New Economy Journal

An Empirical Objection to IPAT: A Reply to Mark Diesendorf

Volume 2, Issue 3

June 9, 2020

By - Duncan Wallace

Piece length: 1,512 words

Cover photo by Pedro Kümmel on Unsplash
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This article is a response to Dr Mark Diesendorf’s article ‘Population is a Driver of Environmental Impact: a Response to Duncan Wallace’ (NEJ, May 2020)

Thank you to Dr Mark Diesendorf for his reply.

He said that I implied, in my original article, that he and others are misanthropes. I don’t think I implied that any individuals were misanthropic – but I did say that the equation, I=PAT, has misanthropic presumptions. In the spirit of reasoned debate, I assume people are not misanthropes, and, if it can be demonstrated that a theory they subscribe to has misanthropic presumptions, I assume that’s something they’ll be concerned about.

I maintain that I=PAT has misanthropic presumptions. Here is why.

Mark Diesendorf says that I=PAT is tautologically true, and “doesn’t need empirical justification any more than 6 = 2 x 3”.

I=PAT is not a purely logical equation in the way 6 = 2 x 3 is. While a purely logical equation doesn’t need empirical justification, it does nevertheless require proof – a logical proof – which is what the study of mathematics is about.

Some equations are not purely logical, but purport to say something about the nature of the world. An example is E = mc2. This is an identity, but it nevertheless needs empirical justification given it claims to explain how the world works. As a scientist involved with a recent empirical test of E = mc2 said,

In spite of widespread acceptance of this equation as gospel, we should remember that it is a theory. It can be trusted only to the extent that it is tested with experiments”

I=PAT is like E = mc2: if it is to claim utility, it needs empirical justification.

Let me explain why I believe this is the case:

In the equation I=PAT, each term in the equation has a lower bound of zero.

Population≥ 0
Affluence> 0
Technology> 0

This means that Impact must necessarily be at or higher than 0:

Impact≥ 0

Thus, an empirical test of IPAT must demonstrate that Impact (I) is necessarily a positive value. If it can be shown that Impact (I) can be a negative value, then IPAT is not empirically justified.

Is there a way that Impact (I) could be a negative value? If it could have a negative value, this would mean that humans not only do damage, but can also be creators. We can think of this in terms of give and take – we are all givers and takers. A tree in a forest takes up resources for itself – it is a taker – but it also provides resources and services to other entities in its ecosystem. It is also a giver.

Humans are also, of course, not just consumers of ecosystem resources, but also providers of ecosystem services. Indeed, each of us are ourselves ecosystems of bacteria – more of the cells in our body are bacterial than are human. It is not hard to demonstrate the innumerable other ways humans provide ecosystem services – not least providing food for worms after we die (the circle of life)!

We do much more than provide food for worms though – we are a part of ecosystems, not dominant over them. Take, for example, the Amazon Rainforest. A journal article published in Science in 2011, with over 40 co-authors, found that the “region’s ecology is a product of 8,000 years of indigenous agriculture”. One of the leaders in the study said we should stop speaking about the Amazon as “pristine”. The Amazon, in fact, was shaped by humans: “human societies increased the abundance and distribution of useful species”, she said. “Perhaps”, said another of the co-authors, “the very biodiversity we want to preserve [in the Amazon] is not only due to thousands of years of natural evolution but also the result of the human footprint. The more we learn, the more the evidence points to the latter.”

We do not live outside ecosystems, having only impacts on them – we are part of them, and not only taking benefits from them, but contributing ecosystem services too. If that was not true, we would have to reject as impossible projects like regenerative agriculture.

(As an aside, a documentary series that is extraordinarily insightful in this regard, is the BBC’s Unnatural Histories).

Returning to I=PAT – if the above has any truth to it at all, PAT can only be one part of the equation – the part representing the fact that human beings take from our environment. It fails to represent the fact humans also give – it cannot account, for example, for a person planting a tree. Planting a tree cannot be accounted for by ‘Affluence’ (A), nor ‘Technology’ (T). Hence we must also recognise another part of the equation – let us call it PSG. This is the part that recognises that humans are also givers – that they perform ecosystem services; that they plant trees. That is:

Population (P)≥ 0
Services (S) (provision of ecosystem services)> 0
Technology (G) (how effective we are at performing services)> 0

Here, we call technology G, to differentiate service technology from affluence technology, which is called T. So, our new equation for “Impact” is:

Impact= PAT – PSG
= P(AT – SG)

This now allows Impact to be a negative value, if SG > AT (though, of course, it may very well be positive – it depends on how we behave!).

By this new identity, there is now no necessary relationship between population size and impact on the environment, given that it is recognised each person may be performing more ecosystem services than the total of the resources they are consuming. At issue is not the size of P, but whether AT is bigger than SG.

Of course, if humans are behaving in such a way that AT is out of balance with SG, then the size of P is relevant. But whether AT is bigger than SG, or visa versa, will depend on the society in question, and will not be uniform geographically or across time.

A further observation: so far, environmental scientists have been focussed on discovering the value of PAT, having assumed that this is equal to impact. However, PAT does not in fact equal I:

Impact= PAT – PSG
Impact + PSG= PAT

We see here that if we ignore the ecosystem services human beings engage in, and focus only on our consumption, we will have a warped understanding of our net impact. If we work out only the value of PAT, it will appear as if our Impact is larger than it is, since we are not working out our net Impact, but are instead working out our net Impact plus the sum total of our ecosystem services: Impact + PSG.

In addition to misleading us about the size of our net impact, I=PAT also blinds us to the fact that we not only need to minimise the harm we cause to environments, but we also need to start ramping up the ecosystem services we perform. It blinds us to what is perhaps our most important defence against ecological destruction – that is, our ability to positively enrich our environment. We cannot just focus on conservation – we must also focus on regeneration.


This demonstrates, if nothing else, that I=PAT requires empirical justification. Advocates of the utility of I=PAT must show empirically that it is to be preferred to, for example, I=P(AT–SG). If they cannot show that, they cannot claim any utility for I=PAT.

I think that I=P(AT–SG) may be better justified empirically than I=PAT. I=PAT, after all, assumes we are all “takers” but never “givers”, which is demonstrably not true. Hence my characterisation of I=PAT in my original essay as misanthropic: I described the equation as assuming all human actions are necessarily “bad” (Diesendorf has pointed out that is an emotive term, so in this reply I have gone for the term “take”, in the aforementioned sense of “give and take”, instead of “bad”).

Nevertheless, while better than I=PAT, I do not claim that I=P(AT–SG) is empirically useful. I think it’s just too hard to put a numerical value on things like affluence or ecosystem services. Also, the way that people interact together creates emergent properties, which cannot be captured by a linear equation.

4 Replies to “An Empirical Objection to IPAT: A Reply to Mark Diesendorf”

  1. You cannot make up your own definitions of mathematical concepts. Yet that’s what you have done in confusing an identity with an equation.
    I = PAT is an identity, a well-know mathematical concept, because it’s true by definition. We can write it as:
    I = P x (GDP/P) x (I/GDP)
    where x denotes multiply and GDP is Gross Domestic Product.
    Cancelling the Ps and GDPs, we obtain I = I.
    In contrast, E = mc**2 is an equation , not an identity, and has to be proven.

    1. In Impact of Population Growth (1971), Ehrlich and Holdren say the following:

      “… each human individual has a negative impact on his environment… The total negative impact of such a society on the environment can be expressed, in the simplest terms, by the relation
      I = P*F
      Where P is the population, and F is a function which measures the per capita impact.”

      Quite explicitly, they are saying the are measuring only the negative impact of human society. This is like watching a football game and only noticing when one of the teams scores, but not noticing when the other does. If you only paid attention to the goals one side scored, you would be almost clueless about the ultimate result of the game. The team whose goals you were following might have scored ten goals – but the only way of determining whether this constitutes a win is if you also know how many goals the other side scored.

      I am saying we need to pay attention to the other side – not just our negative impact, but also our positive impact.
      I am saying that Impact should be thought of as Negative Impact (In) minus Positive Impact (Ip):
      I = In – Ip
      In = PAT
      Ip = PSG
      I = PAT – PSG

      This recognises that there is not just Gross Domestic Product (GDP), but also Gross Domestic Services (GDS), as in ecological services. This allows us to count our consumption and our services in measuring our Impact.

      We can write I = PAT – PSG as:
      I = (P x ((GDP/P) x (In/GDP))) – (P x ((GDS/P) x (Ip/GDS)))
      = P x ((GDP/P) x (In/GDP)) – ((GDS/P) x (Ip/GDS))
      = P x ((In/P) – (Ip/P))
      = In – Ip
      I = I

      Now – show me, empirically, that I=PAT is a better measure of our impact than I = In–Ip (or else, I=PAT-PSG).
      In other words, show me why I should prefer your identity rather than mine.

  2. It’s difficult to have a reasoned discussion with someone who shifts ground whenever someone refutes a point they have made.

    Originally, Duncan’s claim, against all the evidence, was that ‘we do not have a problem with overpopulation’, but failed to present a case that, for example, doubling Earth’s population would not, to first approximation, double environmental impact.

    Instead, he offered a rhetorical attack on the I = PAT identity, accusing indirectly those of us who find it useful conceptual framework of misanthropy. He can’t wriggle out of that by saying that ‘the equation, I=PAT, has misanthropic presumptions’. Presumptions are held by people, not by equations, so he owes us an apology.

    Duncan further confused the issue by claiming that ‘The principal assumption [behind I = PAT] is that human beings are necessarily bad for the environment’, which confuses science with ethics. When I pointed out that environmental impacts are neither ‘good’ nor ‘bad’, he shifted ground to talking about ‘positive’ and negative’ impacts, or ‘give’ and ‘take’ impacts, which still contain similar value judgments to ‘good’ and ‘bad’.

    When he was challenged for confusing the equation E = mc2 with an identity, he shifted ground again and produced his own identity with ‘positive’ and ‘negative’ environmental impacts. However, in a moment of frankness he admitted that ‘I do not claim that I=P(AT–SG) is empirically useful’. I agree, it is not useful and only confuses the issue.

    However, I = PAT is very useful in bringing together the environmental impacts of growth in population and consumption per person (as a measure of ‘affluence’), and technological choice, into a single framework in which each of these factors can be addressed by different policies. It is important to have such a framework because the inhabitants of planet Earth are faced with climate disaster, loss of biodiversity, chemical pollution, land degradation, etc., and, at one conceptual level, the factors, P, A and T, are the drivers of these impacts.

    Of course the I = PAT is inappropriate for describing regenerative activities such as tree planting, which are failing to stop environmental destruction. This does not give valid grounds for rejecting the identity any more than we would reject Newton’s Laws of Motion because they cannot describe relativistic or quantum mechanical phenomena.

    What is more important than arguing about I = PAT is that people come to understand that we must stop the growth in population and consumption per person, as well as clean up our technologies.

    My final comment on this issue: Ethical questions are raised when an editor pushes their own views in the journal they edit. Who assesses whether their articles are of sufficient quality for publication?

    1. I haven’t shifted ground at all – I just tried to make my language more amenable to you to get my point across. I’ve obviously failed to make it amenable, so I am only going to use the language that has been used by I=PAT theorists. In the above comment, I quoted from Ehrlich and Holdren. It is they – not I – that uses the language of “negative” (vs positive):

      “… each human individual has a negative impact on his environment… The total negative impact of such a society on the environment can be expressed, in the simplest terms, by the relation I = P*F” (“I=P*F” is I=PAT).

      I am only pointing out that IPAT is, quite explicitly, meant only to measure human “negative impact”. What I am trying to get across is that we cannot draw conclusions about the effects of human population growth based only on an equation which measures human “negative impact”. For the reasons I described in the above article and the above comment, drawing conclusions about population based only on information about human “negative” impact is to go in half-blind, and so be liable to be misled.

      If, as I showed above, you make an equation for human impact which includes not just “negative impact” (not my words – the words of Ehrlich and Holdren), but also include human “positive impact”, then “population” is no longer a necessarily “negative” force – whether population is a “negative” (not my word – the word is quoted from Ehrlich and Holdren) or “positive” force will depend on whether an individual person’s “negative impact” is bigger or smaller than a person’s “positive impact”.

      Hence my argument that there is no necessary relationship between human population numbers and human “negative impact” (not my word – the word is quoted from Ehrlich and Holdren).

      As to your aspersions about me being someone who “pushes their own views in the journal they edit”, I can’t understand what you mean – the editorial team has always gratefully accepted articles with views which diverge from our own. The tagline, since the first issue, has been: “We hope you disagree with some, take hope from others, and learn from all about how we can build a new, just and sustainable economy”. If you would rather not subject your views to public debate, I don’t understand why you’d want them published in the first place. Incidentally, we were particularly careful with this article given the sensitivities involved, and it was reviewed for publication by three individuals, two of whom are professional ecological economists. All took the view that the article is a worthwhile contribution.

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