letter Network motifs in the transcriptional regulation network of Escherichia coli Shai S. Shen-Orr1 , Ron Milo2 , Shmoolik Mangan1 & Uri Alon1 ,2 Published online : 22 April 2002 , DOI : 10.1038 / ng881 2002 Nature Publishing Group http://genetics.nature.com a feedforward loop X Y Z X Y n b crp araC araBAD c single input module -LRB- SIM -RRB- X X n Z1 Z2 ... Zn Little is known about the design principles1 10 of transcriptional regulation networks that control gene expression in cells . Recent advances in data collection and analysis2 ,11,12 , however , are generating unprecedented amounts of information about gene regulation networks . To understand these complex wiring diagrams1 10,13 , we sought to break down such networks into basic building blocks2 . We generalize the notion of motifs , widely used for sequence analysis , to the level of networks . We define ` network motifs ' as patterns of interconnections that recur in many different parts of a network at frequencies much higher than those found in randomized networks . We applied new algorithms for systematically detecting network motifs to one of the best-characterized regulation networks , that of direct transcriptional interactions in Escherichia coli3 ,6 . We find that much of the network is composed of repeated appearances of three highly significant motifs . Each network motif has a specific function in determining gene expression , such as generating temporal expression programs and governing the responses to fluctuating external signals . The motif structure also allows an easily interpretable view of the entire known transcriptional network of the organism . This approach may help define the basic computational elements of other biological networks . d argR argF argCBH argD argE argI e dense overlapping regulons -LRB- DOR -RRB- X1 X2 X3 ... Xn X1 X2 X3 Xn We compiled a data set of direct transcriptional interactions between transcription factors and the operons they regulate -LRB- an operon is a group of contiguous genes that are transcribed into a single mRNA molecule -RRB- . This database contains 577 interactions and 424 operons -LRB- involving 116 transcription factors -RRB- ; it was formed on the basis of on an existing database -LRB- RegulonDB -RRB- 3,14 . We enhanced RegulonDB by an extensive literature search , adding 35 new transcription factors , including alternative - factors -LRB- subunits of RNA polymerase that confer recognition of specific promoter sequences -RRB- . The data set consists of established interactions in which a transcription factor directly binds a regulatory site . The transcriptional network can be represented as a directed graph , in which each node represents an operon and edges represent direct transcriptional interactions . Each edge is directed Fig. 1 Network motifs found in the E. coli transcriptional regulation network . Symbols representing the motifs are also shown . a , Feedforward loop : a transcription factor X regulates a second transcription factor Y , and both jointly regulate one or more operons Z1 ... Zn . b , Example of a feedforward loop -LRB- L-arabinose utilization -RRB- . c , SIM motif : a single transcription factor , X , regulates a set of operons Z1 ... Zn . X is usually autoregulatory . All regulations are of the same sign . No other transcription factor regulates the operons . d , Example of a SIM system -LRB- arginine biosynthesis -RRB- . e , DOR motif : a set of operons Z1 ... Zm are each regulated by a combination of a set of input transcription factors , X1 ... Xn . DORs are defined by an algorithm that detects dense regions of connections , with a high ratio of connections to transcription factors . f , Example of a DOR -LRB- stationary phase response -RRB- . Z1 rpoS Z2 oxyR ada Z3 Z4 ... Zm rcsA nhaR hns lrp ihf crp proP fis f ftsQAZ katG osmC alkA 1Department of Molecular Cell Biology , 2Department of Physics of Complex Systems , Weizmann Institute of Science , Rehovot 76100 , Israel . Correspondence should be addressed to U.A. -LRB- e-mail : urialon@wisemail.weizmann.ac.il -RRB- . 64 nature genetics volume 31 may 2002 nhaA dps letter Table 1 Statistics of occurrence of various structures in the real and randomized networks Appearances in real network Structure Coherent feedforward loop Incoherent feedforward loop Operons controlled by SIM -LRB- > 13 operons -RRB- Pairs of operons regulated by same two transcription factors Nodes that participate in cycles * * Cycles Appearances in randomized network -LRB- mean s.d. -RRB- 4.4 3 2.5 2 28 7 57 14 0.18 0.6 P value P < 0.001 P 0.03 P < 0.01 P < 0.001 P 0.8 34 6 68 203 0 2002 Nature Publishing Group http://genetics.nature.com include all loops greater than size 1 -LRB- autoregulation -RRB- . P value for cycles is the probability of networks with no loops . from an operon that encodes a transcription factor to an operon that is regulated by that transcription factor . We scanned the network with algorithms aimed at detecting recurring patterns -LRB- see Methods -RRB- . We evaluated the statistical significance of the network motifs by comparison with randomized networks having the same characteristics as the real E. coli network . The probability that a randomized network had an equal or greater number of each of the motifs than the E. coli network was determined by enumerating the motifs found in 1,000 randomized networks . The first motif , termed ` feedforward loop ' , is defined by a transcription factor X that regulates a second transcription factor Y , such that both X and Y jointly regulate an operon Z -LRB- Fig. 1a -RRB- . We term X the ` general transcription factor ' , Y the ` specific transcription factor ' , and Z the ` effector operon -LRB- s -RRB- ' . For example , this motif occurs in the L-arabinose utilization system -LRB- Fig. 1b -RRB- 15 . Here , Crp is the general transcription factor and AraC the specific transcription factor . This motif characterizes 40 effector operons in 22 different systems in the network database , with 10 different general transcription factors . A feedforward loop motif is ` coherent ' if the direct effect of the general transcription factor on the effector operons has the same sign -LRB- negative or positive -RRB- as its net indirect effect through the specific transcription factor . For example , if X and Y both positively regulate Z , and X positively regulates Y , the feedforward loop is coherent . If , on the other hand , X represses Y , then the motif is incoherent . We find that most -LRB- 85 % -RRB- of the feedforward loop motifs are coherent -LRB- Table 1 -RRB- . Feedforward loops are stylized structures that occur much more frequently in the E. coli network than in randomized networks -LRB- Table 1 , P < 0.001 -RRB- . The second motif , termed single-input module -LRB- SIM -RRB- , is defined by a set of operons that are controlled by a single transcription factor -LRB- Fig. 1c -RRB- . All of the operons are under control of the same sign -LRB- all positive or all negative -RRB- and have no additional transcriptional regulation . The transcription factors controlling SIM motifs are usually autoregulatory -LRB- 70 % , mostly autorepression -RRB- , in contrast to only 50 % of the transcription factors in the complete data set . An example is the arginine biosynthesis pathway , where the transcription factor ArgR uniquely controls five operons that encode arginine biosynthesis genes -LRB- Fig. 1d -RRB- . Other amino-acid biosynthesis systems also correspond to this motif . The SIM motif appears in 24 systems in the database -LRB- including only systems with three or more operons -RRB- . Large SIMs occur infrequently in randomized networks -LRB- Table 1 , P < 0.01 -RRB- , because there is a low probability that a large number of operons controlled by a single transcription factor will have no other transcriptional inputs . The third motif , termed ` dense overlapping regulons ' -LRB- DOR -RRB- , is a layer of overlapping interactions between operons and a group of input transcription factors -LRB- Fig. 1e -RRB- that is much more dense than corresponding structures in randomized networks . We find that the sets of genes regulated by different transcription nature genetics volume 31 may 2002 factors in E. coli are much more overlapping than expected at random . This can be quantified by the frequency of pairs of genes regulated by the same two transcription factors -LRB- Table 1 -RRB- . This does not result , however , in a homogenous mesh of dense interconnections ; instead , the network contains several loosely connected , internally dense regions of combinatorial interactions -LRB- DORs -RRB- . As these regions are somewhat overlapping , different criteria can yield slightly different groupings . We used a clustering approach to define DORs . This algorithm detects locally dense regions in the network with a high ratio of connections to transcription factors -LRB- see Methods -RRB- . This defines six DORs . The operons in each DOR share common biological functions . Typically , every output operon is controlled by a different combination of input transcription factors . In rare cases , termed ` multi-input modules ' , several operons in a DOR are regulated by precisely the same combination of transcription factors with identical regulation signs . An example of a DOR is the set of operons regulated by RpoS upon entry into stationary phase -LRB- Fig. 1f -RRB- 16 . Different combinations of additional transcription factors , including transcription factors that respond to various stresses and nutrient limitations , control each of these operons . To fully understand the computation performed by each DOR requires a knowledge of the regulatory logic that controls how multiple inputs are integrated at each promoter17 . A number of DORs as large and dense as in the real E. coli network occurs very rarely in randomized networks -LRB- P0 .001 -RRB- . We note that different clustering rules can give rise to slightly different separations of operons into DORs . The significant finding is that these dense regions of overlapping interactions exist and that they seem to partition the operons into biologically meaningful combinatorial regulation clusters . The fact that the network motifs appear at frequencies much higher than expected at random suggests that they may have specific functions in the information processing performed by the network . One clue to their possible function is provided by common themes of the systems in which they appear . Additional insight may be gained by mathematical analysis of their dynamics . The feedforward loop motif often occurs where an external signal causes a rapid response of many systems -LRB- such repression of sugar utilization systems in response to glucose , shift to anaerobic metabolism -RRB- . The abundance of coherent feedforward loops , as opposed to incoherent ones , suggests a functional design -LRB- Table 1 -RRB- . Mathematical analysis suggests that the coherent feedforward loop can act as a circuit that rejects transient activation signals from the general transcription factor and responds only to persistent signals , while allowing a rapid system shutdown . This can occur when X and Y act in an ` AND-gate ' - like manner to control operon Z -LRB- Fig. 2a -RRB- , as is the case in the araBAD operon in the arabinose feedforward loop -LRB- Fig. 1b -RRB- 15 . When X is activated , the signal is transmitted to the output Z by two pathways , a direct one 65 letter a Fig. 2 Dynamic features of the coherent feedforward loop and SIM motifs . a , Consider a coherent feedforward loop circuit with an ` ANDgate ' like control of the output operon Z . This circuit can reject rapid variations in the activity of the input X , and respond only to persistent activation profiles . This is because Y needs to integrate the input X over time to pass the activation threshold for Z -LRB- thin line -RRB- . A similar rejection of rapid fluctuations can be achieved by a cascade , XYZ ; however , the cascade has a slower shut-down than the feedforward loop -LRB- thin red line in the Z dynamics panel -RRB- . b , Dynamics of the SIM motif . This motif can show a temporal program of expression according to a hierarchy of activation thresholds of the genes . When the activity of X , the master activator , rises and falls with time , the genes with the lowest threshold are activated earliest and deactivated latest . Time is in units of protein lifetimes , or of cell cycles in the case of long-lived proteins . 2002 Nature Publishing Group http://genetics.nature.com b from X and a delayed one through Y . If the activation of X is transient , Y can not reach the level needed to significantly activate Z , and the input signal is not transduced through the circuit . Only when X signals for a long enough time so that Y levels can build up will Z be activated -LRB- Fig. 2a -RRB- . Once X is deactivated , Z shuts down rapidly . This kind of behavior can be useful for making decisions based on fluctuating external signals . The SIM motif is found in systems of genes that function stochiometrically to form a protein assembly -LRB- such as flagella -RRB- or a metabolic pathway -LRB- such as amino-acid biosynthesis -RRB- . In these cases , it is useful that the activities of the operons are determined by a single transcription factor , so that their proportions at steady state can be fixed . In addition , mathematical analysis suggests that SIMs can show a detailed temporal program of expression resulting from differences in the activation thresholds of the different genes -LRB- Fig. 2b -RRB- . Built into this design is a pattern in which the first gene activated is the last one to be deactivated . Such temporal ordering can be useful in processes that require several stages to complete . This type of mechanism may explain the experimentally observed temporal program in the expression of flagella biosynthesis genes18 . The motifs allow a representation of the E. coli transcriptional network -LRB- Fig. 3 -RRB- in a compact , modular form -LRB- for an image of the full network , see Web Fig . A online -RRB- . By using symbols to represent the different motifs -LRB- Fig. 1 -RRB- , the network is broken down to its basic building blocks . A single layer of DORs connects most of the transcription factors to their effector operons . Feedforward loops and SIMs often occur at the outputs of these DORs . The DORs are interconnected by the global transcription factors , which typically control many genes in one DOR and few genes in several DORs . An important step in visualizing the network was to allow each global transcription factor to appear multiple times , whenever it is an input to a structure . This reduces the complexity of the interconnections while preserving all the information . There are few 66 long cascades3 , usually involving - factors , such as cascades of depth 5 in the flagella and nitrogen systems . Over 70 % of the operons are connected to the DORs ; the rest of the operons are in small disjoint systems . Most disjoint systems have only 1 to 3 operons . The remaining disjoint systems have up to 25 operons and show many SIMs and feedforward loops . A notable feature of the overall organization is the large degree of overlap within DORs between the short cascades that control most operons . The layer of DORs may therefore represent the core of the computation carried out by the transcriptional network . Cycles such as feedback loops are an important feature of regulatory networks . Transcriptional feedback loops occur in various organisms , such as the genetic switch in - phage5 . In the E. coli data set , there are no examples of feedback loops of direct transcriptional interactions , except for auto-regulatory loops3 . However , the absence of feedback loops is not statistically significant , as over 80 % of the randomized networks also have no feedback loops -LRB- Table 1 -RRB- . The many regulatory feedbacks loops in the organism are carried out at the post-transcriptional level . We considered only transcription interactions specifically manifested by transcription factors that bind regulatory sites3 ,14 . This transcriptional network can be thought of as the ` slow ' part of the cellular regulation network -LRB- time scale of minutes -RRB- . An additional layer of faster interactions , which include interactions between proteins -LRB- often subsecond timescale -RRB- , contributes to the full regulatory behavior and will probably introduce additional network motifs . Characterization of additional transcriptional interactions may change the present motif assignment for specific systems . However , our conclusions regarding the high frequencies of feedforward loops , SIMs and overlapping regulation compared with randomized networks are insensitive to the addition or removal of interactions from the data set . These features are still highly significant , even when 25 % of the connections in the E. coli network are removed or rearranged at random . The concept of homology between genes based on sequence motifs has been crucial for understanding the function of uncharacterized genes . Likewise , the notion of similarity between connectivity patterns in networks , based on network motifs , may be helpful in gaining insight into the dynamic behavior of newly identified gene circuits . The present analysis may serve as a guideline for experimental study of the functions of the motifs . It would be useful to determine whether the network motifs found in E. coli can characterize the transcriptional networks of other cell types . In higher eukaryotes , for example , there will be many more regulators affecting each gene , and additional types of circuits may be found . The findings presented here also raise the possibility that motifs can be defined in other biological networks7 , such as signal transduction , metabolic19 and neuron connectivity networks . nature genetics volume 31 may 2002 2002 Nature Publishing Group http://genetics.nature.com nature genetics volume 31 may 2002 letter Fig. 3 Part of the network of direct transcriptional interactions in the E. coli data set , represented using network motifs . Nodes represent operons , and lines represent transcriptional regulation , directed so that the regulating transcription factor is above the regulated operons . Network motifs are represented by their corresponding symbols -LRB- Fig. 1 -RRB- . The DORs are named according to the common function of their output operons . Each transcription factor appears in only a single subgraph , except for transcription factors regulating more than ten operons -LRB- ` global transcription factors ' -RRB- , which can appear in several subgraphs . For an image of the entire network , see Web Fig . A online . 67 letter Methods Transcriptional interaction database . Data from RegulonDB -LRB- v. 3.2 , XML format -RRB- included 81 transcription factors , with 624 interactions between transcription factors and sites . For this study , we unified interactions with several promoters for the same operon , as well as interactions of a transcription factor with several binding sites in the same promoter region . Unified interactions of different signs -LRB- negative/positive -RRB- were registered as ` dual ' . We did not include interactions of unknown type or those based solely on microarray data . This reduced the effective number of interactions in RegulonDB to 390 . We extended RegulonDB data by adding 35 new transcription factors , including alternative - factors , and 187 new interactions that we collected through a literature search . In most cases , the new interactions added were supported in the literature both by in vivo genetic experiments and by in vitro DNA binding data . Most -LRB- 58 % -RRB- of the interactions are positive , owing largely to the addition of the alternative factors as transcription factors . Of the 58 autoregulatory interactions -LRB- 50 % of all transcription factors -RRB- , a majority are autorepressors -LRB- 70 % -RRB- . The distribution of the number of transcription factors controlling an operon is compact -LRB- exponential -RRB- , whereas the distribution of the number of operons regulated by a transcription factor is long-tailed10 with an average of approximately 5 . Algorithms for detecting network motifs . The transcriptional network was represented as a connectivity matrix , M , such that Mij = 1 if operon j encodes a transcription factor that transcriptionally regulates operon i , and Mij = 0 otherwise . We scanned all n n submatrices of M , generated by choosing n nodes that lie in a connected graph , for n = 3 and n = 4 . Submatrices were enumerated efficiently by recursively searching for nonzero elements -LRB- i , j -RRB- and then scanning row i and column j for nonzero elements . The P value for the submatrices representing each type of connected subgraph was evaluated by comparing the number of times they appeared in the real network to the number of times they appeared in the randomized ensemble . For n = 3 , the only significant motif is the feedforward loop . For n = 4 , only the overlapping regulation motif , where two operons are regulated by the same two transcription factors -LRB- Table 1 -RRB- , was found to be significant . To detect SIMs and multi-input modules , we searched for identical rows of M. DOR detection . We used an algorithm for detecting dense regions of interactions in the network . All operons regulated by two or more transcription factors were considered . We defined a -LRB- nonmetric -RRB- distance measure between operons k and j , based on the number of transcription factors regulating both operons : d -LRB- k , j -RRB- = 1 / -LRB- 1 + -LRB- n fn Mk , n Mj , n -RRB- 2 -RRB- , where fn = 1/2 for global transcription factors -LRB- transcription factors that regulate more than ten operons -RRB- ; otherwise , fn = 1 . Using this distance measure , the operons were clustered with a standard average-linkage algorithm20 . DORs corresponded to clusters with more than C = 10 connections , with a ratio of connections to transcription factors greater than R = 2 and a splitting distance18 larger than the mean splitting distance . Finally , all additional operons -LRB- those regulated by a single transcription factor -RRB- , which are regulated by transcription factors participating in a single DOR , were included in that DOR . works with precisely the same F -LRB- p , q -RRB- , or the number of nodes with p incoming and q outgoing nodes , as the real network . Mathematical model of network motif dynamics . We used Boolean kinetics4 . The SIM -LRB- Fig. 2b -RRB- was described by dZi/dt = F -LRB- X , Ti -RRB- aZi , where Zi and i = 1,2,3 are the protein concentrations ; the activation thresholds are T1 = 0.1 , T2 = 0.5 , T3 = 0.8 ; the cell-cycle time -LRB- or lifetime for rapidly degradable proteins -RRB- is a = 1 ; and F -LRB- X , T -RRB- = 0 if X < T and 1 if XT . The feedforward loop -LRB- Fig. 2a -RRB- was described by dY/dt = F -LRB- X , Ty -RRB- aY , dZ/dt = F -LRB- X , Ty -RRB- F -LRB- Y , Tz -RRB- aZ , with Ty = Tz = 0.5 , a = 1 . The cascade in Fig. 2a corresponds to dY/dt = F -LRB- X , Ty -RRB- aY , dZ/dt = F -LRB- Y , Tz -RRB- aZ . The dynamics are qualitatively similar if other sigmoidal forms for F are used instead of Boolean kinetics -LRB- such as F -LRB- X , T -RRB- = X / -LRB- T+X -RRB- -RRB- . Data availability . The data set is available at http://www.weizmann.ac.il/ mcb/UriAlon . 2002 Nature Publishing Group http://genetics.nature.com Note : Supplementary information is available on the Nature Genetics website . Acknowledgments We thank J. Collado-Vides and the RegulonDB team for making their invaluable database available . We thank A. Arkin , H.C. Berg , J. Doyle , M. Elowitz , S. Leibler , S. Quake , J. Shapiro , M.G. Surette , B. Shilo , E. Winfree and all members of our lab for discussions . This work was supported by the Israel Science Foundation and the Minerva Foundation . Competing interests statement The authors declare that they have no competing financial interests . 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The corresponding randomized connectivity matrices , Mrand , have the same number of nonzero elements in each row and column as the corresponding row and column of the real connectivity matrix M ; that is : iMrandij = iMij , jMrandij = jMij . We used a previously described algorithm13 to generate the randomized networks . Briefly , the proper number of incoming and outgoing edge ` stubs ' is assigned to each node . Pairs of in/out edge stubs are randomly chosen and joined , generating a directed graph . We obtained identical results using a Markov-chain algorithm21 , based on starting with the real network and repeatedly swapping randomly chosen pairs of connections -LRB- XY1 , X2Y2 is replaced by X1Y2 , X2Y1 -RRB- until the network is well randomized . We verified that this yields net - 13 . 14 . 15 . 16 . 17 . 18 . 19 . 20 . 21 . 68 nature genetics volume 31 may 2002

O B O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O B B O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O B O O O O O O B O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O B O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O B B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


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 is inversely related to seed density . Species were excluded from regression analyses if -LRB- 1 -RRB- seeds passed through the 1-mm trap mesh , -LRB- 2 -RRB- seeds or recruits were recorded at fewer than 10 stations , or -LRB- 3 -RRB- 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 -LRB- simple space limitation -RRB- . 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 -LRB- 66 seedlings m-2 -RRB- . 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 , the addition of 1 before taking logarithms gives b values a downward bias . This effect can be large , 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 b values 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 -LRB- L. Reeve & Co. , Ashford , England , 1930 -RRB- . 2 . Janzen , D. H. Herbivores and the number of tree species in tropical forests . Am . Nat . 104 , 501 528 -LRB- 1970 -RRB- . 3 . Connell , J. H. in Dynamics of Populations -LRB- eds den Boer , P. J. & Gradwell , G. R. -RRB- 298 312 -LRB- Center for Agricultural Publication and Documentation , Wageningen , The Netherlands , 1971 -RRB- . 4 . Augspurger , C. K. Seedling survival of tropical tree species : interactions of dispersal distance , lightgaps and pathogens . Ecology 65 , 1705 1712 -LRB- 1984 -RRB- . 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 -LRB- 1984 -RRB- . 6 . Hammond , D. S. & Brown , V. K. in Dynamics of Tropical Communities -LRB- eds Newbery , D. M. , Prins , H. H. T. & Brown , N. D. -RRB- 51 78 -LRB- Blackwell Science , London , 1998 -RRB- . 7 . Howe , H. F. Survival and growth of juvenile Virola surinamensis in Panama : effects of herbivory and canopy closure . J. Trop . Ecol . 6 , 259 280 -LRB- 1990 -RRB- . 8 . Webb , C. O. & Peart , D. R. Seedling density dependence promotes coexistence of Bornean rain forest trees . Ecology 80 , 2006 2017 -LRB- 1999 -RRB- . 9 . Condit , R. , Hubbell , S. P. & Foster , R. B. Recruitment near conspeci c adults and the maintenance of tree and shrub diversity in a neotropical forest . Am . Nat . 140 , 261 286 -LRB- 1992 -RRB- . 10 . Gilbert , G. S. , Hubbell , S. P. & Foster , R. B. Density and distance-to-adult effects of a canker disease of trees in a moist tropical forest . Oecologia 98 , 100 108 -LRB- 1994 -RRB- . 11 . Hubbell , S. P. , Condit , R. & Foster , R. B. Presence and absence of density dependence in a neotropical tree community . Phil . Trans . R. Soc . Lond . B 330 , 269 281 -LRB- 1990 -RRB- . 12 . Wills , C. & Condit , R. Similar non-random processes maintain diversity in two tropical rainforests . Proc . R. Soc . Lond . B 266 , 1445 1452 -LRB- 1999 -RRB- . 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 -LRB- 1997 -RRB- . 14 . Hubbell , S. P. Seed predation and the coexistence of tree species in tropical forests . Oikos 35 , 214 229 -LRB- 1980 -RRB- . 15 . Wright , S. J. in Handbook of Functional Plant Ecology -LRB- eds Pugnaire , F. I. & Valladares , F. -RRB- 449 472 -LRB- M. Dekker , New York , 1999 -RRB- . 16 . Connell , J. H. Diversity in tropical rain forest and coral reefs . Science 199 , 1302 1309 -LRB- 1978 -RRB- . 17 . Leigh , E. G. Jr Tropical Forest Ecology -LRB- Oxford Univ. . Press , Oxford , 1999 -RRB- . 18 . Schupp , E. W . The Janzen Connell model for tropical tree diversity : population implications and the importance of spatial scale . Am . Nat . 140 , 526 530 -LRB- 1992 -RRB- . 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 -LRB- 1996 -RRB- . 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 -LRB- 1995 -RRB- . 21 . Kitajima , K. Relative importance of photosynthetic traits and allocation patterns as correlates of seedling shade tolerance of 13 tropical trees . Oecologia 98 , 419 428 -LRB- 1994 -RRB- . 22 . Janzen , D. H. Speci city of seed-attacking beetles in a Costa Rican deciduous forest . J. Ecol . 68 , 929 952 -LRB- 1980 -RRB- . 23 . Barone , J. A. Host-speci city of folivorous insects in a moist tropical forest . J. Anim . Ecol . 67 , 400 409 -LRB- 1998 -RRB- . 24 . Coley , P. D. & Barone , J. A. Herbivory and plant defenses in tropical forests . Annu . Rev. Ecol . Syst . 27 , 305 335 -LRB- 1996 -RRB- . 25 . Coley , P. D. & Aide , T. M. in Plant Animal Interactions -LRB- eds Price , P. W. , Lewinson , T. M. , Fernandes , G. W. & Benson , W. W. -RRB- 25 49 -LRB- John Wiley and Sons , New York , 1991 -RRB- . 26 . Hubbell , S. P. et al. . Light-gap disturbances , recruitment limitation , and tree diversity in a neotropical forest . Science 283 , 554 557 -LRB- 1999 -RRB- . 27 . Wright , S. J. , Carrasco , C. , Calderon , O. & Paton , S . The El Nino southern oscillation , variable fruit production , and famine in a tropical forest . Ecology 80 , 1632 1647 -LRB- 1999 -RRB- . 28 . Wright , S. J. , Carrasco , C. , Calderon , O. & Paton , S . The El Nino southern oscillation , variable fruit production , and famine in a tropical forest . Ecology 80 , 1632 1647 -LRB- 1999 -RRB- . 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. Muller-Landau and T. Theimer for constructive criticism of the manuscript . The Andrew W. Mellon Foundation and the Environmental Sciences Program of the Smithsonian Institution provided nancial support . Correspondence and requests for materials should be addressed to S.J.W. -LRB- e-mail : wrightj@tivoli.si.edu -RRB- . ... . The evolution of syntactic communication Martin A. Nowak * , Joshua B. Plotkin * & Vincent A. A. Jansen * Institute for Advanced Study , Princeton , New Jersey 08540 , USA School of Biological Sciences , Royal Holloway , University of London , Egham Surrey , TW20 0EX UK ... . Animal communication is typically non-syntactic , which means that signals refer to whole situations1 7 . Human language is syntactic , and signals consist of discrete components that have their 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 evolution of 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 have not been learned beforehand . Nevertheless , according to our model 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 the elephant 's trunk13 . Human language is as different from animal communication as the elephant 's trunk is from other animals ' nostrils . Yet few biologists worry about the evolution of the elephant 's trunk -LRB- which is a most complex organ that consists of about 6,000 individual muscles and that can perform an unparalleled variety of mechanical tasks -RRB- , 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 -LRB- territorial calls or warning of predators -RRB- ; a continuous analogue signal -LRB- for example , the dance of bees -RRB- ; and a series of random variations on a theme -LRB- such as the song of birds -RRB- . All natural animal communication appears to be non-syntactic ; some caution , however , seems appropriate as the nal verdict on complex 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 communication and 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 495 NATURE | VOL 404 | 30 MARCH 2000 | www.nature.com 2000 Macmillan Magazines Ltd letters to nature words . 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 general equations for the resulting evolutionary dynamics are complicated -LRB- see Methods -RRB- , 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 are memorized 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 Wi xi Ri xi 1 2 xi 2 xi 1 where i 1 ; ; n . The abundance of word Wi spreads by the interaction 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 of memorizing a single word after one encounter , and fi is the frequency of occurrence of word Wi in the -LRB- spoken -RRB- 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 that fi . 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 all words have the same frequency . Thus the maximum number of words 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 can not exceed the total number of word-learning events for each individual . Assuming that word frequency distributions follow Zipf 's law22 ,23 , fi C = i , where C is a constant , we nd that the maximum number of words is roughly given by the equation nmax lnnmax bq -LRB- Fig. 1 -RRB- . 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 of objects , places , times and actions . -LRB- 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 . -RRB- 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 -LRB- Fig. 2 -RRB- . 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 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 . The population dynamics of non-syntactic communication are again given by equation -LRB- 1 -RRB- 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 -LRB- see Methods -RRB- . We now turn to syntactic communication . Noun Ni refers to object i and verb Vj refers to action j , hence the event Eij is described by the sentence NiVj . For the basic reproductive ratios we obtain RN i b = 2qs fN i and RV j b = 2qs fV j . Here f -LRB- Ni -RRB- and f -LRB- Vj -RRB- denote the frequency of occurrence of noun Ni and verb Vj , respectively . The factor 1/2 appears because either the noun or the verb is learned in any one of the b learning events . The probability of memorizing a noun or a verb is given by qs . We expect qs to be smaller than q , which simply means that it is a more dif cult task to learn a syntactic signal than a non-syntactic signal . For both signals , the -LRB- arbitrary -RRB- meaning has to be memorized ; for a syntactic signal one must also memorize its relation to other signals -LRB- whether it is a noun or a verb , for example -RRB- . For noun Ni to be maintained in the lexicon of the population , its basic reproductive ratio must exceed one , implying that fN i . 2 = bqs . Similarly , for verb Vj we nd fV 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 of grammatical sentences , however , which consist of one noun and one verb , is given by -LRB- bqs -RRB- 2/4 . Hence syntax makes it possible to maintain more sentences than the total number of sentences , b , encountered by a learning individual . All words have to be learned , therefore , but syntactic signals enable the formulation of ` new ' sentences that have not been learned beforehand . 100 Maximum lexicon size , nmax 10 Actual Approximation 1 1 10 100 1,000 Learning events , b Figure 1 How many word-learning events per individual are required for a population to maintain 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 a word 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 = Sn 1 = i , the i1 maximum number of words that can be maintained , nmax , is the largest integer , n , which ful 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 -LRB- continuous line -RRB- . Here we have used Euler 's gamma which is g 0:5772 . 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 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 for actions 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 . NATURE | VOL 404 | 30 MARCH 2000 | www.nature.com 2000 Macmillan Magazines Ltd 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 xN i V j , we obtain xN i V j RN i xN i xV j 2 xN i V j RV j xV j xN i 2 xN i V j 2 xN i V j 2 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 -LRB- see Methods -RRB- . Figure 3 shows the tness of syntactic and non-syntactic communication as a function of b for different examples of the event rate matrix , G . When does syntactic communication lead to a higher tness than non-syntactic communication ? Suppose there are n objects and m actions . Suppose a fraction , p , of these mn events occur -LRB- all at the same frequency -RRB- , and the other events do not occur . In this case , RW ij bq = pmn for those events that occur . Making the -LRB- somewhat rough -RRB- assumption that all nouns and all verbs , respectively , occur on average at the same frequency , we obtain RN i bqs = 2n and RV j bqs = 2m . If all involved basic reproductive ratios are well above one , the tness of syntactic communication exceeds the tness of non-syntactic communication provided m2 n mn2 = m2 mn n2 . 2q = pqs -LRB- see Methods -RRB- . 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 the evolution of syntax . For m n , the relevant condition is n . 3q = pqs 1 0 0 0 1 1 0 0 0 0 1 0 0 0 0 1 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 a 5 4 Fitness 3 2 1 100 1,000 Fn Fs 3 10,000 b 5 3 Fitness 2 1 Fn Fs 1 0 1 1 0 1 1 1 0 1 1 0 0 1 1 0 0 1 1 0 0 1 0 1 0 1 0 1 1 0 0 0 1 0 1 1 100 c 60 50 Fitness 40 30 20 10 100 Fs 1 1 0 1 1 1 0 1 0 1 1 1 0 1 1 0 1 0 1 0 0 1 1 0 1 1 0 1 1 1 1 0 1 1 1 0 1 1 1 0 0 1 0 1 1 1 0 0 0 1 1 0 1 0 1 1 1 1 1 1 0 1 0 1 1 0 1 0 1 0 0 1 1 0 1 1 0 0 1 1 1 0 1 1 0 1 1 0 0 1 1,000 1 1 0 1 1 1 0 1 1 1 10,000 Hence , the size of the system has to exceed a critical value for syntactic 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 is required 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 consist of unique pairings of objects and actions . The smaller the value of p , the harder it is for syntactic communication to evolve -LRB- the critical n in equation -LRB- 3 -RRB- is large -RRB- . 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 Syntax winning 0.8 0.6 0.4 0.2 5 10 15 Size n 20 25 Fn 1,000 Learning events , b 10,000 Figure 3 The tness of non-syntactic and syntactic communication , Fn and Fs , as function of the total number of word learning events per individual , b , for three different choices of the 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 than non-syntactic communication . For values of b above 400 , non-syntactic communication wins . Hence , for medium-sized systems the emergence of syntactic communication can be 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 and illustrates the chosen event rate matrix , G. NATURE | VOL 404 | 30 MARCH 2000 | www.nature.com Figure 4 Numerical validation of the approximate threshold condition given by equation -LRB- 3 -RRB- . If this inequality holds then syntax will be favoured by natural selection . There is 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 a single 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 the fraction of times when Fs exceeds Fn . From left to right the curves correspond to the parameter 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 . 497 2000 Macmillan Magazines Ltd letters to nature communication 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 that syntactic communication is always at an advantage . Many animal species probably have a syntactic understanding of the world , but natural selection did not produce a syntactic communication system for these species because the number of relevant signals was below the threshold illustrated by equation -LRB- 3 -RRB- . Presumably the increase in the number of relevant communication topics was caused by changes in the social structure24 and interaction of those human ancestors who evolved syntactic communication . M Received 1 November 1999 ; accepted 26 January 2000 . 1 . Von Frisch , K . The Dance Language and Orientation of Bees -LRB- Harvard Univ. . Press , Cambridge , Massachusetts , 1967 -RRB- . 2 . Marler , P. Birdsong and speech development : could there be parallels ? Am . Sci . 58 , 669 673 -LRB- 1970 -RRB- . 3 . Wilson , E. O. Animal communication . Sci . Am . 227 , 52 60 -LRB- 1972 -RRB- . 4 . Gould , J. L. & Marler , P. Learning by instinct . Sci . Am . 256 , 74 85 -LRB- 1987 -RRB- . 5 . Burling , R. Primate calls , human language , and nonverbal communication . Curr . Anthropol . 34 , 25 53 -LRB- 1989 -RRB- . 6 . Cheney , D. L. & Seyfarth , R. M . How Monkeys See the World : Inside the Mind of Another Species -LRB- Chicago Univ. . Press , 1990 -RRB- . 7 . Hauser , M . The Evolution of Communication -LRB- MIT Press , Cambridge , Massachusetts , 1996 -RRB- . 8 . Bickerton , D. Species and Language -LRB- Chicago Univ. . Press , Chicago , 1990 -RRB- . 9 . von Humboldt , W. Linguistic Variability and Intellectual Development -LRB- Pennsylvania Univ. . Press , Philadelphia , 1972 -RRB- . 10 . Chomsky , N. Aspects of the Theory of Syntax -LRB- MIT Press , Cambridge , Massachusetts , 1965 -RRB- . 11 . Jackendoff , R . The Architecture of the Language Faculty -LRB- MIT Press , Cambridge , Massachusetts , 1997 -RRB- . 12 . Pinker , S. & Bloom , P. Natural language and natural selection . Behav . Brain Sci . 13 , 707 784 -LRB- 1990 -RRB- . 13 . Pinker , S . The Language Instinct . -LRB- Harper Collins , New York , 1994 -RRB- . 14 . Maynard Smith , J. & Szathmary , E . The Major Transitions in Evolution -LRB- Freeman , Oxford , 1995 -RRB- . 15 . Hurford , J. R. , Studdert-Kennedy , M. & Knight , C. Approaches to the Evolution of Language -LRB- Cambridge Univ. . Press , Cambridge , UK , 1998 -RRB- . 16 . Nowak , M. A. & Krakauer , D. C . The evolution of language . Proc . Natl Acad . Sci . USA 96 , 8028 8033 -LRB- 1999 -RRB- . 17 . Chomsky , N. Language and Mind -LRB- Harcourt Brace Jovanovich , New York , 1972 -RRB- . 18 . Chomsky , N. Language and Problems of Knowledge : The Managua Lectures -LRB- MIT Press , Cambridge , Masachusetts , 1988 -RRB- . 19 . Premack , D. Gavagai ! or the future history of the animal language controversy . Cognition 19 , 207 296 -LRB- 1985 -RRB- . 20 . Lieberman , P . The Biology and Evolution of Language -LRB- Harvard Univ. . Press , Cambridge , Massachusetts , 1984 -RRB- . 21 . Bates , E. , Thal , D. & Marchman , V. in Biological and Behavioural Determinants of Language Development -LRB- eds Krasnegor et al. -RRB- -LRB- Erlbaum , Mahwah , NJ , 1991 -RRB- . 22 . Zipf , G. K . The Psychobiology of Language -LRB- Houghton-Mif in , Boston , 1935 -RRB- . 23 . Miller , G. A. & Chomsky , N. Handbook of Mathematical Psychology . Vol . 2 -LRB- eds Luce , R. D. , Bush , R. & Galauter , E. -RRB- 419 491 -LRB- Wiley , New York , 1963 -RRB- . 24 . Dunbar , R. Grooming , Gossip and the Evolution of Language -LRB- Harvard Univ. . Press , Cambridge , Massachusetts , 1996 -RRB- . 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 are de ned by bit strings : 1 means that the corresponding word is known ; 0 means it is not . Let us enumerate them by I 0 ; ; n where n 2n 2 1 . The number I is the integer representation of the corresponding bit string . -LRB- For example , I 6 represents the string 000 0110 . -RRB- Denote by xI the abundance of individuals with internal lexicon I . The population dynamics can be formulated as x I dI 2 x I b Methods ^ ^ x x J0 K0 n n J K QJKI 2 xI xJ QIJK 4 where I 0 ; ; n . We have d0 1 and dI 0 otherwise ; thus all individuals are born not knowing any of the words . Individuals die at a constant rate , which we set to 1 , thereby de ning a time scale . The quantities QIJK denote the probabilities that individual I learning from J will become K. Equation -LRB- 4 -RRB- is a general framework for the population dynamics of the 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 memorized independently of each other , we obtain the speci c system described by equation -LRB- 1 -RRB- . Let us now assume that the world is made up of events Eij consisting of objects i and actions j . The ` event rate matrix ' , G has the entries gij which specify the relative rate of occurrence of event Eij . Denote by fij the frequency of occurrence of event Eij . We have fij gij = Sij gij . Non-syntactic communication uses words , Wij , for events Eij . The basic reproductive ratio of Wij is given by RW ij bqfij . If RW 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 = RW 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 by Fn 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. -LRB- e-mail : nowak@ias.edu -RRB- . ^ x * W g : ij 2 ij i ; j 5 ... . Glutamate spillover suppresses inhibition by activating presynaptic mGluRs Simon J. Mitchell & R. Angus Silver Department of Physiology , University College London , Gower Street , London WC1E 6BT , UK 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 by equation -LRB- 2 -RRB- . The basic reproductive ratios are given by RN i b = 2qs fN i and RV j b = 2qs fV i . The frequencies of occurrence are fN i Sj fij and fV j Si fij . If the basic reproductive ratios , R -LRB- Ni -RRB- and R -LRB- Vj -RRB- , 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 = RN i 1 2 1 = RV j 1 2 1 = RN i RV j 6 At equilibrium , the tness of syntactic communication is given by Fs ^ x * N V g : i j 2 ij i ; j 7 ... . Assuming there are n objects and m actions that give rise to pnm meaningful events that all occur at the same frequency , we obtain RW 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 RN i bq2 = 2n and RV j bqs = 2m . For the tness values , we obtain F n pnm1 2 1 = RW ij 2 and F s pnm1 2 1 = RN i 2 1 2 1 = RV j 2 = 1 2 1 = RN i RV 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 a1 Hence the size of the system has to exceed a critical threshold for syntax to be favoured by natural selection . Metabotropic glutamate receptors -LRB- mGluRs -RRB- found on synaptic terminals throughout the brain are thought to be important in modulating 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 activation of mGluRs on inhibitory terminals within the cerebellar glomerulus , a structure in which GABA -LRB- g-aminobutyric acid -RRB- - releasing inhibitory terminals and glutamatergic excitatory terminals are in close apposition and make axo-dendritic synapses onto granule cells6 . 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 NATURE | VOL 404 | 30 MARCH 2000 | www.nature.com 498 2000 Macmillan Magazines Ltd

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O B O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B B O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O B O O O O B O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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