Ecological Modelling 222 (2011) 2891–2896 Contents lists available at ScienceDirect Ecological Modelling jo ur n al homep ag e: www.elsevier.com/locate/ecolmodel Dispersal vs. stochasticity: Competition for persistence in a reaction-diffusion model with strong Allee dynamics M.A. Budroni a,b , F. Rossi a,b , E. Farris c , R. Filigheddu c , M. Rustici d,∗ a Dipartimento di Chimica, Università di Siena, Via della Diana 2a, Siena 53100, Italy b Polo Universitario di Colle Val d’Elsa, Via Matteotti 15, Colle Val d’Elsa (SI), Italy c Dipartimento di Scienze Botaniche, Ecologiche e Geologiche, Università di Sassari, Via Piandanna 4, Sassari 07100, Italy d Dipartimento di Chimica, Università di Sassari, Via Vienna 2, Sassari 07100, Italy a r t i c l e i n f o Article history: Available online 24 June 2011 Keywords: Allee effect Population dynamics Pseudo-stochastic reaction-diffusion processes Mediterranean plants a b s t r a c t In ecological and population dynamics, the coupling between random perturbations and the Allee effect could drive small and confined populations of rare species to extinction. In this paper, we propose a general model for describing spatio-temporal dynamics characterized by demographic Allee growth. In this approach, we include the combined contribution of stochasticity and spatial processes, typically dispersal, which is scarcely explored in the literature. The model is formulated in a reaction-diffusion framework, where the dynamics is regulated by a typical Allee–dispersal evolution and the resilience to white noise is probed at different perturbation amplitudes. Preliminary results show that dispersal processes can compensate random fluctuations to favor the stabilization of the species establishment. © 2011 Elsevier B.V. All rights reserved. 1. Introduction The long-term survival of small populations of plants can be challenged by a positive correlation between population density and individual fitness. This is one of the possible scenarios for populations influenced by the Allee effect (Allee et al., 1949). In contrast with a pure logistic or multhusian per capita growth curves, the Allee dynamics presents a maximal intrinsic growth rate at intermediate population density. This phenomenon is asso- ciated with a multitude of mechanisms, including failure to locate mates, inbreeding depression, failure to satiate predators, and lack of co-operative feeding. From a mathematical point of view, the density-dependent form of the demographic per capita Allee growth directly derives from the general polynomial formulation f (u) = ∑ ∞ n=0 a n u n , and is given by f (u) = a 1 + a 2 u + a 3 u 2 (1) where a 2 > 0 and a 3 < 0. The Allee growth curve increases at small density (depensation) and, in case of strong Allee dynamics, it is characterized by a negative growth rate (critical depensation) at low population values which determines a threshold population density for the persistence of the species (see Fig. 1). Any fluctu- ation which forces the population to be lower than this critical level, leads the species to extinction (Brauer and Castillo-Chavez, ∗ Corresponding author. E-mail address: rustici@uniss.it (M. Rustici). 2001). Density-dependent processes in plant populations have been demonstrated at multiple scales (Gunton and Kunin, 2009) and considering the Allee effect has been useful for understand- ing both widespread, invasive species (Garrett and Bowden, 2002; Davis et al., 2004; McCormick et al., 2010) and rare, narrow-spread species dynamics (Le Cadre et al., 2008). Furthermore, an Allee effect based approach is helpful when dealing with biodiversity conservation problems related to human induced fragmentation (Colas et al., 2001; Forsyth, 2003; Cheptou and Avendano, 2006; Wagenius et al., 2007; Chen and Lin, 2008; Chen and Hui, 2009). Interesting study cases of the potential Allee effect in small pop- ulations are offered by Mediterranean plants, in particular in biogeographic islands (Gentile and Argano, 2005; Whittaker and Fernández-Palacios, 2007; Brooke, 2010). Here the past geologi- cal history (Dercourt et al., 1986; Gueguen et al., 1998; Krijgsman, 2002) has conditioned the distribution of many plant species, that are rare and confined to narrow ranges, often with scattered, isolated, and small populations (Thompson, 2005). It has been demonstrated that plants confined to narrow ranges are less com- petitive than congeneric, widespread species, and are limited to harsh environments (Lavergne et al., 2004), that are poorly acces- sible, stable and conservative, with minimal disturbance and a high availability of micro-sites (Larson et al., 2000). Within suit- able patches, plants confined to narrow ranges show often a life strategy based more on local persistence than colonization abil- ity (Thompson, 2005). Recently, particular attention has been paid on the density evolution of plant population patches in space and time (García, 2003, 2008; García et al., 2010). Species that occupy small areas are particularly abundant in some Mediterranean plant 0304-3800/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.ecolmodel.2011.05.015