Geospatial effects on phonological complexity in the world’s languages

3.1 Computational model

The computational model for this analysis needs to be capable of detecting and modeling several important aspects of geospatial and linguistic patterns. The model type which can fulfill these requirements is a custom state-of-the-art Bayesian nonlinear multi-level Gaussian Process model. The software we used to create this highly complex model is the Stan programming language.^[2]

Below, we discuss the individual aspects and requirements for the model and how we integrate those as elements in the Gaussian Process model. The specific implementation is outlined below in this section.

4.1 Geographical distances

The geographic distances were derived from each language’s latitudinal and longitudinal values projected on a spheroid earth (Haversine distance) using the R-package geosphere (Hijmans 2022). However, calculating distances between languages on a globe as part of a geospatial or language contact study is problematic. In its raw form, a language in Newfoundland would be equally distant from a language in central Europe and a language in central Asia. However, contact and language spread between central Asia and Europe has been far greater than between North America and Europe (in the latter case, barely any). Yet in the model, both language pairs would be treated as equally mutually influential.^[5] We mitigate the issue through a map transformation in which we artificially inflated the globe by a scale factor of 1.5 and then projected a Pacific-centered map back onto it. This way, we inflated the Atlantic to more than 1.5 its actual size. We calculated that the distortion between each point on the West-East axis from Europe/Africa to the Americas is small, while distances between the East-West Europe/Africa – Americas axis are greatly inflated. This allows the model to run as intended, but strongly discounting any geospatial or contact influence across the Atlantic. Inflating the Atlantic region on the map is a necessary procedure, since the model requires the pairwise distance matrices to be positive definite, which makes editing any individual distances impossible. In other words, the model requires the input data to be distributed on a contiguous surface (a globe in this case) which disallows for manual changes to pairwise distances. In preliminary tests, we tested running the model without the inflated Atlantic and observed a noticeable influence of (West) African language complexity on (Eastern) South American languages. While this would be a genuine model result, we know that since there was no actual historical contact in this case, the influence was likely an overestimation.

For the computational analysis, we used the model of a globe earth described above, but the maps used for examining the model results are Pacific-centered maps.

4.2 Mode of result analysis

The output of the model is, as discussed above, a grid of geographic points on the globe with inferred complexity values for each complexity variable.^[6] This gives us a series of 2-D maps with the inferred complexity values. However, while 2-D maps (one per complexity variable) are useful for a general overview of the global complexity patterns, they are difficult to compare with one another. Additionally, smaller geospatial variations are easily missed. For this reason, we defined seven geographical macroareas which we use to isolate geographical patterns in order to analyze them in more detail.^[7]

The macroareas are drawn from the continent-sized areas of the Autotyp database (Bickel et al. 2022) but differ from those and other large language areas in the literature in that each has an axis of orientation along which we often find that variable values are aligned. The grid points which fall in each area (defined in Figure 2a) can be isolated and plotted as a one-dimensional nonlinear curve against one geographic coordinate. For example, we could isolate the inferred complexity data points that fall in one continent and then plot those values against, for example, latitude. As a result, we can observe the changes in complexity along the latitudinal axis. This is akin to taking a slice out of the world map and looking at the grid points from the side.

Figure 2:

Map of the selected geographical areas. (a) Every polygon corresponds to an area while the blue dots correspond to the locations of the surveyed languages. (b) The grid points used in the model (red crosses) overlaid with the surveyed languages (blue dots). It is important to keep in mind that the model uses and outputs the estimates of this set of grid points instead of complexity values for the individual languages.

The axes of orientation for the most part follow the predominant directionalities of migration and expansion as the human range expanded from Africa to fill the globe: from Africa to Europe and the Near East (for expansions and fallbacks along this axis see Section 6.3); from Southeast Asia to Northeast Asia, populating Siberia; from Southeast Asia to New Guinea–Australia, populating the Pacific; from North America to South America, populating the Americas.

The macroareas, in summary, are used in the analysis of the results, but are not input to the model and calculations. The map in Figure 2 shows the geographical ranges of the macroareas.^[8]

The isolated areas are in detail:

1. American Pacific rim (latitudinal): an area consisting only of languages along the coastal and near-coastal land up to the far side of the major coast range, along the entire coastal length from Alaska to Tierra del Fuego.

2. Americas: all languages located in the Americas.

3. East Asia (latitudinal): an area comprising languages in northern and central East Asia, including the Asian Pacific rim, stretching from northern Siberia to the northern border region of the Indochinese Peninsula.

4. Euro-Africa (latitudinal): all of Africa and Europe, along with some of the Middle East.

5. Northern Eurasia (longitudinal): from western Europe to northeast Asia, south to the Caucasus and Mongolia, and including the entire Eurasian steppe.

6. Southeast Asia and Australasia (diagonal, northeast to southwest): Northwest-Southeast starting in mainland Southeast Asia and ending in southeastern Australia.^[9]

7. North America (latitudinal): all of North America from the Arctic to southern Mesoamerica.

In addition to the nonlinear curves, we give small cropped maps with the mean complexity measures superimposed.

Note also that we did not assess the fit of the model, as this is a purely inferential model rather than a predictive one and we did not have a competing model to which we could compare it. This means that a single-fit metric for model predictions for the existing languages is only useful to assess the predictive power of the model and leave-one-out cross-validation measures can only be interpreted in the context of other competing models of the same data. We calculated that the median absolute difference between the inferred values and the observed languages equals 0.35 standard deviations across all variables: Grades (ranging from 1 to 9), for example, has a standard deviation of 1.29, which means that the median difference between predicted and observed values for Grades is 0.45. As discussed above, it is not possible to put this value into perspective, unless there are other models to which this can be compared or if there is a specific accuracy score that needs to be met for predictions. In this inferential model, neither of these is the case.

5.1 Areal results

In the following, we can examine the area plots to get the model estimates for complexity gradients in those areas along a geographical variable (latitude, longitude, or diagonal). All figures show the mean posterior estimates for the distribution of grid points on the surface by complexity variable with a black median line. Every blue vertical line represents the 95 % credible interval over the grid points at one point on the x-axis. It thus corresponds to the range of complexity at a certain point on the x-axis in the selected area. This means that the larger the vertical line segments are, the more variance in complexity there is at the corresponding point.

Concretely, these graphs are longitudinal or latitudinal slices from the inference of the grid points on the world map. They are oriented in the direction of ascending geographical latitude or longitude. This means the graphs run from south to north or from west to east. As discussed above, the model itself makes inferences in the global context. The closest to this output is what we can see in the heatmaps in Appendix 2. However, since heatmaps of the globe can be difficult to analyze especially for many complexity features, we consider selected areas (a subset of the heatmaps) and plot the distribution of complexity (inferred from the grid points) in that area (landmass only) along a geographical (e.g., latitude/longitude) axis. As a practical example, the complexity distribution for Closure in the North America area (Figure 3) can be read as follows: the blue vertical lines are the ranges which 95 % of complexity values fall in. We look at the graphs according to their west-east longitudinal placement. The black curve in the graphs indicates the median line of all grid points and can be taken as the approximate median average complexity at that latitude/longitude. This is akin to looking from the south and seeing the relief of the complexity distribution in North America. This means the left part of the graph is approximately located in western North America, the part on the right in eastern North America. For this reason, the complexity peak in the left third of e.g. the Closure plot corresponds approximately to the Pacific Rim area.

Figure 3:

Mean posterior estimates for the grid points in the North America area by variable (blue line segments). X-axis is the longitude west to east. The black line indicates the median of the estimates at every increment of the geographical variable.

5.1.1 North America

The North America area shows one dominant pattern: an overall complexity decrease from west to east in all variables except Geminates where complexity instead increases from west to east. Most of these variables show a distinct peak at around 225 degrees which is the result of higher phonological complexity along the North American west coast (Figure 3). The dip at the very left is due to lower complexity in Alaska, which is further east than the west coast.

We can further see that the higher complexity is mostly constrained to the Pacific Northwest with Ancillary having a second peak in the Eastern Part of the United States, while Total Tones and Total Vowels are both higher in the far northwest and in the central parts of North America (Figure 4).

Figure 4:

Heatmap of the mean posterior estimates for the grid points in the North America area by variable superimposed on map outlines. Brighter color (yellow) indicates higher complexity.

5.1.2 The Americas

The latitudinal view of the Americas area shows a steep rise in complexity in the syllable variables (syllable onset, contrastive stress, and syllable coda) from the Equator northwards. Other variables show small or less clearly observable complexity increases (e.g. Pitch, Geminates, Places, Pitch). Notably, geographical variance in this area is generally higher in the north with the exception of Qualities and Total Vowels. Higher complexity in South America is mostly found in the eastern part closer to the Atlantic coast (see Figures 5 and 6).

Figure 5:

Mean posterior estimates for the grid points in The Americas area by variable (blue line segments). X-axis is the latitude south to north. The black line indicates the median of the estimates at every increment of the geographical variable.

Figure 6:

Heatmap of the mean posterior estimates for the grid points in the Americas area by variable superimposed on map outlines. Brighter color (yellow) indicates higher complexity.

5.1.3 American Pacific Rim

The latitudinal view of the American Pacific Rim area suggests a similar, yet distinct pattern from the Americas area (recall that the American Pacific Rim is a subarea of the Americas as a whole) (Figures 7 and 8). The complexity increases at and north of the Equator are more pronounced though some of these variables fall off in the far north. South America is generally of lower complexity. The lower complexity in the south may reflect the settlement history of the Americas: immigrations were very few until the end of glaciation opened up inhabitable land near enough to Siberia that a more varied set of immigrants could enter (see also Section 6.2 below). Geographical variance is smaller than in the Americas overall with the exception of Total Vowels (cf. Figure 5). This can be seen in the blue line segments around the median line being shorter.

Figure 7:

Mean posterior estimates for the grid points in the American Pacific Rim area by variable (blue line segments). X-axis is the latitude South to North. The black line indicates the median of the estimates at every increment of the geographical variable.

Figure 8:

Heatmap of the mean posterior estimates for the grid points in the American Pacific Rim area by variable superimposed on map outlines. Brighter color (yellow) indicates higher complexity.

5.1.4 Euro-Africa

The Euro-Africa area shows a varied set of complexity patterns (Figures 9 and 10). Consonantal, vocalic, and tonal complexity are higher in southern Africa while in the stress and syllable structure variables this pattern is reversed. Because of this strong opposing distributional behavior, which is not found in this many variables in any other region, we can identify a geographical area which is consistently in between the two complexity levels. This area is found between 0° and 25° N and marks the approximate range within which each individual complexity trend starts, ends, or reverses. For example, this area marks the end of the complexity decline in the variables Closure, Grades, Pitch, Places, and Total Tones, while marking the approximate beginning of an ascending trend in the Syllable variables and Places. In the syllable variables, its northern end corresponds to the area with the steepest increase in complexity. It can therefore be seen as a transitional area between opposing gradients of phonological complexity. We call this the Euro-African Transitional Zone (ETZ) and discuss it further in Section 6.3 below. This pattern is unlikely to be an artifact of the model, since there is ample support from various languages in this region (see Figure 2b), and if there were a sudden break in complexity rather than a transition between these areas, we would see a sudden jump in complexity in the model inferences in this region similar to what we can observe in the ContrastiveStress variable in Southeast Asia and Australasia (Figure 15) or the Americas (Figure 5). In those cases, the patterns indicate a sudden step in the complexity gradient which is not found in the ETZ pattern.

Figure 9:

Mean posterior estimates for the grid points in the Euro-Africa area by variable (blue line segments). X-axis is the latitude south to north. The black line indicates the median of the estimates at every increment of the geographical variable. Red vertical lines indicate the extent of the ETZ, to which we now turn.

Figure 10:

Heatmap of the mean posterior estimates for the grid points in the Euro-Africa area by variable superimposed on map outlines. Brighter color (yellow) indicates higher complexity.

The complexity gradient in the Euro-Africa area is mostly latitudinal, with the exception of Places which is higher in the Caucasus region than in western Eurasia.

5.1.5 North Eurasia

The longitudinal view of North Eurasia is marked by very strong stress and syllable complexity patterns as well as Geminates which are very high in Europe and decline towards Eastern Asia. Notable is the peak or trough in complexity around 25° which corresponds approximately to a strong dip or increase in complexity in the Caucasus which breaks the overall pattern (see Figures 11 and 12).

Figure 11:

Mean posterior estimates for the grid points in the North Eurasia area by variable (blue line segments). X-axis is the longitude west to east. The black line indicates the median of the estimates at every increment of the geographical variable.

Figure 12:

Heatmap of the mean posterior estimates for the grid points in the Northern Eurasia area by variable superimposed on map outlines. Brighter color (yellow) indicates higher complexity.

5.1.6 East Asia

The most apparent property of this area is the high variance which dominates the graphs. This indicates that, unlike in the other regions, there are strong differences between the complexity levels throughout the area. The reason for the high variance is probably the sharp interfaces between the three linguistic populations known as Paleosiberian and Altaic in the north, and Southeast Asian in the south. Structurally, all three are internally diverse and different from each other. We discuss this issue more in Section 6.1. Moreover, a consonantal higher-complexity zone can be found in central East Asia (Figures 13 and 14).

Figure 13:

Mean posterior estimates for the grid points in the East Asia area by variable (blue line segments). X-axis is the latitude south to north. The black line indicates the median of the estimates at every increment of the geographical variable.

Figure 14:

Heatmap of the mean posterior estimates for the grid points in the East Asia area by variable superimposed on map outlines. Brighter color (yellow) indicates higher complexity.

Note that the blue line segments here are more widely spaced because the scale is smaller.

5.1.7 SEA and Australasia

Generally, complexity is higher in Southeast Asia and declines towards southeastern Australasia. It is high in the southeast for places because Australian languages tend to have multiple contrastive series among dental, alveolar, palatal, and retroflex consonants. However, there is comparatively more variance especially in the variables Geminates, Total Consonants, and Ancillary (see Figures 15 and 16). There is a strikingly smooth decline in syllable codas, with very little variance, chiefly because Australian languages near-unanimously have very simple syllable structures.

Figure 15:

Mean posterior estimates for the grid points in the SEA and Australasia area by variable (blue line segments). X-axis is the diagonal northwest to southeast. The black line indicates the median of the estimates at every increment of the geographical variable.

Figure 16:

Heatmap of the mean posterior estimates for the grid points in the Southeast Asia and Australasia area by variable superimposed on map outlines. Brighter color (yellow) indicates higher complexity.

5.2 Parameter covariance

Recall that the Bayesian inference model treats each variable effect as an outcome of a correlated process on the level of each grid point. This means the geographic effects are not modeled independently of one another but jointly come from a common underlying Multivariate Normal distribution. If variables are correlated in their effects, they will more often yield similar outcomes on the geographical level. For example, if high complexity in variable 1 often occurs together in the same geographic location with high complexity in variable 2, both are positively correlated. Because of this property of the model, we can extract the correlations from the covariance matrix. Figure 17 shows the mean posterior correlation between the complexity variables (plotted with the R-package corrplot; Wei and Simko 2017).

Figure 17:

Posterior estimates of the pairwise correlations between the complexity variables. Larger dots with more intense colors indicate higher correlation while the color indicates the direction of the correlation.

Here, we can see that most variables are slightly to strongly positively correlated with each other. The highest correlations can be found between Total Consonants and Grades, Places, Pitch, and Closure; Ancillary, Total Vowels, and Qualities; and Closure and Grades. The only exception, albeit very a slight one, is the negative correlation between Qualities and Places/Closure.

This means that in the system overall, many variables seem to be positively correlated to some degree. As a result, they show similar complexity trends in the geospatial context.

As a second check on this predominant positive correlation between the individual variables, we ran a Bayesian Latent Variable Factor Analysis model using the R-package blavaan (Merkle et al. 2021). We found that no complexity measure can be securely determined to be influenced by the latent variable negatively (the compatibility intervals of Quality, Diphthongs, ContrastiveStress, Initial Stress, and Final Stress overlap with zero – all others are positive) which means that all complexity variables are either positively or neutrally associated with a latent complexity measure. However, this basic Factor Analysis is not sufficient to demonstrate any such relationship definitively, because it does not account for the spatial component.^[10] We take this therefore as corroborating our above findings from the more complex spatial model and results of previous studies (see Hartmann forthc.).

5.3 Geographical covariance

Lastly, we can inspect the geographical covariance within each variable. Since the Bayesian model contains a Gaussian Process, we model each point on the geographic surface in relation with all other points. Sometimes, far-away points will influence a point more strongly and sometimes only localized effects are influential. All of this is expressed in the shape of the kernel function (see discussion in Section 3.1) where, when covariance is high in a variable for a large geographical distance, it means that this variable shows more long-distance effects. Figure 18 shows the posterior kernel functions for each variable.

Figure 18:

Posterior kernel functions by variable. The black line is the posterior mean while the colored area represents the 95 % credible interval.

Overall, we can see that five variables show clearly discernible localized effects (represented by a steeper drop-off in covariance). Ancillary, Total Consonants, Grades, Total Tones and Total Vowels show this behavior. Most notably, Total Consonants and Total Vowels decrease steeply and approximate zero by approximately 2,000 km distance. This means there is close to no long-distance influence between the points on the surface beyond 2,000 km.

All other variables show considerably more long-distance influences. Concretely, this means that complexity is more homogeneous over large distances and shows smoother curves. This can be interpreted as these variables being geographically more homogenous and showing less steep changes.

6.1 Distribution of variables across areas

Clear geospatial profiles in total vowel complexity among the areas are generally lacking. This does not necessarily mean that there are no vowel complexity differences associated with any area, but only that the association strengths are smaller or sparse. Vowel complexity (Total Vowels and Ancillary) shows varied complexity levels such as in North Eurasia or less varied patterns as in SEA and Australasia or North America where there is one single peak. An example where we did find clear differences for vowels was the decrease in complexity from Southeast Asia to Australasia (see Figures 15 and 16).

Consonant complexity, stress, and syllable complexity, on the other hand, prove to be good indicators for gradients in geospatial complexity distributions. The more high-level complexity measures (e.g., Total Tones, Total Vowels, and Total Consonants) show clearer geographical profiles, since they are more locally determined (see Figure 18). This means that they are distributed in such a way that there is less inferred similarity with farther-away languages when it comes to these measures. This gives these variables clearer, regionally determined patterns.

As noted in Section 5.1 above (Figure 5), the settlement prehistory of the Americas would seem to predict some of the patterns we see in the distribution of complexity and variance in the Americas. Continental glaciation blocked overland entry to North America north of about the Oregon–Washington border until about 14,000 years ago, when what is known as the Ice-Free Corridor between the Cordilleran and Laurentide ice sheets formed and gradually widened. The first evidence of humans north of the ice appears just before the opening, but there is little or no evidence of actual north-to-south entries via this route (see Dalton et al. 2023, especially Fig. 9; Potter et al. 2014, Willerslev and Meltzer 2021). At that point immigrants from East Asia seeded a diverse North American linguistic population (for a sense of the population density see Anderson et al. 2019, 2010). Coastal movements by watercraft undoubtedly brought earlier settlements south of the ice sheets, probably beginning 25,000 or more years ago (see e.g. Dalton et al. 2023; Gowan et al. 2021 on ice sheet reconstruction over time, Davis and Madsen 2020 on paleodemographic and migration implications, Praetorius et al. 2023 on possible entry times based on sea ice conditions, and Nichols 2024 on linguistic entries). The earlier, glacial-age immigrants, however, were far fewer and must have formed a sparse and highly mobile population.^[11] We know little about the impacts of that population structure and its sociolinguistics on language structure, but we suppose linguistic boundaries may have been fluid and languages may have been affected by generations of language mixture and L2 learning, and of course that population had few entering ancestors to start with. The result could well have been reduced diversity, variance, and complexity compared to languages of the north. We raise this possibility for purposes of hypothesis formation; if it has any reality, it gives us a general identity and age for a linguistic population much older than the Comparative Method can usually trace for descent groups.

More recent population movements may be responsible for the high variance in East Asia (Figures 13 and 14). Here we find a sharp discontinuity between the diverse and often complex languages collectively known as Paleosiberian (Chukotka-Kamchatkan, Eskimo-Aleut, Yukagir, Nivkh, and sometimes also Korean and Japanese) and the three families known collectively as Altaic (Turkic, Mongolic,^[12] and Tungusic). The latter three are known for their structural regularity (e.g. consistent head-final morphology and syntax, simple syllable structure, consistent causativization in the verbal lexicon) which strikes us as well adapted to contact, calquing, and symbiotic bilingualism. For these language groups and an overview see chapters in Vajda (2024). Still different, and complex in different ways, are the languages of mainland Southeast Asia (for a structural overview see Enfield 2014; the two major language families, both old and much diversified, are Sino-Tibetan and Austroasiatic). The meeting of those three very different structural profiles appears to be showing up in the high variance observable in Figure 13.

6.2 Broader and global distribution of variables

Some previous work (Shagal et al. 2019, nd; Nichols 2017; Nichols et al. 2004; Janhunen 2000; and others) has revealed the existence of large-scale gradient distributions of a number of typological properties, running east-west across Eurasia or the entire northern hemisphere. The explanation has been that there is a long-standing westward trajectory of language spreads from northern Asia to Europe via the Eurasian steppe and northern forest, and a similar trajectory of language movements from northern Asia into North America. In such studies, gradient distributions or east-west asymmetries more generally have been observed opportunistically, and other typological features were then examined in searches for possibly confirming evidence. Some of our areas are based on those earlier findings, but here we have made the areas – subsets of the global complexity distributions calculated by the model – central to the interpretation of the results. The most striking feature of the North Eurasia area is that, along the entire West-East axis, we find the most varying and seemingly uncorrelated complexity patterns. Vocalic and tonal complexity measures show many larger and smaller peaks along the extent of the area, while syllable and stress complexity decline from west to east. Consonantal complexity (with the exception of pitch coarticulation), on the other hand, shows no clear patterning, yet has increased variance between the languages in the area around 50° E.

The overall picture of the complexity distributions shows that syllable and consonant complexity are the most clearly geographically distributed. Australasia has very low complexity overall: most complexity variables decrease in the south(east) direction. We also find that South America and Australasia are quite similar in that complexity decreases to the south in both areas. Perhaps more accurately: the further to the southern periphery of these areas’ languages, the more complexity decreases. Euro-Africa is very different, as the same south-north complexity increase does not hold there (see discussion in Section 5.1 and Figures 9 and 10). Instead, we find many opposing complexity directions in different variables.

Concerning South America and Australasia, both are at the far ends of early human migration chains and the far edges of the former human species range, which followed trajectories from Africa across southern Eurasia via Southeast Asia to New Guinea and Australia, and from both Southeast Asia and Europe north to Beringia and then to the Americas (HUGO 2009; Rootsi et al. 2007; Raghavan et al. 2014, and others). That is, the lower complexity in South America and Australasia is an isolation by distance effect: these places are at the far ends of migration trajectories, relatively isolated from large-scale effects, and shielded by natural barriers such as oceans and bottlenecks. It might have been the case that in both areas a dominating earlier complexity level was easily maintained due to the relative isolation. In this view, whether the complexity level is low or high is irrelevant as it is merely the level which first spread into these areas and was trapped in the formation of low-complexity pockets. An alternative hypothesis, which is able to account for the fact that it is low complexity that is prevalent in these areas, is that low complexity is an ancient feature, higher complexity has diffused outward from population centers in Africa and Eurasia, and the later developments have not yet fully penetrated to the ends of the trajectories. Innovations are expected to arise and be propagated in denser networks with unequal distributions of prestige and connections (Fagyal et al. 2010), conditions that have been present longer and more strongly in the Old World than at the younger eastern edge of the human range. An isolation by distance model predicts that some innovations made near the center will fail to reach to the edges, especially innovations dependent on or favored by other features in the same or neighboring languages (such as clicks dependent on or favored by ingressive articulations). Such innovations are more readily lost than gained, and when the innovation is an additive one the consequence will be feature loss in outlying regions.

When comparing the results from the American Pacific Rim to the geographical effects found across the Americas as a whole, we see that the subarea American Pacific Rim exhibits the same gradients and effects as the larger Americas does. On the whole, the American Pacific Rim has considerably more clear gradients. This suggests that the American Pacific rim is a true subset of the Americas as a whole (cf. also Jacobsen 1989). Further, the American Pacific Rim and the western region of the North America area show overlapping complexity peaks compared to the Americas as a whole. This means high phonological complexity is concentrated in the North American Pacific Rim area. The only variable where this trend is broken is the geminates, which strongly increase toward the eastern part of North America.

Two instances where vocalic and tonal complexity are defining properties of areas and their axes involve Southeast Asia, where the two areas SEA–AUS and SEA–NEA overlap. The region of intersection is a vowel complexity peak, with complexity dropoffs in both directions away from it, albeit with much variance in the northern direction. This phenomenon can be seen as a complexity fork.

6.3 The Euro-African transition zone

In Figures 9 and 10, we see the Euro-African Transition Zone (ETZ), a complexity transition zone between the Equator or the southern Sahel in Africa (about 0° to 10° N) and the northern edge of the Sahara Desert (about 25° N), with the northern edge of this area extending into the African Mediterranean coast. This transition zone represents an intermediate area between two opposing complexity regions, where we see high consonantal and tonal complexity, and low complexity of syllable structure, stress, and overall vocalic complexity, in Africa, but roughly the opposite in the Levant, Anatolia, and southern Europe. The main feature of this region is that inside of this transition zone, several complexity variables reach a low point or turning point (the point at which a decreasing complexity trajectory stabilizes or even reverses) or an inflection point (the point at which the rate of change of the curve reverses). For some variables, the region contains languages lower in complexity, while there is higher complexity on both sides. For variables where complexity is continuously rising or falling, the languages here constitute the point at which the speed of the change measured from south to north starts to flatten. For the prehistory and linguistic geography of the ETZ see Hartmann and Nichols (forthc.).

An exact geographic definition of the ETZ proves difficult as the patterns, where present, do not all align. The ETZ is unlike anything we see in the other areas; there are various perturbations elsewhere, but the ETZ is the only case where there is a clear mirror-image pattern between the variables. This calls for an area-theoretical description and an explanation or hypothesis, to which we turn in the following subsections.

6.4 Is complexity adaptive?

Work showing correlations of complexity with other factors, both linguistic and non-linguistic, generally assumes that complexity is adaptive, over time tending to acquire the level that suits the sociolinguistic or extralinguistic context best or is most easily learned (Bentz 2018; Sinnemäki and Di Garbo 2018). Our findings suggest that, at the scale we are investigating, complexity levels are not responsive to any evident contextual factor.

Along the south-north areas (Africa-Europe, Australasia-Southeast Asia, South America-North America), the distribution of complexity is not consistent with what has been said about adaptation. Patterning along these axes, if adaptive, should at least reveal the one kind of geospatially structured complexity that has been previously described: latitudinally conditioned complexity with the extreme levels near the equator and a fall-off polewards in both directions (The cause has to do with increasing density of resources, length of growing season, density of languages, density and diversity of language families, density and diversity of species, population density, etc. toward the equator, vs. greater sparseness toward the poles). This is in fact what is found by Bentz (2016, 2018:125–127) and Maddieson (2013a). It is not what we see in our areas, however; they show increased complexity from south to north, i.e. a gradient extending from pole to pole.

We conclude that, at the global scale of this study, complexity does not appear to be adaptive to either environmental or sociolinguistic contexts. But it also has a large-scale geospatial distribution that is too large and appears too stable to be the result of local sociolinguistic, ecological, etc. factors. Rather, on the face of it the global distribution would suggest that lower complexity is the ancestral state and higher complexity has evolved piecemeal as individual additive innovations have spread out from long-standing centers of population growth and expansion: Africa-Europe and Southeast Asia. There does appear to be evidence of adaptive complexity at lower levels of linguistic population structure, such as language families or local areas (Nichols and Bentz 2018), indicating, consistent with most of the literature, that complexity levels are the result of universal kinds of adaptation to historical contingencies such as sociolinguistic isolation. But the global scale of the present study and the large-scale or global scope of some of our complexity areas suggest that another, equally strong, factor is distance from the western Old World, which we interpreted (Section 3.3 and just above) as meaning distance from early centers of population growth.

6.5 Complexity as a meta-property

We found that the different complexity measures tend to correlate positively or neutrally; there are no strong negative correlations (see Figure 17). The positive correlations are strongest for measures that are inherently related, such as Total Consonants and Grades, Closure and Grades, Tones and Vowels, and Ancillary and Vowels. In general, we find mostly positively covarying variables which behave in similar ways vis-à-vis their geospatial patterning. One of the more surprising covariances can be found in total tones and grades.

We have seen that complexity can pattern similarly with coinciding geospatial trajectories. We see lower complexity in Australasia, South America, and eastern North America in several complexity domains. Higher complexity is found in southern Africa and the northern American Pacific Rim area. This suggests that individual regions not only display a unique complexity profile, but that this profile appears in many variables at the same time. In short, the findings show that the complexity variables considered here are cumulative. This is further supported by the variable covariances detected in the model (see Figure 17), where the covariances of notable strength are exclusively positive. This is true for variables of the same complexity type (e.g., all affecting consonants or all affecting syllables) but also across the types. Given that this is a stable global pattern, it can be taken as an indication that diachronic complexifications and decomplexifications are both geographically sensitive (i.e., they do not occur randomly scattered across all languages) and appear in unison with other complexifications or de-complexifications.

Thus, as many previous studies suggest as well (e.g. Maddieson 2011, 2009), we find that complexity in general seems to be cumulative. More specifically, this means that different complexity measures tend to be predictive of one another, meaning that complexity levels rise and fall in unison. The covariance of individual complexity measures found in Section 5.2 is furthermore relevant to the debate on equi-complexity, which concerns whether complexity differences on the micro-level (i.e. individual complexity measures) compensate one another so that languages are equally complex on the linguistic macro-level. Building on our findings in this paper, we can ascertain that there is little evidence for compensatory or tradeoff behavior between phonological measures, at least for larger geospatial trends (see also Maddieson 2011, 2005/2013a, 2005/2013b, Sinnemäki 2014a). We follow Hartmann (forthc.) in suggesting that the actual differences between the complexity measures, though salient, are constrained by the bounds of what is required for languages to maintain a stable phonological system (the observed complexity levels were never so low as to result in a collapse of discriminative power in lexical and sublexical units in any one language). In other words, it is conceptually difficult to determine compensatory effects in a system that is stable even when the variation in complexity within and across complexity measures is large (see e.g. Sinnemäki 2014a).

The findings of co-occurrence of complexity patterns both in the level of complexity and its geographical extent suggest that phonological complexity can be seen as a single property that manifests in individual observable complexity traits. It is influenced by geography in that historical developments such as migration and contact lines can yield different levels of complexity in different areas. This notion of an abstract property of complexity is further supported by the observation that the individual complexity features are mostly positively correlated. Complexity, therefore, seems to be generally cumulative. As a cumulative feature it can therefore be well explained by a common underlying – i.e. latent – property that propagates outward into individual observable complexity measures at the surface (see discussion in Hartmann, forthc.). A theory of complexity therefore has to account for this apparent unity on the underlying level.