Resource Ecology and Ecosystem Modeling - Models, MSVPA
Multispecies fish stock assessment models that include predation
We have developed a multispecies virtual population analysis (MSVPA) model and its forecasting version (MSFOR) for the eastern Bering Sea (Livingston and Jurado-Molina, 2000; Jurado-Molina and Livingston, 2002a; Jurado-Molina and Livingston, 2002b). These models include predation interactions (Fig. 1) among several commercially important groundfish stocks (walleye pollock, Theragra chalcogramma; Pacific cod, Gadus macrocephalus ; Greenland turbot, Reinhardtius hippoglossoides ; yellowfin sole, Pleuronectes asper ; rock sole, Lepidopsetta bilineata ) and also predation by external predators (arrowtooth flounder, Atheresthes stomias; northern fur seal, Callorhinus ursinus ) on these stocks. The MSVPA is a recursive algorithm that calculates the fishing mortality at age Fa,t, recruitment, stock size, suitability coefficients and predation mortality based on catch-at-age data, predator ration and predator diet information. MSVPA allows the estimation of vital population rates used in the management of fishing resources. One of the advantages of this model is the estimation of the predation mortalities produced by predators on preys species and the annual consumption of prey by predators. MSVPA is an extension of the VPA model that incorporates the predator stomach content data into the virtual population. The predation mortality estimation is based on the following equations:
(1)  ,
where M1 is the residual mortality and M2 is the predation mortality.
(2)  .
Where  represents the average stock size of the predator i of age j. Ri,j is the annual ration of the predator and Sp,a,i,j is the suitability coefficient for each combination of predator-prey-age. This parameter reflects the diet composition of the predator relative to the available food (Sparre 1991). The denominator of equation (2) represents the total suitable biomass available to the predator. In the denominator,  represents the average stock size of the prey p of age a and Wp,a represents the weight at age of the prey in the stomach of the predator. The third equation estimates the suitability coefficients:
(3) 
where Up,a,i,j represents the fraction of prey p of age a found in the stomach of the predator i of age j.
The MSVPA input data includes the catch-at-age data (1979-2002), percent of maturity-at-age, weight-at-age, terminal fishing mortalities, predator stomach content data, over 40,000 stomach samples (Table 1) and residual mortalities.
The terminal fishing mortalities were estimated with cohort analysis and these parameters were chosen to minimize the differences between our population estimates and the ones derived from the stock assessment models used by the AFSC and the ADF&G scientists during 1979-2002. The estimation of the residual mortalities required an initial run of the MSVPA with M1=M (M from single-species). We estimated the average M2 of the adult age classes over the model time series. This average was subtracted from the single-species M to get the residual mortality for the multispecies models.
Results from the MSVPA are deterministic and include adult stock size (Figs 2-7), average class size, 1979-2002 (Figs 8-13, age-0 recruitment (Table 2), fishing mortalities, average predation mortality (Table 3) , prey biomass consumed by predators (Figs 14-19), comparison of biomass consumed by predators and yield (Figs 20-25), and comparison of total mortality z (Figs 26-31) .
For further information contact Kerim Aydin, Program Leader or Jesus Jurado-Molina, Author
A portion of this research was supported by the North Pacific Research Board (NPRB). For more information on the NPRB and this project see the NPRB website (external link not affiliated with the AFSC website)
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