**5. Conclusions**

In this paper, we have presented a model about how lexical variation is affected by societal structure, with an emphasis on shared context. The model validates theories from situations of sign language emergence which find that smaller, insular communities with high degrees of shared context exhibit high degrees of lexical variation, while larger, dispersed communities with more diverse backgrounds (and hence less shared context) exhibit more lexical uniformity. We have shown that shared context, as well as population size, are probable factors influencing lexical variability. Though several additions to the model would yield a more realistic language representation and hence a more valid model, this simple model provides a first step.

**Author Contributions:** Conceptualization, K.M., B.d.B. and C.d.V.; methodology, K.M., B.d.B. and C.d.V.; software, K.M.; analysis, K.M.; visualization, K.M.; writing—original draft preparation, K.M.; writing—review and editing, K.M, B.d.B. and C.d.V.; funding acquisition, B.d.B. and C.d.V.; All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by FWO-NWO gran<sup>t</sup> number [NWO 326-70-002; FWO G0B4317] "The emergence of phonology within six generations" awarded to Bart de Boer, Paula Fikkert, and Connie de Vos, and by ERC under the ERC Starting Grant [ELISA—852352] "Emergence of Language in Social Interaction" awarded to Connie de Vos, as well as by the Flemish AI plan.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Model code and instructions on how to run the model and produce the plots can be found at: https://doi.org/10.6084/m9.figshare.15163872.v1.

**Acknowledgments:** We would like to thank Peter Dekker, Marnix Van Soom and Yannick Jadoul for helpful feedback in the initial stages of model development and to Marnix van Soom, Heikki Rasilo, Andrea and Alex Mudd for feedback on and help with producing the plots.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Appendix A. Parameter Exploration**

*Appendix A.1. Initial Degree of Iconicity*

The fixed parameters during this parameter exploration are: *n\_concepts* = 10, *n\_bits* = 10, *n\_agents* = 10, *n\_steps* = 4000. The parameters that are varied are *n\_groups* and *initial\_degree\_of\_overlap*.

**Figure A1.** The mean lexical variability over the 2000 model stages for different numbers of groups that agents can be assigned to (*n\_groups*): 1, 5 and 10, while varying the degree of overlap between the form and culturally salient features at the start of the run (*initial\_degree\_of\_overlap*). The dark line represents the mean and the shaded area represents the standard deviation of the 100 repetitions. With one exception (*n\_groups* = 1 and *initial\_degree\_of\_overlap* = 1), the higher the initial degree of overlap between form and culturally salient features, the lower the mean lexical variability. In addition, the higher the initial overlap between form and culturally salient features, the higher the degree of iconicity.

As shown in Figure A1, when there is only one group where the form and culturally salient features completely overlap, lexical variability is 0 (i.e., all agents have the exact same form for each concept). Except in this case, for all group sizes, smaller overlaps between the form and culturally salient features (*initial\_degree\_of\_iconicity*) result in a lower level of lexical variability. In other words, less lexical similarity initially leads to more uniform productions. With regards to the degree of iconicity, the degree of iconicity is higher in populations with a more initial overlap between form and culturally salient features.

#### *Appendix A.2. The Number of Concepts*

The fixed parameters during this parameter exploration are: *n\_bits* = 10, *n\_agents* = 10, *n\_groups* = 5, *initial\_degree\_of\_iconicity* = 0.9, *n\_steps* = 2000. The number of concepts is the only parameter that varied.

**Figure A2.** The mean lexical variability over the 2000 model stages for numbers of concepts (*n\_concepts*): 1, 5, 10, 20, 50, 100. The dark line represents the mean and the shaded area represents the standard deviation of the 100 repetitions. When there are more concepts, the initial value of lexical variability increases. While the runs with few concepts quickly stabilize at a fairly high degree of lexical variability, the runs with more concepts have a lexical variability value which continues to decrease. The degree of iconicity is comparable across runs with different numbers of concepts, though runs with more concepts retain a higher degree of iconicity longer before stabilizing.

Figure A2 shows the model results of how a different number of concepts affects lexical variation over time. Beginning with runs with a low number of concepts, the lexical variability value quickly stabilizes near the starting lexical variability value. However, in runs with more concepts, the mean lexical variability initially increases before decreasing. The runs with 50 and 100 concepts do not stabilize after 2000 stages. However, it is clear that runs with a larger number of concepts ultimately results in a lower lexical variability value. Why would this be? When there are 2 concepts and 10 bits, because there are only 2 concepts needed to successfully communicate, there is less pressure for the forms to be identical. With few competing concepts, this means that as long as the form from one is different enough from the form of the other, communication will be successful. However, with more concepts, there is more pressure towards uniformity due to the number of competing concepts. In addition, the final degree of iconicity is comparable across runs with different numbers of concepts. However, for runs with more concepts, the degree of iconicity remains higher for longer before reaching a stable point. This is likely because each step of the model only has one language game and hence one chance to update a form. Thus, with more concepts, it takes longer for all forms in the population to update and move away from the initial level of iconicity.

#### *Appendix A.3. The Number of Bits*

The fixed parameters during this parameter exploration are: *n\_concepts* = 10, *n\_agents* = 10, *initial\_degree\_of\_iconicity* = 0.9, *n\_steps* = 2000. The parameters that are varied are *n\_groups* and *n\_bits*.

Figure A3 shows how lexical variability is affected by the number of bits of the forms and culturally salient features. The number of bits affects lexical variability at stage 0, with more bits yielding a higher lexical variability value. Overtime, the more bits there are the more lexical variability is maintained. When there are few bits (*n\_bits* = 5), the lexical variability value quickly decreases, before stabilizing above 0. It is probable that these stark differences are the result of using a binary distance measure and the amount of stages that the model was run for: With more bits, more time is needed to make the forms the same. The non-binary distance measure would reveal more similarities across forms. There is, of course, a relationship between the number of bits and the number of concepts in the model; for example, with a large number of bits and few concepts not all bits of a form would need to be identical across the population for the same concept. As long as communication is successful given the pressures imposed by the bits and concepts, there will not be pressure for the population to fully converge on the exact same form for each concept. Thus, for when there are many bits for the form and culturally salient features (when there are few concepts), it would make more sense to have a more nuanced distance measure, taking into account the degree of overlap between forms produced across the population for a given concept.

**Figure A3.** The mean lexical variability over the 2000 model stages for runs with a different number of bits (*n\_bits*): 5, 10, 20, 50, 100 and for different numbers of groups that agents can be assigned to (*n\_groups*): 1, 5, 10. The dark line represents the mean and the shaded area represents the standard deviation of the 100 repetitions. The lexical variability value is higher when there are more bits. The number of bits also affects the lexical variability value at stage 0. The more bits, the higher the iconicity level.

Finally, with regards to iconicity, the more bits there are, the higher the degree of iconicity. When the language game ends with a bit update, only one bit is updated regardless of the number of bits. Hence, with more bits, it will take longer for the forms to move away from their iconic starting point. In addition, the level of iconicity interacts with the number of groups: With fewer groups, the iconicity remains higher than with more groups. For instance, when all agents belong to the same group, their forms are similar and they are likely to additionally make use of the iconic–inferential pathway. Without the need for bit updating in the case of communicative failure, the level of iconicity in the population remains high.
