Migration between human populations can affect the cultural repertoire of both immigrant and resident (host) groups in a number of ways. In some cases, immigrants adopt cultural variants that are present in the resident population. For example, the diet of Mexican immigrants in the United States is more similar to the diet of non-Hispanic white Americans than it is to the diet of Mexicans1. Immigrant groups can also influence the resident culture. For example, the immigration of approximately 100,000 Chinese immigrants into nineteenth-century Peru substantially influenced Peruvian cuisine. This is evidenced by the culinary tradition of ‘chifa’, which is rooted in Chinese cuisine but incorporates Peruvian elements, and by the general importance of rice as one of the main carbohydrate staples in contemporary Peru2. Other outcomes are also possible: immigrant and resident culture may mix to produce new cultural variants such as Creole languages, or they may retain much of the original culture and often hardly change over long periods of time, as in ethnic enclaves such as Klein-Ankara in Berlin or Chinatowns in the United States and United Kingdom3.

In the social sciences, cultural changes that take place as a result of migration have traditionally been studied in the framework of ‘acculturation’. Acculturation is defined as 'those phenomena which result when groups of individuals having different cultures come into continuous first-hand contact, with subsequent changes in the original cultural patterns of either or both groups'4. Berry5 distinguishes four different acculturation orientations, as resulting from two tendencies: the tendency to maintain the own cultural identity and the tendency to establish relations with the other cultural groups (Fig. 1). Henceforth, we will refer to these dimensions as ‘degree of cultural conservatism’ and ‘interaction tendency’, respectively. To be clear, we use the term ‘cultural conservatism’ in a strict sense, as the tendency to conserve one’s culture (so not in the broader political sense that is associated with the term ‘conservatism’). According to Berry5, a high degree of cultural conservatism can either result in an integration orientation (in case of high interaction tendency) or in a separation orientation (in case of low interaction tendency), while a low degree of cultural conservatism can result in an assimilation orientation (in case of high interaction tendency) or a marginalisation orientation (in case of low interaction tendency).

Fig. 1 Berry’s classification of acculturation orientations5. The four acculturation orientations result from the two dimensions shown on the axes: how much importance individuals give to maintaining their own cultural identity (‘degree of cultural conservatism’, horizontal axis) and how much importance they give to establishing interactions with other cultures (‘interaction tendency’, vertical axis). The four individual orientations can be interpreted as corresponding to possible outcomes of the acculturation process: immigrants are either participating members of the host society that have kept their cultural identity (integration), participating members of the host society that have adopted the host culture (assimilation), socially segregated members of society that have kept their cultural identity (separation), or socially segregated members of society that have not kept their own culture (marginalisation) Full size image

Although Berry’s classification is useful, its societal implications are not immediately obvious, for at least two reasons. First, acculturation orientations may differ between individuals in both immigrant and resident groups, and may change over time3,5,6. It is far from obvious how the acculturation process might unfold in a population that is mixed and/or dynamic with respect to acculturation orientations. Second, there may be mismatches in the orientations of the immigrant and resident groups; for example, immigrants may prefer to integrate (maintaining their cultural identity), whereas residents may prefer immigrants to assimilate (adopting the resident culture3). The societal outcome of the acculturation process in case of such mismatched acculturation orientations is not straightforward to ascertain. For example, it is not clear under which circumstances a multicultural society, in which both immigrant and resident traits stably coexist, is likely to emerge.

Given the dynamic and complex nature of the acculturation process, it is likely that verbal reasoning alone is insufficient to fully appreciate the societal implications of migration on cultural change. The construction of a formal model requires the identification of the important parts of the system and the relationships between them, and forces the scholar to explicitly consider the assumptions that have to be made when developing theory. This facilitates the development of a sharper intuition about the system, and helps avoid mistakes that are easily made when reasoning verbally about complex dynamic systems (see ref. 7 about the benefits of using formal models in the behavioural sciences). Hence, a theoretical modelling approach is needed to aid our understanding. In this study, we develop a model to investigate the dynamics of cultural change that result from migration, depending on the acculturation orientations that are present in the society. To do this, we make use of ideas and techniques from the field of cultural evolution, where there is a significant tradition of studying cultural change using formal methods.

The study of cultural evolution is based on the idea that cultural change is, to a certain extent, a process analogous to genetic evolution8,9,10,11,12. Cultural change can be considered as a type of adaptive evolution, because it meets the three basic requirements of evolution by natural selection13: variation (cultural traits differ between individuals), differential persistence (some cultural traits may spread more readily than others) and inheritance (cultural traits are transmitted between individuals through forms of social learning). There have been some investigations into the role of migration in the process of cultural evolution9,14,15,16, but the effect of acculturation orientations on cultural change has not yet been investigated within this framework.

As social learning is the mode of cultural transmission, the ways in which individuals learn from each other have received much attention in the field of cultural evolution17. It has been shown that individuals use various social learning strategies, including ‘frequency-based learning’, where the probability of acquiring a cultural trait depends on the frequency of that trait in the population (e.g., conformism), and ‘success-based learning’ where individuals preferentially adopt traits from successful individuals18,19. The social learning strategies people use may differ between individuals19 and between cultures20, and these differences can have substantial ramifications for the outcome of social interactions21. To come to a full appreciation of how cultural traits may change in a population with migration, social learning strategies must be part of the equation.

We present a simple model to systematically assess how acculturation orientations and social learning strategies affect cultural change in populations with continuous immigration. We consider a resident population with a constant influx of immigrants, and assume that these two types originally differ in the cultural traits they express. Over time, individuals’ cultural traits may change through interactions with others in the population, depending on their acculturation orientations. Their interaction tendency determines how likely they are to interact with individuals from the other cultural group, and their degree of cultural conservatism determines how likely they are to change their cultural trait as a result of such interactions. We investigate how the outcome of the model depends on model parameters such as migration rate and the acculturation orientations associated with the resident and immigrant cultures.

We consider three versions of the model, which differ in the assumptions they make on social learning. We start with a simple baseline model, in which we consider two cultural traits (initially associated with residents and immigrants, respectively), that are in principle completely arbitrary (i.e., they do not confer any advantages or disadvantages to the individuals that express them). For example, one might think of the different ways the same ingredient (e.g., potato) is used in the cuisines of various cultures (e.g., poutine in Canada, rösti in Switzerland or stamppot in the Netherlands). In this version of the model, the probability that individuals change their cultural traits is fully dependent on their acculturation orientation (social learning strategies are absent in this case). In the second version of the model, we consider cultural traits that have some kind of functional relevance, considering cases where either the immigrant or the resident cultural trait is more advantageous than the other (i.e., confers a payoff advantage to the individual expressing it, such as the usage of gunpowder weapons in warfare). With this model, we investigate how success-based learning strategies affect the spread of cultural traits. In the third version of the model, we study cases where the payoffs of cultural traits are not constant, but depend on the population constitution. Here, we consider both the case where the most common trait has a payoff advantage (coordination, e.g., driving on the left or right side of the road, or salutations with a handshake vs. a bow), and the case where the least common trait is superior (complementation, e.g., practicing a rare trade and therefore having less competition). Throughout, we track the frequencies of the two cultural traits, and determine whether cultural evolution leads to the fixation of either of the traits, or maintains a multicultural society in which both cultural traits coexist.

We find that both the interaction tendency and the degree of cultural conservatism considerably affect the distribution of resident and immigrant culture, across all scenarios we investigated. Specifically, we find that the stable coexistence of both immigrant and resident culture in a single population (i.e., a multicultural society) is more likely if individuals of both cultural types are relatively willing to interact with each other, and if resident culture is associated with stronger cultural conservatism than immigrant culture. These general patterns hold both in the presence and in the absence of payoff consequences associated with both types of cultural traits. These results show that, at least under the assumptions of our model, acculturation orientations have a robust effect on the stability of multiculturalism.