Evolution of human-driven fire regimes in Africa

Abstract

Human ability to manipulate fire and the landscape has increased over evolutionary time, but the impact of this on fire regimes and consequences for biodiversity and biogeochemistry are hotly debated. Reconstructing historical changes in human-derived fire regimes empirically is challenging, but information is available on the timing of key human innovations and on current human impacts on fire; here we incorporate this knowledge into a spatially explicit fire propagation model. We explore how changes in population density, the ability to create fire, and the expansion of agropastoralism altered the extent and seasonal distribution of fire as modern humans arose and spread through Africa. Much emphasis has been placed on the positive effect of population density on ignition frequency, but our model suggests this is less important than changes in fire spread and connectivity that would have occurred as humans learned to light fires in the dry season and to transform the landscape through grazing and cultivation. Different landscapes show different limitations; we show that substantial human impacts on burned area would only have started ∼4,000 B.P. in open landscapes, whereas they could have altered fire regimes in closed/dissected landscapes by ∼40,000 B.P. Dry season fires have been the norm for the past 200–300 ky across all landscapes. The annual area burned in Africa probably peaked between 4 and 40 kya. These results agree with recent paleocarbon studies that suggest that the biomass burned today is less than in the recent past in subtropical countries.

Fire has been a part of the earth system for billions of years (1), but recently—within the past million years at most—humans have provided a new and different source of ignition. Today, fires in all ecosystems are largely started by human ignitions, whether intentionally (for land management or arson) or by accident.

From studies in modern systems we know that humans can affect fire regimes via their effects on both ignition (frequency, season, and location) and landscape connectivity. However, we lack an understanding of how these different impacts might have emerged as humans learned to control fire and as they spread throughout the globe. Moreover, the degree to which current human-ignited fire regimes differ from historical, lightning-driven regimes is largely unresolved (2).

The question is complicated by the fact that the potential limitations on fire are various and system specific (3), and as one constraint is released, others can come into play. Thus, the number of ignitions can increase without a concomitant increase in area burned (4, 5), and responses of fire to drivers like population density can be nonlinear (6). Most ecosystems in Africa are probably not ignition-limited currently; ignition rates are more than sufficient to burn the available fuel, and climate and landscape connectivity act as the main limitations on fire (5, 7, 8).

Interpreting historical human effects on fire regimes using empirical data has proved challenging. Most paleoecological studies of fire have used temporal changes in charcoal sedimentation rates to examine large-scale patterns (1, 9, 10). Difficulties arise because sedimentation rates respond not only to fire frequency, but also to the type of vegetation burned and the completeness of combustion (11); a change in vegetation or the season of burning could be misinterpreted as a change in fire frequency and vice versa. For this reason, analyses usually limit themselves to descriptive scales such as more biomass burning or less biomass burning (11, 12), which are difficult to relate to particular characteristics of a fire regime (13). Moreover, separating the human signal from variability caused by changes in vegetation and climate over the time periods studied is often impossible (10, 14).

Nonetheless, multiproxy analyses show increases in charcoal density around 60,000 y ago as humans started to spread into more regions of the globe (11). More local analyses also link increases in charcoal to timing of human settlement (14, 15), although it is possible these changes are associated with land cover change rather than alteration of fire characteristics per se.

In African savannas there is disagreement on the extent to which humans have altered the seasonal distribution of fires (16). Currently, fires occur throughout the dry season (2, 8) with very few fires (<5%) in the wet season. Lightning is largely absent in the dry season - being associated with convective wet season thunderstorms and more rarely with dry storms just before the first rains. Thus, a lightning-driven fire regime probably had seasonal fire distributions different from modern ones, with major effects on the size, intensity and atmospheric emissions of fires (17, 18).

The impact of humans on fire regimes depends not only on their ability to manipulate fire but on the importance of this manipulation in the face of other constraints. In reconstructing past fire regimes we therefore need to know when humans could have altered various fire characteristics and the extent to which these were limiting to fire.

Here we present a modeling approach that integrates information on the physics of fire spread (19–21), the effect of humans on different components of fire spread (8, 22, 23), and the paleoecology of modern humans (24–26). We use conceptual links between (i) known advances in human manipulation of fire, population growth, and spread and (ii) the parameters of a spatially explicit fire propagation model, to explore the types of impacts humans could have had on fire regimes as they learned to manipulate fire, their environment, and their landscapes. We propose this approach will improve our ability to reconstruct expected fire regime changes over time in Africa, and will aid interpretation of charcoal records.

We focus here on Africa as the continent with the longest continuous history of human use of fire. We also limit our analysis to grass-fueled savanna and woodland environments, which cover 70% of the land surface and where fire is a common and in some cases essential component (27). Our focus means that we are not simulating the effect of fires associated with land transformation (28), but our analysis should lend insights into the extent to which human manipulation of fire alone (without concurrent land-cover change) can alter forest/savanna boundary dynamics. We ask three questions:

• i) What technological/demographic changes during human evolution would be expected to affect fire characteristics?

• ii) Which of these changes is likely to be most important in determining savanna fire regimes?

• iii) Were savanna systems ever ignition limited?

Modelling Framework.

The fire propagation model is based on three key parameters, which reflect ecological processes affecting the extent of fire (see Materials and Methods for more details). Cells are either flammable, or not, and fire spreads to flammable cells with a predefined probability. The proportion of flammable cells (ρ) represents spatial processes controlling percolation through a landscape—the connectedness of fuels. Once a cell is on fire, the probability of spreading to an adjacent cell (λ) represents temporal processes controlling percolation through a landscape—seasonal/diurnal changes in the flammability of fuels. The parameter μ is the number of ignition events in a landscape. Humans can affect ρ by changing the proportion of cultivated and grazed land, or by building roads, μ by igniting more fires, and λ by altering the times of year when fires occur.

These impacts would probably have become important at different times during hominin evolution (Fig. 1). The effect on μ is the least easy to reconstruct; theoretically, people could have altered μ from the first time they were recorded as making use of lightning fires 1–1.5 Mya (29), but μ is more likely to have increased when hominins developed the technology to ignite their own fires (30) 200–400 kya, or when rapid population growth began ∼40–70 kya (24, 31). It is also unclear when humans started using fire as a tool for landscape manipulation, rather than purely for heating and cooking (32). We assume here that if humans were able to ignite grassy fuels and apply fire to the landscape then they did (see Discussion). The probability of fire spread (λ) could only have been altered by people after they learned to ignite their own fires, were no longer dependent on lightning, and could have spread ignitions into the dry season when fuels are highly flammable; this probably started ∼200–400 kya in a range of different hominin groups (32, 33). Altering ρ only became possible once humans began domesticating cattle (reducing fuel loads) and cultivating land (creating barriers to spread), which happened 2–4 kya in Africa and earlier in other parts of the world (34).

Fig. 1.

Stages of human evolution defined by their ability to manipulate μ (frequency of ignition events), λ (timing of ignition events), and ρ (the connectivity of the fuel bed). The gray line represents reconstructed global population size. The thickness of the colored lines gives a rough representation of the magnitude of the effect.

The modeling framework was first evaluated for its qualitative behaviors and then run for parameters that were quantified for six stages in the evolution of human technologies and population growth and spread. The relevant stages of human-evolved fire regimes were defined (Table 1) such that the first stage represents a time period before hominins used fire, and lightning was the only ignition source (>1.5 Mya). The second stage represents a time when hominins could potentially have increased the frequency of fire through making use of lightning fires, but did not alter the season of burning (1.5 Mya to 300 kya). In the third stage, hominins could alter the season of burning with ignition events independent of lightning (300–70 kya). The fourth stage represents human population expansion and associated increase in ignitions throughout the year (70–4 kya). In the fifth stage (4,000–200 B.P.), agropastoralism had spread to Africa, and humans were altering fuel loads (through grazing) and fuel beds (through cultivation). This effect is magnified in the sixth stage, where rapid recent population expansion significantly increased these impacts on the landscape (200 B.P. to present). The dates chosen here are illustrative; specific dates when these transitions occurred are still debated in the archaeological literature. For the sake of comparison, we assume that population densities are the same in stages 2 and 3 and in stages 4 and 5. See Materials and Methods for more on this and for details about the calculation of the parameters.

Table 1.

Six stages of human evolution and reconstructed values of μ, λ, and ρ for each stage

Stage	Population density	Ignition frequency, μ*	Spread probability, λ	Fraction transformed	Connectivity, ρ
1. <1.5 Mya	9.2 × 10−6	0.01	Wet season	0	0.62 0.80 0.98
2. 1.5 Mya–300 kya	8.4 × 10−5	0.01 + 0.005	Wet season	0	0.62 0.80 0.98
3. 300–70 kya	8.4 × 10−5	0.01 + 0.005	Wet and dry season	0	0.62 0.80 0.98
4. 70–4 kya	1.3 × 10−3	0.01 + 0.02	Wet and dry season	0	0.62 0.80 0.98
5. 4 kya–200 B.P.	1.3 × 10−3	0.01 + 0.02	Wet and dry season	0.06	0.56 0.74 0.92
6. 200 B.P.+	4.9 × 100	0.01 + 0.04	Wet and dry season	0.16	0.40 0.58 0.76

Stages were delimited with reference to Fig. 4 showing the timing of key innovations in human mastery of fire and the landscape. These results represent a fivefold increase in μ, an increase of 20% in the median value of λ, and a 20–30% decrease in ρ from stage 1 to stage 6.

*Fires per km²/y.

Results

Deterministic Model Behaviors.

Model responses to variations in spread probability (λ) and landscape connectivity (ρ) are consistent with percolation theory, as expected (35, 36), and show threshold behaviors. As the proportion flammable area (ρ) decreases below ∼0.6, fires suddenly cannot spread and the total burned area drops to zero (Fig. 2A). Similarly, fires can only spread when λ is greater than ∼0.6. Below this value the landscape will not burn irrespective of the value of ρ (Fig. 2A).

Fig. 2.

Sensitivity analysis showing thresholds of fire spread controlled by λ and ρ. Panels represent 1, 5, and 100 ignitions, respectively. Dashed line represents the maximum possible area burned for each value of ρ. With a single ignition, landscapes will only burn when both λ and ρ are >∼0.6; increasing the number of ignitions can compensate for this to some extent.

Increasing μ (ignition frequency) can compensate for these thresholds to a certain extent (Fig. 2 B and C). However, because fire size drops off exponentially as ρ and λ drop below 0.6, μ needs to increase exponentially to make any difference to the total landscape burned (Fig. 2 B and C); this can be quantified by calculating the deviation from the maximum possible burned area across all values of ρ and λ (difference from the 1:1 line in Fig. 2). Increasing μ by an order of magnitude (from 1 to 10) can increase burnt area by 6%; increasing this again from 10 to 100 adds another 4%.

To conceptualize the effect of humans in this system, consider how the number of ignitions required to burn 50% of the flammable area changes under different conditions of ρ and λ (Fig. 3). Moving toward dry season burning increases spread probability (λ), increasing the area under cultivation and pasture decreases the proportion of the landscape that is flammable (ρ), and changing population density alters ignition frequency (μ) (Fig. 3).

Fig. 3.

The effect of different human activities on fire spread. When ρ and λ are above their threshold values, one or two ignitions can burn the landscape. Below the threshold, the ignitions required to burn 50% of the landscape rapidly increase to unrealistic numbers. When close to these thresholds, decreasing ρ through grazing and cultivation could make preiously flammable landscapes inflammable. Similarly, increasing λ through dry season burning could make previously inflammable landscapes flammable.

Clearly, ρ and λ are complements of each other; one represents spread probability in space and one in time, and, because only their product matters (SI Materials and Methods), each parameter can compensate for the effect of the other (Fig. 3). Thus, at any spread threshold, a reduction in λ requires an equivalent increase in ρ for fires to continue to spread. A first obvious conclusion is that by altering the season of burning, it is possible to connect previously unconnected landscapes and to make fires spread through landscapes that would otherwise be below the percolation threshold. Conversely, if landscapes become less connected, flammability of fuels would have to increase for fires to spread. It is also clear from Fig. 3 that μ is not a strong driver of change in this system: when spread rates and connectivity are high, one or two ignitions are sufficient to burn the entire landscape. As ρ and λ decrease below the percolation threshold, the number of ignitions required to burn the landscape quickly becomes unrealistically high.

The importance given to increases in population densities in altering fire regimes appears misguided from the above analysis. The major impacts humans would have had would have been when they started lighting fires in the dry season, and again when they started cultivating crops and domesticating cattle. In the first instance, humans might have increased the probability of large fires, and caused fires to spread in landscapes that were previously too disconnected to carry fires. In the second instance, they would have reduced the probability of fire spread by reducing landscape connectivity.

Stochastic Model Predictions: Human-Driven Changes in Fire Regimes.

The extensive literature on savanna fire behavior enabled us to relate landscape connectivity (ρ), fire spread probability (λ), and ignition frequency (μ) to variables such as fuel moisture and population density, and to changes in these variables during human evolution. We used this information to run stochastic simulations broadly representative of six stages of hominin evolution (Table 1 and Fig. 4) in three different landscapes of increasing ρ.

Fig. 4.

Broadly showing the six stages of human evolution used to determine parameters for the stochastic model runs. The parameters μ and ρ were derived from published relationships between population density and fire density (B) and population density and land transformation (D), respectively; λ was determined from field data on fire spread probability in the wet and dry seasons in a savanna national park (C). See Table 1 and Materials and Methods for more details on the parameterization. In B and D the data represent medians with 75th and 25th percentiles.

Results indicate that area burned increased from stage 1 through stage 4, regardless of landscape connectivity, with maximum area burned over all landscapes occurring around stage 3–4 of human evolution (∼300 to ∼4 kya; Fig. 5A). Africa was probably at its most fire prone in the period ∼40–4 kya, when the effect of humans on ignition frequency and season were pushing fire into landscapes previously rarely burned, and were increasing the scale of burning in open landscapes (Fig. 5A). Percent burned area subsequently decreased as agropastoralist societies started reducing landscape connectivity. By stage 6, total area burned has decreased in open landscapes to less than that characterizing stage 1, although burned area remains slightly higher in closed landscapes. These results are consistent with empirical evaluations of charcoal that show recent declines in tropical areas inferred to be caused by land modification and fragmentation (9).

Fig. 5.

Percentage of area burned (A) and the percent contributed by dry season fires (B) for three savanna landscapes (with high, medium, and low values of ρ) across six stages of human evolution (Table 1). (A) Slight increases in burned area are associated with dry season ignitions (stage 3 onward), but the largest effect is the reduction in burned area with the beginning of agriculture and pastoralism (stage 5 onward). Only the least connected (high tree cover, more dissected) landscapes showed a response to increased ignition (stage 4), indicating that these were ignition limited at certain stages of our evolution. (B) Once humans started lighting fires throughout the year (stage 3 onward), all landscapes became dominated by dry season fires. Points give the median, boxes the 25th and 75th quantiles, and dashed lines the extremes.

Contrary to expectations from the sensitivity analysis discussed above, increasing ignition frequency can have an impact under some conditions. In closed landscapes, burned area was substantially higher in stage 4 than in stage 3. The higher μ associated with population expansion in stage 4 allowed fire to burn 4× more of the landscape than before (Fig. 5A). However, in more open landscapes, ignition frequency (μ) was not important; area burned depended more on dry season human ignitions (λ) (stage 3+) and even more strongly on landscape connectivity (ρ).

The area burnt in the dry season changed from ∼25% under a lightning regime to ∼90% today (Fig. 5B). This switch occurred suddenly, after stage 3 (200–300 kya), which suggests that plants in African savannas have been exposed to fires throughout the dry season for the past ∼300,000 y. Observations from the paleorecord do record a change in the nature of fire at this time, which has been ascribed to human intervention (37).

Discussion

Our model illustrates how population changes, dry season burning, and the expansion of agropastoralism would affect fire in African savanna ecosystems, through impacting ignition frequency, spread probability, and landscape connectivity, respectively (Fig. 3). Our model shows that over the past ∼1 million years, changes in land connectivity associated with agropastoralism have probably had the most significant impacts on area burned, particularly within the past 4,000 y (Fig. 5A). If correct, these results suggest that current area burned and CO₂ emitted from fires in Africa are lower than they have been since savanna landscapes first spread on the continent. Charcoal data from Marlon (9) support this finding, showing a dramatic global decline in charcoal index in the last 200 y, especially in the tropics and extratropics, where land transformation has been extensive.

The estimated impact of shifts to dry season ignitions on area burned was less substantial than expected from the theoretical model. It seems the infrequent (∼10%) lightning ignitions that do occur when fire-spread probability is high are sufficient to burn well-connected open landscapes. As a result, total area burned during a lightning-ignition regime (stage 2) and a human-ignition regime (stage 3) are more similar than expected from theory (Fig. 5A), even though the seasonal distribution of fires changed dramatically over this period (Fig. 5B).

Changes in ignition frequency seldom seem to make a difference in savanna landscapes. A single fire, burning under favorable conditions for spread, can burn as much if not more of the landscape than 100 fires burning under suboptimal conditions (Fig. 2). However, in highly fragmented landscapes close to the percolation threshold, ignition frequency can substantially increase burned area, particularly when fire spread probability (λ) is high enough to compensate for low connectivity (ρ)—i.e., primarily during the dry season (Fig. 5). Thus, landscapes low in connectivity are more responsive to changes in fire season and ignition frequency than open landscapes. Areas that are highly dissected by river channels, where the vegetation has increased moisture content (38); areas with insufficient (<200 gm⁻²) grass cover (39); or areas of sufficiently high forest/thicket cover, as occurs in savanna-forest mosaics (40), seem to have intrinsically low landscape connectivity. The spatial distribution of these barriers can affect the precise percolation threshold (SI Materials and Methods) (41) but should not qualitatively change the results. It is therefore likely that human activities spread fire further into these disconnected systems in the past, as is certainly the case in forest-grassland mosaics today (42), and, because fire acts to prevent forest encroachment into savannas, that this could have affected the rates of forest expansion and contraction associated with wetting and drying cycles in Africa.

The threshold responses of fire to parameters ρ and λ are consistent with observed patterns. Archibald et al. (5) found burned area to decrease suddenly when 40% of the landscape is inflammable (covered with trees), and Hennenberg et al. (43) also found thresholds (around 40% tree cover) where fire cannot spread. Similarly, below a critical fireline intensity (FI; ∼1,400 kW⋅m⁻¹), fires will not burn in savannas (16, 44).

This model necessarily presents a simplified perspective on the evolution of human-driven fire regimes. We have largely ignored people's motivations for starting fires and the effect these have had on spatial and temporal patterns of ignition. Hunter-gatherers light fires to attract game to the green regrowth and to improve visibility and movement (2), whereas pastoralists light fires to improve grazing land, and to reduce tick loads (45). By contrast, agricultural communities light fire breaks to protect their crops, and use fire to open new land for cropping and to burn agricultural residue (46). In general, human ignitions are clustered around settlements and concentrated in space (23). These factors may have ramifications for the impacts that humans have had on fire regimes, although we are inclined to suggest that clustering of ignitions, particularly in areas that have been intensively fragmented by humans, are likely to compound the effects of landscape fragmentation observed herein.

Testing these results could extend beyond correlations with charcoal data. Population-genetic studies of plants expected to respond to dry season burning could corroborate the timing of the predicted shift in fire regimes ∼200–300 kya. Carbon isotope studies might test predictions of responsiveness to human ignitions across landscapes of varied connectivity. Better quantification of spread probability (λ) diurnally, as well as seasonally, would be useful, as would comparative studies in systems where the timing of human impacts was different.

Implications.

These results have profound implications for our understanding of fire regimes not only in the modern global context, but for predictions about further evolution of fire regimes in the face of extensive climate and land-use change. We suggest that the extent of burning has declined in the past millennium and (if vegetation and climate remained constant) would currently be lower than in the past million years. Characteristic fire regime seasonality has also changed in favor of dry season fires, which have lower emissions of methane and carbon monoxide (17). The role of wildfire in the global carbon cycle is probably less significant now than in the recent past. Of course, this finding needs to be weighed against evidence for increased burning of fuel wood associated with Iron Age smelting of metal tools in Africa (which also started 2,000–4,000 y ago) if we are to assess changes in total biomass burning due to human interventions.

This work raises a note of caution in the face of our attempts to isolate the effects of humans on the global fire cycle, and to manipulate fire regimes through human interventions. Statistical analyses that exclude process are unlikely to be useful predictors of past or future fire regimes. Only methods that explicitly include the potential and actual effects humans have had via their effect on ignitions, fire season, and landscape fragmentation can provide any insights into the continuing evolution of human-driven fire regimes in Africa and elsewhere.

Materials and Methods

A 100 × 100 cell spatially explicit fire propagation model was set up with no interaction on the diagonals and no wrapping at the edges. Obstructions to fire (nonflammable cells) were randomly laid down on this grid with proportion ρ. Calculations of μ assume a 500-m grid cell, which results in a landscape of 250,000 ha and allowed us to use 500 m remotely sensed fire data to parameterize the stochastic model. Ignitions occurred randomly in the grid, and if an ignition occurred in a flammable cell its probability of spreading to an adjacent flammable cell was λ. Each model run occurred over one growth year; there was no regrowth of fuels, and a cell that burned remained burned until the end of the model run. Similarly, there was no carryover effect of fires from year to year, and the landscapes had no memory (see ref. 45 for justification).

We assumed constant environmental conditions over the time period considered (1.5 Mya to present), which allowed us to avoid the inherent complexity of empirical analyses and to focus only on changes associated with human use of fire. Though rainfall amount is known to have varied substantially and periodically over this time period (47), with associated expansion and contraction of forest vegetation (48, 49), seasonal rainfall regimes, and the open grassy environments in which fire occurs have been present for at least the last 2.5 Mya in Africa (50, 51). Seasonality and grassy fuels are the key assumptions of the model. The documented variations in rainfall and forest extent would affect the parameters λ and ρ, as discussed, but would not invalidate the model.

The deterministic behavior of the model was explored with a sensitivity analysis using all combinations of ρ and λ from 0.1 to 1 (using a step of 0.1) and increasing levels of μ from 1 to 500. Then a stochastic version of the model was run representing six stages in human development (see Table 1 and main text for details). The model requires three parameters to simulate savanna fire regimes.

Spread Probability.

In savanna and woodland landscapes, spread probability (λ) is controlled by the moisture content of the fuels, increasing in the dry season when grassy fuels are flammable, and decreasing in the wet season. Weather conditions also modify λ and contribute toward higher spread probabilities in the dry season. Diurnal changes in λ are ignored for this analysis, but are the subject of future research. Humans can alter λ by altering the ignition season, and this would first have occurred when they were able to ignite their own fires (∼200,000–400,000 y ago).

In the stochastic model, the value of λ for each fire was drawn from distributions of wet season and dry season fireline intensity (FI: energy released by a moving fire front) from the Kruger National Park (38) (Fig. 4C). FI can be related to λ using published relationships between FI and percent of landscape burned (44) (SI Materials and Methods). Median λ is below the percolation threshold in the wet season and above the percolation threshold in the dry season (Fig. 4C). Lightning fires were drawn from these wet (November to April) and dry (May to October) season datasets in proportion to the number of lightning strikes recorded in the wet and dry season in subtropical Africa (0.11 and 0.89, respectively; calculated using lightning strike data from the Global Hydrology Resource Centre (GHRC; http://thunder.nsstc.nasa.gov/data/). Human-ignited fires were assumed to have a uniform distribution and were drawn randomly from both datasets.

Landscape Connectivity.

In savannas, landscape connectivity (ρ) is controlled by the amount of grassy fuel as well as barriers to spread (which can include clumps of trees, agriculture, bare ground, roads, topographic features, or rivers). Humans would first have altered ρ when they started to domesticate cattle (reduce fuels below the spread threshold) and cultivate land. Spatial arrangement of barriers could be important (41). Here we only consider randomly distributed barriers, but the analysis shows similar behavior, but a higher percolation threshold, when barriers to spread are clumped (SI Materials and Methods).

The effect of humans on ρ was determined from data in Archibald et al. (8), which link population density to the fraction of transformed land (Fig. 4D). In untransformed savanna landscapes, ρ ranges from 1 to close to 0.6, depending on bare ground, tree and shrub cover, and river density. Connectivity could also have changed over time with forest expansion and contraction (48, 49). To represent this variability we ran the stochastic model in three different landscapes with ρ values of 0.62, 0.8, and 0.98, respectively. The final ρ value was calculated by subtracting the fraction of transformed land from the initial landscape connectivity (Table 1).

Ignition Frequency.

Lightning and human ignitions are the only sources considered. Lightning ignitions were calculated from the GHRC data, assuming that 0.2 of lightning strikes hit the ground and 0.04 of these start a fire (52). Estimating human ignition frequencies (μ) over time requires knowledge of (i) the expected number of fires at different population densities and (ii) prehistoric changes in population densities. The first was available from relationships in Archibald et al. (8) (Fig. 4B). Reconstructing prehistoric population trends is complicated by lack of data and the fact that people live in settlements, so low regional population densities might still have meant locally high population densities. Powell (53) argues that the social complexity of African societies in the past 100 kya could only have occurred at regional densities >3.2714 × 10⁻⁴⋅km⁻². The estimated population of the first city-state in southern Africa, Mapungubwe (∼700–1,100 y ago), was 9,000 people in an area of ∼30,000 km² (54), giving a local density of 0.3 people/km⁻². Currently, regions with <0.5 people/km⁻² are rare in Africa (8), and median rural population densities are 10 people/km⁻². Assuming exponential growth between these three estimates, we predict regional densities of 9.2 × 10⁻⁶, 8.4 × 10⁻⁵, 1.3 × 10⁻³, 1.3 × 10⁻², and 4.9 × 10⁰ for the time periods considered, which translate to human ignitions of 0.005, 0.005, 0.05, 0.02, and 0.04 km⁻²⋅year⁻¹ (Table 1). The sum of lighting and human ignitions gives μ.