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. 2017 Apr 28;12(4):e0176163. doi: 10.1371/journal.pone.0176163

Fig 5. Eco-social Model 4 for Management and Exploitation Areas for Benthic Resources (MAEBRs), Open Access Areas (OAAs), and sustainable scenario (SS).

Fig 5

D = demand, F = fishers, X = macroalgae, Y = herbivores, Z = carnivores, and p(λ) = characteristic polynomial. The community (Jacob-Levins) matrix with the semi-quantitative effect of j variable to i variable and the Hessian matrix are shown. The local stability measures of Routh-Hurwitz and Levins (Fn) criteria for MEABRs, OAAs and sustainable scenarios are also summarized. First criterion (1°C) describes stability condition of the system, the second criterion (2°C) determine asymptotic or oscillation condition. The Fn is defined by holistic sustainability [25].The assumptions included were changes in the self-dynamic (damped ‘-‘ [small circle] and/or enhanced ‘+’ [small arrow]) for fishers, macroalgae, herbivores and carnivores.