Skip to main content
Article thumbnail
Location of Repository




Noninvadability implies noncoexistence for a class of cancellative systems ∗ Jan M. Swart † There exist a number of results proving that for certain classes of interacting particle systems in population genetics, mutual invadability of types implies coexistence. In this paper we prove a sort of converse statement for a class of one-dimensional cancellative systems that are used to model balancing selection. We say that a model exhibits strong interface tightness if started from a configuration where to the left of the origin all sites are of one type and to the right of the origin all sites are of the other type, the configuration as seen from the interface has an invariant law in which the number of sites where both types meet has finite expectation. We prove that this implies noncoexistence, i.e., all invariant laws of the process are concentrated on the constant configurations. The proof is based on special relations between dual and interface models that hold for a large class of one-dimensional cancellative systems and that are proved here for the first time

Topics: , parity preservation
Year: 2013
OAI identifier: oai:CiteSeerX.psu:
Provided by: CiteSeerX
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • (external link)
  • (external link)
  • Suggested articles

    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.