From Bacteria to Black-Scholes: testing the neutrality of competition with time-series data
Event Description:
First Colloquium Fall 2015
Thursday 8/27/2015 at 3:30pm in SMLC 356
Speaker: Alex Washburne (Duke University)
Title: From Bacteria to Black-Scholes: testing the neutrality of competition with time-series data
Abstract:
Competition is a ubiquitous process. Trees compete for space, companies compete over capital, and both genes and cultural memes compete for places in the population of humans. Competition can lead to exclusion/extinction of and tradeoffs between competing groups, thus understanding the stochastic time-evolution of competitive systems is important for reserve design and management of multi-species communities, investment portfolio design, and egalitarian governance of multicultural societies and institutions.
An urn process constructed in biology’s Neutral Theory and its Ito-process analog, the Wright-Fisher Process (WFP), have been proposed as null models of competition among equal competitors. Rejecting such neutral models in a competitive system helps us understand the non-neutral forces governing the system. Current tests of neutral competition vs. other models have performed comparative tests on stationary rank-abundance distributions (or the analogous capital distribution curves in finance), but much more information is contained in time-series data, and more powerful and insightful tests can be constructed using the WFP as a null model for time-series data.
In this talk, I will discuss the relation between Neutral Theory and the WFP, show how to test the quadratic covariation between neutral competitors through constant-volatility transformations of the WFP, and demonstrate how to apply this test and other tools I have developed to understand the non-neutrality of community dynamics in the human microbiome and the S&P 500.
About the speaker:
Alex Washburne got his PhD in Ecology and Evolutionary Biology from Princeton University in Spring 2015, under the direction of Prof. Simon Levin. Alex is posed to join Duke University as a postdoc in Fall 2015. Alex received his BS in Mathematics and Biology from UNM in 2010, while at UNM he worked with Helen Wearing on his Honor's Thesis, and was an MCTP participant in various roles: Summer camp participant, REU participant, and a TA for the next Summer camp.
