Predicting Shannon’s information for genes in finite populations: new uses for old equations
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This study provides predictive equations for Shannon’s information in a finite population, which are intuitive and simple enough to see wide scale use in molecular ecology and population genetics. A comprehensive profile of genetic diversity contains three complementary components: numbers of allelic types, Shannon’s information and heterozygosity. Currently heterozygosity has greater resources than Shannon’s information, such as more predictive models and integration into more mainstream genetics software. However, Shannon’s information has several advantages over heterozygosity as a measure of genetic diversity, so it is important to develop Shannon’s information as a new tool for molecular ecology. Past efforts at making forecasts for Shannon’s information in specific molecular ecology scenarios mostly dealt with expectations for Shannon’s information at genetic equilibrium, but dynamic forecasts are also vital. In particular, we must be able to predict loss of genetic diversity when dealing with finite populations, because they risk losing genetic variability, which can have an adverse effect on their survival. We present equations for predicting loss of genetic diversity measured by Shannon’s information. We also provide statistical justification for these models by assessing their fit to data derived from simulations and managed, replicated laboratory populations. The predictive models will enhance the usefulness of Shannon’s information as a measure of genetic diversity; they will also be useful in pest control and conservation.
KeywordsConservation genetics Population genetics Isolated populations Small populations Entropy Simulations
I would like to thank Zlatko Jovanoski, Mark Tanaka and Russell Bonduriansky for providing helpful criticism and comments throughout the duration of writing this paper. Flydata were obtained from a previous study that was funded by the Australian Research Council Discovery Grant A10007270 to Sherwin, Oakeshott, Barker and Frankham. Jyoutsna Gupta participated significantly in the experiments that lead to Flydata.
GDO did the simulation design, programming and analysis. WBS conceived and supervised the project. FJ developed Jabot’s equation (in the Supplement S5.1) and all theoretical backing for its use. MRG conducted the study that produced the ‘Flydata’.
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