O'Farrell and Satterthwaite: Inferred historical fishing mortality rates of Oncorhynchus tshawytscha 
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fisheries in the 2000-2012 period were largely closed 
during these months. To infer contact rates per unit 
of effort for these strata, we used historical SRWC 
harvest data derived from marked (fin-clipped) nat- 
ural-origin fish from the brood years 1969-1970 that 
were recovered in ocean fisheries as age-3 fish during 
the calendar years 1971-1972 (CDFG 8 ). Recreational 
fisheries in SF and MO in 1971-1972 opened in mid- 
February with a 22-in (56-cm) minimum size limit, and 
this timing of the start of the season and this mini- 
mum size restriction were similar for recreational fish- 
ing seasons through 1983. The average proportion of 
the recreational harvest of age-3 SRWC south of Point 
Arena that was taken in February-March for the years 
1971-1972 (00 was 0.33. This proportion was assumed 
to be representative of the average fraction of the rec- 
reational harvest south of Point Arena that was taken 
in February and March for the years 1978-1983 ( 02 R 
Assuming that the contact rate per unit of effort was 
equivalent for February and March, and in manage- 
ment areas SF and MO, we used the root finding func- 
tion uniroot in the R statistical software, vers. 3.0.0 
(R Core Team, 2013) to identify the value of contact 
rate per unit of effort that resulted in the difference 
between tpi and 02 that equaled zero. Put another way, 
we solved iteratively for the contact rates per unit of 
effort for February-March that resulted in 33% of the 
total recreational sector harvest occurring in Febru- 
ary-March, on average, for the years 1978-1983. 
Data sufficient for estimation of contact rates per 
unit of effort also do not exist for the commercial sec- 
tor in SF or MO in April and for the recreational sector 
in MO in October because fisheries in the 2000-2012 
period were largely closed for these months. In the case 
when SF and MO commercial fisheries began in April, 
the estimate of contact rate per unit of effort for May 
was assumed. In the case when MO recreational fisher- 
ies extended into October, the contact rate per unit of 
effort for September was assumed. These assumptions 
had little effect on the results because April commer- 
cial fisheries and MO recreational fisheries in October 
were relatively rare, were short in duration, and at- 
tracted little effort. 
The proportion of SRWC expected to be of legal size 
for retention was determined on the basis of a size- 
at-age model derived for SRWC, described in O’Farrell 
et al. (2012a, 2012b), and the specified minimum size 
limit for retention in a fishery. For the growth mod- 
el, the size-at-age of individual fish in each month is 
assumed to be normally distributed, and the propor- 
tion of legal-size fish is estimated by evaluating the 
cumulative normal distribution at the minimum size 
limit, given the estimated mean and standard devia- 
tion. When a large minimum size limit is in effect for 
months when SRWC size-at-age is smallest (i.e., Febru- 
ary-May), very low estimates of the proportion of legal- 
8 CDFG (Calif. Dep. Fish Game). 1989. Unpubl. report. De- 
scription of the winter Chinook Ocean Harvest Model. Ocean 
Salmon Project, Calif. Dep. Fish Game, Santa Rosa, CA. 
size fish can result. This scenario can translate into 
unrealistically low levels of harvest per contacted fish, 
and, conversely, into a very large estimate of contacts 
based on a single retained and sampled fish. As a re- 
sult, a lower bound on the proportion of legal-size fish 
of 0.035 is assumed. The value of 0.035 corresponds 
to the condition where a single coded-wire tag recov- 
ery results in contacts approximately equivalent to the 
lowest reconstructed abundance of age-3 fish estimated 
from cohort reconstruction (O’Farrell et ah, 2012a). Use 
of this lower bound value reduces the probability that 
an entire hatchery-origin cohort would be estimated 
to be contacted by the fishery in order to produce one 
harvested and sampled fish. Table 1 displays the size- 
at-age model parameters and the proportion of legal- 
size fish estimated for commonly employed minimum 
size limits in both the commercial and recreational 
fisheries. 
Release mortality rates were assumed to be 0.26 for 
the commercial sector and 0.14 for the recreational sec- 
tor, reflecting the conventional values used for the an- 
nual assessment of SRWC and other Chinook salmon 
stocks (PFMC 4 ). An exception exists in the recreational 
sector, where release mortality rates for 1990-2012 
were estimated on the basis of prevalence of mooching 
(drifting a hooked bait in the California recreational 
sector), and fish contacted with mooching gear expe- 
rience a higher rate of gut hooking and, therefore, a 
higher release mortality rate than that of troll-contact- 
ed fish (Grover et al., 2002). Derived from the results 
in Grover et al. (2002), estimates of the recreational 
release mortality rate range from 0.14 to 0.57 between 
1990 and 2012 (Grover 9 ). 
The dropoff mortality rate was assumed to be 0.05 
for all months, areas, and sectors, reflecting the con- 
ventional value used for PFMC Chinook salmon assess- 
ment (PFMC 4 ). 
The natural mortality rate was assumed to be 0.018, 
the monthly rate corresponding to an annual natural 
mortality rate of 0.20. The annual natural mortality 
rate of 0.20 is commonly assumed in many stock as- 
sessments (Quinn and Deriso, 1999) and is consistent 
with many PFMC Chinook salmon assessments (e.g., 
O’Farrell et al., 2012a, 2012b). 
Bootstrap 
A key source of uncertainty in the hindcasting of impact 
rates is variation in estimates of contact rates per unit 
of effort across years. To account for this variation, we 
performed 20,000 replicate computations of the impact 
rate for the years 1978-2012 by randomly sampling, 
with replacement, estimates of the contact rate per 
unit of effort from the years 2000-2012. This procedure 
effectively makes the assumption that annual variation 
in contact rate per unit of effort in 2000-2012 is rep- 
resentative of the entire time series for 1978-2012. For 
9 Grover, A. 2013. Personal commun. Institute of Marine 
Sciences, Univ. Calif., Santa Cruz, Santa Cruz, CA 95064. 
