Sociology memo

Team Assembly Mechanisms Determine Collaboration Network Structure and Team Performance

Roger Guimerà,1* Brian Uzzi,2* Jarrett Spiro,3

Luı́s A. Nunes Amaral1.

Agents in creative enterprises are embedded in networks that inspire, support, and evaluate their work. Here, we investigate how the mechanisms by which creative teams self-assemble determine the structure of these collaboration networks. We propose a model for the self-assembly of creative teams that has its basis in three parameters: team size, the fraction of newcomers in new productions, and the tendency of incumbents to repeat previous collaborations. The model suggests that the emergence of a large connected community of practitioners can be described as a phase transition. We find that team assem- bly mechanisms determine both the structure of the collaboration network and team performance for teams derived from both artistic and scientific fields.

Teams are assembled because of the need to

incorporate individuals with different ideas,

skills, and resources. Creativity is spurred

when proven innovations in one domain are

introduced into a new domain, solving old

problems and inspiring fresh thinking (1–4).

However, research shows that the right bal-

ance of diversity on a team is elusive. Al-

though diversity may potentially spur creativity,

it typically promotes conflict and miscom-

munication (5–7). It also runs counter to the

security most individuals experience in working

and sharing ideas with past collaborators (8).

Successful teams evolve toward a size that is

large enough to enable specialization and

effective division of labor among teammates

but small enough to avoid overwhelming

costs of group coordination (9). Here, we

investigate empirically and theoretically the

mechanisms by which teams of creative

agents are assembled. We also investigate

how these microscopic team assembly mech-

anisms determine both the macroscopic

structure of a creative field and the success

of certain teams in using the resources and

knowledge available in the field. We develop

a model for the assembly of teams of cre-

ative agents in which the selection of the

members of a team is controlled by three

parameters: (i) the number, m, of team mem-

bers; (ii) the probability, p, of selecting incum-

bents, that is, agents already belonging to the

network; and (iii) the propensity, q, of incum-

bents to select past collaborators. The model

predicts the existence of two phases that are

determined by the values of m, p, and q. In

one phase, there is a large cluster connecting

a substantial fraction of the agents, whereas

in the other phase the agents form a large

number of isolated clusters.

We analyzed data from both artistic and

scientific fields where collaboration needs

have experienced pressures such as differen-

tiation and specialization, internationaliza-

tion, and commercialization (4, 10, 11): (i)

the Broadway musical industry (BMI) and

(ii) the scientific disciplines of social psy-

chology, economics, ecology, and astronomy

(Table 1). For the BMI, we considered all

2258 productions in the period from 1877 to

1990 (12, 13). Productions are defined as

musical shows that were performed at least

once in Broadway. The team members com-

prise individuals responsible for composing

the music, writing the libretto and the lyrics,

designing the choreography, directing, and

producing the show, but not the actors that

performed in it. For each of the scientific dis-

ciplines, we considered all collaborations that

resulted in publications in recognized journals

within the fields studied (14): seven social

psychology journals, nine economics journals,

10 ecology journals, and six astronomy jour-

nals (Table 2). Collaboration networks (15–19)

were then built for each of the journals in-

dependently and for the whole discipline by

merging the data from the journals within a

discipline (Materials and Methods).

The evolution of team sizes in the BMI

bears out the expectation that team size and

composition depend on the intricacy of the

creative task. In the period from 1877 to

1929, when the form of the Broadway musi-

cal show was still being worked out through

trial and error (12), there was a steady in-

crease in the number of artists per produc-

tion, from an average of two to an average of

seven (Fig. 1A). This increase in size suggests

that teams evolved to manage the complexity

of the new artistic form. By the late 1920s, the

Broadway musical reached the form we know

today, as did team composition (4). Since then,

the typical set of artists creating a Broadway

musical have been choreographer, composer,

director, librettist, lyricist, and producer. For

the following 55 years, a period that includes

the Great Depression, World War II, and the

postwar boom, the average size of teams re-

mained around seven (20).

We find similar scenarios for the evolution

of team size in scientific collaborations. The

four fields experienced an increase in team size

with time (Fig. 1, B to E). The increase has

been roughly linear in social psychology and

economics and faster than linear in ecology

and astronomy. For social psychology, team

size growth rate was greater for high-impact

compared with low-impact journals, suggesting

that team size not only depends on the intri-

cacy of the enterprise but also that successful

teams might adapt faster to external pressures.

The analysis of team size cannot capture

the fact that teams are embedded in a larger

network (3). This complex network (21–26),

which is the result of past collaborations and

1Department of Chemical and Biological Engineering, Northwestern University, Evanston, IL 60208, USA. 2Kellogg School of Management and Department of Sociology, Northwestern University, Evanston, IL 60208, USA. 3Graduate School of Business, Stanford University, Stanford, CA 94305, USA.

*These authors contributed equally to this work. .To whom correspondence should be addressed. E-mail: amaral@northwestern.edu

Table 1. Global network properties of the fields studied. The sources for the BMI are (12) and (13). The data analyzed excludes revivals and focus on the steady-state period from 1940 to 1985. The data for scientific publications was obtained from the Web of Science. We selected recognized journals in each of the different scientific fields (Table 2). For each field, we show the total number of productions

and agents in all the periods considered, the values of p and q estimated with the model from the data, the f

R , the size, N, of the network in the last year of the period

considered, the value, N mod

, predicted by the model, the fraction, S, of agents that belong to the largest cluster, and the value, S

mod , predicted by the model. S takes

values between 0 and 1 and does not depend on the size of the network (31).

Field Period Productions Agents p q f R

N N mod

S S mod

BMI 1877–1990 2258 4113 0.52 0.77 0.16 428 420 0.70 0.80 Social psychology 1955–2004 16,526 23,029 0.56 0.78 0.22 11,412 14,408 0.68 0.67 Economics 1955–2004 14,870 23,236 0.57 0.73 0.22 9527 11,172 0.54 0.50 Ecology 1955–2004 26,888 38,609 0.59 0.76 0.23 23,166 26,498 0.75 0.84 Astronomy 1955–2004 30,552 30,192 0.76 0.82 0.39 18,021 22,794 0.92 0.98

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the medium in which future collaborations

will develop, acts as a storehouse for the pool

of knowledge created within the field. The

way the members of a team are embedded in

the larger network affects the manner in

which they access the knowledge in the field.

Therefore, teams formed by individuals with

large but disparate sets of collaborators are

more likely to draw from a more diverse res-

ervoir of knowledge. At the same time and

for the same reasons, the way teams are or-

ganized into a larger network affects the like-

lihood of breakthroughs occuring in a given

field.

The agents composing a team may be

classified according to their experience. Some

agents are newcomers, that is, rookies, with

little experience and unseasoned skills. Other

agents are incumbents. They are established

persons with a track record, a reputation, and

identifiable talents. The differentiation of agents

into newcomers and incumbents results in

four possible types of links within a team:

(i) newcomer-newcomer, (ii) newcomer-

incumbent, (iii) incumbent-incumbent, and

(iv) repeat incumbent-incumbent. The dis-

tribution of different types of links reflects

the team_s underlying diversity. For exam- ple, if teams have a preponderance of repeat

incumbent-incumbent links, it is less likely

that they will have innovative ideas because

their shared experiences tend to homogenize

their pool of knowledge. In contrast, teams with

a variety of types of links are likely to have more

diverse perspectives to draw from and therefore

to contribute more innovative solutions.

Because quantifying the emergence and

the effects of team diversity (2, 9, 27–29) is

more difficult than measuring team size, we

consider next a model for the assembly of

teams. In our model, we assemble N teams in

temporal sequence. The assembly of each

team is controlled by three parameters: m, p,

and q. The first parameter, m, is the number

of agents in a team. In our investigations of

the model, we considered three situations:

(i) keep m constant, (ii) draw m from a dis-

tribution, or (iii) use a sequence of m values

obtained from the data. For the theoretical

analysis of the model, we kept m constant,

whereas comparison with an empirical data

set was done with the use of the sequence of

m(t) values in the corresponding data set.

The second parameter, p, is the probabil-

ity of a team member being an incumbent.

Higher values of p indicate fewer opportu-

nities for newcomers to enter a field. The

third parameter, q, represents the inclination

for incumbents to collaborate with prior

collaborators rather than initiate a new col-

laboration with an incumbent they have not

worked with in the past.

We start at time zero with an endless pool

of newcomers. Newcomers become incum-

bents the first time step after being selected

for a team. Each time step t, we assemble a

new team and add it to the network (Fig. 2).

We select sequentially m(t) different agents.

Each agent in a team has a probability, p, of

being drawn from the pool of incumbents and

a probability, 1 j p, of being drawn from the

pool of newcomers. If the agent is drawn from

the incumbents’ pool and there is already

another incumbent in the team, then (i) with

probability q the new agent is randomly se-

lected from among the set of collaborators of

a randomly selected incumbent already in the

team; (ii) otherwise, he or she is selected at

random among all incumbents in the network.

Table 2. Journal-specific network structure. We present the same information as in Table 1 for each of the journals studied. We ranked journals within each field according to their impact factor (IF). For some low-impact journals, the f

R is too high to be reproducible with the model. In those cases, which we

represent by q 9 1, simulations of the model are done with q 0 1. The model still reproduces the empirical results quite well for these cases.

Journal IF Period Agents p q f R

S S mod

Social psychology J. Pers. Soc. Psychol. 3.862 1965–2003 9112 0.56 0.74 0.20 0.75 0.79 J. Exp. Soc. Psychol. 2.131 1965–2004 2133 0.40 0.76 0.11 0.44 0.07 Pers. Soc. Psychol. B 1.839 1976–2004 4339 0.45 0.74 0.14 0.54 0.47 Eur. J. Soc. Psychol. 1.060 1971–2004 1790 0.41 0.93 0.15 0.44 0.08 J. Appl. Soc. Psychol. 0.523 1971–2004 4602 0.33 1.00 0.10 0.06 0.02 J. Soc. Psychol. 0.291 1956–2004 6294 0.32 91 0.12 0.05 0.01 Soc. Behav. Personal. 0.227 1973–2004 1981 0.26 91 0.08 0.03 0.01

Economics Q. J. Econ. 4.756 1956–2004 2320 0.37 0.58 0.08 0.26 0.05 Econometrica 2.215 1965–2004 3351 0.45 0.67 0.13 0.26 0.05 J. Polit. Econ. 2.196 1956–2004 3464 0.30 0.88 0.07 0.06 0.01 Am. Econ. Rev. 1.938 1956–2004 6807 0.42 0.84 0.15 0.27 0.02 Econ. J. 1.295 1956–2004 4528 0.31 0.99 0.09 0.08 0.01 Eur. Econ. Rev. 1.021 1969–2004 2585 0.35 0.85 0.10 0.15 0.02 J. Econ. Theory 0.833 1969–2004 2062 0.28 91 0.08 0.51 0.03 Econ. Lett. 0.337 1978–2004 5129 0.31 0.98 0.10 0.01 0.01 Appl. Econ. 0.200 1969–2004 4488 0.26 91 0.08 0.01 0.01

Ecology Am. Nat. 4.059 1955–2004 4990 0.44 0.70 0.13 0.49 0.19 Ecology 3.701 1965–2003 8885 0.48 0.71 0.15 0.56 0.65 Oecologia 3.128 1969–2004 10,545 0.44 0.81 0.15 0.51 0.36 Ecol. Appl. 2.852 1991–2004 3417 0.29 0.99 0.08 0.30 0.06 J. Ecol. 2.833 1955–2004 3639 0.43 0.91 0.15 0.40 0.19 Funct. Ecol. 2.351 1989–2004 2873 0.36 91 0.13 0.05 0.02 Oikos 2.142 1961–2004 6589 0.43 0.84 0.15 0.48 0.11 Biol. Conserv. 2.056 1977–2004 5821 0.27 91 0.09 0.08 0.01 Ecol. Model. 1.561 1978–2004 5260 0.35 91 0.13 0.14 0.02 J. Nat. Hist. 0.497 1967–2004 2631 0.36 91 0.04 0.13 0.01

Astronomy Astron. J. 5.647 1965–2003 10,832 0.78 0.86 0.40 0.96 0.99 Publ. Astron. Soc. Pac. 3.529 1955–2004 6769 0.58 0.78 0.22 0.85 0.89 Icarus 2.611 1983–2004 4357 0.72 0.90 0.38 0.89 0.97 Publ. Astron. Soc. Jpn. 2.312 1965–2004 2432 0.77 0.95 0.44 0.95 0.99 Astrophys. Space Sci. 0.522 1968–2004 10,823 0.55 1.00 0.29 0.60 0.05 IAU Symp. 0.237 1984–2004 10,185 0.60 0.75 0.23 0.80 0.92

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Fig. 1. Time evolution of the typical number of team members in (A) the BMI and scientific collab- orations in the disciplines of (B) social psychology, (C) economics, (D) ecology, and (E) astronomy.

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Lastly, agents that remain inactive for

longer than t time steps are removed from the network. This rule is motivated by the obser-

vation that agents do not remain in the network

forever: agents age and retire, change careers,

and so on. The removal process enables the

network to reach a steady state after a transient

time. Our results do not depend in the specific

value of t (Materials and Methods). Through participation in a team, agents

become part of a large network (30). This fact

prompted us to examine the topology of the

network of collaborations among the practi-

tioners of a given field. More specifically,

we asked, BIs there a large connected cluster comprising most of the agents or is the net-

work composed of numerous smaller clus-

ters?[ A large connected cluster would be supporting evidence for the so-called invisible

college, the web of social and professional

contacts linking scientists across universities

proposed by de Solla Price (31) and Merton

(32). A large number of small clusters would

be indicative of a field made up of isolated

schools of thought. For all five fields con-

sidered here, we find that the network con-

tains a large connected cluster.

As is typically done in the study of per-

colation phase transitions (33), we use the

fraction S of agents that belong to the largest

cluster of the network to quantify the tran-

sition between these two regimes: invisible

college or isolated schools. We explore sys-

tematically the (p,q) parameter space of the

model. We find that the system undergoes

a percolation transition (33) at a critical line,

p c (m,q). That is, the system experiences a

sharp transition from a multitude of small

clusters to a situation in which one large clus-

ter, comprising a substantial fraction S of the

individuals, emerges: the so-called giant com-

ponent (Fig. 3). The transition line p c (m,q)

therefore determines the tipping point for the

emergence of the invisible college (34). Our

analysis shows that the existence of this

transition is independent of the average number

of agents bmÀ in a collaboration, although the

precise value of p c (m,q) does depend on m.

The proximity to the transition line, which

depends on the distribution of the different

types of links, determines the structure of the

largest cluster (Fig. 3A). In the vicinity of the

transition, the largest cluster has an almost

linear or branched structure (Fig. 3A) ( p 0 0.30). As one moves toward larger p, the

largest cluster starts to have more and more

loops (Fig. 3A) (p 0 0.35), and, eventually, it becomes a densely connected network (Fig.

3A) ( p 0 0.60). Networks with the same fraction, S, of

nodes in the largest cluster do not necessarily

correspond to networks with identical prop-

erties. Each point in the (p,q) parameter space

is characterized by both S and the fraction,

f R , of repeat incumbent-incumbent links. For

example, in Fig. 3C, the line f R 0 0.32 cor-

responds to those values of p and q for which

32% of all links in new teams are between

repeat collaborators (35). The f R

has a nota-

ble impact on the dynamics of the network.

When f R

is large, collaborations are firmly

established, and therefore the structure of the

network changes very slowly. In contrast, low

values of f R

correspond to enterprises with

high turnover and very fast dynamics. Inter-

mediate values of f R

are related to situations

in which collaboration patterns with peers are

fluid (Materials and Methods).

For each of the five fields for which we

have empirical data, we measure the relative

size of the giant component S (Materials and

Methods). For all fields considered, S is

larger than 50% (Table 1). This result pro-

vides quantitative evidence for the existence

of an invisible college in all the fields. In-

triguingly, the relative sizes of the giant com-

ponent is similar for three of the four fields

considered: S 0 0.70, S 0 0.68, and S 0 0.75 for BMI, social psychology, and ecology,

respectively. However, for astronomy S was

significantly larger (0.92), whereas for eco-

nomics it was significantly smaller (0.54).

To gain further insight in the structure of

collaboration networks, we used our model

to estimate the values of p and q for each

field. Given the temporal sequence of teams

producing the network of collaborations, one

can calculate the fraction of incumbents and

the fraction of repeat incumbent-incumbent

links. These fractions and the model enable

us to then estimate the values of p and q that

are consistent with the data (36).

We estimated p and q for each field and

then simulated the model to predict the key

properties of the network of collaborations,

including the degree distribution of the

network and the fraction S of nodes in the

Fig. 2. Modeling the emergence of collaboration networks in creative enterprises. (A) Creation of a team with m 0 3 agents. Consider, at time zero, a collaboration network comprising five agents, all incumbents (blue circles). Along with the incumbents, there is a large pool of newcomers (green circles) available to participate in new teams. Each agent in a team has a probability p of being drawn from the pool of incumbents and a probability 1 j p of being drawn from the pool of new- comers. For the second and subsequent agents selected from the incumbents’ pool: (i) with probability q, the new agent is randomly selected from among the set of collaborators of a randomly selected incumbent already in the team; (ii) otherwise, he or she is selected at random among all incumbents in the network. For concreteness, let us assume that incumbent 4 is selected as the first agent in the new team (leftmost box). Let us also assume that the second agent is an incumbent, too (center-left box). In this example, the second agent is a past collaborator of agent 4, specifically agent 3 (center-right box). Lastly, the third agent is selected from the pool of newcomers; this agent becomes incumbent 6 (rightmost box). In these boxes and in the following panels and figures, blue lines indicate newcomer- newcomer collaborations, green lines indicate newcomer-incumbent collaborations, yellow lines indi- cate new incumbent-incumbent collaborations, and red lines indicate repeat collaborations. (B) Time evolution of the network of collaborations according to the model for p 0 0.5, q 0 0.5, and m 0 3.

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largest cluster. By comparing predictions of

the model with the empirical results, we are

able to test and validate the model. We first

compare the degree distribution of the col-

laboration networks with the predictions of

the model (Fig. 4, A to E) and find that the

model predicts the empirical degree distri-

butions remarkably well. In Table 1, we

compare the predictions of the model for S

with the measured values. The model cor-

rectly predicts that an invisible college con-

taining more than 50% of the nodes exists in

all cases. Additionally, the values of S pre-

dicted by the model are in close agreement

with the empirical results.

To investigate how changes of the team

assembly mechanism affect the structure of the

network, we used the model to generate net-

works with the same sequence of team sizes as

the data but with different values of p and q.

We show in Fig. 4, F to J, that four out of the

five creative networks we consider are very

close to the tipping line at which an invisible

college emerges. The exception is astronomy.

We also find that, for astronomy, the f R

is

significantly larger than for the other fields.

If diversity affects team performance and

our model correctly captures how diversity is

related to the way teams are assembled, then

the parameters p and q must be related to team

performance. To investigate this issue, we con-

sidered for the four scientific fields how teams

publishing in different journals are assembled.

We used each journal_s impact factor as a proxy for the typical quality of teams’ output.

We then studied the different journals sepa-

rately to quantify the relationship between team

assembly mechanisms and performance.

In Fig. 5, we show the values of p, q, and

S for the journals in each of the fields as a

function of the impact factor of the journal.

We found that p was positively correlated

with impact factor for economics, ecology,

and social psychology, whereas q was nega-

tively correlated with impact factor for the

Fig. 3. Predictions of the model. (A) Phase transition in the structure of the collaboration network. We plot only the largest cluster in the network. For small p, the network is formed by numerous small clusters ( p 0 0.10). At the critical point p

c , the tipping point, a large cluster emerges, that is, a

cluster that contains a substantial fraction of the agents. In the vicinity of the transition, the largest cluster has an almost linear or branched structure ( p 0 0.30). As p increases, the largest cluster starts to have loops ( p 0 0.35) and eventually becomes a densely connected cluster containing essentially all nodes in the network ( p 0 0.60). We show results for q 0 0.5 and m 0 4, where m is the number of agents in a team. (B) The transition described in (A) can be characterized by the fraction S of nodes that belong to the giant component, the order parameter, and the average size bsÀ of the other clusters, the susceptibility (33). The model displays a second-order percolation transition as the fraction p of incumbents increases from 0 to

1. The transition occurs for p 0 p c , which coincides with the maximum of

bsÀ. Note that p c

is a decreasing function of m. We show results for q 0 0.5 and m 0 4 and m 0 8. (C) We display graphically the value of S as a function of p and q for m 0 4. For any value of q, the model displays the percolation transition, and the critical fraction p

c depends on q, de-

fining a percolation line p c (m,q). The critical line p

c (m,q) is an increasing

function of q. Even though the order parameter S is an important param- eter to quantify the structure of the network, not all points with the same S, that is, all points represented with the same color, correspond to fields with identical properties. This result is made clear by the lines of equal f

R . The upper-right corner of the ( p,q) plane is characterized

by f R

close to one, whereas the lower-left corner corresponds to f R

close to zero. As we show in Fig. 4, all fields considered have parameter values above the transition line.

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same fields. The result for p implies that suc-

cessful teams have a higher fraction of incum-

bents, who contribute expertise and know-how

to the team, whereas the result for q implies

that teams that are less diverse typically have

lower levels of performance.

The relative size S of the giant compo-

nent in a journal was also associated with

performance for ecology and social psychol-

ogy. Teams publishing in journals with a high-

impact factor typically give rise to a large

giant component, whereas teams publishing in

low-impact journals typically form small iso-

lated clusters. This suggests that teams publish-

ing in high-impact journals perform a better

sampling of the knowledge within a field and

thus are able to more efficiently use the re-

sources of the invisible college. Surprisingly,

neither p, q, or S were significantly correlated

with impact factor in astronomy. This distin-

guishes astronomy from the other creative

enterprises considered.

We have shown that team size evolves

with time, probably up to an optimal size as

in the case of the BMI. A similar process

may be occurring for the parameters quanti-

fying expertise, p, and diversity, q. Four of

the five fields considered, all except astron-

omy, have very similar values of p and q,

thus suggesting that a Buniversal[ set of

Fig. 4. Network structure of different creative fields. Degree distributions for (A) the BMI, (B) the field of social psychology, (C) the field of eco- nomics, (D) the field of ecology, and (E) the field of astronomy. We carried out with the use of the sequence {m(t)} of team sizes found in the empirical data and with the values of p and q estimated from the measured fractions of the different types of links. We present the pre- dictions of the model with the lines and the empirical degree dis- tributions with the open circles. For all cases considered, the data falls within the 95% confidence intervals of the predictions of the model. The ( p,q) parameter space of the network of collaborators is shown for (F) the BMI, (G) the field of social psychology, (H) the field of economics, (I) the field of ecology, and (J) the field of astronomy. The solid lines

separating the red and the blue regions indicate the values of p and q for which 50% of the nodes belong to the largest cluster, that is, the percolation transition at which a giant component, the invisible college, emerges. The distance from the percolation line predicts the overall structure of the network. For example, the networks in astronomy are well above the tipping line and have a very dense structure (Table 1). In contrast, all other fields are close to the transition and have rela- tively sparse giant components. Another important characteristic of the network is provided by the value of f

R . To help with the inter-

pretation of the results, we plot with dotted lines the curves for f R 0 0.32.

For four of the creative networks considered, we find f R G 0.25. For

astronomy, we find f R 0 0.39.

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%8.0 = ) r(P s

%5.0 = )

2.0

3.0

4.0

5.0

6.0

p

ygolohcysp laicoS

2.0

3.0

4.0

5.0

ygolocE

5.0

6.0

7.0

8.0

ymonortsA

2.0

3.0

4.0

5.0

scimonocE

r(P s

%1 = ) r(P s

%33 = )r(P s

%5 = ) r(P s

%4 = )

Fig. 5. Relation between team assembly mechanisms, network structure, and performance. We calculate the values of p, q, and S for several journals in each of the four scientific fields con- sidered. In a few cases, q should be larger than one in order to reproduce the empirical values of f

R ;

in these cases, q is considered one and the corresponding points are shaded. We plot the values of p, q, and S as a function of the impact factor of the journal and then use the Spearman rank-order correlation coefficient r

s to determine significant correlations. Shaded graphs indicate significantly

correlated variables at the 95% confidence level.

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optimal values might exist. The fact that in

astronomy there are no correlations between

p, q, or S and the impact of journals also

indicates that this field is different from the

others. Whether these differences are caused

by the needs imposed by the creative enter-

prise itself or to historical or other reasons is

a question that we cannot answer conclusively.

References and Notes 1. M. S. Granovetter, Am. J. Sociol. 78, 1360 (1973). 2. R. Reagans, E. W. Zuckerman, Organ. Sci. 12, 502

(2001). 3. R. Burt, Am. J. Sociol. 110, 349 (2004). 4. B. Uzzi, J. Spiro, Am. J. Sociol., in press. 5. J. R. Larson, C. Christensen, A. S. Abbott, T. M. Franz,

J. Pers. Soc. Psychol. 71, 315 (1996). 6. A. Edmondson, Adm. Sci. Q. 44, 350 (1999). 7. K. A. Jehn, G. B. Northcraft, M. A. Neale, Adm. Sci. Q.

44, 741 (1999). 8. G. Stasser, D. D. Stewart, G. M. Wittenbaum, J. Exp.

Soc. Psychol. 31, 244 (1995). 9. J. R. Katzenback, D. K. Smith, The Wisdom of Teams

(Harper Business, New York, 1993). 10. J. M. Ziman, Prometheus Bound (Cambridge Univ.

Press, Cambridge, 1994). 11. J. R. Brown, Science 290, 1701 (2000). 12. S. Green, K. Green, Broadway Musicals Show by Show

(Hal Leonard, Milwaukee, WI, 1996), ed. 5. 13. R. Simas, The Musicals No One Came to See: A Guide-

book to Four Decades of Musical-Comedy Casualties on Broadway, Off-Broadway and in Out-Of-Town Try- Out, 1943–1983 (Garland, New York, 1988).

14. We imposed several requirements on the journals we selected for analysis. First, the main subject category of the journal must be the desired one. For example, we consider only those ecology journals whose sub- ject category is either ecology or ecology and bio- diversity and conservation according to the Journal

Citation Reports. We disregarded more specialized journals, such as Microbial Biology, whose subject category is more specific. We also required that jour- nals contain a sufficiently large number of papers, typically larger than 1000.

15. M. E. J. Newman, Proc. Natl. Acad. Sci. U.S.A. 98, 404 (2001).

16. A.-L. Barabási et al., Physica A 311, 590 (2002). 17. M. E. J. Newman, Proc. Natl. Acad. Sci. U.S.A. 101,

5200 (2004). 18. K. Börner, J. T. Maru, R. L. Goldstone, Proc. Natl.

Acad. Sci. U.S.A. 101, 5266 (2004). 19. J. J. Ramasco, S. N. Dorogovtsev, R. Pastor-Satorras,

Phys. Rev. E 70, 036106 (2004). 20. This stationary state remains until the mid-1980s,

when size drops again precisely at the time when a rash of revivals and revues conceivably simplified production.

21. A.-L. Barabasi, R. Albert, Science 286, 509 (1999). 22. D. J. Watts, S. H. Strogatz, Nature 393, 440 (1998). 23. L. A. N. Amaral, A. Scala, M. Barthélémy, H. E. Stanley,

Proc. Natl. Acad. Sci. U.S.A. 97, 11149 (2000). 24. R. Albert, A.-L. Barabási, Rev. Mod. Phys. 74, 47

(2002). 25. M. E. J. Newman, SIAM Rev. 45, 167 (2003). 26. L. A. N. Amaral, J. Ottino, Eur. Phys. J. B 38, 147

(2004). 27. H. Etzkowitz, C. Kemelgor, M. Neuschatz, B. Uzzi,

J. Alonzo, Science 266, 51 (1994). 28. D. A. Harrison, K. H. Price, M. P. Bell, Acad. Manage. J.

41, 96 (1998). 29. S. G. Barsade, A. J. Ward, J. D. F. Turner, J. A. Sonnenfeld,

Adm. Sci. Q. 46, 174 (2001). 30. The teams and the agents are the nodes in a bipartite

network. Technically, agents are connected only to teams and vice versa. However, this bipartite network can be projected onto a network comprising only agents and in which there is an edge (connection) between two nodes (agents) if the agents have been connected to at least one common team.

31. D. J. de Solla Price, Little Science, Big ScienceI and Beyond (Columbia Univ. Press, New York, 1963).

32. R. K. Merton, The Sociology of Science (Univ. of Chicago Press, Chicago, 1973).

33. D. Stauffer, A. Aharony, Introduction to Percolation Theory (Taylor and Francis, ed. 2, London, 1992).

34. M. Gladwell, The Tipping Point: How Little Things Can Make a Big Difference (Little, Brown, Boston, 2000).

35. Figure 3C shows that large f R

occurs when p and q are large and corresponds to a network in which collab- orations among incumbents are firmly established and opportunities for newcomers are few. Conversely, small f

R , which occurs when p and/or q are small,

indicates plentiful opportunities for newcomers to join new projects. In this case, newcomers are the norm and collaborations are rarely repeated. Lastly, inter- mediate values of f

R suggest intermediate values of

both p and q, that is, a situation for which there is a balance between seasoned incumbents and new- comers with fresh ideas.

36. The value of p is directly given by the fraction of incumbents in new creations. The value of q must be obtained numerically by simulating the model with different tentative values of q until the fraction f

R of

repeat incumbent-incumbent links predicted by the model coincides with the value measured from the data.

37. We thank K. Börner, V. Hatzimanikatis, A. A. Moreira, J. M. Ottino, M. Sales-Pardo, and D. B. Stouffer for nu- merous suggestions and discussions. R.G. thanks the Fulbright Program and the Spanish Ministry of Education, Culture, and Sports. L.A.N.A. gratefully ac- knowledges the support of a Searle Leadership Fund Award and of a NIH/National Institute of General Medical Studies K-25 award.

Supporting Online Material www.sciencemag.org/cgi/content/full/308/5722/697/ DC1 Materials and Methods Figs. S1 and S2

13 October 2004; accepted 10 February 2005 10.1126/science.1106340

The Dynamics of Interhemispheric Compensatory Processes

in Mental Imagery A. T. Sack,1* J. A. Camprodon,2 A. Pascual-Leone,2 R. Goebel1

The capacity to generate and analyze mental visual images is essential for many cognitive abilities. We combined triple-pulse transcranial magnetic stimulation (tpTMS) and repetitive TMS (rTMS) to determine which distinct aspect of mental imagery is carried out by the left and right parietal lobe and to reveal inter- hemispheric compensatory interactions. The left parietal lobe was predom- inant in generating mental images, whereas the right parietal lobe was specialized in the spatial comparison of the imagined content. Furthermore, in case of an rTMS-induced left parietal lesion, the right parietal cortex could immediately compensate such a left parietal disruption by taking over the specific function of the left hemisphere.

Mental imagery refers to the experience of

a perception in the absence of a corre-

sponding physical stimulus. In our everyday

life, mental imagery represents a crucial ele-

ment of numerous cognitive abilities, such as

object recognition, reasoning, language com-

prehension, and memory. Because of its im-

portance, the exact processes associated with

imagery have long occupied cognitive psychol-

ogists and been a matter of debate and con-

troversy (1).

Mental imagery is accompanied by the

activation of frontoparietal networks (2–5),

but the exact brain areas engaged in imagery

depend on the specific features of the imagery

task (6). When spatial comparisons between

imagined objects are required, most functional

imaging studies show bilateral parietal activa-

tion in homologous intraparietal sulcus areas of

the left and right hemispheres (3). However,

neuropsychological studies on patients with

focal brain lesions generally support a domi-

nant role of the left hemisphere in imagery

E(7), but see (8)^. Time-resolved functional magnetic reso-

nance imaging (fMRI) has been used to address

this apparent contradiction between functional

imaging studies and findings in focal brain

injury patients (4). An earlier cluster of ac-

tivation in both parietal cortices (with left

predominance) can be separated from a late

cluster confined to the right parietal cortex

(Fig. 1). These results support the involve-

ment of both parietal lobes in mental imagery

but suggest that each parietal lobe has a

distinct functional role at different moments

in time. The sequential parietal activation

might represent a transition from an earlier

more distributed processing stage of image

generation to a later right-hemispheric later-

alized stage of spatial analysis of the images

(4). In a combined fMRI and rTMS study, only

rTMS to the right parietal lobe led to an

impairment of spatial imagery performance

1Department of Cognitive Neuroscience, Faculty of Psychology, Maastricht University, Post Office Box 616, 6200 MD Maastricht, Netherlands. 2Center for Non-invasive Brain Stimulation, Beth Israel Deacon- ess Medical Center and Harvard Medical School, 330 Brookline Avenue, Kirstein Building KS 452, Boston, MA 02215, USA.

*To whom correspondence should be addressed. E-mail: a.sack@psychology.unimaas.nl

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29 APRIL 2005 VOL 308 SCIENCE www.sciencemag.org702

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Performance Team Assembly Mechanisms Determine Collaboration Network Structure and Team

Roger Guimerà, Brian Uzzi, Jarrett Spiro and Luís A. Nunes Amaral

DOI: 10.1126/science.1106340 (5722), 697-702.308Science

ARTICLE TOOLS http://science.sciencemag.org/content/308/5722/697

MATERIALS SUPPLEMENTARY http://science.sciencemag.org/content/suppl/2005/04/22/308.5722.697.DC1

CONTENT RELATED http://science.sciencemag.org/content/sci/308/5722/639.full

REFERENCES

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