From 1932 to 1955, he headed the entomology department at the
Rothamsted Experimental Station. When he joined the staff in 1932, Sir John Russell was the director. Russell had earlier invited
R. A. Fisher and Williams was able to study quantitative aspects of insect populations. Williams became one of the pioneers of the statistical study of
biodiversity patterns. For example, he showed that
Charles Elton's observation that the species-to-genus ratio was lower on islands than on mainlands could be expected from chance alone and hence that Elton's interpretation (
competitive exclusion) was redundant (which had already been shown three decades earlier by
Alvar Palmgren and
Arthur Maillefer). In his 1964 book, "Patterns in the Balance of Nature", Williams gave a still valuable overview of this discipline. With Fisher, Williams was able to establish patterns in the diversity and numbers of insects caught in light traps. He noticed that logarithmic patterns were widespread, an idea which was later developed by other ecologists like
Frank W. Preston. Williams used this pattern to predict the number of head lice on people using data on counts of lice from prisoners in a South Indian jail. Williams calculated that the number of persons with only one louse must be 107 and the actual was 106 and he wrote
so Nature was only one wrong. He continued to work after his retirement on many aspects of insect ecology. == Miscellaneous ==