THIS POST IS PART OF OUR SERIES ON URBAN METABOLISM.

Co-authored with Katie Marshall

How do we define the beginning of the Anthropocene?  This question invites controversy because it depends on what metric you happen to like using.  Some researchers argue for a sociological measure of the Anthropocene (Ellis et al., 2016), while others are content to use the mark left in the geological record (Zalasiewicz, Waters & Head, 2017). This controversy has led to much discussion (Lewis & Maslin, 2015), with suggested dates associated with moments in human history ranging from the onset of fossil fuel use, the development of the atomic bomb, or even the dawn of agriculture.  But it is clear that the question is interdisciplinary–it sits squarely at the intersection of social science, geology, physiology, and ecology. What common currency do these different fields have?  Marina Fischer-Kowalski and her colleagues suggest using metabolism.

Metabolism is a central concept in biology.  It is the sum of all chemical reactions that take place in the body, involving all the fuels that are broken down for their chemical energy and all the waste byproducts that are produced.  Of course, measuring every chemical reaction that takes place in an organism is incredibly difficult, so biologists will often measure the rate of oxygen consumption or carbon dioxide production, both of which are useful indicators of how much fuel is being used in central metabolic pathways.

Biologists find that measuring metabolic rate is useful because it provides an indication of animals’ energy usage–how much fuel do they need to maintain their bodies, to grow, and to reproduce?  As a result, James Brown and Jamie Gillooly posited the Metabolic Theory of Ecology: the metabolic rate of individual organisms governs their ecological interactions, because it reflects how much energy the organism needs from the environment to allocate to its life processes (Enquist et al., 2003; Brown et al., 2004). This theory explains the scaling of energetic needs from the individual to the ecosystem, providing a bridge between the physical and chemical processes within individuals to the ecological interactions that govern how entire systems function.

In recent years, social scientists have developed the concept of “urban metabolism:” an analogy that applies the idea of metabolism to the city.  Humans are, after all, just another type of organism that lives in large, complex ecosystems. Indeed, the relationship between total energy use of a city and the ambient temperature of the environment looks almost identical to how that relationship scales for an individual organism (Hill, Munich, & Humphries, 2013).  Humans have just outsourced their individual energetic needs to the city (see Katie’s post on that idea).

If metabolism is a useful conceptual framework for describing both cities and organisms, might the models that we use to study populations of organisms also be useful for describing populations of cities? This question was on our mind as we read the paper by Fischer-Kowalski and her colleagues.

Fischer-Kowalski et al. use quantitative estimates of societal metabolism rates to explore Ehrlich’s classic formula, I = P x A x T. That formula describes the impact of humans on the environment (I) as the product of population size (P), affluence (A), and a technology factor (T) that describes a society’s level of resource use. The authors make some careful estimates of these parameters for three general modes of subsistence (Hunter and gatherer, Agrarian, and Industrial), and then reconstruct time series estimates of the total population in each mode of subsistence from 10,000 BC to 2000 AD.

This is a compelling analysis, but data availability forced the authors to make their best estimates for some calculations. Are there tools and models from population biology that could offer complementary insights? For example, suppose we consider the number of people in each  of the three modes of subsistence as a populations of organisms. Each population has its own intrinsic growth rate, and we might also assume that there is some conversion rate at which hunter-gatherers become agrarian, and at which agrarians become industrial. How could we model that?

Lotka-Volterra predator-prey dynamics

One approach would be to use the classical Lotka-Volterra (“L-V”) predator-prey equations from biology:  a set of first-order differential equations that describe the dynamics of predators and prey. In the L-V model, each population has a growth rate, and the model includes parameters that describe the interactions of the two populations. In our analogy, we would consider a set of three equations: one for the hunter-gatherer population (i.e., “prey”, unfortunately, in this metaphor), one for the agrarian population (i.e., a predator on the hunter-gatherer population, since hunter-gatherer societies become agrarian over time), and one for the industrial population (i.e., the top-level predator). This model is straightforward to solve, and the data in the paper could provide reasonable estimates of any parameters we’d need.

With this model in hand, we might ask: can it explain the long-term dynamics of these three populations (e.g., Fig. 2 in Fischer-Kowalski) using reasonable values for the growth rates of each population? If not, does that fact provide any insights into how populations grow and transform among these three modes of subsistence?

The Conclusions section of the paper provides some ideas for adding a little more sophistication to this modeling exercise. When discussing the limitations of the IPAT model, the authors explain “It cannot be assumed that the three components – population, affluence and technology – are independent from one another. On the contrary: they are functionally deeply interlinked, but in ways that differ between sociometabolic regimes” (p. 27). They go on to say:

In the hunter gatherer regime, population numbers basically are constrained by available food energy, and the availability of food from ecosystems can hardly be controlled by humans. In the agrarian regime, the relation between food and population becomes more complex: While food energy still constrains population numbers, population growth allows investing more labour and drives technological progress increasing the overall amount of food energy available from agro-ecosystems… In the industrial regime, the link between land and energy availability is largely disrupted, as well as the link between available energy and population dynamics. (p. 27)

All of those assertions sound reasonable, but we could also test them by extending our Lotka-Volterra model. For example, the above quote suggests that hunter-gatherer populations should have some fixed carrying capacity determined by their environment; that in agrarian societies the carrying capacity should be a function of both the environment and the population size; and in industrial societies there should be effectively no carrying capacity. We could readily modify the L-V model along these lines, and again see if it is possible to explain the long-term dynamics of these three populations (e.g., Fischer-Kowalski, Fig. 2) using reasonable values for parameters. If not, would that be grounds for questioning some of the assertions in the above block-quote?

Metabolism is a compelling conceptual framework for describing both cities and organisms. It provides a common currency for linking disparate academic disciplines, and Fischer-Kowalski convincingly use it to propose a definition for the beginning of the Anthropocene and illustrate changing anthropogenic impacts through time. As biologists, it makes us wonder: how far does this metaphor go? What other similarities are there between cities and organisms, and what other tools and models from biology could be brought to bear on the study of cities?