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Seppelt, R., A. M. Manceur, J. Liu, E. P. Fenichel, and S. Klotz. 2014. Synchronized peak-rate years of global resources use. Ecology and Society 19(4): 50.

Synchronized peak-rate years of global resources use

1UFZ - Helmholtz Centre for Environmental Research, Department Computational Landscape Ecology, 2iDiv - German Centre for Integrative Biodiversity Research, 3Institute of Geoscience & Geography, Martin-Luther-University Halle-Wittenberg, Halle (Saale), Germany, 4UFZ - Helmholtz Centre for Environmental Research, Department Community Ecology, 5Center for Systems Integration and Sustainability, Michigan State University, 6Yale School of Forestry and Environmental Studies, Yale University, 7UFZ - Helmholtz Centre for Environmental Research, Department of Community Ecology


Many separate studies have estimated the year of peak, or maximum, rate of using an individual resource such as oil. However, no study has estimated the year of peak rate for multiple resources and investigated the relationships among them. We exploit time series on the appropriation of 27 global renewable and nonrenewable resources. We found 21 resources experienced a peak-rate year, and for 20 resources the peak-rate years occurred between 1960-2010, a narrow time window in the long human history. Whereas 4 of 7 nonrenewable resources show no peak-rate year, conversion to cropland and 18 of the 20 renewable resources have passed their peak rate of appropriation. To test the hypothesis that peak-rate years are synchronized, i.e., occur at approximately the same time, we analyzed 20 statistically independent time series of resources, of which 16 presented a peak-rate year centered on 2006 (1989-2008). We discuss potential causal mechanisms including change in demand, innovation and adaptation, interdependent use of resources, physical limitation, and simultaneous scarcity. The synchrony of peak-rate years of multiple resources poses a greater adaptation challenge for society than previously recognized, suggesting the need for a paradigm shift in resource use toward a sustainable path in the Anthropocene.
Key words: limits to growth; peak-rate year; synchrony


Sustainable appropriation of nonrenewable and renewable resources is required for society’s long-term well-being. Four decades ago, Meadows’ limits to growth model reignited the old Malthusian debate about the limits of the world’s resources (Mathus 1798, Bardi 2000, Griggs et al. 2013). Limits to growth of specific resources such as oil (Hallock et al. 2014) or fossil water (Gleick and Palaniappan 2010) have been analyzed separately, by estimating the peak-rate, or maximum, year, defined as the year of maximum resource appropriation rate. For which renewable and nonrenewable resources can a peak-rate year be identified given the most up-to-date time series of human resource appropriation? Exploring the relation among peak-rate years for multiple resources then raises an important second question: are global peak-rate years synchronized, i.e., occurring at approximately the same time in the long history of human civilization? Calculating the appropriation rate of resources allows the detection of the maximum increase year or peak-rate year, which indicates the timing of scarcity or change in demand (Fig. 1). We analyzed peak-rate years for many of the world’s major resources and found synchrony in the peak-rate years of statistically independent resources by a method that is standardized, nonparametric, generalizable, and allows analysis of nonrenewable and renewable resources (Table 1), and we will conclude by giving clear implications for sustainable development goals (Arrow et al. 1995).

We focused on 27 nonrenewable and renewable resources essential for human well-being and daily needs, e.g., energy and food. These resources are also the focus of global policy bodies such as the United Nations and the World Bank. Nonrenewables include the fossil fuels, i.e., coal, gas, oil, supplying 87% of the energy consumed by the 50 wealthiest nations (Tollefson and Monastersky 2012). Renewables include staple crops, e.g., cassava, maize, rice, soybeans, and wheat, which the Food and Agriculture Organization of the United Nations identified as providing 45% of global caloric intake (FAO 2013). Combined with data on the consumption of animal products, the main sources of food are included in our analysis. We also evaluated resources with a long history of use, e.g., cropland and domesticated species, and renewable energy sources, which may be increasingly important in the future. Furthermore, we considered two global drivers of resource use, population and economic activity (world GDP). The database consists of time series of 27 global resources, 2 global drivers, and 13 national resources/drivers. The data sources are listed in Table 2. All data is accessible at Figshare The raw data and smoothed times series of the bootstrap resamples (see Methods) are plotted in Figure 2.


Peak-rate year estimation

We used a method that is standardized, nonparametric, generalizable, and allows analysis of nonrenewable and renewable resources. Renewable resources regenerate on shorter time scales, i.e., harvest rate and regrowth have comparable time scales, and have a human scale, and annual production is the response variable that was analyzed. Nonrenewables are regenerated on geological time scales, and the response variable is the accumulated amount extracted. This choice of response variables allowed the analysis of all resources with the same mathematical method (Table 1, Fig. 1). To estimate a peak-rate year, the maximum increase rate of the time series must be calculated. It is possible to use a parametric model, e.g., a logistic curve or its derivative. However, nonparametric curve fitting offers advantages regarding the bias and does not require parametric assumptions or that a functional model be postulated, e.g., stationarity of rate of resource appropriation. This means that the different resources and drivers need not follow the same increase process (Gasser et al. 1984). Further, by using a bootstrap resample to estimate the uncertainty of the peak rate year estimate, we avoided distributional assumption. However, no prediction outside the range of the data can be performed.

Time series analysis of peak-rate years and synchrony testing

We do provide a summary of the statistical analysis of the time series. Appendix 1 provides detailed documentation of conducted steps. Figure A1.1 in the appendix provides a graphical overview.

The time series of the 27 global resources, 2 global drivers, and 13 national resources/drivers (with length n = 12 - 112, see Table 2) were subjected to a cubic smoothing spline to find the peak rate of resource appropriation, based on the maximum of the first derivative. This nonparametric method has no distributional assumptions, but does not enable predictions. We performed 5000 bootstrap resamples, and the 50th percentile (2.5 and 97.5th) was taken as the peak-rate year (uncertainty), unless the 50th percentile was equal to the last year in the time series, in which case we concluded the rate of resource appropriation was still increasing.

To test the hypothesis of synchrony, we selected statistically independent time series. We performed ARIMA modelling of the 27 global resource time series and tested the residuals with a Box-Pierce test of white noise. Haugh’s test of dependence on all pairs of resources was performed on cross-correlation coefficient of the white noise residuals (Haugh 1976). We selected 20 statistically independent time series of resource, of which 16 presented a peak-rate year. A peak-rate year from the 5000 bootstrap resamples for each of the 16 resources was randomly selected, and the mode of the resulting smoothed distribution of 16 peak-rate years obtained. This process was repeated 5000 times, and we estimated the synchrony as the median of the 5000 modes. A nonparametric goodness of fit test was performed with a uniform distribution as a null hypothesis, i.e., no mode implies no synchrony, and a critical value obtained by Monte Carle simulation (5000). The statistical tests were performed at a Type I error rate of 0.05.


We observed that for 21 of the 27 global resources and for the 2 global drivers of resource use, there was a peak-rate year. For the 21 resources that had a peak-rate year (Table 3), all but 1 (cropland expansion) lay between 1960 and 2010 (Fig. 3). Given the long human history, this is a very narrow time window. The available data suggest that peak-rate years for several nonrenewable resources, i.e., coal, gas, oil, and phosphorus, have not yet occurred. This implies a continued acceleration of extraction, which is in accordance with earlier analysis for oil (Hallock et al. 2014) and phosphorus (Cordell et al. 2009).

Individual countries have detectable impacts on the global nonrenewable resource extraction rate. For example, in 2011 the rate of coal extraction for China was 7.2% (5.7-7.4), whereas the rate for the world without China was 3.7 % (3.5-3.8). The values for natural gas in 2011 were 10.1% (7.6-10.3) and 4.4% (4.0-4.4) with and without China, respectively. A peak-rate year for renewable energy has not occurred.

Figure 3 shows that the peak rate of earth surface conversion to cropland occurred in 1950 (1920-1960), and the expansion of cropland recently stabilized at the highest recorded levels, about 1.8 x 106 ha (Ramankutty and Foley 1999). We find peak-rate years recently passed for many agricultural products: soybeans in 2009 (1977-2011), milk in 2004 (1982-2009), eggs in 1993 (1992-2006), caught fish in 1988 (1984-1999), and maize in 1985 (1983-2007). Two major factors of agricultural productivity, N-fertilizers and the area of irrigated land, show peak-rate years in 1983 (1978-2010) and 1978 (1976-2003), respectively. Water is a resource that many world policy bodies are concerned with and is largely understood as a renewable resource. But not all water is renewable. ‘Fossil water’ stocks are isolated water resources, which are consumed faster than are naturally renewed. There is currently a lack of time-series data at the global scale on the status of hydrological resources (Fan et al. 2013). As an example of national trends, the greatest rate of groundwater extraction occurred in 1975 in the USA (1975-2005). Water conservation and rationing rules likely reduced the rate of ground water extraction (Gleick and Palaniappan 2010). For maize, rice, wheat, and soybeans, the yield per area is stagnating or collapsing in 24-39% of the world’s growing areas (Ray et al. 2012), which may explain why the peak-rate years have passed at a global level. The peak-rate years of renewable resources collectively suggest challenges to achieving global food security (Foley et al. 2011). We identified a sequence in the peak-rate years of resources associated with food production: 1950 for conversion to cropland, 1978 for conversion to irrigated land, 1983 for fertilizer use. Because all peak-rate years for food resources appeared afterward, we inferred that the strategies to increase food production changed from land expansion to intensification of production. Furthermore, the pattern of peak-rate years occurring in land, food, and not yet for nonrenewable resources suggests that sustained intensification of agricultural production is not limited by energy but rather by land.

Following the observation of an apparently simultaneous pattern of peak-rate years in Figure 3, we tested the hypothesis of synchrony among peak-rate years on 20 statistically independent time series of resources, of which 16 presented a peak-rate year. We found that peak-rate years appeared clustered around 2006 (1989-2008), given the uncertainty surrounding the peak-rate year estimate of each resource (Fig. 4). It is unlikely that the synchrony is a statistical artefact because there is less than a 1 in 1000 chance that the distribution in Figure 4 would have been obtained if it were sampled from a uniform distribution, i.e., null hypothesis of no synchrony is rejected.


Why is there a synchrony of peak-rate years? Some explanations follow. The overall hypothesis is that multiple resources become scarce simultaneously, which can be driven by two mechanisms.

First, multiple resources, e.g., land, food, energy, etc., are consumed at the same time to meet different human needs. For example, people require food for nutrition; water for drinking, irrigation, and cleaning; land for housing, recreation, food production, infrastructure; and energy for cooking food, transportation, heating, cooling, etc.

Second, producing one resource requires the use of other resources. For example increasing food production requires more land and water whose scarcity in turn leads to limited food production increases, as the sequence of peak-rate years associated with food production shows (see above). Furthermore, the continued increase in extraction for less accessible resources results in an increased ecological and economic cost per unit extracted (Davidson and Andrews 2013), thus reducing availability of the remaining resources. For example, pollution exacerbates water shortages because polluted water is not suitable. These two mechanisms provide the most parsimonious explanation for simultaneous scarcity leading to synchrony of peak-rate years.

Are there other factors causing synchronized peak-rate years? Besides scarcity, passing an individual peak-rate year may be caused by two possible reasons: availability of substitutes or less demand, e.g. less resource is needed because of more efficient use, taste changes, or institutional and regulatory changes (Fig. 1). It is unlikely that substitution has a substantial influence on synchronization. Strong support for the hypothesis that substitution synchronized the peaks would require that substitution took place for all or most of the resources with synchronized peak-rate years. However, among the 16 resources with synchronized peak-rate years in our database, which contains most of the critical global resources, only a few resources may have substitutes. For instance, contrary to expectation there is little evidence that farmed fish substitutes for caught fish (Asche et al. 2001). In contrast, poultry products serve as a substitute for beef because they are cheaper and better adapted to changing tastes (Eales and Unnevehr 1988). However, evidence suggests that meat as a category is not being substituted by plant protein on a global scale (Daniel et al. 2011). Finally, there is little evidence that renewable energy, which did not show a peak-rate year, substitutes for fossil energy. In the last 50 years, the general global trend was that a unit of energy sourced from nonfossil fuels substituted less than one quarter of a unit of fossil fuel-based energy, possibly as a consequence of economic and social complexity (York 2012).

A global synchronous reduction of demand is also an unlikely driver. Despite a declining global population growth rate, i.e., peak-rate year passed in 1989 in accordance with preceding reports (Lutz and K. C. 2010), the global population continues to grow. In most developed countries, we identified peak-rate years in household intensity, i.e., number of households per 100 people (Table 2). Additionally, the peak rate of meat consumption in the USA occurred in 1955 (1909-1999). Nevertheless, the rate of resource appropriation is not expected to decline because consumption in developing countries increases because of lifestyle changes (Brown 2012, Liu 2014), and the land area used for urban settlements and household numbers continue to increase (Liu et al. 2003, Seto et al. 2011). These shifts in resource-intensive living likely more than offset the declining rate of population growth. Declining demand would have to come from broad scale changes in individual preferences for conservation, which continue to seem unlikely.

Finally, constraints on production may not be alleviated unless there is disruptive innovation. For example, although there is phenotypic plasticity in plants, which is exploited by agronomic research, e.g. breeding, particular biochemical mechanisms were not as of now disrupted or constructed de novo in a commercial setting: nitrogen fixation for cereals remains elusive (Charpentier and Oldroyd 2010) and further increase in photosynthetic efficiency is expected to be hard to achieve (Zhu et al. 2010). Further, a basic constraint on breeding is biological diversity. The rate of domesticating species, the biological foundation of food provisioning, began to slow around 2600 B.C. (3600-1500 B.C.), well before our era.

Synchrony among the peak-rate years suggests that multiple planetary resources have to be managed simultaneously, accounting for resource distribution and utilization (Steffen et al. 2011, Liu et al. 2013). Synchrony does not necessarily imply a tipping point that leads to disastrous outcomes because trade-offs are possible (Seppelt et al. 2013), and adaptation, such as the current increasing rate of renewable energy generation or shifting diets (Foley et al. 2011), potentially can be accelerated. Synchrony also suggests that the debate about whether humans can devise substitutes for individual natural capital needs to be broadened to assess simultaneous substitutability (Barbier et al. 2011). Whether substitution and recycling will alleviate constraints to future economic growth (Neumayer 2002) remains an open question, especially because maintaining the innovation rate requires increasing expenditures on human capital (Huebner 2005, Fenichel and Zhao 2014). Arrow et al. (2012) estimated that the growth rate of human capital in the United States could be as low as 0.35%, which is 15-44% of the growth rate of conventional reproducible capital, e.g., infrastructure, and China’s rate of human capital growth ranges between 1.1% and 2%, but is only 10-17% of the rate of growth in reproducible capital.

The synchronization of peak-rate years of global resource appropriation can be far more disruptive than a peak-rate year for one resource. Peak-rate year synchrony suggests that the relationship among resource appropriation paths needs to be considered when assessing the likelihood of successful adaptation of the global society to physical scarcity.


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We are grateful to Anna Cord, Jörg Priess, Nina Schwarz, Dagmar Haase, and Burak Guneralp for providing comments on earlier versions of the manuscript. We also thank Karen Seto and Burak Gunneralp for providing access to the urban growth data. The work was funded by grant 01LL0901A "Global Assessment of Land Use Dynamics, Greenhouse Gas Emissions and Ecosystem Services - GLUES" (German Ministry of Research and Technology) under the Helmholtz Program "Terrestrial Environmental Research," U.S. National Science Foundation, and Michigan AgBioResearch. This article contributed to the Global Land Project (


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