Goodness of fit to a mathematical model for Drosophila sleep behavior is reduced in hyposomnolent mutants

The conserved nature of sleep in Drosophila has allowed the fruit fly to emerge in the last decade as a powerful model organism in which to study sleep. Recent sleep studies in Drosophila have focused on the discovery and characterization of hyposomnolent mutants. One common feature of these animals is a change in sleep architecture: sleep bout count tends to be greater, and sleep bout length lower, in hyposomnolent mutants. I propose a mathematical model, produced by least-squares nonlinear regression to fit the form Y = aX(∧)b, which can explain sleep behavior in the healthy animal as well as previously-reported changes in total sleep and sleep architecture in hyposomnolent mutants. This model, fit to sleep data, yields coefficient of determination R squared, which describes goodness of fit. R squared is lower, as compared to control, in hyposomnolent mutants insomniac and fumin. My findings raise the possibility that low R squared is a feature of all hyposomnolent mutants, not just insomniac and fumin. If this were the case, R squared could emerge as a novel means by which sleep researchers might assess sleep dysfunction.