North American Journal of Fisheries Management 27:634–642, 2007
! Copyright by the American Fisheries Society 2007
DOI: 10.1577/M06-094.1
[Management Brief]
An Improved Sibling Model for Forecasting Chum Salmon and
Sockeye Salmon Abundance
STEVEN L. HAESEKER,*1 BRIGITTE DORNER, RANDALL M. PETERMAN,
AND
ZHENMING SU2
School of Resource and Environmental Management, Simon Fraser University,
8888 University Drive, Burnaby, British Columbia V5A 1S6, Canada
Abstract.—The sibling model is often one of the best
methods for calculating preseason forecasts of adult return
abundance (recruits) for populations of Pacific salmon
Oncorhynchus spp. This model forecasts abundance of a
given age-class for a given year based on the abundance of the
previous age-class in the previous year. When sibling relations
fit historical data well, the sibling model generally performs
better than other forecasting methods, such as stock–
recruitment models. However, when sibling relations are
weak, better forecasts are obtained by other models, such as
naı̈ve models that simply use an historical average. We
evaluated the performance of a hybrid model that used
quantitative criteria for switching between a sibling model and
a naı̈ve model when generating forecasts for 21 stocks of
chum salmon O. keta and 37 stocks of sockeye salmon O.
nerka in the northeastern Pacific Ocean. Compared with the
standard sibling model, the hybrid model reduced the root
mean square error (RMSE) of forecasts by an average of 27%
for chum salmon stocks and 28% for sockeye salmon stocks.
Compared with a naı̈ve model, the hybrid model reduced the
RMSE of forecasts by an average of 16% for chum salmon
stocks and 15% for sockeye salmon stocks. Our results
suggest that hybrid models can improve preseason forecasts
and management of these two species.
Fishery management agencies often generate preseason forecasts of returns of Pacific salmon Oncorhynchus spp. for initial guidance on the fishing regulations
that may be needed to achieve spawner abundance
(escapement) or harvest-rate goals. The fishing industry
has also used these forecasts to regionally allocate
harvesting and processing equipment and personnel.
However, the predictive performance of preseason
forecasts is often poor (Adkison and Peterman 2000;
Haeseker et al. 2005), due in part to high interannual
variation in survival and recruitment rates (Peterman
1987; Bradford 1995). As a result of forecasting error,
* Corresponding author: steve_haeseker@fws.gov
1
Present address: U.S. Fish and Wildlife Service, Columbia
River Fishery Program Office, 1211 Southeast Cardinal Court,
Suite 100, Vancouver, Washington 98683, USA
2
Present address: Institute for Fisheries Research, 1109
North University Avenue, 212 Museums Annex Building,
Ann Arbor, Michigan 48109-1084, USA
Received March 24, 2006; accepted September 20, 2006
Published online April 26, 2007
management agencies may have difficulty achieving
escapement goals or harvest-rate targets, and the fishing
industry may experience economic losses (Bocking and
Peterman 1988; Eggers 1993).
The standard sibling model (Peterman 1982) has
often demonstrated relatively good forecasting ability
for sockeye salmon O. nerka and chum salmon O. keta
(Bocking and Peterman 1988; Wood et al. 1997). Adults
of both species return to their natal streams and rivers
across two or more ages (e.g., as 4–5-year-olds), but the
proportion at each age is not constant across years,
thereby creating a challenge for forecasting total
abundances. Furthermore, juvenile sockeye salmon rear
in lakes for 1 or 2 years before migrating to the ocean;
thus, the number of years spent in freshwater (i.e., before
ocean entry) varies. Ages of sockeye salmon and chum
salmon are designated as x.y, where x is the number of
winters spent in freshwater and y is the number of
winters spent in the ocean. The chum salmon stocks
evaluated in this analysis mainly consisted of ages 0.2,
0.3, and 0.4 (Table 1), while the sockeye salmon stocks
mainly consisted of ages 1.1, 1.2, 1.3, 2.1, 2.2, and 2.3
(Table 2). The sibling model forecasts the abundance of
adult recruits of a given age returning in year t from the
abundance of the previous adult age-class that returned
in year t ! 1. By using data on such siblings from the
same brood year that also spend the same number of
winters in freshwater (but one less winter in salt water),
the sibling model takes advantage of the covariation in
response to critical environmental influences that these
age-groups of fish share during their early life stages
(Peterman et al. 1998; Pyper et al. 2002, 2005).
Nevertheless, there are examples of naı̈ve time series
models outperforming sibling models (Noakes et al.
1990; Wood et al. 1997). In this context, naı̈ve models
are those that do not require statistical parameter
estimation but rather simply summarize past observations to make forecasts. For example, naı̈ve models
could be based on average recruitment over the
previous 5 years or the prior year’s recruits. Recently,
some biologists have adopted hybrid approaches that
use both sibling and naı̈ve models for forecasting the
age-specific components of salmon returns (Eggers
2003). However, there is little guidance on when to use
a sibling model, a naı̈ve model, or a hybrid approach.
634
635
MANAGEMENT BRIEF
TABLE 1.—Chum salmon stocks used in a comparison of recruit abundance models (abbreviations used in figures are in
parentheses), number of years of data available for estimation (n), number of years forecasted (nf), ages that could and could not
be forecasted using a sibling model, and variance thresholds that achieved the minimum root mean squared error (RMSEmin) for
each stock.
Ages
Chum salmon stock
Washington
Willapa (WIL)
Grays Harbour (GRH)
Skagit (SKA)
Nooksack (NOK)
Stillaguamish (STI)
Hood Canal (HC)
South sound–fall (SSF)
South sound–early (SSE)
South sound–winter (SSW)
British Columbia
Fraser total (FTO)
Fraser inner (FIN)
Area 8 (A8)
Area 6 (A6)
Alaska
Prince William Sound (PWS)
Nushagak (NUS)
Togiak (TOG)
Yukon (YUK)
Anvik (ANV)
Andreafsky (ADR)
Kwiniuk (KWI)
Kotzebue (KOT)
Non-sibling
Thresholds achieving
RMSEmin
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
7.27–7.30
2.68–2.74
0.00–1.06
0.44–0.88
1.54–1.55
0.00–1.42
0.55–0.56
0.00–1.46
0.49–0.50
0.3,
0.3,
0.3,
0.3,
0.4
0.4
0.4
0.4
0.2
0.2
0.2
0.2
0.64
1.14–10.00
0.84
0.92–1.01
0.3,
0.3,
0.3,
0.3,
0.3,
0.3,
0.3,
0.3,
0.4,
0.4,
0.4,
0.4,
0.4,
0.4,
0.4,
0.4,
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
6.53–6.58
0.73
0.00–0.28
0.30
0.51–0.58
0.84–10.00
0.74
0.29–10.00
n
nf
27
24
30
30
30
30
30
29
29
16
11
16
16
16
16
16
16
16
0.3,
0.3,
0.3,
0.3,
0.3,
0.3,
0.3,
0.3,
0.3,
35
35
21
17
24
24
11
7
29
21
19
22
22
24
31
19
18
8
5
10
10
12
19
8
To improve the accuracy of preseason forecasts for
chum salmon and sockeye salmon, we retrospectively
evaluated the performance of a hybrid model that used
the sibling model when sibling relations were strong
(small residual variation) and a naı̈ve model when
sibling relations were weak (large residual variation).
We developed quantitative criteria for determining
whether to use a sibling model or a naı̈ve model for
generating a forecast in a particular year, stock, and
age-stanza. Finally, we compared the performance of
this hybrid sibling model with that of both the standard
sibling model and a naı̈ve model to determine whether
the hybrid model improves upon existing methods for
forecasting chum salmon and sockeye salmon returns.
Methods
Data.—We analyzed previously compiled data on
age-specific recruitment of 21 chum salmon stocks and
37 sockeye salmon stocks in the northeast Pacific
Ocean, distributed from northwestern Alaska to
northwestern Washington and including British Columbia (Tables 1, 2). Abundances of recruits included
both catch and spawning escapement of both sexes.
The time series ranged in duration from 17 to 50 years;
the average was 26 years for chum salmon stocks
within the period 1962–1998 and 43 years for sockeye
salmon stocks within the period 1951–2001. Further
Sibling
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
details on sources and derivation of data can be found
in Peterman et al. (1998), Mueter et al. (2002), and
Pyper et al. (2002).
Forecasting models.—The sibling model (Peterman
1982) assumes a linear relation between raw abundances of two sibling groups in log space,
loge ðRd;t Þ ¼ a þ bloge ðRc;t!1 Þ þ et ;
ð1Þ
where Rd,t is the abundance of the later-returning
siblings of age d in year t, Rc,t!1 is the abundance of the
earlier-returning siblings of age c in year t ! 1 (where c
¼ d ! 1), a and b are estimated parameters, and et
;N(0, r2e ). This form of error term is based on the
frequently observed multiplicative lognormal variation
of marine survival rates of salmon (Peterman 1981).
Because of the occasional presence of zeros in the agespecific return data, a constant of 1 was added to the
Rd,t and Rc,t!1 observations to allow for logarithms.
The linear regressions were fit using maximum
likelihood estimation, minimizing the error sum of
squares. We did our analyses for both chum salmon
and sockeye salmon using data series aligned such that
the later and earlier returns (Rd,t and Rc,t!1) spent the
same number of winters in freshwater but the earlier
returns spent one winter less in salt water and thus
returned 1 year earlier. For instance, one sibling model
for sockeye salmon reflected the relation between
636
HAESEKER ET AL.
TABLE 2.—Sockeye salmon stocks used in a comparison of recruit abundance models (abbreviations used in figures are in
parentheses), number of years of data available for estimation (n), number of years forecasted (nf), ages that could and could not
be forecasted using a sibling model, and variance thresholds that achieved the minimum root mean squared error (RMSEmin) for
each stock.
Ages
Sockeye salmon stock
Washington
Lake Washington (LWA)
British Columbia
Adams (ADA)
Birkenhead (BIR)
Bowron (BOW)
Chilko (CHL)
Cultus (CUL)
Gates (GAT)
Horsefly (HOR)
Nadina (NAD)
Pitt (PIT)
Portage (POR)
Raft (RAF)
Seymour (SEY)
Stellako (STO)
Stuart–early (STE)
Stuart–late (STL)
Weaver (WEA)
Long Lake (LOL)
Skeena (SKE)
Nass (NAS)
Alaska
Copper (COP)
Cook (COK)
Ayakulik (AYA)
Frazer (FRA)
Early Upper Station (EUS)
Late Upper Station (LUS)
Black (BLA)
Chignik (CHI)
Branch (BRA)
Egegik (EGE)
Igushik (IGU)
Kvichak (KVI)
Naknek (NAK)
Nuyakuk (NUY)
Togiak (TOG)
Ugashik (UGA)
Wood (WOD)
n
nf
27
15
1.2, 1.3
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
21
46
26
37
37
37
37
37
35
37
37
37
33
37
37
37
37
37
37
8
26
15
1.2,
1.2,
1.2,
1.2,
1.2,
1.2,
1.2,
1.2,
1.2,
1.2,
1.2,
1.2,
1.2,
1.2,
1.2,
1.2,
1.3
1.2,
1.3,
1.3,
1.3,
1.3
1.3,
1.3,
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.3
35
31
30
30
26
26
48
48
45
45
45
45
45
32
45
45
45
23
15
19
19
15
14
34
34
30
30
30
30
30
17
30
30
30
1.2,
1.2,
1.2,
1.2,
1.2,
1.2,
1.2,
1.2,
1.2,
1.2,
1.3,
1.2,
1.2,
1.3,
1.3,
1.2,
1.2,
1.3,
1.3,
1.3,
1.3,
1.3,
1.3,
1.3,
1.3,
1.3,
1.3,
1.4,
1.3,
1.3,
1.4,
2.3
1.3,
1.3,
Sibling
1.1
2.2
2.2, 2.3
2.2, 2.3
2.2
1.3
2.3
abundances in ages 1.2 and 1.3. The model was
parameterized using data from numerous brood years
for which both sibling groups had already returned and
for which abundances were estimated. Generating
^ &d;t ) based on equation (1)
forecasts of adult recruits (R
required back-transformation to estimate the forecasted
mean number of recruits on the arithmetic scale.
Accounting for the well-known bias associated with
back-transforming lognormally distributed variables
(Hayes et al. 1994), forecasts were generated using
the equation
!
"
^ 2e
r
&
^
^
;
Rd;t ¼ exp Rd;t þ
2
Non-sibling
ð2Þ
1.4,
1.4,
2.2,
2.2,
2.2,
2.2,
1.4,
1.4,
2.2,
1.4,
2.3
2.2,
1.4,
2.3
2.2,
2.2,
2.3
2.3
2.3
2.3
2.2,
2.2,
2.3
2.2,
2.3
2.3
2.3
2.3
2.3
2.3
2.2, 2.3
1.4, 2.2, 2.3
1.4, 2.2, 2.3
Thresholds achieving
RMSEmin
1.42
1.1,
1.1,
1.1
1.1,
1.1,
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.2,
1.1
1.2,
2.1
2.1
0.3,
0.3,
0.3,
1.1,
0.3,
0.3,
1.1,
1.1,
1.1,
0.3,
0.3,
1.1,
1.1,
0.3,
0.3,
0.3,
0.3,
1.1,
1.1,
1.1,
2.1
1.1,
1.1,
2.1
2.1
2.1
1.1,
1.2,
2.1
2.1
1.2,
1.2,
1.1,
1.1,
2.1
2.1
2.3, 3.1
2.2
2.1
2.1
2.1, 3.2
2.1
2.1
2.1, 3.2
2.2
2.2
2.2
2.1
2.1
0.88
0.79–0.80
0.43
4.14–4.31
0.54
2.57–2.58
8.31–8.41
2.50–2.51
0.96–10.00
2.98
0.00–0.19
0.00–0.86
0.44
1.18
3.32
0.46–0.65
0.47–10.00
0.38
0.48–0.49
0.69
0.58
2.36–2.41
1.86–1.99
0.48–0.49
0.62
0.88
3.39–3.49
2.21–2.30
9.24–9.26
2.42–2.57
4.18–4.27
1.05–10.00
2.41–10.00
0.54
2.36–2.38
6.73–6.75
^ & is the forecast of the mean number of age-d
where R
d;t
^ 2e is
recruits in year t, R̂d,t is the estimate of Rd,t and r
the variance of the residuals estimated from fitting
equation (1).
The sibling model can be used to make forecasts for
older age-classes that have younger siblings, but other
methods must be used to forecast abundance of ageclasses for which no data exist on abundance of
younger siblings. For example, if a stock is composed
of ages 1.1, 1.2, and 2.1, a sibling model can be used to
forecast the abundance of age-1.2 returns based on the
age-1.1 returns from the previous year, but other
methods would have to be used to estimate the
abundance of age-1.1 and age-2.1 returns. To forecast
the total annual abundance of returns, some method is
MANAGEMENT BRIEF
necessary to generate a forecast for all age-classes in a
given return year. In practice, stock–recruit relations
and naı̈ve time series models (e.g., long-term averages)
have been used to forecast those age-classes that cannot
be forecasted using sibling models (Wood et al. 1997;
Eggers 2003). To forecast such age-classes, we used a
naı̈ve time series model referred to as R(yr ! 4):
Rd;yr ¼ Rd;yr!4 þ wyr ;
ð3Þ
where Rd,yr is the abundance of age-d fish returning in
year yr, Rd,yr!4 is the abundance of age-d fish in year yr
! 4, and wyr ;N(0, r2w ). In an initial exploratory
analysis that compared retrospective model performance for various naı̈ve models, the R(yr ! 4) model
typically matched or outperformed other naı̈ve models.
For sockeye salmon, the root mean square error
(RMSE) of the forecasts was on average 29% greater
for the R(yr ! 3) model than the R(yr ! 4) model and
28% greater for the R(yr ! 5) model than the R(yr ! 4)
model. For chum salmon, the RMSE of the forecasts
was on average 12% greater for the R(yr ! 3) model
than the R(yr ! 4) model and 23% greater for the R(yr
! 5) model than the R(yr ! 4) model. Because this
model does not assume lognormal errors, no backtransformation (e.g., equation 2) was required when
making forecasts.
In our preliminary research that used retrospective
analyses (described below), we observed that the
sibling model had smaller forecasting errors than the
R(yr ! 4) model when the estimated sibling relations
were strong (i.e., characterized by high coefficient of
determination [R2] values and low mean square error or
^ 2e ). However, when sibling relations
residual variance, r
were weak, the R(yr ! 4) model often performed better
than the standard sibling model. These observations
provided the rationale for developing the hybrid model
that used a sibling model when the sibling relation was
strong for a particular stock and age-stanza but used a
naı̈ve R(yr ! 4) model when the sibling relation was
weak. Our derivation of the hybrid sibling model
involved determining the optimal quantitative criteria
for strong sibling relations (i.e., when to choose one
model over the other).
We used retrospective analysis to evaluate performance of the standard sibling model, the hybrid sibling
model, and the naı̈ve R(yr ! 4) model. In this
retrospective analysis, we attempted to simulate the
implementation of the modeling approaches as if they
had been implemented historically. That is, only the
data that would have been available to make a forecast
for some past year were used to estimate model
parameters and generate the forecast of total adult
returns across ages for that year. Each sibling
637
regression based initial parameter estimates on the first
10 years of data. By sequentially adding a year to the
data set used for parameter estimation, generating a
forecast, and comparing the forecast with the observed
value, our retrospective analysis produced a time series
of forecasting errors for each model. This method
produced ‘‘out-of-sample’’ forecasts, thereby providing
a rigorous assessment of each forecasting model’s
performance as if it had been used historically. We
^ 2e (in units of
calculated the variance of the residuals, r
loge[fish]2), for the loge!loge relation in equation (1)
and assessed model performance based on the RMSE
of the forecasts of total adult recruits. One advantage of
using RMSE as the performance metric is that errors
are expressed in the same units as the response variable
(i.e., in numbers of fish). The number of years for
which abundances were forecasted varied among
stocks, ranging from 5 to 37 years (average ¼ 14 years
for chum salmon stocks, 29 years for sockeye salmon
stocks; Tables 1, 2). In total, 295 stock-years were
forecasted for chum salmon and 1,080 stock-years
were forecasted for sockeye salmon.
^ 2e estimated
For the hybrid sibling model, we used r
for each year and age-stanza during the retrospective
analysis to determine whether to use the naı̈ve R(yr !
4) model or the sibling model to make the age-specific
forecasts for the subsequent year. If the most recent
estimated residual variance for an age-stanza was
below a threshold, then the sibling model was used to
generate the forecast of abundance for that stanza’s
predicted age-class in the next year. If the residual
variance estimate was above that threshold, then the
naı̈ve R(yr ! 4) model was used to generate the
forecast. For each stock, we examined thresholds for
^ 2e ranging from 0 to 10 in increments of 0.01 and
r
calculated the RMSE of the resulting forecasts
associated with each threshold. The same variance
threshold was used for all age-stanzas for a given stock.
For example, if (1) the residual variance for the 1.2
versus 1.3 age-stanza in a given year of the
retrospective analysis was 0.8 and the residual variance
for the 1.3 versus 1.4 age-stanza was 1.7 and (2) we
were evaluating a residual variance threshold of 1.5,
then the sibling model would be used to forecast the
abundance of age-1.3 fish and the naı̈ve R(yr ! 4)
model would be used to forecast the age-1.4 fish
abundance for that particular stock and year. We
defined the optimum threshold for each stock as that
which minimized the RMSE of forecasts for that stock.
In contrast, we used two criteria to determine which
threshold for residual variance was optimal across all
stocks within a species for sockeye salmon and chum
salmon. We developed these criteria in an effort to
derive a forecasting method that could be applicable
638
HAESEKER ET AL.
FIGURE 1.—The sum of relative root mean square errors (RMSEs; solid line) and the number of stocks (count) within 10% of
their minimum RMSEs (dashed line) across candidates for the variance threshold in a hybrid sibling model of chum salmon
^ 2e .
recruit abundance. The vertical dashed line denotes the resulting optimum variance threshold, r
generally to sockeye salmon and chum salmon and that
would not be limited to only those stocks considered in
this analysis. First, for each stock, we calculated the
relative RMSE as follows:
Relative RMSEi ¼ RMSEi =RMSEmin ;
ð4Þ
where RMSEi is the RMSE of the hybrid sibling model
using threshold value i and RMSEmin is the minimum
RMSE across all threshold values explored for that
stock. To determine the appropriate residual variance
threshold across stocks within each species, we
summed the relative RMSE values across all stocks.
For a given species, the best threshold was defined as
the one that minimized the sum of the relative RMSE
values across stocks within a species. Because the
profiles of this ‘‘relative RMSE sum’’ across thresholds
did not always have well-defined minima (Figures 1,
2), we developed a second criterion that counted the
number of stocks for which the RMSEi was within
10% of the RMSEmin. The threshold that maximized
this count was judged to be best for this criterion.
Results
For chum salmon stocks, the sum of relative RMSEs
was minimized at variance thresholds of 1.08 and 1.09,
but it was nearly as low for a wide range of candidate
thresholds from 0.5 to 7.5 (Figure 1). The count of
stocks within 10% of their stock-specific RMSEmin was
maximized with candidate thresholds of 1.08–1.16
(Figure 1). Therefore, we judged 1.08 and 1.09 to be
appropriate thresholds for use in the hybrid sibling
model across chum salmon stocks because both
objective functions were met with these values. We
also determined the stock-specific optimum thresholds
(i.e., those candidate thresholds that, when applied to
all age-stanzas, achieved RMSEmin; Table 1). In some
stocks, a wide range of thresholds gave almost the
same RMSEmin.
For sockeye salmon stocks, the minimum sum of
relative RMSEs was better defined; candidate variance
thresholds of 0.7–3.0 resulted in the lowest values
(Figure 2). While the minimum was achieved with a
candidate threshold of 2.41, values from 2.40 to 2.54
were within 1% of the minimum. The count of stocks
within 10% of their stock-specific RMSEmin was
maximized with candidate thresholds of 2.31–2.34,
2.38–2.39, and 2.53–2.54 (Figure 2). Because the
threshold of 2.53 maximized the count of stocks within
10% of RMSEmin and also achieved a near-minimal
sum of relative RMSEs, we judged it to be an
appropriate threshold for use in the hybrid sibling
model across sockeye salmon stocks. However, stockspecific optimum thresholds for sockeye salmon varied
considerably among stocks (Table 2).
Using general thresholds of 1.09 for chum salmon
and 2.53 for sockeye salmon, we found that switching
between the sibling model and the naı̈ve R(yr ! 4)
model during the time series occurred in 16% of the
age-stanzas for sockeye salmon and 18% of the agestanzas for chum salmon. Thus, for the majority of age-
639
MANAGEMENT BRIEF
FIGURE 2.—The sum of relative root mean square errors (RMSEs; solid line) and the number of stocks (count) within 10% of
their minimum RMSEs (dashed line) across candidates for the variance threshold in a hybrid sibling model of sockeye salmon
^ 2e .
recruit abundance. The vertical dashed line denotes the resulting optimum variance threshold, r
stanzas (84% for sockeye salmon, 82% for chum
salmon), the model chosen at the onset of the time
series was used throughout the time series. Therefore,
the thresholds generally determine at the onset whether
a sibling model or a naı̈ve model should be used for a
particular age-stanza, although switching between
models during the time series based on changes in
the residual variance does occur.
We compared the RMSEs for four cases: the
standard sibling model, the hybrid sibling model using
the general across-stock thresholds as determined
above, the hybrid sibling model using the stockspecific optimum thresholds (Tables 1, 2), and the
naı̈ve R(yr ! 4) model. The general hybrid sibling
model with a threshold of 1.09 for chum salmon and
2.53 for sockeye salmon performed the same as or
better than (i.e., had a lower RMSE) the standard
sibling model in 20 of 21 chum salmon stocks (Figure
3) and 33 of 37 sockeye salmon stocks (Figures 4, 5).
On average, the general hybrid sibling model reduced
the RMSE by 27% for chum salmon stocks and 28%
for sockeye salmon stocks relative to the standard
sibling model. The naı̈ve R(yr ! 4) model had an
average RMSE reduction of 10% compared with the
standard sibling model for chum salmon stocks and a
reduction of 9% compared with the standard sibling
model for sockeye salmon stocks. The naı̈ve R(yr ! 4)
model performed as well as or better than the standard
sibling model in 13 of 21 chum salmon stocks and 19
of 37 sockeye salmon stocks. Compared with the naı̈ve
R(yr ! 4) model, the general hybrid sibling model
reduced the RMSE by 16% on average for chum
salmon and by 15% for sockeye salmon; the general
hybrid model performed as well as or better than the
naı̈ve R(yr ! 4) model in 18 of 21 chum salmon stocks
and 30 of 37 sockeye salmon stocks. Finally, use of the
hybrid model with stock-specific optimal thresholds
(rather than the across-stock optimal values) improved
the hybrid model RMSE by a further 5% on average for
chum salmon and 8% for sockeye salmon.
Discussion
We have proposed quantitative criteria for an
algorithm to decide for each year whether to use a
sibling model rather than a naı̈ve model to generate
preseason forecasts when data to estimate sibling
relations are available. Our findings suggest that there
are cases when sibling relations are uninformative for
generating forecasts of a given age-class due to the
model’s large previous residual variance; in those
situations, it may be prudent to use a naı̈ve time series
model to forecast that age-class. In several chum
salmon and sockeye salmon stocks, much of this
unexplained variance was due to estimates of zero
returns for particular age-classes. However, our
findings also suggest that there are cases when the
sibling relations are highly informative and should
therefore be used. Using our criteria for thresholds in
residual variance of the general sibling model, the
RMSE of forecasts from the hybrid sibling model was
640
HAESEKER ET AL.
FIGURE 3.—Root mean square error (RMSE) values for the naı̈ve model, general hybrid sibling model, and stock-specific
hybrid sibling model of chum salmon recruit abundance; each RMSE value is divided by the RMSE for the standard sibling
model. The horizontal line at 1.0 represents the RMSE for the standard sibling model; therefore, models with values below that
line made better forecasts.
less than or equal to that of the standard sibling model
for 53 of the 58 stocks analyzed. The RMSE of the
naı̈ve R(yr ! 4) model was lower than that of the
general hybrid sibling model in only 10 of the 58
stocks analyzed. These results suggest that there is little
chance of degrading forecasts by adopting the general
hybrid sibling model instead of the standard sibling
model or the naı̈ve R(yr ! 4) model.
FIGURE 4.—Root mean square error (RMSE) values for the naı̈ve model, general hybrid sibling model, and stock-specific
hybrid sibling model of sockeye salmon recruit abundance in stocks from Lake Washington and British Columbia (see Table 2
for stock code descriptions); each RMSE value is divided by the RMSE for the standard sibling model. The horizontal line at 1.0
represents the RMSE for the standard sibling model; therefore, models with values below that line made better forecasts.
MANAGEMENT BRIEF
641
FIGURE 5.—Root mean square error (RMSE) values for the naı̈ve model, general hybrid sibling model, and stock-specific
hybrid sibling model of sockeye salmon recruit abundance in Alaska (see Table 2 for stock code descriptions); each RMSE value
is divided by the RMSE for the standard sibling model. The horizontal line at 1.0 represents the RMSE for the standard sibling
model; therefore, models with values below that line made better forecasts.
Although additional reduction in RMSE can be
achieved by using stock-specific optimal thresholds
within the hybrid sibling model for the stocks listed,
the average improvement in RMSE over the speciesspecific hybrid sibling model is only 5–8% on average.
This result supports the view that the optimal acrossstock variance thresholds determined here (1.09 for
chum salmon; 2.53 for sockeye salmon) could be used
to generate forecasts of abundance for stocks not
included in this analysis and that those species-specific
thresholds represent a reasonable trade-off between
generality across stocks in the northeastern Pacific
Ocean and accuracy for individual stocks. However, if
it is feasible, stock-specific values should be derived by
analysts for their stocks of interest. We also investigated using optimized age-stanza-specific variance
thresholds but found little improvement in precision
of forecasts over the across-stanza variance thresholds.
Variability and uncertainty in escapement, reproduction, freshwater survival, and marine survival all
contribute to the difficulty of making accurate
preseason forecasts of salmon returns (Fried and Yuen
1987). Forecasts based on stock–recruitment models
are typically fitted from data on escapement and adult
returns, which include all of these sources of error. The
advantage of sibling models (Alaska Department of
Fish and Game 1981; Peterman 1982; Bocking and
Peterman 1988) is that many of these sources of error
are avoided by using age-specific return data in
successive years; the relative abundances of different
adult age-classes have already been largely determined
by the demographic factors listed above during periods
when siblings that mature at different ages share
common environmental conditions. The only exception
is marine survival during the last year of life.
Despite these intuitive reasons why standard sibling
models should perform well, they do not always
outperform stock–recruitment-based forecasting models or naı̈ve models, perhaps due to inaccuracies in the
age-specific return data, inherently weak sibling
relations, or temporally changing parameters of
component relations (Noakes et al. 1990; Wood et al.
1997; Holt and Peterman 2004). In such cases, naı̈ve
time series models (e.g., moving averages or lagged
returns) can outperform sibling models as well as other
forecasting methods (Noakes et al. 1990; Haeseker et
al. 2005; S.L.H., unpublished data). Because the hybrid
sibling model examined here includes both types of
models, it can perform better across stocks and agestanzas than either model alone.
While the hybrid sibling model presented shows
some promise for improving the accuracy of preseason
forecasts for chum salmon and sockeye salmon,
considerable uncertainty remains. Recognizing this
642
HAESEKER ET AL.
uncertainty, a precautionary approach to managing
chum and sockeye salmon stocks is warranted (FAO
1995). Implementing a precautionary approach would
involve explicit accounting of the uncertain components of a fishery system, including the large
uncertainties in preseason forecasts of abundance,
when evaluating fishing regulation options. Appropriate adjustments to early-season fishing plans can be
determined through consideration of such uncertainties
by means of risk assessments or decision analyses (e.g.,
Robb and Peterman 1998).
Acknowledgments
We thank the numerous biologists and technicians in
various management agencies for gathering and
processing the lengthy time series data used here and
providing them to us. This research was supported by
the Natural Sciences and Engineering Research
Council of Canada.
References
Adkison, M. D., and R. M. Peterman. 2000. Predictability of
Bristol Bay, Alaska, sockeye salmon returns one to four
years in the future. North American Journal of Fisheries
Management 20:69–80.
Alaska Department of Fish and Game. 1981. Preliminary
forecasts and projections for 1981 Alaskan salmon
fisheries. Alaska Department of Fish and Game, Division
of Commercial Fisheries, Informational Leaflet 190,
Juneau.
Bocking, R. C., and R. M. Peterman. 1988. Preseason
forecasts of sockeye salmon (Oncorhynchus nerka):
comparison of methods and economic considerations.
Canadian Journal of Fisheries and Aquatic Sciences
45:1346–1354.
Bradford, M. J. 1995. Comparative review of Pacific salmon
survival rates. Canadian Journal of Fisheries and Aquatic
Sciences 52:1327–1338.
Eggers, D. M. 1993. Robust harvest policies for Pacific
salmon fisheries. Pages 85–106 in G. Kruse, D. M.
Eggers, R. J. Marasco, C. Pautzke, and T. J. Quinn II,
editors. Proceedings of the International Symposium on
Management Strategies for Exploited Fish Populations.
Alaska Sea Grant College Program, Report 93–02,
University of Alaska, Fairbanks.
Eggers, D. M. 2003. Run forecasts and harvest projections for
2003 Alaska salmon fisheries and review of the 2002
season. Alaska Department of Fish and Game, Regional
Information Report 5J03–01, Juneau.
FAO (Food and Agricultural Organization of the United
Nations). 1995. Precautionary approach to fisheries. Part
1. Guidelines on the precautionary approach to capture
fisheries and species introductions. FAO Fisheries
Technical Paper 350/1. Available: www.fao.org/
DOCREP/003/V8045E/V8045E00.htm. (April 2007)
Fried, S. M., and H. J. Yuen. 1987. Forecasting salmon returns
to Bristol Bay, Alaska: a review and critique of methods.
Pages 273–27 in H. D. Smith, L. Margolis, and C. C.
Wood, editors. Sockeye salmon (Oncorhynchus nerka)
population biology and future management. Canadian
Special Publication of Fisheries and Aquatic Sciences 96.
Haeseker, S. L., R. M. Peterman, Z. Su, and C. C. Wood.
2005. Retrospective evaluation of pre-season forecasting
models for pink salmon. North American Journal of
Fisheries Management 25:897–918.
Holt, C. A., and R. M. Peterman. 2004. Long-term trends in
age-specific recruitment of sockeye salmon (Oncorhynchus nerka) in a changing environment. Canadian
Journal of Fisheries and Aquatic Sciences 61:2455–2470.
Mueter, F. J., R. M. Peterman, and B. J. Pyper. 2002. Opposite
effects of ocean temperature on survival rates of 120
stocks of Pacific salmon (Oncorhynchus spp.) in northern
and southern areas. Canadian Journal of Fisheries and
Aquatic Sciences 59:456–463. (Errata. Canadian Journal
of Fisheries and Aquatic Sciences 60:757).
Noakes, D. J., D. W. Welch, M. Henderson, and E. Mansfield.
1990. A comparison of preseason forecasting methods
for returns of two British Columbia sockeye salmon
stocks. North American Journal of Fisheries Management 10:46–57.
Peterman, R. M. 1981. Form of random variation in salmon
smolt-to-adult relations and its influence on production
estimates. Canadian Journal of Fisheries and Aquatic
Sciences 38:1113–1119.
Peterman, R. M. 1982. Model of salmon age structure and its
use in preseason forecasting and studies of marine
survival. Canadian Journal of Fisheries and Aquatic
Sciences 39:1444–1452.
Peterman, R. M. 1987. Review of the components of
recruitment of Pacific salmon. Pages 417–429 in M.
Dadswell, R. J. Klauda, C. M. Moffitt, R. L. Saunders,
R. A. Rulifson, and J. E. Cooper, editors. Common
strategies of anadromous and catadromous fishes.
American Fisheries Society, Symposium 1, Bethesda,
Maryland.
Peterman, R. M., B. J. Pyper, M. F. Lapointe, M. D. Adkison,
and C. J. Walters. 1998. Patterns of covariation in
survival rates of British Columbian and Alaskan sockeye
salmon (Oncorhynchus nerka) stocks. Canadian Journal
of Fisheries and Aquatic Sciences 55:2503–2517.
Pyper, B. J., F. J. Mueter, and R. M. Peterman. 2005. Acrossspecies comparisons of spatial scales of environmental
effects on survival rates of Northeast Pacific salmon.
Transactions of the American Fisheries Society 134:86–
104.
Pyper, B. J., F. J. Mueter, R. M. Peterman, D. J. Blackbourn,
and C. C. Wood. 2002. Spatial covariation in survival
rates of Northeast Pacific chum salmon. Transactions of
the American Fisheries Society 131:343–363.
Robb, C. A., and R. M. Peterman. 1998. Application of
Bayesian decision analysis to management of a sockeye
salmon (Oncorhynchus nerka) fishery. Canadian Journal
of Fisheries and Aquatic Sciences 55:86–98.
Wood, C. C., D. T. Rutherford, D. Peacock, S. Cox-Rogers,
and L. Jantz. 1997. Assessment of recruitment forecasting methods for major sockeye and pink salmon stocks in
northern British Columbia. Canadian Technical Report of
Fisheries and Aquatic Sciences 2187.