Fig. 4: Relation between maximum 2-link loop weight \({w}_{max}^{(2)}\) and critical level of self-regulation s* in empirical systems. | Communications Biology

Fig. 4: Relation between maximum 2-link loop weight \({w}_{max}^{(2)}\) and critical level of self-regulation s* in empirical systems.

From: Competitive hierarchies in bryozoan assemblages mitigate network instability by keeping short and long feedback loops weak

Fig. 4

The critical level of self-regulation s* represents the factor by which observed intraspecific interaction strength has to be multiplied to obtain stability; s* > 1 means that a system is unstable, and s* = 1 represents the threshold between stability and instability. The maximum weight of 2-link loops is denoted as w(2)max, where \({w}^{2}=\sqrt{\frac{{a}_{{ij}}{a}_{{ji}}}{\left|{a}_{{ii}}{a}_{{jj}}\right|}}\). Regression analysis: n = 30 bryozoan assemblages, R2 = 0.95, y = −0.11 + 1.13x, p < 0.001.

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