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Appendix 



Fecundities 



Fecundities were size-specific, but the general form 

 of the equation relating size to fecundity varied from 

 species to species. The specific relationships are listed 

 in Table 1 as /•. These r values were set to zero for all 

 classes smaller than the size at maturity. 



Larval survival 



We used equations developed by Houde ( 1989) that 

 relate ambient temperature during development to 

 duration of larval stage, daily mortality risk, and prob- 

 ability of surviving through the entire larval stage. 



D = 952.5 7^ 



1 .07.52 



Z = 0.0003149 7 



(11 

 (2) 

 (3) 



where T = ambient temperature during develop- 

 ment, in degj-ees Celsius; 

 D = duration of larval stage, in days; 

 Z = probability of mortality, per day; and 

 A'^ = probability of surviving through the en- 

 tire larval stage. 



Adult survival 



We assumed that newly settled fish experienced den- 

 sity dependence. Thus, instead of surviving at a rate 

 L'j like individuals in other size classes, their survival 

 was weighted by a density-dependent function of the 

 form e '' '^ where p = the population density and K = 

 a measure of carrying capacity arbitrarily set at 1000 

 due to a lack of information on carrying capacities 

 for the fish we studied. Note that size-class- 1 indi- 

 viduals included new recruits that survived and grew 

 as well as old size-class-1 individuals that survived 

 but did not grow to size class 2. Thus, at time t, the 

 densities of size-class-1 individuals in the reserve 

 iSj ^) and the fishing area (F^ ^) are 



Si, = V(,piO}Sof_-^e~^ 

 F,j=VopiO}Foj_,e~ 



+ ri(l-p(l))Si,,_i (4) 



,/A- 



+ v,(l- 



P<1>)^1,M. (5) 



where v = the density-independent survival rate for 

 individuals in size class .v. 



Note that the density in the fishing area is de- 

 creased later in the program to account for fishing 

 mortality but only for size classes larger than the size 

 at fisheiy recioiitment. Also note that other size classes 

 experience the density-independent survival rate v^. 



Growth 



We began with standard von Bertalanffy equations 

 (Ricker, 1975 1, relating length to age and weight to 

 length (Fig. 2) and categorized them as described by 

 Figure 2. Through algebraic manipulation, we estab- 

 lished a formula for g(B^J, the size of an individual 

 projected one year in the future: 



^(Bj^e-^'S +(l-e-''')L,„^- 



(6) 



We used this formula to establish the following cal- 

 culation forp(.x'), the probability that an individual 

 in size class x grows to size class x+l by next year. 



pix) 



S. 





B 



ill. (7) 



