Abstract
One of the main challenges in ecology is to determine the cause of population fluctuations. Both theoretical and empirical studies suggest that delayed density dependence instigates cyclic behavior in many populations; however, underlying mechanisms through which this occurs are often difficult to determine and may vary within species. In this paper, we consider single species population dynamics affected by the Allee effect coupled with discrete time delay. We use two different mathematical formulations of the Allee effect and analyze (both analytically and numerically) the role of time delay in different feedback mechanisms such as competition and cooperation. The bifurcation value of the delay (that results in the Hopf bifurcation) as a function of the strength of the Allee effect is obtained analytically. Interestingly, depending on the chosen delayed mechanism, even a large time delay may not necessarily lead to instability. We also show that, in case the time delay affects positive feedback (such as cooperation), the population dynamics can lead to self-organized formation of intermediate quasi-stationary states. Finally, we discuss ecological implications of our findings.
Highlights
The classical theory of population dynamics predicts that the smaller the population, the less individuals will suffer from constraints of intraspecific competition
This paper aims to address the interplay between time delays and the Allee effect
Using the single-species context, we study two different models of population dynamics where the effects of competition and cooperation are taken into account in either a multiplicative or additive way
Summary
The classical theory of population dynamics predicts that the smaller the population (or the lower its density), the less individuals will suffer from constraints of intraspecific competition. A less appreciated and frequently overlooked mechanism through which Allee effects emerge are predator-prey interactions It has been shown, that size-selective predation on prey regulated through density-dependence leads to a positive relationship between predator density and population growth, through intraspecific competition in the prey population (De Roos and Persson 2002, De Roos et al 2003, van Kooten et al 2005 ). That size-selective predation on prey regulated through density-dependence leads to a positive relationship between predator density and population growth, through intraspecific competition in the prey population (De Roos and Persson 2002, De Roos et al 2003, van Kooten et al 2005 ) Such an Allee effect is known as “emergent”, as it results from the predator induced changes in prey size distribution and is essentially a consequence of the feedback of predator feeding on its own performance.
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