Patrick A. P. Moran, 1917–1988: In memorium

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

the frequency profile wanders around in the allele space with time, a variance-like quantity settles to a constant mean value at equilibrium.

From the mid-1960s Pat became interested in psychiatric genetic disorders. He examined the possible basis of the schizophrenic polymorphism and developed models to examine the stability of schizophrenia over time and place. Further he considered the estimation of psychiatric genetic differences between classes and races and the effect of maternal and paternal age in several genetic diseases. Pat was also the first to point out the difficulties of defining a concept of heritability when genetic and environmental factors are correlated and when relatives share a closer environment than individuals in general. The debate on this concept was heated in the 1970s, but has now led to the introduction of a variety of more realistic and complex models.

Pat Moran was born in Sydney, Australia, July 14, 1917. He was educated at St. Stanislaus College, Bathurst, and at the Universities of Sydney and Cambridge. He held positions as Experimental Officer, Ministry of Supply, 1940 Supply, -1942;; Australian Scientific Liaison Officer, London, 1942 -1945; Baylis Student, University of Cambridge, 1945 -1946; Senior Research Officer, Institute of Statistics, Oxford University 1946 -1951; Lecturer in Mathematics, Trinity College, Oxford, 1949-1951, and Pat's list of publications, more than 170 in number, reflect his considerable contributions to many areas of science. This list (until 1981) can be found in Gani and Hannan [1982] . Just twenty percent of his publications relate to genetics. His other influential books were The Theory of Storage, Methuen [ 19601; Geometric Probability (with M.G. Kendall), Griffin [ 19621; and Introduction to Probability Theory, Oxford [1968] .

Around him Pat created a warm, calm, and intellectually stimulating atmosphere. He was ever willing to give advice, and its breadth and wisdom will always be treasured by those of us who were fortunate enough to know him well.

University Lecturer 1951; and Professor of Statistics, Institute of Advanced Studies, Australian National University, 1952-1982. During his thirty years at ANU, Pat Moran played a unique role in the training of several generations of Australian statisticians. After his retirement he stayed on at ANU as Visiting Fellow in the National Health and Medical Research Council Social Psychiatry Research Unit. Pat was honoured for the excellence of his research by election to the Australian Academy of Science in 1962 and the Royal Society in 1975. He was awarded the Lyle Medal of the Australian Academy of Science in 1963 and the Pitman Medal of the Statistical Society of Australia in 1982. He became an Honorary Life Fellow of the Royal Statistical Society in 1970 and an Honorary Life Member of the Statistical Society of Australia in 1978. Pat was a foundation Honorary Life Member of the Human Genetics Society of Australasia.