“Effective Population Size for Culturally Evolving Traits”, 2021-09-10 (; backlinks):
Population size has long been considered an important driver of cultural diversity and complexity. Results from population genetics, however, demonstrate that in populations with complex demographic structure or mode of inheritance, it is not the census population size, N, but the effective size of a population, Ne, that determines important evolutionary parameters. Here, we examine the concept of effective population size for traits that evolve culturally, through processes of innovation and social learning.
We use mathematical and computational modeling approaches to investigate how cultural Ne and levels of diversity depend on (1) the way traits are learned, (2) population connectedness, and (3) social network structure.
We show that one-to-many and frequency-dependent transmission can temporally or permanently lower effective population size compared to census numbers. We caution that migration and cultural exchange can have counter-intuitive effects on Ne. Network density in random networks leaves Ne unchanged, scale-free networks tend to decrease and small-world networks tend to increase Ne compared to census numbers. For one-to-many transmission and different network structures, effective size and cultural diversity are closely associated. For connectedness, however, even small amounts of migration and cultural exchange result in high diversity independently of Ne.
Our results highlight the importance of carefully defining effective population size for cultural systems and show that inferring Ne requires detailed knowledge about underlying cultural and demographic processes.
Author Summary: Human populations show immense cultural diversity and researchers have regarded population size as an important driver of cultural variation and complexity. Our approach is based on cultural evolutionary theory which applies ideas about evolution to understand how cultural traits change over time. We employ insights from population genetics about the “effective” size of a population (ie. the size that matters for important evolutionary outcomes) to understand how and when larger populations can be expected to be more culturally diverse. Specifically, we provide a formal derivation for cultural effective population size and use mathematical and computational models to study how effective size and cultural diversity depend on (1) the way culture is transmitted, (2) levels of migration and cultural exchange, as well as (3) social network structure.
Our results highlight the importance of effective sizes for cultural evolution and provide heuristics for empirical researchers to decide when census numbers could be used as proxies for the theoretically relevant effective numbers and when they should not.
…To understand what we gain from the effective size, even if we are not particularly interested in Wright-Fisher models, let us assume there are two populations, A and B, that produce a particular cultural trait with many possible variants. We now want to know whether population size affects the number of different traits in a population. Population A has a large census population size of 1,000 individuals, population B has a smaller census size of just 500. Using a theoretical model of a cultural evolutionary process [eg. 2001, 2004, et al 2009, et al 2017], we conclude that larger populations should have larger or more complex cultural repertoires. Can we expect to find this demographic relationship in data on census population sizes and cultural repertoire sizes from both populations [eg. 1976]? The answer is that—regardless of how good the model is—the relationship is unlikely to be found unless these real populations are identical in some evolutionarily important ways. If they do not have the same age structure, demographic history, or, as we show below, cultural transmission mechanisms and interaction patterns, the populations are not directly comparable, except through their relation to a simpler model—through their effective population sizes.
Imagine we now discover that, 10 generations ago, population A had a population bottleneck where its census size fell to only 10 individuals before recovering to its current value of 1,000. Genetic evolution will be affected by this bottleneck for a number of generations (culture might recover from such events much faster than genetics [2020]). Both populations are otherwise identical and conform to the assumptions of the Wright-Fisher model, which we detail below.
Accordingly, the effective population size of the small, stable population B is 500, the same as its census size. The effective size of population A, however, is only around 92 (see Appendix 1 for calculation). We can now use results from population genetics to calculate how many cultural traits we expect to see in each population, given certain transmission mechanisms and innovation rates. For population B with Ne = 500, the expected number of traits is 223. For population A with Ne ≈ 92, we expect to see on average 41 traits in a given generation (see Appendix 1 for full details). Thus, although a relationship exists between effective population size and cultural diversity, a straightforward relationship does not exist between census size and diversity. Using census numbers or more informal definitions of effective size will produce incorrect results.
…We have systematically examined effective population size, a concept derived from theoretical population genetics, for culturally evolving traits. The effective size allows us to compare populations, where it would otherwise be difficult to do so. We showed that both modes of cultural transmission and relevant elements of population structure can change the effective size compared to the census size, sometimes considerably. One-to-many and frequency-dependent transmission can substantially lower effective population size with the strongest effects of frequency dependence occurring when the system is out-of-equilibrium. Investigating different forms of connectedness between populations, we found that migration as we define it does not increase Ne and cultural exchange among groups increases inbreeding effective number but not variance effective number. This implies that considerable precision and caution is needed in defining cultural effective sizes.
Finally, while random networks with varying densities leave Ne unchanged, scale-free networks tend to decrease and small-world networks tend to increase Ne compared to the census number…Our results show that, when there are a few highly influential individuals who—through transmission modes—strongly influence the cultural makeup of the population, the census size and the effective size can diverge. Similarly, where populations are organized into social networks in which individuals are heterogeneous with respect to their degree, the ratio between census and effective size can either increase or decrease depending on network structure. These results also highlight that even relatively small populations might be able to maintain comparatively high levels of cultural diversity if connections are structured in a certain way. [see selection amplifiers]