Fig. 4: R–N stability response to increasing interaction strength.

Time series showing R density following a perturbation that lowered R density to 50% of equilibrium density for a low (\({a}_{{RN}}=0.8\)), b intermediate (\({a}_{{RN}}=1\)), and c high maximum rate of nutrient uptake (\({a}_{{RN}}=2.8\)). d Local stability (dominant eigenvalue; \({\lambda }_{{\max }}\)) of the R–N subsystem as \({a}_{{RN}}\) is increased for \({l}_{N} \, > \, {l}_{R}\), \({l}_{N}={l}_{R}\), and \({l}_{N} < {l}_{R}\), where \({l}_{R}\) and \({l}_{N}\) are the rate at which nutrients are lost to the external environment from compartment R and N, respectively. Solid lines are real parts and dashed lines are complex parts of \({\lambda }_{{\max }}\).