This shows the relationship between life expectancy and fertility rates; colours code regions, point sizes indicate infant mortality rates. If you follow this link, you can easily modify the graph, use a slider to instantly look at historical, and cook up your own examples.
Sorry if this is a bit off-topic, but I was so impressed by this tool that I’m hoping other mathematicians might like to explore it too. The particular graph I’ve shown is something I’ve been interested in for a while. Consider the very simple model in which parents want to be 95% certain that they have at least two children that survive to adulthood. Pretending this is the only determining factor in fertility rates, you can now compute fertility rates as a function of infant mortality. Tools like this provide amazing access to data, to quickly confirm or invalidate models like this, and to suggest other models.