In this paper we study a model of the competition of annual and perennial plants proposed by Crawley and May. Specifically, we calculate the asymptotic behavior of the critical value for coexistence in the biologically reasonable limit in which annual seeds are dispersed over a large number of sites. Our results are related to earlier work of Durrett and Swindle and prove a conjecture made in that paper.
"Asymptotic Critical Value for a Competition Model." Ann. Appl. Probab. 3 (4) 1047 - 1066, November, 1993. https://doi.org/10.1214/aoap/1177005272