Carbon, Climate, and Collapse: Coupling Climate Feedbacks and Resource Dynamics to Predict Societal Collapse

Abstract

Anthropogenic climate change threatens production of essential natural resources, including food, fiber, and fresh water, and provisioning of ecosystem services such as carbon sequestration, increasing the risk of societal collapse. The Human and Nature Dynamics (HANDY) model simulates the effect of resource overexploitation on societal collapse but lacks representation of feedbacks between climate change and resource regeneration in ecological systems. We extend the HANDY model by integrating models of climate change and ecological function to examine the risk of societal collapse. We conducted a sensitivity analysis of our expanded model by systematically varying key parameters to examine the range of plausible socio-ecological conditions and evaluate model uncertainty. We find that lowered greenhouse gas emissions and resilient ecosystems can delay societal collapse by up to approximately 500 years, but that any scenario with greater than net-zero greenhouse gas emissions ultimately leads to societal collapse driven by climate-induced loss of ecosystem function. Reductions in greenhouse gas emissions are the most effective intervention to delay or prevent societal collapse, followed by the conservation and management of resilient ecological systems to sequester atmospheric carbon.

1. Introduction

Resource consumption and greenhouse gas (GHG) emissions have accelerated since the onset of industrialization, driving the potential for societal collapse. Overshooting the carrying capacity of the natural environment, or overutilization of natural resources to the point of scarcity, has been a common cause of societal collapse in the past. Surpassing carrying capacity has been studied by many academics [1,2,3,4,5], notably coined as Malthusian catastrophe [6], Tragedy of the commons [7], and overshoot and collapse [8]. Some modern scholars believe that modern society may have already reached that point [9,10].

Motesharrei et al. present a conceptual and mathematical model to simulate and study the factors associated with such collapse [1]. Their Human and Nature Dynamics (HANDY) model examines how class inequality and income distribution may affect trends of population dynamics and societal collapse. The HANDY model recreates two patterns of societal collapse driven by inequality and resource overuse and shows that collapse can be avoided when resource depletion and social inequality are low [1]. While HANDY explores the effect of societal inequity on societal collapse, it does not consider the feedback between anthropogenic climate change and ecosystem function.

Contemporary society faces even greater challenges from environmental change than past collapsed societies [11]. Anthropogenic climate change can induce a reinforcing feedback that alters the potential for ecological systems to sequester carbon. These feedbacks can reinforce climate change through altered disturbance regimes, decreased ecosystem function, and decreases in carbon sequestration capacity [12,13,14,15]. Changing temperature associated with climate change has already led to phenological mismatches, range shifts, biodiversity loss, extinctions, and loss of crop photosynthetic capacity [13,16], all of which reduce carbon sequestration and access to ecosystem services. Declines in ecosystem services could drive societal derailment, i.e., disruption of social and economic systems and declines in human population, leading to reductions in anthropogenic GHG emissions through reductions in economic activity, in a balancing feedback that could reduce the rate of climate change [17].

HANDY does not represent this potential feedback between climate change and ecosystem function that could contribute to societal collapse. We represent this missing component by expanding the HANDY model to include a simple climate model [18] and a feedback between climate and ecosystem function in the carbon, climate, and collapse (or C³) model. We use carbon emissions as a proxy for GHG emissions and carbon intensity (I_C)—Defined as carbon use per unit of wealth accumulation—As a proxy for a society’s balance of fossil fuel and renewable energy sources. Our model represents the declining capacity of ecosystems to sequester carbon with climate change, along with reduced regeneration of ecosystem services, reflecting potential declines in production of food, fiber, fresh water, and other vital ecosystem services. We use the yearly change in global mean surface temperature as a proxy for climate change and refer to the two interchangeably throughout this paper.

We use the expanded model of human and ecological dynamics to evaluate how carbon intensity and ecological resilience influence societal dynamics and the risk of societal collapse. Our simulations vary four key parameters to capture uncertainty in carbon intensity and ecological resilience: (1) Carbon intensity (I_C), or the degree of societal reliance on fossil fuels versus renewable energy sources, (2) ecological niche breadth (σ), which determines ecosystem resilience to changes in climate, (3) maximum carbon sequestration (S_rM), representing the greatest rate of atmospheric carbon that ecosystems can remove under optimal temperature conditions, and (4) the functional relationship (r) between ecosystem resilience and climate change to reflect how ecosystem function may decline as temperature rises. We assess societal resilience to feedbacks between climate change and ecosystem function using collapse or time to collapse in simulations while factorially varying model parameters to assess model sensitivity to parameter uncertainty.

2. Materials and Methods

The HANDY model was created to simulate societal collapse [1]. It uses the predator-prey model [19,20] to investigate human and nature dynamics (Equations (A1)–(A4)) such that the human population serves as “predator” while nature serves as “prey”, and humans “predate” on natural resources to grow their population (see Appendix A.1). HANDY expands on this concept by introducing complexity through class stratification and wealth accumulation. It includes two populations of humans: commoners, who use natural resources to generate wealth, and elites, who consume this wealth to increase their population (see Appendix A.2). Motesharrei et al. use the HANDY model to explore how social structures and scales of resource depletion influence societal dynamics (Equations (A5)–(A13)) [1]. Their simulations run for 1000 years and show that societies of all levels of inequality can collapse or reach equilibrium, depending on resource usage.

The climate component of C³ is designed to capture the change in global mean surface temperature as a function of changing atmospheric carbon (Figure 1). This model element consists of a gray atmosphere radiative transfer module and a temperature simulation module [18]. The atmosphere component computes the net solar flux at the Earth’s surface as a function of planetary albedo, incoming solar radiation, and atmospheric opacity (Equations (A14)–(A19)). Then, the temperature module uses this net solar flux to calculate the global mean surface temperature and the difference from the previous year (see Appendix A.3).

In our C³ model, we use the HANDY equitable society scenario, initializing our joint HANDY-climate model with a ratio of 4:1 commoners to elites, starting populations of 100 commoners and 25 elites, and an inequality factor of 1 (with no difference in commoner and elite salaries). Because the society is equitable, with equal pay for commoners and elites, our model does not include wealth inequality, only labor inequality. Following Motesharrei and colleagues, our simulations were 1000 years long to explore both the long-term and near-term consequences of GHG emissions from fossil fuel usage. We added temporal specificity by beginning in the year 1850 to simulate the rise in industrialization and GHG emissions.

The HANDY and climate models are joined through the creation of an atmospheric carbon stock (Figure 1). Atmospheric carbon (A_C) is initialized at 501 PgC, the equilibrium value for the climate model. A_C is increased through carbon emissions and decreased through sequestration:

DA_C/dt = E − S

(1)

Emissions are proportional to the amount of accumulated wealth and the carbon intensity (I_C) of the society, or the amount of carbon in petagrams emitted per ecodollar of accumulated wealth (w):

E = I_C × w

(2)

Carbon intensity thus represents the “greenness” of a society. Lower values of carbon intensity correspond to a society that relies less on fossil fuel consumption. Higher values correspond to heavy reliance on fossil fuels to generate wealth.

We define ecosystem resilience to include three distinct parameters: σ, r, and S_rM. Each parameter represents a facet of resilience and robustness of ecosystem function to climatic change, represented as temperature change. The critical thermal maximum, or σ, refers to the temperature at which ecosystem function ceases, defining the range of temperature niche breadth. This parameter controls the regenerative capacity of natural resources by modifying ecological carrying capacity. Therefore, σ encompasses both niche breadth and regenerative capacity. In addition, we explore the conservation of ecosystem function through varying two carbon sequestration parameters (r and S_rM). S_rM is the maximum sequestration rate, representing the maximum amount of carbon that can be removed from the atmosphere per year per unit of ecosystem resources when the ecosystem is at its optimal climate condition (e.g., optimal temperature).

Sequestration, or the removal of carbon from the atmosphere through photosynthesis, is proportional to the amount of available natural resources (y) as a proxy for ecosystem services and the sequestration rate, (S_r), or the amount of carbon sequestered per year by one ecodollar of natural resources (Figure 1). This assumes that natural resources represent Earth’s photosynthesizing vegetation:

S = S_r × y

(3)

Sequestration rate changes with change in temperature (ΔT), as increasing temperature can put stress on vegetation through reduction in photosynthetic capacity, as well as phenological mismatch, range shift, biodiversity loss, or even extinction [13,21]:

S_r = S_rM × (1 − ΔT/6)^r

(4)

where r is a steepness parameter used to control the functional relationship between temperature and sequestration, and S_rM is the maximum amount of carbon that can be sequestered at the optimal temperature, or ΔT = 0. The steepness parameter (r) represents the possible functional forms of how temperature can reduce the photosynthetic capacity of vegetation, such that (1 − ΔT/6)^r equals a number between 0 and 1 to modify the photosynthetic rate as ΔT increases from 0. Steepness can be varied to explore these functional relationships. This introduces a reinforcing feedback whereby increasing atmospheric carbon creates higher temperatures, making the sequestration capacity of ecosystems lower, leading to even more atmospheric carbon (Figure 1).

Temperature change (ΔT) can also affect the ability of ecosystems to regenerate after being utilized for the production of wealth [13]. The ecosystem carrying capacity (λ), or the ecosystem function an environment can sustain over time, is adjusted via a normal cumulative density function (CDF, Φ):

∆λ = 1 − 2 × Φ (ΔT − σ)

(5)

where σ is the niche breadth of vegetation, or the amount of warming that vegetation can tolerate before regeneration stops. We use the normal CDF to calculate the likelihood that a given change in temperature remains within the tolerance limits specified by an ecosystem’s niche breadth. Values close to 1 represent a temperature anomaly within a vegetation’s tolerable range and values close to 0 represent a temperature anomaly outside or nearly outside this range. The latter results in a lower carrying capacity because of limits on regenerative potential [13].

In the original HANDY model, natural resources have a fixed carrying capacity (λ). Our λ_adjusted parameter implements the cumulative density function to limit carrying capacity based on change in temperature:

λ_adjusted = ∆λ × λ

(6)

which effectively lowers the maximum ecosystem functionality, as well as its ability to regenerate.

Sensitivity Analysis

C³ is not calibrated to a specific dataset but we instead examine model response across parameter values drawn from literature-informed ranges (see Appendix B,

Table A1. Parameter samples for sensitivity analysis.

Parameter	IC	σ	r	SrM
Sample range	{0, 1}	{1, 5}	{0.01, 1, 30}	{0, 0.01}
Justification	After running shortened simulations from 1850 to 2022, we found that a value of 0.4–0.5 led to similar anthropogenic emissions to observed data since the industrial revolution. Therefore, we made 0.5 the mean value of CI. We chose 0 as a lower bound to show the impact of net-zero GHG emissions, and 1 as the upper bound to show extreme GHG emission scenarios and keep the mean sample at 0.5.	We chose this range to represent realistic warming scenarios over the next 1000 years. We also use this range to test a variety of possible “tipping point” temperatures (at which reinforcing ecological feedbacks begin) proposed by Armstrong McKay et al., (2022).	The range of r designates the functional form of the relationship between temperature and ecosystem function. We use photosynthetic capacity, as we are specifically interested in how climate change might limit carbon sequestration. The three values represent extreme possibilities of this functional relationship, including steep exponential decay with increasing temperatures, linear decay, and gradual logistic decay.	The maximum sequestration rate, or the rate at which natural resources can sequester carbon, is a representation of the maximum functional capacity of ecosystem services in terms of carbon sequestration. We bookended the range of tested values with 0, or no carbon sequestration, and 0.01, which often yielded unrealistically low atmospheric carbon concentrations
Source	[22]	[12,30]	None	[30]

). We ran a 648-sample sensitivity analysis varying carbon intensity (I_C) and ecological resilience parameters σ, r, and S_rM (

Table 1. Important C³ parameters, parameter samples for sensitivity analysis.

Parameter	IC	σ	r	SrM
Process Represented	Anthropogenic emissions	Critical Thermal Maximum	Decreased photosynthetic Capacity	Carbon Sequestration
Affects	Atmospheric Carbon (Climate)	Adjusted carrying capacity (HANDY)	Atmospheric Carbon (Climate)	Atmospheric Carbon (Climate)
Number of Samples	6	6	3	6
Sample range	{0, 1}	{1, 5}	{0.01, 1, 30}	{0, 0.01}

), and recorded 1000 simulated years of commoner and elite populations, global mean surface temperature, natural resources, and accumulated wealth. Parameter values were chosen to bracket the range of supported values, and we varied parameters across these ranges to examine model sensitivity to parameter uncertainty.

Carbon intensity samples ranged from 0 to 1 petagrams of carbon per ecodollar per year (Table A1) with a value of 0.4 giving similar cumulative carbon emissions to current society [22]. Niche breadth ranged from tolerating 1 to 5 °C increase from pre-industrial global mean surface temperature (Table A1). Varying this parameter examines the sensitivity of ecosystem function to temperature change, allowing us to see how widening or narrowing niche breadth affects long-term feedbacks between climate change and resources. We used three values of r, which define the functional relationships between temperature and sequestration rate: 30 (rapid initial decline and a limit of zero), 1 (linear), and 0.01 (gradual initial decline followed by acceleration) (Table A1). Finally, the maximum sequestration rate, or the amount of carbon sequestered per ecodollar of natural resources per year, ranged from 0, or no sequestration, to 0.01. Values higher than 0.01 often led to decreasing atmospheric carbon to below equilibrium values, which we deemed not representative of plausible ecological conditions, and therefore truncated the range there (Table A1).

Two regression trees were run on the results of the sensitivity analysis to determine feature importance.

3. Results

3.1. Change in Temperature

The sensitivity analysis yielded clustered temperature change results with clusters largely driven by niche breadth and stratification driven by carbon intensity (Figure 2), as confirmed by a regression tree (Figure 3). Simulations with wider niche breadths tended to yield larger increases in temperature than those with more narrow niche breadths. Similarly, simulations with high values of carbon intensity yielded larger temperature increases than those with low carbon intensity. Functional form and maximum sequestration also drove more granular stratification within these clusters with varying effects. Some simulations reached equilibria, and some runs peaked and started to decrease between years 2100 and 2250 (Figure 2). A stable temperature equilibrium was achieved in some simulations following societal collapse.

3.2. Time to Population Collapse

All populations were initially increasing in model simulations (see Appendix C). For each run where GHG emissions were greater than zero (I_C > 0), populations peaked around the year 2100 and collapsed before the end of the 1000-year run (Figure A1 and Figure A2). Only populations with no reliance on fossil fuels (i.e., 0 GHG emissions or I_C = 0) reached an equilibrium. The inequality factor for all simulations was held constant at 1, and so the proportion of commoners to elites remained at 1:4 for the entire run, and the trajectories of both groups were the same within each run.

There was some clustering in both populations driven by a combination of carbon intensity and niche breadth (Figure A1 and Figure A2). We define collapse as a population with <1 person. Commoner populations that collapsed did so between years 2394 and 2850, with a mean collapse date of 2544 and a median of 2537 (

Table A2. Mean time to collapse across values of carbon intensity (CI) and niche breadth (σ).

	Carbon Intensity
Niche Breadth	0.2	0.6	1
1	2466.6	2421.1	2427.7
2.6	2654.9	2497.7	2423.9
5	2845.3	2667.2	2591.6

). The mean collapse time with an I_C of 0.2 was 2649, while a CI of 1 led to a mean collapse time of 2481. The mean collapse time with a niche breadth of 1 was 2430, while a niche breadth of 6 led to a mean collapse time of 2661. As niche breadth widened, both the number of years to collapse and the spread of possible times to collapse increased (Figure 4). Carbon intensity created stratification within this distribution of outcomes, with lower values of carbon intensity delaying collapse (Figure 4). A regression tree examining the time to collapse for commoner populations branched only on niche breadth and carbon intensity (Figure 5).

4. Discussion

4.1. Summary of Findings

We used a coupled model of humans, climate, and ecosystems to examine long-term societal dynamics while varying carbon intensity of the human system and resilience of ecological systems. We found that reinforcing feedbacks between declines in ecosystem function and climate change amplified overshoot of human carrying capacity. Our simulations illustrate the potential effects of continued GHG emissions on societal outcomes. Net emissions greater than 0 led to societal collapse in all of our simulations, with higher carbon intensities leading to earlier collapse. The combined effects of GHG emissions and ecological stress in our model simulations reinforces the need for timely reductions in anthropogenic emissions with a goal of net-zero emissions.

Reducing GHG emissions is the most immediate and actionable step society can take to delay collapse. Our results also illustrate that societal outcomes also depend on ecological resilience—especially niche breadth which, in our C³ model, reflects how much climatic change ecosystems can tolerate before their function declines. Increases in global temperature are a consequence of any amount of GHG emissions, and so the ability of ecological systems to function in the face of climate change is a critical factor in societal resilience or collapse. This points to the need for a concomitant focus on fostering ecological resilience to climate change in addition to achieving net-zero GHG emissions.

4.2. Paradox of Resilience

Counterintuitively, a narrow niche breadth in our model simulations led to lower overall temperature increases than did wide niche breadth. This is because a narrow niche breadth was associated with faster resource depletion and societal collapse, which in turn meant less overall anthropogenic GHG emissions. In contrast, when niche breadth was wide, ecosystems could tolerate relatively more climate change, which supported larger human populations and economic activity, and ultimately led to more GHG emissions and increased climate change. Greater ecosystem resilience allows society to emit more GHGs and drive more climate change before societal collapse. This apparent paradox, that greater ecosystem resilience allows humans to engage in unsustainable behaviors for longer before ecological systems collapse, could provide time and opportunity to achieve sustainability, but could also be mistakenly interpreted as society being resilient and sustainable. This is reminiscent of the observation that those societies most responsible for emissions often avoid their most immediate effects [23] and represents a potential “system trap” of high ecosystem resilience.

Although high levels of ecological resilience and lowered dependence on fossil fuels may postpone societal collapse, any net emissions of GHGs inevitably lead to societal collapse. The implication is that the use of non-renewable fossil fuels can make renewable resources less renewable: In our C³ model simulations, GHG emissions reduced the resilience of ecological systems, reducing the regeneration of renewable resources.

4.3. Limitations and Future Directions

Our C³ model is a greatly simplified Earth system model that does not account for many important processes, for example, socio-behavioral feedbacks to GHG emissions, technological development that reduces carbon intensity of economic activities, and regional variation in ecological impacts that could affect global ecological resilience. Our model is nonspatial and so does not account for regional variation in climate change nor variation in ecosystem function. Other unrepresented effects on ecological function could arise with warming as well, including increased incidence of disease [24], natural disasters [25], and heat waves [26], which in turn could directly affect population sizes. Finally, our model does not explicitly include the socio-behavioral effects of climate change, societal derailment, and political instability sparked by resource insecurity [17], nor perceived risk and policy interventions that continued climate change may bring about [27,28]. Our C³ model presents a simplified and abstract representation of ecosystem resilience that allows us to examine feedbacks between ecosystems, humans, and climate using a low-dimensional model to better understand interactions between system components. Technological advancements, dynamic socio-behavioral responses and changing ecological responses that reduce GHG emissions over time are not included in the model, though a dynamic carbon intensity parameter would only delay collapse in the absence of achieving 0 net emissions. For projections or predictions of likely societal trajectories, more complex and complete representations of ecological, social, or economic systems would be needed.

Our model is a mean field approximation that does not include spatial heterogeneity, which can lead to complex feedbacks between emissions and the impacts of climate change mediated by the human perception of risk, and more complex ecosystem responses that could impact system resilience. Future enhancements to our model could include adding spatial heterogeneity, human behavioral components, international policy or climate interventions [28], or explicit economic models [29]. Inequality or consumption rates can also be varied alongside our case of an equitable society, as in Motesharrei et al., to examine how socioeconomic inequality affects system behavior [1]. These increases in model complexity could allow the model to better explore the effects of economic, social, geographical, and political heterogeneity on ecosystem–climate feedbacks.

5. Conclusions

Historically, societal collapse could often be attributed to overutilization of localized resources. Today, societal impacts on global climate mean that our models must account for the compounding effects of reinforcing feedbacks between ecosystem function and climate change. Integrating climate change into socio-ecological models is crucial for capturing these feedbacks. We expanded upon an existing societal collapse model to include the impacts of climate change. In our simulations, reinforcing feedbacks between climate change and ecological systems amplified the effects of societal overshoot. Higher carbon intensity of economic activities led to faster resource depletion because of declining ecosystem function driven by climate change, accelerating societal collapse. While reducing fossil fuel use to net-zero emissions is a necessary step to achieving a sustainable society, our simulation outcomes were also dependent on ecosystem resilience to climate change. Conservation and management of ecosystems can also bolster resilience of ecosystem services and contribute to long-term sustainability of the coupled human and Earth system.