Event Detail

Event Type: 
Applied Mathematics and Computation Seminar
Friday, June 4, 2010 - 05:00 to 06:00
Gilkey 113

When brush mice, fruit flies, and other animals disperse from their natal site, they are immediately tasked with selecting new habitat, and must do so in such a way as to optimize their chances of survival and breeding. Interestingly, observations indicate a strategy that occurs with a certain prescribed statistical regularity. It has been demonstrated (Stamps, Davis, Blozis, Boundy-Mills, Anim. Behav., 2007) that brush mice and fruit flies employ a refractory period: a period wherein a disperser, after leaving its natal site, will not accept highly-preferred natural habitats.

The Best Choice Problem (also known as the Secretary Problem) might provide a mathematical explanation for the existence of the refractory period. In the classical Best Choice problem, a selector must view the elements of a sequence one-by-one, seeing only their relative ranks, and choose the largest or ``best'' element. The selector cannot return to previously viewed elements, and must choose an element immediately after viewing it. The process ends when the selector selects an element or views the last one. The optimal strategy, to wait the number of turns equal to the next integer after n/e, and then pick the next element that is (relatively) the best, might demonstrate why such refractory periods have adaptive benefit. Our preliminary research has identified extensions to the Best Choice Problem that may better account for ecological aspects of habitat selection; we formalize an extension that allows equivalence and incomparability of sites, as well as an extension where the goal is to select one of the $r^{th}$ best sites, instead of the best. In each extension we determine the role played by the refractory period.