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Paul T. Jacobson
f (i−j) = fraction of returning females that return at age (i−j)
j = {0, 1, 2, . . . , j max }
k = {0, 1, 2, . . . , k max }
i = {0, 1, 2, . . . , k max + j max }
j max = number of cohorts stocked − 1
k max = maximum age at which fish return
N(µ, σ) = a normal distribution having a mean of µ and a standard deviation of
σ. Values of h i , r j , and s j falling below zero were set equal to zero.
The return rate implicitly incorporates all sources of mortality that are not included in the harvest rate. Model year 0 begins when the first cohort of eggs
hatches; thus, the first stocking of fish occurs in year 1. For each replication
(iteration) of the model, the number of strays in each stream was tabulated.
Frequencies for each combination of number of streams and number of strays
were calculated on the basis of 50,000 replications of the model. Year-specific
probabilities associated with a given outcome were then calculated as the proportion of model replications in which the outcome occurred.
There are several assumptions pertaining to the behavior and ecology of the fish
that are explicit in the model. Within each replication of the model, straying rate is
held constant for a given cohort, regardless of the year in which those fish return.
This assumption is consistent with Shapovalov and Taft’s (1954) observation that
“the rate of straying from a given stream is fairly constant for a given year class
(over all years in which returns occur), but may vary considerably from year class
to year class.” Return rate is also held constant for a given cohort in each replication of the model. This assumption is based on evidence that overall survival is
most heavily influenced by factors operating relatively early in the cohort’s marine life rather than by ecological conditions at the time of return (Mathews and
Buckley 1976; Neilson and Geen 1986; Holtby et al. 1990).
Derivation of Model Parameters
Harvest Rate
The harvest rate mean, µ h , and standard deviation, σ h , for all three species were
estimated from returns and harvest of the 1968–1984 brood years in the New
Hampshire Coho fishery (R.S. Fawcett, New Hampshire Fish and Game Department, personal communication). Any fishery established in the Delaware River
and estuary is more likely to be similar to the New Hampshire fishery than to those
of the Great Lakes and the west coast of North America, where large numbers of
many salmonid species are sought.
Return Rate
As with harvest rate, the mean return rate, µ r , and standard deviation, σ r , for each
species was derived from the New Hampshire Coho fishery. Mean return rate for
Coho Salmon was estimated from a linear regression of number of returns against
the number of smolts stocked (Fig. 5.2; returns = 0.005002 (released) + 229.7,
Paul T. Jacobson
f (i−j) = fraction of returning females that return at age (i−j)
j = {0, 1, 2, . . . , j max }
k = {0, 1, 2, . . . , k max }
i = {0, 1, 2, . . . , k max + j max }
j max = number of cohorts stocked − 1
k max = maximum age at which fish return
N(µ, σ) = a normal distribution having a mean of µ and a standard deviation of
σ. Values of h i , r j , and s j falling below zero were set equal to zero.
The return rate implicitly incorporates all sources of mortality that are not included in the harvest rate. Model year 0 begins when the first cohort of eggs
hatches; thus, the first stocking of fish occurs in year 1. For each replication
(iteration) of the model, the number of strays in each stream was tabulated.
Frequencies for each combination of number of streams and number of strays
were calculated on the basis of 50,000 replications of the model. Year-specific
probabilities associated with a given outcome were then calculated as the proportion of model replications in which the outcome occurred.
There are several assumptions pertaining to the behavior and ecology of the fish
that are explicit in the model. Within each replication of the model, straying rate is
held constant for a given cohort, regardless of the year in which those fish return.
This assumption is consistent with Shapovalov and Taft’s (1954) observation that
“the rate of straying from a given stream is fairly constant for a given year class
(over all years in which returns occur), but may vary considerably from year class
to year class.” Return rate is also held constant for a given cohort in each replication of the model. This assumption is based on evidence that overall survival is
most heavily influenced by factors operating relatively early in the cohort’s marine life rather than by ecological conditions at the time of return (Mathews and
Buckley 1976; Neilson and Geen 1986; Holtby et al. 1990).
Derivation of Model Parameters
Harvest Rate
The harvest rate mean, µ h , and standard deviation, σ h , for all three species were
estimated from returns and harvest of the 1968–1984 brood years in the New
Hampshire Coho fishery (R.S. Fawcett, New Hampshire Fish and Game Department, personal communication). Any fishery established in the Delaware River
and estuary is more likely to be similar to the New Hampshire fishery than to those
of the Great Lakes and the west coast of North America, where large numbers of
many salmonid species are sought.
Return Rate
As with harvest rate, the mean return rate, µ r , and standard deviation, σ r , for each
species was derived from the New Hampshire Coho fishery. Mean return rate for
Coho Salmon was estimated from a linear regression of number of returns against
the number of smolts stocked (Fig. 5.2; returns = 0.005002 (released) + 229.7,