XVIIIth Fisher Memorial Lecture Delivered at the Natural History Museum, London, on Thursday, 20th October, 1994 Fiducial Inference and the Fundamental Theorem of Natural Selection

The International Biometric Society owes much to the initiative of R. A. Fisher, its first President, and the Fisher Memorial Trust owes much to the British Region of the Society, which was one of the cofounders and which contributes three representatives to the Trust. The other cofounders are the Royal Statistical Society and the Genetical Society, each with two representatives, and the Royal Society with one. Fisher served as President of each of these Societies except the Royal Society, from which he received the Royal Medal, the Darwin Medal, and the Copley Medal. It has long been a custom of the Trust to encourage its supporting societies to host Fisher Memorial Lectures, but alone amongst them the Biometric Society has not so far been involved. Today we repair this omission. I am as grateful to the Society for allowing me to deliver my Presidential address in Fisher format as I am to my fellow Trustees for inviting me to deliver the XVIIIth Memorial Lecture. The Trust exists primarily to promote the Lectures, but, insofar as it has residual resources to do so, also to support the application of mathematics to biology. In this connexion I am very happy to announce that the Trust has decided to offer the British Region funds to enable it to establish a number of travel bursaries to help young members attend the next International Biometrics Conference due to take place in Amsterdam in 1996. If I might be allowed to postpone the difficult subjects of my talk for another few moments-no doubt to your relief-I should like also to thank the British Region for inviting me to be its President two years ago. The pleasure I derived from this was all the greater because of a coincidence I would like to describe. Sixteen years ago I was made a Reader at Cambridge, and was encouraged to choose for my title Mathematical Biology. I was never very happy with it, and as the years went by became even less so as the phrase came to be identified with differential-equation biology. So I had the title changed to Biometry, influenced partly by the name of the Society but also by the fact that the two distinguished university posts in Britain which had used the title-the Readership in Biometry at Oxford held years ago by N. T. J. Bailey and the Weldon Professorship of Biometry at University College London vacated not long ago by C. A. B. Smith-were no longer current (though the latter has since been filled). It seemed only right that if Oxford and London did not want to use Biometry, Cambridge should reclaim it, the word having been coined there by William Whewell in 1831. For the new Cambridge Reader in Biometry to find himself President of the British Region of the Biometric Society almost immediately afterwards seemed like magic. And magic is what both fiducial inference and the fundamental theorem of natural selection have seemed to be to many people. My title is in fact a quotation from 0. Kempthorne (1983), who wrote: