Eigenvalue estimations for the system with four species on 15 patches. We consider loss of stability as a result of the change of two different parameters, governing the nonlinearity of primary production, ϕ (a,c) and the nonlinearity of the functional response of attack rate to prey density, γ (b,d). The leading eigenvalue of the Jacobian was reconstructed from time series for fixed parameters (a,b) and parameter transects (c,d). The steady state under consideration is unstable subsequent to a Hopf bifurcation (region shaded grey). For the transects estimates are shown in the centre of the sampling window (window width is indicated by blue area). See electronic supplementary material for parameters and details.(Online version in colour.)