Hart: Yield and biomass-per-recruit analysis of rotational fisheries 



57 



Appendix 



Basic yield-per-recruit model 



This appendix describes the basic yield-per-recruit model 

 used for a cohort. In this model, recruits start at a specified 

 shell height (or length) /((,. The shell height is converted 

 into a starting age Oq by using a von Bertalanffy growth 

 equation. The shell height at time t is also obtained by 

 using the von Bertalanffy growth cui-ve. The shell height 

 is converted into a meat weight by using a shell-height/ 

 meat weight formula: 



w = exp(o -(- h ln(/?)), 



(7) 



where w and h are in units of grams and millimeters, 

 respectively. 



Natural mortality occurs at a rate M, assumed for these 

 simulations to be constant for all ages (M=0. 1 ). The fishing 

 mortality rate F(h} on a scallop of shell height /; is given 

 by Fih) = FffJ(h), where Fq is the fully recruited fishing 

 mortality rate and J(h> is the selectivity of the gear. J(h) 

 was taken to be if /; is less than a minimum shell height 

 ^min' 1 'f ' '^ greater than a fully recruited threshold size 

 hr^ii, and interpolated linearly as 



Jih)-. 



h-K 



H, 



full 



Aim 



(8) 



^f'min < '' < /'full- Individuals that are caught by the gear 

 but are smaller than a maximum cull size hj, are dis- 

 carded and are subject to a discard mortality d. In these 

 simulations, d is taken to be 0.2 (DuPaulM; however, the 

 results are not very sensitive to the exact value of this 

 parameter All individuals caught at a size greater than 

 hj are assumed to be landed and are included in the total 

 yield. F^(h) denotes the rate at which scallops of shell 

 height h are caught and retained (i.e. not discarded). 



The possibility has been raised that some scallops may 

 be killed but not captured by the gear (Caddy, 1973; My- 

 ers et al. 2000). Caddy (1973) estimated that 15-20% of 

 the scallops remaining on the bottom in the path of a 

 scallop dredge are killed but not captured by the dredge. 

 Murawski and Serchuk^ estimated that less than 59; of 

 the scallops remaining in the path of the dredge suffered 

 incidental (noncatch) mortality. In order to use the above 

 studies to estimate the relationship between incidental 

 fishing mortality F, and the fully recruited capture fish- 

 ing mortality rate F^^, it is necessary to know the efficiency 



'* DuPaul, W. D. 2000. Personal commun. Virginia Institute 

 of Marine Science, P.O. Box 1346, Gloucester Point, VA 23062- 

 1346. 



■• Murawski, S. A., and F. M. Serchuk. 1989. Environmental 

 effects of offshore dredge fisheries for bivalves. ICES CM. 

 1989/K:27. 



e of the dredge on a fully recruited individual. Denote by ; 

 the fraction of scallops that suffer mortality among those 

 that were in the path of the dredge but that were not 

 caught, so that / is estimated at 0.15-0.2 by Caddy (1973), 

 and less than 0.05 by Murawski and Serchuk.' The ratio 

 R of fully recruited scallops in the path of the dredge that 

 are caught to those killed but not caught is 



R = el\i(l-e)\. 



(9) 



If fully recruited scallops suffer capture fishing mortality 

 at rate F^, then the rate of incidental fishing mortality will 

 be 



F, = FJR 



F,J (l-e)/e. 



(10) 



If e is taken as 50% (estimated as the average scallop 

 dredge efficiency on Georges Bank^), then F, would be in the 

 range 0.15 F^ to 0.2 F,, according to Caddy (1973) and less 

 than 0.05 Fg according to Murawski and Serchuk. -^ To ascer- 

 tain the effects of incidental fishing mortality on the 5aeld- 

 per-recruit calculations, model runs were performed with no 

 incidental mortality, and also when F| = 0.15 F^; incidental 

 fishing morality was applied to all size groups. 



Let Z(h) be the total mortality rate at shell height /; (i.e. 

 the sum of natural mortality, and discard, indirect, and 

 landed fishing mortality). Then the fraction of recruits re- 

 maining t years after the beginning of the simulation is 



S(n = exp 



Z{T}dT 



(11) 



Total yield- and biomass-per-recruit are calculated by 

 the formulas: 



Y= [s(t)F^{h{t))w(h(t}}dt 

 B= [S(t)w{hit))dt, 



(12) 



(13) 



where a^ = the ending age of the simulation, taken to be 

 30 -^a^. 



For convenience in these simulations, a^ is taken to be 2 

 years; this age is assumed to correspond to a shell height 

 of precisely 40 mm. In the rotational simulations reported 

 in this study, the fully recruited landed fishing mortalities 

 Fjh> (h>hf^i^) are assumed to vary periodically and are 

 given in year k by F^^^, where > is the year that the cohort 

 reaches the starting age Oq. 



Rago, P. J. 2001. Personal commun. Northeast Fisheries 

 Science Center, 166 Water St., Woods Hole. MA 02543. 



