Carrying capacity by numbers

The application of mathematics to the prediction of population dynamics has challenged demographers for at least two hundred years. Various proponents have developed formulae for both the calculation of population growth as well as the potential limits to such growth. While these formulae on their own have not always been able to accurately predict human carrying capacity limits, in many cases they have contributed to the development of more complex carrying capacity models.[i] As such, they have often been theoretic in nature, rather than having direct applicability to a particular landscape.

One of the earliest known equations relating to population dynamics was Thomas Malthus’ exponential growth theory of 1798. According to Malthus,[ii] “[p]opulation, when unchecked, increases in a geometric ratio,” while its means of subsistence, namely its food supply, increases only in a linear or arithmetic manner. The exponential growth formula is relatively simple and can be given as;

P(t) = P_o e^rt,

where P(t) is the population at a point in time, P_o is the initial population, e is the base of natural logarithms (2.718...), r is the growth rate and t is time. This formula generates a j-shaped curve with population reaching to infinity (figure 1a). However, according to Malthus, this infinite growth is inevitably halted by the inability of food production to keep up with the population’s exponential expansion (figure 1b).

Figure 1a. (left): Malthusian exponential growth curve showing how the population increases infinitely. Figure 1b. (right): Malthus’ exponential population growth curve limited by the linearly increasing food supply. The assumed carrying capacity is the point at which the population projection intersects with the food supply projection. The carrying capacity is assumed in this instance because Malthus did not refer to it as carrying capacity.

The meaning of carrying capacity

The first known use of the term carrying capacity occurred in 1845 in a report by the U.S. Secretary of State declaring that a new tax would differentiate between cargos transported on sailing- and steam-boats because of their differing carrying capacities.[i] While probably initially used just as two discrete words to best describe a ship’s maximum payload, the term carrying capacity subsequently gained its own unique meaning through increasingly frequent use. Firstly applied to just ships, then to other modes of transport such as trains, the term began to take on a broader meaning by the late 1800s. Sayre[ii] explains that eventually, “the term shed its connection to the levying of duties” and, “refers to the amount of X that Y was designed to carry.”

Aims of the Carrying Capacity Dashboard

In its broadest sense, research around the Carrying Capacity Dashboard aims to highlight how society’s understanding of constraints to the productive capacity of its resource base is vital to its long-term survival. A growing mainstream awareness in the importance of linking a population to the carrying capacity of its landscape has to date, largely been rhetorically rather than empirically tackled. For instance, while both the Redlands City[i] and Sunshine Coast Regional Councils[ii] have publicly committed to living within their carrying capacities, they don’t currently have the tools to determine the actual extent of these limits.

This research aims to identify, examine and compare existing approaches to carrying capacity assessment and consider their relevance to future spatial and infrastructure planning. It raises the following questions: Which carrying capacity assessment models are best suited for determining future sustainable land-use and community infrastructure? What gaps in existing research need to be addressed? Is it possible to achieve a practical model for assessing regional human carrying capacity?

This research aims to add practical application to what are currently well-intentioned but untested emerging societal aspirations concerning carrying capacity assessment. Basic questions such as, “How much land does a population require for its minimum resource requirements?” are currently not easily measurable. It is anticipated that the carrying capacity model developed through this research, can more accurately define the variables inherent in this question, and more clearly articulate possible outcomes. For example, the model might suggest that a certain region’s population may currently be within the carrying capacity of its landscape for one year of average production given existing consumption patterns, but perhaps it may be over-capacity if longer timeframes or different consumption patterns are applied. Carrying capacity assessment thus offers a dynamic tool for ascertaining population thresholds and potential future population distributions, as well as providing important guidelines for living within these physical limits. As such, it has the potential to influence urban and rural planning policy at all levels of government. It can also be useful for researchers and educators in highlighting system boundaries and physical limits to design proposals. Perhaps above all else, it can help individuals and local communities to more clearly define lifestyle changes necessary to ensure more resilient and sustainable societies in the future.