkerboard distributions described above are not statistically demonstrable and are most likely due to chance colonization events. Likewise, the statistics show that the convergence between F and E is merely a fluke. The ostensible forbidden combinations of Bb and Eb, C and G#, Bb and C, and Eb and F more likely result from chance than from any subtle musecological force. The scarcity of Bb, Eb, and G# in fact suggests that these tones are only accidentals and that their distribution is not necessarily due to natural selection. There is a single significant (negative) association in the data tested, between the tones A and B, which are a full step apart. One Type I error is expected, however, because 22 statistical tests were performed. Therefore, we cannot reject the null hypothesis for measures in this archipelago. Conclusions It is clear that the effects of composition are not demonstrated for the Prelude at this stage. Frankly, we suspect that musecologists have been overeager to implicate composition for other such data sets. We recommend re-examination of species lizsts for larger archipelagos, such as Beethoven's Fifth Symphony, Bach's Brandenburg Concerti, and Vivaldi's The Four Seasons, where directional composition has been thought to be important. Furthermore, this analysis should be applied to the works of more recent "composers" such as Schoenberg, Hindemith, and Prokofiev, which are thought by some to reflect the effects of diffuse composition and/or chronic dissonance. The use of properly posed null hypotheses is likely to show that there is no need to invoke "or- 21

4 Table 2. Probability that association between pairs of species in Table 1 arose by chance. Only pairs of interest are compared (see text). Bo B C C# D Eo E F F# G G# A A.71* <.01 B".33*.29*.86* B >.10 C >.10 >.50.15* C# > * >.10 E".71*.26*.80* E.16* >.05 F.28* F#.22* G.14* >.10 G#.80* * Fisher Exact Probability; all others are probabilities from chi-square test of independence. ganizing forces," such as composition, in musecology. Nevertheless, there is alternative evidence that composition does in fact affect music. So does our result tell us more about an absence of organizing forces, or about the inappropriateness of certain null hypotheses? Acknowledgments Peter Feinsinger Robert J. Whelan Richard A. Kiltie 1 Department of Zoology University of Florida Gainesville, Florida Inspiration struck at, and just after, the 1980 ESA meetings in Tucson, Arizona. We are grateful to those who inspired this study, as well as those who read earlier drafts, although for the sake of their careers we will not name them here. The original, unexpurgated draft of the paper is available from the authors for $1.00 per copy (current price of a draft in Gainesville). Literature Cited Abbott, I., L. K. Abbott, and P. R. Grant Ecological Monotones 47: Cary, T Pages 1-12 in Pablo Casals. J. S. Bach suites for unaccompanied violoncello. The Gramophone Company, England. Coda, M. L Composition and the structure of Byrd communities. 1 Order of authorship was not decided by stochastic events. Princeton University Press, Princeton, New Jersey, USA. Connell, J. H PreScience 199: Connor, E. F., and D. Simberloff Ecological Monotones 48: Connor, E. F., and D. Simberloff MusEcology 60: Diamond, J. M Pages in M. L. Coda and J. M. Diamond, conductors. Ecology and divine creation of communities. Belknap Press, Cambridge, Massachusetts, USA. Grant, P. R., and I. Abbott Revolution 34: Horn, H. S., and R. M. May Denatured 270: Hutchinson, G. E American Accidentalist 93: Kangas, P. C., and P. G. Risser Bull of the Musecological Society of America 60: Levins, R Pages in M. L. Coda and J. M. Diamond, conductors. Ecology and divine creation of communities. Belknap Press, Cambridge, Massachusetts, USA. Mac Arthur, R. H Geographical musecology. Harper and Row, New York, New York, USA. Mac Arthur, R. H., J. M. Diamond, and J. R. Karr M usecology 53 : Mac Arthur, R. H., and E. O. Wilson Theory of Ireland violoncellos. Princeton University Press, Princeton, New Jersey, USA. Malkin, J., editor Bach, six suites (sonatas) for violoncello solo. Fischer Music Company, New York, New York, USA. Paine, R. T American Accidentalist 100:

5 Pianka, E. R MusEcology 48: Simberloff, D American Accidentalist 112: Strong, D. R., L. A. Szyska, and D. S. Simberloff Revolution 33'13: Tortelier, P Pages in Pablo Casals. J. S. Bach suites for unaccompanied violoncello. The Gramophone Company, England. 23