Defining fitness in an uncertain world.

The recently elucidated definition of fitness employed by Fisher in his fundamental theorem of natural selection is combined with reproductive values as appropriately defined in the context of both random environments and continuing fluctuations in the distribution over classes in a class-structured population. We obtain astonishingly simple results, generalisations of the Price Equation and the fundamental theorem, that show natural selection acting only through the arithmetic expectation of fitness over all uncertainties, in contrast to previous studies with fluctuating demography, in which natural selection looks rather complicated. Furthermore, our setting permits each class to have its characteristic ploidy, thus covering haploidy, diploidy and haplodiploidy at the same time; and allows arbitrary classes, including continuous variables such as condition.

Foundations of a mathematical theory of darwinism.

This paper pursues the 'formal darwinism' project of Grafen, whose aim is to construct formal links between dynamics of gene frequencies and optimization programmes, in very abstract settings with general implications for biologically relevant situations. A major outcome is the definition, within wide assumptions, of the ubiquitous but problematic concept of 'fitness'. This paper is the first to present the project for mathematicians.

Novel isomenthone-derived 1,3-diol ligands identified through parallel synthesis and screening catalyse an asymmetric aldol reaction.

A library of new (+)-isomenthone-derived 1,3-diol ligands, containing 5 contiguous stereocentres (3 fixed, 2 variable), was prepared in 2 steps by parallel synthesis. Evaluation in parallel identified several different ligands from the library for catalysing a Mukaiyama aldol reaction with 87-90% e.e.

Synthesis, stereostructure, and conformations of novel bi- and trifunctional (+)-isomenthone derivatives.

[reaction: see text] Following protection, keto alcohols 4 [from (+)-isomenthone] undergo reduction to 1,3-diol 6 (S configuration at the new stereocenter). Organometallic C-nucleophiles add to the carbonyl with the same facial selectivity as hydride, providing multifunctional derivatives, e.g.

Measurement of the 5-hydroxyindoleacetic acid/creatinine ration in the urine of patients with coeliac disease.

Urinary excretion of 5-hydroxyindoleacetic acid and creatinine has been measured in 8-hour collections from adult patients with coeliac disease, and results have been compared with a group of healthy adult controls. Results were expressed as 5-HIAA/creatinine and significantly higher values of this ratio were found in patients with coeliac disease. Measurement of this ratio is a non-invasive technique which is useful in selecting patients with suspected coeliac disease for further investigation.