Using a signature function to determine resonant and attenuant 2-cycles in the Smith–Slatkin population model

John E. Franke, Abdul-Aziz Yakubu
2007 Journal of difference equations and applications (Print)  
We study the responses of discretely reproducing populations to periodic fluctuations in three parameters: the carrying capacity and two demographic characteristics of the species. We prove that small 2-periodic fluctuations of the three parameters generate 2-cyclic oscillations of the population. We develop a signature function for predicting the responses of populations to 2-periodic fluctuations. Our signature function is the sign of a weighted sum of the relative strengths of the
more » ... s of the three parameters. Periodic environments are deleterious for populations when the signature function is negative, while positive signature functions signal favorable environments. We compute the signature function for the Smith-Slatkin model, and use it to determine regions in parameter space that are either favorable or detrimental to the species.
doi:10.1080/10236190601078987 fatcat:nnfcwi5mdvgsrah5wymoctw6hu