Population biology phenomena such as the spread of alleles in populations, the coexistence of competing species in an ecological community, the branching patterns in phylogenetic trees, and the dynamics of infectious disease are situated in different biology subdisciplines, e.g. demography, ecology, epidemiology, or evolution. However, these disparate phenomena are modeled using shared mathematical approaches. These approaches draw from diverse areas of mathematics, including stochastic processes, mathematical statistics, combinatorics, and dynamical systems. Across biological disciplines, population biologists share interests in the identification and analysis of equilibria, investigation of mechanistic dynamics, network-based methods and spatial modeling, modeling of stage transitions, biological optimality arguments, and the precise mathematical formulation and exploration of the consequences of verbal models. Some mathematical approaches are unique to population biology phenomena, e.g. the exponential amplification of initially rare beneficial variants such that the law of large numbers never applies poses a profound challenge, one which continues to call for new math in the area of stochastic processes.

 

This workshop aims to crystallize central ideas common across mathematical modeling and theory in population biology; to disseminate mathematical innovations from one biological subdiscipline to another; to promote mathematical studies at intersections among biological subdisciplines, and to deepen interactions among scientists working on similar problems but separated by disciplinary structures within biology, or between biology and the mathematical sciences. The goals are to build a community of theoretical population biologists that spans biological subdisciplines, invite new entrants to the field, encourage early-career scientists, showcase outstanding research, demonstrate impact in societally relevant problems, and uncover promising new directions where modeling and theory can make a difference in studying new types of biological data obtained at the level of populations.