Sladek Nowlls and Roberts: Fisheries benefits and optimal design of marine reserves 



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lOO'y^ growth for new settlers to O'vf for fish in 

 the largest size class. 



Adults in the fishing area that grew larger than 

 the minimum catch size experienced fishing mor- 

 tality. We represented fishing mortality using the 

 parameter u, equal to the proportion of fishery- 

 recruited individuals caught per year, and related 

 to the more common F by the equation: 



1 



We independently varied the two key parameters 

 in our models: fishing mortality (;/) and reserve 

 proportion (s). 



We made settlement a density-dependent pro- 

 cess by incorporating a negative exponential 

 function into survivorship for new settlers dur- 

 ing their first year (see Appendix for equation). 

 There is evidence to suggest that shelter is lim- 

 iting for coral reef fish, especially new settlers 

 (Hixon, 1991; Hixon and Beets, 1993; Hixon and 

 Carr, 1997) — a process that would fit well with 

 our density dependence assumptions. We also 

 performed runs in which larval rather than new 

 settler survivorship was density-dependent and 



range of sizes 

 next year 



g(B2) g(B3) 

 1 



—r 





l-inf 



67% of 



range so 



p(2) = 0.67 



Figure 2 



Determination of growth probabilities. The probability pf.ri that 

 a fish of size class x grows to size class .v+1 is the proportion of 

 the range of sizes that size class .r individuals will span one 

 year later. Using von Bertalanffy growth parameters (see Ap- 

 pendix), we determined one year in the future the size of the 

 smallest and largest fish in size class .v. All other fish in x would 

 fall between these two values. We then determined what pro- 

 portion of these sizes fell into size class .r-t-l. 0.67 in the case 

 illustrated. In this hypothetical example, we would assume that 

 p(x) = 0.67, or that GT'i of the fish from size class x grew to 

 class .v-t-l by the next year L, represents the sizes attained at 

 age t and B represents the lower bounds of each size class. We 

 begin counting age at the moment of settlement (so Lg = Bq). 



