Alternative harvest rates for Pacific halibut were evaluated using a definition of exploitable biomass that is consistent with the stock assessment of 1996, and incorporating the effect of bycatch of sublegal fish as pre-recruit mortality. The effects of different exploitation rates on future trends in biomass and yield depend critically on how average recruitment varies with the size of the spawning biomass. Historical trends in recruitment show major, persistent changes in productivity with no clear relationship to spawning biomass. Based on historical performance, we cannot predict long-term average yields with any reasonable level of certainty, as biomass levels will depend to a large extent on prevailing future environmental conditions affecting growth and recruitment. However, it is still possible to select a harvest rate that will perform adequately under a variety of recruitment scenarios. Simulation results indicate that harvest rates ranging from 0.20 to 0.25 may achieve close to maximum yields under different hypotheses about future stock productivity, while having a low probability of driving the stock below the historical minimum achieved in the early 1970s. The analysis of harvesting strategies will be revisited during 1997 when possible changes in the legal size limit will be considered, together with strategies that involve lowering the exploitation rate in response to anticipated low stock levels.

Catch quota recommendations made by IPHC have been based on applying a constant exploitation rate of 0.30 to the exploitable biomass, i.e. the biomass that is fully recruited to the fishery. The choice of a 0.30 exploitation rate was based on an analysis of historical trends in biomass conducted in 1992 using the latest estimates of abundance and growth available at the time. Since then, major changes in the stock and the assessment methodology have taken place, which require a re-evaluation of the harvesting strategy. The dramatic reduction in halibut body growth rate observed in recent years implies that the average reproductive contribution made by each recruit will be substantially smaller than it used to be if growth rates stabilize or decrease even further. This is because egg production is proportional to fish size and we assume that natural mortality has not changed. Harvest rates should be adjusted to account for this effect. In addition, reduced size at age has also resulted in lower selectivity (i.e., the fraction of each age-class that is recruited to the fishery and is part of the "exploitable" biomass) of the younger age classes, a development that conflicted with assumptions made by the old assessment method. Changes in methodology introduced mainly to account for trends in size-at-age resulted in substantially higher estimates of biomass and recruitment, and lower estimates of selectivity. Exploitable biomass is now a smaller fraction of the total biomass of adult fish. The choice of harvest rate had to be re-considered, as harvest rates are now applied to a different definition of exploitable biomass computed using lower selectivities. An additional reason for revising the harvest rate is the implementation of a new procedure for accounting for pre-recruit bycatch mortality through adjustment of the harvest rate (see Clark, this volume).

Alternative harvest rates are evaluated by simulating, based on historical performance, how the stock might respond in the future to different levels of exploitation. In order to simulate future trends in stock biomass, we need to specify how the production of young halibut (recruitment) will change on average as the size of the spawning stock increases or decreases. Indeed, the performance of different harvest rates depends critically on the assumptions made about the relationship between spawning biomass and future recruitment. Not all eggs spawned survive to become young halibut, and more spawning does not necessarily mean more recruitment. In fact, if we look at the historical trends in recruitment and spawning biomass (Figure 1), it appears that recruitment has fluctuated independently of stock size, at least over the range of biomass levels that we have observed. The number of recruits produced per unit of reproductive biomass has changed by a factor of four, showing persistent periods of low and high productivity. Peaks in productivity coincide with periods of low and high parental stock abundance and so cannot be readily explained by changes in parental biomass. In particular, recruitment levels estimated for 1985-1996 (year-class 1977 and subsequent) are on average about twice the mean recruitment level estimated for the preceding 40 years. While the estimates for the last few years are particularly uncertain, the increase in recruitment coincides with major changes in climatic regime across the North Pacific, which have been shown to have affected productivity of other fish stocks.

Because the environment has played a major role in driving recruitment variability at least within the range of stock levels observed, it is impossible to predict future recruitment trends. What we can do is postulate various possible recruitment scenarios and evaluate management choices across them. In all the stock-recruitment models explored, a great deal of recruitment variability is caused by the environment, and so it is not under management control. Two such models are discussed below:

1) a dome-shaped model with gradual changes in environmental effects: average recruitment increases with more spawning, reaches a maximum at an intermediate level of spawning biomass, and slightly decreases thereafter (Fig. 2a); environmental conditions affecting juvenile survival are similar from one year to the next and change gradually over time. A few recruitment trajectories simulated with this model are shown in Figure 2a.

2) a flat model affected by abrupt shifts in climatic regime: average recruitment is insensitive to changes in spawning biomass for a wide range of biomass levels and it is controlled by prevailing environmental conditions which shift between two very different regimes every 20 years. Expected recruitment for good and poor conditions, and a few illustrative recruitment trajectories are shown in Figure 2b. This model is a simple prototype of a stock-recruitment relationship affected by major shifts in climatic regime controlling carrying capacity; it is used here just to explore the performance of different harvest rates under such scenario, without any presumption that halibut stocks will indeed behave precisely in this manner.

Both models predict that recruitment would decrease gradually as spawning biomass decreases to levels lower than the historical minimum. Predictions made about how juvenile production would change if the stock dropped to unprecedented stock levels are extremely uncertain, as they are based on an extrapolation beyond the range of historical experience.

Pacific halibut have undergone a dramatic reduction in body growth (Fig. 3, top). Because the numbers of eggs produced by female halibut depend on their body mass, the observed reduction in size at age results in a decrease in the average contribution that recruits make to reproduction throughout their life. Figure 3 shows how changing growth rates would affect the average life-time reproductive contribution (biomass) per recruit for a range of exploitation rates (using current estimates of selectivity); the three lines in the bottom panel show average reproductive contribution for weights at age as estimated in 1980, 1991 and 1996. With current weights-at-age, an exploitation rate of 0.25 results in lower reproductive biomass per recruit than would be obtained with a 0.30 exploitation rate and weights-at-age as observed five years ago, when the harvesting strategy was last evaluated.

Other things unchanged (stock-recruitment dynamics, selectivity) the exploitation rates that result in adequate levels of spawning are lower when the growth and average reproductive contribution per recruit decline. Because it is not possible to anticipate future trends in halibut growth, alternative harvest rates have been evaluated assuming that weights at age and selectivity would remain constant at the current values. When unforeseeable changes in growth and selectivity do take place, their magnitude may be sufficient to justify adjusting the harvest rate. For example, when harvesting strategies were evaluated in 1992, the mean reproductive contribution per recruit corresponding to the chosen harvest rate of 0.30 was 17% larger than it would be with current weights at age. Interestingly, a harvest rate of 0.25 applied to the exploitable biomass computed using current selectivities and weights at age, and accounting for the reduction in future recruitment due to bycatch, results in the same reproductive contribution per young-of-the-year as that produced by a harvest rate of 0.30 using the old higher selectivities, higher weights-at-age as observed in 1991, and ignoring bycatch. So, adjusting harvest rates to maintain the same reproductive contribution per recruit in response to changes in growth, selectivity, and the incorporation of pre-recruit bycatch mortality would result in lowering the harvest rate from 0.30 to 0.25.

We will continue to monitor future changes in size at age and selectivity, and we can anticipate that the harvest rate may need to be adjusted in response to those changes in order to maintain adequate levels of reproductive contribution per recruit.

Alternative exploitation rates were evaluated by simulating how the stock might respond to different harvest rates ranging from 0.0 to 0.50. A model of the Pacific halibut stock was used to simulate future trends in abundance and catches under the different harvesting regimes. Recruitment was generated according to one of the stock-recruitment models described above, which represent recruitment productivity in the absence of bycatch. Simulated recruitments were reduced by 10% to account for pre-recruit mortality induced by bycatch. Weights at age were assumed to be fixed at the values estimated from the catch of 1996, so the possibility of future trends in growth was ignored. Age-specific selectivities were the average of the age-specific selectivities estimated for areas 2A+2B and 3A in the assessment of 1996, weighted by the respective abundance in those areas. These selectivity values are lower than those used in previous assessments. As a result, the exploitation fractions applied to this new definition of exploitable biomass cannot be compared directly to the 0.30 level used in the past. Further details about the methods used in this analysis are provided elsewhere (Parma, 1997).

Stock trajectories were simulated for 200 years, and performance of the alternative harvest rates was evaluated in terms of:

(1) mean long-term yield,

(2) mean level of reproductive biomass, and

(3) the probability that the reproductive biomass dropped below 125 million lbs, approximately the minimum record attained in the early 1970s over the first 20 years of simulation.

While the exploitation rate that resulted in maximum long-term yield differed for the two models considered (0.23 compared to 0.32, Table 1), a range of harvest rates between 0.20 and 0.30 resulted in average yields that where within 10% of the respective maxima in both cases (Fig. 4, Table 1). Even under a very optimistic scenario in which recruitment carrying capacity would remain at the high level indicated by the last 11 estimates (i.e. a flat stock-recruitment model with carrying capacity stable at the most productive level), yields produced under a 0.25 harvest rate were only 17% lower than the maximum yield obtained with a harvest rate close to 0.50. Considering the major trends in productivity exhibited by halibut stocks in the past, future yields cannot be predicted with any reasonable level of confidence. However, the simulation results show that it is still possible to determine a range of harvest rates that will achieve close-to-maximum yields under various stock-recruitment scenarios.

Long-term average reproductive biomass for harvest rates between 0.20 and 0.25 ranged between 200 and 270 million pounds, well above the historical minimum of around 125 million pounds reached in the mid 1930s and again in the early 1970s. Minimum levels of reproductive biomass attained in the simulated trajectories depend on the recruitment model. Under the dome-shaped model with gradual changes in environmental effects, the probability that the stock dropped below the historical minimum over the first 20 years of simulation was small (less than 10%) for harvest rates of 0.24 and lower, and it increased substantially when the harvest rate was raised above 0.25 (Fig. 4, bottom panel, Table 1). A similar but more drastically increasing trend occurred under the flat model when carrying capacity for the next 20 years was assumed to be at the low level. When, instead, high recruitment levels were assumed for the next 20 years, this probability was close to zero. These two cases are shown by the dashed lines in Figure 4 (bottom panel). Estimated risks are probably optimistic as they are based on assuming that successive errors in the estimates of stock abundance are independent from year to year. Further evaluation of the performance of the new assessment method will be conducted over the next year, which will allow to characterize better the uncertainty associated with the biomass estimates.

Clark, W.G. Long-term changes in halibut size at age. Report of Assessment and Research Activities, this volume.