The Sustainability Nexus

Professor of Physics Emeritus, Ryerson University, Toronto
Submitted contribution to the No-growth Roundtable at York University, 2010 May 6-7th

Sustainability, the nexus of population, consumption and technology is the overarching issue at the global and at the local level. One well defined measure for sustainability is the deviation of the ecological footprint from the ecological capacity. The Global Footprint Network 1 has analyzed the footprint and the ecological capacity of many nations, covering a large part of the world population. According to this study, only few nations have are still sustainable, while most are not, and altogether the footprint of humankind is surpassing the Earth’s ecological capacity already by more than 30%. Population migration is not a desirable solution, as the migrants in improving their personal condition will increase their own ecological footprint, and thus migration will reduce global sustainability. Therefore the opposite of growth is indicated in population and in the economy; in addition a change to green technology is urgent for creating a sustainable civilization.

The sustainability analysis can be quantified by the use of the Ehrlich Holdren equation 2 for the human environmental impact ‘I’ and a simplified global wealth distribution.

The Ehrlich Holdren equation for the human environmental impact is:

I = P A T = X T . (1)

Where ‘P’ is the number of humans, ‘A’ is the per capita consumption of goods, X = P A is the total consumption of goods, and ‘T’ is the environmental damage caused by the production of one unit of consumer goods with the current technology.

George Montbiot 3 and David Satterthwaite 4 state that overconsumption by the rich is causing the large footprint of humankind, and population size does not matter much. There is truth in this view; Share International5 gives the present population and consumption statistics in a simplified form, which indicates that at present 80% of world’s poor population consume only 20% of the resources, and 20% of the population consume 80% of the resources. However, in a just and equitable society of the future, where the poor are legitimately consuming more, and the rich are substantially reducing consumption population numbers become relevant.

According to the Global Footprint Network, using current technology, today’s global resource consumption X needs to be reduced in order to reduce the global ecological footprint to fit the Earth’s ecological capacity and to limit the environmental impact to a sustainable level. The sustainable level of total resource consumption ‘Xs’ is:

Xs = 0.77 X. (2)

Using algebra and the simplified 80/20 global population and consumption statistics, today’s average per capita consumption ‘Aav‘ can be expressed as a fraction of the per capita consumption of today’s rich countries ‘Ar‘, and as a multiple of the per capita consumption ‘Ap‘, of today’s poor. The global average is:

Aav = X/P = 0.25 Ar , and Aav = 4 Ap , and Ar = 16 Ap . (3)

The sustainable global average per capita consumption ‘Asav‘ is less than our present global average. With (2) it is:

Asav = 0.77 Aav . (4)

Assuming globally just and equitable society, where the rich consume less and the poor consume more until the per capita consumption of all humans converges toward a common average, equation (1) represents the connection between population, per capita consumption and technology.

Keeping present day carbon based technology, the relation between a sustainable world population ‘Ps‘ and the resource consumption per capita A in relation to per capita resource consumption of today’s rich. is with (2), (3), and (5):

*Ps A = Xs = 0.77 X = 0.77 P Aav = 0.77 P 0.25 Ar = 0,19 P Ar, or: Ps (A / Ar) = 0.19 P* (5)

This relation is represented in the red series of Fig. 1.

The Global Footprint Network states, that carbon footprint is half of the total ecological footprint. Therefore, the sustainable population can be doubled by changing energy technology to all renewable energy resources with zero carbon emissions:

Ps (A / Ar) = 0.38 P (6)

A graph of how the sustainable population depends on the per capita consumption is given in the green series of Fig 1.

Figure 1 shows that maintaining today’s world population of over 6 billion people, the world average consumption of goods must be 20 % of the per capita consumption of today’s rich. The world average per capita consumption would have to be reduced from presently 25% to 20 % of the per capita consumption of today’s rich.


In a just and sustainable world using carbon based technology with today’s population of 6.5 billion, the rich would have to reduce per capita consumption to 20% of today’s level, while the poor could increase consumption by some 300 %. If renewable energy technology was introduced, together with reduced consumption, some increase in world population seems feasible. However, the sustainability criteria presented by the Global Footprint Network, which are the basis of the above analysis may be too optimistic, as they do not do not sufficiently include the loss of biodiversity.

Fig. 1
The vertical axis gives the sustainable world population in billions as a function of the ratio of per capita consumption of resources to the per capita consumption of today’s rich (A/Ar). The red series assumes present day carbon based technology, the green series assumes zero carbon, total renewable resource based energy technology.


[1] Global Footprint Network: World Footprint. (2009-10-27)

[2] P.R. Ehrlich and J. Holdren, The Impact of Population Growth, Science, Vol. 171, (1971) p.1212

[3] George Monbiot: The Population Myth. (2009-09-30)

[4] David Satterthwaite of the International Institute for Environment and Development: The implications of population growth and urbanization for climate change. (2009-10-27)

[5] Share International (2009-12-06)