Larger communities create more systematic languages

Abstract

Understanding worldwide patterns of language diversity has long been a goal for evolutionary scientists, linguists and philosophers. Research over the past decade has suggested that linguistic diversity may result from differences in the social environments in which languages evolve. Specifically, recent work found that languages spoken in larger communities typically have more systematic grammatical structures. However, in the real world, community size is confounded with other social factors such as network structure and the number of second languages learners in the community, and it is often assumed that linguistic simplification is driven by these factors instead. Here, we show that in contrast to previous assumptions, community size has a unique and important influence on linguistic structure. We experimentally examine the live formation of new languages created in the laboratory by small and larger groups, and find that larger groups of interacting participants develop more systematic languages over time, and do so faster and more consistently than small groups. Small groups also vary more in their linguistic behaviours, suggesting that small communities are more vulnerable to drift. These results show that community size predicts patterns of language diversity, and suggest that an increase in community size might have contributed to language evolution.

1. Introduction

Almost 7000 languages are spoken around the world [1,2], and the remarkable range of linguistic diversity has been studied extensively [3,4]. Current research focuses on understanding the sources for this diversity, and attempts to understand whether differences between languages can be predicted by differences in their environments [5–11]. If languages evolved as a means for social coordination [12,13], they are bound to be shaped by their social environment and the properties of the cultures in which they evolved. Indeed, cross-linguistic and historical studies have suggested that different linguistic structures emerge in different societies depending on their size, network structure and the identity of their members [5,14–18].

One social property, community size, might play a particularly important role in explaining grammatical differences between languages. First, an increase in human group size was argued to be one of the drivers for the evolution of natural language [19]. Second, cross-linguistic work that examined thousands of languages found that languages spoken in larger communities tend to be less complex [5]. Specifically, these languages have fewer and less elaborate morphological structures, fewer irregulars and overall simpler grammars [5]. In addition to shaping grammar, community size could affect trends of convergence and stability during language change [14–18].

While there is correlational evidence for the relation between community size and grammatical complexity, cross-linguistic studies cannot establish a causal link between them. Furthermore, the relationship between bigger communities and linguistic simplification can be attributed to other social factors that are confounded with community size in the real world. In particular, bigger communities tend to be more sparsely connected and more geographically spread out, have more contact with outsiders, and have a higher proportion of adult second language learners [14–16]. Each of these factors may contribute to the pattern of reduced complexity, and thus provide an alternative explanation for the correlation between community size and linguistic structure [5–8,20,21]. In fact, many researchers assume that this correlation is accounted for by the proportion of second language learners in the community [5–7,20] or by differences in network connectivity [15–17,21] (see discussion).

Here, we argue that community size has a unique and casual role in explaining linguistic diversity, and show that it influences the formation of different linguistic structures in the evolution of new languages. Interacting with more people reduces shared history and introduces more input variability (i.e. more variants), which individuals need to overcome before the community can reach mutual understanding. Therefore, interacting with more people can favour systematization by introducing a stronger pressure for generalizations and transparency. That is, larger communities may be more likely to favour linguistic variants that are simple, predictable and structured, which can, in turn, ease the challenge of convergence and communicative success. Supporting this idea, language learning studies show that an increase in input variability (i.e. exposure to multiple speakers) boosts categorization, generalization and pattern detection in infants and adults [22–29].

While existing studies cannot establish a causal link between community structure and linguistic structure or isolate the role of community size, teasing apart these different social factors has important implications for our understanding of linguistic diversity and its origins [30]. Some computational models attempted to isolate the effect of community size on emerging languages using populations of interacting agents, but their results show a mixed pattern: while some models suggest that population size plays little to no role in explaining cross-linguistic patterns [21,31,32], others report strong associations between population size and linguistic features [33–35].

To date, no experimental work has examined the effect of community size on the emergence of language structure with human participants, although it was suggested several times [36–38]. We fill this gap by conducting a behavioural study that examines the live formation of new communicative systems created in the laboratory by small or larger groups. A couple of previous studies investigated the role of input variability, one of our hypothesized mechanisms, using an individual learning task, yet found no effect of learning from different models [39,40]. Another related study compared the complexity of English descriptions produced for novel icons by two or three people, but reported no differences between the final descriptions of dyads and triads [41]. These studies, however, did not test the emergence of systematic linguistic structure. Here, we examine how group size influences the emergence of compositionality in a new language, and assess the role of input variability in driving this effect. In addition to examining changes in linguistic structure over time, we track other important aspects of the emerging systems (e.g. communicative success and the degree to which languages are shared across participants), shedding light on how community size affects the nature of emerging languages.

2. The current study

We used a group communication paradigm inspired by [42–47] to examine the performance of small and larger microsocieties (figure 1). Participants interacted in alternating pairs with the goal of communicating successfully using only an artificial language they invented during the experiment. In each communication round, paired partners took turns in describing novel scenes of moving shapes, such that one participant produced a label to describe a target scene, and their partner guessed which scene they meant from a larger set of scenes. Participants in small and larger groups had the same amount of interaction overall, but members of larger groups had less shared history with each other by the end of the experiment. All other group properties (e.g. network structure) were kept constant across conditions.

Figure 1.

Group communication paradigm. We tested fully connected groups of either four (a) or eight (b) participants. Panels (c,d) show the producer's and guesser's screens, respectively. (Online version in colour.)

We examined the emerging languages over the course of the experiment using several measurements (see Measures): (1) communicative success; (2) convergence, reflecting the degree of alignment in the group (3) stability, reflecting the degree of change over time; and (4) linguistic structure, reflecting the degree of systematic mappings in the language. With these measures, we can characterize the emerging communication systems and understand how different linguistic properties change over time depending on community size.

Our main prediction was that larger groups would create more structured languages, given that they are under a stronger pressure for generalization due to increased input variability and reduced shared history. We also predicted that larger groups would show slower rates of stabilization and convergence compared to smaller groups. Furthermore, we ran analyses to test our proposed mechanism, namely, that larger groups create more structured languages because of greater input variability and reduced shared history.

3. Methods

(a). Participants

Data from 144 adults (mean age = 24.9 years, s.d. = 8.9 years; 103 women) were collected over a period of 1 year in several batches, comprising 12 small groups of four members and 12 larger groups of eight members. Participants were paid €40 or more depending on the time they spent in the laboratory (between 270 and 315 min, including a 30 min break). Six additional small groups took part in a shorter version of the experiment [47], which included only eight rounds. These additional groups showed similar patterns of results when compared with the larger groups. Their results are reported in electronic supplementary material, appendix B. All participants were native Dutch speakers. Ethical approval was granted by the Faculty of Social Sciences of the Radboud University Nijmegen.

(b). Materials

We created visual scenes that varied along three semantic dimensions: shape, angle of motion and fill pattern (see also [44,45,47]). Each scene included one of four novel shapes, moving repeatedly in a straight line from the centre of the frame at an angle chosen from a range of possible angles. The four shapes were unfamiliar and ambiguous in order to discourage labelling with existing words. Angle of motion was a continuous feature, which participants could have parsed and categorized in various ways. Additionally, the shape in each scene had a unique blue-hued fill pattern, giving scenes an idiosyncratic feature. Therefore, the meaning space promoted categorization and structure along the dimensions of shape and motion, but also allowed participants to adopt a holistic, unstructured strategy where scenes are individualized according to their fill pattern. There were three versions of the stimuli, which differed in the distribution of shapes and their associated angles (see electronic supplementary material, appendix A). Each version contained 23 scenes and was presented to two groups in each condition. The experiment was programmed using Presentation.

(c). Procedure

Participants were asked to create a fantasy language and use it in order to communicate about different novel scenes. Participants were not allowed to communicate in any other way besides typing, and their letter inventory was restricted: it included a hyphen, five vowel characters (a,e,i,o,u) and 10 consonants (w,t,p,s,f,g,h,k,n,m), which participants could combine freely.

The experiment had 16 rounds, comprising three phases: group naming (round 0), communication (rounds 1–7; rounds 9–15) and test (round 8; round 16).

In the naming phase (round 0), participants generated novel nonsense words to describe eight initial scenes, so that each group had a few shared descriptions to start with. Eight scenes were randomly drawn from the set of 23 scenes (see Materials) under the constraint that each shape and quadrant were represented at least once. During this phase, participants sat together and took turns in describing the scenes, which appeared on a computer screen one by one in a random order. Participants in larger groups named one scene each, and participants in small groups named two scenes each. Importantly, no use of Dutch or any other language was allowed. An experimenter was present in the room throughout the experiment to ensure participants did not include known words. Once a participant had typed a description for a scene, it was presented to all group members for several seconds. This procedure was repeated until all scenes had been named and presented once. In order to establish shared knowledge, these scene–description pairings were presented to the group twice more in a random order.

Following the naming phase, participants played a communication game (the communication phase): the goal was to earn as many points as possible as a group, with a point awarded for every successful interaction. The experimenter stressed that this was not a memory game, and that participants were free to use the labels produced during the group naming phase, or create new ones. Paired participants sat on opposite sides of a table facing each other and personal laptop screens (see electronic supplementary material, appendix A). During this phase, group members exchanged partners at the start of every round, such that by end of the experiment, each pair in the small group has interacted at least four times and each pair in the large group has interacted exactly twice.

In each communication round, paired participants interacted 23 times, alternating between the roles of producer and guesser. In each interaction, the producer saw the target scene on their screen (figure 1c) and typed a description using their keyboard. The guesser saw a grid of eight scenes on their screen (the target and seven distractors), and had to press the number associated with the scene they thought their partner referred to. Participants then received feedback on their performance.

The number of target scenes increased gradually over the first six rounds, such that participants referred to more scenes in later rounds. While round 1 included only the eight initial scenes selected for the group naming phase, three new scenes were added in each following round until there were 23 different scenes in round 6. No more scenes were introduced afterwards, allowing participants to interact about all scenes for the following rounds. This method was implemented in order to introduce a pressure for developing structured and predictable languages [47], and resembles the real world with its unconstrained meaning space.

After the seventh communication round, participants completed an individual test phase (round 8), in which they typed their descriptions for all scenes one by one in a random order. After the test, participants had seven additional communication rounds (rounds 9–15) and the additional test round (round 16). These two individual test rounds allowed us to get a full representation of participants' entire lexicon at the middle and end of the experiment. Finally, participants filled out a questionnaire about their performance and were debriefed by the experimenter.

Due to a technical error, one large group played only six additional communication rounds instead of seven. Additionally, data from one participant in a large group were lost. The existing data from these groups were included in the analyses.

(d). Measures

(i). Communicative success

Measured as binary response accuracy in a given interaction during the communication phase, reflecting comprehension.

(ii). Convergence

Measured as the similarities between all the labels produced by participants in the same group for the same scene in a given round: for each scene in round n, convergence was calculated by averaging over the normalized Levenshtein distances between all labels produced for that scene in that round. The normalized Levenshtein distance between two strings is the minimal number of insertions, substitutions and deletions of a single character that is required for turning one string into the other, divided by the number of characters in the longer string. This distance was subtracted from 1 to represent string similarity, reflecting the degree of shared lexicon and alignment in the group.

(iii). Stability

Measured as the similarities between the labels created by participants for the same scene on two consecutive rounds: for each scene in round n, stability was calculated by averaging over the normalized Levenshtein distances between all labels produced for that scene in round n and round n + 1. This value was subtracted from 1 to represent string similarity, reflecting the degree of consistency in the groups' languages.

(iv). Linguistic structure

Measured as the correlations between string distances and semantic distances in each participant's language in a given round, reflecting the degree to which similar meanings are expressed using similar strings [43,44,47]. First, scenes had a semantic difference score of 1 if they differed in shape, and 0 otherwise. Second, we calculated the absolute difference between scenes' angles, and divided it by the maximal distance between angles (180°) to yield a continuous normalized score between 0 and 1. Then, the difference scores for shape and angle were added, yielding a range of semantic distances between 0.18 and 2. Finally, labels' string distances were calculated using the normalized Levenshtein distances between all possible pairs of labels produced by participant p for all scenes in round n. For each participant, the two sets of pair-wise distances (i.e. string distances and meaning distances) were correlated using the Pearson product-moment correlation. While most iterated learning studies use the z-scores provided by the Mantel test for the correlation described above [43,44], z-scores were inappropriate for our design since they increase with the number of observations, and our meaning space expanded over rounds. Therefore, we used the raw correlations between meanings and strings as a more accurate measure of systematic structure [47,48].

(v). Input variability

Measured as the minimal sum of differences between all the labels produced for the same scene in a given round. For each scene in round n, we made a list of all label variants for that scene. For each label variant, we summed over the normalized Levenshtein distances between that variant and all other variants in the list. We then selected the variant that was associated with the lowest sum of differences (i.e. the ‘typical' label), and used that sum as the input variability score for that scene, capturing the number of different variants and their relative difference from each other. Finally, we averaged over the input variability scores of different scenes to yield the mean variability in that round.

(vi). Shared history

Measured as the number of times each pair in the group interacted so far, reflecting the fact that members of small groups interacted more often with each other. In small groups, pairs interacted once by round 3, twice by round 6, three times by round 10 and four times by round 14, and started to interact for the fifth time in round 15. In larger groups, pairs only interacted once by round 7 and twice by round 15.

(e). Analyses

We used mixed-effects regression models to test the effect of community size on all measures using the lme4 [49] and pbkrtest [50] packages in R [51]. All models had the maximal random effects structure justified by the data that would converge. The reported p-values were generated using the Kenward–Roger approximation, which gives more conservative p-values for models based on small numbers of observations. The full models are included in electronic supplementary material, appendix C. All the data and the scripts for generating all models can be openly found at https://osf.io/y7d6m/.

Changes in communicative suceess, stability, convergence and linguistic structure were examined using three types of models: (I) models that analyse changes in the dependent variable over time; (II) models that compare the final levels of the dependent variable at the end of the experiment; and (III) models that examine differences in the levels of variance in the dependent variable over time.

Models of type (I) predicted changes in the dependent variable as a function of time and community size. Models for communicative success included data from communication rounds only (excluding the two test rounds). In models for communicative success, convergence and stability, the fixed effects were condition (dummy-coded with small group as the reference level), round number (centred), item current age (centred) and the interaction terms condition × item current age and condition × round number. item current age codes the number of rounds each scene was presented until that point in time, and measures the effect of familiarity with a specific scene on performance. round number measures the effect of time passed in the experiment and overall language proficiency. The random effects structure of models for communicative success, convergence and stability included by-scene and by-group random intercepts, as well as by-group random slopes for the effect of round number. Models for stability and communicative success also included by-scene random slopes for the effect of round number. As structure score was calculated for each producer over all scenes in a given round, the model for linguistic structure did not include item current age as a fixed effect, and included fixed effects for round number (quadratic, centered), condition (dummy-coded with small group as the reference level) and the interaction term condition × round number. Following Beckner et al. [52], who found that linguistic structure tends to increase nonlinearlly, we included both the linear and the quadratic terms (using the poly() function in R to avoid colinearity). The model for linguistic structure included random intrecepts and random slopes for the effect of round number with respect to different producers who were nested in different groups.

Models of type (II) compared the mean values of the final languages created by small and larger groups in rounds 15–16. The fixed effect in these models was a two-level categorical variable (i.e. small groups versus larger groups), dummy-coded with small groups as the reference level. In models for communicative success, stablity and structure, the random effects structure included random intercepts for different groups and different scenes. In models for linguistic structure, the random effect structure included random intercepts for different producers nested in different groups.

Models of type (III) predicted the degree of variance in the dependent variable across groups and time. For linguistic structure, variance was calculated as the square standard deviation in participants' average structure scores across all groups in a given round. For communicative success, convergence and stability, variance was calculated as the square standard deviation in the dependent variable on each scene across all groups in a given round. These models included by-scenes random intercepts and slopes for the effect of round number. All models included fixed effects for round number (centred), condition (dummy-coded with small group as the reference level) and the interaction term condition × round number.

We also examined changes in input variability as a function of time and community size. This model included fixed effects for round number (centred), condition (dummy-coded with small group as the reference level) and the interaction between them. There were by-group random intercepts and by-group random slopes for the effect of round number. Finally, we examined changes in linguistic structure scores over consecutive rounds as a function of (a) input variability, (b) shared history or (c) both. In all three models, the dependent variable was the difference in structure score between round n and n + 1, and there were random intercepts for different producers nested in different groups. In model (a), the fixed effect was mean input variability at round n (centred). In model (b), the fixed effect was shared history at round n (centred). Model (c) was a combination of models (a) and (b).

4. Results

We report the results for each of the four linguistic measures separately, using three types of analyses (see Methods). Figure 2 summarizes the average differences in the performance of small and larger groups over the course of all 16 rounds. Note that all analyses were carried over all data points and not over averages. All analyses are reported in full in electronic supplementary material, appendix C using numbered models, which we refer to here.

Figure 2.

Changes in (a) communicative success, (b) convergence, (c) stability and (d) linguistic structure over time as a function of community size. Thin lines represent average values for each group in a given round. Data from small and larger groups are plotted in blue and red, respectively. Thick lines represent the models' estimates, and their shadings represent the models' standard errors.

(a). Communicative success

Communicative success increased over time (Model 1: β = 0.08, s.e. = 0.02, t = 4, p < 0.0001; figure 2a), with participants becoming more accurate as rounds progressed. This increase was not significantly modulated by group size (Model 1: β = 0.04, s.e. = 0.03, t = 1.76, p = 0.078), with small and larger groups reaching similar accuracy scores in the final communication round (Model 2: β = 0.14, s.e. = 0.08, t = 1.8, p = 0.083). Small and larger groups differed in variance: while all groups became increasingly more varied over time (Model 3: β = 0.002, s.e. = 0.0004, t = 5.18, p < 0.0001), larger groups showed a slower increase in variance (Model 3: β = −0.002, s.e. = 0.0005, t = −4.2, p < 0.0001) and lower variance overall (Model 3: β = −0.007, s.e. = 0.002, t = −3.48, p < 0.001). These results indicate that while small groups varied in their achieved accuracy scores, and even more so as the experiment progressed, larger groups tended to behave more similarly to one another throughout the experiment.

(b). Convergence

Convergence increased significantly across rounds (Model 4: β = 0.007, s.e. = 0.003, t = 2.31, p = 0.029; figure 2b), with participants aligning and using more similar labels over time. Convergence was also better on more familiar scenes (Model 4: β = 0.004, s.e. = 0.001, t = 2.62, p = 0.014). Group size had no effect on convergence (Model 4: β = −0.06, s.e. = 0.04, t = −1.37, p = 0.18), so that small and larger groups showed similar levels of convergence by the end of the experiment (Model 5: β = −0.03, s.e. = 0.05, t = −0.63, p = 0.54). Interestingly, larger groups were not less converged than small groups, despite the fact that members of larger groups had double the amount of people to converge with and only half the amount of shared history with each of them. Variance increased over rounds (Model 6: β = 0.001, s.e. = 0.003 t = 4.32, p < 0.0001), but there was significantly less variance in the convergence levels of larger groups than across small groups throughout the experiment (Model 6: β = −0.04, s.e. = 0.002 t = −23.68, p < 0.0001). That is, larger groups behaved similarly to each other, showing a slow yet steady increase in convergence over rounds, while small groups varied more in their behaviour: some small groups reached high levels of convergence, but others maintained a high level of divergence throughout the experiment, with different participants using their own unique labels.

(c). Stability

Stability significantly increased over time, with participants using labels more consistently as rounds progressed (Model 7: β = 0.009, s.e. = 0.003, t = 3.26, p = 0.003; figure 2c). Labels for more familiar scenes were also more stable (Model 7: β = 0.004, s.e. = 0.001, t = 3.68, p = 0.001). Group size affected stability (Model 7: β = −0.08, s.e. = 0.04, t = −2.08, p = 0.047), with larger groups' languages being less stable (i.e. showing more changes). However, by the end of the experiment, the languages of small and larger groups did not differ in their stability (Model 8: β = −0.06 s.e. = 0.05, t = −1.21, p = 0.24). As in the case of convergence, larger groups showed significantly less variance in their levels of stability compared to small groups throughout the experiment (Model 9: β = −0.018, s.e. = 0.001, t = −16.99, p < 0.0001), reflecting the fact that smaller groups differed more from each other in their stabilization trends.

(d). Linguistic structure

Linguistic structure significantly increased over rounds (Model 10: β = 4.55, s.e. = 0.48, t = 9.46, p < 0.0001; figure 2d), with participants' languages becoming more systematic over time. This increase was nonlinear and slowed down in later rounds (Model 10: β = −3, s.e. = 0.38, t = −7.98, p < 0.0001). As predicted, the increase in structure was significantly modulated by group size (Model 10: β = 1.92, s.e. = 0.63, t = 3.06, p = 0.004), so that participants in larger groups developed structured languages faster compared to participants in small groups. Indeed, the final languages developed in larger groups were significantly more structured than the final languages developed in small groups (Model 11: β = 0.11, s.e. = 0.04, t = 2.93, p = 0.006). Variance did not significantly decrease over time (Model 12: β = −0.0009, s.e. = 0.0005, t = −1.73, p = 0.094), yet larger groups varied significantly less overall in how structured their languages were (Model 12: β = −0.015, s.e. = 0.004, t = −4.28, p = 0.0002). That is, while small groups differed in their achieved levels of structure throughout the experiment, different larger groups showed similar trends and reached similar structure scores.

Although all groups started out with different random holistic labels, compositional languages emerged in many groups during the experiment. Many groups developed languages with systematic and predictable grammars (see figure 3 for one example; electronic supplementary material, appendix D for more examples), in which scenes were described using complex labels: one part indicating the shape, and another part indicating motion.¹ Interestingly, groups differed not only in their lexicons but also in the grammatical structures they used to categorize scenes according to motion. While many groups categorized angles based on a two-axis system (with part-labels combined to indicate up/down and right/left), other groups parsed angles in a clock-like system, using unique part-labels to describe different directions. Importantly, while no two languages were identical, the level of systematicity in the achieved structure depended on group size.

Figure 3.

An example of the final language produced by a participant in a large group, along with a ‘dictionary' for interpreting it on the right. Box colours represent the four shapes, and the grey axes indicate the direction in which the shape moved. Font colours represent different meaningful part-labels, as segmented by the authors for illustration purposes only. For example, the label in the black circle (wowo-ik) described a scene in which shape 4 moved in a 30° angle. It is composed of several parts: wowo (indicating the shape) and ik (indicating the direction, composed of two meaningful parts: i for ‘up' and k for ‘right').

We also tested our hypothesis that group size effects are driven by differences in input variability and shared history. First, we quantified the degree of input variability in each group at a given time point by measuring the differences in the variants produced for different scenes in different rounds. Then, we examined changes in input variability over time across conditions. We found that input variability significantly decreased over rounds (Model 13: β = −0.1, s.e. = 0.01, t = −8, p < 0.0001), with a stronger decrease in the larger groups (Model 13: β = −0.08, s.e. = 0.2, t = −4.42, p = 0.0001). Importantly, this analysis also confirmed that larger groups were indeed associated with greater input variability overall (Model 13: β = 1.45, s.e. = 0.09, t = 15.99, p < 0.0001)—a critical assumption in the literature [8,14,16,39] and a premise for our hypothesis. We also quantified the degree of shared history between participants. Then, we examined the role of input variability and shared history in promoting changes in linguistic structure by using these measures to predict differences in structure scores over consecutive rounds. We found that more input variability at round n induced a greater increase in structure at the following round (Model 14: β = 0.015, s.e. = 0.003, t = 4.8, p < 0.0001). Similarly, less shared history at round n induced a greater increase in structure at the following round (Model 15: β = −0.017, s.e. = 0.004, t = −4.18, p = 0.0004). When both predictors were combined in a single model, only input variability was significantly associated with structure differences (Model 16: β = 0.011, s.e. = 0.004, t = 2.76, p = 0.012), while the effect of shared history did not reach significance (Model 16: β = −0.008, s.e. = 0.005, t = −1.42, p = 0.17)—suggesting that input variability was the main driver for the increase in structure scores.

5. Discussion

We used a group communication paradigm to test the effect of community size on linguistic structure. We argued that larger groups were under stronger pressure to develop shared languages to overcome their greater communicative challenge, and therefore created more systematic languages. We found that while all larger groups consistently showed similar trends of increasing structure over time, some small groups never developed systematic grammars and relied on holistic, unstructured labels to describe the scenes. Importantly, linguistic structure increased faster in the larger groups, so that by the end of the experiment, their final languages were significantly more systematic than those of small groups. Our results further showed that the increase in structure was driven by the greater input variability in the larger groups. Remarkably, the languages developed in larger groups were eventually as globally shared across members, even though members of larger groups had fewer opportunities to interact with each other, and had more people they needed to converge with compared with members of small groups. Finally, the languages of small groups changed less over time, though larger groups reached an equal level of stability by the end of the experiment. Together, these results suggest that group size can affect the live formation of new languages.

The groups in our experiment were smaller than real-world communities. The results, however, should scale to real-world populations since the meaning space and speakers' life span scale up proportionally. Concordantly, our results are consistent with findings from real developing sign languages, which show that given the same amount of time, a larger community of signers developed a more uniform and more systematic language compared with a small community of signers [14]. It also resonates with psycholinguistic findings that show how input variability can affect generalization [22]: participants typically don't generalize over variants when they are able to memorize all of them individually, but do generalize when there are too many variants to remember. Similarly, greater input variability in larger groups promoted generalizations of the linguistic stimuli in our experiment, consistent with language change theories that argue for more systematicity in big communities of speakers for the same reasons [8,15–17].

The proposed mechanism assumes a close relationship between our linguistic measures, and is based on the hypothesis that linguistic structure can facilitate convergence and comprehension. We assumed that larger groups compensated for their greater communicative challenge by developing more systematic languages, which enabled them to reach similar levels of convergence and accuracy by the end of the experiment. Therefore, one may wonder whether more structure indeed facilitated convergence and communicative success in our experiment. To this end, we examined the relation between our measures of communicative success, convergence and linguistic structure after controlling for the effect of round (see electronic supplementary material, appendix C). One model predicted convergence as a function of time and linguistic structure. The model included round number (centred), structure score (centred) and the interaction between them as fixed effects. Another model predicted communicative success as a function of time, convergence and linguistic structure scores, with fixed effects for round number (centred), structure score (centred), mean convergence (centred) and the interaction terms structure × round and convergence × round. Both models included by-group random intercepts and by-group random slopes for all fixed effects. Indeed, we found that more linguistic structure predicted better convergence across different rounds (Model 17: β = 0.018, s.e. = 0.008, t = 2.32, p = 0.027). Additionally, communicative success was predicted by structure (Model 18: β = 0.436, s.e. = 0.06, t = 7.48, p < 0.0001) and convergence (Model 18: β = 0.189, s.e. = 0.06, t = 2.95, p = 0.008), so that better group alignment and more systematic structure predicted higher accuracy scores across rounds. Moreover, the relationship between structure and accuracy became stronger over rounds (Model 18: β = 0.051, s.e. = 0.008, t = 6.38, p < 0.0001). These additional analyses provide important empirical evidence in support of the underlying mechanisms we proposed, and shed light on the nature of the group size effects reported in this paper.

Another important aspect of our results concerns the effect of group size on variance in behaviour. We found significantly more variance in the behaviours of small groups across all measures: some small groups reached high levels of communicative success, convergence, stability and linguistic structure, while others did not show much improvement in these measures over time. By contrast, larger groups all showed similar levels of communicative success, stability, convergence and linguistic structure by the end of the experiment. These results support the idea that small groups are more vulnerable to drift [18,35]: random changes are more likely to occur in smaller populations, while larger populations are more resilient to such random events and often show more consistent behaviours. This result may be underpinned by basic probability statistics: small samples are typically less reliable and vary more from each other, while larger samples show more normally distributed patterns and are more representative of general trends in the population (‘the law of large numbers' [53]).

Our findings support the proposal that community size can drive the cross-linguistic and historical findings that larger societies have more simplified grammars [5,8,14–17], and suggest that differences in community size can help explain and predict patterns and trajectories in language formation and change. Our results show that the mere presence of more people to interact with introduces a stronger pressure for systemization and for creating more linguistic structure, suggesting that an increase in community size can cause languages to lose complex holistic constructions in favour of more transparent and simplified grammars. As such, our results are in line with the idea that increasing community size could have been one of the drivers for the evolution of natural language [19].

Our findings also stress the role of the social environment in shaping the grammatical structure of languages, and highlight the importance of examining other relevant social properties alongside community size. Particularly, network structure and connectivity are typically confounded with community size, and have been argued to play an important role in explaining cross-cultural differences in linguistic complexity. Specifically, theories of language change suggest that differences in network density may be the true underlying mechanism behind language simplification [15–17]. This idea is supported by computational work showing that networks' structural properties, such as their degree of clustering and hierarchy, can influence linguistic complexity and modulate the effect of population size [21] (but see [35]). Future work should examine the individual role and mutual influence of these factors to provide a full understanding of how the social environment shapes language evolution.

Ethics

Ethical approval was granted by the Faculty of Social Sciences of the Radboud University Nijmegen.

Data accessibility

All the data and the scripts for generating all models can be openly found online at: https://osf.io/y7d6m/.

Authors' contribution

L.R. designed and performed the research, analysed the data and wrote the paper; A.M. and S.L.-A. designed the research and wrote the paper.

Competing interests

We declare we have no competing interests.

Funding

We received no funding for this study.