letters to nature
germination. We evaluated the seed±recruit relationship using linear regression of log
transformed values of R  1 and S  1 to normalize residuals. In these regressions, the®tted constant b takes values of less than 1 if the per seed probability of recruitment isinversely related to seed density.
Species were excluded from regression analyses if (1) seeds passed through the 1-mm
trap mesh, (2) seeds or recruits were recorded at fewer than 10 stations, or (3) seed or
recruit density varied less than a factor of four among stations Fifty-three species remained
including 28 trees, 20 lianas and ®ve shrubs. These 53 focal species account for 60.3% of
the seed rain and 80.4% of recruits. None of the 53 species persist for more than one year in
the soil seed bank.
To insure that the regression results were not spurious or artefactual, we conducted
several additional tests. First, some traps received many more seeds than could possibly
recruit into adjacent seedling plots (simple space limitation). Second, in many instances,seedlings of a given species recruited into some seedling plots, but no seeds of that species
were found in the adjacent seed traps. Either or both of these effects would lower b-value
estimates and in¯ate the apparent importance of density dependence. Third, empty
stations, lacking both seeds and recruits, introduce an opposing bias, and raise the b-value
estimates. To control for the effect of space limitation, we conducted analyses excluding
stations in which single species seed densities exceeded the maximum single species recruit
density (66 seedlings m-2). To control for the other biases, we conducted analyses after
excluding stations lacking conspeci®c seed. We then eliminated all of these effects by
including only stations with non-zero seed densities less than 66 seed m-2. Finally, theaddition of 1 before taking logarithms gives b values a downward bias. This effect can belarge, particularly when the ratio of seeds to recruits is large. To evaluate the effect of this®nal potential bias, we compared 95% con®dence intervals of the observed b values with bvalues predicted in the absence of density dependence. Observed b values were signi®cantly less than predicted b values for every species. In all cases, these more conservative
tests substantiated the pervasive and strong effects of negative density dependence on
seedling recruitment.
Received 21 December 1999; accepted 10 February 2000.
1. Ridley, H. N. The Dispersal of Plants Throughout the World (L. Reeve & Co., Ashford, England, 1930).
2. Janzen, D. H. Herbivores and the number of tree species in tropical forests. Am. Nat. 104, 501±528(1970).
3. Connell, J. H. in Dynamics of Populations (eds den Boer, P. J. & Gradwell, G. R.) 298±312 (Center for
Agricultural Publication and Documentation, Wageningen, The Netherlands, 1971).
4. Augspurger, C. K. Seedling survival of tropical tree species: interactions of dispersal distance, lightgaps and pathogens. Ecology 65, 1705±1712 (1984).
5. Clark, D. A. & Clark, D. B. Spacing dynamics of a tropical rainforest tree: evaluation of the Janzen±
Connell model. Am. Nat. 124, 769±788 (1984).
6. Hammond, D. S. & Brown, V. K. in Dynamics of Tropical Communities (eds Newbery, D. M., Prins,
H. H. T. & Brown, N. D.) 51±78 (Blackwell Science, London, 1998).
7. Howe, H. F. Survival and growth of juvenile Virola surinamensis in Panama: effects of herbivory andcanopy closure. J. Trop. Ecol. 6, 259±280 (1990).
8. Webb, C. O. & Peart, D. R. Seedling density dependence promotes coexistence of Bornean rain forest
trees. Ecology 80, 2006±2017 (1999).
9. Condit, R., Hubbell, S. P. & Foster, R. B. Recruitment near conspeci®c adults and the maintenance oftree and shrub diversity in a neotropical forest. Am. Nat. 140, 261±286 (1992).
10. Gilbert, G. S., Hubbell, S. P. & Foster, R. B. Density and distance-to-adult effects of a canker disease oftrees in a moist tropical forest. Oecologia 98, 100±108 (1994).
11. Hubbell, S. P., Condit, R. & Foster, R. B. Presence and absence of density dependence in a neotropicaltree community. Phil. Trans. R. Soc. Lond. B 330, 269±281 (1990).
12. Wills, C. & Condit, R. Similar non-random processes maintain diversity in two tropical rainforests.
Proc. R. Soc. Lond. B 266, 1445±1452 (1999).
13. Wills, C., Condit, R., Foster, R. B. & Hubbell, S. P. Strong density- and diversity-related effects help
to maintain tree species diversity in a neotropical forest. Proc. Natl Acad. Sci. USA 94, 1252±1257 (1997).
14. Hubbell, S. P. Seed predation and the coexistence of tree species in tropical forests. Oikos 35, 214±229(1980).
15. Wright, S. J. in Handbook of Functional Plant Ecology (eds Pugnaire, F. I. & Valladares, F.) 449±472(M. Dekker, New York, 1999).
16. Connell, J. H. Diversity in tropical rain forest and coral reefs. Science 199, 1302±1309 (1978).
17. Leigh, E. G. Jr Tropical Forest Ecology (Oxford Univ. Press, Oxford, 1999).
18. Schupp, E. W. The Janzen±Connell model for tropical tree diversity: population implications and theimportance of spatial scale. Am. Nat. 140, 526±530 (1992).
19. Condit, R., Hubbell, S. P. & Foster, R. B. Changes in tree species abundance in a Neotropical forest:
impact of climate change. J. Trop. Ecol. 12, 231±256 (1996).
20. Hammond, D. S. & Brown, V. K. Seed size of woody plants in relation to disturbance, dispersal, soil
type in wet neotropical forests. Ecology 76, 2544±2561 (1995).
21. Kitajima, K. Relative importance of photosynthetic traits and allocation patterns as correlates ofseedling shade tolerance of 13 tropical trees. Oecologia 98, 419±428 (1994).
22. Janzen, D. H. Speci®city of seed-attacking beetles in a Costa Rican deciduous forest. J. Ecol. 68, 929±
952 (1980).
23. Barone, J. A. Host-speci®city of folivorous insects in a moist tropical forest. J. Anim. Ecol. 67, 400±409(1998).
24. Coley, P. D. & Barone, J. A. Herbivory and plant defenses in tropical forests. Annu. Rev. Ecol. Syst. 27,
305±335 (1996).
25. Coley, P. D. & Aide, T. M. in Plant±Animal Interactions (eds Price, P. W., Lewinson, T. M., Fernandes,
G. W. & Benson, W. W.) 25±49 (John Wiley and Sons, New York, 1991).
26. Hubbell, S. P. et al. Light-gap disturbances, recruitment limitation, and tree diversity in a neotropicalforest. Science 283, 554±557 (1999).
27. Wright, S. J., Carrasco, C., CalderoÂn, O. & Paton, S. The El NinÄo southern oscillation, variable fruit
production, and famine in a tropical forest. Ecology 80, 1632±1647 (1999).
28. Wright, S. J., Carrasco, C., CalderoÁn, O. & Paton, S. The El NinÄo southern oscillation, variable fruit
production, and famine in a tropical forest. Ecology 80, 1632±1647 (1999).

NATURE | VOL 404 | 30 MARCH 2000 | www.nature.com

Acknowledgements
We dedicate this study to the memory of Eduardo Sierra: his ability to identify seedlings of
700 plant species was indispensable. We thank B. Arnold, J. Connell, J. Dalling, J. Eberhard,
C. Gehring, P. Green, S. Hubbell, P. Juniper, H. MuÈller-Landau and T. Theimer forconstructive criticism of the manuscript. The Andrew W. Mellon Foundation and theEnvironmental Sciences Program of the Smithsonian Institution provided ®nancial
support.
Correspondence and requests for materials should be addressed to S.J.W.
(e-mail: wrightj@tivoli.si.edu).

.................................................................
The evolution ofsyntactic communication

Martin A. Nowak*, Joshua B. Plotkin* & Vincent A. A. Jansen²* Institute for Advanced Study, Princeton, New Jersey 08540, USA² School of Biological Sciences, Royal Holloway, University of London, Egham
Surrey, TW20 0EX UK..............................................................................................................................................

Animal communication is typically non-syntactic, which meansthat signals refer to whole situations1±7. Human language is
syntactic, and signals consist of discrete components that havetheir own meaning8. Syntax is a prerequisite for taking advantage
of combinatorics, that is, ``making in®nite use of ®nite means''9±11.
The vast expressive power of human language would be
impossible without syntax, and the transition from non-syntactic
to syntactic communication was an essential step in the evolutionof human language12±16. We aim to understand the evolutionary
dynamics of this transition and to analyse how natural selection
can guide it. Here we present a model for the population dynamics
of language evolution, de®ne the basic reproductive ratio of words
and calculate the maximum size of a lexicon. Syntax allows larger
repertoires and the possibility to formulate messages that havenot been learned beforehand. Nevertheless, according to ourmodel natural selection can only favour the emergence of syntax
if the number of required signals exceeds a threshold value.
This result might explain why only humans evolved syntactic
communication and hence complex language.
The uniqueness of language has been compared to that of theelephant's trunk13. Human language is as different from animalcommunication as the elephant's trunk is from other animals'
nostrils. Yet few biologists worry about the evolution of theelephant's trunk (which is a most complex organ that consists ofabout 6,000 individual muscles and that can perform an unparalleled variety of mechanical tasks), whereas many philosophers,
linguists and biologists have great dif®culties in imagining how
language could have arisen by darwinian evolution17±21.
A challenge for evolutionary biology, therefore, is to provide a
detailed mathematical account of how natural selection can enable
the emergence of human language from animal communication.
Animal communication is based on three basic designs: a ®nite
repertoire of calls (territorial calls or warning of predators); a
continuous analogue signal (for example, the dance of bees); anda series of random variations on a theme (such as the song of birds).
All natural animal communication appears to be non-syntactic;
some caution, however, seems appropriate as the ®nal verdict oncomplex vocalization patterns of certain primate species or dolphins has not been reached. In contrast, human language is clearly
syntactic: messages consist of components that have their own
meaning. We compare non-syntactic and syntactic communicationand evaluate their relative performance in an evolutionary setting.
First, we formulate a mathematical model for the population
dynamics of language evolution. Suppose a language contains n© 2000 Macmillan Magazines Ltd

495

letters to naturewords. Each individual is born not knowing any of the words, but
can acquire words by learning from other individuals. Individuals
are characterized by the subset of words that they know. The generalequations for the resulting evolutionary dynamics are complicated(see Methods), but an analytical approach is possible if we describe
the process in terms of independent, elementary steps on the basis of
two assumptions: ®rst, in any one interaction between two individuals only a single new word can be learned; second, words arememorized independently of each other. With these assumptions,
we obtain for the population dynamics of xi, which is the relative
abundance of individuals who know word WixÇi  Ri xi 1 2 xi  2 xi

1

where i  1; ¼; n. The abundance of word Wi spreads by theinteraction of people who know the word with people who do
not know the word; hence its rate of increase is proportional to the
product xi 1 2 xi . The rate constant, Ri  bqfi , is the basic reproductive ratio of word Wi. This is the average number of individuals
who acquire word Wi from one individual who knows it. The
parameter b is the total number of word-learning events per
individual per lifetime. The parameter q is the probability ofmemorizing a single word after one encounter, and fi is thefrequency of occurrence of word Wi in the (spoken) language.
The term -xi denotes a constant death rate, setting the average
lifetime of each individual as one time unit.
For a word to be maintained in the lexicon of the population, its
basic reproductive ratio must exceed one, which implies thatfi . 1= bq. Suppose Wi is the least frequent word. We certainly
know that fi is less than 1/n, which is the frequency of a word if allwords have the same frequency. Thus the maximum number ofwords is nmax  bq. Note that this number is always less than the
total number of words, b, that are presented to a learning individual.
Hence, the lexicon of the population cannot exceed the total
number of word-learning events for each individual.

Maximum lexicon size, nmax

100

10

ActualApproximation
1
1

10

100

1,000

Learning events, b
Figure 1 How many word-learning events per individual are required for a population tomaintain a certain number of words in its combined lexicon assuming that word
frequencies follow Zipf's law? Zipf's law states that the frequency fi of occurrence of aword is inversely proportional to its position, i, in a frequency ranking. Zipf's law seems to
be a very good approximation for every human language. Nobody knows its signi®cance.
It can be shown, however, that a random source emitting symbols and spaces also
generates word frequency distributions following Zipf's law23. Assuming that n words
follow a frequency distribution as in Zipf's law, fi  C n =i where C n  1=Sni1 1=i, themaximum number of words that can be maintained, nmax, is the largest integer, n, whichful®ls the inequality fn  C n =n . 1=bq. The ®gure shows nmax versus b for q  0:1. The
exact relationship is a step function because both b and nmax are integers. The equation
n max g  ln n max   bq is an excellent approximation (continuous line). Here we haveused Euler's gamma which is g  0:5772¼ . For example, to maintain a lexicon of 100
words, we need about bq  520 successful word-learning events per individual. For
q  0:1, this implies that a total of roughly b  5;200 word-learning events per
individual are required.
496

Assuming that word frequency distributions follow Zipf 's law22,23,
fi  C=i, where C is a constant, we ®nd that the maximum numberof words is roughly given by the equation nmax ln nmax   bq (Fig. 1).
We now use this mathematical framework to analyse how natural
selection can guide the transition from non-syntactic to syntactic
communication. Imagine a group of individuals who communicate
about events in the world around them. Events are combinations ofobjects, places, times and actions. (We use `object' and `action' in a
general way to represent everything that can be referred to by nouns
and verbs of current human languages.) For notational simplicity,
suppose that each event consists of one object and one action. Thus,
event Eij consists of object i and action j. Non-syntactic communication uses words for events, whereas syntactic communication
uses words for objects and actions (Fig. 2). Events occur at different
rates, which are speci®ed by the entries of an `event rate matrix', G.
For natural selection to operate on language design, language
must confer ®tness. A plausible assumption is that correct communication about events provides a ®tness advantage to the interacting
individuals. In terms of our model, the ®tness contribution of alanguage can be formulated as the probability that two individuals
know the correct word for a given event summed over all events andweighted with the rate of occurrence of these events.
The population dynamics of non-syntactic communication areagain given by equation (1) with word Wij referring to event Eij. As
before, the maximum number of words that can be maintained in
the population is limited by bq. We calculate the ®tness of
individuals using non-syntactic communication (see Methods).
We now turn to syntactic communication. Noun Ni refers to
object i and verb Vj refers to action j, hence the event Eij is describedby the sentence NiVj. For the basic reproductive ratios we obtain
R N i   b=2qs f N i  and R V j   b=2qs f V j . Here f(Ni) andf(Vj) denote the frequency of occurrence of noun Ni and verb Vj,
respectively. The factor 1/2 appears because either the noun or theverb is learned in any one of the b learning events. The probability ofmemorizing a noun or a verb is given by qs. We expect qs to besmaller than q, which simply means that it is a more dif®cult task tolearn a syntactic signal than a non-syntactic signal. For both signals,
the (arbitrary) meaning has to be memorized; for a syntactic signal
one must also memorize its relation to other signals (whether it is anoun or a verb, for example).
For noun Ni to be maintained in the lexicon of the population, its
basic reproductive ratio must exceed one, implying thatf N i  . 2= bqs . Similarly, for verb Vj we ®nd f V j  . 2= bqs .
This means that the total number of nouns plus verbs is limited
by bqs, which is always less than b. The maximum number ofgrammatical sentences, however, which consist of one noun and one
verb, is given by (bqs)2/4. Hence syntax makes it possible to maintainmore sentences than the total number of sentences, b, encounteredby a learning individual. All words have to be learned, therefore, but
syntactic signals enable the formulation of `new' sentences that havenot been learned beforehand.

Wij
Eij = Oi + Aj
Ni

Vj

Figure 2 To understand the essence of the evolution of syntax, we imagine a world where
each event consists of one object and one action. Event Eij consists of object Oi and action
Aj. A non-syntactic language has words, Wij, that refer to events, Eij. A syntactic language
has words for objects and actions, Ni and Vj. Words for objects are called nouns, words foractions are called verbs. Our mathematical analysis can also be adapted to more
complicated situations, where events consist of several objects, actions, places or times,
but the equations become more clumsy. The principles remain the same.

© 2000 Macmillan Magazines Ltd

NATURE | VOL 404 | 30 MARCH 2000 | www.nature.com

letters to nature
For calculating the ®tness of syntactic communication, note that
two randomly chosen individuals can communicate about event Eij
if they both know noun Ni and verb Vj. If we denote the relative
abundance of individuals who know Ni and Vj by x N i V j , we
obtainxÇ N i V j   R N i x N i x V j  2 x N i V j 
 R V j x V j x N i  2 x N i V j  2 x N i V j 

2The abundance of individuals who know noun Ni and verb Vj
increases if someone who knows Ni meets someone who knows
Vj but not Ni. Similarly, the abundance increases if someone

5aFitness

4
Fn

3

Fs

n . 3q= pqs 2
1 1 0 00 1 0 00 0 1 00 0 0 1

1
100

1,000

10,0005bFitness

3
Fn

2

Fs
1 1 0 1 0 0
0 1 1 0 1 0
1 0 1 0 0 1
1 1 0 1 1 0
0 1 0 0 1 1
1 0 1 1 0 1

1

100

1,000

10,00060c50
Fitness

who knows verb Vj meets someone who knows Ni but not Vj.
We calculate the equilibrium abundances and thence the ®tness of
individuals using syntactic communication (see Methods). Figure 3
shows the ®tness of syntactic and non-syntactic communication as afunction of b for different examples of the event rate matrix, G.
When does syntactic communication lead to a higher ®tness thannon-syntactic communication? Suppose there are n objects and m
actions. Suppose a fraction, p, of these mn events occur (all at thesame frequency), and the other events do not occur. In this case,
R W ij   bq= pmn for those events that occur. Making the (somewhat rough) assumption that all nouns and all verbs, respectively,
occur on average at the same frequency, we obtain R N i   bqs = 2n
and R V j   bqs = 2m. If all involved basic reproductive ratios arewell above one, the ®tness of syntactic communication exceeds the®tness of non-syntactic communication provided m2 n  mn2 =
m2  mn  n2  . 2q= pqs  (see Methods). If this inequality
holds then syntactic communication will be favoured by natural
selection; otherwise non-syntactic communication will win.
Observe that m $ 3 and n $ 3 are necessary conditions for theevolution of syntax. For m  n, the relevant condition is4030

1 1 0 1 0 1 0 0 1 1
1 1 1 0 1 0 1 1 0 1
0 0 1 1 0 1 0 1 1 0
1 1 0 1 1 0 1 0 1 1
1 1 1 1 1 1 1 1 0 1
1 0 1 0 1 1 0 1 1 1
0 1 0 1 0 1 1 0 1 0
1 0 1 1 0 1 0 0 0 1
0 1 1 1 0 1 1 1 0 1
1 0 1 0 1 1 0 1 1 1

Hence, the size of the system has to exceed a critical value forsyntactic communication to evolve. For example, if it is twice as
hard to memorize a syntactic signal than a non-syntactic signal,
q=qs  1=2, and if a fraction p  1=3 of all noun verb combinations
describe meaningful events, then at least an 18 3 18 system isrequired for syntactic communication to have any chance of
evolving. Figure 4 shows the excellent agreement between our
approximative analytical results and exact numerical computations.
The parameter p quanti®es to what extent the perceived world has
a compositional structure. A small p means that events often consistof unique pairings of objects and actions. The smaller the value of p,
the harder it is for syntactic communication to evolve (the critical nin equation (3) is large).
Our results suggest that the crucial step that guided the transition
from non-syntactic to syntactic communication was an increase in
the number of relevant events that could be referred to. `Relevant
event' means there is a ®tness contribution for communication
about this event. As the number of such `relevant communication
topics' increased, natural selection could begin to favour syntactic

1.0

Fs
100

Syntax winning

20
10

Fn
1,000

10,000

Learning events, b
Figure 3 The ®tness of non-syntactic and syntactic communication, Fn and Fs, as functionof the total number of word learning events per individual, b, for three different choices ofthe event rate matrix, G. The entries of G are the numbers gij which characterize the rates
at which the various events occur. a, There are four objects and four actions. Each object
is associated with a speci®c action; in addition object 1 also occurs with action 2. All
possible events occur at the same rate. Thus the event rate matrix is a binary 4 3 4 matrix
with 5 non-zero entries, p  5=16. For b ranging from 50 to 10,000, F n always exceeds
Fs. b, There are six objects and six actions, the event rate matrix has 20 non-zero entries,p  5=9. For values of b less than 400, syntactic communication has a higher ®tness thannon-syntactic communication. For values of b above 400, non-syntactic communication
wins. Hence, for medium-sized systems the emergence of syntactic communication canbe prevented by increasing the number of learning events per individual. c, There are 10
objects and 10 actions, 65 of 100 combinations occur, p  13=20. In this case, syntactic
communication wins for any choice of b. Each panel shows Fn and Fs as function of b andillustrates the chosen event rate matrix, G.
NATURE | VOL 404 | 30 MARCH 2000 | www.nature.com

3

0.8
0.6
0.4
0.2
5

10

15
Size n20

25

Figure 4 Numerical validation of the approximate threshold condition given byequation (3). If this inequality holds then syntax will be favoured by natural selection. Thereis communication about n objects and m actions. A fraction, p of the nm object±action
combinations refers to events that occur in the world. The parameters q and qs denote,
respectively, the probability of memorizing a non-syntactic and a syntactic signal after asingle occurrence. We choose n  m, b  5;000 and q  0:1. The values of n range
from 2 to 25. For each n we compute Fs and Fn for 1,000 randomly chosen event-rate
matrices G, whose entries are 1 with probability p or 0 otherwise. The y-axis shows thefraction of times when Fs exceeds Fn. From left to right the curves correspond to theparameter values p  0:5, q s  0:1; p  0:5, q s  0:07; p  0:25, q s  0:1;
p  0:25; q s  0:07. The straight lines indicate the predicted threshold values n  6,
8.6, 12, 17.1.

© 2000 Macmillan Magazines Ltd

497

letters to naturecommunication and thereby lead to a language design where
messages could be formulated that were not learned beforehand.
Syntactic messages can encode new ideas or refer to extremely rare
but important events. Our theory, however, does not suggest thatsyntactic communication is always at an advantage. Many animal
species probably have a syntactic understanding of the world, butnatural selection did not produce a syntactic communication
system for these species because the number of relevant signals
was below the threshold illustrated by equation (3). Presumably theincrease in the number of relevant communication topics wascaused by changes in the social structure24 and interaction of
those human ancestors who evolved syntactic communication. M

Methods

Suppose there are n words. Individuals are characterized by the subset of words they know.
There are 2n possibilities for the internal lexicon of an individual. Internal lexica arede®ned by bit strings: 1 means that the corresponding word is known; 0 means it is not. Let
us enumerate them by I  0; ¼; n where n  2n 2 1. The number I is the integer
representation of the corresponding bit string. (For example, I  6 represents the string
000¼0110.) Denote by xI the abundance of individuals with internal lexicon I. The
population dynamics can be formulated asxÇI  dI 2 xI  bnn^^ x x Q 2x x Q 
J K

JKI

I J

IJK

4

J0 K0where I  0; ¼; n. We have d0  1 and dI  0 otherwise; thus all individuals are born notknowing any of the words. Individuals die at a constant rate, which we set to 1, therebyde®ning a time scale. The quantities QIJK denote the probabilities that individual I learningfrom J will become K. Equation (4) is a general framework for the population dynamics ofthe lexical aspects of language. Assuming that in any one interaction between two
individuals only a single new word can be acquired and that words are memorizedindependently of each other, we obtain the speci®c system described by equation (1).
Let us now assume that the world is made up of events Eij consisting of objects i andactions j. The `event rate matrix', G has the entries gij which specify the relative rate ofoccurrence of event Eij. Denote by fij the frequency of occurrence of event Eij. We havefij  gij =Sij gij .
Non-syntactic communication uses words, Wij, for events Eij. The basic reproductive
ratio of Wij is given by R W ij   bqfij. If R W ij  . 1, the word Wij will persist in the
population, and at equilibrium the relative abundance of individuals who know this word
is given by x* W ij   1 2 1=R W ij .
The ®tness contribution of a language can be formulated as the probability that two
individuals know the correct word for a given event summed over all events and weighted
with the rate of occurrence of these events. Hence, at equilibrium, the ®tness of individuals
using non-syntactic communication is given byFn ^x* W  g :
2

ij

ij

5

i;j

For syntactic communication, we assume the event Eij is described by the sentence NiVj.
The population dynamics of individuals knowing both Ni and Vj are described byequation (2). The basic reproductive ratios are given by R N i   b=2qs f N i  andR V j   b=2qs f V i . The frequencies of occurrence are f N i   Sj fij and f V j   Si fij .
If the basic reproductive ratios, R(Ni) and R(Vj), are greater than one, the equilibrium
frequency of individuals who know both Ni and Vj is given by
x* N i V j  

1 2 1=R N i 1 2 1=R V j 
1 2 1=R N i   R V j 

6^x* N V  g :
i

j

2

ij

7

i;j

Assuming there are n objects and m actions that give rise to pnm meaningful events that
all occur at the same frequency, we obtain R W ij   bq= pnm. If we also assume that the
combinations of objects and actions are arranged in a way that all nouns and all verbs,
respectively, have about the same frequency, we can write R N i   bq2 = 2n andR V j   bqs = 2m. For the ®tness values, we obtain F n  pnm1 2 1=R W ij 2 andF s  pnm1 2 1=R N i 2 1 2 1=R V j 2 =1 2 1= R N i   R V j 2 . Assuming that all
involved basic reproductive ratios are well above one, we obtain for F s , F n the condition
m2 n  mn2 = m2  mn  n2  . 2q= pqs . De®ning the ratio, a  m=n, we can rewrite
this condition as


2q
1
1
:
8
1 2
n.
pqs
a a1
Hence the size of the system has to exceed a critical threshold for syntax to be favoured bynatural selection.

498

1. Von Frisch, K. The Dance Language and Orientation of Bees (Harvard Univ. Press, Cambridge,
Massachusetts, 1967).
2. Marler, P. Birdsong and speech development: could there be parallels? Am. Sci. 58, 669±673 (1970).
3. Wilson, E. O. Animal communication. Sci. Am. 227, 52±60 (1972).
4. Gould, J. L. & Marler, P. Learning by instinct. Sci. Am. 256, 74±85 (1987).
5. Burling, R. Primate calls, human language, and nonverbal communication. Curr. Anthropol. 34, 25±
53 (1989).
6. Cheney, D. L. & Seyfarth, R. M. How Monkeys See the World: Inside the Mind of Another Species(Chicago Univ. Press, 1990).
7. Hauser, M. The Evolution of Communication (MIT Press, Cambridge, Massachusetts, 1996).
8. Bickerton, D. Species and Language (Chicago Univ. Press, Chicago, 1990).
9. von Humboldt, W. Linguistic Variability and Intellectual Development (Pennsylvania Univ. Press,
Philadelphia, 1972).
10. Chomsky, N. Aspects of the Theory of Syntax (MIT Press, Cambridge, Massachusetts, 1965).
11. Jackendoff, R. The Architecture of the Language Faculty (MIT Press, Cambridge, Massachusetts, 1997).
12. Pinker, S. & Bloom, P. Natural language and natural selection. Behav. Brain Sci. 13, 707±784 (1990).
13. Pinker, S. The Language Instinct. (Harper Collins, New York, 1994).
14. Maynard Smith, J. & Szathmary, E. The Major Transitions in Evolution (Freeman, Oxford, 1995).
15. Hurford, J. R., Studdert-Kennedy, M. & Knight, C. Approaches to the Evolution of Language (Cambridge Univ. Press, Cambridge, UK, 1998).
16. Nowak, M. A. & Krakauer, D. C. The evolution of language. Proc. Natl Acad. Sci. USA 96, 8028±8033(1999).
17. Chomsky, N. Language and Mind (Harcourt Brace Jovanovich, New York, 1972).
18. Chomsky, N. Language and Problems of Knowledge: The Managua Lectures (MIT Press, Cambridge,
Masachusetts, 1988).
19. Premack, D. Gavagai! or the future history of the animal language controversy. Cognition 19, 207±296(1985).
20. Lieberman, P. The Biology and Evolution of Language (Harvard Univ. Press, Cambridge, Massachusetts, 1984).
21. Bates, E., Thal, D. & Marchman, V. in Biological and Behavioural Determinants of Language
Development (eds Krasnegor et al.) (Erlbaum, Mahwah, NJ, 1991).
22. Zipf, G. K. The Psychobiology of Language (Houghton-Mif¯in, Boston, 1935).
23. Miller, G. A. & Chomsky, N. Handbook of Mathematical Psychology. Vol. 2 (eds Luce, R. D., Bush, R. &Galauter, E.) 419±491 (Wiley, New York, 1963).
24. Dunbar, R. Grooming, Gossip and the Evolution of Language (Harvard Univ. Press, Cambridge,
Massachusetts, 1996).

Acknowledgements
This work was supported by the Leon Levy and Shelby White Initiatives Fund, the Florence
Gould Foundation, the J. Seward Johnson Sr Charitable Trusts, the Ambrose Monell
Foundation, the National Science Foundation, the Wellcome Trust and the Alfred P. Sloan
Foundation.
Correspondence and requests for materials should be addressed to M.A.N.
(e-mail: nowak@ias.edu).

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Glutamate spillover suppresses
inhibition by activatingpresynaptic mGluRs
Simon J. Mitchell & R. Angus Silver
Department of Physiology, University College London, Gower Street,
London WC1E 6BT, UK

At equilibrium, the ®tness of syntactic communication is given byFs Received 1 November 1999; accepted 26 January 2000.

..............................................................................................................................................

Metabotropic glutamate receptors (mGluRs) found on synaptic
terminals throughout the brain are thought to be important inmodulating neurotransmission1,2. Activation of mGluRs by synaptically released glutamate depresses glutamate release from excitatory terminals3±5 but the physiological role of mGluRs on
inhibitory terminals is unclear. We have investigated activationof mGluRs on inhibitory terminals within the cerebellar glomerulus, a structure in which GABA (g-aminobutyric acid)-releasing
inhibitory terminals and glutamatergic excitatory terminals are
in close apposition and make axo-dendritic synapses onto granulecells6. Here we show that `spillover' of glutamate, which is released
from excitatory mossy ®bres, inhibits GABA release from Golgi
cell terminals by activating presynaptic mGluRs under physiological conditions. The magnitude of the depression of the© 2000 Macmillan Magazines Ltd

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