Molecular Ecology (2006) 15, 2857–2869 doi: 10.1111/j.1365-294X.2006.02992.x © 2006 The Authors Journal compilation © 2006 Blackwell Publishing Ltd Blackwell Publishing Ltd Measurement of biological information with applications from genes to landscapes WILLIAM B. SHERWIN,*† FRANCK JABOT,*‡ REBECCA RUSH * and MAURIZIO ROSSETTO § *School of Biological Earth and Environmental Science, University of New South Wales, Sydney, NSW 2052, Australia, †Institut Des Sciences de l’Evolution, Université Montpellier 2, cc 065, Place Eugène Bataillon, 34095 Montpellier, Cedex 05 France, ‡Ecole Polytechnique 91128 Palaiseau, Cedex Paris, France, §National Herbarium of New South Wales, Botanic Gardens Trust, Mrs Macquarie’s Road, Sydney, NSW 2000, Australia Abstract Biological diversity is quantified for reasons ranging from primer design, to bioprospect- ing, and community ecology. As a common index for all levels, we suggest Shannon’s S H, already used in information theory and biodiversity of ecological communities. Since Lewontin’s first use of this index to describe human genetic variation, it has been used for variation of viruses, splice-junctions, and informativeness of pedigrees. However, until now there has been no theory to predict expected values of this index under given genetic and demographic conditions. We present a new null theory for S H at the genetic level, and show that this index has advantages including (i) independence of measures at each hier- archical level of organization; (ii) robust estimation of genetic exchange over a wide range of conditions; (iii) ability to incorporate information on population size; and (iv) explicit relationship to standard statistical tests. Utilization of this index in conjunction with other existing indices offers powerful insights into genetic processes. Our genetic theory is also extendible to the ecological community level, and thus can aid the comparison and integra- tion of diversity at the genetic and community levels, including the need for measures of community diversity that incorporate the genetic differentiation between species. Keywords: biodiversity, dispersal, population genetics, Shannon information, subdivision Received 8 February 2006; revision accepted 18 April 2006 Introduction There is enthusiasm for merging biodiversity databases over a range of levels: ecosystems, species, genes (Sugden & Pennisi 2000). There is also interest in explicitly comparing genetic and species diversity between areas (Vellend 2005). However, there has been little attention to providing common measures for biodiversity at different levels, thus risking comparisons of ‘apples with oranges’. Crist et al. (2003) said that ‘Despite a growing empirical interest in diversity partitioning, however, its use is still descriptive with little theoretical basis for interpreting the observed patterns of α and β diversity … or statistical methods for testing null hypotheses on observed diversity partitions.’ There have been a number of formulations of hierarchical biodiversity (Whittaker 1972), with various uses of the terms α, β and γ. It is now accepted that criteria for a good diversity measure include (i) additivity, so that the highest level γ is equal to the sum of diversity at local level, α, plus diversity between localities β; (ii) concavity, so that total diversity up to and including a particular level of organization is always greater or equal to diversity at the lower level, and thus α, β and γ are never negative; (iv) low bias, the systematic deviation between the estimate and the true value; (v) low imprecision, often expressed as the coefficient of variation of the estimate (CV); and (vi) low root mean square error (RMSE), a summary of the combined effects of bias and imprecision (Allen 1975; Routledge 1979; Lande 1996; Watve & Gangal 1996; Hubalek 2000; Lande et al. 2000; Crist et al. 2003). There has been less attention to the question ‘Does the index measure what we want to measure?’ In our opinion, this stems from the lack of biological basis to most of the measures — except in limited and extreme cases, we do not know what values we expect to see in a population or community with a particular history. We first discuss the statistical properties of some common indices, then summarize available theoretical expectations Correspondence: William B. Sherwin, Fax: 61 (0)2-9385-1558; E-mail: w.sherwin@unsw.edu.au