Research Document - 2014/089
Estimating Regional Distributions of Freshwater Stock Productivity, Carrying Capacity, and Sustainable Harvest Rates for Coho Salmon Using a Hierarchical Bayesian Modelling
By Josh Korman and Arlene Tompkins
Abstract
We estimated regional distributions of freshwater stock productivity (smolts/spawner at low spawning stock size) and carrying capacity (smolts/km when spawners are not limiting) for Coho salmon to support a simulation analysis intended to describe the tradeoff between harvest and conservation in mixed-stock fisheries. The objectives of this analysis are to: determine the most suitable form of a freshwater stock-recruitment model using information theoretic and other criteria; estimate and compare regional distributions of freshwater stock-recruitment parameters from alternate models; estimate regional distributions of sustainable harvest rates under different marine survival regimes; and to determine the validity of applying the estimated regional stock-recruitment distributions to streams in the Georgia Basin West (GBW) management unit and the Thompson River drainage.
We compiled spawner-to-smolt data from 16 coastal streams supporting Coho salmon in Oregon, Washington, and BC (n=251). We used a hierarchical Bayesian modeling approach because it correctly weighs the contribution of each stream to the regional distribution based on its information content. Hierarchical Beverton-Holt (BH), Ricker (RI), and Logistic Hockey Stick (LHS) models fit the data well and were consistent with the assumed lognormal error structure. There was considerable shrinkage in all hierarchical models, as evidenced by the relatively low number of effective parameters (pD= 17-23) relative to the total number of parameters that were estimated (K=37 and 55 for standard and depensatory models, respectively). Although an additional 18 parameters were estimated for the depensatory BH model, the effective number of parameters was similar to values for non-depensatory models. This indicated little evidence for depensation in the data. Estimates of the depensation parameter were largely determined by the prior distribution. The Beverton-Holt model had a substantially lower deviance information criteria (DIC) statistic than the Ricker (DDIC=43.2) and Logistic Hockey Stick (DDIC=70.6) models, indicating that the former model had the best out-of-sample predictive power. The mean and standard deviation of the lognormal regional distributions for stock productivity for the BH model was 71 smolts/spawner (sa=0.49) and 1564 smolts/km (sa=0.67), respectively. The form of the stock-recruitment function had a significant influence on the regional distributions of stock productivity, but little effect on distributions for carrying capacity. Regional distributions of stock productivity based on LHS and RI models had lower means (31 and 49 smolts/spawner, respectively) and lower variability (sa = 0.32 and 0.38, respectively) compared to the distribution based on the BH model.
Regional distributions of harvest rate (Umsy) that resulted in maximum sustainable yields were computed based on samples from the marginal predictive distributions of stock productivity and carrying capacity from the Beverton-Holt model. As expected, Umsy declined considerably at lower marine survival rates (ms). In the worst scenario (ms=0.025), 15% of the streams represented in the regional distributions could not sustain a viable population, even in the absence of harvest. Modal Umsy values at ms=0.025, 0.05, and 0.10 were 0.25, 0.45, and 0.65, respectively.
The product of mean smolt capacity per km of stream from the predictive regional distribution (2052 smolts/km) and total accessible stream length (1335 and 2268 km for GBW and Thompson, respectively) under predicted adult recruitment at full seeding by about 2-fold for GBW and overestimated recruitment by a similar magnitude for the Thompson River drainage. In the case of the Thompson, it is possible that the total amount of stream length used for rearing was overestimated because larger mainstem reaches comprised about 50% of the total. There was good agreement between predicted and escapement-based estimates of adult recruitment when 6th and 7th order reaches were removed (total length after removal = 1105 km). In the case of GBW, where recruitment at full seeding was underestimated, accessible stream length could have been underestimated, as many productive side-channel habitats would not be shown on a 1-50,000 map-scale. Comparison of map- and field-based estimates of habitat for Black Creek however suggests the latter method underestimates habitat by only about 15%. Thus, other factors must have contributed to the discrepancy between escapement- and habitat-based carrying capacity estimates. We suspect that the historical escapement data overestimates wild stock capacity because it includes an unknown, but potentially large component of hatchery-origin fish. In the absence of reliable estimates of naturally produced escapement, the comparison of predicted and observed carrying capacities for GBW remains inconclusive.
Simulated aggregate escapement trends, driven by historical exploitation and marine survival rates and random draws from the marginal distributions of spawner-to-smolt stock-recruitment parameters, agreed well with the observed aggregate trend for the Thompson drainage. Simulations also matched the observed decline in escapement in GBW until the late 1980s, but substantially under predicted escapement from 1990 to the present. As marine survival for wild stocks for this latter period in GBW is likely reasonably well defined by index stocks and has a declining trend, and there is no indication from the stock-recruitment analysis that freshwater productivity has declined, it seems likely that the aggregate escapement trend for GBW does not represent the trend for wild stocks, or is at least inconsistent over the time series. Further analysis would benefit from a rigorous review of GBW escapement data that would include removing the hatchery component. In general, the simulations tend predict the extent of declines in abundance relative to what has been observed, even in the case of the Thompson drainage, where hatchery returns are removed from escapement estimates. Thus, there was no indication from the simulation analysis that the regional distribution of freshwater productivity estimated from the hierarchical stock-recruitment analysis over-represents more productive stocks in GBW or the Thompson drainage.
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