Empirical phenomena and universal laws

In 1943 Fisher, together with Corbet and Williams, published a study on the relation between the number of species and the number of individuals, which has since been recognized as one of the most influential papers in 20th century ecology. It was a combination of empirical work backed up by a simple theoretical argument, which describes a sort of universal law governing random partitions, such as the celebrated Ewens partition whose original derivation flows from the Fisher-Wright model. This talk will discuss several empirical studies of a similar sort, including Taylor's law and recent work related to Fairfield-Smith's work on the variance of spatial averages.