54 



Fishery Bulletin 101(1) 



Donald and Thompson, 1986). If this is the case, optimal 

 rotational periods would be shorter than calculated here, 

 although the jdeld-per-recruit formalism would remain 

 valid. More serious problems would be caused if there is 

 density-dependent mortality of adults or if high adult den- 

 sities inhibited recruitment because rotational closures 

 can induce higher densities than would constant fishing. 

 If either of these processes occur, shorter rotation periods 

 would be advisable to minimize this problem. For sea scal- 

 lops, however, observations of areas that have been closed 

 to fishing for a number of years give no indication that 

 such density-dependent processes are occurring (Fig. 2b in 

 Hart 2001, and Table B5-8 in NEFSC^). 



An extreme case of rotational fishing is true pulse 

 fishing, where all exploitable individuals are removed at 

 periodic intervals (see e.g. Sluczanowski, 1984). Thus, true 

 pulse fishing corresponds to pulse rotation (as defined 

 in the present study) with an infinite fishing mortality. 

 Such pulse fishing is not optimal for sea scallops, as can 

 be seen by the slight decline of yield-per-recruit at high 

 fishing mortalities in Figure 1 because at very high fish- 

 ing mortalities, the partial selectivity of the gear loses its 

 effectiveness and all individuals that are even slightly 

 selected to the gear (i.e. that are even slightly greater 

 than /in,,,,) will be removed. To put it another way, at high 

 fishing mortality rates, the additional (i.e. marginal) catch 

 obtained from a further increase in F will disproportion- 

 ately consist of small animals, thereby reducing yield- 

 per-recruit. Pulse fishing would be optimal if knife-edge 

 selectivity is assumed. For this reason, the assumption of 

 knife-edge selectivity would lead to unrealistic results for 

 cases such as sea scallops, where gear selectivity increases 

 more gradually with size. Proper application of rotational 

 theory therefore requires a careful examination of fishing 

 selectivity with size. 



Pulse fishing can be related to the classic Faustmann 

 theory of forest rotation (see e.g. Reed, 1986; Clark, 1990). 

 In this theory, if a stand of trees in an area that has last 

 been harvested t years previously has value Vit), then the 

 optimal time to harvest the trees satisfies 



V'(t) = 8(V(t)-c) + 5 



V{t)- 



exp(&)- 1 



(6) 



where 5 

 c 



the discount rate; and 

 the cost of harvesting. 



In the case of a fishery, Vit) would represent the expected 

 value of the exploitable stock (e.g. those of shell height 

 greater than /!„„„) at time t. (Note that in this context, 

 unlike the original forest application, it is not necessary to 

 assume that all exploitable individuals arc the same age.) 

 In the case of scallops, assuming all scallops command the 

 same price per unit weight, c = 0, and 5 = 0.1, this formula 

 would give an optimal rotation period of about 6.1 years 

 (the optimal period would be moderately longer for realis- 

 tic positive values of c). This value corresponds well to the 

 rotation time of 6 years that optimizes discounted yield- 

 per-recruit (see Fig. 2). However, the yield-per-recruit for 



6-yr pulse fishing, V(6), is less than 80% of the maximal 

 yield-per-recruit obtained by fishing uniformly. Again, the 

 reduced yield-per-recruit is due to the fact that pulse fish- 

 ing induces knife-edge selectivity at h^^^. rather than the 

 usual gradual increase in vulnerability to the gear 



Symmetric rotational strategies appear to give less 

 benefit than does pulse rotation. However, optimal pulse 

 rotation would require high, and possibly impractical, lev- 

 els of effort in an area when it is opened (e.g. F of about 

 1.7 for a 6-yr pulse rotation). In addition, such a strategy 

 would require that areas be closed most of the time, pos- 

 sibly inducing social-economic disruptions by closing 

 traditional fishing grounds for long periods. Compared to 

 pulse rotation, symmetric rotation requires less concen- 

 trated effort, allows areas to be open half the time, and 

 is less sensitive to the assumption of constant natural 

 mortality. One possible compromise between pulse and 

 symmetric rotation is to close an area for half the time 

 and then gradually increase effort during the opening. 

 For example, an area might be closed for three years and 

 then fished for the next three years at Ffj^^, 2Fjj^^, and 

 ■^^MAX- respectively. 



(Questions have been raised regarding the appropriate- 

 ness of the use of whole-stock fishing mortalities as tar- 

 gets or reference points for fisheries of sedentary stocks 

 that include rotational or long-term closures (or both) 

 (NEFSC-). The solid line in Figure 9 gives the whole stock 

 (biomass-weighted) fishing mortality (assuming constant 

 recruitment everywhere) for a pulse rotational system 

 consisting of six areas, one of which is fished each year 

 in turn. This whole-stock fishing mortality was obtained 

 by simply dividing the yield-per-recruit for a 6-yr pulse 

 rotation by the corresponding biomass-per-recruit. The x 

 axis is F^vG' which should be proportional to true effort. As 

 can be seen, whole-stock fishing mortality is proportional 

 to effort for low fishing mortalities, but then flattens to a 

 maximum of just under 0.4. 



A similar situation can happen even if an area is fished 

 uniformly, except that a portion of the area is set aside as 

 an indefinite closure. The dashed line in Figure 9 gives an 

 example for the case when lO"^'; of the area is permanently 

 closed and is allowed to equilibrate to the biomass-per-re- 

 cruit corresponding to zero fishing mortality Whole-stock 

 fishing mortality shows a relationship to the actual fishing 

 effort (the fishing effort in the open area only) in the open 

 areas that is similar to that of rotational fishing. In both 

 cases, closed area biomass dominates the whole-stock fish- 

 ing mortality calculation at high fishing effort. The yield 

 at high fishing effort is essentially derived from incoming 

 recruitment, which is not sensitive to fishing effort for 

 very high effort levels. Therefore, the whole-stock fishing 

 mortality becomes nearly constant when effort is high. 



^ NEFSC (Northeast Fisheries Science Center). 1999. Report 

 of the 29th northeast reffional stock assessment workshop (29th 

 SAW). Stock Assessment Review Committee (SARC) consen- 

 sus summary of assessments. NEFSC Ref Doc. 99-14, 347 

 p. [Available from NEFSC, 166 Water St., Woods Hole, MA 

 02543.1 



