I began research into pair approximation as a new graduate student at the University of Maine under the direction of David Hiebeler.  Pair approximation is a method for deriving ordinary differential equations that describe stochastic, lattice-based dynamics by allowing the considering both the frequency of “individuals” as well as the frequency of pairs of “individuals”. It follows naturally from considering birth processes (like the spread of plants and animals). It is well understood that the clustering of habitat affects the persistence of such species (fragmented landscapes have a deleterious effect on persistence).  There are not satisfactory ways to model this using the mean field approximation (typical differential equations assume this and it is synonymous with the well mixing assumption).  However, pair approximation is a way to capture “cellular” interactions (those between individuals in a discrete sense) using differential equations.

I swear I usually do a better job explaining this.

*: Denotes an undergraduate researcher

• Buhr M*, Garcia O*, Reyes T*, Sumdani H*, Barley K, Smith A, Morin B, Mubayi A. Dynamics of Glial Cell Defense Mechanisms in Response to Ischemic Hypoxia in the Brain. MTBI Technical Reports, 2014. (link)
• Larios-Ferrer JL*, Peterson J*, Vargas A*, Arriola L, Golinski M, Morin B. A New Perspective on Modeling Forest Fires. MTBI Technical Reports, 2010. (link)
• Merckens J*, van de Geijn B*, Hociota I*, Tadaya D*, Morin B. The Dynamics of a Spatial Cyclic Competition System. MTBI Technical Reports, 2009. (link)
• Hiebeler DE, Morin BR. The effect of static and dynamic spatially structured disturbances on a locally dispersing population. Journal of theoretical biology. 2007 May 7;246(1):136-44. (link)
• Ayala-Valenzuela MA*, Pawling CL*, Smith AN*, Gao L, Hiebeler D, Morin BR. An Epidemiological Approach to the Dynamics of Chytridiomycosis on a Harlequin Frog Population. MTBI Technical Reports, 2006. (link)