2.1 Procedure

All our experiments consist of 135 rounds. At each round, one participant is the sender and the other is the receiver; these roles switch after every round. The sender is shown two meanings, represented by English nouns (see Section 2.2) and is instructed to communicate one of those meanings to the receiver, using a single word from an artificial lexicon (see Section 2.3). The receiver is then shown the same pair of meanings (in random order) and the sender's signal and has to guess which of the two meanings the signal represents. After taking a guess, both participants are shown an identical feedback screen which informs them whether the receiver guessed correctly; (see Table 1 for an illustration). The game ends with a screen showing both participants their total score, asking them for optional feedback, and leaving them with instructions on how to claim their monetary reward.

The participants never see more than two meanings on the screen at any time. In each game, there are 10 meanings, among them three “target pairs” consisting of two highly similar meanings, for example, motor and engine. The remaining four meanings serve as distractors that have low similarity scores to all other meanings, including the targets (see below for details). The signal space consists of seven artificial words such as fuwo or qohe. Since there are fewer signals than meanings, participants must colexify some meanings. We assume it takes a while to establish stable meaning correspondences, so we consider the first one third of the rounds as a “burn-in” phase and only analyze the final 90 rounds of the experiment.

2.2 Stimuli: Meanings

The meanings to be communicated are English common nouns of three to seven characters in length, drawn from the Simlex999 dataset (Hill, Reichart, & Korhonen, 2015), which consists of pairs of words and their crowdsourced similarity judgments. We use Simlex999, as it was built for evaluating models of meaning with the explicit goal of distinguishing genuine similarity (synonymy) from associativity (the dataset incorporates a subset of the USF Free Association Norms for that purpose; cf. Nelson, McEvoy, & Schreiber, 2004). Our target pairs are required to have a Simlex similarity score of at least 8 out of 10, but a free association score below 1 out of 10. This should yield meanings which are near synonymous and not simply contextually associated. For example, arm and leg have a high association score of 6.7, that is when people hear arm they are likely to think of leg—but these two are not synonyms (reflected in the Simlex similarity score of only 2.9). plane and jet have high similarity (8.1), but they also appear to be highly associated terms (6.6). In contrast, abdomen and belly have high similarity (8.1) but at the same time low associativity (0.1), therefore, making them suitable for our stimulus set.

Since Simlex does not have scores for all possible word pairs in its lexicon, we also used publicly available pretrained word embeddings (fasttext trained on Wikipedia; cf. Bojanowski, Grave, Joulin, & Mikolov, 2017) to obtain additional computational measures of similarity. We use these to ensure low similarity across the board in the distractor set, which was sampled so that no two distractors and no distractor–target pair would have vector cosine similarity above 0.2 (out of 1). Furthermore, no two nouns were substrings of each other, nor otherwise similar in form (we used a Damerau–Levenshtein edit distance^1. threshold of 3), and targets were not allowed to share the same first letter. This filtering yielded 13 eligible target pairs: abdomen-belly, area-zone, author-creator, bag-purse, coast-shore, couple-pair, danger-threat, drizzle-rain, engine-motor, fashion-style, job-task, journey-trip, noise-racket. The meaning space for each dyad consists of three target pairs selected at random from this set of 13 possible pairs, plus an additional four distractor meanings, drawn from the remaining 475 possible meanings (see Fig. 2a).

2.3 Stimuli: Signals

For each dyad in Experiments 1–3, we generated a set of seven signals, according to the following constraints (Experiment 4 has an extended signal space of 10 signals). Each signal had a length of four characters and was composed of two consonant–vowel syllables, constructed from a set of consonants and vowels . We further constrained the artificial language so that the initial letters of the signals would not overlap with any initial letters of the meanings (English nouns) in a given stimulus set. We used a large English word list to make sure there was no overlap between the artificial signals and actual English words, and furthermore made sure all signals were at least three edits distant from the meanings (the English nouns) in the same game, as well as from other signals in the game (see Fig. 2b).

2.4 Experimental manipulation of communicative need

The experiments have two conditions: the baseline or control condition, where communicative need is uniform, and the target condition where we manipulate communicative need, creating a situation where colexifying certain (similar) concepts would hinder the accurate exchange of messages. This applies to all experiments except for Experiment 3, which only has a (modified) target condition (see details in Section 5).

In the baseline condition, the distribution of meaning pairs (e.g., drizzle-rain, style-fashion, payment-bull, rain-payment, rain-fashion) is uniform—each possible combination is shown to the participants exactly three times. Based on cross-linguistic tendencies (cf. Xu et al., 2020a), in this condition we would expect participants to colexify similar meanings. In the target condition, all possible meaning pair combinations still occur in the game, but, crucially, we manipulate the occurrence frequencies so that the target (similar-meaning) pairs occur together more often than the distractor pairs. The target pairs (e.g., drizzle-rain, style-fashion) are shown 11 times each, and the pairs consisting of distractor meanings (e.g., payment-bull) five times each. Pairs consisting of a meaning from a target pair plus another meaning are shown two times (e.g., rain-payment or rain-fashion).

The nonuniform distribution of meaning pairs in the target condition entails that to communicate successfully, participants are required to select signals which allow their partner to differentiate between drizzle and rain 11 times, but are only required to differentiate between rain and payment two times. The increased co-occurrence of similar meanings in the target condition simulates communicative need. If a pair of similar meanings never or seldom need to be distinguished, then it is efficient to colexify them, both from a learning and communication perspective. In contrast, if the communicative context often requires disambiguating between two similar meanings or referents—such as rain and drizzle in a culture obsessed with talking about poor weather—then colexifying them as rain or blending them into something like rainzzle would obviously be detrimental to communicative success. We expect this to be reflected in the outcomes of the target condition: participants should avoid colexifying the similar concepts, as that would make it difficult to distinguish them and hinder communicative efficiency.

These pairs are displayed in a randomized order, but randomized separately for the burn-in (first third) and post-burn-in part of the game. In other words, we make sure that if rain-fashion is supposed to appear three times over the course of the game, then it will appear once in the burn-in and twice afterwards. Of course not all values are divisible by 3, so the distribution of stimuli between burn-in and the rest of the game is not perfect, but we optimize it to be as good as numerically possible.^2.

The meaning pair frequency distribution used in both conditions ensures that individual meanings all occur exactly the same number of times (which is 27). It is necessary to control for individual frequencies in this manner, as simply making target pairs more frequent would also mean making the individual meanings in those pairs more frequent than the distractors. This would introduce a confound: another reasonable hypothesis could be that it is occurrence frequency that drives colexification (i.e., colexifying frequent meanings is preferred, or avoided; cf. Xu et al., 2020a), over and above communicative need or word similarity.

2.5 Participants and exclusion criteria based on communicative accuracy

All our experiments were approved by the Ethics Committee of the School of Philosophy, Psychology and Language Sciences of the University of Edinburgh. All participants provided informed consent on the online game platform prior to participating and were compensated monetarily for their time. We do not include all the data in our analysis, as the communicative accuracy of some dyads is at or near random chance. Low accuracy in guessing the meanings of the signals transmitted indicates a given dyad did not manage to converge on a lexicon they could use with reasonable success to communicate—such data are not informative in terms of our research question.

We calculate the communicative accuracy of a dyad as the percentage of correct guesses out of all guesses made in the game after the burn-in period (see Section 2.1). We make the assumption that dyads with a total accuracy score above 59%, that is guessing correctly in of the trials, were unlikely (binomial ) to be signaling or guessing randomly. Dyads scoring below this threshold were excluded from analysis; all excluded dyads still received full payment. The instructions also included a request not to make any notes or write anything down during the experiment, and participants were asked at the end of the experiment whether they had taken written notes; no participants were excluded on the basis of having admitted to taking written notes.

2.6 Quantifying colexification

We are interested in what participants do with the target meaning pairs. If they colexify target meanings in the baseline condition (e.g., use the same signal for rain and drizzle), that would support the cross-linguistic findings of Xu et al. (2020a), that similar meanings are most often colexified. If participants avoid colexifying target meaning pairs in the target condition, then this would support the hypothesis we intend to test, that given high enough communicative need to distinguish similar meanings, they will not be colexified (see Fig. 3 for an illustration). We, therefore, need a method to operationalize these signal-meaning associations in a manner that would allow us to test our hypothesis via rigorous statistical analysis, while preferably also capturing possible changes in lexification choices over the course of each game.

Data from each game is converted into a new dataset suitable for statistical analysis, consisting only of colexifications involving one of the target meanings. We introduce a new binomial variable, “colexification with synonym” and assign values to it using the following procedure. We start by iterating through all the messages sent in the post-burn-in part of the game that signal one of the target meanings. We check if the most recent usage of a given signal by the same player in the same game lexified another meaning, and if that meaning belongs to the same target pair or not. For example, given Player 1 signals rain using pami at round number 53, we check the most recent usage of pami by Player 1 in all preceding rounds of the game where Player 1 was the signaler. Let us say this happened at round 39, and Player 1 used pami to also signal rain. This does not count as a colexification—it has the same meaning—so this case is not added to the new dataset. At some point later in the game, at round 127, Player 1 signals rain using pami again. The previous usage of pami by Player 1 was round 121, where they used it to signal style. This counts as a colexification, and so this case is added to the new dataset. As style is not a synonym of rain, the value assigned to the new “colexification with synonym” variable is “no.” If instead of style, the most recent meaning signaled by pami had been drizzle—a highly similar meaning belonging to the same target pair with rain—then this value would be set as “yes.”

This procedure is repeated for all dyads that score above our previously described accuracy threshold. We do not include the data from the burn-in period (first one third of the game) in the statistical analysis of the results but do take the burn-in into account when checking for the most recent usage of signals, as players do not start from a clean slate after the end of the burn-in, but already have some experience with the language and likely at least some signal–meaning associations in place. This is not the only way to operationalize and analyze such data, but it does provide insights into participant behavior while allowing for explicit comparison of the conditions in terms of the likelihood of target pair colexification, and for modeling changes in lexification over the course of the game.

The distributions of meanings occurring in the game—the input data for the participants—are carefully balanced, and all games consist of exactly 135 rounds, as described in Section 2.4. Note, however, that under this operationalization, the amount of output data yielded by different dyads varies somewhat (see Fig. 4). The exact number of data points per dyad depends on their colexification behavior: if they converge on a system where most of the target meanings get their own unique signal, then there will be fewer colexifications and as such fewer data points. If they colexify the target meanings, either with their near-synonyms or with unrelated meanings, then there will be more colexifications to analyze. This is by design as we prioritize balancing the input and is controlled for in our statistical analyses below, ensuring that the overall results are not driven by a few data-rich dyads.

2.7 Statistical modeling approach

We used mixed effects logistic regression models (using the lme4 package in R; Bates, Mächler, Bolker, & Walker, 2015) to model all the datasets derived using the approach described in Section 2.6 above. The model has the same effects structure across all experiments. A condition (baseline or target) is treatment coded, with the baseline condition set as the reference level (with the exception of Experiment 3; this is discussed in the relevant section). A round number (scaled to a range of ) is centered at round 68, the middle of the game. The binomial colexification variable is set as the response, predicted by condition, round number, and their interaction. The interaction with round accounts for possible changes in lexification preferences. To account for the repeated measures nature of the data and the fact that the number of data points per dyad is variable, we set random intercepts for meaning and sender (the latter nested in dyad) and a random slope for condition by meaning.³ A full random effects structure would be desirable, but could not be included due to model convergence issues.

3.1 Methods

The setup of our first experiment matches the overview in Section 2: There is a baseline and a target condition, and in both cases participants are provided with seven signals which they can use to lexify the 10 meanings. We operationalize the data for statistical modeling using the procedure as described in Section 2.6 and illustrated in Fig. 4.

3.2 Results

The data-processing procedure described in Section 2.6 yields a dataset of 1214 cases (597 in the baseline, 617 in the target condition), a median of 30 per dyad (illustrated in Fig. 4). In the mixed effects regression model (see Section 2.7), the dependent variable is the derived binomial colexification measure. The fixed effects consist of the condition, round number, and the interaction of the two. The interaction is included to account for possible changes over the course of the game (cf. Fig. 4). Random effects are included to control for repeated measures of meanings, dyads, and players, as outlined in Section 2.7. In the model described in Table 2, the intercept value of stands for the log odds of target meaning pairs being colexified, in the baseline condition, midgame (i.e., a probability of .45; recall that we centered round number). By midgame, the model is not picking up a significant difference between the conditions (). Each passing round does increase the probability of colexification in the baseline condition (, ). Importantly, the interaction between condition and round is in the opposite direction (, ), indicating participants were less likely to colexify related meanings in the target condition, where these related meanings frequently co-occurred and needed to be distinguished from one another. By the end of a game, the estimated average probability of colexifying target pairs is only 0.29 in the target condition, compared to 0.69 in the baseline condition. In short, these results support our communicative need hypothesis (for further illustration, see Fig. 5, the leftmost columns).

Table 2. The fixed effects from the mixed effects regression model applied to data from Experiment 1, predicting the value of the colexification variable (reference level: “no”) by the interaction between condition (reference: baseline) and round number. The latter is included to account for progress over the course of the experiment. The results indicate a statistically significant difference in participant behavior between the two conditions, supporting the hypothesis that communicative need can drive lexification preferences above and beyond conceptual similarity

Colexification	Estimate	SE
intercept (baseline condition, midgame)	−0.22	0.37	−0.59	.56
+ condition (target)	−0.52	0.51	−1.03	.3
+ round	1.02	0.27	3.84	.01
+ condition (target) round	−1.18	0.37	−3.17	.01

3.3 Discussion

Human memory is not infinite, and neither is time that can be used for learning. An unlimited number of signals or signal-meaning associations cannot be stored in the brain. We emulated these natural conditions in our artificial communication experiment by providing the participants with a signal space that is smaller than the provided meaning space. The results from the baseline condition provide experimental support for the cross-linguistic findings of Xu et al. (2020a)—that people indeed tend to colexify similar meanings. Yet when faced with a situation where there is elevated communicative need to distinguish certain meaning pairs more often than others, people are more likely to colexify other pairs or clusters of meanings to maintain communicative efficiency—even if this requires colexifying unrelated meanings. This in turn supports the hypothesis suggested by Xu et al. (2020a) and is in line with previous research on communicative need in general (cf. Section 1).

It should be noted that this setup possibly puts a heavier cognitive load on the participants in the target condition. In the baseline condition, participants can colexify similar meanings (like rain and drizzle) without paying an additional communicative cost. It is probably safe to assume similarity-driven pairings are easier to remember. In the target condition, participants are encouraged to colexify meanings which are maximally dissimilar by design (e.g., dentist and fashion).^5. In that sense, Experiment 1 constitutes a strong test of the communicative need hypothesis—we predict that given high enough communicative need, speakers would even colexify unrelated meanings rather than sacrifice communicative efficiency. However, actual differences in average communicative accuracy in Experiment 1 turn out to be negligible.^6. Fig. 6 illustrates this, as well as the accuracy levels of the rest of the experiments, which we will discuss further in the next sections. There was also no difference in game length (on average 29 min in both conditions).

Regardless, we will still explore the weaker hypothesis in a follow-up experiment, where participants are provided with less frequently co-occurring but still similar meanings to colexify (Experiment 3 in Section 5). We will also describe an experiment with an expanded signal space (Experiment 4 in Section 6). However, in the next section, we will first replicate the initial study on a different, slightly larger sample of participants.

4.1 Methods

4.2 Results

The analysis procedure for Experiment 2 is identical to that of Experiment 1: We operationalize colexification (see Section 2.6; yielding a dataset of 1659 cases, a median of 32 per dyad) and apply the same mixed effects logistic model (Section 2.7). Experiment 2 successfully replicated the results of Experiment 1 with the condition-round interaction coefficient being significantly negative (, ; see Table 3; refer back to Fig. 5 for visual comparison). This value indicates participants were again less likely to colexify related meanings in the target condition which simulated communicative need (average probability of .46 by the end of the game), compared to the baseline condition, where there was no such pressure, and where participants more often colexify related meaning pairs (.72 probability).

Table 3. The fixed effects from the mixed effects regression model applied to data from Experiment 2, predicting the value of the colexification variable (reference level: “no”) by the interaction between condition (reference: baseline) and round number. The results replicate those of Experiment 1

Colexification	Estimate	SE
intercept (baseline condition, midgame)	−0.2	0.29	−0.68	.49
+ condition (target)	−0.44	0.36	−1.24	.22
+ round	1.14	0.24	4.82	.01
+ condition (target) round	−0.66	0.31	−2.11	.03

4.3 Discussion

The successful replication gives us additional confidence in the overarching hypothesis concerning the role of communicative need in lexification choices. We now turn to two more experiments to gain a better understanding of how communicative need and simplicity preferences shape the behavior of our participants, testing a weaker version of the communicative need hypothesis in Experiment 3 and relaxing the signal space constraint in Experiment 4.

5.1 Methods

5.2 Results

To obtain a point of comparison, we combine the data collected in this experiment with the baseline and target condition data from Experiment 2 (totaling 2527 cases, of those 868 from the weaker hypothesis target condition of Experiment 3). We fit a mixed effects logistic regression model with the same structure as before but set the new, “weaker” target condition as the reference level for the condition effect. We find that as with the previous target condition, there is still a significant difference from the baseline condition (the condition round interaction ). However, participant behavior does not differ from the target condition of Experiment 2, that is , our manipulation of the meaning space did not elicit a meaningful difference (; see Table 4 and Fig. 5).

Table 4. The fixed effects from the mixed effects regression model applied to combined data from Experiments 2 and 3, predicting the value of the colexification variable (reference level: “no”) by the interaction between condition (reference: new weaker target condition) and round number. Participant behavior does not differ significantly between the original target condition and the new weaker-hypothesis target condition

Colexification	Estimate	SE
intercept (weaker target condition, mid-game)	−0.22	0.25	−0.9	.37
+ condition (baseline)	0.04	0.34	0.12	.9
+ condition (target)	−0.39	0.34	−1.16	.24
+ round	0.14	0.2	0.68	.49
+ condition (baseline) round	0.95	0.3	3.11	.01
+ condition (target) round	0.3	0.29	1.06	.29

5.3 Discussion

We once again observe the same general trend (echoing the cross-linguistic findings of Xu et al., 2020a) that participants colexify any similar-meaning pairs even if it causes the occasional miscommunication, but change their behavior if that cost becomes too high, as evidenced once more by the significant difference between the baseline condition of Experiment 2 and the new target condition of Experiment 3. We also expected that participants would colexify target pairs even less often than in the target conditions of Experiment 2, since alternative similar pairs were available among the distractors, removing one of the assumed barriers to avoiding colexifying target pairs. The data do not support this hypothesis; we see the same (relatively low) rate of colexification of target pairs in our new data. One explanation may be that the difference between co-occurrence frequencies is simply not stark enough for participants to see a benefit (consciously or subconsciously) in colexifying the distractors—and there is still the option to colexify target-distractor pairs, which co-occur less often (twice each, vs. the five of the distractor-only pairs).

6.1 Methods

6.1.2 Procedure

This setup is the same as that of Experiment 1 and 2: There is a baseline and a target condition, and the meaning space and its associated occurrence distributions are arranged as discussed in Section 2.1). The single difference is that participants are not forced to colexify any meanings, as the size of the signal space is 10, equal to the meaning space (illustrated in Fig. 7).

6.2 Results

The results of applying the mixed effects logistic regression model to the data from Experiment 4 (1306 cases after operationalizing colexification) show that when the requirement to colexify is removed, by allowing a larger signal space, the difference between the baseline and target condition disappears (; see Table 5; see also Fig. 5 for a visualization across all conditions). Communicative accuracy is roughly the same as in the other Mechanical Turk samples (recall Fig. 6).

Table 5. The fixed effects from the mixed effects regression model applied to data from Experiment 4, predicting the value of the colexification variable (reference level: “no”) by the interaction between condition (reference: baseline) and round number. Here, in contrast to previous experiments, the conditions yield similar results

Colexification	Estimate	SE
intercept (no-pressure baseline condition, midgame)	−0.73	0.27	−2.74	.01
+ condition (target)	0.24	0.36	0.68	.5
+ round	0.19	0.24	0.78	.44
+ condition (target) round	−0.3	0.33	−0.89	.37

6.3 Discussion

When the signal space is larger, the difference between the baseline and the target condition disappears. Participants behave in the baseline condition similarly to participants in the target conditions, avoiding colexification of the target pairs. We also quantified signal usage entropy for all dyads across all conditions. The results show that in the no-pressure conditions with the expanded signal space, in absolute terms more signals were used on average (Fig. 8). In relative terms, signal usage in Experiment 4 was not that different from the previous experiments, with some dyads making use of most of the signal space (notches close to the limit lines in Fig. 8) and others being more conservative and colexifying instead.

It appears participants favored the effort of remembering a few extra signals over having a simpler but more ambiguous language. While the signaling options are visible in the game at all times, the entire meaning space is never revealed all at once (recall Table 1). Participants here seem to have picked up on the relative abundance of the signals; nevertheless, and unlike in the weaker hypothesis condition, participants did not colexify similar meanings to the same extent. These results solidify the original findings of Experiments 1 and 2: the size of the signal space clearly makes a difference in participant behavior and allows for making inferences into speakers' lexification preferences. Naturally, our signal spaces are tiny compared to real lexicons that humans are able to memorize, not least because our signal space is designed for a lexicon that is to be conventionalized and used in the span of about half an hour. And like in natural languages, the complexity of the lexicon, the number of signals, has a limit. It is just that this limit is cognitive in nature in the real world and appears to be largely artificial (i.e., driven by our constraint on the size of the signal space) in our experiments.

7.1 Extensions and implications

Future research could look into a number of aspects and parameters of the communicative need game, beyond the exploration in our two follow-up studies (Experiments 3 and 4). In terms of setup and procedure, we chose what we assumed would be a reasonably sized meaning space for an experiment of this length, but this, as well as the length itself, is of course arbitrary, as is the chosen co-occurrence distributions that emulate the pressure of communicative need. It would be interesting to see both the effect of stronger and weaker pressures than employed here. Need could also be gradually increased over the course of a longer game to probe the strength of the pressure required for participants to modify an already established artificial communication system (which would loosely correspond to natural language users changing their language over their lifespan; cf. Sankoff, 2018).

In this study, we chose direct similarity or synonymy as the semantic relationship to explore. Xu et al. (2020a) show that conceptual associativity (i.e., the car, engine type) also correlates with cross-linguistic colexification patterns, roughly to the same extent. It would be interesting to use our paradigm to investigate whether dyads preferentially colexify based on associativity or similarity. Another possible predictor, related to associativity, could be co-occurrence probability (or mutual information), which could be inferred from a large text corpus and then tested experimentally. Differences between more fine-grained relationships like register-varying synonymy (abdomen, belly) and hyponymy (bag, purse) could also be probed, as well as how these preferences may correlate with historical patterns of sense formation and expansion (cf. Ramiro et al., 2018).

Xu et al. (2020a) also discuss a potential role of frequency, namely that more commonly referred-to senses may be more likely colexified. We control for frequency in our experiment by making sure the occurrence distribution of meanings is uniform in all games. Future research could let frequency vary systematically to determine its importance. Previous research (cf. Atkinson, Mills, & Smith, 2018; Blythe & Croft, 2021; Raviv, Meyer, & Lev-Ari, 2019; Raviv, de Heer Kloots, & Meyer, 2021; Segovia-Martín, Walker, Fay, & Tamariz, 2020) has also demonstrated that community size and links between individuals has an effect on (artificial) language formation, learnability, and change. Another potentially interesting extension would be to run the colexification experiment using a larger speaker group than a dyad, perhaps also manipulating the connections between participants to investigate the proposed network effects. In our experiment, the participants were only presented with two possible meanings to guess between, to facilitate convergence on systematic associations in a short-time frame. This also means it was trivial to achieve 50% guessing accuracy. In a longer experiment, the number of choices could be increased.

Our work may also have potentially interesting implications for historical linguistics. Population-level changes large enough to register on historical timescales must also start with differential utterance selection on the individual level, before they can compound over time and larger groups to become the norm (cf. Baxter, Blythe, Croft, & McKane, 2006; Croft, 2000). If the mechanisms discussed and experimented with here are representative of utterance selection dynamics in natural languages, then the next interesting question would be: To what extent does communicative need constitute selection in language change? (cf. Andersen, 1990; Baxter et al., 2006; Newberry, Ahern, Clark, & Plotkin, 2017; Reali & Griffiths, 2010; Steels & Szathmáry, 2018). A comprehensive understanding of lexical evolution, and language evolution in general, would benefit from merging the perspectives of individual mechanisms and population-level consensus changes.

7.2 Complexity, information loss, and communicative need

In more broad terms, our study interfaces with a growing body of work on the interplay between the orthogonal pressures of simplicity and informativeness in language evolution. The former relates to ease of learning; while the latter relates to low information loss or communicative cost (the terminology and foci vary between authors and disciplines, cf. Beckner, Pierrehumbert, & Hay, 2006; Bentz, Alikaniotis, Cysouw, & Ferrer-i Cancho, 2017; Carr et al., 2020; Carstensen, Xu, Smith, & Regier, 2015; Denić, Steinert-Threlkeld, & Szymanik, 2021; Fedzechkina et al., 2012; Gasser, 2004; Haspelmath, 2021; Kemp & Regier, 2012; Kirby & Hurford, 2002; Kirby et al., 2015; Nölle et al., 2018; Smith, 2020; Steinert-Threlkeld & Szymanik, 2020; Uegaki (in preparation); Winters et al., 2015; Zaslavsky, Regier, Tishby, & Kemp, 2019b). Thesestudies have yielded converging evidence that languages which are learned and used in communication—the real-world ones, the artificial ones grown in the lab, as well as those evolved by computational agents—all aspire to balance these two pressures, ending up somewhere along the optimal frontier.

Our results provide support for the argument that culture-specific communicative needs may modulate the location of a language on that frontier (cf. Kemp et al., 2018). The pressure for simplicity in lexicons can be relaxed in favor of more expressivity, given high enough communicative need (which we emulated in the target condition, and the no-pressure conditions)—while informativeness can give way to simplicity when a less expressive lexical subspace does the job (cf. our baseline condition).

To allow for systematic statistical testing of the hypothesis in the previous sections, we applied a transformation to the data (outlined in Section 2.6) that operationalized colexification the most objective manner we could think of. Fig. 9 is a reanalysis of data from Experiment 1 along the axes of complexity and expressivity, using an alternate coding scheme. To simplify things, we ignore the sender here and treat the language of each dyad as a collaborative effort. Each message containing a target meaning is assigned a simplified cognitive cost score and communicative cost score between [0,2], which depends on the last most recent reference to the same meaning and the last reference to the synonym (target pair member) of the current meaning. Fig. 9 displays the mean scores for each target meaning pair used by each dyad in Experiment 1, across all their respective utterances. We also simulate the full possibility space of the results under this coding scheme, using a simple agent-based model (shown as gray blocks in Fig. 9). This is to provide meaningful dimensionality to the graph: given the number of signals and meanings, it would be impossible to obtain a maximal score simultaneously on both axes. The technical details of both procedures are further described in the Appendix.

In summary, dyads tend towards the optimal frontier between complexity and expressivity (or in this case, the two optimal points at (1,0) and (0,1); positioning near the bottom left diagonal just indicates mixed strategies). Baseline dyads favor simplicity (having the luxury to do so), while target condition dyads sacrifice simplicity to reduce communicative cost (in response to our manipulation driving them to do so).

7.3 Beyond small subsystems

Extrapolating the communicative need argument beyond the grammatical and lexical subsystems mentioned in Section 1 to the scale of entire languages, we would expect semantic spaces of different languages to be mostly uniform in density—how many words are used to express shades of any given concept or meaning subspace—but differ in exactly where culture-specific communicative needs of the time either require more detail, or where fewer words will suffice (analogous to uniform information density on the level of utterances; cf. Levy, 2018). Previous research has focused on delimited domains of language like tense or kinship. This makes sense both from a data collection and computational point of view: quality cross-linguistic data are not trivial to acquire, and neither is computing complexity, information loss or expressivity, the larger the system under scrutiny. This is then the next challenge: understanding these pressures and the evolution of lexicons and grammars, over time, and cross-linguistically, on the scale of entire languages (as opposed to isolated domains). This would require combining explicitly quantified metrics of simplicity and expressivity (cf. Bentz et al., 2017; Mollica et al., 2020; Piantadosi, Tily, & Gibson, 2011; Steinert-Threlkeld & Szymanik, 2020; Zaslavsky et al., 2019b), some estimate of communicative need (cf. Karjus, Blythe, Kirby, & Smith, 2020; Regier, Kemp, & Kay, 2015), some measure of density or colexification (see Chapter 5.4 of Karjus, 2020, for one potential approach), and if using a machine learning–driven approach such as word embeddings, either a joint semantic model of multiple languages allowing for direct cross-linguistic comparison of lexical densities and colexification (e.g., Chen & Cardie, 2018; Rabinovich, Xu, & Stevenson, 2020; Thompson et al., 2018), or language-specific diachronic semantic models to observe changes in colexification over time (e.g., Dubossarsky, Hengchen, Tahmasebi, & Schlechtweg, 2019; Rosenfeld & Erk, 2018; Ryskina, Rabinovich, Berg-Kirkpatrick, Mortensen, & Tsvetkov, 2020).