APPENDIX A— A PROCESS FOR ADJUSTING EGG-TO- 

 PRESMOLT SURVIVAL WHEN HATCHERY FISH ARE 

 INTRODUCED 



I. Definitions pi = probability of survival of naturally produced eggs with no additional 



hatchery fish 



p2 = pi adjusted for presence of hatchery fish 



p3 = p2 adjusted for time period 



N(£) = natural fry alive at time t 



H(£) = hatchery fry alive at time t 



ul = instantaneous mortality rate 



u2 = adjusted mortality rate 



E( • ) = denotes expectation 



Binomial{N,p} = function call that generates a random number from 

 a binomial distribution. 



Beta{p,cv} = function that generates a random number from a beta 

 distribution 



f[x] = function call to density-dependent relationship that defines p 

 as a function of x 



All other definitions are as defined within the text. 



II. Calculations Calculations take place in sequence 



1. ul = -log(pl)/100 



2. N(reltime) = Binomial{EGGS,exp(-ul*reZ£irae) 



3. H(reltime) = Bmomial{hatfry,hintsv 



4. E(p2) = f{EGGS+H(reltime)} 



5. u2 = -log(p2)/100 



6. E(p3) = exp(-u2*(100-reZ^'me)) 



7. p3 = Beta{E(p3),ci;e£si;} 



8. PRESMOLT = Binomial{N(reZ^'me)+H(reZ^me),p3} 



25 



