Are bigger populations more innovative? There are lots of reasons to think they should be.
More brains means more ideas
More people means more specialization(?)
More consumers means more profit for innovators
There’s also an argument that small populations are not just stagnant - they are actually vulnerable to technological regress. Joseph Henrich has an influential model of cultural evolution, where technological progress (in pre-modern societies) occurs via tinkering and retention of successful modifications. In these models, transmission of good ideas from one generation to the next is crucial for cumulative technological progress to occur. But transmission is noisy, usually resulting in inferior copies. This tends to lead to the steady accumulation of errors, until technologies are degraded to the point where they are useless. What keeps cumulative technological progress going is the random appearance of especially talented individuals who do not merely copy but improve on existing technology. Since their appearance is more or less random, they will tend to be more of them in big populations.
This argument was put to a lab test in Derex et al. (2013). Derex and coauthors ask groups of 2, 4, 8, and 16 people to perform a simulated task where they “construct” arrowheads and fishing nets on a computer. “Construction” of the arrowhead is relatively simple, while the fishing net is complex. After participants are shown how to create each object, the groups go through 15 rounds. In each round, they can observe a group member create the digital object, they choose which to try and create themselves, and they receive a score based on the quality of their creation. It’s also possible to “discover” higher scoring designs by tweaking the models. Consistent with expectation, the bigger the group, the more likely they are to improve the simple arrowhead creation (figure 2) and maintain (though not improve) the complex fishing net creation (figure 3).
But that’s just a lab experiment. Turning from the lab to the real world, a host of papers test the link between cultural complexity and population size in the distant past, with mixed results. One challenge with testing this model is that populations are rarely truly isolated. When distinct populations still have contact with each other, then a small population can learn from a large one (and vice-versa), resulting in no apparent connection between population size and technology. The trouble is, if populations can interact, then we really only have one population to observe - that of the entire planet.
A famous exception is Kline and Boyd (2010), which studies the link between indigenous technology and population for a set of 10 relatively isolated islands in Oceania (10 is not a lot of observations, but better than 1). They find that bigger populations tend to have more tools, and that the tools they have are more complex (as measured by the number of components comprising them). Even in this setting though, the islands are not completely isolated. However, they have some measures of contact between islands, and they do find that small islands in contact with big islands tend to have more and more-complex technology than isolated ones.
Can we go beyond the lab and idiosyncratic islands though? Michael Kremer gives it a shot in an ambitious 1998 paper (summary here). Rather than attempt to calculate the technological complexity of different societies, he assumes that better technology allows a given resource base to support a larger population. Since bigger populations also have more ideas, this leads to a self-catalyzing cycle, where more people beget more ideas, which beget more people.
This model makes two predictions. First, the rate of population growth should be increasing in the absolute size of the population. He tests this on data on global population, going back to 1,000,000 B.C.
Not bad, at least until the demographic transition!
Second, suppose two regions are connected to each other and have access to all the same technology. In the kind of argument that surely drives anthropologists and archeologists up the wall, Kremer argues this is probably a good enough characterization of the ice age, when land-bridges connected Eurasia/Africa to the Americas, Australia, Tasmania, and Flinder’s Island. When the ice melted, these regions became separated by the rising sea until the 1500s, when large ocean-going ships were invented. Until that time, they evolved in relative isolation.
While they might have had access to similar technologies at the end of the ice age, they differed in the extent of their land mass. All else equal, bigger landmasses can support larger populations. So Kremer’s model predicts these regions will have faster technological progress and hence higher population density.
He checks this prediction by comparing population density across these regions when they again came into contact with each other.
Granted, this is 5 observations, but at least they are consistent with his hypothesis. The bigger the landmass, the larger the population density!