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Data S1 Comparison of analytic and simulation results for mean herbivore biomass under rotating protection.

Data S2 Comparison of static, rotational and subset MPA strategies under the assumption that herbivore biomass declines linearly on fished reefs.

Figure S1 Comparison of the equilibrium mean herbivore biomass of a rotational MPA system, calculated by; (a) a deterministic analytic solution (black line), and (b) stochastic simulation (coloured bars). Simulations were conducted for three different periods of rotation; monthly (red), annually (blue), and every 2 years (green). Dots indicate mean biomass across all reefs. Bars show the range of biomass values across all reefs. In all cases, herbivore populations on protected reefs are assumed to recovery linearly.

Figure S2 Comparison of the equilibrium mean herbivore biomass of a rotational MPA system, calculated by; (a) a deterministic analytic solution (black line), and (b) stochastic simulation (coloured bars). Simulations were conducted for three different periods of rotation; monthly (red), annually (blue), and every 2 years (green). Dots indicate mean biomass across all reefs. Bars show the range of biomass values across all reefs. In all cases, herbivore populations on protected reefs are assumed to recovery asymptotically.

Figure S3 Comparison of the equilibrium mean herbivore biomass of a rotational MPA system, calculated by; (a) a deterministic analytic solution (black line), and (b) stochastic simulation (coloured bars). Simulations were conducted for three different periods of rotation; monthly (red), annually (blue), and every 2 years (green). Dots indicate mean biomass across all reefs. Bars show the range of biomass values across all reefs. In all cases, herbivore populations on protected reefs are assumed to recovery logistically.

Figure S4 Comparison of the equilibrium mean herbivore biomass on the average reef under both static and rotational MPAs, with increasing levels of system protection. The black line represents static protection under all recovery models and the remaining lines represent rotational protection under different possible herbivore recovery models; logistic (red), asymptotic (blue) and linear (green) growth. The dotted red line indicates the hysteretic mean biomass under logistic recovery if the mean system biomass either begins or is allowed to decline too low.

Figure S5 Comparison of expected mean herbivore biomass across a system of 100 reefs, under three different protected area strategies: static MPAs (black line), MPAs rotated amongst all 100 reefs (blue line) and MPAs rotated amongst the optimal subset number (dashed grey line). All herbivore populations are assumed to recover asymptotically and decline linearly. The x-axis indicates the number of reefs able to be reserved.

Figure S6 Comparison of expected mean herbivore biomass across a system of 100 reefs, under three different protected area strategies: static MPAs (black line), MPAs rotated amongst all 100 reefs (red line) and MPAs rotated amongst the optimal subset number (dashed grey line). All herbivore populations are assumed to recover logistically and decline linearly. The x-axis indicates the number of reefs able to be reserved.

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