Many mathematicians and statisticians have had great influence on evolutionary theory and population genetics. Patrick A.P. Moran was one who made major contributions to this theory.
Pat Moran began his career as a pure mathematician but soon became interested in statistical inference, and gradually broadened his range of interests. Fifteen years later, in the late 1950s, he moved on to mathematical genetics. His work over the next thirty years included several major contributions in this field.
In population genetics he is perhaps best known for the introduction of a model that has proved to be particularly amenable to analysis. Moran models have overlapping generations, can incorporate mutation and selection, and enable explicit expressions for many quantities of evolutionary interest to be obtained. Thirty years later, these models are still important. Then his consideration of the complications of two sexes led to the introduction of quasi-Markovian variables whose study has been mathematically and biologically fruitful. Pat's well-known and scholarly book on mathematical genetics, The Random Processes of Evolutionary Theory [Oxford, 1962; (translated into Russian in 1973)], contained many novel results. A controversial consequence of his consideration of the effect of population subdivision was to cast some doubt on the evolutionary theory favoured by Sewell Wright. Later, Pat was to examine Fisher's Fundamental Theorem of Natural Selection, which stated that the increase in mean fitness from one generation to another is non-negative. It came as a surprise when Pat showed that, in certain circumstances, decreases in mean fitness can occur when fitness depends on the genes an individual carries at two loci. This led both to the genetical development of multilocus theory and to the mathematical study of principles that are "almost always" true. The Fundamental Theorem is, in some sense, "usually" true. At the molecular level, in the 1970s, Pat examined stepwise mutation models arising from experimental measurements of the charge level on a gene. These models have interesting stationarity properties. Pat showed that although the mean position of