
==== Front
Proc Natl Acad Sci U S A
Proc Natl Acad Sci U S A
PNAS
Proceedings of the National Academy of Sciences of the United States of America
0027-8424
1091-6490
National Academy of Sciences

38466852
202312207
10.1073/pnas.2312207121
research-articleResearch Articleanthro-socAnthropologyenv-sci-bioEnvironmental Sciences402
417
Social Sciences
Anthropology
Biological Sciences
Environmental Sciences
The long-term expansion and recession of human populations
Freeman Jacob jacob.freeman@usu.edu
a b 1 https://orcid.org/0000-0001-7402-8450

Robinson Erick c d e https://orcid.org/0000-0002-0789-3724

Bird Darcy f g https://orcid.org/0000-0003-3466-6284

Hard Robert J. h https://orcid.org/0000-0001-5920-2836

Mauldin Raymond P. i https://orcid.org/0000-0002-3631-0479

Anderies John M. e j https://orcid.org/0000-0002-0138-8655

aAnthropology Program, Utah State University, Logan, UT 84321
bThe Ecology Center, Utah State University, Logan, UT 84321
cNative Environment Solutions LLC., Boise, ID 83701
dDivision of Atmospheric Sciences, Desert Research Institute, Reno, NV 89512
eSchool of Human Evolution and Social Change, Arizona State University, Tempe, AZ 85281
fDepartment of Anthropology, Washington State University, Pullman, WA 99164
gUniversity of Florida, Florida Museum of Natural History, Gainesville, FL 32611
hDepartment of Anthropology, University of Texas at San Antonio, San Antonio, TX 78249
iDepartment of Anthropology, The Center for Archaeological Research, University of Texas at San Antonio, San Antonio, TX 78249
jSchool of Sustainabilty, Arizona State University, Tempe, AZ 85281
1To whom correspondence may be addressed. Email: jacob.freeman@usu.edu.
Edited by George Milner, The Pennsylvania State University-University Park Campus, University Park, PA; received August 5, 2023; accepted January 31, 2024

11 3 2024
19 3 2024
11 9 2024
121 12 e231220712105 8 2023
31 1 2024
Copyright © 2024 the Author(s). Published by PNAS.
2024
https://creativecommons.org/licenses/by-nc-nd/4.0/ This article is distributed under Creative Commons Attribution-NonCommercial-NoDerivatives License 4.0 (CC BY-NC-ND).

Significance

A revolution in archaeological research now reveals that human populations grew exponentially during periods of the Holocene, disrupted by periods of recession. This deep history of long-term population expansion and recession requires an explanation. In this paper, we propose an explanation that unifies the population growth dynamics of human societies across environments. We argue that human populations face tradeoffs between innovations that massively scale-up human well-being and unintended punctuated recessions. The recessions occur when innovation slows and competition suddenly degrades key resources. The theory and data analysis provide a framework for understanding diverse trajectories of human population growth. Explaining this diversity in the past provides context for understanding the factors that may impact population dynamics in the coming centuries.

Over the last 12,000 y, human populations have expanded and transformed critical earth systems. Yet, a key unresolved question in the environmental and social sciences remains: Why did human populations grow and, sometimes, decline in the first place? Our research builds on 20 y of archaeological research studying the deep time dynamics of human populations to propose an explanation for the long-term growth and stability of human populations. Innovations in the productive capacity of populations fuels exponential-like growth over thousands of years; however, innovations saturate over time and, often, may leave populations vulnerable to large recessions in their well-being and population density. Empirically, we find a trade-off between changes in land use that increase the production and consumption of carbohydrates, driving repeated waves of population growth over thousands of years, and the susceptibility of populations to large recessions due to a lag in the impact of humans on resources. These results shed light on the long-term drivers of human population growth and decline.

human population
human ecology
demographic transitions
radiocarbon
National Science Foundation (NSF) 100000001 IBSS-L:1520308 Jacob FreemanRobert J. HardRaymond P MauldinJohn Martin Anderies National Science Foundation (NSF) 100000001 BCS-1535841 Jacob FreemanRobert J. HardRaymond P MauldinJohn Martin Anderies
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pmcThe last 20 y have witnessed a revolution in the ability of archaeologists to describe long-term patterns of population growth (e.g., refs. 1–17). This research explosion demonstrates two general findings. First, most regions of the world display long periods of positive, exponential-like growth. For example, Zahid and colleagues illustrate a similar rate of exponential population increase from 12,000 to 6,000 cal BP among archaeological regions inhabited by hunter-gatherers and agriculturalists (7). More widely, Freeman and colleagues document that human populations experienced correlated, exponential-like growth, regardless of technological and climate differences, throughout the Holocene (9). These correlated patterns suggest that a similar underlying process of population growth operated across different types of physical environments and human economies during the Holocene. Second, following periods of expansion, human populations often display oscillations and the magnitude of these oscillations vary over space and time (e.g., refs. 2, 8, 10–12, 16 and 18–20). For instance, in NW Europe, human populations experienced a sustained expansion beginning with the spread of agriculture followed by a recession of population for hundreds of years (2). Similar “expansions and recessions” occur worldwide (21).

The above findings suggest two fundamental questions. i) What mechanisms enable human populations to often display positive, exponential-like growth over thousands of years, and ii) why do some regions display more stability (less violent oscillations) than other regions? To help answer these questions, we use controlled comparisons of large datasets of radiocarbon ages associated with human activity (e.g., ref. 22) and data on changes in the production of resources to test an Adaptive Capacity Tradeoff Hypothesis. This hypothesis synthesizes the basic insights of many models of long-term population growth (e.g., refs. 23–35), providing a potential explanation for both positive, exponential-like growth over a few thousand years and variation in population stability. Our results contribute to a general theory of innovation-driven demographic transitions in human societies and suggest that innovations, such as the adoption of intensive agriculture, that massively increase human well-being in the shorter-run require larger recessions in the longer-run due to lags in the impacts of competition for resources on ecosystems.

Adaptive Capacity Tradeoff Hypothesis

Following the strategy of Cohen (23), we use a cartoon model to help illustrate a general Adaptive Capacity Tradeoff. This model describes four key processes in human populations: The amplifying feedback of population growth, the balancing feedback of competition, population escapes through innovations that impact the production of resources, and, finally, the delayed impact of human populations on ecosystems. All four processes occur, though not always in the same model, in a class of formal models called Malthus–Boserup models of human population growth (e.g., refs. 23, 24, 29–34, and 36). To capture these processes, we build on a modified version of the logistic model (37),[1] p˙(t)=rp(t)−Sp(t)2K,

where p˙(t) is the change in human population in a given area at time t; r (1/time) is the per capita rate of population growth in the absence of environmental or social constraints (i.e., the “intrinsic” growth rate); S (1/time) is the cost of social integration, 0<S≤1, and K is the maximum population that a given area can support based on the productivity of the resources used by humans. In Eq. 1, rp captures the tendency of a population to increase exponentially (38), amplifying feedback], and −Sp(t)2K captures the dampening effect of competition for resources on population growth (38), balancing feedback]. If S were zero, then human populations could achieve the level of social integration necessary to exploit resources at arbitrarily large scales. The same effect occurs by making K arbitrarily large. The key feature of Malthus–Boserup models is a description of the race between environmental constraints imposed by a fixed K (Malthus) and endogenous innovations in technology and land use that increase K over time (Boserup).

A critical insight of previous models is that innovations in the production of resources may be driven by population pressure (24, 30, 31, 34, 36, 39). Population pressure is defined as the minimum tolerable fitness (well-being) greater than the fitness necessary for a population to replace itself. Whenever per capita fitness crosses the minimum tolerable threshold, populations receive signals of intolerable competition for key resources that provide incentives to adopt alternative forms of social organization and infrastructure for producing food. However, it is not well understood whether innovations occur as a linear function of the background rate of cultural evolution (34), continuously ratcheting a population higher and higher, or whether innovations in the production of food diminish in their effectiveness over time as landscapes become transformed and occupied (23, 30, 31, 36). Recent evidence among hunter-gatherers suggests that changes in resource extraction that raise K may, in fact, saturate over time (40). Two problems arise: i) over hundreds of years, innovations that up-scale food production, and, thus, population to a higher equilibrium level only provides temporary increases in well-being (e.g., refs. 24, 25, 30, and 31). This occurs because population growth fills-in the new niche and results in the system re-entering a state of population pressure. ii) More interestingly, over hundreds to thousands of years, populations may hit an innovation ceiling, becoming so specialized that individuals invest in making their current systems more efficient and more entrenched rather than innovating (29, 31, 40).

To capture the up-scaling of a population system to a higher K and the effect of an innovation ceiling, we first divide both sides of Eq. 1 by p(t) to calculate the mean per capita fitness, f of a population:[2] f≡p˙(t)/p(t)=r−Sp(t)K.

Next, we write the change in environmental constraints on a population due to the productivity of resources as a function of time,[3] Ki(t)=Ai−Bip(t−d)+C,

where Ai describes the effect of human-made infrastructure on the productivity of resources in a set of ecosystems over the climate controlled resources available to culturally unaided primates (C). For example, the climate-controlled net primary productivity of terrestrial ecosystems impacts the population density of ethnographically recorded hunter-gatherers, agriculturalists, and modern countries in the same way (41). However, holding net primary productivity equal, increasing specialization on agriculture results in much higher population densities (41, 42) due to the augmentation of productivity on the landscape by individuals and communities. Bi describes the relationship between the productivity of resources and population density for strategy i; and (t−d) defines the delay of a population’s impact on resources.

In the standard continuous time logistic model, a population always displays a smooth convergence to equilibrium. Oscillations in the dynamics of human population, as with other species, only occur in the presence of delays initiated by predator–prey interactions (33). Here, to create a general framework for comparison, we use a simple delay function to capture the effect of a lag between harvest pressure on prey and prey response (37). In real social–ecological systems, the delay may occur because ecosystems have the capacity to withstand and respond to harvest pressure and humans adjust their behavior to dampen resource degradation. For example, in the classic logistic model formulation, if a population adopts shifting rice agriculture, it takes time for a population to grow and fill-in potential places where shifting agriculture produces well. Once these areas become occupied, then mature vegetation cover declines and farmers experience declines in surplus production and, thus, per capita fitness. However, in real systems farmers may adjust their behavior to such a situation by spending more time weeding their gardens and increasing the tempo of garden rotation, delaying a decline in the output of agricultural surplus. Together, both processes can create a delay in the impact of increasing population density on surplus production.

Finally, we add an “if, then, else” function to capture the process of innovation stimulated by population pressure that leads to transitions in the production of resources. If fmin<f, then K1(t), else K2(t). For convenience, we study two functions, K1(t) and K2(t), to capture the demographic transition dynamics of the model driven by an innovation in productive capacity. A demographic transition refers to a situation in which population density and the mean fitness of a population shift from a negative to a positive and then back to a negative relationship. Note that the transition from K1(t) to K2(t) captures an “easy” innovation in productive capacity, whereas the lack of a K3 denotes an innovation ceiling. We hold C, r, and Bi constant and study how changes in A, S, and d impact the system. Here, we assume that A1<A2 and B1>B2. We make these assumptions to simulate the effects of humans adopting infrastructures that allow them to extract more resources from ecosystems, though at the cost of greater impacts on ecosystems in the future.

Model Dynamics.

Fig. 1 illustrates the dynamics of the model for three experiments. Fig. 1 A and B document the following: In the absence of a delay, a larger innovation in the productivity of resources generates larger, longer demographic transitions and a smooth transition into a higher equilibrium population density. For instance, in Fig. 1B, at about 20 generations, the population increases upward from the A = 0 curve (no innovation, baseline population model). The length of increase and equilibrium population displayed after the 20 generation mark is determined by the positive value of A=A2−A1.

Fig. 1. (A) Per capita fitness vs. population density, illustrating demographic transitions as a function of A, with all other parameters held constant: r=0.25 (per generation which is equivalent to roughly 1-2% annual growth rate depending on generation times), S=0.5 (per generation), d=0, C=1, A1=0, B1=0, B2=−0.25, and A1<A2. As A increases, the productivity of resources increases. (B) Illustration of population dynamics over time. The A=0 curve illustrates population dynamics with no demographic transition due to the adoption of infrastructure that increases productivity. Higher values of A result in larger and longer demographic transitions. (C) Same as graph A but with delayed impact (d>0) and other parameters held constant as above. The delayed impact of human populations on the resource stock results in an overshoot and recession displayed by the hook shape of each curve. (D) Population dynamics over time with a delay. As A increases, the overshoot and recession intensifies. (E) Per capita fitness vs. population density as S varies. All parameters are the same as above and A=1.5. As S increases, equilibrium population density increases, the length of the demographic transition increases, and population stability decreases. (F) Population dynamics over time for different S.

Fig. 1 C and D replicate the figures above, except that now population size has a delayed effect on the productivity of resources. In panel C, again, a larger innovation in the productivity of resources generates a longer demographic transition. However, the larger innovation also magnifies the impact of the delay. This is denoted by the hooked shape of the curves in Fig. 1C; the larger hooks reaching lower negative per capita fitness. Fig. 1D illustrates the expansion–recession pattern over time. The population expansion and recession occurs because the combination of a greater increase in energy extraction and a delay weakens the balancing feedback of competition on population growth. Thus, growth races ahead of competition until the resource constraint suddenly hits and per capita fitness turns negative. This occurs until the amplifying feedback of growth once again balances competition and the system enters equilibrium.

Finally, Fig. 1 E and F replicate panels C and D; however, we hold A equal and change the costs of social integration, S. Fig. 1E illustrates that as S increases, the length of the demographic transition, equilibrium population size, and population recession become larger. This last dynamic is illustrated over time in Fig. 1D by the sudden uptick in population growth around 20 generations and the increasingly humped shape of the curve as S increases. Again, the innovation-driven overshoot occurs because the lower cost of social integration weakens the balancing feedback of competition for resources. Consequently, population growth races ahead of competition until the population hits a sudden “competition cliff.” At this point, the balancing feedback overpowers growth, population declines, and the system eventually enters equilibrium.

In summary, both the long-term population expansion and overshoot-recession pattern documented in many archaeological regions require an explanation (e.g., refs. 4, 7, 9, 19, 21, and 43). We propose that these patterns result from i) waves of “demographic transitions” as populations increase their ability to extract resources from ecosystems over time; ii) however, given the potential delays in the negative impacts of human populations on ecosystems, a greater ability to augment the productivity of ecosystems and/or a lower cost of social integration results in longer periods of expansion and rapid recessions when populations hit an innovation ceiling. Greater investments in constructing highly productive niches create greater adaptive capacity now, generating longer and more robust population growth, but results in population decline and pain later, rather than a smooth transition into an equilibrium. This argument suggests three expectations in the context of deep time population dynamics.

First, population expansion over thousands of years results from increases in the ability of populations to extract more resources from ecosystems, especially shifts toward the production of energy-dense carbohydrates that require less area per person. Second, periods of positive growth are longer in regions where populations adopted more productive economies, like agriculture, than in regions where populations focused resource extraction on hunting and gathering techniques. Finally, population recessions should be larger in regions where populations adopted agriculture and had greater levels of social integration (e.g., through large ceremonial centers). These last two expectations follow from the model dynamics discussed above. Larger innovations in the productivity of resources and higher levels of social integration weaken the balancing feedback of competition, leading to larger overshoots and recessions, if populations approach an innovation ceiling. If populations did not approach an innovation ceiling, then populations would simply grow continuously with no oscillations (e.g., ref. 34).

Results

To evaluate the above expectations, we conduct comparisons at two scales (Fig. 2). First, we conduct a controlled comparison of the Middle Mississippi River Valley and Central Texas in N. America. This controlled comparison assesses the population dynamics of regions with similar ecosystems (grassland to wooded savanna), abundant evidence of changes in resource production over the last 3,500 y, and significant differences in social–ecological adaptations. People in the Middle Mississippi River Valley adopted agriculture and, eventually, large centers of population aggregation that should have lowered the costs of social integration [e.g., Cahokia (44, 45)]. The people of Central Texas intensified their production of wild resources, especially wild tubers and bulbs over the last 3,500 y, and remained mobile hunter-gatherers with little evidence of large-scale ritual centers. Second, we compare eight ArchaeoGlobe Regions (46) from the Lower 48 US states. This larger comparison allows us to use estimates of changes in land use made in the ArchaeoGlobe dataset to evaluate the presence of adaptive capacity tradeoffs (i.e., larger innovations in production due to agriculture create longer periods of increases in fitness but require larger recessions) among regions that adopted agriculture to various degrees over the last 3,500 y.

Fig. 2. Map of radiocarbon data from the eight ArchaeoGlobe Regions (Albers equal area projection) used in this study. Dashed circles highlight the Central Texas and Middle Mississippi River Valley case studies.

Scale 1.

Fig. 3 compares the change in population density (A and B), individual fitness (C and D), and resource extraction technology and diet (E and F) over time in the Middle Mississippi River Valley and Central Texas. In the Middle Mississippi River Valley and Central Texas, we track changes in resource production using stable isotopes associated with human bone from 354 individuals (Mississippi Basin) and 78 individuals (Central Texas). Changes in δN15 allow us to track the trophic position of consumers, with higher values indicating more consumption of protein (e.g., American bison, deer, and/or fish) and lower values indicating less consumption of these resources. Further, in the Middle Mississippi River Valley, we use an index of cultigens relative to nuts to estimate changes in the specialized production of carbohydrates from domesticated plants (14). In Central Texas, we use the ratio of large earth oven middens that result from the repeated baking of wild roots to small cooking features as an estimate of specialization in the production of carbohydrates. In both cases, the higher the index, the more effort people invested in producing and consuming energy-dense carbohydrates that require longer processing times.

Fig. 3. Time-series of population, resource extraction technology, and diet in the Middle Mississippi River Basin and Central Texas. (A and B) Mean kernel density estimates (KDE) and 95% confidence envelope of 200 KDE simulations (gray shading). (C and D) Per capita growth rates of mean KDE’s in the Middle Mississippi River Basin and Central Texas. Gray shading is the 95% confidence envelope of simulated KDE growth rates. (E and F) Violin plots of δN15 values from 354 individuals in the Middle Mississippi River Basin and 78 in Central Texas. Each violin plot is shaded by the median cultigen index (Mississippi) or midden index (Texas) during cultural historical time periods (Data and Methods). The change in color of the violin plots indicates changing technology over time from less (red) to more to intensive carbohydrate processing (blue). The black dots indicate the median of the distribution and illustrate the changing physiological impact of a shift to more carbohydrate production. These two lines of evidence indicate innovative processes that sequentially increased K (i.e., moving from K1 to K2 in our model). Error bars are shown at 95 % of the distribution.

In both regions, we observe population curves that increase in a non-linear way over 3,500 y, with a peak at about 800 cal BP (Fig. 3 A and B). Although both cases display a curve-linear increase from 3,500 to 800 cal BP, this growth is distributed differently. In the Middle Mississippi River Valley, populations experienced a positive per capita growth rate, on average, for 23.3 consecutive 30-y generations. For example, the mean and 95% CI of per capita growth remain positive in the Middle Mississippi from 2,300 to 800 cal BP (see the dashed box on Fig. 3C). Conversely, Central Texas populations only display positive per capita growth, on average, for 7.42 consecutive generations, and the 95% confidence envelop of per capita growth is much more variable between 2,300 and 1,400 cal BP (compare dashed boxes on Fig. 3 C and D). Finally, the exponential-like increase in population, in both regions, associates with a step-wise increase in the production of energy-dense carbohydrates and a significant decline in protein consumption near the peak of each curve. In Fig. 3E, δN15 values remain stable between Periods 1 and 2; however, the cultigen index increases from 0.027 to 0.19 from Period 1 to 2. From period 2 to 3, we observe a significant decrease in δN15 values (W = 1,353, P-value < 0.05) and, again, an increase in the cultigen index from 0.19 to 0.77. During Period 5, when the population of the Mississippi River Basin declines, the cultigen index decreases to 0.61, and we observe a significant increase in δN15 values (W = 2473.5, P-value < 0.05). A very similar pattern occurs in Central Texas (Fig. 3F). δN15 values remain unchanged from Period 1 to 2, but the midden index increases from 0.27 to 0.31. Near the peak of population during Period 3, we observe a major increase in the midden index to 0.51 and a significant decline from period 2 to 3 in δN15 values (W = 187.5, P-value < 0.05). Finally, as the population curve declines during Period 4, we observe a decrease in the midden index to 0.11 and a significant increase in δN15 values (W = 22.5, P-value < 0.05).

In summary, our controlled comparison presents evidence consistent with expectations. Both regions experienced population growth over thousands of years associated with step-wise increases in carbohydrate production and a decline in δN15 values near peak population densities. Further, greater commitment to agriculture and larger-scale social integration in the Middle Mississippi River Valley associates with longer periods of positive per capita growth but a more dramatic population recession. The agricultural system achieved exponential expansion through successive demographic transitions in which per capita growth remained positive until the population hit a demographic cliff at 800 cal BP, declining for 300 y. The hunter-gatherer system achieved exponential-like growth via moderate periods of positive per capita growth interspersed by many short periods of negative per capita growth. In Central Texas, populations declined after 800 cal BP less rapidly and severely. In both cases, population decline after 800 cal BP associates with an increase in protein consumption and decline in carbohydrate production, as we would expect in a dynamic predator–prey system as human population decline released pressure on resources and ecosystems recovered.

Scale 2.

Recall that we expect larger innovations in productive capacity to generate longer demographic transitions but also require larger population recessions, if an innovation ceiling occurs (as illustrated in the case studies above). In Fig. 4, we use the presence of extensive agriculture over hunting and gathering and intensive agriculture in addition to extensive agriculture as a proxy for larger innovations in the productivity of resources among eight ArchaeoGlobe regions. Partly consistent with expectations two and three, Fig. 4 illustrates that regions practicing agriculture experience longer periods of consecutive positive per capita growth than populations practicing hunting and gathering. In particular, the large increase in energy extraction afforded by intensive agriculture leads to longer periods of population expansion. Similarly, investing in extensive and intensive agriculture leads to more extreme recessions (estimated by the minimum negative per capita growth experienced in a region). For example, just as with the comparison of the Middle Mississippi and Central Texas, populations experienced extreme recessions in the Southwest and Midwest ArchaeoGlobe regions around 800 cal BP after adopting intensive agriculture in the preceding centuries. Conversely, the Western ArchaeoGlobe region, dominated by hunter-gatherer adaptations, experienced more frequent and much smaller recessions (SI Appendix, Part III).

Fig. 4. The relationship between length of population expansion and severity of subsequent population recession. (A) Length of consecutive positive per capita growth rates among ArchaeoGlobe regions by subsistence land use categories. HG = hunting, gathering, and fishing. Min. Agg = extensive agriculture only. Moderate Agg. = extensive and intensive agriculture land use types. (B) The lowest per capita growth rate associated with periods of negative growth in the eight ArchaeoGlobe regions. HG = hunting, gathering, and fishing. Min. Agg = extensive agriculture only. Moderate Agg. = extensive and intensive agriculture land use types. A and B together suggest that the longer the growth phase, the more intense the subsequent recession.

Discussion

The proliferation of open access archaeological data and synthesis of large radiocarbon datasets (e.g., refs. 2, 9, 10, 18, 22, and 47–49) is changing archaeology. Over the past 20 y, two dominant patterns have emerged from an analysis of these datasets. First, human populations often display exponential-like growth over a few thousand years. Second, following these periods of expansion, human populations sometimes display recessions and oscillations. In this paper, we developed and began to evaluate a general explanation for these patterns. Human populations face an unintended Adaptive Capacity Tradeoff. Large innovations in the ability to extract resources from ecosystems, such as the adoption of intensive agriculture, generate large and consistent gains in well-being in the shorter-run. However, such large innovations require populations to “pay” with large declines in well-being—population recessions—in the longer-run. Mechanistically, the transformation of social–ecological landscapes causes a delay in the feedback from resource conditions to decisions about investments in capital and innovation. These delays may lead to a doubling down on existing forms of production rather than innovations, potentially producing population recessions.

Our analysis is partly consistent with the Adaptive Capacity Tradeoff explanation at two scales. First, comparing the Middle Mississippi River Valley and Central Texas reveals that populations in both regions increased their use of energy-dense carbohydrates in a step-wise process over time. This increased production and consumption of carbohydrates associates with persistent population growth, waves of increases in mean fitness over 3,000 y, and a marked decline in protein consumption very near peak population density in each region (Fig. 3). Further, the evolution of the agricultural system (Mississippi River Valley) displays longer periods of consecutive positive per capita growth and a very large final population recession. The hunter-gatherer system displays shorter periods of positive per capita population growth interspersed by shorter periods of negative growth. These patterns are consistent with model dynamics indicating that large innovations in resource productivity, for example, due to agriculture, lead to the capacity to sustain positive per capita growth rates now, but also introduces delays that require larger population declines in the future. Second, we observe similar dynamics among the eight ArchaeoGlobe regions of the modern US. More transformation of land use to include extensive and intensive agriculture results in longer periods of positive per capita growth and more severe population recessions.

Our study raises important questions for future research and understanding when and why human populations display successive waves of expansion and periodic recess. First, our approach focuses on general systems dynamics as opposed to individual decisions in the context of life history theory (43). Ultimately, we need a multi-scalar theory of human population growth that explains both the long-term expansion of populations over thousands of years and shorter-term fluctuations. This multi-scalar theory informed by deep time archaeological data will be essential for understanding the long-term implications of the demographic dynamics humans are currently experiencing. The key to understanding long-term population expansion is an ability to explain why rates of innovation and people’s affinity for adopting innovations change over time. Certainly, this will require understanding both systems dynamics and how individual preferences for novelty shift with changing demographic and social circumstances.

Second, our analysis focused on two scales. The first was a controlled comparison of two regions with distinct economies and culture histories. This scale of analysis links to a long-standing interest in reorganization/collapse in archaeology and beyond. For instance, in the Middle Mississippi River Valley and surrounding area, researchers have long proposed that climate change and/or social stresses were integral components of the expansion of population around 1,000 cal BP, nucleation of populations in centers such as Cahokia, and then the decline of these centers and population around 770 cal BP (17, 50–52). Our point here is not to provide an alternative to such explanations. Rather, we argue that in many cases, “population collapses” are notable recessions of the carrying capacity of a region that has its antecedents not simply in the decades and centuries prior, but in the transformation of human infrastructure systems over millennia. Given that human populations embed within and create multiple interacting complex adaptive systems, the immediate antecedents to such recessions will always have a unique path dependence and confluence of local factors. But the general pattern driving growth and creating a vulnerability to recessions is the same, we argue, across regions with cultural evolutionary histories as different as Central Texas and the Middle Mississippi River Valley. A comparison of dozens of cases at this scale will help evaluate the ultimate merit of this hypothesis.

The second scale of analysis focused on comparing ArchaeoGlobe regions from within the modern US political boundaries. This scale of analysis averages over many different ecosystems and cultural histories, even within any one ArchaeoGlobe region. For example, the Western US and Northern Rocky Mountains were dominated by hunter-gatherer land use strategies throughout the Holocene. However, hunter-gatherer land use, just as in Central Texas, changed over time and in different ways across these regions. Thus, future research should document the different trajectories of hunter-gatherer population change and compare these trajectories with areas where people adopted agriculture. Further, no doubt many North American archaeologists may point to the different climates across the continent as a key driver of population growth patterns. As evidenced by the inclusion of climate in Eq. 2, we suspect that climate plays an important role, potentially impacting the process of integrating innovations in food production into extant social and economic patterns. Clearly, more work is needed to refine archaeological chronologies to the resolution necessary to document and understand the role of climate in the process of innovations, or lack thereof, in food production.

Third, we qualitatively suggest that the Middle Mississippi River valley developed a lower cost of social integration than Central Texas, and the same for the US Southwest, Midwest, and Southeast relative to the other ArchaeoGlobe regions at a larger scale. The evidence for this is that, in these regions, people developed more integrative ritual centers and widespread iconography associated with centers (e.g., Cahokia, Chaco Canyon, Hohokam platform mounds) (e.g., refs. 44, 45, and 53–55). Thus, we suggest that S became lower over time within these systems, supercharging population overshoots. However, much more work is needed to measure S, archaeologically. We need better theory that connects the costs of social integration with material remains and quantitative time-series of relevant archaeological remains.

Importantly, shared rituals and centers that lower the costs of social integration (e.g., build trust, social capital) always do so for some (in-groups) but not others (out-groups). Thus, social mechanisms, such as increases in the scale of shared rituals, may also associate with more warfare, and disentangling these effects on population requires more work. For example, Kondor and colleagues recently proposed an agent-based model to help explain expansion and recession dynamics in Mid-Holocene Europe (18). They conclude that a model with social conflict (war) better reproduces fluctuating population dynamics than a model that relies on climate perturbations to agricultural carrying capacity alone. Although on the surface quite different from our approach, ultimately the expansion–recession patterns in their model are caused by delays between population growth and the density-dependent feedback of direct competition for resources and warfare. Future research needs to investigate the interaction of changes in the productive capacity of a resource due to innovations, integrative social structures that impact the costs of social integration, and conflict between in and out-groups.

In the end, we argue that the long-term expansion of human populations and recessions may be interrelated. Innovations in the production of food, especially carbohydrate-dense plants, drive waves of long-term positive growth over thousands of years. However, innovations that provide adaptive capacity now also generate long-term trajectories of population growth that transform landscapes. Such landscape transformations may create delays in the effect of density-dependent competition for resources and result in eventual large population recessions. Particularly important in this context is the role of incremental innovations in social integration and productive capacity that only raise a region’s carrying capacity a little (Central Texas) vs. large innovations that raise a region’s potential carrying capacity a lot (Mississippi River Valley). Large increases in integration and productivity where human impacts on ecosystems have a delay lead to a competitive cliff. Populations experience larger scale and longer-term expansion, but at the expense of more painful population recessions (see also refs. 10 and 11). Such dynamics in population systems provide one empirical example of the tradeoff in complex adaptive systems between suppressing variability (i.e., learning) to gain productivity, perhaps for a long time, but at the expense of greater fragility to slow environmental change in the future (e.g., refs. 11 and 56–59).

matseccnt1

Data and Methods

Materials and Methods

The formal model in Eqs. 1–3 was analyzed numerically in XPPAUT (60) (SI Appendix, Part I). All other data are available at ref. 61. To evaluate the Adaptive Capacity Tradeoff Hypothesis, we used previously published data from the Middle Mississippi River Valley and Central Texas (Fig. 2) (14, 62–66). We divided the two above archaeological cases into cultural historical phases identified by archaeologists in each region. In the Middle Mississippi River Valley, which includes the American Bottom, Illinois River Valley, and sites into Missouri, we divided the sequences into Middle Woodland, Early Late Woodland, Late Late Woodland, Mississippian, and Oneota Phases. Fig. 3E compares the distribution of isotope values by each cultural historical phase (n=354 individuals), and we used a Mann–Whitney U test to evaluate the null hypothesis that the distribution of isotope values between consecutive phases comes from the same distribution. We consider a P-value of less than 0.1 as sufficient evidence to reject the null hypothesis. We focus here on changes in δN15, which allow us to track the trophic position of consumers. Higher values potentially indicate more consumption of large to medium-sized animals and/or more fish, and lower values potentially indicate less use of these resources (SI Appendix, Part II).

Once we developed a database of human bone isotopes in the Middle Mississippi, we used an index of nuts to cultigens found in archaeological sites in this region over the last 5,000 y cal BP published by Milner and Boldsen (14). We selected sites that overlap geographically with the sites from which the isotope data were recorded, and we then calculated the median cultigen index by each cultural historical phase. Note that our results do not change if we use the whole dataset, which encompasses sites from Eastern N. America more broadly (SI Appendix, Part II). The cultigen index provides an estimate of the production and use of small domesticated seeds, such as amaranth and maize, relative to nuts higher in protein and fats. The index is calculated as the percentage of cultigens found in site ethnobotanical samples divided by nuts plus cultigens. In general, the domesticated seeds provide lower returns per person hour than nut resources (67). Thus, higher index values indicate more production and use of lower return rate carbohydrates with less protein and fat.

In Central Texas, we divided the sequence into four phases: Early Late Archaic, Terminal Late Archaic, Early Late Prehistoric (Austin Phase), and Late Late Prehistoric (Toyah Phase). Fig. 3F compares the distribution of isotope values by each cultural historical phase (n=78 individuals), and we used a Mann–Whitney U test to evaluate the null hypothesis that the distribution of isotope values between successive phases comes from the same distribution. To track the production of carbohydrates in Central Texas, we used a database of 303 dated fire-cracked rock features that resulted from suspected earth oven cooking (40). Earth ovens are a general cooking technology; however, substantial evidence indicates that the remains of such ovens in Central Texas were used to bake root species for prolonged periods of time (e.g., refs. 40 and 68–70). We ran a cluster analysis of the features, identifying two clusters of feature size: those that cluster around 1 square meter and those that cluster around 100 square meters in surface area. Surface area serves as an estimate for the size of cooking oven and the number of times a cooking feature was reused, generating more fire-cracked rocks (SI Appendix, Part II). Thus, the more that foragers in Central Texas baked roots in the same location, the larger middens should have become. To estimate commitment to the production of root species, we calculated an index of large middens divided by the number of large middens plus small features. The higher this index, the more frequently foragers bulk processed roots in the same locations. The smaller the index, the more small, unique cooking sites foragers created on the landscape.

To reconstruct the population dynamics of the Middle Mississippi River Valley and Central Texas, we used archaeological radiocarbon. We pulled and analyzed 3,167 archaeological radiocarbon ages from Bird et al. (22) that overlap with the geographic distribution of sites with human bone isotopes discussed above, and we used the 1,762 radiocarbon ages published from Central Texas by Freeman et al. (40). We used the R package rcarbon to construct Kernel Density Estimates (KDEs) to estimate changes in population in each region over the last 3,500 y cal BP (71) (SI Appendix, Part II). While radiocarbon records are subject to potential biases, archaeologists have developed models and techniques to control for the biases of sampling intensity, preservation, and the non-linear radiocarbon calibration curve (e.g., refs. 4, 5 and 71–76). To help address these concerns, we constructed mean KDEs in each region by running 200 simulations with a bandwidth of 50 and then calculated the mean of the 200 KDEs. We then summed the KDEs into 30 y bins. Both of these procedures smooth the KDE to capture the long-term trend over time and reduce intra-generational fluctuations over shorter time-scales induced by calibration and/or biases introduced by site over-sampling (SI Appendix, Part II for alternative methods). Further, we constructed these KDEs to 200 cal BP and then trimmed the sequences to 410 cal BP. We end the sequences at 410 cal BP to avoid biases potentially associated with a lack of radiocarbon dating of material remains in N. America after European manufactured items become common and, potentially, useful to date archaeological sites (SI Appendix, Part II, Edge Effects and Taphonomy). In both cases, we are conservative and do not use a global taphonomic adjustment proposed by (77) because the adjustment introduces complexity and uncertainty into the data (SI Appendix, Part II, Edge Effects and Taphonomy). We used Intcal2020 to calibrate the radiocarbon ages (78).

We analyzed the mean KDE in two ways. First, we fit a logistic model to capture the trend over time in the mean KDEs. We use the logistic model because the Adaptive Capacity Tradeoff Hypothesis proposes that population growth over thousands of years follows innovations that, at first raise a population’s limit a lot, but then display diminishing returns, leading to a slowing of increases in a population’s limit as an innovation ceiling is approached. Second, we calculated the per capita growth rates of the mean KDEs as ln(MKDEt+1/MKDEt). We then calculated the number of consecutive generations that each case displayed positive per capita growth, and we recorded the minimum and maximum per capita growth rates in each period of consecutive growth or decline.

To scale our analysis up to ArchaeoGlobe regions, we analyzed archaeological radiocarbon ages documented from eight ArchaeoGlobe regions in the lower 48 contemporary United States. We did this by joining archaeological radiocarbon synthesized by Bird et al. (22) with ArchaeoGlobe shape files. We then constructed KDEs for each region following the same procedures outlined above. Next, we integrated ArchaeoGlobe estimates of land use (46) with the mean KDE data. In particular, ArchaeoGlobe uses a consensus of expert opinions to estimate how widespread types of land use were at 1,000 y intervals. In our cases, land use types include hunting, gathering, and fishing, extensive agriculture, intensive agriculture, and urbanism (or a high degree of settlement nucleation). We assume, based on ethnographic evidence (e.g., ref. 41), that agricultural land use, on average, has a higher productive potential than hunting and gathering land use. To capture differences in land use, we coded each case and 1,000 y time period as HG = hunting and gathering land use only, Minimum Agg. = the presence of extensive agriculture; Moderate Agg. = the presence of extensive and intensive agricultural land use.

Once we integrated the KDE and ArchaeoGlobe data, we calculated the per capita growth rates of the mean KDE in each region as ln(MKDEt+1/MKDEt). We counted the number of consecutive generations with positive per capita growth in each case by the land use categories of HG, Minimum Agg., and Moderate Agg. If a given set of positive per capita growth rates crossed land use boundaries, we used the more productive land use category. For example, in the Northeast US region, one period of positive growth begins at 3,090 and ends at 2,820 cal BP. During this time period, extensive agricultural land use begins at 3,000 cal BP in the ArchaeoGlobe data. We recorded this period of growth as occurring in the Minimum Agg. category. Finally, we recorded the minimum and maximum per capita growth rate in each block of consecutive growth or decline (SI Appendix, Part III).

Supplementary Material

Appendix 01 (PDF)

We are grateful for financial support from the NSF, Grants: BCS-1535841 and IBSS-L:1520308. This study was also undertaken by J.F., E.R., and D.B. as part of PEOPLE 3000, a working group of the Past Global Changes (PAGES) project, which in turn received support from the Swiss Academy of Sciences and the Chinese Academy of Sciences. Finally, we would like to thank three anonymous reviewers and the editor for their helpful comments and suggested improvements on previous versions of the manuscript.

Author contributions

J.F. and E.R. designed research; J.F., D.B., R.J.H., R.P.M., and J.M.A. performed research; J.F. analyzed data; and J.F., E.R., D.B., R.J.H., R.P.M., and J.M.A. wrote the paper.

Competing interests

The authors declare no competing interest.

Data, Materials, and Software Availability

Raw and processed radiocarbon data and other stable isotope data have been deposited in NorthAmericaAdaptiveCap2 (https://doi.org/10.5281/zenodo.8217599) (61).

Supporting Information

This article is a PNAS Direct Submission.

Although PNAS asks authors to adhere to United Nations naming conventions for maps (https://www.un.org/geospatial/mapsgeo), our policy is to publish maps as provided by the authors.
==== Refs
1 J.-P. Bocquet-Appel, O. Bar-Yosef, The Neolithic Demographic Transition and Its Consequences (Springer, 2008).
2 S. Shennan , Regional population collapse followed initial agriculture booms in mid-Holocene Europe. Nat. Commun. 4 , 2486 (2013).24084891
3 S. Shennan, “Population processes and their consequences in early Neolithic Central Europe” in The Neolithic Demographic Transition and Its Consequences (Springer, 2008), pp. 315–329.
4 S. Shennan, Demographic continuities and discontinuities in Neolithic Europe: Evidence, methods and implications. J. Archaeol. Method Theory 20 , 300–311 (2013).
5 E. R. Crema, Statistical inference of prehistoric demography from frequency distributions of radiocarbon dates: A review and a guide for the perplexed. J. Archaeol. Method Theory 29 , 1–32 (2022).
6 R. L. Kelly, T. A. Surovell, B. N. Shuman, G. M. Smith, A continuous climatic impact on Holocene human population in the Rocky Mountains. Proc. Natl. Acad. Sci. U.S.A. 110 , 443–447 (2013).23267083
7 H. Jabran Zahid, E. Robinson, R. L. Kelly, Agriculture, population growth, and statistical analysis of the radiocarbon record. Proc. Natl. Acad. Sci. U.S.A. 113 , 931–935 (2016).26699457
8 A. Bevan , Holocene fluctuations in human population demonstrate repeated links to food production and climate. Proc. Natl. Acad. Sci. U.S.A. 114 , E10524–E10531 (2017).29158411
9 J. Freeman , Synchronization of energy consumption by human societies throughout the Holocene. Proc. Natl. Acad. Sci. U.S.A. 115 , 9962–9967 (2018).30224487
10 D. Bird , A first empirical analysis of population stability in North America using radiocarbon records. Holocene 30 , 1345–1359 (2020).
11 J. Freeman , Landscape engineering impacts the long-term stability of agricultural populations. Hum. Ecol. 49 , 369–382 (2021).
12 A. Palmisano , Holocene landscape dynamics and long-term population trends in the Levant. Holocene 29 , 708–727 (2019).
13 P. V. Kirch , Reprint: Building and testing models of long-term agricultural intensification and population dynamics: A case study from the leeward Kohala Field system, Hawai’i. Ecol. Model. 241 , 54–64 (2012).
14 G. R. Milner, J. L. Boldsen, Population trends and the transition to agriculture: Global processes as seen from North America. Proc. Natl. Acad. Sci. U.S.A. 120 , e2209478119 (2023).36649404
15 G. R. Milner, D. G. Anderson, M. T. Smith, “The distribution of Eastern Woodlands peoples at the prehistoric and historic interface” in Societies in Eclipse: Archaeology of the Eastern Woodland Indians, A.D. 1400–1700, D. S. Brose, C. Wesley Cowan, C. Robert Manifort, Jr., Eds. (Smithsonian Institution Press, Washington, DC, 2001), pp. 9–18.
16 G. R. Milner, The Moundbuilders: Ancient Societies of Eastern North America (Thames & Hudson, London, UK, ed. 1, 2004).
17 D. G. Anderson, Examining prehistoric settlement distribution in eastern North America. Archaeol. East. N. Am. 19 , 1–22 (1991).
18 D. Kondor , Explaining population booms and busts in mid-Holocene Europe. Sci. Rep. 13 , 9310 (2023).37291136
19 E. A. Peralta , Past maize consumption correlates with population change in Central Western Argentina. J. Anthropol. Archaeol. 68 , 101457 (2022).
20 M. Lima , Ecology of the collapse of Rapa Nui Society. Proc. R. Soc. B 287 , 20200662 (2020).
21 M. Lima , Positive feedbacks in deep-time transitions of human populations. Philos. Trans. R. Soc. B: Biol. Sci. 379 , 20220256 (2024).
22 D. Bird , p3k14c, a synthetic global database of archaeological radiocarbon dates. Sci. Data 9 , 1–19 (2022).35013360
23 J. E. Cohen, Population growth and earth’s human carrying capacity. Science 269 , 341–346 (1995).7618100
24 R. D. Lee, “Malthus and Boserup: A dynamic synthesis” in The State of Population Theory: Forward from Malthus, D. Coleman, R. Schofield, Eds. (Blackwell, Oxford, UK, 1986), pp. 96–130.
25 C. T. Lee, S. Tujapurkar, Population and prehistory. I: Food-dependent population growth in constant environments. Theor. Popul. Biol. 73 , 473–482 (2008).18439637
26 C. T. Lee, C. O. Puleston, S. Tuljapurkar, Population and prehistory. III. Food-dependent demography in variable environments. Theor. Popul. Biol. 76 , 179–188 (2009).19540865
27 C. O. Puleston, S. Tuljapurkar, Population and prehistory. II. Space-limited human populations in constant environments. Theor. Popul. Biol. 74 , 147–160 (2008).18598711
28 C. Puleston, S. Tuljapurkar, B. Winterhalder, The invisible cliff: Abrupt imposition of Malthusian equilibrium in a natural-fertility, agrarian society. PLoS ONE 9 , e87541 (2014).24498131
29 P. S. Meyer, J. H. Ausubel, Carrying capacity: A model with logistically varying limits. Technol. Forecast. Soc. Change 61 , 209–214 (1999).
30 J. W. Wood, A theory of preindustrial population dynamics: Demography, economy, and well-being in Malthusian systems. Curr. Anthropol. 39 , 99–135 (1998).
31 J. Wood, The Biodemography of Subsistence Farming: Population, Food and Family (Cambridge University Press, Cambridge, UK, 2020), vol. 87 .
32 J. M. Anderies, Economic development, demographics, and renewable resources: A dynamical systems approach. Environ. Dev. Econ. 8 , 219–246 (2003).
33 J. M. Anderies, Culture and human agro-ecosystem dynamics: The Tsembaga of New Guinea. J. Theor. Biol. 192 , 515–530 (1998).9680724
34 P. J. Richerson, R. Boyd, R. L. Bettinger, Cultural innovations and demographic change. Hum. Biol. 81 , 211–235 (2009).19943744
35 P. J. Richerson, R. Boyd, Homage to Malthus, Ricardo, and Boserup toward a general theory of population, economic growth, environmental deterioration, wealth, and poverty. Hum. Ecol. Rev. 4 , 85–90 (1998).
36 J. Freeman, R. J. Hard, R. P. Mauldin, J. M. Anderies, Radiocarbon data may support a Malthus–Boserup model of hunter-gatherer population expansion. J. Anthropol. Archaeol. 63 , 101321 (2021).
37 V. I. Yukalov, E. P. Yukalova, D. Sornette, Punctuated evolution due to delayed carrying capacity. Physica D 238 , 1752–1767 (2009).
38 T. R. Malthus, An Essay on the Principle of Population: Or, a View of Its Past and Present Effects on Human Happiness (Reeves and Turner, London, UK, 1888).
39 E. Boserup, Population and Technological Change? A Study of Long-Term Trends (University of Chicago Press, Chicago, IL, 1981).
40 J. Freeman, R. P. Mauldin, M. Whisenhunt, R. J. Hard, J. M. Anderies, Repeated long-term population growth overshoots and recessions among hunter-gatherers. Holocene 33 , 1163–1175 (2023).
41 J. Freeman , The global ecology of human population density and interpreting changes in paleo-population density. J. Archaeol. Sci. 120 , 105168 (2020).
42 J. Freeman, The socioecology of territory size and a “work-around’’ hypothesis for the adoption of farming. PLoS ONE 11 , e0158743 (2016).27391955
43 S. Shennan, R. Sear, Archaeology, demography and life history theory together can help us explain past and present population patterns. Philos. Trans. R. Soc. B 376 , 20190711 (2021).
44 G. R. Milner, The Moundbuilders: Ancient Societies of Eastern North America (Thames & Hudson, London, UK, ed. 2, 2004).
45 T. R. Pauketat, S. M. Alt, J. D. Kruchten, The emerald acropolis: Elevating the moon and water in the rise of Cahokia. Antiquity 91 , 207–222 (2017).
46 L. Stephens , Archaeological assessment reveals Earth’s early transformation through land use. Science 365 , 897–902 (2019).31467217
47 R. L. Kelly , A new radiocarbon database for the lower 48 states. Am. Antiq. 87 , 581–590 (2022).
48 E. C. Kansa , The Digital Index of North American Archaeology: Networking government data to navigate an uncertain future for the past. Antiquity 92 , 490–506 (2018).
49 J. J. Wells , Web-based discovery and integration of archaeological historic properties inventory data: The Digital Index of North American Archaeology (DINAA). Lit. Linguist. Comput. 29 , 349–360 (2014).
50 L. V. Benson, T. R. Pauketat, E. R. Cook, Cahokia’s boom and bust in the context of climate change. Am. Antiq. 74 , 467–483 (2009).
51 B. W. Bird, J. J. Wilson, W. P. Gilhooly III, B. A. Steinman, L. Stamps, Midcontinental Native American population dynamics and late Holocene hydroclimate extremes. Sci. Rep. 7 , 41628 (2017).28139698
52 C. R. Cobb , The beginning of the end: Abandonment micro-histories in the Mississippian vacant quarter. J. Archaeol. Method Theory, 1–25 (2023).37359278
53 R. Gwinn Vivian, Chacoan roads: Function. KIVA 63 , 35–67 (1997).
54 L. Sebastian, The Chaco Anasazi: Sociopolitical Evolution in the Prehistoric Southwest (Cambridge University Press, 1996).
55 D. R. Abbott, A. M. Smith, E. Gallaga, Ballcourts and ceramics: The case for Hohokam marketplaces in the Arizona desert. Am. Antiq. 72 , 461–484 (2007).
56 S. R. Carpenter, W. A. Brock, E. H. van Carl Folke, Nes, and Marten Scheffer, Allowing variance may enlarge the safe operating space for exploited ecosystems. Proc. Natl. Acad. Sci. U.S.A. 112 , 14384–14389 (2015).26438857
57 N. N. Taleb, Antifragile: Things that Gain from Disorder (Random House Incorporated, 2012), vol. 3 .
58 J. M. Anderies, A. A. Rodriguez, M. A. Janssen, O. Cifdaloz, Panaceas, uncertainty, and the robust control framework in sustainability science. Proc. Natl. Acad. Sci. U.S.A. 104 , 15194–15199 (2007).17881574
59 L. B. Jorde, H. C. Harpending, Cross-spectral analysis of rainfall and human birth rate: An empirical test of a linear model. J. Hum. Evol. 5 , 129–138 (1976).
60 B. Ermentrout, Xppaut 5.96 (2006).
61 J. Freeman, Adaptive Capacity Tradeoff Data (2023) N.AmericaAdaptiveCap2. https://zenodo.org/records/10163554. Deposited 20 November 2023.
62 J. Freeman, R. Mauldin, R. J. Hard, people3k/Texas-Adaptive_Capacity: AdaptCapatTradeoff (1.0). Zenodo. 10.5281/zenodo.7757792 (Accesses 30 July 2023).
63 R. M. Tubbs, Ethnic Identity and Diet in the Central Illinois River Valley (Michigan State University, 2013).
64 S. H. Ambrose, J. Buikstra, H. W. Krueger, Status and gender differences in diet at Mound 72, Cahokia, revealed by isotopic analysis of bone. J. Anthropol. Archaeol. 22 , 217–226 (2003).
65 F. Rose, Intra-community variation in diet during the adoption of a new staple crop in the Eastern Woodlands. Am. Antiq. 73 , 413–439 (2008).
66 K. Hedman, E. A. Hargrave, S. H. Ambrose, Late Mississippian diet in the American Bottom: Stable isotope analyses of bone collagen and apatite. Midcont. J. Archaeol. 27 , 237–271 (2002).
67 B. Winterhalder, C. Goland, On population, foraging efficiency, and plant domestication. Curr. Anthropol. 34 , 710–715 (1993).
68 R. McAuliffe, R. P. Mauldin, S. L. Black, “Central Texas plant baking” in Earth Ovens and Desert Lifeways: 10,000 Years of Indigenous Cooking in the Arid Landscapes of North America, C. W. Koenig, M. R. Miller, Eds. (University of Utah Press, Salt lake City, UT, 2022), pp. 33–60.
69 R. P. Mauldin, D. L. Nickels, C. J. Broehm, Archaeological testing to determine the National Register eligibility status of 18 prehistoric sites on Camp Bowie, Brown County, Texas (Archaeological Survey Report, Center for Archaeological Research, The University of Texas at San Antonio, San Antonio, TX, 2003), vol. 334 .
70 S. L. Black, D. G. Creel, “The Central Texas burned rock midden reconsidered” in Hot Rock Cooking on the Greater Edwards Plateau: Four Burned Rock Midden Sites in West Central Texas, Studies in Archeology 22, S. L. Black, L. W. Ellis, D. G. Creel, G. T. Goode, Eds. (Texas Archeaological Research Laboratory, The University of Texas at Austin, Austin, TX, 1997), pp. 269–301.
71 E. R. Crema, A. Bevan, Inference from large sets of radiocarbon dates: Software and methods. Radiocarbon 63 , 23–39 (2021).
72 J. Freeman, D. A. Byers, E. Robinson, R. L. Kelly, Culture process and the interpretation of radiocarbon data. Radiocarbon 60 , 453–467 (2018).
73 E. R. Crema, A. Bevan, S. Shennan, Spatio-temporal approaches to archaeological radiocarbon dates. J. Archaeol. Sci. 87 , 1–9 (2017).
74 A. Timpson , Reconstructing regional population fluctuations in the European Neolithic using radiocarbon dates: A new case-study using an improved method. J. Archaeol. Sci. 52 , 549–557 (2014).
75 N. Williams Alan, The use of summed radiocarbon probability distributions in archaeology: A review of methods. J. Archaeol. Sci. 39 , 578–589 (2012).
76 T. A. Surovell, J. B. Finley, G. M. Smith, P. Jeffrey Brantingham, R. Kelly, Correcting temporal frequency distributions for taphonomic bias. J. Archaeol. Sci. 36 , 1715–1724 (2009).
77 L. E. Bluhm, T. A. Surovell, Validation of a global model of taphonomic bias using geologic radiocarbon ages. Quatern. Res. 91 , 325–328 (2019).
78 P. J. Reimer , The IntCal20 northern hemisphere radiocarbon age calibration curve (0–55 cal kbp). Radiocarbon 62 , 725–757 (2020).
