Supplement 1. Mathematica code to calculate the overcompensation and consumer–resource stability boundaries of the semi-discrete model.

File List StabilityAnalysisSemi-DiscreteLogistic.nb - Mathematica code <br> StabilityAnalysisSemi-DiscreteLogistic.pdf - PDF of the code Description Mathematica (version 5) code to calculate the overcompensation and consumer-resource stability boundaries of the semi-discrete model as a function of mu and alpha, for different values of rho. The analysis is decsribed in Appendix A. The code calculates the stability boundaries in sections.<br> data1 - bottom part of the consumer-resource boundary (heavy solid line in Fig. 2a of the main text);<br> data2 - top part of the consumer-resource boundary (dotted line in Fig. 2a);<br> data3 - top of the left arm of the overcompensation boundary (dashed line in Fig. 2a) until it crosses the consumer-resource boundary;<br> data4 - bottom of the left arm of the overcompensation boundary (dashed line in Fig. 2a) until the minimum of the boundary;<br> data5 - right arm of the overcompensation boundary (dashed line in Fig. 2a). Some parameter definitions:<br> J11, J12, J21, J22 - elements of the Jacobian from the linear stability analysis of the model.<br> Cond1 - condition for existence of a positive equilibrium;<br> Cond2 - transition from stability to overcompensation cycles;<br> Cond3 - transition from stability to consumer - resource cycles;<br> Period - period of population cycles on the consumer - resource stability boundary (for a discussion of caclulating boundary conditions and the period see Gurney, W. S. C., and R. M. Nisbet. 1998. Ecological Dynamics. Oxford University Press, New York, New York, USA)