Their hypothesis is that in places where disease is rampant, it behoves groups not to mix with one another more than is strictly necessary, in order to reduce the risk of contagion. They therefore predict that patterns of behaviour which promote group exclusivity will be stronger in disease-ridden areas. Since religious differences are certainly in that category, they specifically predict that the number of different religions in a place will vary with the disease load. Which is, as they report in the Proceedings of the Royal Society, the case.
Proving the point involved collating a lot of previous research.
Even defining what constitutes a religion is fraught with difficulty. But using accepted definitions of uniqueness, exclusivity, autonomy and superiority to other religions they calculated that the average number of religions per country is 31. The range, though, is enormous—from 3 to 643. Côte d’Ivoire, for example, has 76 while Norway has 13, and Brazil has 159 while Canada has 15. They then did the same thing for the number of parasitic diseases found in each country. The average here was 200, with a range from 178 to 248.
Obviously, some of the differences between countries are caused by differences in their areas and populations. But these can be accounted for statistically. When they have been, the correlation between the number of religions in a place and how disease-ridden it is looks impressive. There is less than one chance in 10,000 that it has come about accidentally.