Here is one speculation of what could explain the prevalence of heavy-tailed distributions in what you call ‘hierarchical classification schemes’:
Suppose that the causal mechanism generating the relevant classes has the property that new members are more likely to be added to a class the more members it already has (e.g. if people were more likely to move to a city the higher its population). Under some such conditions it’s then a mathematical consequence that the size distribution (i.e. number of members across classes) will converge to a power law.
This has been popularized as “preferential attachment” by the ‘network science’ people around Barabasi since the end of the 1990s to explain various observations on the Internet and other networks (though the related academic cottage industry has recently received some good criticism). But the maths and potential real-world cases are much older; indeed, the perhaps first major case for which this explanation was proposed was one of your examples—biological taxa -, by Yule in the 1920s.
Here is one speculation of what could explain the prevalence of heavy-tailed distributions in what you call ‘hierarchical classification schemes’:
Suppose that the causal mechanism generating the relevant classes has the property that new members are more likely to be added to a class the more members it already has (e.g. if people were more likely to move to a city the higher its population). Under some such conditions it’s then a mathematical consequence that the size distribution (i.e. number of members across classes) will converge to a power law.
This has been popularized as “preferential attachment” by the ‘network science’ people around Barabasi since the end of the 1990s to explain various observations on the Internet and other networks (though the related academic cottage industry has recently received some good criticism). But the maths and potential real-world cases are much older; indeed, the perhaps first major case for which this explanation was proposed was one of your examples—biological taxa -, by Yule in the 1920s.
For a survey of other generating mechanisms of power laws, see Newman (2005) and this blog post by Terence Tao.