The role of speaker population size in shaping patterns and rates of language and cultural evolution has been much discussed, but few generalities have been agreed upon. It has been suggested that larger populations should have higher rates of language change, because populations containing more individuals provide more opportunity for innovations to arise (Richerson et al., 2009; Kline and Boyd, 2010; Baldini, 2015). Large populations might also be less prone to random sampling effects that can cause elements of language and culture to be lost (Shennan, 2001; Henrich, 2004; Kline and Boyd, 2010; Collard et al., 2013) and they may have less stringent norm enforcement allowing them to change faster (Bowern, 2010; Trudgill, 2011). Larger populations might also have more robust transmission systems: having more people to learn from might increase fidelity of information transition (Derex et al., 2013), possibly because learners in large populations have a large set of potential models to learn from (Henrich, 2004; Kline and Boyd, 2010). Exposure to more people may make learning more robust, potentially allowing retention of a wider range of linguistic diversity (Trudgill, 2004; Hay and Bauer, 2007; Atkinson, 2011; Wichmann et al., 2011; Derex et al., 2013), although this effect is not universally supported (Caldwell and Millen, 2010; Read, 2012).

Other researchers have proposed that rates of change should be fastest in small populations due to the more rapid diffusion of new features (Nettle, 1999). Languages spoken by small speaker populations might be able to develop and retain greater linguistic complexity (Nettle, 2012). Smaller populations may have greater tolerance of diversity (Milroy and Milroy, 1985, 1992) and more malleable linguistic representations (Lev-Ari, 2017) which could speed up rates of change. Further, it has been suggested that the rate of language change may be accelerated by serial founder effects as new languages are started from relative small populations (Atkinson et al., 2008), which could increase the rate of loss of language elements from the ancestral language (Trudgill, 2004; Atkinson, 2011). Small speaker populations may also be more influenced by language contact through trade and marriage across groups, which might increase rates of language change (Bowern, 2010).

In contrast, other studies have found little or no significant effect of population size on the rate of language change or phoneme inventory size (Wichmann and Holman, 2009; Moran et al., 2012). If languages evolve in a purely stochastic manner, analogous to neutral molecular evolution, then rates of change might be independent of population size (Neiman, 1995; Shennan and Wilkinson, 2001; Bentley et al., 2004). The controversial claim that the average rate of word turnover is essentially the same in all languages, has led to much-disputed attempts to date language diversification by assuming a uniform rate of change over time (for examples of contributions to this debate see: Swadesh, 1952, 1955; Hoijer, 1956; Rea, 1958; Bergsland and Vogt, 1962; Sankoff, 1970; Blust, 2000). A similar effect has been suggested for cultural evolution because, for a variety of cultural traits from Neolithic pottery motifs to modern American pop songs, the frequency of variants matches the predictions of a purely stochastic model such that the rate of change is reasonably regular (Bentley et al., 2007).

So, despite many studies on a wide range of languages and language features, there is no consensus on whether population size has a consistent influence on patterns and rates of linguistic evolution (Bowern, 2010; Greenhill, 2014). The lack of a consistently predictable influence of population size on language change might indicate that it is not a universally important factor in rates of language change. Alternatively, the inconsistent patterns might also be due to complicated patterns of change. For example, if rates of word gain show different relationships with population size than rates of word loss, then overall rates of change may show no consistent pattern, and the patterns uncovered in any study might depend on the mode of measuring language change (Bromham et al., 2015a). The diversity of conclusions in published studies could also arise from the diversity of languages studied, data types analyzed, or methodological approaches.

Testing these hypotheses has been challenging for several reasons. Most studies analyzing rates of language change have focused on features within one language (e.g., Johnson, 1976), or relied on simulations (e.g., Nettle, 1999), making it difficult to draw general conclusions about language change. Comparative studies of language change also need a way of overcoming the problem of statistical non-independence due to relatedness. Since languages evolve and diversify from shared ancestors, closely related languages are likely to be more similar to each other in many ways. This similarity by descent means that any association between the two traits might simply be due to the co-occurrence of the traits in a common ancestor, even if there is no functional connection between the two. Therefore, statistical tests cannot treat each language as an independent piece of evidence about the relationship between population size and the patterns of language evolution. This methodological problem, often referred to as Galton's problem, can confound attempts to find relationships between language and demographic factors (Moran et al., 2012; Roberts and Winters, 2013).

Our aim in this paper is to examine the influence of one aspect of demography (size of speaker population) on one aspect of language evolution (the gain and loss of words from basic vocabulary). Specifically, we wish to test whether the association between population size and rates of word gain and loss noted in a study of 10 pairs of Polynesian languages reflects a general pattern. The study of Polynesian languages compared the gain and loss of cognate terms for basic vocabulary and demonstrated greater rates of word gain in larger populations and greater rates of word loss in smaller populations (Bromham et al., 2015a). In many ways, Polynesia represents a perfect “laboratory” of language evolution, with a recent, well-characterized history of colonization of previously uninhabited islands (Goodenough, 1957). Most Polynesian languages are restricted to clearly-defined groups of islands, and the population size of speakers is closely correlated with the area inhabited (Bromham et al., 2015a). As they are the product of a recent human expansion (Spriggs, 2010), Polynesian cultures, and languages share many similarities (Pawley, 1967) and are largely found in similar environments (Kirch and Green, 1987). While these features make Polynesia an ideal case study in language evolution, it also makes it difficult to extrapolate from the patterns observed in Polynesia to general patterns of language evolution. Do languages spoken in other parts of the world by much larger groups of people with wider continental distributions show similar patterns?

To test the generality of the relationship between population size and rates of word gain and loss, we chose 153 pairs of closely related sister languages from three of the largest language families, Austronesian, Indo-European, and Niger-Congo (Bantu subfamily). The languages in our analysis are from a wide geographic area, from the North Atlantic to the South Pacific (Figure 1). These language pairs span a huge range of speaker population sizes, from Perai to Aputai spoken on the island of Wetar in the Maluku province of Indonesia (spoken by 280 and 150 people, respectively), to Sambaa and Bondei spoken in the mountain regions of Northern Tanzania (664,000 and 50,000 people), to German and Luxembourgish in continental Europe (spoken by 69,800,000¹ and 266,000 people respectively). For each of these families, we used published linguistic databases of basic vocabulary to evaluate relative rates of word gain and loss, using a technique that explicitly accounts for non-independence due to the relatedness of the languages.

The Poisson regression of population size and rates of change in the Indo-European language family (14 pairs) suggests that languages with smaller speaker population sizes had significantly higher rates of word loss (Table 4, Figure 3). Least squares regression also suggests a significant negative relationship between contrasts in population size and contrasts in the rate of word loss (coefficient = −0.13, P = 0.05, R² = 0.22). However, this result is no longer significant when a single shallow pair, Upper and Lower Sorbian (Lusatian_U and Lusatian_L) are removed following the Welch & Waxman test (Table 5, Figure 4).

We found no evidence of a significant association between rate of word gain and population size in the Indo-European language pairs, nor in gains or losses for the Austronesian and Bantu data (Tables 4, 5, Figure 4). One possible explanation for the observation of a significant relationship between rate of language change and population size only in the Indo-European languages is that we expect this dataset to have relatively higher power to detect differences in rates of change. Although the Indo-European dataset has many fewer pairs than the Austronesian or Bantu datasets, the Indo-European word list contains more cognates per category: that is, there are more synonymous lexemes per word (see Table 6). The test we use to detect rate differences is broadly based on the Tajima test (Tajima, 1993), the power of which is dependent on the number of variable sites, which are columns in DNA alignments in which the sequences being compared differ from each other (Bromham et al., 2000). It may be that the more synonyms recorded per lexical category, the more likely we will record a true gain and less likely we will record a false loss (i.e., a synonym is used less frequently in a language but not completely lost). This may be a particular problem for the Bantu dataset which has the fewest synonyms as it was collected following Swadesh's (1952, 1955) approach whereby only the most frequent word was entered for each lexical category. This means that cognates may be retained in lineages even if not recorded, if there are in less frequent usage than a more predominant form. A gain, in this case, may represent the rise in frequency of one cognate over alternatives, therefore may not involve the loss of an alternative form. Given the differences in the nature of the recorded data, we do not know whether the lack of significant relationships for the Bantu and Austronesian data is due to lack of a consistent association between population size and rates of word gain and loss in these language groups, or due to biases in counts of word gain and loss and thus insufficient power to detect rate differences for these datasets.

Languages evolve, creating patterns of descent and relatedness reminiscent of biological species. Because of this, tools from evolutionary biology are being increasingly applied to studying language change (Levinson and Gray, 2012; Gavin et al., 2013; Bromham, 2017). However, we cannot assume that the mechanisms underlying change, or the observed patterns and rates of change, will be the same for both languages and biological lineages.

Evolutionary theory makes clear predictions about the relationship between population size and rates and patterns of genetic change. Selection is more efficient in large populations, so deleterious mutations should be removed more effectively, and advantageous mutations should more rapidly go to fixation. However, in smaller populations, random sampling effects can have a comparatively greater impact on the frequency of genetic variants, so that positively selected mutations may be reduced in frequency by chance, and may thus occasionally be lost rather than going to fixation. Conversely, in small populations, slightly deleterious changes may increase in frequency by chance, and may eventually drift to fixation, leading to the loss of other variants at that locus (Charlesworth, 2009; Lanfear et al., 2014).

In contrast, the effects of population size on language evolution are not as straightforward to predict, and many alternative hypotheses have been suggested. Large populations of organisms generate more mutations per generation because there are more genomes in the population that can undergo change. Languages with large speaker populations might be expected to generate more innovations (Kline and Boyd, 2010; Collard et al., 2013), however unlike genetic mutation, the processes that create new language variants are not well understood, and may occur by a wider range of mechanisms. Unlike mutation, which is random with respect to utility, introduction of new language variants can be guided by perceived need, and can be regulated by social convention or top-down rules (see Bromham, 2017). Similarly, rates of language change may show different patterns to genetic change if the process of substitution is by horizontal spread of variants through the population, rather than by inheritance (Reali and Griffiths, 2010). So, unlike adaptive genetic change in biological populations, it is possible that smaller speaker populations might have a greater rate of adoption of innovations because it is easier for new words to diffuse to all speakers and replace all other variants (Nettle, 1999). It is therefore difficult to predict whether smaller or larger speaker populations should have greater rates of language change, whether patterns should be the same or different for both gains and losses of language elements, and whether we expect similar patterns across all language families or more idiosyncratic associations, particular to given language groups.

Our analysis suggests that, as for Polynesian languages, smaller Indo-European languages have greater rates of word loss from basic vocabulary. This result is consistent with the claim that smaller populations are at greater risk of loss of language elements, and other aspects of culture, due to effects of incomplete sampling of variants over generations. However, we note that the relatively small sample size for this dataset complicates the interpretation of this result. Least squares regression after Welch & Waxman test has the same false positive rate but has much less power than Poisson regression when sample size is small (~ten or fewer pairs, Hua et al., 2015). This makes it difficult to interpret the inconsistent results of these two analyses, as they may be due to their difference in the statistical power. Hence, the negative relationship between rates of loss and population size for Indo-European languages would benefit from additional investigation. We do not find evidence for a negative relationship between population size and word loss rates in the Austronesian and Bantu groups. This finding suggests that either these datasets contain too few language variants to have sufficient power to detect rate differences, or that the increased loss rate in small populations is not a universal phenomenon, or that it is a relatively weak force in some language groups and thus may be overwhelmed by other social, linguistic or demographic factors.

One factor that may be playing a role in the uncertainty in our results, and in the wider debate in general, is that measuring speech community size is notoriously difficult. How exactly does one delimit a speech community (Crystal, 2008) and what degree of proficiency in a language is sufficient to be part of the community (Bloomfield, 1933)? This task is made harder as there are few national censuses that collect detailed speaker statistics. Further, speaker population size can change rapidly with many modern world languages (especially the Indo-European languages) experiencing rapid growth over the last few hundred years (Crystal, 2008), while others have experienced catastrophic declines (Bowern, 2010). For the same reasons, the difficulty of obtaining accurate population estimates is also a problem in biology. Furthermore, the relevant parameter for genetic change—the effective population size—is difficult to estimate directly, even when accurate census information is available (Wang et al., 2016). Likewise, there may be an important role played by population and network density—tight-knit networks may inhibit change, while loosely integrated speech communities (regardless of their size), may facilitate change (Granovetter, 1973; Milroy and Milroy, 1992). One way forward here is perhaps to simulate rates of change over a range of population sizes and network topologies (c.f. Reali et al., 2018).

Despite the obvious challenges in obtaining an accurate measure of speaker population size, several previous studies have reported that empirical estimates of population size do correlate with aspects of language change (Hay and Bauer, 2007; Lupyan and Dale, 2010; Bromham et al., 2015a). Therefore, either census population size, as reported in databases such as the Ethnologue, are sufficiently accurate reflections of speaker population size that they are able to reveal significant patterns of language change, or census population size is reflecting some aspect of languages that is connected to change. In either case, the reported relationships with speaker population size invite further investigation.

We can draw two conclusions from these results. Firstly, we provide some evidence that rates of language change can be affected by demographic factors. Even if the effect is not universal, the finding of significant associations between population size and patterns of linguistic change in some languages urges caution for any analysis of language evolution that makes an assumption of uniform rates of change. These results also potentially provide a window on processes of language change in these lineages, providing further impetus to investigate the effect of number of speakers on patterns of language transmission and loss. A more detailed study of language change for a larger number of comparisons might clarify the relationship between population size and word loss rates, particularly within the Indo-European language family.

Secondly, we have shown that the significant patterns of language change identified in a previous study are not a universal phenomenon. Unlike the study of Polynesian languages, we did not find any significant relationships between word gain rate and population size, and the association between loss rates and population size was not evident for all language families analyzed. The lack of universal relationships suggests that it may be difficult to draw general conclusions about the influence of demographic factors on patterns and rates of language change. Many other factors have been proposed to influence rates of language change (Greenhill, 2014) including population density, social structure (Nettle, 1999; Labov, 2007; Ke et al., 2008; Trudgill, 2011), degree of contact, and connectedness with other languages (Matras, 2009; Bowern, 2010), degree of language diffusion within a speech community (Wichmann et al., 2008), degree of bilingualism or multilingualism (Lupyan and Dale, 2010; Bentz and Winter, 2013), language group diversity (Atkinson et al., 2008) and environmental factors such as habitat heterogeneity and latitude (Bowern, 2010; Blust, 2013; Amano et al., 2014). These factors might mediate or overwhelm the effect of speaker population size.

We find no evidence to support the hypothesis that uptake of new words should be faster in small populations, which is based on the assumption that new words can diffuse more efficiently through a smaller speaker population than a larger one (Nettle, 1999). Nor do we find support for the suggestion that large, widespread languages have a tendency to lose linguistic features a greater rate (Lupyan and Dale, 2010). However, this latter hypothesis is predominantly expected to explain loss of complex linguistic morphology (such as case systems), which may be harder for non-native speakers to learn, rather than basic vocabulary studied here which may be comparatively easier for second language learners to acquire (but see Kempe and Brooks, 2018). Further, our results cannot be interpreted as confirmation of previous studies that suggest there is no effect of population size on rates (Wichmann and Holman, 2009). The detection of significant patterns in rates of lexical change with population size variation in the Polynesian and Indo-European languages, but the failure to identify similar patterns in the Bantu and Austronesian data, suggests that patterns of rates may need to be investigated on a case-by-case basis.

The failure to find a consistent association between population size and rate of change for languages means that analogies drawn between biological and linguistic evolution must be carefully considered to make sure that they are appropriate for linguistic evolution (Bowern and Evans, 2014). For example, patterns of human migration can leave similar traces on both genetic and linguistic diversity (Hurles et al., 2003; Hunley et al., 2007, 2008; Longobardi et al., 2015), but even though the patterns are the same, the underlying mechanisms may not be identical. The observation of decreasing phoneme inventories along chains of human migration has been attributed to serial founder effects (Trudgill, 2004; Atkinson, 2011). While founder effect is likely to influence genetic variability, because a small number of colonists cannot carry all of the genetic variation of the parent population, it might not have the same effect on language variants, as the founding population may use all the main variants in basic vocabulary. Similarly, while a correlation between lineage diversity and rate of change has been reported for both genetic and linguistic evolution (Pagel et al., 2006; Atkinson et al., 2008; Lanfear et al., 2010; Bromham et al., 2015a), it may not reflect a shared mechanism: while formation of new languages may drive higher rates of word turnover, speciation itself is unlikely to drive faster mutation rates in molecular evolution. Our results suggest that the population size effects may be another example of a pattern that is superficially similar between linguistic and biological evolution, yet may be driven by different mechanisms.

However, although the processes underlying language change and genetic change may be different, many of the same analytical tools can be used in the study of both biological and language evolution (see Bromham, 2017). This point was well recognized by early promoters of cross-disciplinary dialogue between evolutionary biology and historical linguistics (Morpugo Davies, 1975), such as Charles Darwin, August Schleicher, and Charles Lyell (Lyell, 1863; Schleicher, 1869; Darwin, 1871). For example, Schleicher's analogy between borrowing from a foreign language and biological cross-breeding did not imply the same mechanism for both, yet both have the effect of confounding attempts to represent evolutionary history as a bifurcating phylogeny (List et al., 2014). Yet the same solutions may apply to both processes, regardless of their mechanistic origin, such as representation of relationships as a network rather than a tree. Similarly, the shared problem of phylogenetic non-independence due to shared inheritance applies to both languages and species despite the many differences in mode of evolutionary change. While some solutions may be more readily applied to cross-species analysis, due to the availability of phylogenies for many groups, other solutions can be applied more readily to both languages and species, even in the absence of a phylogeny. We demonstrate here that sister pairs analysis is a viable solution to Galton's problem, and it can be applied using information from widely available language taxonomies.

Our results show that some of the variation of rates of lexical change in languages can, in some cases, be attributable to differences in speaker population size. Significant correlations between population size and rate of word loss were identified for Indo-European languages, but not for Austronesian and Bantu languages. One possible explanation for the negative relationship between speaker population size and loss rates is that language evolution shares similar mechanisms with genetic evolution, because both show patterns of greater rates of loss of variation in small populations. However, the lack of significant relationships between word gain and loss in two other large language groups—Austronesian and Bantu—warns that we cannot reliably predict variation in rates of linguistic evolution by extrapolation from general principles. By demonstrating that differences can exist in rates of change even between closely related languages, our results caution against assuming uniform rates of change across all languages, and suggest that in some cases the rates of change may be consistently influenced by demographic factors.

LB, CW, XH, and SG: Conceived the project and wrote the paper; SG, CW, and HS: Collected data; XH: Analyzed data.