Knowledge of the spawner-recruit relation for a population is necessary to accurately estimate the harvest rates consistent with specific goals such as maximum recruitment or maximum sustainable yield (MSY). Spawner-recruit relations reflecting recent conditions in the Columbia River Basin have been estimated for two wild populations of spring chinook salmon in Oregon�the John Day River (Lindsay et al. 1986) and the Warm Springs River (Lindsay at al. 1989). I estimated these relations for wild fish from the Snake, Methow, Entiat, and Wenatchee Rivers.

For this analysis, I assumed that all hatchery fish returned to hatcheries, and I estimated the number of fish spawning in each river by subtracting the number of fish returning to hatcheries and taken in terminal fisheries from the total number of fish returning to a river (estimated from counts at dams on the Columbia or Snake River). Number of recruits was estimated by dividing the number of fish returning to each river by the proportion of upriver spring chinook salmon escaping the fisheries in the Columbia River (Zones 1-6). I assigned recruits to year classes by either using age composition data from spawning surveys for Snake River fish or adding half the recruits in year n + 4 and half the recruits in year n + 5 (because annual age composition data for wild fish were lacking) for fish from the Entiat, Methow, and Wenatchee Rivers.

Survival of molts declined between 1964 and 1977 with the construction of mainstem dams in the Columbia and Snake River, and increased after 1979 because of enhancement activities (Raymond 1988). To develop relations applicable to current conditions (assumed to be reflected by the survival of smolts migrating in 1982-84), I multiplied the number of recruits from each year class by 0.0237/s_n, where 0.0237 was the mean survival for Snake River molts migrating in 1982-84 and s_n was Raymond's (1988) estimated survival for Snake River fish of year class n.

Ricker spawner-recruit relations (R = aSe^-bS, where R = recruits, S = spawners, and a and b are parameters of the model) were fitted by least squares linear regression of ln(R/S) on S (Table 1). I subjectively chose values for a that I considered more reasonable than the estimated values for three reasons: 1) the productivity parameter a is often substantially overestimated for stocks with low productivity (Walters and Ludwig 1981; Reisenbichler 1989); 2) estimated values of a for chinook salmon not exposed to numerous hydroelectric dams on their downstream and upstream migrations typically lie between 7 and 9 (Reisenbichler 1987); and 3) mortality of wild downstream migrants at and between dams may remain, on average, 12-15% per project (F. Young, Oregon Department of Fish and Wildlife, personal communication). I then calculated the corresponding values for b (Table 1).

The Snake River population probably consists of a number of stocks with different productivities; consequently, the estimated harvest rate for MSY (35%) would probably deplete or eliminate some of the stocks. Furthermore, Reed (1979) showed that maximum sustained yields calculated from deterministic analyses (as above) are too high for randomly fluctuating (i.e., real) populations. For these reasons, and because the quality of the sport fishery (measured as catch per unit of effort) increases with the number of fish (e.g., Lindsay at al. 1989), managers would probably choose a harvest rate nearer 25% (Fig. 1).

Outplanting (releasing hatchery fish into natural areas to compensate for low numbers of naturally spawning fish) is expected to provide substantial increases in the number of adult fish produced from the Columbia River system. I used the model of McIntyre and Reisenbichler (1986) to estimate the appropriate harvest rate and the associated harvestable surplus when fry from hatcheries in the Snake River Basin are outplanted.

The expected hatchery production of spring chinook salmon smolts in the Snake River Basin is about 7 million per year (D. Herrig, U.S. Fish and Wildlife Service, personal communication). I assumed that 5,000 adults would be required to produce 7 million smolts, and that the smolt-to-adult survival rate for hatchery fish would be 0.2%, resulting in 14,000 returning adults. I also assumed that 1) hatchery fish we genetically, physically, and behaviorally equivalent to wild fish; 2) hatchery fish are outplanted as fry and we released throughout the available rearing habitat; and 3) a female spawned in the hatchery produces four times the number of fry that the same female would produce spawning naturally. When these data and assumptions about hatchery fish were applied, the model indicated the harvest rate consistent with a given escapement goal for naturally spawning fish (Fig. 2).

I repeated the analysis assuming that each adult spawned in the hatchery produced in average of 1.9 recruits rather than 2.8 recruits (as above). With 1.9 recruits per spawner (probably the more realistic expectation), the harvest rate for maximum catch was only slightly greater than that with no outplanting (Fig. 3). The allowable catch, of course, increases with the success of the hatchery program (measured in recruits per spawner), but it falls short of the catch from wild fish alone if the survival of downstream migrants is doubled (Fig. 3). One should realize that the assumptions for outplanting, such as no differences between hatchery and wild fish,¹ will probably not be met; hence, the allowable catch and acceptable harvest fractions a overestimated to an unknown extent.

Outplanting in the Methow River system would involve collecting wild adults each year, spawning them in a hatchery, and releasing their offspring back into the Methow River as smolts (W. Hopley, Washington Department of Fisheries, personal communication). I assumed that 1) no adults will be collected at escapements with less than 500 fish; 2) no more than either 1,000 or one-third of the returning adults (whichever is less) will be taken for the hatchery each year; 3) on average, each adult spawned in the hatchery would produce two returning adults; and 4) hatchery fish are genetically, physically, and behaviorally equivalent to wild fish. The results were similar to those for outplanting in the Snake River system (Fig. 4).

Clearly, some populations can accommodate a higher harvest rate than others. The John Day River population may become extinct at a 10% harvest rate, and the 64% harvest rate estimated for MSY of Wenatchee River fish would deplete or eliminate the populations from the Entiat, Methow, and Snake Rivers. Accordingly, managers can allow only limited fishing in the main-stem Columbia River if each stock is to persist. This would require that there be almost no harvest below the John Day River until improvements in downstream migrant survival have substantially increased the productivity of the population and perhaps 25% harvest rate below the Snake River, even with successful (2:1) outplanting.

The estimates of population productivity given here, or anywhere else, may, of course, be wrong and may suggest harvest rates substantially different from optimum rates. For this reason, and because population productivity varies from year to year and among populations, minimum escapement goals should be established for each population in the system and escapements should be monitored to avoid both loss of populations from overfishing and generation of genetic problems resulting from small effective population size. Harvesting populations in their home tributaries, rather than in the Columbia or Snake River, would allow for protection of the less productive populations, and would provide the greatest total catch.

Successful outplanting will increase production and allowable catch, although optimum harvest rates may change little. Outplanting program should be planned and evaluated carefully because outplanting is not a proven technology; it can eliminate endemic populations, and may produce few or no additional fish over an extended period of years.

¹Indeed, the more general, implicit assumption that outplanting will produce any additional fish over an extended period of time remains to be verified.

Lindsay, R. B., W. J. Knox, M. W. Flesher, B. J. Smith, E. A. Olsen, and L. S. Lutz. 1986. Study of wild spring chinook salmon in the John Day River system. Oregon Department of Fish and Wildlife, Final Report to Bonneville Power Administration, 119 p. (Available from ODFW, P.O. Box 59, Portland, OR 97207.)

Lindsay, R. B., B. C. Jonasson, R. I- Schroeder, and B. C. Cates. 1989. Spring chinook salmon in the Deschutes River, Oregon. Oregon Department of Fish and Wildlife Information Report 89-4, 92 p. (Available from ODFW, P.O. Box 59, Portland, OR 97207.)

McIntyre, J. D., and R. R. Reisenbichler. 1986. A model for selecting harvest fraction for aggregate populations of hatchery and wild anadromous salmonids. In R, H. Stroud (editor), Fish culture in fisheries management, p. 179-189. Am. Fish. Soc., Bethesda, Maryland. 481 p.

Raymond, H. L. 1988. Effects of hydroelectric development and fisheries enhancement on spring and summer chinook salmon and steelhead in the Columbia River basin. N. Am. J. Fish. Manage. 8:1-24.

Reed, W. J. 1979. The steady state of a stochastic and deterministic harvesting model. Math. Biosci. 41:273-307.

Reisenbichler, R. R. 1987. Basis for managing the harvest of chinook salmon. N. Amer. J. Fish. Manage. 7:589-591.

Reisenbichler, R. R. 1989. Utility of spawner-recruit relations for evaluating the effect of degraded environment on the abundance of chinook salmon, Oncorhynchus tshawytscha. In C. D. Levings, L. B. Holtby, and M. A. Henderson (editors) Proceedings of the national workshop on effects of habitat alteration on salmonid stocks, p. 21-32. Can. Spec. Publ. Fish. Aquat. Sci. 105.

Walters, C. J., and D. Ludwig. 1981. Effects of measurement errors on the assessment of stock-recruitment relationships. Can. J. Fish. Aquat. Sci. 38:704-710.

Table 1. Estimated parameters for Ricker spawner-recruit relations, R = aSe^-bS, where R = recruits, S = spawners, a and b are parameters; m_s is the harvest rate for maximum sustainable yield, and m_m is the harvest rate for maximum recruitment.

^aDeschutes River drainage. Lindsay at al. (1989) did not account for prespawning mortality. I used the mean prespawning mortality for 1977-79 and 1983-86 (40%) to adjust their values.

^bGeometric mean value for four areas in the John Day River system for 1970-79. Mean a = 6.1 for 1959-69, before completion of John Day Dam.

^cMaximum recruitment occurs to the right of the replacement line with no harvest.

Figure 1. Spawner-recruit relation for spring chinook salmon in the Snake River; R = 2.2Se^-0.000017S, where R = recruits and S = spawners. Solid lines indicate harvest levels of 0%, 25%, and 35%. Expected population levels are where the solid lines intersect the curve. Points are identified by year class.

Figure 2. Harvest rate, with outplanting to achieve different escapement goals (values for wild deficit at harvest rate = 1) for spring chinook salmon in the Snake River when the hatchery programs produce 2.8 recruits per spawner.

Figure 3. Expected catch of spring chinook salmon from the Snake River at different harvest rates. Curves illustrate natural (wild) production under recent conditions (current) and when survival of downstream migrants is doubled, and natural and hatchery production with outplanting when hatchery programs produce 1.9 (2:1) or 2.8 (3:1) recruits per spawner.

Figure 4. Expected catch of spring chinook salmon from the Methow River at different harvest rates. Curves illustrate natural (wild) production under recent conditions (current) and when survival of downstream migrants is doubled, and natural and hatchery production with outplanting when hatchery programs produce two (2:1) or 3 (3:1) recruits per spawner.

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