Article Biomath Communications 1 (2014) Biomath Communications www.biomathforum.org/biomath/index.php/conference Allee Effects in Population Dynamics 1 ¨ Unal Ufuktepe Izmir University of Economics, Department of Mathematics unal.ufuktepe@ieu.edu.tr Keywords: Population biology, Predator-prey, Beddington. Introduction. The Allee effect is a phenomenon in biology charac- terized by a positive correlation between population density (size) and its per capita growth rate [1]. In their book, Courchamp et al [3], the au- thors described the Allee effect in a straightforward manner: “The more the merrier”. This effect is simply a casual positive relationship between the number of individuals in a population and their “overall individual fit- ness.” The more individuals there are, up to a point, the better they fare. So as population size approaches a threshold, favorable influences stimu- late its growth, and when it goes below it, unfavorable influences inhibit its growth. From their point of view, the Allee effect may be described as a notion of positive density dependence in which the “overall individual fitness”, or one of its components, is positively related to population size or density [3]. However, Lidicker [8] recently proposed that Allee effect may be described and defined in terms of demographic processes. He explained that “Allee effects are expressed at the population level of organization, and the parameters of interest are the population proponents of growth rates, recruitment rates, loss rates, equilibrium densities, and perhaps, success in establishing new populations.” Some authors make a distinction between strong Allee effect and weak Allee effect: a strong Allee effect refers to a population that exhibits a “critical size or density” below which population declines to extinction and above which it survives; while a weak Allee effect refers to a population that lacks a “critical density”, but where, at lower densities, the population growth rate rises with increasing densities (Stephens et al [11], Lidicker [8]) Stephens et al [11] made the distinction between the component Allee effect, of particular interest to behaviorists, and the demographic Allee ef- fect, of overriding concern to conservationists. From these authors’ point of view, the benefits of conspecific presence may include one or more preda- tor dilution or saturation; antipredator vigilance or aggression; cooperative 1 An invited talk given during BIOMATH 2014. Citation: Ufuktepe, ¨ U.: Allee Effects in Population Dynamics. Biomath Communica- tions 1/1 (2014), 12–19. http://dx.doi.org/10.11145/j.bmc.2014.08.012 12