Price of Prostatectomy

Three different urological units found that transurethral prostatectomy required a hospital stay at least one week shorter than open Millin or transvesical prostatectomy. By making transurethral resection more widely available there could be a substantial financial saving; but more surgeons would have to specialize in urology.     

Grafen,the Price equations,fitness maximization,optimisation and the fundamental theorem of natural selection

This paper is a commentary on the focal article by Grafen and on earlier papers of his on which many of the results of this focal paper depend. Thus it is in effect a commentary on the “formal Darwinian project”, the focus of this sequence of papers. Several problems with this sequence are raised and discussed. The first of these concerns fitness maximization. It is often claimed in these papers that natural selection leads to a maximization of fitness and that this view is claimed in Fisher’s “fundamental theorem of natural selection”. These claims are refuted, and various incorrect statements about the meaning and interpretation of the fundamental theorem of natural selection, in this sequence and in other papers by other authors, are discussed. Next, much of the work in this sequence rests on the first Price equation. In the deterministic (infinite population) case this equation is no more than the standard classical equation relating to changes in gene frequencies. In the stochastic case the equation gives the change in gene frequencies as the sum of two terms (the second of which vanishes in the deterministic case). These two terms are of essentially equal importance in the situation considered in the focal article, yet one of Grafen’s results ignores the second term in the stochastic analysis. This is associated with a wavering between deterministic and stochastic analyses and the use of the Price fitness concept and the classical fitness concept. These comments cast doubts on Grafen’s optimization theory.     

Integrating physiological, ecological and evolutionary change: a Price equation approach

We use a general quantitative framework – the Price equation – to partition phenotypic responses to environmental change into separate physiological, evolutionary and ecological components. We demonstrate how these responses, which potentially occur over different timescales and are usually studied in isolation, can be combined in an additive way; and we discuss the main advantages of doing this. We illustrate our approach using two worked examples, concerning the emergence of toxin resistance within microbial communities, and the estimation of carbon uptake by marine phytoplankton in high-CO₂ environments. We find that this approach allows us to exclude particular mechanistic hypotheses with regard to community-level transformations, and to identify specific instances where appropriate data are lacking. Thus Price's equation provides not only a powerful conceptual aid, but also a means for testing hypotheses and for directing empirical research programmes.