From: alanm@igc.apc.org (Alan McGowen)
Newsgroups: sci.environment
Subject: I=PAT, and a little sci-fi
Date: 21 Nov 92 06:09:00 GMT
Nf-ID: #N:cdp:1466601925:000:8480
Nf-From: cdp.UUCP!alanm    Nov 20 22:09:00 1992


Some thoughts on ecosystem impacts and the I = PAT eqn. [I = 
impact, P = population size, A = mean "affluence" or consumption, 
T = impact of technology used to provide consumed goods or 
services.]

The I = PAT idea is due to Ehrlich and Holdren [1].

Some posters have criticised the idea on the grounds that the
factors are not in general completely independent, i.e they say 
that we might have A = A(P,T), T = T(P,A) or dependencies on 
derivatives. It has also been suggested that only physical 
scientists would ever notice such a complex situation ;-). 
Actually, the problem may be that physical scientists have 
inappropriate expectations about the generality which can be 
expected from any detailed model in the life sciences. 

I = PAT is *not* a detailed model -- it is a template for 
building detailed models -- it is a *class* of models, if you 
like. To build a detailed model, we need to specify the exact 
impact and the factors of technology and affluence which are 
relevant to it. It is also important to remember that the 
response of ecosystems to impacts is not in general linear, even 
though there are *qualitative* similarities of response to 
impacts of different *kinds* (which is why the concept of impacts 
is useful).

For example, consider the impact of logging on a forest 
ecosystem. Very selective logging on a small scale may closely 
approximate the normal effects of trees falling -- especially if 
the wood is used within the ecosystem, so that its nutrients are 
not permanently removed from the total capital. This is the 
situation with traditional use of trees by indigenous forest 
people. Here the impact may be smaller than what the ecosystem 
can absorb without change of character ("loss of function"). At 
the opposite extreme is clearcut logging on a scale affecting 
entire watersheds. 

The different *techniques* of logging give the different factors 
of T. Note that T should be measured as some specific type of 
important impact -- e.g. as a rate of habitat conversion per unit 
of time per dollar in the case of nonselective logging. 
Quantification is difficult but not impossible. For techniques 
which produce extreme degredation remote sensing can be used to 
measure extent of habitat destruction. For less destructive 
techniques there are a panoply of diversity measures which could 
be used to quantify impacts.            

A is simply the average consumption of forest products of the 
population responsible for the logging.  In an earlier post about 
this subject, one objection raised was that the T for logging in 
one area (say Indonesia) was multiplied by the A in another area 
(say Japan) -- this violated the intuitions of one poster. 
However, the As which are relevant are the ones which are 
responsible for the logging operation -- i.e. the As at the 
sources of consumption. A has to be modified if there are 
nonmarket factors such as regulations restricting the use of a 
given technology or its use in certain areas, since this reduces 
consumption.  

P is just the number of people with the A characteristic, i.e. PA 
is the total consumption of the forest products produced by the 
technology with impact T per unit of consumption. The result? 

I(rate of habitat destruction due to clearcut logging) 
= P(consumers of forest products from the logging)X
  A(mean consumption of forest products from the logging)X
  T(rate of habitat destruition for the given technology and the 
    given ecosystem per unit of consumption)

Like more than a few basic ideas in science, this is scarcely 
anything more than than bookeeping. Moreover, the factors are 
independent enough to permit some prediction -- for example of 
the likely effects on a specific ecosysem of a regulation 
changing T (specifying logging methods) or A (restricting take).
Likewise, for cases where P is increasing rapidly and T is 
changing slowly if at all (South American farmers with 
chainsaws), again prediction is possible without considering 
complex implicit dependencies among the factors.

Michael Tobis wonders whether my position is that I is an order of 
magnitude too great, and that P has to come down by this much. 
Actually, I from all sources is probably 2-3 orders of magnitude 
above what would be stable in the sense of a coevolutionary 
stable state. I don't believe that any one of the three factors P, 
A, or T could be expected to absorb the entire reduction, and 
would advocate an order of magnitude reduction in P, and another 
roughly two orders in AT. The technologial optimists of course 
think that T can be brought as low as you please, but history 
points the other way: T has been increasing, not decreasing. A 
Brazilian farmer with a chain saw and a little gasoline has a 
vastly greater T at his disposal than Spanish Conquistador or a 
native of the rainforest. Technology has tended to evolve to make 
it easier for humans to rearrange things, and that is the whole 
problem. If we are to get huge reductions in T we are going to 
need some stong nonmarket incentives (i.e. regulations) to get 
the same level of service at much lower impacts.

To address the worries that we can't think about the future with 
I = PAT because the "real" model is something like

I(t) = P(t, A, T, dP/dt, dA/dt, dT/dt, I, dI/dt) x
       A(t, P, T, dP/dt, dA/dt, dT/dt, I, dI/dt) x
       T(t, P, A, dP/dt, dA/dt, dT/dt, I, dI/dt)

which roughly means "its too complicated to think about", I'd 
like to conclude with a philosphical tale which I will present as 
a science fiction story.

     A Dialogue of the Dead and the Not-Yet Dead

The Space Empire Empidonax, deciding that they prefer Earth's 
rainforests to Earth's humans, determines to end human 
technology. They send their latest model space-time cruiser to 
Earth, and after stopping a few cars on rural roads, cutting six 
or seven crop circles, and leaving kindred signs of Higher 
Intelligence, they kidnap four people who post in this group:
an ECONOMIST, a PHYSICIST, a COMPUTER SCIENTIST and a 
METEOROLOGIST. The four are transported back in time to the late 
17th century, where they are brought face to face with the 
English scientist Robert Hooke, president of the Royal Society of 
London, who has been busy measuring springs and is about to give 
the world Hooke's Law -- the force of a spring is directly 
proportional to its displacement from equilibrium. The four time 
travelers are dismayed at his simplemindedness.

PHYSICIST: "Look, Hooke, you've fastened onto the first silly 
model you've come across. The real situation is far more 
complicated. Nonlinear oscillators, chaos... you have no concept. 
Just look at what happens when you stretch your spring too far -- 
it breaks. Start by modelling that. Have you thought about what 
happens if the oscillation occurs in a non-Euclidean manifold, 
or if energy is quantized? I didn't think so. It's utterly 
useless."

ECONOMIST: "Not only that, Hooke, but you have committed a 
logical error: you say that EVERY spring obeys your law, but you 
haven't examined EVERY spring. You've only examined a FEW 
SPRINGS. Your conclusion doesn't follow from your premises."

COMPUTER SCIENTIST: "You don't seem to know how to use 
statistics. I think your relation is emotive -- you discard the 
cases you don't like. You should study some arithmetic. He who 
refuses to --"

METEOROLGIST (cutting in): "Yes, I'm convinced that scientific 
objectivity (which has nothing whatsoever to do with history or 
cultural background) forces me to conclude that the situation 
is probably more complex than Mr. Hooke thinks it. Real springs 
are not linear, except in some very local applications."

HOOKE: "Gentlemen, I'm amazed at how simple I have been. You have 
quite convinced me."

[Vast upheaval, in which the four time travelers cease to exist. 
Hooke never publishes his law, no theory of harmonic oscillators 
is ever developed, no electrodynamics, quantum mechanics, 
electronic devices or computers are ever developed. The Earth in 
the 20th century is quite safe for rainforests.

The Space Empire of the Empidonax is greatly pleased.]


The moral: thou shalt not multiply implicit variables beyond 
empirical necessity without well-supported and *applicable* 
theoretical cause, or in other words Keep It Simple, Stupid.
  

[1] P.R. Ehrlich and J.P. Holdren, "Impact of Population Growth," 
Science, vol. 171, pp. 1212-17 (1974)

------------
Alan McGowen