(Quarterly Report for Oct-Nov-Dec 1998)
James M. Murphy and Herbert J. Jaenicke
Empirical relationships between
spawning stock size and subsequent harvest levels (recruitment) can show extreme
variability. Measurement error and factors independent of the spawner-recruitment
relationship mask underlying regenerative processes of fish populations and introduce
uncertainty in efforts to define optimal harvest strategies. Factors acting
independently of spawning stock levels (e.g., environment) are often the predominant
source of variability in recruitment when a fishery such as Pacific salmon (Oncorhynchus
spp.) is managed for constant spawning stock levels. Methods and approaches used to
define and account for uncertainty in the spawner-recruitment relationship have,
therefore, been the subject of much of the literature on Pacific salmon.
Environmental conditions during the early life history stages of pink salmon (O. gorbuscha) are thought to be the most critical to survival. Winter severity (e.g. streambed freezing and ice thickness) during the freshwater incubation stage is particularly important to the survival of southeastern Alaska pink salmon stocks due to freezing winter temperatures throughout most of Alaska and the life history of the fish. Pink salmon in southeastern Alaska spawn during late summer and their eggs overwinter in streambed gravel. Eggs hatch the following spring and the fry make their way up through the streambed gravel, migrate downstream, and enter the marine environment between April and May. Due to their small size at ocean entry, pink salmon are vulnerable to a broad spectrum of predators. However, the fish grow rapidly in productive estuarine habitats before beginning their 1-year residency in the Gulf of Alaska.
Winter severity during the freshwater incubation stage and growth during the early marine stage are two factors used to forecast harvest levels for southeastern Alaska pink salmon stocks. Estimates of these factors were included in environmentally dependent spawner-recruitment models and their significance examined in light of the stocks recent increase in natural production.
Pink salmon harvest and escapement rates for the northern (NSE) and southern (SSE) fishing districts of southeastern Alaska were provided by the Alaska Department of Fish and Game (ADF&G). Hatchery contributions to the commercial fishery were removed from harvest data, and all commercial harvest data were used regardless of gear type. Reliable escapement data are available only from 1960 to present; therefore data prior to 1960 were not included in spawner-recruitment models. The escapement index was estimated by summing peak counts of pink salmon from surveyed streams and adjusted for streams not surveyed within each fishing district.
Air temperatures from 1948 to 1998 were obtained from the National Climate Data Center for the Annette Island, Sitka, and Juneau weather stations located in the southern, central, and northern regions, respectively, of southeastern Alaska. Average minimum daily temperatures in January (the coldest month of the year) were used as a measure of winter severity.
Scales collected from late-run adult pink salmon returning to Auke Creek in Juneau, Alaska, from 1979 to 1997 were measured for growth. No scales were collected in 1990; therefore, scale growth in 1990 was estimated by averaging data from 1989 and 1991. The highest quality scales from a sample of 50 female pink salmon were selected each year for measurement. Female pink salmon were selected due to the greater tendency of scale resorption in males. All scales were collected from the preferred body region2 to 3 scale rows above the lateral line and posterior of the dorsal fin. A Cal Comp digitizing tablet was used to count and measure distances between scale circuli between 1979 and 1996; an OPTIMAS based optical recognition system was used to digitize the 1997 scale samples. Measurements were taken along the anterolateral line of the scale.
Ricker and generalized Ricker models were used to examine the relationship between stock and recruitment. A Ricker model is defined as:
where R = recruitment (harvest + escapement), S = number of spawners, and a and b are the productivity and density-dependence parameters. The Ricker model can be generalized through the addition of a third parameter, g:
to add more flexibility in the shape of the stock-recruitment curve.
The generalized form of the Ricker model is also known as an unnormalized gamma function and hereafter is referred to as a gamma model.
Extrapensatory or environmental factors contributing to mortality can be added to the Ricker and gamma models as:
where Xi is a measurable
source of extrapensatory mortality and qi its relationship to recruitment.
Nonmeasurable or unmeasured sources of mortality are contained in the multiplicative
error term, .
Robust regression techniques were used to estimate spawner-recruitment model parameters through iteratively reweighted least-squares. An initial fit was determined using least trimmed squares regression. This method was chosen over ordinary least squares because of its ability to correct for high leverage data points. After the initial fit, each datum was weighted by its residual distance using a Cauchy weighting function, 1/(1 + (u/c)2), where u is the vector of standardized residuals, and c is a tuning constant. New regression parameters and residual weights were computed using ordinary weighted least-squares and repeated until parameter estimates converged. A value of c = 2.385 was used for all analyses. Spawner-recruitment models were selected based on biological interpretation of model parameters and Akaike Information Criterion (AIC) values from the regression analysis.
Two time series of pink salmon escapement and harvest were used and differed only in the number of years considered. The first series included data between 1962 and 1997 and was modeled with winter air temperatures. The second series included data between 1979 and 1997 and was modeled with winter air temperatures and measurements of early marine growth. The two data series were required as growth data are available only between 1979 and 1997.
Pink salmon harvest and escapement in southeastern Alaska have increased substantially over the last 20 years (Figure 1). The same general pattern of increase is present in both northern and southern fishing districts. The Juneau, Sitka, and Annette Island weather stations exhibited similar patterns in minimum January air temperature; however temperatures were coolest at the Juneau station (Figure 2). A cyclical pattern is present in winter temperatures, and temperatures were above average between 1979 and 1997.
Differences in scale growth were found between years of high harvest (1979-82, 1984, 1987, 1988) and low harvest (1983, 1985, 1986, 1989-97) (Figure 3). The largest difference in growth occurred during early marine residence (first circuli intervals). Little difference in growth was observed between the eighth (C8) and fifteenth circuli (C15) where supplemental checks typically form on pink salmon scales. Differences in growth between years of high and low harvest were again evident from C15 to C19. Growth during early marine residence (C1-C6) was positively correlated with pink salmon harvest (Figure 4); however, growth during the later coastal ocean residency (C15-C19) was not. Recent studies conducted by the Auke Bay Laboratory of juvenile chum salmon (O. keta) growth in southeastern Alaska show that early marine growth rates are similar for chum salmon stocks originating from different locations in southeastern Alaska. Due to the migratory behavior of juvenile salmon, it is likely that much of the variability in growth occurs over time rather than space. Hence, scale growth of Auke Creek pink salmon may be a reasonable approximation of growing conditions throughout much of southeastern Alaska. The significant and positive relationship between early marine scale growth and harvest suggests that growth or environmental conditions affecting growth during the early marine residence may be important to the survival of southeastern Alaska pink salmon.
Stock-recruitment models were fit to southeastern Alaska pink salmon harvest and escapement data from the NSE, SSE, and pooled (SE) fishing districts (Table 1 and Table 2). Biologically meaningful results were only obtained with gamma models when fit to the full spawner-recruitment data set (1962-97); beta parameter estimates (density-dependence) for all Ricker models were either very close to zero or negative, resulting in exceptionally high or infinite escapement estimates (Sm) for maximum yield. Gamma models also fit spawner-recruitment data better than Ricker models when the reduced data series (1979-97) was used; Ricker models produced biologically meaningful results (b > 0), but values of Sm were still unrealistically high for SSE pink salmon. Values of Sm estimated with gamma models were similar for both data sets, suggesting that the gamma model was not sensitive to the removal of earlier data. All gamma models had g parameters greater than one, which would occur if depensatory mortality exists at low spawning levels. Depensatory mortality at low spawning levels exists if the productivity of a population declines as the spawning stock approaches zero.
Inclusion of winter air temperatures significantly improved the gamma model fit (lower AIC) to the full spawner-recruitment data series for NSE pink salmon but not SSE pink salmon (Table 1). The regional difference in the significance of winter air temperatures suggests that severe winter conditions during freshwater incubation may be more important to NSE stocks than to SSE stocks. When SSE data were pooled with NSE, winter air temperatures still significantly improved the gamma model fit; however, winter temperatures could not account for the high catch rates in recent years (Figure 5).
Inclusion of early-marine growth significantly improved the fit of spawner-recruitment models of the reduced data series (Table 2). The poorest fitting models (highest AIC) resulted from inclusion of winter air temperatures, suggesting that the significance of winter air temperatures to stock-recruitment models may be primarily due to conditions that existed prior to 1979. Gamma models with early-marine growth accounted for much of the variability in the spawner-recruitment relationship of the reduced data series
Pink salmon are unique to most commercially-harvested fish species in that they return to spawn and are harvested always as 2 year-old fish. The semelparous nature of pink salmon prevents the use of sibling and cohort methods commonly used to obtain estimates of survival and define harvest strategies. Management and preseason forecasts of pink salmon is therefore dependent on the spawner-recruitment relationship and environmental indices of survival.
The treatment of error in statistical models of the spawner-recruitment relationship can have a substantial effect on the resulting fit and interpretation of model results. Outliers, or single data points that have a substantial effect on model parameters, are often present in fisheries data. A reasonable tradeoff between arbitrarily removing outliers or highly influential data points and ignoring possible violations of model assumptions of error is to use robust methods when fitting spawner-recruitment models. Robust regression methods are an important complement to classical least-squares in that they provide answers similar to least-squares when the data are linear with normally distributed errors and yet are robust to violations in the assumption of normality.
Assumptions on the nature of the spawner-recruitment relationship are important to the interpretation of survival when only harvest and escapement data are available. One can assume no relationship exists, or use one-, two-, or three-parameter spawner-recruitment models. Gamma models (three parameter models) consistently fit the spawner-recruitment data better than Ricker models (two parameter models), which suggests that a more generalized spawner-recruitment model may be warranted for southeastern Alaska pink salmon. An important aspect of the gamma model is that it can account for depensatory mortality at low spawning levels. Depensatory morality at low spawning levels may be important to salmon production through:
loss of nutrient enrichment from spawner carcasses
reduction of fine sediment removal in spawning substrate through redd-digging activities
increased risk of predation through the loss of predator-swamping capabilities and smaller school sizes
Both bias and measurement error are
known to exist in estimates of pink salmon escapement in southeastern Alaska. Before
depensation can be fully implicated, corrections for these uncertainties will need to be
Winter severity during the freshwater incubation stage is of particular importance for Alaska salmon stocks due to the freezing winter temperatures that occur throughout much of Alaska. Our estimates of winter severity (average daily minimum air temperature during the month of January) added significantly to the spawner-recruitment relationship of NSE pink salmon, where winter temperatures were the coolest, but not to the spawner-recruitment realtionship of SSE pink salmon. Winter conditions also appeared to be most important to survival during the years prior to 1979, when winter temperatures were below average. These patterns in significance may be largely due to a nonlinear relationship between winter temperature and survival. Winter temperatures may only be significant to survival once temperatures drop below a particular threshold.
A large number of factors are thought to affect the survival of juvenile salmon during their early marine life. We used growth as an index of conditions present during this critical marine period. Growth can be a powerful tool to reduce high dimensionality inherent in the environment by bioenergetically integrating environmental conditions over space and time. Early marine growth of Auke Creek pink salmon did not show an apparent density-dependence (growth and production increased) and was significantly related to survival of southeastern Alaska pink salmon (added significantly to spawner-recruitment models) between 1979 and 1997. Early marine growth of Auke Creek pink salmon may reflect environmental conditions important to the survival of southeastern Alaska pink salmon or it may be directly related to survival through size-selective mortality.
At present, early marine conditions in southeastern Alaska appear to be more important to pink salmon survival than winter severity during freshwater incubation. However, the cyclical nature of winter temperatures suggests that an increase in winter severity should be anticipated. An increase in winter severity could shift the life-history stage affecting survival from early marine to fresh water in at least the NSE pink salmon stocks. Shifts in the critical life-history stage will make it difficult to identify a single environmental factor that can account for variability in the spawner-recruitment relationship with time. However, such shifts may be an important component of regime shifts identified in Alaskan salmon production.
The possibility for depensatory mortality to exist in southeastern Alaska salmon emphasizes the need to ensure that adequate escapement levels are maintained during time periods of poor environmental conditions. If escapements are reduced to the level that depensatory mortality plays a significant factor in their production dynamics, pink salmon stocks in southeastern Alaska will either not respond or will be sluggish to respond to improved environmental conditions.