Correspondence/Amendment 5 Comments - New England Fishery ...

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of body weight was mult¡pl¡ed by we¡ght to obta¡n the total daily rat¡on at
weight (DRt"t"l,w):
DRtot"¡w : DRww,w'W.
Subfituting length for weight ¡n th¡s equat¡on prov¡ded an est¡mate of total
daily ration of haddock as a function of length (DRtot"r.J. The linal step in
calculating the index of haddock predat¡on intens¡ty (PD was to sum the
products of the abundance-atlength of the haddock population (lV¿) for
a year and the total daily consumption at length (DR1q1"¡,¿):
pt :DNL.DRþE:.L.
Population Model. We used an age-based populat¡on model to evaluate the
effect of egg predation by haddock and fishing mortality on herring populat¡on
dynamics. This model !s divided into three components representat¡ve
of different herring life stages (F¡9. 53). The first component is the egg
predation model, which is used to pred¡ct larval abundance as a funct¡on of
haddock predat¡on intens¡ty and herring spawning stock biomass. The second
component is an asymptotic Beverton-Holt model descr¡b¡ng the relationship
between larval abundance (L/) and recruitment (R) at age 2 y:
- sLl
t.: þ+u'
where a and þ arc the two model parameters. Th¡s component is d¡rectly
comparable to the stock-recruitment curve in trad¡t¡onal fisheries population
models. except recru¡tment is described as a function of the number
of eggs that hatch (i.e., early rtage larval abundance) rather than of the
number of eggs produced. The third component accounts for processes that
affect the adult stage of herríng, including growth, maturity, físhing mortal¡ty,
and natural mortality (see 5/ Iext for full equat¡ons and parameters).
Equat¡ons and parameters for these functions were obtained from the most
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recent benchmark herring stock assessment (17). ln combination, the first
and second model components are used to predict recru¡tment as a function
of herring spawning stock b¡omass and haddock predation intensity. The
th¡rd component is used to calculate the recru¡tment necessary to maintain
a population at â stable-equil¡brium level given a specified fishing morality
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by subtract¡ng the t¡me-ser¡es mean from each data point and then
dividing by the t¡me-ser¡es 5D. The annual mean of the standardized
anomalies was then calculated. Year-to-year changes were calculated after
applying a LOWEss smoother to the mean standardized anomalies.
ACKNOWTEDGMEMTS. We thank R. Cowen, J. Deroba, M. Hauff. R. Langton,
J. Llopiz, J. Manderson, and 5. Sponaugle for reviewing an earlier draft of
this paper and everyone who collected the ¡chthyoplankton, food habits and
trawl survey data, and contributed to the herr¡ng and haddock stock
assessments. J. Collie, A. Malek, and D. Byrne generously prov¡ded timeseries
data. This work was supported by National Marine Fisheries Service
Fisheries and the Environment Grant 07-1.
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