The three horses of sustainability – population , 2 affluence and technology 3

The IPAT equation holds that the total impact of economic and social activity is a function of 11 population size (P), level of affluence (A) and an energy or technology factor (T) [9-11]: 12 13 Impact = f (Population, Affluence, Technology Equation (1) 14 15 Most simply, population, affluence and technology are multiplied together, providing a strong 16 first approximation of the classic photographs of weekly food consumed in countries with different 17 cultures, but also principally different levels of wealth [30]. The argument is made here at the level 18 of national economies and households in different countries, though it could apply to any entity such 19 as an organization, and individuals. 20 21 Population, Affluence (consumption of goods and services) and Technology (or energy/material 22 cost), can and have been framed differently by different authors [14,19,50] (and see main text). Here, 23 Population is given by the world population (fig. S1a). Affluence is approximated by the United 24 Nations Development Programme's (UNDP) Human Development Index (HDI, fig. S1b), where the 25 direct access to ecosystem services and other natural assets in lower income countries (e.g. through 26 local or home production of food) compensates for the mainly market access to these services in richer 27 countries. Technology is approximated by Gross National Income (GNI, fig. S1c), as a proxy for access 28 to and use of energy and manufactured products in richer vs. poorer countries. Quantitative 29 improvements can be made to this parametrization, that also deal better with correlation among the 30 factors, but the focus here is on broad properties [37]. 31


Figures S1 and S2
Tables S1 and S2 Text S1: The IPAT model The IPAT equation holds that the total impact of economic and social activity is a function of population size (P), level of affluence (A) and an energy or technology factor (T) [9][10][11]: Most simply, population, affluence and technology are multiplied together, providing a strong first approximation of the classic photographs of weekly food consumed in countries with different cultures, but also principally different levels of wealth [30].The argument is made here at the level of national economies and households in different countries, though it could apply to any entity such as an organization, and individuals.
Population, Affluence (consumption of goods and services) and Technology (or energy/material cost), can and have been framed differently by different authors [14,19,50] (and see main text).Here, Population is given by the world population (fig.S1a).Affluence is approximated by the United Nations Development Programme's (UNDP) Human Development Index (HDI, fig.S1b), where the direct access to ecosystem services and other natural assets in lower income countries (e.g. through local or home production of food) compensates for the mainly market access to these services in richer countries.Technology is approximated by Gross National Income (GNI, fig.S1c), as a proxy for access to and use of energy and manufactured products in richer vs. poorer countries.Quantitative improvements can be made to this parametrization, that also deal better with correlation among the factors, but the focus here is on broad properties [37].The model proceeds on two premises, with three simplifying assumptions:  Premise 2 -country populations can be described by the model of demographic transition [51].
They start at low population densities where birth and death rates are high (stage 1).As affluence increases first death rates decline first (stage 2) then birth rates (stage 3), which results in rapid increases in population growth in stage 2 and into stage 3, due to the differential between these.In stage 4 when affluence is high, birth and death rates equilibrate at low levels, so population growth slows and halts.Finally, in stage 5, at high affluence and ageing populations, death rates may exceed growth rates, resulting in population decline.
Assumption 1 -Population growth is based on median projections established by the United Nations (fig.S1a) [32].
Assumption 2 -Equity -all countries aspire to, and have the right to achieve, equivalent living standards to those experiencing the highest quality of life.Also by this principle countries should not be expected to accept a decline in living standards, so all must eventually converge towards the highest living standards, as currently experienced in Very High HDI and high GNI countries.To simplify calculations, the model caps HDI and GNI at current levels in Very High HDI countries (fig.S1b,c), as projecting these several decades into the future is not possible simply.
Assumption 3 -the principle of 'common but differentiated responsibilities' as accepted in the United Nations Framework Convention on Climate Change [52], holds that effort in reducing total impact should be proportional to current wealth (and this also reflects contribution to past impact)i.e.wealthier countries adopt higher efficiency targets to reduce their total impact, while poorer countries adopt lower targets, and with later timelines.Over time, as wealth equilibrates across countries, they will converge towards the same efficiency targets.
For this application, the IPAT equation is modified by a coefficient 'e', where e varies between 0 and 1 (0  e < 1; presented in the text as a percentage).e represents a reduction in total impact achieved by reducing population, affluence, or technology, or a combination of these, below reference levels.
Thus, (1-e) enables calculation of the resulting Impact.The parameters population, affluence and technology are multiplied together as the most simple expression of the model.The IPAT equation is thus modified to: The model is used to consider two basic scenarios (figs.1a,b), applied through varying the coefficient e (fig.1c): Business as usual -current trends in population, HDI and GNI continue into the future.e = 0.
Using Assumption 2 to simplify calculations, HDI and GNI are capped at current levels in Very High HDI countries.
Sustainable future -total Impact is capped at 2020 levels, achieved by varying e between 0 and 1. Assumption 3 is applied by applying different levels of e by HDI class such that Very High HDI countries adopt higher and earlier efficiencies than Low HDI countries.

Text S2: exploration of the model factors, limitations and some assumptions for further research
The three major factors each have a fundamental contribution, some key aspects of these being explored in the following text.
Population -the model uses median estimates of population growth, but the same source provides lower and upper confidence limits for growth (fig.S2).At higher growth rates, population will be growing in all income categories in 2100, and Low HDI countries still show accelerating growth rates.At lower growth rates, population in all HDI categories is stabilized and decreasing by 2100, with global population having peaked at under 9 billion in 2050, and declined to under 8 billion, just over today's levels, in 2100.Adjustment of the model to lower population levels (not presented in detail here) lessens the efficiency required from all countries, e.g. from 70 to 50 per cent for Very High and High HDI countries, from 60 to 40 per cent for Medium HDI countries, and from 50 to 30 percent for Low HDI countries, representing significantly less effort needed.By contrast, higher population projections require correspondingly higher reductions in affluence and technology.Of critical importance with respect to political will across all countries is that differentiating these population-based scenarios does not occur until after 2030 in Very High HDI countries and after 2050 in Low HDI countries, a dramatic 10 -30 year lag that makes garnering political and social commitment to putting in place these long term solutions now extremely challenging.HDI is a step in this direction.

High
Technology -reductions in technology impact are perhaps the easiest to implement in that the physical, chemical and biological costs of production and consumption can be dramatically reduced through transforming the way energy and materials are used and recycled.Potential solutions for businesses and the corporate world are currently best expressed in the concept of circular economy 2 .
This transforms the linear business model -that extracts natural resources as essentially free goods and emits waste products with limited accounting of their impacts -into a circular one that does two fundamental things.First, it accounts for all raw material inputs from nature, such that all impacts are reduced to zero and/or mitigated in full.Second, waste is reduced to as close to zero as possible by making all outputs an input to another business process, such as in recycling material waste, or scrubbing carbon dioxide from emissions.These are viewed as costs in the linear model and therefore minimized to maximize profit of the business entity; however the costs they impose through pollution (or e.g.climate change) are borne by others, and may be much higher than the initial direct cost.In a circular model they reflect opportunities for investment and further generation of wealth and jobs -in another business, another sector, or in societal or other benefits (e.g. a clean environment).
Further exploration of the premises, assumptions and corollaries of the model is possible (Table S1) but beyond the scope of this paper.
Table S1.Some assumptions and caveats about the model, of interest for further exploration.

Issue Description Within-country application
Within countries and economies, similar principles can apply among businesses, income classes and households, to achieve sustainability solutions in an equitable and transparent way.Current global footprint exceeds 1 planet earth Though capping affluence and technology at today's levels, the model also provides for potential reductions.The need for greater reduction is explicit in that humanity's footprint today is 1.5 planet earths (WWF 2016), and this needs to reduce to under 1 for true sustainability.This is also illustrated by the need to reduce atmospheric carbon dioxide concentrations from today's level of 407 ppm to below the safe limit of 350 ppm that was passed before 1990 [55].

HDI and GNI cap (Assumption 2)
The assumption that caps HDI at current levels in Very High HDI countries could be relaxed, which would require greater efficiencies to be put in place.However, once transformations in P, A or T are underway, allowing HDI to grow may not have the same impact implications as it currently has.

Measures of affluence and technology
Use of HDI as the measure of affluence, and GNI for technology rather than affluence, may be debatable and provides avenues for improved parametrization of this model.

Does reducing impacts cost?
One assumption embedded within the principle of common but differentiated responsibilities (Assumption 3) is that there is a cost to reducing impact.This may not always be the case, as there may be multiple and broader benefits that stakeholders may obtain from more equitable approaches to reducing impact that transforms apparent costs into benefits, and this may be true for both richer [56]  costs associated with reduction of impacts at source may be less than costs associated with those impacts borne by broader society, but not well-costed or accurately attributed, so this may be a matter of just attribution of costs.
The IPAT model has been debated extensively in the past and does have its weaknesses.These are summarized as follows [58]: "IPAT itself has been criticized because it does not account for interactions among the terms (e.g., increasing affluence can lead to more efficient technologies); it omits explicit reference to important variables such as culture and institutions (e.g., social organization); impact is not linearly related to the right side variables (there can be important thresholds); and it can simply lead to wrong conclusions."The intent here is not to ignore these problems, as they can be addressed in specific circumstances.Rather, the intent is to return to a simpler expression of causal relationships [37] that through their relevance and accessibility to people, businesses and politics, can stimulate behaviour change [8].12/secretary-generals-remarks-the-closing-of-the-high-level-segment-of-the-talanoa-dialoguecop-24-delivered.

References
See in main text.

Figure S1 .
Figure S1.Factors in the IPAT equation -population, affluence and technology.a) global population (in millions), b) Human Development Index (HDI) and c) Gross National Income (GNI, $ per capita) in Very High, High, Medium and Low HDI countries.Impact (IPAT) is a product of these three, see fig. 1. Numbers up to 2015 are measured data, after 2015 are projections [31,32].

Figure S2 .
Figure S2.Population growth rates projected by the United Nations for total world population, split by HDI levels: Very High, High, Medium and Low[31,32].In each figure, the black line shows the median, and the grey lines the 80% and 95% percentile estimates of population.