population growth

Population, technological progress and the evolution of innovative potential

In his seminal paper Population Growth and Technological Change: One Million B.C. to 1990, Michael Kremer combined two basic concepts to explain the greater than exponential population growth in human populations over the last million years.

The first concept is that more people means more ideas. A larger population will generate more ideas to feed technological progress.

The second concept is that, in a Malthusian world, population is constrained by income, with income a function of technology. Population can only increase if there is technological progress, with any increase in income generated by technological progress rapidly consumed by population growth.

When you combine these two concepts, a larger population generates more ideas, which in turn eases the constraint on additional population growth, which further accelerates the production of ideas. The result is population growth being in proportion to the population size. The following diagram illustrates the feedback loop.

Kremer model

When I first read Kremer’s paper, the title caught my attention, particularly the reference to One Million B.C. Humans have evolved markedly in the last one million years. One million years ago, Homo sapiens did not exist as a distinct species, with Homo erectus found in Africa, Europe and Asia. Since then, cranial capacity (a proxy for brain size) has increased from around 900 cubic centimeters to 1,350 cubic centimeters. And not only have humans evolved, but adaptive human evolution appears to be accelerating. As more people means more mutations, natural selection has greater material on which it can act.

It was this consideration that forms the basis of my latest working paper, Population, Technological Progress and the Evolution of Innovative Potential, co-authored with my supervisors Juerg Weber and Boris Baer.

In the spirit of Kremer’s original paper, we develop a model of population growth and technological progress, but add an extra element, which we call “innovative potential”. Innovative potential is any trait that results in the production of ideas that advance the technological frontier. Innovative potential might incorporate IQ, willingness to invest in innovation, participation in productive activities in which innovation may occur, risk preference, time preference and so on. At this stage, we do not specify the precise trait, but it is not hard to see what the likely traits are.

As more people means more mutations, mutations that increase the innovative potential of the population will occur with greater frequency in a larger population. As the population grows, so too does the rate of evolution of innovative potential.

Incorporating the evolution of innovative potential into the model creates a second element to the feedback loop, as is shown below. Population growth is now proportional to both the size and innovative potential of the population.

Collins et al model

One of the more interesting results of the model can be seen when we partition the drivers of the acceleration of population growth between increasing population size and the increasing innovative potential of the population. As the population evolves, the relative contribution of continuing growth in innovative potential to the acceleration of population growth declines. Continuing population growth becomes the main driver of technological progress and further population growth. However, this does not mean that innovative potential is not important, as the level of innovative potential continues to have a material effect. Populations with higher innovative potential will have much faster population growth.

The reason this change occurs is that population growth is driven by both increasing population size and the increasing innovative potential of the population, whereas innovative potential only increases with population size. As the innovative potential reaches a higher level, each new person is more innovative and generates more ideas, but they will only generate the same number of mutations as they always have.

One issue with introducing innovative potential into a model of this kind is that ideas are non-excludable. Suppose I invent some new technology that increases my ability to procure resources. If someone else sees and copies this idea, I wont have an evolutionary edge. In the first version of the model presented in the paper, we handwave around this issue, and suggest that innovative people may have higher fitness due to prestige, the ability to keep secrets or some other avenue of reaping the benefits of the innovation. Although this handwaving likely has an element of truth, we introduced a version of the model in which those who are more innovative are also more productive in using those ideas. The results are robust to inclusion of this element.

One other observation from the model is the robustness of the population to technological shocks. Through human history, population did not undergo a simple increase, but underwent shocks and bottlenecks. For example, a change in climate could reduce the carrying capacity of the land (through reducing the effective level of technology), reducing population size.

In Kremer’s model, shocks of this nature are a strong setback to population growth and technological progress. As the population is smaller, idea production will be slower. In fact, population growth and technological progress will resemble the levels of growth when the population was last of that size. A population experiencing consistent technological shocks may never grow to a substantial size.

Where there is evolution of innovative potential, a technological shock is a setback to population growth, but the clock is not fully wound back to the time when the population was last of that size. The population now has higher innovative potential and the population recovers faster from each successive technological shock. This effect is particularly strong where higher innovative potential also increases the productivity of the population in using the new technologies.

Finally, two assumptions that we include in the model are that population instantaneously adjusts to the carrying capacity of the land, and that the spread of mutations is instantaneous. The first is a weak assumption given the time spans over which the model operates. The second is much stronger. As a result, we also consider the time it takes for a mutation to spread through the population in a dynamic model and an agent-based simulation. Delaying the spread of a mutation does not substantively change the model results, although it prevents an explosion in the innovative potential of the population at the time that the population explodes. But as noted above, even where mutations spread instantaneously, the contribution of continuing evolution of innovative potential to the acceleration of population growth drops to near zero when the population explodes. The delay in the spread of mutations simply strengthens that result.

If you would like to play with the agent-based model, code for the model is contained at the end of the working paper, or you can download the model here. I developed the model in NetLogo, an open source agent-based programming environment, which you can download from here.

As is always the case, I would appreciate any comments, ideas or criticisms about the working paper.

World economic history in two diagrams

Gregory Clark opens A Farewell to Alms with a strong claim:

The basic outline of world economic history is surprisingly simple. Indeed it can be summarized in one diagram: figure 1.1.

Clark (2007) Figure 1.1

I like Clark’s claim, but I’m now convinced that we need a second. From Michael Kremer’s Population Growth and Technological Change: One Million B.C. to 1990:

Figure I plots the growth rate of population against its level from prehistoric times to the present.

Kremer (1993) population growth

Even though there was negligible per person income growth through the Malthusian era, technological change was accelerating. As more people leads to more ideas (as there are more people to come up with them), a larger population leads to faster technological progress. Technological progress in turn allows for further population growth. The resulting pattern is faster than exponential growth in technology and population – a dynamic that does not show up in Clark’s chart.

If I were to stretch it to a third diagram I would want something that captures the dynamism of the Malthusian era – population bottlenecks, different rates of growth across different populations and the like – but I’m not sure what that chart would look like yet.

Fertility is going to go up

In my latest working paper, co-authored with Oliver Richards, we argue that recent fertility increases in developed countries may only be the beginning. From the abstract:

We propose that the recent rise in the fertility rate in developed countries is the beginning of a broad-based increase in fertility towards above-replacement levels. Environmental shocks that reduced fertility over the past 200 years changed the composition of fertility-related traits in the population and temporarily raised fertility heritability. As those with higher fertility are selected for, the “high-fertility” genotypes are expected to come to dominate the population, causing the fertility rate to return to its pre-shock level. We show that even with relatively low levels of genetically based variation in fertility, there can be a rapid return to a high-fertility state, with recovery to above-replacement levels usually occurring within a few generations. In the longer term, this implies that the proportion of elderly in the population will be lower than projected, reducing the fiscal burden of ageing on developed world governments. However, the rise in the fertility rate increases the population size and proportion of dependent young, presenting other fiscal and policy challenges.

We’re certainly not the first to hint at the idea that selection of high fertility individuals will increase fertility. Fisher noted the power of higher fertility groups in The Genetical Theory of Natural Selection. I’ve seen Razib Kahn, Robin Hanson and John Hawks mention the idea in blog posts. There is one great paper by Murphy and Wang (which I will blog about soon) that has part of this argument buried in the micro-simulation. Many papers on the heritability of fertility hint at it. Rowthorn’s paper on fertility and religiosity also points in this direction. But what we couldn’t find was someone who sought to tie down the idea – particularly in the way we have.

I actually thought a paper of this nature would already be written. We were interested in the economic implication of the argument, but because there was no clear statement of the evolutionary foundations that we could use in the way we wanted, we decided to build our argument from the ground up. We’re hoping that this working paper receives some solid critique that will allow us to decide whether our angle of attack is useful or can be improved. We have constructed three basic genetic models, but are they useful? Are there better alternatives? Once we address those questions, we have some ideas for empirical tests and we hope to use the concept in some more detailed economic and cultural analysis. Ultimately, this paper will need to be tied in with a large and growing literature on the biosocial basis of fertility.

I’m the first to admit we could be wrong in the prediction of a fertility increase. What other shocks are still to come? Will the continually changing environment drown out the underlying evolutionary dynamics? Our instinct is that most of the shocks that can affect fertility have played out in the developed world – increased incomes, effective contraception, female choice and so on. But what further shocks could reduce fertility?

In presenting this paper, we tend to receive  two major classes of response. The first and obvious question is whether these dynamics will play out in time frames that matter. As its been 200 years since some populations underwent the demographic transition, there has  been enough time for selection to have occurred on a trait as important to fitness as fertility (in some populations we have evidence of this). The more interesting question is what will be the magnitude of the effect over the next 50 or 100 years? I’m not sure of the answer to this, but even a small total fertility rate increase of 0.1 children per female can have material effects on population size and structure.

The other response we tend to receive is that fertility is affected by policy, incentives, female opportunities and so on. Any trend we see today is a response to those factors. And that may be true. But to the extent there is variation in the response to the policy, incentives or opportunities and there is a genetic basis to that variation, we can see selection of those with higher fertility.

Having said that, throughout the paper we are deliberately agnostic about the merits of the various theories of what has caused the fertility decline in the developed world to date. For the purposes of our hypothesis, it is sufficient to know that there was a decline in fertility and that variation in fertility is heritable after the decline. As the first law of behaviour genetics is that all human behaviour is heritable, its not a very high bar to clear. It would be difficult if it was otherwise, particularly when you consider the raft of current theories. And even if you believe a certain factor is behind the decline, what is the causative pathway? As an example, consider the spread of the pill and the factors which are relevant to it reducing fertility. First, there is desire of someone with access to the pill to have children. Then there is their desire to take the pill to control pregnancy. Do they take the pill as instructed (possibly related to conscientiousness)? Is the pill physiologically effective? Do they experience side-effects that deter continued use? Variation along any of those dimensions would affect fertility.

The biggest simplification in the way we present our models is that, unlike our models, developed countries did not receive a single fertility shock across the population. Rather, multiple shocks hit different parts of the population at different times. This is why fertility has generally declined for much of the last 200 years, rather than suddenly suffering a single large drop. Of note, fertility tended to decrease among the wealthy first. As our framework would suggest that fertility rates will increase first among groups that experienced the shock earlier, we would predict that groups with a history of higher socioeconomic status will tend to increase their fertility rates earlier.

Immigration also presents some interesting issues. Immigrants tend to have higher fertility when arriving in a country that has undergone the demographic transition. But our framework would suggest that following generations will experience a decline as they undergo the fertility shock. To the extent that the immigrant population has not been exposed to the shock before, their fertility may decline and recover later than native populations.

These issues offer some basis for testing the hypothesis. But first, we’re keen to nail down some good ways of thinking about the problem. The working paper and the models within are part of that process. So, if you have any thoughts or criticisms, we’d be grateful to hear them.