## Info

Note that we have already learned something valuable about the system: I — u(1 - a) is an invariant for the marine reserve in the sense that the steady state takes the same value, regardless of individual values of u and a as long as the product remains the same. Thus for example, if we have a large reserve (making a big) then we can allow a high fraction of take in the harvest zone and vice versa (i.e. a higher fraction of a smaller available population in the fishing region). This observation, also noted by Hastings and Botsford (1999), suggests that there is an equivalence between protecting area and reducing catch.

One objective for the design of a reserve could be that the steady state given by Eq. (6.32) is a fixed fraction f of the carrying capacity. The value of that fraction is not something that can be set by quantitative analysis; it is a policy decision. For example, for a relic population f = 0.1 (or even 0.05 - definition of relic is an open topic); we might want to ensure that the population is at worst depleted and setf = 0.35 or we might want to ensure that the population is in its optimal sustainable range and setf= 0.6. If we set N = fK and solve the resulting equation for f, we obtain

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