Projections for Port Susan Pacific hake population

Conditions that prevailed during the 1982 to 1999 period were assumed to continue for the projections. Population productivity was assumed to not change. Warm conditions have prevailed since 1976 (Fig. 6). These conditions may have lowered productivity. Conditions may become cooler in the future (1999 and early 2000 were cool). If so, productivity may be higher than assumed for the projections and the results may be too pessimistic. Human consumption was assumed to be zero. Consumption of Pacific hake by California sea lions during the 1986-1999 period was assumed to continue at the same rate. As previously described, it appears that numbers of California sea lions in Puget Sound increased until 1986 and then fluctuated without trend. Consumption of Pacific hake by harbor seals was assumed to be at 1999 levels. Harbor seal counts had increased in the Puget Sound and Eastern Bays, but Steve Jeffries (S. Jeffries[35]) expressed the opinion that they may have reached their carrying capacity in the Sound. If the harbor seal populations continue to increase after 1999, Pacific hake consumption is likely to increase and projection results would tend to be too optimistic. Pacific hake biomass was projected for 100 years starting in 2000 for each of the hypothetical 10 levels of predation by pinnipeds. 1000 runs were made for each level of projections.

The first projections were made using equation (1) to describe stock productivity. Biomass in year (i+1) was projected to be:

Bio(i+1) = (1+ Prod(i))Bio(i) - (Csl(i) + Chs)                (4)

Prod(i) was drawn randomly with equal probability from the 1982-1998 set of productivities shown in Table 11. When i was greater than 1999, Csl(i) was drawn randomly with equal probability from the 1986-1999 set of consumption by sea lions at the specified hypothetical level shown in Table 9. When i was 1999 Csl(i) was set to the value shown in Table 9 for 1999. Chs was set at consumption by harbor seals at the specified hypothetical level shown in Table 10. Results indicate that the probability of extinction of the Port Susan population within a short period of time is high, if the assumed model is valid (Fig. B-1).

Projections were next made using equation (2) to describe stock productivity. Biomass in year (i+1) was projected to be:

Bio(i+1) = Bio(i)e-(Z(i)).                (5)

Where,

Z(i)  = M +F(i) - G(i),

M    = Constant instantaneous rate of natural mortality,

F(i)  = Instantaneous rate of exploitation mortality from all causes in year i,

F(i)  = Fsl(i) + Fhs(1999),

Fsl(i)  = Instantaneous rate of mortality caused by exploitation by sea lions in year i,
                         (Drawn randomly from 1986-1999 set in Table B-1, except set to value for 1999 when i =1999.)

Fhs(1999) = Instantaneous rate of mortality caused by exploitation by harbor seals in 1999
                        (from Table B-2), and

G(i)  = Instantaneous rate of productivity in year i. It includes migration to and from other populations, and was drawn randomly from 
                       1982-1998 set in Table 12.
 

The population never actually reached 0 when equation 5 was used. Summarizations were made of probabilities of the biomass falling below 10 kg, 1 mt, or 50 mt or approximately 100, 10,000, or 500,000 fish. (In recent years the average weight of Port Susan Pacific hake was about 0.1 kg, Table 7.)  Pacific hake usually occur in loose aggregations (if not dense schools). Individual trawl catches can be as large as 50 mt. A biomass of 10 kg probably would be undetectable and when breeding populations fall to around 100 individuals, genetic bottlenecks are likely. The IUCN proposed that populations of marine fish be considered vulnerable when numbers drop below 10,000 animals (Musik 1999). Results of the projections indicate that the probability of biomass falling to less than 1 mt is below 0.5 for 100 years (Figs. B-2, B-3). However the probability of biomass falling to less than 50 mt exceeds 0.5 in about 55 years under the highest hypothetical level of predation by pinnipeds (Fig. B-4).

Generation time for Port Susan Pacific hake was estimated to be about 4 years. Musick (1999) suggested examining trends in numbers over three generations as an indicator of risk. Projected 12 year trends of average biomasses under model 2 range from increasing under the lowest level of pinniped predation to very little change under the highest level of pinniped predation (Fig. B-5). However the averages can be misleading because average values are strongly influenced by relatively very robust results of some of the replications. Projected 12 year trends of median biomasses under model 2 indicate that 50% or more of the replicates had negative 12 year trends (Fig. B-6).

In summary, results of the hypothetical projections indicate that uncertainty about rates of predation of Pacific hake by pinnipeds and the form of the relationships between Pacific hake predation by pinnipeds and commercial fishing precludes definitive conclusions concerning the risk of extinction of the Port Susan Pacific hake population. It seems unlikely that reality will be as pessimistic as projected using model 1. Even if sea lions continue to target Pacific hake in a model 1 fashion on the Port Susan spawning grounds if Pacific hake biomass falls to very low levels, it seems that model 2 would be more appropriate for other spatial-temporal situations. However, model 2 may be too optimistic because Pacific hake and pinniped behavior may result in pinnipeds being able to increase exploitation rates on Pacific hake with positive net energy results even when overall Pacific hake abundance falls to very low levels.
 
 

Table B-1. Ten hypothetical levels of Fsl(i) in Puget Sound. Ten levels are based on assumptions detailed in text.
 

        Year                                                                                                  Ten hypothetical levels of Fsl(i)

Table B-2. Ten hypothetical levels of Fhs(1999) in Puget Sound and Eastern Bays combined. Ten levels are based on assumptions detailed in text.
 

Figure B-2 Estimates of probability that biomass of the Port Susan population of Pacific hake is less than 10 kg using Model 2 and 10 hypothetical levels of pinniped predation.

Figure B-3 Estimates of probability that biomass of the Port Susan population of Pacific hake is less than 1 mt using Model 2 and 10 hypothetical levels of pinniped predation.

Figure B-4 Estimates of probability that biomass of the Port Susan population of Pacific hake is less than 50 mt using Model 2 and 10 hypothetical levels of pinniped predation.

Figure B-5 Projected 12 year trends in average Port Susan Pacific hake biomass using Model 2 under 10 hypothetical levels of pinniped predation.

Figure B-6 Projected 12 year trends in median Port Susan Pacific hake biomass using Model 2 under 10 hypothetical levels of pinniped predation.