The Genetic Code and Zipf's LawAuthor(s): M. L. Bender and Pritmohinder GillReviewed work(s):Source: Current Anthropology, Vol. 27, No. 3 (Jun., 1986), pp. 280-283Published by: The University of Chicago Press on behalf of Wenner-Gren Foundation for AnthropologicalResearchStable URL: http://www.jstor.org/stable/2742889 .Accessed: 29/06/2012 06:12

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are currently unable to identify indigenous groups over such an extended period, and this forces us to be cautious in our eth- nographic interpretations (Michielli 1984). Indigenous groups in South America tended to be migratory, with few settle- ments, and it is to this preurban phase that the majority of rock art belongs, beginning at 17,000 B.P. in eastern Brazil and 9,000 B.P. in southern Argentina (Guidon 1981, Gradin et al. 1977). The San Luis rock art, which includes both painting and engraving, is generally geometric in design. This does not simply represent the influence of Andean art but is consistent with the broader traditions of South American art as a whole. Four pictographic and five petroglyphic styles, the earliest dat- ing to 4000 B.C., have been identified. Some of them reflect influence from as far away as the Chilean Andes, the Argen- tine Northwest, and Patagonia (Consens 1985).

We consider it wrong, with few exceptions, to correlate art styles or artefact types with ethnic groups. Nor are terms such as "hunter's art" or "pastoralist art" helpful, since they confuse concepts of subsistence with semiotic relationships. The vari- ety of the environment, from the sierras to the pampas, and the utilisation of the area as a traditional migration route allowed San Luis artists to draw on a vast repertoire of sources which never amalgamated to form a distinctive regional style. San Luis is therefore particularly well-suited to the testing of hy- potheses on influence, diffusion, and adaptation between areas that differ in geographical and archaeological character.

References Cited ALVAREZ, E. 1985. "Metodologia del tratamiento estadfstico de los

datos de la investigaci6n de arte rupestre," in "Utilizaci6n de la inform6tica en la determinaci6n de estilos de arte rupestre: Un ejem- plo de analisis factorial de correspondencia." Actas de las Primeras Jornadas de Arte y Arqueologia, Santiago de Chile, 1983. In press.

CONSENS, M. 1980. "Sobre algunos aspectos fisico-tecnicos de la inves- tigaci6n de arte rupestre." Programs and Abstracts, 43d Interna- tional Congress of Americanists, p. A25.

. 1985. San Luis: El arte rupestre de sus sierras. San Luis: Direcci6n de Cultura de la Provincia de San Luis.

GAMBIER, M. 1981. Instalaci6n humana prehispanica en la region de Cuyo. Instituto de Investigaciones Arqueol6gicas y Museo, Univer- sidad de San Juan, Publicaciones 9:1-5.

GRADIN, C. J., et al. 1977 Investigaciones arqueol6gicas en la Cueva de las Manos, Estancia Alto Rio Pinturas. Relaciones de la Sociedad Argentina de Antropologia, n.s., 10:3-52.

GUIDON, M. 1981. Datao6es pelo C-14 de sitios arqueol6gicos em Sao Raimundo Nonato, sudeste do Piaui (Brasil). Clio 4:35-38.

MICHIELLI, C. T. 1984. La regi6n de Cuyo y sus naturales a traves de la cr6nica de Ger6nimo de Bibar y su confrontaci6n con otras fuentes. Instituto de Investigaciones Arqueol6gicas y Museo, Un- iversidad Nacional de San Juan, Publicaciones 10:1-16.

PAGER, H. 1976a. The rating of superimposed rock paintings. Almoga- ren 5-6:205-18.

. 1976b. Quantitative analysis elucidates the motives of the South African rock painters. Almogaren 5-6:219-26.

The Genetic Code and Zipf's Lawl

by M. L. BENDER and PRITMOHINDER GILL Department of Anthropology, Southern Illinois University at Carbondale, Carbondale, Ill. 62901, U.S.A. 19 VII 85

As a powerful and versatile information-carrying system, the genetic code is a test case for displaying the necessary proper- ties of such systems. Most fundamental perhaps is the relation- ship known as Zipf's Law: the product of rank order and frequency of elements in a code is a constant. A second relationship discovered by Zipf is that more frequent items in a code are more highly polysemous than less frequent ones in accordance with a simple mathematical formula. Both of these properties are examined here for several organisms whose DNA structures have been completely worked out.

The genetic code, as its name implies, is a system of elements which communicates information in the formal sense of the term (Cherry 1978, Shannon and Weaver 1949). As such, it shows interesting parallels with other codes, e.g., human speech. At the lowest structural level, the nitrogen bases of nucleotides (adenine [A], cytosine [C], guanine [G], thymine [T], uracil [U]) can be seen as parallel to phonetic features (about 40 in number, including presence or absence of nasali- zation or vocalization, degree of aspiration, etc.). Strings of three nucleotides make up codons (43 or 64 in number) parallel to phones (sets of phonetic features, probably fewer than 300 for any given language). Of the 64 codons, equivalence sets exist, with the result that there are 20 distinct amino acids and a boundary signal (e.g., alanine is represented by GCA, GCC, GCG, or GCT in the genetic code for messenger RNA) parallel to the natural classes of phones making up phonemes (12-70

1 ? 1986 by The Wenner-Gren Foundation for Anthropological Re- search, all rights reserved 0011-3204/86/2703-0008$1.00. We are happy to acknowledge comments from Jack Parker, DuWayne Eng- lert, and Robert Corruccini and aid with statistical computations from Robert Corruccini. None of them is responsible for any errors herein.

280

for any language). (For more details on the genetic code, see standard sources such as Crick 1966 or Dobzhansky et al. 1977.) The parallel could be taken farther (see Doerfler 1982), but for present purposes we shall restrict our attention to the levels just mentioned.

Statistical properties of codes have been studied in depth (Cherry 1978). One of the pioneering findings is Zipf's (1949) R x F = C; where R is rank order and F is frequency of an element in a code, C is a constant for the code in question. Zipf shows that this relationship holds for the words of James Joyce's Ulysses and for many other information-conveying sys- tems (Cherry 1978, Zipf 1949). In logarithmic terms, this be- comes log R + log F = log C, or in other terms x + y = c, i.e., a straight line of slope - 1 and y-intercept c on log paper, (logarithm to any convenient base).

Zipf also investigated the question of meanings per token, finding that more frequent items are more highly polysemous than less frequent ones-for example, more frequent pho- nemes have more allophones, more frequent words have more homophones (such as bear [animal], bear [carry], bare). In fact, the relationship in this case is that of a straight line 2y + x = c (where y is log F and x is log R). The only difference between this and the first Zipf finding, then, is that the slope is - 1/2 instead of - 1. This means that there is a more gradual falling off of frequency than in the first case.

Given that the genetic code is an information-transmitting system par excellence, if Zipf's relationships are really univer- sal, they should hold for it. As far as we are aware, no one has presented a test of this expectation, though several have dis- cussed the DNA-language parallel (e.g., Doerfier 1982, Jakob- son 1970).

We examined the codon structure of the 5,375-nucleotide DNA of the bacterial virus 4X 174 the complete sequence of which has been published by Fiddes (1977). The sequence in- cludes nine identified genes (labelled A, B, C, D, E, F, G, H, J). B is included in A, E is included in D, C overlaps with A and D, and J overlaps with D; F, G, and H are disjoint from the others. Each gene encodes a protein with a given function (e.g., E for lysis-disrupting a host cell's outer membrane, G for part of the production of spikes in the virus's protein coat).

CURRENT ANTHROPOLOGY

TABLE 1

FREQUENCIES AND RANKS OF AMINO ACIDS AND CODONS IN THE NINE GENES OF THE BACTERIAL VIRUS 4X 174

AMINO ACID In In AMINO ACID In In AND CODONS FREQUENCY FREQUENCY RANK RANK AND CODONS FREQUENCY FREQUENCY RANK RANK

Alanine ............ 168 5.12 1 0 CTT ............ 55 4.01 13 2.56 GCA ............ 17 2.83 41 3.71 TTA ............ 24 3.18 32 3.47 GCC ............ 29 3.37 27 3.30 TTG ............ 39 3.66 22 3.09 GCG ............ 19 2.94 36 3.58 Lysine ............. 115 4.75 8 2.08 GCT ............ 103 4.64 1 0 AAA ............ 69 4.23 4 1.39

Arginine ........... 114 4.74 9 2.20 AAG ............ 46 3.83 18 2.89 CGA ............ 6 1.79 59 4.06 Methionine (also CGC ............ 36 3.64 23 3.14 initiator) ....... 58 4.06 17 2.83 CGG ............ 8 2.08 55 4.01 ATG ............ 58 4.06 10 2.30 CGT ............ 49 3.89 16 2.77 Phenylalanine ...... 91 4.51 11 2.40 AGA ............ 11 2.40 51 3.93 TTC ............ 32 3.47 26 3.26 AGG ............ 2 .69 63 4.14 TTT ............ 59 4.08 9 2.20

Asparagine ......... 91 4.51 12 2.48 Proiine ............ 78 4.36 15 2.71 AAC ............ 35 3.55 24 3.18 CCA ............ 8 2.08 54 3.99 AAT ............ 56 4.02 11 2.40 CCC ............ 9 2.20 53 3.97

Aspartic acid ....... 123 4.81 6 1.79 CCG ............ 22 3.09 34 3.53 GAC ............ 52 3.95 14 2.64 CCT ............ 39 3.66 21 3.04 GAT ............ 71 4.26 3 1.10 Serine ............. 134 4.89 3 1.10

Cysteine ........... 26 3.26 19 2.94 AGC ............ 7 1.96 56 4.03 TGC ............ 12 2.48 50 3.91 AGT ............ 12 2.48 48 3.87 TGT ............ 14 2.64 47 3.85 TCA ............ 22 3.09 35 3.56

Giutamic acid ...... 88 4.48 13 2.56 TCC ............ 15 2.71 44 3.78 GAA ............ 32 3.47 25 3.22 TCG ............ 18 2.89 39 3.66 GAG ............ 56 4.02 12 2.48 TCT ............ 60 4.09 8 2.08

Glutamine ......... 92 4.52 10 2.30 Threonine ......... 126 4.84 5 1.61 CAA ............ 45 3.81 19 2.94 ACA ............ 14 2.64 45 3.81 CAG ............ 47 3.85 17 2.83 ACC ............ 24 3.18 31 3.43

Giycine ............ 126 4.84 4 1.39 ACG ............ 28 3.33 28 3.33 GGA ............ 18 2.89 37 3.61 ACT ............ 60 4.09 7 1.95 GGC ............ 41 3.71 20 3.00 Tryptophan 23 3.14 20 3.00 GGG ............ 4 1.39 61 4.11 TGG ............ 23 3.14 33 3.50 GGT ............ 63 4.14 6 1.79 Tyrosine ........... 67 4.21 16 2.77

Histidine .......... 35 3.55 18 2.89 TAC ............ 17 2.83 42 3.74 CAC ............ 9 2.20 52 3.95 TAT ............ 50 3.91 15 2.71 CAT ............ 26 3.26 29 3.37 Vaiine ............. 116 4.75 7 1.95

Isoleucine .......... 88 4.48 14 2.64 GTA ............ 12 2.48 49 3.89 ATA ............ 6 1.79 58 4.08 GTC ............ 18 2.89 38 3.64 ATC ............ 15 2.71 43 3.76 GTG ............ 14 2.64 46 3.83 ATT ............ 67 4.20 5 1.61 GTT ............ 72 4.28 2 .69

Leucine ............ 167 5.12 2 .69 Terminators ........ 10 2.30 21 3.04 CTA ............ 7 1.96 57 4.04 TAA ............ 3 1.10 62 4.13 CTC ............ 17 2.83 40 3.69 TAG ............ 1 0 64 4.16 CTG ............ 25 3.22 30 3.40 TGA ............ 6 1.79 60 4.09

NOTE: Order of codons is alphabetical. Ties are listed in alphabetical order (e.g., ACT is 7th, TCT is 8th). Amino acids are listed alphabetically exceptfor terminators (last).

Overlapping works because of "phase differences," e.g., Gene B begins with ATGGAA, while Gene A reads TGG as a codon in this stretch. In addition to the genes, there are intermediate "untranslated" regions which deal with operational matters such as terminating transcription (for details see Fiddes 1977).

In this study, only the genes are dealt with. Their lengths vary greatly; codons involved number per gene as follows: A, 514; B, 121; C, 87; D, 153; E, 92; F, 425; G, 176; H, 329; J, 39 (total 1,936). Table 1 tabulates the frequencies and ranks of amino acids and their codons. In figures 1 and 2 the two sets of data are graphed on scales of ln (natural logarithm) of rank (x-axis) vs. ln frequency (y-axis). For amino acids (fig. 1) the goodness of fit to a straight line is far from impressive; much better would be a broken-line approximation with a segment of shallow negative slope from (0, 5.12) to (2.64, 4.48) and a segment of steep negative slope from (2.64, 4.48) to (3.04, 2.30). Even so, a least-squares approximation y = -0. 64x + 5.73 has a correlation coefficient of -0.73. Not surprisingly, for the larger data set, that of codons, a somewhat sharper result is obtained; the concave curve of figure 2 can be approxi-

Vol. 27 * No. 3 * June 1986

mated by y = 0. 80x + 5.62 with r = -0. 83. Finally, table 2 shows the data for the codon composition of each amino acid, and figure 3 displays them graphically (ln F, where F is num- ber of codons per amino acid vs. ln R, where R is rank). The straight line joining the extreme points (0, 1.79 vs. 3.04, 0) has equation y = - 0.59x + 1. 79, which is a fair approximation to the expected y = - 0.5x + c. A least-squares approximation gives y = - 0.59x + 2.31 (same slope, higher intercept) with r = -0.88. It may be argued that a major-axis regression fit is more appropriate than a least-squares one, since measurement error may be involved in both x and y variates. Without taking a stand on which method to prefer, we found that the reduced- major-axis slopes are -0.88 for amino acids and -0.956 for codons, which are closer approximations to the theoretical ex- pectation of - 1.0 (see table 3).

Since the human genetic code carries a description of the human language mechanism (oral-aural organs, brain speciali- zations, etc.), the genetic code contains a description of the language code and vice versa (since human language can pre- sumably succeed in describing the genetic code). If the relation-

281

45-_

40 ____ T+_ 35

30

25

InF

20

0 5 1 0 1 5 20 25 30 35 40 45 InR

FIG. 1. Natural logarithm of rank vs. natural logarithm of frequency of amino acid occurrences in nine genes of the bacterial virus XX 174. Least-squares approximation y = -0. 64x + 5. 73, r = -0. 73.

ships discovered by Zipf are necessary properties of efficient coding systems, it would seem that the genetic code should be a strong exemplar of those relationships. In fact, the results for the bacterial virus 4X 174 are not as impressive as some of Zipf's examples, e.g., words in Ulysses (Zipf 1949:23-25). But this is not really surprising, since the number of different words in Ulysses is about 29,899, more than 467 times the number of tokens in our test. Because codons are limited to 64 and amino acids to 20, the only way to sharpen the results is to examine other organisms, especially more complex ones (e.g.,

5.5-

5.0

4.5

4.0-

InF

3.5

3.0

2.5

InR FIG. 2. Natural logarithm of rank vs. natural logarithm of frequency of codon occurrences in nine genes of the bacterial virus fX 174. Least-squares approximation y = -O. 80X + 5. 62, r = -0. 83.

282

TABLE 2

CODON COMPOSITIONS OF THE AMINO ACIDS

NUMBER OF In In AMINO ACID CODONS NUMBER RANK RANK

Arginine .......... 6 1.79 1 0 Leucine .......... 6 1.79 2 .69

Serine ............ 6 1.79 3 1.10

Alanine .......... 4 1.39 4 1.39

Glycine ........... 4 1.39 5 1.61 Proline ........... 4 1.39 6 1.79 Threonine ........ 4 1.39 7 1.95

Valine ............ 4 1.39 8 2.08 Isoleucine ......... 3 1.10 9 2.20

Terminators ...... 3 1.10 10 2.30

Asparagine ....... 2 .69 11 2.40

Aspartic acid ...... 2 .69 12 2.48

Cysteine .......... 2 .69 13 2.56

Glutamic acid ..... 2 .69 14 2.64

Glutamine ........ 2 .69 15 2.71 Histidine ......... 2 .69 16 2.77

Lysine ........... 2 .69 17 2.83 Phenylalanine ..... 2 .69 18 2.89 Tyrosine .......... 2 .69 19 2.94

Methionine ....... 1 0 20 3.00

(initiator) Tryptophan ....... 1 0 21 3.04

according to Dobzhansky et al. [197 7:72-74], bacteria have on the order of 106 nucleotides, mammals on the order of 109). Two such analyses were undertaken. The first of these dealt with mouse mitochondrial DNA (Bibb et al. 1981) and the second with E. coli (Alff-Steinberger 1984). Interestingly, the pattern of curve for amino acids and codons in these two exam- ples was very similar to the one seen in figures 1 and 2 for 4X 174. The statistical results for all three examples are summarized in table 3. In all cases except for the smallest sample (amino acids of 4X 174), slope is nearer to - 1 than -0.75, and the best results are generally for the larger sam- ples. Correlations all hover around -0.7 or -0.8, and re- duced major axis (except for E. coli codons) is near - 1. Thus, the curves can all be approximated fairly well by straight lines of slopes near - 1, but a better approximation would be ob- tained by a broken graph having a line of shallower slope for high frequencies and steeper slope for lower frequencies. This means that in the case of genetic coding, a modified version of Zipf's Law seems to hold in which frequent tokens are very frequent indeed and infrequent tokens rare. A biological expla- nation should be sought for this situation.

2.0

1 5

InF 1.

.5-

OI 0 .5 1.0 1.5 2.0 2.5 3.0 3.5

InR FIG. 3. Natural logarithm of frequency (number of codons per amino acid) vs. natural logarithm of rank of amino acids in terms of the above . Least-squares approximation y = 0. 59X + 2.31, r = - 0.88.

CURRENT ANTHROPOLOGY

TABLE 3 SUMMARY OF GRAPHIC RESULTS FOR THREE ORGANISMS

AMINO ACIDS CODONS

,X 174 Mouse Mitochondrial DNA E. coli ,X 174 Mouse Mitochondrial DNA E. coli (N = 1,936) (N = 3,816) (N = 16,351)

Slope (m) ......... - 0.644 - 0.846 -0.751 - 0.798 - 0.839 - 0.874 Intercept (y) ..........5.737 6.75 8.05 5.62 6.45 7.93 Correlation (r) ........ - 0.732 -0.781 - 0.742 - 0.835 - 0.799 - 0.706 Reduced major axis .. . -0.88 - 1.08 - 1.01 -0.956 - 1.05 - 1 238

References Cited ALFF-STEINBERGER, C. 1984. Evidence for a coding pattern on the

non-coding strand of the E. coli genome. Nucleic Acid Research 12:2235-41.

BIBB, M. J., R. A. VAN ETTEN, C. T. WRIGHT, M. W. WALBERG. 1981. Sequence and gene organization of mouse mitochondrial DNA. Cell 26:167-80.

CHERRY, COLIN. 1978. 3d ed. On human communication. Cambridge: M.I.T. Press.

CRICK, F. H. C. 1966. The genetic code. 3. Scientific American 215 (4):55-62.

DOBZHANSKY, T., F. J. AYALA, G. L. STEBBINS, and J. W. VALEN- TINE. 1977. Evolution. San Francisco: Freeman.

DOERFLER, W. 1982. In search of more complex genetic codes: Can linguistics be a guide? Medical Hypotheses 9:563-79.

FIDDES, J. C. 1977. The nucleotide sequence of a viral DNA. Scientific American 237 (6):54-67.

JAKOBSON, ROMAN. 1970. Main trends in the science of language. New York: Harper and Row.

SHANNON, CLAUDE E., and WARREN WEAVER. 1949. The mathemat- ical theory of communication. Urbana: University of Illinois Press.

ZIPF, GEORGE K. 1949. Human behavior and the principle of least effort. Cambridge: Addison-Wesley.

Proposals for Anthropology in the Nuclear Agel

by PETER WORSLEY 22 Northchurch Terrace, London Ni 4EG, England. 26 XI 85

Two years' work with the Commission on the Study of Peace of the International Union of Anthropological and Ethnological Sciences (IUAES) has convinced me that there is widespread receptivity to any ideas that anthropologists are able to con- tribute to the analysis of the major international conflicts and especially of the threat of nuclear warfare.

The sources of the arms race lie in conflicts of interests and in "images of the Other" which are often based on ignorance and stereotypes similar in kind to those which anthropologists have so effectively analysed in studies of interethnic relations. Beliefs about an innate human propensity to aggression, for instance, or Manichaean ideas about the intrinsic evil-ness of believed enemies, which have been studied in the anthropology of witchcraft in very sophisticated ways, are highly relevant to suspicions of the intentions of the U.S.S.R. or the U.S.A. The study of war making, and of peace making, by anthropolo- gists, in both state and acephalous societies, also points to mechanisms-of mediation, confidence building, alternatives to war-which have their analogues in superpower or other kinds of international hostility. The institutional making of war, including military organization, and the social forces which generate peace movements are further appropriate fields of research. (In the U.S.A., for example, Donna Brasset- Shearer is engaged in an anthropological study of top U.S. military leaders.)

The Peace Commission has now contributed to several ma- jor academic conferences. An initial collection of papers from the XIth International Congress of Anthropological and Eth- nological Sciences at Vancouver in 1982 will come off the presses as a book any minute (Peace and War: Cross-cultural Perspectives, Transaction Books). Carol Greenhouse of Cor- nell University, one of the cochairpersons of the Peace Com- mission, is contributing on behalf of our discipline to the

1 ? 1986 by The Wenner-Gren Foundation for Anthropological Re- search, all rights reserved 0011-3204/86/2703-0009$1.00.

Vol. 27 * No. 3 - June 1986

volume The Quest for Peace, which is the outcome of a multi- disciplinary meeting of the International Social Science Coun- cil held at UNESCO headquarters in Paris last year. That meeting was both cheering and depressing-depressing be- cause the 11 social sciences represented there (by the presidents or secretaries, usually, of their international organizations) all reported that no serious sustained work on the issue of nuclear war had been developed until the last couple of years. In con- trast, the natural sciences have played a major role-for in- stance, in researching the medical consequences of nuclear war or the prospect of a "nuclear winter." Here, too, scenarios of likely social responses to nuclear devastation have been left largely to social psychologists.

In the U.S.A., important contributions to symposia on inter- national conflicts (at the American Association for the Ad- vancement of Science in Los Angeles last May and at the De- cember 1985 annual meeting of the American Anthropological Association) have already been undertaken, and more are planned. The Soviet Academy of Sciences, similarly, invited the Peace Commission to a very open and rewarding discussion in Moscow this August and has accepted its suggestion of a conference involving East European and West European an- thropologists in London on the subject of urban ethnicity.

Conferences build confidence and promote interpersonal and institutional contacts without which we remain ignorant and usually suspicious of colleagues from whom we are divided by political and cultural barriers. I believe that anthropology, of all disciplines, is best fitted to do the following even more important things:

1. To multiply, on a greatly increased scale, fieldwork- based studies both by established anthropologists and by grad- uate students of the kind Caroline Humphrey has done in the U.S.S.R. and Jack Potter in China-which, so far, no East European or Chinese anthropologist has been encouraged to do in the West.

2. To embark upon a program of exchanges of teachers in which they would equip themselves to teach courses in their home universities on "The Peoples (plural) of the U.S.S.R." (before long, an English-language textbook, prepared by an American anthropologist, will be available) or "The Peoples of the U.S.A./Western Europe. "

3. To exchange graduate students, trained to first-degree level in their home countries, who would pursue graduate

283