In the last few days two new papers were published which had EcoMinga staff as coauthors:

** Magnolia vargasiana (Magnoliaceae), a new Andean species, and a key to Ecuadorian species of subsection Talauma, with notes in its pollination biology** J. Antonio Vasquez-Garcia, David A. Neill, Mercedes Asanza & Luis Recalde

Luis Recalde, one of our reserve caretakers whose photographic work appears often on this blog, was coauthor of this paper. It describes one of two new species of *Magnolia* discovered recently in our Rio Zunac Reserve. These Magnolias open mainly at night, so buds need to be collected from high in the canopy during the day and brought to earth for observation. Luis risked his life multiple times to obtain flower buds from the canopy of this tree, free-climbing a thick aerial root of a hemi-epiphyte growing high in the tree’s crown. The effort exhausted him, the first time I’d ever seen him tired.

Luis’ salary is financed by the World Land Trust’s “Keepers of the Wild” program, thanks to a donation to the WLT from Puro Coffee. Thanks very much, WLT and Puro!!

**Expected Shannon Entropy and Shannon Differentiation between Subpopulations for Neutral Genes under the Finite Island Model** Anne Chao, Lou Jost, T. C. Hsieh, K. H. Ma, William B. Sherwin, Lee Ann Rollins

This paper derives some fundamental results on the relationship between Shannon entropy and evolution. Shannon entropy is an important theoretical quantity in many sciences, including physics and information theory. It can be partitioned into within- and between-group components, and these components can be used to contruct a measure of the degree of genetic differentiation between two or more subpopulations of a species. Unlike previously-used measures of genetic differentiation, this one has mathematical properties that make it always increase when a gene in one subpopulation mutates into a new gene. That is how speciation starts–two subpopulations that don’t mix very much will gradually accumulate new mutations and so become genetically distinct. Thus the entropy-based measure of differentiation can accurately describe the beginnings of the speciation process.

But we’d like not only to merely *describe* the degree of differentiation between subpopulations, but to know the *causal role *of the genetic and demographic factors (subpopulation size, number of subpopulations, migration rate between subpopulations, mutation rate, strength of natural selection ) that control the process. To figure that out, geneticists use a simple mathematical model of the subpopulations, ignoring natural selection for now. This model is called the “finite island model”. Subpopulations that obey this model always reach an equilibrium amount of genetic differentiation that is completely determined by the genetic and demographic parameters of the model. The challenge, then, is to figure out the formula for the equilibrium amount of differentiation in terms of the model parameters.

The first step is to figure out a formula for the entropy of a single population at equilibrium. Some progress had been made on that problem by William Sherwin and his colleagues, but the breakthrough came when Anne Chao discovered that the entropy at equilibrium was given by a very elegant mathematical function (called the digamma function) of a certain combination of the model parameters. From there it was possible to formulate the entropy of a subdivided population, and the entropy of the subpopulations. And from this we could derive the entropy-based measure of genetic differentiation in terms of the model parameters. The result showed that under a broad range of conditions, the main factor determining the amount of differentiation at equilibrium was the ratio of migration rate to mutation rate. Under other conditions, other factors also had important effects. This result can help us better understand the mechanisms of speciation.

The paper contains many other interesting results, including a novel test to check if a set of genes is being acted on by natural selection, and a novel connection between different mutation models. Interested readers can get the paper free on PLoS1. I’d like to thank my coauthors for a really wonderful and productive collaboration. I’d also like to thank Tom Leinster and the Centre de Recerca Matematica, Universitat Autonoma de Barcelona, Catalunya, for hosting Bill and I as visiting fellows for a month and for bringing Anne as well to the wworld’s first Mathematics of Biodiversity conference there.

Lou Jost

http://www.loujost.com