This paper presents a simple model of linguistic priming between languages in contact, based on the utterance selection model (USM) for language change of Baxter et al. (2006). It will be shown that the emergence or the non-emergence of a new contact language depends on the way potentially bilingual agents choose a language to communicate.
One major factor driving language evolution is the interaction of its speakers. In our paper, we consider a situation where speakers of two different communities are in contact, and where (at least some of) the speakers of the two groups need to communicate with one another. There are basically two ways of resolving the communicative problem in such cases: speakers can either use (some variant of) their community languages or a contact language can emerge — which corresponds to neither of the two community languages. This new language, which can take the form of a pidgin, is not random and highly correlates with the two languages it originates from. The fine-grained processes controlling this process are poorly understood. In this paper, we provide a simple computational simulation of the stochastic dynamics of a contact situation. We show that the way agents choose a language when they interact partly controls the emergence of a contact language.
In order to capture the stochastic aspects of
linguistic interactions, Baxter et al. (2006) designed
the utterance selection model (USM) for language
change
We study a simple extension of the USM that models potentially bilingual agents and explicitly takes into account a priming effect between the two languages to model a situation of language contact. In particular, we study how the choice of a specific language in the interaction can lead either to the coexistence of the two group languages or to the emergence of a new contact language. 2
Our model is an extension of the USM for language
change
U h, λ u(i) u(j)
h, λ U x(j)
In order to communicate, an agent i produces an utterance u(i) of length L from a production process U (u := U x). The process U is defined by
1
U x = L MMulti(L; x); (1) where M is a matrix representing production errors or innovations and Multi(L; x) is a vector counting the outcome of L multinomially sampled variables.
During an interaction, two connected agents are randomly selected. Then, they both produce an utterance u and update their usage frequency distribution x by
x(i);new = x(i);old + x(i); where the increment x(i) is defined by x(i) = [(1 h) u(i) + hu(j) x(i);old]; where is a usually small learning parameter and the attention parameter h controls the relative importance of the utterance u(j) of the other agents with respect to her own utterance u(i). The presence of u(i) accounts for a self-monitoring process and the presence of u(j) accounts for an accommodation process. This learning rule assumes communicative success.1
1One way of interpreting this is to assume that the context and non-verbal communication provide sufficient clues for the interpretation. (2) (3)
The USM has been used to study the conditions
under which a consensus can be achieved in a
population
In order to model a language contact situation, the USM needs to take into account the possibility that agents become bilingual. We assume that each agent belongs to a group labelled by capital letters (A; B; : : : ) and every agent knows the group membership of every other agents. An agent belonging to some group Y is able to represent two languages and we denote the corresponding frequency vectors xY for the group language Y and xY¯ for the non-group language Y¯ . With this modification, the utterance production and learning rules have to be adapted.
During an interaction, if two agents belong to the same group, they interact as usual using the standard USM production and learning rules. If the two agents belong to different groups, we consider two scenarios:
agents of different groups interact, they both adapt to the other agent. For example if agent i of group A and agent j of group B interact, they both use their non-group language, i.e. A¯ and B¯, respectively.
Scenario 2: Unilateral adaptation When two agents of different groups interact, for each interaction they randomly choose a group language to use, either A (with probability p) or B (with probability 1 p), and the agent who doesn’t know the language uses his non-group language. For example, if agent i belongs to group A and agent j belongs to group B, then one language is chosen randomly, say language of group A, then agent i uses her group language and j her non-group language B¯.
When an agent uses her group language, her knowledge of the language is assumed to be perfect and she uses the corresponding frequency vector. However, when an agent needs to use a non-group language, her knowledge is only partial and the non-group language is primed by the group language. This priming is implemented by the rule that whenever a non-group language has to be used, instead of using the frequency vector xA¯ purely, the group language frequencies modifies the distribution through xA¯;eff = (1 ) xA¯ + xA: (4) The priming parameter models the degree of mixing between languages A and A¯. If = 0, then there is no priming and the effective frequency vector boils down to xA¯ and if = 1, then priming is total and the effective frequency distribution xA¯;eff = xA. In the production rule (1), it is the effective frequency vector xA¯;eff that is sampled. The learning rule (2) is the same but is only applied to the languages associated with the interaction.
The social structure used in our model is made of two random regular graphs of degree 3, containing 20 agents each, connected with each other by 5 connexions, see Fig. 2. The agents situated at an end of an intergroup connexion are the potentially bilingual agents, the other agents are monolingual, since they never use their non-group language. We measure the outcome of the simulation by computing Pearson’s correlation coefficient between the time series of the averaged use of a language by each group. Note that the non-group languages are only used by agents with intergroup connexions and only these agents are updating their non-group language and can, therefore, become bilinguals.
We introduce the following notation: rXY correlation between language X of group A and language Y of group B, illustrated in Fig. 3. If rXY is close to 1, then the two languages can be considered Group A xA x A¯ rAB as being the same. If rXY is close to 0, the two languages are independent. For medium values of rXY the languages are different but correlated. 3
For the simulation of the two scenarios, we used the network topology discussed in Sec. 2.2 and illustrated in Fig. 2. The parameters are N = 40 agents with 5 intergroup connexions, the number of variants is V = 3, and the utterance length is L = 2. The learning parameter = 0:1 and the attention parameter h = 0:5. The matrix M used to simulate errors and innovations is of the form 21 6 M = 66 q 66 0 4 q 1 q 0 q 1 q 3
7 0 77 ;
7 q7 5 (5) where q = 3 10 4. The structure of this matrix is such that the innovations are ordered and variant 1 can only be transformed into variant 2, but not into variant 3, and similarly for the other variants. The pattern of mutation/innovation should be read columnwise. The simulations have been performed for T = 5000 full network updates and the priming parameter is varied.
In Scenario 1, two interacting agents of different groups used their non-group language. Results are displayed in Fig. 4 and we observe that the correlation between xA and xB (r AB) is close to zero for all values of the priming parameter ; the correlation between xA¯ and xB¯ (r A¯B¯ ) is close to one for all values of the priming parameter ; the other correlation coefficients grow from 0 to about 0:7 when is increased. From these results, one can conclude that there are three languages in these settings, the language of group A, the language of group B, and a new contact language A¯ = B¯ partly correlated with both languages.
In Scenario 2, when two agents of different groups interact, at each interaction, they choose language A with probability p and language B 10−3 10−2 10−1 Priming Parameter ρ 100 with probability 1 p. Here p = 0:5 and the two languages are equivalent. Results are displayed in Fig. 5 and we observe that r AB¯ and r A¯B are close to one for all values of and the other correlation coefficients increase from zero to one as increases. In this situation, there are only two languages present, the two group languages. When is large enough, the two languages converge to the same language and there is a single language remaining. 4
We have shown that the decision of which language to use has an important impact on the outcome of the simulation, and can lead either to the emergence of a contact language, or to the stable cohabitation of the two group languages. Compared to the naming rAB rA B¯ rAB game model of Tria et al. (2015), the agents of our model do not instantaneously learn or forget a language but gradually adapt their behaviour. As a result, the emergence of a contact language, or absence thereof, is more gradual and better accounts for the influence of the stance that agents take during intergroup communication.
Our model makes a number of idealising assumptions. First of all, we assume that there is no reason to choose one language rather than the other for intergroup communication — which implies the absence of any hierarchy between the languages (or groups). This is probably a rather rare setting in the wild. There are different degrees of divergence from this configuration: instead of a perfectly symmetric situation with a probability p = 0:5 for using each language, there may be a different p tilted towards one group language. In extreme cases, if p = 1 or 0, or when the priming parameter = 1, the agents of one group do not adapt to the language of the other group at all. Therefore, their group language will always be used, forcing the agents of the other group to adapt. Furthermore, in our model, the preferences and attitudes of the agents as well as the network structures do not evolve over time (bilinguals cannot switch group allegiance, etc.).
That being said, in which circumstances of reallife language contact would we expect the two scenarios we have considered to arise? Notice first that the asymmetric scenario should have a lower cognitive cost than the symmetric one, since only one agent in an intergroup interaction needs to adapt his behaviour, whereas scenario 1 requires both agents to do so. Using this argument, scenario 2 should be preferred overall and no contact language should emerge. One can also argue that an asymmetric scenario will take longer to reach a consensus through the population. As a consequence, if the pressure for communication is strong enough, the more costly, but more rapidely converging scenario 1 would be preferred and a contact language is likely to emerge. The additional cognitive cost of a symmetric adaptation should be partly compensated by the fact that contact languages are usually simpler than fully-fledged languages.
To conclude, scenario 1 is expected if communication pressure is strong and the group languages are unrelated. Otherwise, we expect scenario 2. This is consistent with the conclusions of Tria et al. (2015) concerning the influence of population structure on communicative needs and creole-formation. We would like to thank the three anonymous reviewers for their comments on a previous version of the paper. We would also like to thank the members of the project “Parallel Evolutions”, on whom we inflicted a first version of this paper. All remaining errors and omissions are ours alone.