2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/212275We show that renormalized two-dimensional Lotka--Volterra models near criticality converge to a super-Brownian motion. This is used to establish long-term survival of a rare type for a range of parameter values near the voter model.Published in at http://dx.doi.org/10.1214/07-AAP453 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)Probability60K35, 60G57 (Primary) 60F17, 60J80 (Secondary)text