July 6, 2010

Human fertility, population growth, energy usage, and intellectual dishonesty

Posted in Uncategorized at 2:53 pm by Chris

I recently unearthed a paper that I read years ago and have been pondering ever since. On re-reading, I find that I disagree with almost everything in it, but the reasons are interesting enough that I thought I’d write about it anyway.

The paper is “Allometry of human fertility and energy use”, by Melanie Moses and James Brown, published in 2003 in Ecology Letters 6. No, not that James Brown. Very briefly, they fit a relationship between per-capita energy use and fertility rates, for a large number of countries, and across nearly thirty years. Their fitted relationship is a -1/3 power relationship between energy use per capita and fertility, i.e. there’s a slight negative trend between energy use and fertility: countries with very low fertility have very high energy use and vice versa. This is an extension, they say, of the relationship between metabolic rate (mostly determined by body size) and fecundity in the animal kingdom.

I have misgivings about all this. The very first one is a fairly high level of bio-math geekery, so feel free to skip the next paragraph if that doesn’t interest you.

This paper is one from a whole slew by a relatively small group of people, using scaling laws based on fractal dimensions (3/4 powers, in particular) to explain (they say) a host of biological phenomena. In general this crew are just a bit too keen to have their results support the underlying theory, which is obviously a bit circular. It’s particularly bothersome because some of the basics of the underlying theory are debatable: they take it as a given, for instance, that metabolic rates scale as a 3/4 power of body mass; which is true, if you pool lots of datasets together. If you look at datasets for individual groups of organisms (just reptiles, for instance) then there are some very knowledgeable physiologists who are adamant that the line is flatter than that, maybe a 2/3 power. If you pile a up whole lot of 2/3 power lines, scatter data around each of them, and then fit a line through the whole mess, you can fit a 3/4 power, but it doesn’t have any biological meaning. So any beautiful tower of reason and logic built on the existence of a universal 3/4 power scaling law in biology is going to be… wrong.

OK, the rest of you can start reading again here. Leaving aside my bio-geek concerns, I don’t think the relationship they claim to have fitted does a very good job of explaining the data. It’s not robust enough to be predictive in any useful way, and I’ve swiped a figure out of the paper to prove my point. Per capita power consumption is along the bottom (in Watts, which is inappropriate) and fertility rate in births per thousand goes up the side. Empty circles are “outliers”, excluded from the analysis:

Notice that there’s a LOT of scatter in the relationship. A robust predictive method based on hard physical constraints wouldn’t, to my mind, allow variation to the tune of “somewhere between 9 and 30” in the predicted value. If you’re talking human birth rates, that’s a pretty big difference.

But more disturbing are the “outliers”, and those are in fact the reason that I put the words intellectual dishonesty in the title of this post. Let me quote what they say about these data points in the text: “Ten oil-producing nations with extremely high per capita energy production (Oman, Qatar, Saudi Arabia, United Arab Emirates, Bahrain, Kuwait, Netherlands Antilles, Brunei, Libya and Turkmenistan) are significant outliers in most years and are excluded from regression equations”. Excuse me? Sorry guys, you don’t get to throw out data points just because they inconvenience you. You’re talking about using technological energy use to predict biological responses, and those points at the far end of the energy-use spectrum are the most important to proving your case! Four of them are right past the end of all your other points, you have no other data at all in that region; calling what you do have an outlier is indefensible without a damn good reason. And just quietly, the figure is produced so small in the original paper that the empty circles aren’t at all obvious until you blow it up for a blog post. That’s sloppy at the very least, if not outright dishonest.

OK, so I don’t like their analysis, nor their conclusions, nor the way they present their data. Why am I still talking about this paper? Because if you ignore the conceptual arm-bending going on, there is some interesting stuff here. Look at that graph, ignoring the silly trend line and taking all the points as being equal. There’s very clearly a limiting line in human fertility, what we bio-geeks call a factor ceiling:  no matter how great your resources, you can only sustain a certain birth rate, somewhere between 40 and 50 births per thousand. Going in the other direction, it doesn’t seem like low per capita energy and low fertility are mutually compatible, although a couple of other graphs in the paper have Latvia and Bosnia as “outliers” in this region during the 1980s (anyone know what was special about Latvia and Bosnia in the eighties?). But the very lowest fertility rates are at around half the maximum per capita energy consumption, maybe even less. What gives?

What I suspect is really going on here is to do with demographic transition. Moses and Brown mention this concept, but they clearly don’t understand it very well. Demographic transition is probably the single most important phenomenon in human population dynamics, and occurs when women stop having vast numbers of babies who may or may not die in childhood, and start having just a few, who are much less likely to die young. Not to put to fine a point on it, this is the major dividing line between the first and third worlds. It tends to happen pretty quickly, and it happened in living memory in the West: how many people out there have grandparents who were one of five or ten children? My mother was one of ten children, and she was born in the 1950s.

The single biggest driver of demographic transition, leaving all other factors way in its dust, is female education. Educated women have fewer children, and educated women drag all the other social indicators along with them. Or to put it in a less deterministic way: a society that educates woman is also a society that has hospitals (or at least clinics) and the rule of law (or at least social stability), and all the other trappings of modern civilisation (and I have pondered before on the limited extent to which any of this depends on energy use). Educating woman doesn’t require air-conditioners or V8 shopping trolleys, in fact you can have all those things without educating women (hence Oman, Qatar, etc). I don’t have figures to hand, but compare this map and this map with this map to see the shape of those relationships. I think you can probably make the argument that this is deterministic, though; having a big pool of educated women changes social dynamics. Women tend to get things done, that’s why lots of those micro-loan and local aid groups prefer to deal with women, no matter how much it irritates the men.

The thing is, these ideas matter. Energy use is a huge topic at the moment, for reasons I don’t need to expand on. The extent to which energy use is related to population size and standards of living is something that needs to be examined at length, not least (as George Monbiot so rightly points out) so that we can shut up those tedious self-apologists who go on about the teeming millions somewhere else being to blame for every ecological woe. If we take it as a given that demographic transition requires lots of energy, then we’re in trouble. If, on the other hand, demographic transition is traditionally correlated with a whole bunch of energy-intensive activities, but doesn’t depend on them, then the future is manageable, or least hopeful.

We suffer from an incomplete sample here. I don’t know which countries occupy the lower edge of that graph, but I suspect that most of them share a similar history. We don’t know if that history represents the only pathway towards a stable population and decent standards of living for everyone, but I don’t think that enshrining it in some sort of shonky mathematical doctrine is helpful.



  1. Gordon said,

    Chris –
    1. In the description of the paper the authors (or maybe you) make reference to energy USE. The outliers in the figure are energy PRODUCERS.
    2. Latvia and Bosnia were not in existence (as sovereign states anyway) in the 80s. The latter was part of Yugoslavia and Latvia was part of the USSR. In Latvia’s case independence movements started in the mid to late 1980s.

    But perhaps more importantly – why was this part of academic research? Surely the results are obvious? The less power available the less power consumed – and the less power available means no artificial means of heating or electronic means of entertainment. In a case like this what are people to do, except what comes naturally? Hence an increase in births, representing an (assumed) increase in fertility. 🙂

  2. Chris said,

    Hi Gordon,

    I thought this might be up your alley. Energy-producing states tend to be massive domestic energy consumers as well, presumably because they can and energy is ridiculously cheap there (don’t a lot of the oil-producing states have subsidised petrol on the local market?).

    I had a feeling that there was something funny about that Latvia and Bosnia thing. I’m going to have to look up the original dataset, aren’t I?

    Looking forward to future scientific papers validating the inverse relationship between artificial lighting and fertility 🙂 Blackout babies need not apply.

  3. Gordon said,

    Yup you are going to have to go and find the original dataset and hope that Latvia was not simply a subset of the USSR!

    On the production/use conundrum. Energy producers may also be massive energy consumers, but I am not sure that there is a direct (i.e. statistically significant) correlation between the two figures. One is not necessarily in proportion to the other.

    So I am afraid the authors of the paper, if they were using these two sets of data, and did not take cognisance of the difference are royally screwed.

    And probably don’t have any birth to show for it!

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: