for applying algorithms to those data at regional and global scales, there has been a recent upsurge of research interest in urban delineation. This has led to the development and application of several new algorithms for the more accurate and consistent delineation of urban areas across countries (see, _inter alia_ , Uchida and Nelson 2009; Dijkstra and Poelman 2014; Zhou, Hubacek, and Roberts 2015; Ch, Martin, and Vargas 2021; Dijkstra et al. 2021).

One shortcoming that most of these algorithms share, however, is that they rely on one or more, essentially arbitrary, thresholds to delineate an urban area. For example, the widely used “degree of urbanization” approach (Dijkstra and Poelman 2014; Dijkstra et al. 2021) relies on two such thresholds to identify urban settlements – namely, an overall population threshold for the settlement and a population density threshold for each 1 km<sup>2</sup> population grid cell that belongs to it.<sup>8, 9</sup> To overcome this shortcoming, we instead apply a modified version of the de Bellefon et al. (2021) “dartboard” algorithm. This algorithm has the advantage that it grounds the identification and delineation of urban areas in a statistical approach which avoids the _a priori_ specification of arbitrary, and globally uniform, population (density) thresholds. In essence, and after performing smoothing, the algorithm identifies urban areas as clusters of statistically significant peaks of population or built-up density. This is done by comparing the actual spatial distribution of population or built-up density with the counterfactual spatial distributions that would result if population / built-up density were instead randomly distributed across a country’s potentially inhabitable (or “livable”) area.

Whereas de Bellefon et al. originally applied their algorithm to France using detailed data on every building footprint in the country as input, we instead apply the algorithm on a much larger spatial scale – i.e., to the entire SSA region – using constrained WorldPop data for 250 m*250 m grid cells as input. We also modify the algorithm to exclude deserts from the definition of a country’s potentially inhabitable area. While excluding deserts is not important for France, it is for SSA countries such as Mauritania, Niger, Mali, and Chad. For all four of these countries, more than 50 percent of their land areas are desert.<sup>10</sup> Not excluding deserts would mechanically decrease the counterfactual density and make these countries appear more urbanized overall than they really are. Our exclusion of deserts, and, more generally, of uninhabitable areas, also distinguishes our application of the “dartboard” algorithm from the version applied by Henderson et al. (2022) in their analysis of SSA urbanization dynamics.<sup>11</sup> Another notable advantage of the “dartboard” algorithm over other approaches for delineating urban areas is that the counterfactual density threshold to be considered significantly urban is specific to each cell and, most importantly, relative to a country’s own overall density instead of being common to all countries. Therefore, the approach much better discriminates urban areas. This is especially so for either very densely populated countries, which appear as very highly urbanized, or very sparely populated countries, which appear little urbanized partly by construction in the degree of urbanization and similar approaches.

The third, and final, literature to which our paper contributes is the descriptive literature on the structures of both urban systems and the internal structures of urban areas. This includes the extensive

> 8 The degree of urbanization uses a variety of such thresholds to distinguish different types of urban area. In “level 1” of the approach, a distinction is drawn between urban areas (“towns and suburbs”) that satisfy an overall population threshold of 5,000 and a population density threshold of 300 people per km<sup>2</sup> , and urban centers (“cities”) that satisfy thresholds of 50,000 people and 1,500 people per km<sup>2</sup> for overall population and population density respectively (Dijkstra et al. 2021).

> 9 As mentioned above, the Africapolis data utilized by OECD/SWAC (2020) uses a population threshold of 10,000 to identify urban areas.

> 10 The dartboard algorithm also excludes water bodies and both areas at extreme elevations and which have extreme slopes from the definition of potentially inhabitable area.

> 11 Henderson et al. (2022) also impose thresholds that are constant over time, fixing them to those of the last year of observation, 2014, in their data. Given that built-up area has generally expanded overtime, this mechanically increases the number of settlements that are identified over time. The full dartboard approach would have allowed for an assessment relative to each year’s overall development.

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