A simulation model to investigate the potential effects of marine and freshwater fisheries on the Thompson River

steelhead trout population (Oncorhynchus mykiss)

Robert Bison

Fish & Wildlife Branch, BC Ministry of Environment, Kamloops, BC, V2C 5Z5

August 8, 2007

Abstract: A simulation model was designed to monitor trends in fishing mortality as well as

gain insight on the cumulative effects of fisheries that sequentially intercept the interior Fraser

River steelhead population along its migration routes. The model uses well-known algorithms to

determine cumulative losses due to immediate and latent fishing mortality effects. As input, the

model uses effort data for the largest commercial, native and sport fisheries. Fishery parameters

are based on salmon catch records and/or steelhead observer programs. Published information on

steelhead and salmon biology, abundance data from field surveys, environmental records, results

from tagging programs, and expert advice were used to determine the most likely values and the

bounds of all parameters. Simulations are conducted using actual records of fishing schedules,

and corresponding levels of effort, and sets of hypotheses concerning migration patterns for

1992-2006. Simulation results obtained under deterministic conditions indicate that exploitation

rate declined considerably during 1994-2000, but has increased since then. Concurrent

abundance trends are suggesting that abundance may be continuing to decline despite

management efforts to date. For the most recent years, simulations results that account for some

well-known sources of uncertainty show considerable variation in the plausible range of fishing

effects. In light of such findings, and the low escapement levels observed in recent years, it

seems advisable to seek opportunities to ensure that steelhead exploitation is reduced and

remains low so as to stem further decline in abundance and foster a rebuilding of the stock. The

model limitations are identified and recommendations are given on how to improve its

performance given the seemingly unavoidable data gaps concerning fishery effects on this

relatively small stock from the Fraser River.

1. Introduction

Steelhead that spawn in the Thompson River and its tributaries are considered as a

‘summer run’ population because they enter the Fraser River as immature fish during August-

November (Anon. 1998). They approach the Fraser River using marine migration patterns that

overlap with those of salmon species, and are intercepted by commercial net fisheries targeting

salmon along the way. In recent years, increased conservation concerns over the state of the

Fraser River summer runs lead the British Columbia Ministry of Environment (MoE)1 and the

Canadian Department of Fisheries & Oceans (DFO) to develop and implement fishery

management plans to reduce the steelhead by-catch. Initially, this was achieved through time

and area restrictions. More recently this has been attempted by reducing handling mortality in

gillnet and seine fisheries that have been reintroduced onto the mid and later portion of the

steelhead run.

While considerable efforts have been made to improve the quality and quantity of data on

the composition and abundance of steelhead populations that spawn in the Thompson River

tributaries (collectively referred to as the Thompson River steelhead), data on exploitation

patterns in marine waters is scarce, fragmented, and incomplete, with potential biases difficult to

quantify. Anon. (1998) summarized the existing data, and provided preliminary figures on

catches in the major gillnet and seine interception fisheries at Nitinat, Johnstone Strait, Juan de

Fuca Strait, the Fraser River mouth, and in US waters of Juan de Fuca Strait and north Puget

Sound. Steelhead catches in commercial fisheries are generally less than those of other salmon

species caught simultaneously. And unlike major salmon production releases, most steelhead

stocks are not routinely coded-wire tagged (CWT), or systematically sampled in commercial

landings for physical and biological markers. Consequently, there are very few scientifically

defensible catch estimates for most interception fisheries, which preclude the rigorous

application of the conventional stock-assessment procedures as commonly used to determine

exploitation rates on Pacific salmon stocks.

1 During 1996-2005, management of provincial fisheries was conducted by staff of the BC Ministry of Air, Water and Land Protection (WALP)

2

No rigorous monitoring program has been implemented to determine the overall effect of

marine and fresh water fisheries on Fraser River steelhead populations since the implementation

of the non-retention policy in 2002. Granted, implementing a scientifically credible, coast-wide

steelhead catch monitoring program for this purpose may be hard to justify, given the costs

involved, the low catches of steelhead relative to salmon in salmon fisheries, the absence of

steelhead landing statistics, and the difficulty of obtaining reliable estimates of gear induced

mortalities once steelhead are released.

To improve this state of affairs, a harvest simulation model was developed to provide a

method of monitoring relative trends in fishing induced mortality as well as provide some insight

on the ‘plausible’ level of fishing mortality on steelhead that spawn in the Fraser River

tributaries upstream of Hell’s Gate (collectively termed the interior Fraser River steelhead

stocks). The computational framework of this simulation model (termed ‘simulator’ in the

following sections) is partly based on those developed to manage Fraser River sockeye fisheries

(Cave and Gazey 1994), and Skeena River fisheries that intercept sockeye, coho and steelhead

(Cox-Rogers 1994).

In this relatively ‘data-poor’ context, most of the steelhead-specific estimates of

exploitation and gear-specific mortality required to parameterize the simulation model are

characterized by considerable uncertainty, or are simply not available. When parameter values

are lacking, investigators often rely on information from ‘meta-analyses’ (Fernandez-Duke and

Valeggia 1994), which involves combining parameter estimates from similar species and under

similar contexts. And for Bayesian analyses, when reliable priors are lacking, investigators often

rely on ‘expert-based’ priors, which involves combining and weighting the opinions of several

experts (see Morris 1977). For the present study, the ‘missing’ parameter values were determined

through similar approaches which involved (i) obtaining pertinent figures from the literature, (ii)

deriving these (if necessary) from available ones for co-migrating salmon species given

similarities in behavior and morphology, and (iii) requesting the opinions of biologists and

fishery scientists with considerable knowledge on the issues when doubt remained after the first

two steps, so as to pinpoint the most plausible mode and range of parameter values.

3

The simulator uses information obtained via the above process, in conjunction with the

actual fishery openings schedules, corresponding fishing effort levels, environmental conditions,

and survey records with regard to run timing and migration rates to provide deterministic indices

of relative exploitation rates separately for each year of interest. Obviously, one would expect

some variation in the baseline parameter values used given annual changes in exploitation

patterns, run timing, environmental conditions, fishing practices, and gear adjustments. The

simulator allows users to explore the effects of some parameter variation on the predictions. The

simulator was not used to quantify the combined impacts of a wide spectrum of parameters

subject to variation, or describe the plausible impacts associated with a multitude of scenarios

that could possibly occur in the future. But the effects of variation in some ‘key’ parameters are

explored via Monte Carlo simulations for the post-2002 fishing seasons because of the additional

uncertainty associated with the non-retention policy (must account for mortalities after release).

The results presented will show that the simulator is an investigative tool that can assist

with the determination of data collection priorities, help gain better insight on the likely effect of

the fisheries, and help gain better insight on how the overall fishing mortality rate is trending

from year to year.

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2. Symbols and notation a, b generic regression coefficients d 24 h interval corresponding to a specific calendar day f single gear fishery operating in a DFO or US fishing region, during a certain period k group of fish (or block) that migrate together during a period t time interval of a specified size (context specific) Cfdk catch in fishery f, obtained during day d, from block k D last calendar day of the fishing season E fishing effort in a single fishery and single day context Efd fishing effort deployed in fishery f, day d Ffdk instantaneous rate of fishing mortality applied by fishery f, during day d, on block k Nfdk number of fish available to fishery f, at the beginning of day d, from block k NDk number of fish alive on the last day of the fishing season, in block k ND+1 total escapement after the entire fishing season, all blocks combined N average abundance, between the start and the end of a period NE number of fish exposed to fishing NC number of fish not exposed to fishing N0 population size at the start of the fishing season N’0 number of fish that enter Georgia Strait through the northern route N”0 number of fish that enter Georgia Strait through the southern route Rfdk removals (deaths) caused by fishery f, during day d, on block k SD survival rate after D days Td water temperature (oC), day d Uf exploitation rate of fishery f on the total population

fkd average migration date (calendar day) through fishery f, by block k h harvest rate on fish in a single fishery and single day context hfdk harvest rate of fishery f, day d, on block k q catchability coefficient for a single fishery in a single day context qf catchability coefficient for fishery f rfk residence period (in days) in fishery f, for block k mfd migration rate (km·d-1) through fishery f, day d mfdk migration rate (km·d-1) through fishery f, day d, for block k u elemental harvest rate in a single fishery and single day context ufdk elemental harvest rate of fishery f, day d, on block k σfk standard deviation of the run time distribution (in days), through fishery f, for block k θf average mortality rate per encounter, in fishery f (immediate + subsequent deaths) θfd mortality rate per encounter, by fishery f, on day d (immediate + subsequent deaths) ε random error from a specified distribution Λ diversion rate, or portion of the total steelhead population that enters Georgia Strait through Johnstone Strait Rand() function that produces a random value from a specified distribution given a variable

5

3. Description of the simulator components

3.1 Model structure

Cave and Gazey (1994) described a procedure used to reconstruct sockeye stock sizes at

various times during a fishing season, starting with abundance levels on spawning grounds, and

recursively updating abundances backwards in time/space based on catch and effort of fisheries

that intercept sockeye along their migration. Once the population sizes have been reconstructed

prior to their entry into each fishery, and fishery-specific harvest rates have been estimated,

forward projections of expected catches are made given a sequence of fishery openings to assess

the effects on various fishery management scenarios.

The simulator is a simpler version of that described by Cave and Gazey (1994). It does

not (and cannot) reconstruct population sizes because (i) historical steelhead catch records are

unreliable and (ii) fishing effort acting on steelhead is unlikely to be identical to that on the

salmon species targeted due to differences in spatial migration patterns. The simulator simply

computes expected steelhead catches using the algorithm of Cave and Gazey (1994) using

fishery-specific harvest rate estimates for other salmon stocks in the same fisheries, and

hypothesized combinations of gear-specific mortality rates and migration patterns. The simulator

does not determine the best combination of parameters, but can be used to determine the

plausible effects of a set of hypotheses (like alternative fishing schedules), and determine data

collection priorities for future evaluations.

3.2 Movement model

An algorithm is required to account for the movement of the population through the

fisheries it traverses on its way to the spawning grounds. During the summer-fall, interior Fraser

River steelhead stocks move through several marine and fresh water fisheries before reaching the

spawning grounds during the fall. There are about 27 fisheries in southern BC that can intercept

steelhead, but previous surveys indicate that only some of these have a substantial impact on the

interior Fraser River stocks. The major marine fisheries (Fig. 1) take place between the mid

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Fraser River and the entrances to Strait of Georgia, starting at Cape Caution on the north-east

coast of Vancouver Island above Johnstone Strait (Area 11), and off Nitinat on the south-west

coast of Vancouver Island near Juan de Fuca Strait (Area 21).

The terminology proposed by Cave and Gazey (1994) is used to describe how the

simulator accounts for steelhead movement. All steelhead that move through a fishery on a given

day are collectively referred to as a ‘block’. Successive blocks moving through a fishery (a

unique combination of fishing region and gear) can be thought of as railroad cars moving past a

train station, which explains the term ‘boxcar model’ often used to describe this modeling

approach. All fish in a block are considered to be equally susceptible to harvest in the fishery

they move through. The definition helps distinguish the impact of a fishery on a block (harvest

rate) from its impact on the entire population (exploitation rate).

Fraser River steelhead return via Johnstone Strait (northern route) or via Juan de Fuca

Strait (southern route). During the mid-1980s, Parkinson (1984) noted that Thompson River

steelhead used mainly the southern route, while those from the Chilcotin River used mainly the

northern route. The term ‘diversion rate’ denotes the percentage of the total population using the

northern entrance. This rate still cannot be forecasted with certainty before each fishing season,

so sensitivity analyses are conducted to determine its influence on steelhead exploitation rates.

Given a known or hypothesized diversion rate, the population returning to the Fraser River must

first be split into groups that enter through each route;

(1) Λ= 0'0 NN

(2) '00

"0 NNN −=

It is often assumed that salmon run timing through a region or fishery conforms to a

normal distribution (Cave and Gazey 1994, Hilborn et al. 1999). The same assumption is made

here. Given two groups (N’0, N”0) heading to Georgia Strait, the simulator first determines the

numbers available for capture on day (d) in the first fisheries encountered.

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(3) ⎥⎥⎦

⎤

⎢⎢⎣

⎡ −−= 2

2'0

2)(

exp2 fk

fk

fkfdk

ddNN

σπσ for d>0, k = 1 to x, f = 1

(4) ⎥⎥⎦

⎤

⎢⎢⎣

⎡ −−= 2

2"0

2)(

exp2 fk

fk

fkfdk

ddNN

σπσ for d>0, k = x+1 to K, f ≠ 1

Since N’0 and N”0 are split into distinct and uniquely numbered blocks, that move

through uniquely numbered fisheries, the is no further need for superscripts (‘ and “) when

referring to blocks, so these are omitted from now on for purposes of clarity.

Run timing distribution parameters ( fkfkd σ, ) are based on test-fishery records collected

at Albion above the Fraser River mouth (Bison and Ahrens, 2003). These figures, used in

conjunction with published estimates of steelhead migration rates, provide approximate dates of

entry and passage times through the first two fisheries encountered (in Areas 12 and 21).

Examination of past observer based catch records for these fisheries supports that the

approximate dates are realistic. Passage times through these and other fisheries subsequently

encountered are determined using migration rates.

Migrating steelhead travel about 17.0 km·d-1 in marine waters (Ruggerone et al. 1990). In

freshwater, migration rates tend to vary according to river temperature (Renn et al. 2001). Over

a typical range of river temperatures during the freshwater migration period, for example at

temperatures of 18, 12, and 6oC, the respective migration rates computed by a regression

relationship are 29, 17, and 6 km·d-1. These estimates are similar to those from tagging

programs on Skeena River steelhead and coho (Lough 1981, Spence 1989, Koski et al. 1995).

The freshwater migration rate is also similar to that of chum salmon in the Fraser River

(Anderson and Beacham 1983). No evidence has been found to support the notion that steelhead

may hold in areas at sea or in the Fraser River mouth. However, the simulator adjusts the

freshwater migration rate using water temperature records, according to the radio-telemetry

results obtained by Renn et al. (2001). The fishery-specific migration rates used to determine the

next block locations are

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(5) marine fisheries (f = 1 to x) 10.17 −⋅= dkmmfd

(6) in-river fisheries (f = x+1 to F) 1)1358.5875.1( −⋅−= dkmTm dfd

As in Cave and Gazey (1994), the movement model is used to express space in units of

time, so the length of each fishing region is described by the time required for a species to travel

though. Eq. 5-6 also serves to move steelhead through regions with no fishing activity. The

simulator simply sets fishing effort to zero, so no depletion occurs when blocks move through.

3.3 Exploitation model

Gulland (1983) relates catch, average abundance, harvest rate, fishing effort and gear

catchability such that EqNhNC == . When the exploitation period can be split into short

intervals (≤1d), and the catch is taken over a portion of each interval, there is no need to account

for the average abundance. And in the absence of natural mortality, the catch can be computed

from the abundance at the start of the interval (Hilborn and Walters 1992, p. 360)

(7) fdkfdkfdkfdkfdkfdk qENhNC ==

All gear-induced mortalities are assumed to occur shortly after capture or release, and

before the next day, due to greater susceptibility to predation, accumulated stress, physiological

problems (scale loss), or progressive loss of blood. The simulator keeps track of all block

removals (i.e losses), the survivors, the overall exploitation rates, and the total escapement via

(8) fdfdkfdk CR θ=

(9) fdkfdkkdf RNN −=+ )1( if fd+1 = fd

(10) fdkfdkkdf RNN −=++ )1(1 if fd+1 ≠ fd

(11) for all k impacted by f ∑∑= =

=D

d

K

kfdkf RR

1 1

9

(12) 0N

RU f

f =

(13) ∑=

++ =K

kkDD NN

1,11

3.4 Computational adjustments

The movement and exploitation models described in the preceding sections form the

basic bookkeeping procedure of the simulator. However, two additional refinements are required

to apply the boxcar model algorithms in the current context. First, Cave and Gazey (1994)

forecast fishery-specific catches using harvest rate estimates obtained via the stock

reconstruction procedure. Some of their published equations were found to be typographically

incorrect, so the correct forms and derivations are given in the Appendix (Section 1). Irrespective

of this minor finding, the authors decompose the harvest rate h because they hypothesize that a

block (NE) that enters or leaves an area during a fishing period is subject to a lower harvest rate

than a block (NC) that remains in an area for the entire fishing period. The authors define an

elementary harvest rate (u) for partially exposed blocks, to distinguish it from the harvest rate h

acting on fully exposed blocks (see Appendix, Section 2 for derivations).

Many find this concept confusing (W. Gazey, pers. comm.), so an illustration is provided

to help the reader visualize the process (see Appendix, Section 3). Given that steelhead and

sockeye can move through some fisheries in 1 d, the simulator uses elementary harvest rates to

compute catches in 1 d time steps. The relation between fishing effort, catchability rates, harvest

rates, and elementary harvest rates is

(14) fdkfdkfdkfdk qEhu −−=−−= 1111

Cave and Gazey (1994) account for changes in vessel distribution during a sockeye

fishery opening. The authors apply context-specific relations between fishing effort and

catchability. When catchability increases linearly with effort, Eq. 14 holds since (u = qE). But for

some fisheries, catchability seems to be limited by effort saturation (u = a + bLn(E)), so the

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simulator substitutes Efdkqfdk by (af + bfLn(Efdk)) in Eq. 14, using the scaled fishery-specific

catchability coefficients (bf) published in annual reports.

A second adjustment is required because the average population size (as in Eq. 7) during

fishing periods >1 d is rarely known. Usually, the size of the population before a fishery opening

is estimated through some analytical procedure, and the instantaneous form of the catch equation

is used given a corresponding rate of instantaneous fishing mortality. In the absence of natural

mortality during short fishing periods (<1d), the standard equation reduces to

(15) ( )fdkFfdkfdk eNC −−= 1

As in Cox-Rogers (1994), the simulator uses Eq. 15 instead of Eq. 7 to compute daily

catches. For this purposes, it makes the necessary conversions between ufdk and hfdk, (or Efdkqfdk)

before computing the rightmost component of Eq. 15 (see Appendix, Section 4 for derivations).

Before doing the conversion, the simulator uses either a steelhead elementary harvest rate

derived from the estimate for a salmon species in the same stratum (fishery/period), or the

fishing effort level combined with a steelhead catchability derived from an estimate for a salmon

species in the same stratum.

Since all steelhead released are thought to be subject to ‘delayed’ mortality, with perhaps

a substantial, fishery-independent, over-wintering mortality after passing through the ‘terminal’

Thompson River sport fishery, the simulator uses Eq. 8 to compute all block removals and

update the block sizes for purposes of consistency.

To help the reader visualize the sequential application of the simulator functions, Fig. 2

provides the pseudo-code used for the initialization, distribution, movement, depletion and

computation of fishery impacts of steelhead populations moving through the marine and fresh

water fisheries on their way up to the over-wintering and spawning grounds.

4. Parameter values and sources

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The effort levels, elemental harvest rates and catchability coefficients used to compute

the net fishery catches are given in Tables 1-2. Fisheries thought to have minor or unquantifiable

impacts are not listed and not used to simulate recent fishery impacts. These include traditionally

important ones such as gillnet and seine fisheries in Area 21, gillnet fisheries in Areas 4b-5-6c,

the lower Fraser River sport, and First Nation fisheries upstream of Sawmill Creek.

The major data sources used include the results of sockeye exploitation assessments (Hill

et al. 2000), sockeye run reconstruction results (Cave and Gazey 1994), published information on

movement patterns of steelhead, sockeye and chum salmon, test-fishing statistics and observer

records. What follows is a description of the procedures and justifications used to determine the

exploitation and mortality parameters.

4.1 Exploitation parameters

4.1.1 Sport fisheries

The simulator accounts for the impacts of the major sport fishery in the Thompson River.

For lack of sufficient data, the simulator does not account for the incidental catches of steelhead

by anglers in marine waters and the lower Fraser although these fisheries are considered to have

negligible effects. The Thompson River sport fishery has been rigorously monitored for over 20

years, and is the last (or ‘terminal’) major fishery before steelhead reach their over-wintering and

spawning grounds. This fishery has been subject to catch-and-release restrictions since the late

1980’s. It used to be open by the time steelhead arrived, and was traditionally closed on

December 31. Steelhead could be caught as soon as they entered the Thompson River. Observed

catches (i.e. fish hooked/released) correlate well with escapement levels each year (Morris and

Bison 2004), with slightly higher catch-to-escapement ratios in years of reduced flows and

turbidity levels (Renn and Bison 2002).

Total angler catches are generally estimated using roving survey methods (Renn & Bison

2001). Post-season angler reports are also solicited annually by the BC Fish & Wildlife Branch.

The figures reported are corrected for well-known reporting biases before the final catches are

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estimated (DeGisi 1999). For seasons when no roving surveys were conducted, catches are

computed based on regressions of previous roving surveys figures against previous post-season

angler survey figures. Since total catches (and releases) are estimated directly, the simulator does

not compute catches using elementary harvest rates, as for other fisheries.

4.1.2 Set-net fisheries

In the lower Fraser River between Sawmill Creek and Agassiz, there are aboriginal

fisheries using set-nets (or stationary gillnets). The effectiveness of this gear is related to the

morphology and swimming speed of the species caught. It is thought to be lower for steelhead

than for sockeye because the former is larger and less readily gilled by nets with non-optimal

mesh size. This assumption is supported by analyses of gillnet selectivity patterns for sockeye

(Jim Cave, PSC, pers., comm.). For simulation purposes, set-nets are assumed to be ≈40% less

effective at catching steelhead than sockeye, because the mesh size commonly used for sockeye

fishing (5.75 in., 14.61 cm) is smaller than the most effective size for steelhead (6.75 in., 17.15

cm) in the size range captured (≈ 68-80 cm orbital-fork length). This assumption is considered

‘plausible’ (J. Cave, PSC, pers. comm.). Lower effectiveness is accounted for by first setting the

steelhead elementary harvest rate to 60% of the sockeye estimate in same fisheries.

With regards to swimming speed, when nets are deployed in areas requiring >1 d to move

through, the fastest swimming species should get caught in more nets than slower ones. Sockeye

tend to travel faster than steelhead in fresh water (Renn et al. 2001). If sockeye travel twice as

fast as steelhead, the elementary harvest rates for steelhead is 0.106 when that of sockeye is 0.2.

The proof given in Appendix (Section 5) is based on the hypothesis that sockeye swim twice as

fast as steelhead. This is not always the case since steelhead migration rates are adjusted for

water temperatures, so the simulator adjusts the coefficient (b of Eq. 5.7) during the simulations

given the ratio of swimming speeds between the two species in the fisheries traversed and the

water temperatures at such times.

For in-river net fisheries above Mission that occur during the chum salmon fishing season

(Table 2, categories 16-18), far fewer nets are deployed than during the sockeye fishing season.

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Consequently, the derived harvest rates are further adjusted for those periods to account for the

reduced effort. This is accomplished by multiplying the derived harvest rate by chum/sockeye

fishing effort ratio. Typically, during the chum fishery, fishing effort is about 10-20% of that

during the sockeye fishery, so the multiplicative factor (fishing effort ratio) that is determined

dynamically by the simulator during each simulation is about ≈ 0.1-0.2.

4.1.3 Area 29 fisheries

For late season commercial and drift gillnet fisheries (after Sept. 20), sockeye estimates

of elementary harvest rates cannot be used as they apply to fleet sizes much larger than those

intercepting steelhead. So steelhead catchability figures are derived from those estimated for

chum salmon.

The lower Fraser River test-fishing records are considered to be accurate and reliable.

These were used with escapement records (Tables 3-4) and hypothesized movement patterns to

determine the catchability coefficients for both species in the test-fishery, using the procedure

described by Bison and Ahrens (2003). The authors assumed that test-fishery catches are subject

to random variation (escapements are accurate), and that movement conforms to the model

described by Hilborn et al. (1999). Given a normally distributed run timing, a total run size, and

an error structure for variation in test-fishery catches, Bison and Ahrens (2003) compute the

number of fish moving past the test-fishing area each day, the daily catch time series, and the

overall gillnet catchability rate. Based on the fits obtained and the distribution of residuals, the

pseudo-Poisson error assumption was rejected. Results obtained using a lognormal error

structure showed good fit to non-zero catches, but the predicted run timing variance was

unrealistically large. Given a normal error structure, sets with no steelhead catches could be used

to compute the fits which were better, so this error structure was preferred. Since then, the error

models in the original likelihood functions were substituted by the Poisson and the Negative

Binomial (for testing purposes), and the Poisson error structure produced better fits between the

predicted and observed values than all other error structures (see Bison 2006 for likelihood

function). Consequently, this procedure was used to conduct the simulations described here.

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Maximum likelihood estimates of peak migration dates past Albion, standard deviation in

run timing, and catchability were generated for both species. Predicted tends conformed fairly

well to the observed catch trends (Fig. 3), and the average catchability for steelhead was found to

be ≈3.2 times greater than for chum (Table 5). This could be viewed as support for the

hypothesis that chum are less susceptible to capture in the lower Fraser River gillnet fisheries

because they swim closer to the bottom relative to steelhead (J.O. Thomas & Assoc. 1997, 1998)

and are less vulnerable to gillnets when fishermen tend to avoid sweeping the bottom of the river

for fear of snagging on submerged debris. Other hypotheses (size or behavior differences) might

also explain the results, but even if this was the case, the test fishery catch-to-escapement ratios

for both species indicate that steelhead catchability tends to be greater than that of chum salmon.

The 3.2:1 catchability ratio applies only to the test-fishery. For the commercial gillnet

fishery, an overall daily catchability rate for chum salmon was determined using the gillnet catch

and effort time series obtained at the peak of the chum run through Area 29 over 1990-2003. In

1998, a federally sponsored ‘buy-back program’ reduced the fleet size. It is not known if this

changed the composition and effectiveness of the fleet, so estimates of daily catchability rates

were generated for each period separately (pre/post 1998) by linearly regressing daily harvest

rates against fishing effort (in boats). The best fitting chum catchability rates were 0.0010 for the

first period, and 0.0014 for the later. Multiplying these by 3.2 translates into steelhead

catchability rates of 0.0032 and 0.0045 respectively.

Given these coefficients, and total escapements and run timing estimates based on the

Albion test-fishery data, commercial catches were computed for some Area 29 openings subject

to catch monitoring by observers (Table 6). Chum catches based on the two catchability rates

were 49-93% of observed catches for the first period, 71% during the second, and 71% over both

periods. For steelhead, the figures are 70-93%, 134%, and 98% over both periods. Despite some

discrepancy, the comparison to observed catches suggests that the approach is useful in

estimating the magnitude of the catch. From a steelhead catch estimation perspective, this is

encouraging given that conventional catch reporting is often biased to a degree where it is of

little practical use.

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Starting in 2002, the lower Fraser gillnet fishery changed, with a reduction in net length

and soaking period. To account for changes in nominal effort (the area·time covered by a set),

both catchability rates are linearly adjusted for changes in the nominal effort ratio (pre-post

2002). For example, if shorter nets are used (100 fathoms instead of 200), the baseline

catchability is reduced by half before the simulator computes catches.

4.1.4 Area 21 fisheries

Fishing vessels in this area target mainly chum salmon returning to the hatchery during

October as they aggregate near the Nitinat River mouth. There used to be a sizeable by-catch of

steelhead and coho that transit through this area during the fishing period. These two species stay

further offshore than chum and are subject to different harvest rates (Anonymous 1996, Bison

1992). For these fisheries, overall catchability rates for steelhead could not be derived from those

estimated for other species.

For lack of a better alternative, a fishery-specific elementary harvest rate for the gillnet

fishery was determined based on a standard run-reconstruction method using the 1989 observer

program results. Given a spawning population of 2200 steelhead, and accounting for sequential

losses thought the fisheries ‘backward over time’, the size of the population that entered the Area

21 fishery was determined under the following hypotheses; (i) a fixed harvest rate of 30% in all

‘upstream fisheries’, established based on a review of the exploitation indices for that period, (ii)

a 20% diversion rate (Parkinson 1984), and (iii) an interior Fraser stock contribution to Area 21

catches of 80% (Beacham et al. 1999). The fixed harvest rate figure was determined based on

crude catch and escapements figures for the mid-1980s that indicated harvest rates of about 60%,

which declined to <25% by 1993 according to the simulation results obtained with the present

model. On this basis, the fixed harvest rate was arbitrarily set to 30%. Having reconstructed the

abundances prior to the fishery, forward projections were done to determine catches in the Area

21 fishery over a range of harvest rates. For u = 0.1, the predicted and observed catches where

very similar to the observed catch in 1989 (Table 7).

16

In 1996, the Nitinat gillnet fishing was limited to near-shore areas to minimize steelhead

and coho interception further offshore. In 1998, the southern part of the fishing area was closed

to reduce impacts on steelhead and coho that aggregate there. The fishery opening was delayed

until October 1, beyond the historical peak migration period of Interior Fraser steelhead. Total

fishing effort decreased to about 80% of what it was in the early 1990’s, largely due to

unfavorable economic conditions (low prices, higher fuel costs, etc.). This fishery was largely

reduced since 1999, so for subsequent seasons, the Area 21 GN fishery harvest rates were

considered to be negligible, and are not accounted for by the model.

4.2 Induced mortality

Fishery-specific mortality impacts account for deaths when the fishing gear is retrieved,

plus subsequent ones caused by injuries and handling stress after release. For gillnet fisheries,

the figures used are largely based on observer records (Table 8). For commercial gillnet sets

operated in a traditional manner (i.e. without operational adjustments intended to reduce

mortality rates of bycatch), about half of the steelhead tend to die before retrieval. There are no

standard figures on losses due to predation while the nets are soaking. Predation losses are highly

variable, and often related to net handling practices. In the absence of survey data, average losses

due to predation cannot be quantified with certainty, so no effort was made to account for them

in the simulations.

Concerning post-release mortalities from gillnet fishing, some radio-telemetry studies

(Anonymous 1992, Renn et al. 2001) showed that steelhead caught and released in brackish

waters (estuaries) are subject to higher mortality than those released in marine or fresh water

environments. During the 1990’s, new gillnet fishing practices were established to reduce by-

catch mortality (assuming full compliance). For estuary sets, revival boxes and short set times

were shown to reduce gillnet mortality for coho (Farrell et al. 2001) if implemented effectively.

For gillnet fishing operations conducted in this manner, Winther (in prep) found that coho

mortality was about 26% after being held for 24 h. The author found that mortality increased

with fish size (0% for <45 cm, to 80% for >70 cm), because smaller fish were not close to the

optimal size of capture for the mesh used. Based on figures reported in the literature and

17

discussions with regional biologists having experience in salmon tagging operations, it is

assumed that traditional, commercial gillnet fishing practices induce, on average, about 80%

mortality on the steelhead intercepted (all fishing locations combined). For First Nation gillnet

fisheries, mortality is assumed to be 100%, because historically, there were no incentives to

release steelhead in those fisheries.

Adjustments to mortality rates to account for improved gillnet fishing practices were

provided by DFO staff and based on information compiled several years ago for a wide range of

conditions (see Anon. 2001, 2002b). For Areas 12 and 20, the pre-1995 mortality rates of 80%

are reduced to 50% for later years to account for the effects of new release regulations for by-

catch species and stricter catch monitoring programs (Table 9). For Area 21, mortality rates are

reduced over 1994-98 for the same reason. For the Area 29 commercial fishery, mortality rates

are reduced in 1998 and 2000 to account for the effects of shorter soak periods and the

mandatory use of revival tanks. For US fisheries (Areas 7-7a), mortality rates are reduced

gradually during 1994-98 due to the implementation of practices to decrease by-catch,

particularly of Puget Sound coho. For the aboriginal drift net fisheries, it is assumed that

mortality rates are lower in 1993 and 1999, because of improved handling practices and greater

awareness of stock conservation issues.

With regards to purse seine catches, Winther (in prep) found that mortality of chinook

held for 24 h was inversely related to fish size, and ranged from ≈70% for <45 cm fish, to ≈18%

for 70-100 cm fish. This suggests that mortality is lower for mature fish. Winther (in prep) found

much lower mortality rates for coho. Radio-tagging operations conducted by Spence (1989) and

Koski et al. (1995) showed mortality rates of about 30% for steelhead caught by purse seine

vessels near the Skeena River mouth during the peak migration period. For radio-tagged coho,

Koski et al. (1995) observed mortality rates of about 45%. Fraser River sockeye were also

subject to radio-tagging operations like those described by Koski et al. (1995) and Spence

(1989). Early-run sockeye mortality after release was 65% in 2002, and 54% in 2003 (English et

al. 2004). Mortality rates tended to decrease as the season progressed; reaching 25% in 2002, and

33% in 2003 for late-run sockeye. Mortality rates of sockeye tagged with acoustic devices late in

the season was only 19%.

18

Salmon mortality induced by seining operations is generally considered to be a function

of the specific gear used and the catch retrieval method. Since 2000, brailing has been mandatory

in Canadian seine fisheries, even in the south coast. In the DFO fishing areas 3 & 4 (near Prince

Rupert), surveys have shown that brailing induces about 5-10% mortality, whereas ramping can

be ≈30% (S. Cox-Rogers, DFO, pers. comm.). These figures are considered as minimal rates,

since they account only for short term mortalities (died on board), and not for deaths after

release. In principle, steelhead radio-tagging operations (Koski et al. 1995) can account for death

after release, and provide better estimates of mortality. However, even those estimates may be

biased due to the potential effects of tag regurgitation, tag malfunction, straying, losses due to

predation, and fish selection (only fish that survive and are in top condition are radio-tagged).

Furthermore, anecdotal reports suggest that in the absence of observers or taggers, brailing is

generally done with less care, so the immediate and post release mortality rates are likely higher

than observed under ideal conditions.

Steelhead mortality rates induced by marine purse seine fisheries were therefore set based

on such considerations, and discussions with several regional fisheries scientists (DFO, MoE).

For US fisheries where brailing is not common practice, the average induced mortality was set to

30%, with the lower and upper bounds being 20% and 40% respectively (distributions specified

in following sections). For Canadian commercial seine fisheries, the average induced mortality

was set to 20% with the lower and upper bounds being 10% and 40% respectively (Table 9).

Steelhead mortality caused by angling activities has been estimated on many occasions

during hatchery broodstock collection operations conducted using gear and catch-and-release

practices as commonly used by anglers (Anonymous 1998). Mortality-per-encounter was

estimated to average ≈3% (range: 0.3-5.1%) for operations conducted in the Chilliwack,

Thompson, Coquihalla and Squamish rivers. Some experts believe such figures are obtained

under ideal conditions, and are not representative of fishing periods involving many non-

experienced anglers and gear types. In a subsequent review of the Thompson River sport fishery,

Labelle (2004) accounted for the mortality induced by different gear types (bait, lure, and flies),

effort levels by angler category, and multiple recaptures. His simulation results indicated that

19

overall mortality induced by catch and release operations were about 5.4% (range: 4-7%), but

decreased to 5.1% (range: 3.7-6.6%) from 2003 onwards with the implementation of fishery

closure during October 1-15. This level of mortality affects only steelhead that are available to

anglers during the fishing period. Telemetry studies indicate that a considerable portion of the

population (20-30%) can move past the fishing areas prior to, or after the sport fishing season

(Renn et al. 2001). Consequently, the above figures are thought to be slightly greater than the

actual impact of this fishery on the escapements. So for modelling purposes, the lower bounds,

means and upper bounds of the mortality were respectively set to 3%, 4.4% and 6% for years

prior to 2003, and 2.7%, 4.1% and 5.6% for all years since then.

5. Monte Carlo simulations

For stochastic projections (years 2004, 2005 and 2006), the simulator uses values that can

vary according to some distribution. Sometimes, the expert opinions solicited diverged

considerably as to which distribution was most suitable. This is not surprising since there is little

empirical data to identify the best distribution systematically. So final decisions were

occasionally based on various considerations that include; does a certain distribution provide the

random variates needed (continuous vs. discrete), can it serve to provide a most plausible value

and associated bounds, are all parameter values equally likely (uniform vs. non-uniform), is the

distribution likely skewed (symmetrical vs. asymmetrical), could some values be <0 (log-normal

vs. others), and etc. After a ‘suitable’ set of distributions was selected, computations are made

for each combination of randomly chosen parameter values. The parameters allowed to vary

were (i) the peak date of arrival at the northern tip of Vancouver Island, (ii) the standard

deviation of run timing, (iii) the diversion rate, (iv) the migration rate in marine waters, (v) the

migration rate in fresh water above and below Hope, (vi) the gear catchability, and (vii) the gear-

specific mortality. The justifications for selecting the particular distributions to account for

patterns of variation are given below, with details summarized in Table 10.

5.1 Variation in run timing

20

The historical run timing patterns derived from test-fishery catches at Mission (Table 11),

suggest that the peak of the steelhead run can be as much as two weeks earlier than average in

some years, or up to 3 weeks later than average in others. The Weibull distribution was used to

represent this positively skewed run timing patterns (Fig. 4). The peak arrival date for a

particular realization of the fishery is taken as a random deviate from this distribution under the

assumption there is no within-season variation. The average standard deviation in run timing is

also closer to the minimum estimate that to the maximum estimate, so the variation in the

standard deviation of run time is also assume to conform to a Weibull distribution.

5.2 Variation in diversion rate

The impacts of the marine fisheries are influenced by the diversion rate. This rate is

thought to be highly variable and cannot be predicted before the season. There is no evidence to

indicate that all steelhead ever enter the Strait of Georgia through a single passage. In light of

such facts, a platykurtic Beta distribution is used to generate random deviates of diversion rates

for each fishery realization under the assumption there is no within-season variation. Given

parameter values of α = 1.7, β = 1.7 and scale = 1.0, this distribution has a nearly semi-circular

form (Fig. 5). The greatest probability is associated with a diversion rate of 0.5. Lower

probabilities are associated with diversion rate of 0.3-0.7, and zero probabilities of obtaining

extreme diversion rates (0.0, 1.0).

5.3 Variation in migration rate

Instead of using a constant [baseline] marine migration rate of 17 km·d-1, the marine rate

is represented by a random deviate from a normal distribution with a mean of 17, and a standard

deviation of 0.6 (Fig. 6). A unique random value is generated for each fishery realization. The

middle 95% percentile range of such a distribution of random values is ≈ 15.5-18.5 km·d-1, which

amounts to ±1.5 km·d-1 or ± 9% of the baseline rate. The average migration rate used within each

realization is subject to additional stochasticity to allow each block to migrate through a fishery

at a slightly different rate during the same fishery realization. For this purpose, a series of

21

random error values (εfdk) are taken from a uniform distribution with the bounds being ±10% of

the baseline rate. Block-specific daily migration rates in marine waters are thus obtained from

(14) fdkfdfdk mRandm ε+= )(

Daily fresh water migration rates are adjusted for water temperatures, which allows for

variation in migration rates between days and seasons. Further stochastic variation is allowed

under the assumption that block movements do not always conform to that predicted by the

physiological-temperature model. For each day, a random error variate (εfdk) is obtained from a

uniform distribution with bounds that are ±5% of the daily migration rate obtained with Eq. 6.

Block-specific daily migration rates in fresh water are thus obtained from

(15) fdkfdfdk mm ε+=

5.4 Variation in gear catchability

Catchability of purse seine and gillnet gears are allowed to vary during the fishing

periods within each realization, as if there is small day-to-day or set-to-set variation. Purse seine

catchability is assumed to be more variable than that of gillnets. For purse seines fisheries,

catchability variation is modeled by multiplying an elementary harvest rate by a random variate

from a uniform distribution with bounds 0.8-1.2, so the adjusted daily harvest rates are within

±20% of the elementary rates. For gillnet fisheries, the same approach is used, with the bounds

being 0.9 and 1.1, so the adjusted daily harvest rates are within ±10% of the elementary rates.

5.5 Variation in mortality

For some fisheries, the most reasonable figure proposed tended to be closer to lower

bound (best conditions), than the upper (exceptionally bad conditions). Consequently, the

distribution of mortality rates is represented by a Beta distribution, parameterized to have a

22

skewed profile for some fisheries, and a symmetrical profile for others. Stochastic simulations

were conducted for years 2004-2006, so distributions chosen reflect the implementation of

improved fishing practices. For the Area 12 gillnet fishery, the most plausible mortality was set

to 0.5, with the bounds being 0.3-0.8 (Fig. 7). This set of distribution parameters is denoted as

(0.3, 0.5, 0.8). As noted earlier, purse seine fisheries are thought to cause less mortality that

gillnet fisheries, for the Area 12 PS fishery, the distribution parameters were (0.2, 0.3, 0.4). The

set of parameters for the other fisheries; Area 13 PS (0.2, 0.3, 0.4), Area 13 GN (0.3, 0.5, 0.8),

Area 21 PS (0.2, 0.3, 0.4), Area 21 GN (0.3, 0.5, 0.8), Area 20 PS (0.2, 0.3, 0.4), Area 7 Native

PS (0.4, 0.5, 0.6), Area 7 non-Native PS (0.4, 0.5, 0.6), Area 7a Native PS (0.4, 0.5, 0.6), Area

29 GN (0.4, 0.6, 0.8), Area 29 to Port-Mann Aboriginal Driftnet AD (0.8, 0.9, 1.0), Port-Mann to

Mission GN (0.4, 0.6, 0.8), Port-Mann to Mission AD (0.8, 0.9, 1.0), and Aboriginal SN from

Mission to Hope were set to 1.0 (no substantial variation implied). For the sport fishery, the

mortality induced by catch-and-release activities represented by a Beta distribution with

parameters (0.027, 0.041, 2.0 and 2.1) for an average mortality rate of 4.1% since 2003.

The above figures account for US PS fisheries induced slightly greater mortalities than

Canadian ones, and that aboriginal driftnet fisheries cause greater mortalities due to relatively

greater retention rates and immediate losses. For each realization, the fishery-specific rates are

allowed to vary independently from each other even if they have the same baseline parameter

values. Each fishery-specific rate is then subject to some additional stochastic variation since it

would likely not be constant throughout any given fishing period. This is achieved by taking a

random error variate (εf) from a uniform distribution with bounds of ±10% of the fishery-specific

rate. Omitting the subscript denoting a realization, the daily mortality rates are computed from

the fishery-specific rate, subject period-specific (within season) variation

(16) fdffd εθθ +=

5.6 Stochastic simulations for 2004-2006

Stochastic simulations are conducted only for the 2004-2006 fishing season because they

are the most recent, and the exploitation rates are the most uncertain given the assumed mortality

23

rate and harvest rate adjustments intended to account for improved fishing practices. Previous

exploratory analyses indicated that the overall exploitation rates were influenced by well-known

factors such as fishing effort levels, fishery opening schedules, diversion rates, peak migration

times, and fresh water temperatures that influence migration rates. So the inter-seasonal changes

in these conditions are described below to best interpret their combined impacts on the

simulation results, and the resulting changes in exploitation rates.

In terms of run timing, peak migration at Albion was latest in 2004, earliest in 2005, and

again later than average in 2006 (Oct. 22, 2 and 18 respectively), and consequently, so were the

peak arrival dates at the northern tip of Vancouver Island (Sept. 27, 8 and 25 respectively). The

run was much shorter in 2004 than during 2005-2006 (SD = 8.2, 13.0 and 21.0 d respectively).

Average water temperatures in the Fraser River from Sept. 1 to November 20 (main steelhead

run period) were substantially lower in 2004 than during 2005-2006 (10.2, 11.3, and 11.1 C

respectively). From 2004 to 2006, there were more fishing days in Area 12 (PS &GN), in area 13

(PS & GN), in Area 7-7A (PS & GN), in Area 29 (GN), in the aboriginal fishery (DN) from

Mission to Steveston, and in the set-net fishery from Mission to Sawmill Creek (Table 12). In all,

there were 137 daily net fishery openings during 2004, 175 in 2005, and 218 in 2006 during the

period of interior Fraser steelhead migration (Table 12). There was also a fishery opening in

Johnstone Strait during mid-September, 2005, but none in the other years.

o

The Monte Carlo simulations involved conducting 10,000 fishery realizations. The first

simulation was done with all-but-one stochastic process disabled. The second was done with all

stochastic processes enabled. This shows the singular effect of each variable on the overall

exploitation impact, and their combined effect under more realistic conditions (i.e, akin to doing

a sensitivity analysis).

6. Results

For the years since the recent implementation of the non-retention policy, simulations

were conducted with all stochastic processes enabled. The 2004 distribution of exploitation rates

24

had a mean of 20.0%, and a 95% inter-percentile range (or bounds) of ≈12-30%. For 2005, the

mean was 14.5%, with bounds of ≈9-21%. For 2006, the mean was 19.0%, with bounds of ≈10-

29%. This suggests that exploitation effects varied between years, and by as much as 30% (or ≈

5 percentage points) between 2005 and the two adjacent seasons (Fig. 8).

The number of fishery openings increased during 2004-2006, but the 2005 exploitation

rate was lower. Sensitivity analysis showed that the major determinants of exploitation rates in

2004 were the peak migration date and the spread of the run (Table 13). For 2005, peak

migration date was a distinctly important factor, but diversion rate and the marine migration rate

were also notable factors. For 2006, the spread of the run was a distinctly important factor.

The sensitivity analysis indicated that peak migration date was negatively correlated in

2004 and positively correlated in 2005 and 2006. This is the result of the timing of the run

relative to the timing of those fisheries having relatively large exploitation effects like the first

Area 12/13 chum fishery and the first Area 29 chum fishery. It is apparent that if the steelhead

peak date happens to occur late enough in the season, like in 2004, the peak of the run occurs on

or after the occurrence of the larger fisheries and their effect diminishes as peak migration date is

advanced. Under early or more average peak migration date scenarios, like 2004 and 2006

respectively, the correlation between peak migration date and exploitation rate is positive which

is consistent with the observation that most fisheries tend to occur during the later part of the

steelhead run when chum salmon are peaking in abundance.

The importance of the spread of the run in 2004 and 2006 is also a notable result. The

importance of this parameter is related to the later-than-average peak migration dates for those

years and the coinciding occurrence of the larger fisheries on those “blocks” containing

relatively large numbers of fish. Increasing the spread of the run diminishes the number of fish

in these blocks and since the fisheries having the larger exploitation effects are short in duration

(usually one day openings, e.g. Johnstone Strait seine), the reduced number of fish in these

blocks is quite pronounced and results in a reduction in the overall proportion of the run that is

subjected to fishing effects. The importance of the spread of the run in 2006 is especially large

because the value and variation in this parameter was largest in 2006 (Table 10). Whether this

25

parameter value was overestimated due to difficult test fishing conditions in 2006 is a possibility,

but remains a matter of speculation. It is interesting therefore to conduct the 2006 Monte Carlo

simulation using what may be a more realistic parameter value and variation for the spread of

run. If we conduct the 2006 Monte Carlo simulation using the 2005 values for this parameter,

spread of run remains the most important factor and remains negatively correlated with

exploitation rate, but the coefficient is lower at -0.63 which is similar to the result for 2004.

Interestingly, peak migration date increases in importance and ranks second with a coefficient of

0.37, again similar to the results for 2004. Mortality rates in Area 29 gillnet fishery also

increased in importance ranking third and fourth for the area downstream and upstream of Port

Mann, respectively indicating that there is potential for an increasing trend in the importance of

this fishery on steelhead exploitation in the future should future values for spread of run be less

than estimated for 2006.

The relative influence of strongly correlated factors is best viewed by manually adjusting

their corresponding values in the simulator (one at the time), and comparing the deterministic

outcomes (Table 14). For 2004, lower exploitation would have resulted from a more protracted

run, earlier peak run time, and lower purse seine fishing effort in Area 12. For 2005, lower

exploitation would result from an earlier run time, greater diversion rate, and greater marine

migration rates, perhaps because it could reduce the number of fisheries encountered. For 2006,

lower exploitation rates again would result from a more protracted run (as in 2004), lower gillnet

fishing effort in Area 29, and reduced sport fishing effort.

The deterministic simulation results obtained with a fixed diversion rate of 50% suggest

that relative exploitation rates decreased considerably during the 1990s, from >40% in 1994 to

<10% in 2000 (Fig. 9). The exploitation indices increased progressively since then to reach about

19% in 2006. Given that little information exists on steelhead diversion rate, it is fortunate that

this trend happens to be similar regardless of the diversion rate assumption used. Note that the

annual figures differ from those computed with all stochastic processes enabled, because they do

not account for the plausible variation of several factors operating simultaneously that can

influence the overall impacts via multiplicative effects.

26

The relative exploitation rates computed deterministically also exhibit year-to-year

variation, but suggest trends that are consistent with trends in fishing schedules. Third order

polynomials were fitted to the exploitation and corresponding escapement time series. The trends

show a progressive reduction in exploitation impacts during 1992-2001, but these have increased

since which is consistent with the earlier scheduling of fisheries during the month of October in

the lower Fraser River and in north Puget Sound. Escapement also decreased substantially up to

1999, remained relatively stable until 2004, and has been decreasing since then to reach the

lowest level observed historically.

7. Discussion

Ideally, for in-season fishery management purposes, it would be desirable to rely on a

fishery/stock assessment model, couched in a Bayesian framework that estimates key parameters

while keeping track of the accumulating losses during the season. Unfortunately, in this data-

poor context, there is too little information to apply an integrated assessment model. For lack of a

better alternative, the simulator was designed and used to monitor relative trends in fishing

induced mortality and the outcomes of fishery management plans by using information from

various sources. Obviously, the results depend on many assumptions about movement patterns,

gear-induced mortalities, fishery-specific catchability rates, and run timing patterns. If this

simulator is to be relied upon to provide fishery management guidelines while more

sophisticated procedures are being developed, it would seem desirable to focus attention on

reducing the sources of uncertainty.

Peak migration date at the northern tip of Vancouver Island and the spread of run stand

out as a major determinants of exploitation rates. Both parameters are derived from the Albion

test fishery data. Because the test fishery is located “upstream” of fisheries in the lower Fraser

River that affect the later segments of the steelhead runs, the peak migration date estimated from

test fishery data could be biased. In spite of this limitation, and in the absence of test fishery data

from interception fisheries in the two entrances to Georgia Strait, run timing data from the

Albion test fishery will continue to serve as a crucial source of data for the present model.

27

Although diversion rate consistently ranks among the more important factors determining

exploitation rate, the correlation coefficients in the sensitivity analysis are consistently much

smaller than the most dominant factors: peak migration date and spread of run. This is fortunate

since diversion rate is a parameter for which we admitted a large amount of uncertainty given

that little information exists about it. The simulation results imply that the effect and timing of

fisheries along both migration routes have been roughly similar, at least to date, and explains

why the deterministic trends in exploitation rate over time are similar regardless of the diversion

rate assumption used. This seems reasonable since almost all of the fisheries are targeting Fraser

chum salmon so fisheries which happen to have roughly similar cumulative exploitation effects

tend to be scheduled on roughly similar parts of the steelhead run regardless of the migration

route.

The results of deterministic simulations indicate that considerable progress was made

since 1992 to reduce the fishing mortality on the Thompson River steelhead population.

Unfortunately, the simulation results suggest that exploitation rates have increased lately. In

2004, the DFO determined that maximum exploitation [or induced mortality] on steelhead

should limited to 15%, while the MoE recommended that it be limited to 10%. The Integrated

Fisheries Management Plan of the DFO for Southern BC salmon stocks for June 2006 to May

2007 states that [for Canadian fisheries] “the objective for Interior Fraser River Steelhead is to

limit fishing mortality rates within Canada to recent year levels of less than 13%”. A substantial

portion of the simulated exploitation impacts exceeded this figure in 2004-2006. As noted

previously, the two sets of figures are not directly comparable. The simulation outputs are

exploitation rate indices, and are not absolute measures of exploitation rates or even genuine

estimates. However, they still provide a consistent index over the period of interest and when

linked to the escapement trends, they can assist in alerting managers to seek additional

opportunities to conserve steelhead in an attempt to reverse a declining trend in abundance in the

event that the abundance is below a target or limit reference point (Johnston et al. 2002).

During October 2006, the simulator structure and the results produced were subject to a

PSARC review. One of the major criticisms was that the simulator does not account for all the

28

underlying uncertainty of the system under study, including that associated with the harvest rate

estimates obtained from various sources. However, few bio-statistical models (if any) account for

all underlying uncertainties, since such models are by nature, simplified representations of reality

(see Brown and Rothery 1993). Even complex and detailed ‘operational models’ of well-known

fisheries and stock-assessment contexts do not (NRC 1988; Labelle 2002, 2005). Subsequent

requests for additional data simply confirmed that the confidence intervals for harvest rates on

sockeye salmon runs simply are unavailable. The Pacific Salmon Commission (PSC) staff does

conduct ‘hindcasting’ studies to determine the extent of potential biases in harvest rates. But the

variances of the fishery-specific harvest rates cannot be quantified as they cannot be attributed

with certainty to the stock-reconstruction procedure, the pre-season planning model, other factors

yet to be determined, or a mixture of these (see Cave 2006).

Another criticism expressed during the same PSARC review was that the simulator relies

on a single set of harvest rate parameters to determine catches, but should use year-specific

parameter values to determine fishery impacts each season. This would be the ideal situation, but

subsequent requests for such data simply confirmed that the PSC has not had sufficient resources

to determine and publish estimates of elementary harvest rates for each fishery/year shortly after

each season. Furthermore, given the limitations of the methods used and various data set

uncertainties, no efforts have been made to determine if there are statistical differences between

the elementary harvest rates for different periods (J. Cave, PSC, pers. comm.).

During the PSARC review, it was also suggested that a backward reconstruction could

provide more accurate results of the run timing distribution at Albion (and other fisheries

‘downstream’), because it can [theoretically] account for all losses further upstream starting from

the escapement. In the absence of reliable estimates of catches and parameter values to conduct

both types of analyses, it seems pointless to conjecture about the pseudo-merits of the backward

reconstruction over the forward projection approach adopted years ago by DFO-MoE scientists.

However, one should emphasize that in recent years, total incidental losses in fisheries upstream

of Albion amount to <10% or less of the total population. In light of this fact, the uncertainty

associated with the available statistics, and the low level of observer coverage, it seems doubtful

that a backward reconstruction would provide a substantially better picture of the run-timing

29

distribution at Albion. However, this exercise still might be a useful, as it would provide

alternative indices of exploitation trends that could eventually be used to compare the

performance, merits and crucial data requirements of both approaches.

In the meantime, the results suggest improvements are best achieved by improving our

understanding of the migration biology of Thompson steelhead and in particular improving

estimates of run timing parameters. One viable option would be to simply collect more data at

Albion. The test fishing activities were reduced in 1998, supposedly to reduce the incidental kill

of coho (Anonymous, 2002). There is no evidence that the incidental kill on total coho

escapement has effectively been reduced, but reduced test fishing has substantially reduced the

amount of data available for the assessment and in-season management of steelhead. Ironically,

it was noted years ago that “the value of the test fishery for management of Fraser River

watershed salmon stocks, far out weights the impact it could have on any individual coho or

steelhead stock in [the] watershed” (Anon. 2002). The Thompson River sport fishery has

recently been subject to severe gear/time/area regulations to reduce incidental mortality in this

catch-and-release fishery, and recent escapement levels are near minimum conservations levels,

so there is now an even greater need for reliable escapement indices from the Albion test-fishery.

Resuming daily test fishing operations would help increase sample size, provide more

information on the shape of the run timing curve, and provide more data for the application of

the in-season sport fishing management model used by the MoE. Alternatively, run timing

parameters could also be obtained via the use of fish wheels. If the catch records from

fishwheels over a few trial years end up being highly correlated with those of the test fishing

gear, it may be possible to infer abundance information from these data. Steelhead radio-tagging

operations should also be conducted below Albion to provide better estimates of the catchability

coefficient of this test-fishing gear, and losses due to in-river fisheries above Mission. Tagging

operations could also provide information on the behavior, catchability and run strengths of weak

coho stocks subject to conservation concerns that co-migrate with steelhead stocks.

Another potentially viable option would be to tag surviving steelhead kelts with acoustic

transmitters in order to directly measure diversion rate and migration rate parameters upon their

second returning migration to the Fraser and Thompson rivers. The operation of acoustic

30

listening lines along the North American coast as part of the Pacific Ocean Shelf Tracking

project (POST) makes this option possible. In the absence of any practical means of capturing

steelhead at sea prior to reaching the North American coast, tagging kelts is the next best

potential alternative while technologies continue to improve.

As currently structured, the simulator accounts for more of the underlying uncertainties

than the original (PSARC approved) model used by the DFO staff in North Coast for similar

purposes (see Cox-Rogers, 1994). The later has since been updated each year with the addition

of new data and assumptions (Cox-Rogers, 2007). Similar adjustments could be made to the

simulator if additional efforts were made to obtain key data for this purpose.

8. Acknowledgements

Sincere thanks are owed to several persons who made substantial contributions to this

investigation: Marc Labelle for developing much of the text and conducting the Monte Carlo

simulations, Ryan Hill for developing the original model, Tom Johnston for statistical advice,

and Vic Palermo for suggesting other model improvements. Data on gear-specific mortality rates

were provided by Leroy Hop Wo (southern seines), Melanie Sullivan (southern gillnets), Barbara

Mueller (Area 29 gillnets), Ivan Winther (northern gillnet and seine), Jim Renn (other gillnet).

Pieter Van Will, Michael Folkes, Don Noviello, Jim Cave, Steve Cox-Rogers, Paul Starr, and

William Gazey provided background data and reviews. Paul Ryall, Al Martin, Ian McGregor,

and Ted Down provided support for this investigation. Kim Haytt provided some

encouragements to pursue the investigation following the initial PSARC review of a prior draft

in October 2006. Financial assistance was provided by the Habitat Conservation Trust Fund

(HCTF) for the steelhead migration studies, escapement monitoring and angler surveys in the

Thompson River. Additional funds were provided by the BC Ministry of the Environment, and

the Pacific Salmon Foundation (PSF).

31

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32

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34

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35

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36

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37

10. TABLES

38

Table 1. Effort figures (in vessels) for fisheries targeting chum salmon, 1992-2002. These effort

values are also used to quantify steelhead exploitation levels, after adjustments (see text

for details). Areas 7-7a equivalencies based on 1 purse seine boat·day equals 5 gillnet

boat·days on summer run sockeye, and 10 gillnet boat·days on late run sockeye.

Fishery 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002Area 12 gillnet 200 200 200 200 200 200 200 200 200 200 200Area 12 purse seine 200 200 200 200 200 200 200 200 200 200 200Area 13 gillnetArea 13 purse seine 100 100 100 100 100 100 100 100 100 100 100Areas 7-7a, non-treaty gillnetAreas 7-7a, non-treaty purse seine 40-90 40-50 40-50 40-50 40-50 40-50 40-50 40-50 40-50 40-50 14-14Areas 7-7a, treaty gillnetAreas 7-7a, treaty purse seine 100-50 100-50 100-50 100-50 100-50 100-50 100-50 100-50 100-50 100-50 10-10Area 29 to Port Mann, driftnetArea 29 to Port Mann, gillnet 200 200 200 200 200 200 200 150 100 100 100Port Mann to Mission driftnetPort Mann to Mission, gillnet 150 150 150 150 150 150 150 110 80 80 80Mission to Agassiz, setnetAgassiz to Hope, setnet

Effort converted to seine effort equivalencies, and included in the figures below

Effort converted to seine effort equivalencies, and included in the figures below

Effort converted to seine effort equivalencies, and included in the figures below

effort by individual opening within each season

effort by individual opening within each season

effort by individual opening within each season

effort by individual opening within each season

39

Table 2. Exploitation parameter values for all net fisheries (GN = gillnet, PS = purse seine) used

by the simulator. The total fishing effort deployed is denoted by label E.

Category Fishery Exploitation parameters Estimate source

[1a] Area 12 GN u = (0.0002015*E) + 0.01424 Sockeye run reconstructions (Cave and Gazey 1994), revised by the Pacific Salmon Commission in 2000.

[1b] Area 12 GN after Sept. 20 u = 1-SQRT(1-(0.0003*E+ 0.0013)) Chum run reconstruction estimates (VanWill, pers. comm.).

[2] Area 12 SN u = (0.0012*E) + 0.2334 As in [1a].

[3a] Area 13 GN u = 1-SQRT(1-(0.0003*E+ 0.0013)) Sockeye run reconstructions (Cave and Gazey 1994), revised by the Pacific Salmon Commission in 2000.

[3b] Area 13 GN after Sept. 20 u = (0.0002015*E) + 0.01424 Chum run reconstruction estimates (VanWill, pers. comm.).

[4] Area 13 SN u = (0.001*E) + 0.2243 Sockeye run reconstructions (Cave and Gazey 1994), revised by the Pacific Salmon Commission in 2000.

[5] Area 21 GN u = 0.1 Least-squares fit to 1989 observed steelhead catches. See text for details.

[6] Area 20 PS u = 0.5Average value, based on sockeye run reconstructions (Cave and Gazey 1994), revised by the Pacific Salmon Commission for a range of diversion rates.

[7] Area 7 Indian u = (0.0928*Ln(E)) - 0.1823 From sockeye run reconstruction (Cave and Gazey 1994).

[8] Area 7 Non-indian u = (0.00088*E) + 0.0443 As in [6].

[9] Area 7a Indian u = (0.212*Ln(E)) - 0.3602 As in [6].

[10] Area 7a Non-indian u = (0.00378*E) + 0.0405 As in [6].

[11] Area 29 GN (pre-1998) q = 0.0032 Forward projection fits to chum catches, adjusted for steelhead:chum catchability ratio.

[12] Area 29 GN (1998 onwards) q = 0.0045 Forward projection fits to chum catches, adjusted for steelhead:chum catchability ratio.

[13] Area 29 GN (100 fathom nets) q = 0.0023 As in [11], adjusted for a reduction in net length.

[14] Drift GN Aboriginal Area 29 to Port Mann q = 0.00192 As in [11], adjusted for fishery duration and net length.

[15] Drift GN Aboriginal Port Mann to Mission q = 0.0008 As in [11], adjusted for smaller net length.

[16] Set GN Aboriginal Mission to Agassiz u = 0.036Baseline figure from 1995 sockeye run reconstructions. Further adjusted for differences in morphology, plus swimming speed (during sockeye fishery), plus sockeye/chum effort ratio (after sockeye fishery)

[17] Set GN Aboriginal Agassiz to Hope u = 0.03 As in [16].

[18] Set GN Aboriginal Hope to Sawmill Cr. u = 0.20 As in [16].

40

Table 3. Albion test fishery catches and total escapements of Interior Fraser River steelhead. Spring spawners 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007Thompson 1135 3544 2426 1675 1500 1671 1200 1200 900 2955 2660 2591 1019 1470 2419 835 1880 1672 1490 1000 2200 1800 1000Chilcotin 1133 3149 1992 2328 2342 610 403 466 542 1546 917 830 500 1373 672 744 739 1258 1113 917 254 384 552Thompson Chilcotin 2268 6693 4418 4003 3842 2281 1603 1666 1442 4501 3577 3421 1519 2142 3163 1574 3138 2785 2407 1254 2584 2352Test Fishing Steelhead Catch DataDate 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006

01-Sep 0 0 0 0 0 0 0 0 002-Sep 0 1 0 0 003-Sep 0 0 0 0 0 0 0 0 004-Sep 0 1 0 0 005-Sep 0 0 0 1 2 1 0 0 106-Sep 0 0 0 0 007-Sep 0 0 0 0 1 1 0 0 0 008-Sep 0 0 0 0 009-Sep 0 0 0 1 1 1 0 0 010-Sep 0 1 0 3 111-Sep 1 0 0 0 0 1 1 0 0 012-Sep 2 1 0 1 113-Sep 1 0 0 0 0 0 0 0 0 014-Sep 1 0 0 1 215-Sep 0 0 1 0 0 2 0 0 2 0 1 0 0 016-Sep 0 1 1 1 0 1 0 2 817-Sep 0 0 4 0 0 0 0 0 3 0 0 0 2 018-Sep 0 0 3 0 0 0 0 0 119-Sep 1 6 0 0 0 0 1 0 0 0 0 1 120-Sep 0 3 1 0 1 0 0 1 121-Sep 2 2 6 0 0 0 0 1 0 1 1 0 4 022-Sep 0 8 0 2 0 0 3 223-Sep 3 2 6 2 0 0 1 1 0 0 0 0 0 024-Sep 0 1 0 0 1 1 0 0 025-Sep 0 1 6 1 3 1 0 1 12 3 0 0 4 026-Sep 0 3 4 1 0 2 0 2 027-Sep 2 2 0 2 1 0 0 1 7 1 2 0 1 028-Sep 2 1 8 2 0 2 0 1 229-Sep 0 0 2 0 0 3 1 0 1 3 1 0 0 130-Sep 1 4 3 1 0 5 0 2 001-Oct 17 0 7 0 3 1 1 3 0 0 8 0 1 1 4 1 0 2 002-Oct 6 14 2 3 2 0 2 2 0 0 0 3 1 203-Oct 11 0 2 4 0 0 4 1 0 1 6 0 1 3 0 0 1 0 004-Oct 2 14 10 0 2 4 2 2 5 2 0 1 0 205-Oct 4 2 1 0 0 0 2 3 1 2 8 0 2 8 1 1 0 11 206-Oct 0 19 11 1 1 6 1 5 1 2 0 2 0 107-Oct 10 8 0 3 0 1 2 2 0 5 1 2 0 9 0 0 0 0 108-Oct 1 6 0 2 3 1 4 0 2 0 4 009-Oct 1 5 4 4 4 0 1 1 1 2 2 0 1 0 1 0 2 0 0 1 1 010-Oct 0 1 2 1 0 2 4 1 0 3 211-Oct 0 7 3 3 0 1 1 5 0 2 0 2 6 2 0 4 1 2 0 0 0 1 012-Oct 0 2 7 12 2 0 5 2 0 2 4 6 1 313-Oct 1 0 7 2 2 2 0 0 1 0 4 3 1 1 5 0 2 1 0 0 1 114-Oct 1 3 5 7 1 2 3 2 2 0 1 0 2 215-Oct 0 5 4 0 2 0 1 5 0 3 1 2 0 0 2 2 0 0 0 2 016-Oct 2 6 6 0 0 1 0 0 4 1 3 117-Oct 0 4 10 0 3 2 0 1 2 1 1 0 2 0 1 1 1 2 0 0 0 018-Oct 1 1 9 8 2 0 4 4 3 3 3 2 2 2 019-Oct 2 2 0 4 1 4 1 3 4 0 0 1 5 0 2 1 8 2 0 0 1 020-Oct 1 1 6 0 0 1 3 3 0 1 1 0 0 2 221-Oct 2 2 7 4 0 3 2 1 3 4 1 3 4 10 0 1 1 3 0 0 1 0 022-Oct 1 7 14 3 1 4 2 2 0 3 0 9 0 1 2 0 2 1 023-Oct 0 4 10 0 1 2 0 0 0 3 3 2 1 2 1 0 0 0 0 1 124-Oct 0 3 3 0 2 1 5 0 1 0 1 1 1 2 1 0 0 0 4 1 025-Oct 2 4 2 0 0 1 1 1 1 1 1 0 1 2 0 0 0 1 0 0 3 1 026-Oct 1 5 2 3 0 1 2 1 1 1 0 0 0 0 0 0 0 0 0 1 027-Oct 0 9 2 5 1 1 1 4 2 2 2 0 3 2 0 0 0 1 0 0 0 028-Oct 1 3 0 1 0 1 5 9 1 0 0 5 1 2 0 0 0 1 2 0 2 0 029-Oct 0 1 1 4 1 3 3 1 1 0 0 2 1 2 0 2 1 0 0 0 0 2 1 030-Oct 2 9 2 4 0 0 2 1 2 1 0 1 0 4 0 0 0 3 0 0 0 031-Oct 0 13 4 2 1 1 0 0 1 1 0 0 3 0 0 1 0 1 1 0 0 0 001-Nov 2 10 6 0 0 3 0 0 0 1 1 0 1 7 0 0 0 0 0 0 0 0 002-Nov 0 9 2 1 0 3 2 1 1 1 0 5 5 3 1 2 0 0 0 0 0 003-Nov 1 9 1 0 0 1 1 0 0 0 0 5 3 1 0 0 0 0 2 0 004-Nov 0 4 4 1 2 1 2 0 0 1 3 1 1 1 0 1 0 0 0 0 0 0 0 305-Nov 1 6 3 1 2 5 0 0 0 3 0 0 4 0 1 1 0 0 1 0 0 006-Nov 2 0 5 2 0 0 0 0 0 3 1 0 0 0 3 0 0 0 1 1 0 0 007-Nov 1 1 5 0 0 1 3 0 1 1 0 0 0 0 0 0 0 0 1 0 0 008-Nov 0 2 2 0 1 1 1 0 1 3 0 0 0 4 0 1 0 0 0 1 1 1 0 009-Nov 0 4 4 0 1 0 0 1 2 0 0 1 0 0 0 0 0 0 0 110-Nov 0 5 0 4 0 0 0 2 2 0 1 0 1 1 1 0 0 1 0 0 0 011-Nov 0 3 0 2 1 2 0 0 1 1 1 0 0 0 0 1 0 0 0 0 012-Nov 0 5 2 2 0 1 0 0 0 4 0 0 2 1 0 0 0 0 1 0 0 213-Nov 0 5 1 2 1 1 0 0 0 1 0 0 0 3 0 0 0 0 0 0 0 0 114-Nov 0 0 0 0 1 0 1 0 1 1 0 0 1 2 0 0 0 0 0 0 0 0 0 115-Nov 0 1 1 0 4 1 0 0 1 0 1 0 0 1 1 0 0 0 2 2 0 0 116-Nov 0 1 2 0 1 0 0 0 0 2 1 1 0 0 0 1 0 0 0 0 0 0 0 017-Nov 0 1 1 0 0 0 0 1 0 0 2 0 0 0 0 0 0 0 0 0 0 0 018-Nov 0 2 4 1 0 0 0 0 2 0 0 0 2 1 0 0 0 0 0 0 0 0 019-Nov 0 2 2 0 0 0 1 0 0 3 0 0 0 0 0 0 0 0 0 0 020-Nov 0 0 1 0 0 0 1 1 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0

41

Table 4. Albion test fishery catches and total escapements of Fraser River chum salmon. Blank

cells indicate that no records are available. Actual escapements not reported. Test Fishing Chum Catch DataDate 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006

01-Sep 0 1 0 0 0 5 0 0 1 002-Sep 0 1 0 0 003-Sep 0 1 0 1 2 5 0 0 0 104-Sep 0 2 0 1 105-Sep 1 0 0 2 1 5 1 0 006-Sep 1 1 0 2 207-Sep 2 1 0 5 4 7 1 0 6 508-Sep 0 0 0 4 409-Sep 1 1 1 6 3 7 0 5 6 710-Sep 1 5 1 2 811-Sep 7 1 0 6 4 15 2 4 116 1612-Sep 1 4 0 6 613-Sep 6 4 1 14 6 18 0 13 16 114-Sep 8 1 0 13 1215-Sep 3 1 5 7 8 0 3 5 36 4 6 23 216-Sep 4 2 2 3 10 7 2 20 2317-Sep 6 3 3 2 8 6 5 28 3 50 5 0 25 1018-Sep 5 4 5 1 0 4 4 1 2319-Sep 1 8 1 21 7 4 80 10 79 10 7 37 1220-Sep 4 10 1 9 10 7 7 19 3821-Sep 8 9 11 26 17 6 10 61 22 58 22 30 122 15822-Sep 12 6 16 12 0 2 32 2723-Sep 13 2 4 18 15 9 4 72 25 91 44 36 83 19024-Sep 40 17 0 16 33 21 4 47 5125-Sep 38 20 5 13 42 17 58 50 157 60 39 126 15026-Sep 29 22 9 11 18 20 7 78 8827-Sep 30 16 2 18 28 31 8 150 83 149 134 51 100 11528-Sep 40 6 9 10 65 32 9 135 9029-Sep 35 21 6 36 53 11 135 133 195 189 66 267 19030-Sep 31 51 22 15 36 67 15 168 24901-Oct 101 123 30 24 95 40 117 3 188 149 266 162 57 186 21902-Oct 53 35 97 80 70 36 137 27 90 323 25203-Oct 0 0 72 121 41 27 180 57 108 4 264 182 436 175 136 199 23204-Oct 36 74 24 151 75 20 125 26 34 280 35105-Oct 0 0 59 119 59 28 84 38 115 10 162 282 323 135 204 176 32506-Oct 75 93 104 123 115 55 123 58 52 540 26007-Oct 0 63 100 105 97 62 156 65 75 2 243 449 247 325 227 38608-Oct 54 0 154 136 65 45 167 42 100 51809-Oct 68 118 130 126 46 67 158 48 52 26 530 208 182 519 263 390 371 78710-Oct 131 0 138 48 54 152 99 100 28211-Oct 49 147 184 148 84 70 160 96 83 126 416 261 188 488 210 305 233 33712-Oct 0 73 224 300 46 106 159 127 76 52313-Oct 91 93 219 327 21 40 175 131 92 87 931 230 166 239 352 341 313 42014-Oct 97 96 258 226 106 118 224 121 52 31015-Oct 116 107 256 126 88 160 94 147 138 504 322 265 645 300 463 256 32216-Oct 120 142 131 118 314 64 156 47917-Oct 82 63 272 253 148 96 386 183 145 51 471 313 377 596 205 621 332 42418-Oct 132 66 233 292 137 116 380 372 160 156 44219-Oct 95 155 125 239 157 155 245 182 95 20 476 463 283 573 502 459 384 28920-Oct 86 198 101 149 239 189 302 258 84 648 449 77521-Oct 57 160 158 151 74 144 224 656 161 701 466 117 404 714 6 680 532 44022-Oct 92 139 276 106 71 347 346 99 677 272 269 165 400 652 40923-Oct 39 121 43 77 105 315 359 90 57 376 478 278 358 294 43 429 71224-Oct 82 133 50 71 157 86 379 205 70 432 232 222 406 574 362 30525-Oct 62 56 39 84 201 745 219 48 414 329 423 126 365 351 73 729 233 28626-Oct 108 36 168 75 136 253 315 204 108 284 362 134 294 449 455 22727-Oct 140 86 286 113 124 285 231 13 302 353 118 307 319 456 657 202 28828-Oct 73 104 246 166 126 70 367 248 29 334 363 201 471 717 293 401 313 38529-Oct 83 78 347 127 112 69 442 181 116 239 435 227 143 641 801 176 533 214 33330-Oct 116 124 246 202 150 140 308 195 162 242 302 152 493 395 502 420 51931-Oct 32 296 190 117 142 479 170 24 276 44 67 321 374 298 477 323 31401-Nov 44 243 368 57 252 123 167 171 286 257 108 322 259 134 529 237 19502-Nov 36 110 62 215 65 118 118 79 414 164 224 65 201 167 299 414 22803-Nov 35 76 90 25 146 148 156 204 301 19 205 167 866 225 17304-Nov 50 252 89 14 358 269 165 169 147 44 83 150 24 146 97 458 178 47805-Nov 152 174 6 140 418 152 86 114 106 57 14 213 132 379 292 198 36306-Nov 140 120 33 36 111 166 15 159 106 141 27 44 531 315 181 383 88 23407-Nov 189 155 117 71 22 103 275 245 75 87 28 61 511 257 278 224 7908-Nov 122 108 168 93 50 163 189 67 116 320 76 33 60 33 248 56 2909-Nov 77 64 75 53 137 150 85 61 12 370 56 56 128 2210-Nov 37 51 94 136 127 98 274 173 61 198 82 13 217 163 175 65 25211-Nov 76 85 148 50 77 217 575 229 221 35 14 111 163 94 139 18 16612-Nov 21 180 48 120 77 386 76 66 1 1 70 100 98 56 41 25013-Nov 16 90 6 81 58 45 109 243 105 35 5 2 90 102 45 14 12414-Nov 52 174 4 109 47 13 42 57 16 287 30 2 2 156 86 64 0 11915-Nov 23 264 45 166 114 26 20 18 110 104 15 1 4 156 95 28 8 10516-Nov 8 237 203 108 91 49 19 76 46 22 33 35 3 42 72 128 28 8 517-Nov 19 107 244 9 27 80 51 122 71 86 17 4 86 36 76 34 6 10818-Nov 119 97 27 75 120 61 3 31 19 25 1 9 52 75 38 33 3 2919-Nov 45 123 110 90 136 21 38 5 23 1 38 11 41 4 11 1820-Nov 46 44 177 45 84 84 10 46 2 34 11 22 6 13 31 17 12 7 321-Nov 38 75 131 91 33 58 21 11 3 16 35 0 8 25 10 37 4 1922-Nov 38 12 153 64 18 17 9 1 4 21 8 1 8 12 6 17 2 323-Nov 61 29 71 53 34 6 66 26 0 35 1 0 4 5 1 4 0 324-Nov 101 26 54 30 131 4 0 0 60 1 0 2 5 2 0 0 025-Nov 115 50 2 37 9 116 9 0 18 3 0 7 12 2 0 0 026-Nov 140 48 54 112 20 3 90 9 2 1 18 1 0 3 6 2 0 0 027-Nov 157 47 207 134 10 11 91 12 0 0 38 1 0 0 8 0 0 0 028-Nov 123 53 206 130 12 5 25 20 0 0 15 0 0 0 7 1 1 0 029-Nov 77 93 61 5 30 0 1 0 8 0 0 0 0 10 0 0 030-Nov 52 181 6 73 11 1 5 0 2 0 6 1 0 0 5 6 0 0 0

9

0

2

2

42

Table 5. Estimates of catchability coefficients for steelhead and chum for the Albion test-fishery.

For some years, no figures are provided, as none were obtained, or those obtained were

considered to be unreliable or un-informative.

Survey steelhead chum ratio

year (q) (q) steel/chum1990 0.038 0.0106 3.61991 0.029 0.0085 3.41992 0.022 0.0078 2.819931994 0.018 0.0071 2.51995 0.031 0.0055 5.619961997 0.010 0.0076 1.31998 0.022 0.0055 4.019992000 0.036 0.0115 3.12001 0.027 0.0093 2.9

Average 0.026 0.008 3.2

Table 6. Predicted and observed catches of chum and steelhead in the Area 29 commercial gillnet

fishery, 1990-2001. Reported catch figures adjusted for sale slip omissions.

Catchability Run size Species Opening Effort Predicted Observed

(q) (No) dd/mm/yy (vessels) catches catches0.0010 1,000,000 Chum 23/10/90 520 49,088 n/a0.0032 2,400 Steelhead 23/10/90 520 354 4250.0010 900,000 Chum 28/10/91 346 28,096 30,7510.0032 2000 Steelhead 28/10/91 346 178 2660.0010 800,000 Chum 27/10/92 362 26,674 54,8950.0032 5,300 Steelhead 27/10/92 362 305 2270.0014 1,900,000 Chum 08/11/01 180 20,057 28,3590.0045 3,600 Steelhead 08/11/01 180 46 n/a

43

Table 7. Predicted and observed catches of steelhead in the Area 21 commercial gillnet fishery,

in 1989. Figures obtained with an entering run of 3440 subject to u of 0.1.

Opening Effort (# vessels each day) Predicted catch Observed catchSept. 18-21 335, 176, 105, 80 79 229Sept. 25-28 275, 277, 200, 125 91 95Oct. 4-10 200, 315, 234, 210, 170, 190, 165 141 82

Table 8. Estimates of steelhead mortality rates based on observer records and radio-tagging

program results. Figures that are not available denoted by ‘n/a’.

Gear Fishing Survey Investigation Total Dead at Dead Post-releasetype location year caught capture Poor Good mortalitiesGill net Skeena 1989 Beere 1991 113 55 49% 9 49 41Gill net Skeena 1992 Anonymous 1992 62 45 73% n/a n/a n/aGill net Fraser 1992 McGregor 1993 227 149 66% n/a n/a n/aGill net Nitinat 1996 Anonymous 1996 160 95 59% 57 8 8Gill net Nitinat 1997 Anonymous 1997 26 17 65% n/a n/a n/aGill net Nitinat 1998 Anonymous 1998 39 20 51% n/a n/a n/a

Condition of live fish

Table 9. Mortality rate per encounter figures used for simulation purposes, by fishery and year.

Fishery gear types and labels are; gillnets (GN), drift net (DN), set net (SN) and purse

seine (PS). Mortality rates of 1.0 indicates no post-release survival (all catches retained).

Fishery (Area & Gear) 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006Area 12 GN 0.8 0.8 0.8 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5Area 12 PS 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.2 0.2 0.2 0.2 0.2 0.2Area 13 PS 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.2 0.2 0.2 0.2 0.2 0.2Area 20 GN 0.8 0.8 0.8 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5Area 20 PS 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.2 0.2 0.2 0.2 0.2 0.2Area 21 GN 1.0 1.0 1.0 0.9 0.8 0.6 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5Area 21 PS 1.0 1.0 1.0 0.9 0.8 0.6 0.5 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3Areas 7-7a, Non-Treaty GN 1.0 1.0 1.0 0.9 0.8 0.6 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5Areas 7-7a, Non-Treaty PS 1.0 1.0 1.0 0.9 0.8 0.6 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5Areas 7-7a, Treaty GN 1.0 1.0 1.0 0.9 0.8 0.6 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5Areas 7-7a, Treaty PS 1.0 1.0 1.0 0.9 0.8 0.6 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5Area 29 to Port Mann DN 1.0 0.9 0.9 0.9 0.9 0.9 0.9 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8Area 29 to Port Mann GN 0.8 0.8 0.8 0.8 0.8 0.8 0.7 0.7 0.6 0.6 0.6 0.6 0.6 0.6 0.6Port Mann to Mission DN 1.0 0.9 0.9 0.9 0.9 0.9 0.9 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8Port Mann to Mission SN 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.8 1.0 0.8 0.8Port Mann to Mission GN 0.8 0.8 0.8 0.8 0.8 0.8 0.7 0.7 0.6 0.6 0.6 0.6 0.6 0.6 0.6Mission to Agassiz SN 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0Agassiz to Hope SN 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0

44

Table 10. Assumed parameter distributions and values used to represent stochastic processes for

simulation purposes. Lower and upper bounds respectively denoted by lb and ub. Weibull

location parameters are expressed either as the mean date of entry into top end of

Johnstone Straight, or as the number of days.

Variable Distribution Parameters ValuesPeak date of entry Johns. Strait (2004) Weibull Location, Scale, Shape Sept.22, 10.0, 2.2Peak date of entry Johns. Strait (2005) Weibull Location, Scale, Shape Aug. 27, 15.0, 4.0Peak date of entry Johns. Strait (2006) Weibull Location, Scale, Shape Sept.8, 21.0, 3.4SD run time Johns. Strait (2004) Weibull Location, Scale, Shape 5.5, 5.0, 1.6SD run time Johns. Strait (2005) Weibull Location, Scale, Shape 9.5, 5.3, 1.9SD run time Johns. Strait (2006) Weibull Location, Scale, Shape 10.0, 15.0, 2.0Diversion rate Beta lb, ub, alpha, beta 0.0, 1.0, 2.0, 2.0Daily migration rate in marine fisheries Normal mean, SD 17.0, 0.6Daily migration rate in fresh water Regr. + uniform lb, ub 0.95, 1.05Catchabilty PS gear Uniform lb, ub 0.8, 1.2Catchability GN gear Uniform lb, ub 0.9, 1.1Area 12 GN mortality Beta lb, ub, alpha, beta 0.3, 0.8, 2.0, 2.6Area 12 PS mortality Beta lb, ub, alpha, beta 0.1, 0.3, 2.0, 2.0Area 13 PS mortality Beta lb, ub, alpha, beta 0.1, 0.3, 2.0, 2.0Area 13 GN mortality Beta lb, ub, alpha, beta 0.3, 0.8, 2.0, 2.6Area 21 PS mortality Beta lb, ub, alpha, beta 0.2, 0.4, 2.0, 2.0Area 21 GN mortality Beta lb, ub, alpha, beta 0.3, 0.8, 2.0, 2.6Area 20 PS mortality Beta lb, ub, alpha, beta 0.2, 0.4, 2.0, 2.0Area 7 Native PS mortality Beta lb, ub, alpha, beta 0.4, 0.6, 2.0, 2.0Area 7 non-Native PS mortality Beta lb, ub, alpha, beta 0.4, 0.6, 2.0, 2.0Area 7a Native PS mortality Beta lb, ub, alpha, beta 0.4, 0.6, 2.0, 2.0Area 7a non-Native PS Mortality Beta lb, ub, alpha, beta 0.4, 0.6, 2.0, 2.0Area 29 GN mortality Beta lb, ub, alpha, beta 0.4, 0.8, 2.0, 2.0Area 29 to Port-Mann AD mortality Beta lb, ub, alpha, beta 0.8, 1.0, 2.0, 2.0Port-Mann to Mission GN Beta lb, ub, alpha, beta 0.4, 0.8, 2.0, 2.0Port-Mann to Mission AD Beta lb, ub, alpha, beta 0.8, 1.0, 2.0, 2.0Terminal Sport (1992-2003) Weibull Location, Scale, Shape 0.026, 0.020, 3.0Terminal Sport (2004-2006) Weibull Location, Scale, Shape 0.023, 0.020, 3.0

45

Table 11. Estimates of steelhead run timing patterns based on Albion test fishery catches and

escapement records (based on Bison and Ahrens 2003). The mean date corresponds to the

number of days after August 31. Standard deviations expressed in number of days.

Figures that are not-available are represented by blank cells. Estimates based on the

Poisson error structure are used for simulation purposes. Estimates based on the normal

error structure are provided for reference purposes.

Escapement Test fishing Normal Error Normal Error Poisson Error Poisson Error Coeff.Year Year Mean date Standard Dev. Mean Date Standard Dev. Variation1984 19831985 19841986 19851987 1986 31.2 24.2 32.4 20.2 0.6241988 19871989 19881990 19891991 19901992 1991 44.7 14.1 44.1 14.8 0.3361993 1992 39.5 19.7 40.9 21.8 0.5351994 19931995 1994 44.3 11.2 43.9 11.9 0.2721996 1995 46.8 17.0 44.8 17.7 0.3961997 19961998 1997 59.3 9.5 59.5 15.7 0.2641999 1998 34.2 21.9 35.2 22.2 0.6302000 1999 36.7 18.2 36.1 17.9 0.4972001 2000 32.6 10.9 31.4 11.5 0.3642002 2001 29.3 20.8 31.0 17.3 0.5562003 2002 29.7 19.4 28.5 26.9 0.9462004 20032005 2004 53.9 2.7 52.2 8.0 0.1532006 2005 31.8 11.5 32.6 12.8 0.3922007 2006 46.7 28.0 48.1 20.8 0.432

Mean 40.0 16.4 40.0 17.1 0.457sd 9.5 6.7 9.1 5.1min 29.3 2.7 28.5 8.0 0.153max 59.3 28.0 59.5 26.9 0.946

46

Table 12. The number of daily net fishery openings of discrete fisheries (as defined in the model)

during the Thompson steelhead migration period. Area 12/13 is defined as containing 4

discrete fisheries (2 areas and 2 net types). Area 7/7a is defined as containing 4 fisheries

(2 areas each divided by "Treaty" and "Non-Treaty"). Area 29 is defined as containing 2

discrete fisheries (2 areas, one upstream of Port Mann and one downstream). Lower

Fraser Drift Net is defined as containing 2 fisheries (one upstream of Port Mann and one

downstream of Port Mann). Lower Fraser Set Net is defined as containing 3 fisheries,

Mission to Agassiz, Agassiz to Hope, and Hope to Sawmill Cr.).

Year Area 12/13 Area 7/7a Area 29 Lower Fraser Drift Net Lower Fraser Set Net Total (Aug 15-Oct 30) (Sept 1-Nov 20) (Sept 1-Nov 20) (Steveston to Mission,

Sept 1-Nov 20)(Mission to Sawmill,

Sept 1-Nov 20)2004 24 56 4 25 28 1372005 32 69 4 30 40 1752006 40 82 8 38 50 218

Table 13. Effects of each variable on overall exploitation for the 2004-2006 fishing seasons.

Coefficients of the rank correlations between each variable and the exploitation rate are

given under the label Corr. See text for additional details.

Rank Variable (2004) Corr. Variable (2005) Corr. Variable (2006) Corr.21 Aborig. driftnet mort u/s P.Mann 0.00 Slope of migr.-temp. regression 0.00 Catchability noise for seine 0.0020 Area 7 mortality Treaty Indian -0.01 Area 7a mortality Treaty Indian 0.00 Catchability noise for gillnet 0.0019 Area 21 gillnet mortality -0.01 Aborig. driftnet mortality u/s P.Mann -0.01 Aborig. driftnet mortality u/s P.Mann 0.0118 Area 29 mortality u/s P.Mann 0.01 Catchability noise for seine -0.01 Area 7 mortality Non-Indian 0.0117 Area 7a mortality Non-indian 0.01 Catchability noise for gillnet -0.01 Area 7a mortality Treaty Indian 0.0116 Slope of migr.-temp. regression -0.01 Area 13 gillnet mortality 0.01 Area 21 gillnet mortality 0.0215 Marine migration rate 0.02 Spread of run 0.02 Area 7a mortality Non-Indian 0.0214 Area 7 mortality Non-Indian 0.02 Area 21 gillnet mortality 0.02 Slope of migr.-temp. regression -0.0213 Area 13 gillnet mortality 0.02 Area 7 mortality Non-Indian 0.03 Area 7 mortality Treaty Indian 0.0212 Catchability noise for gillnet -0.02 Area 7a mortality Non-Indian 0.03 Aborig. driftnet mortality d/s P.Mann 0.0311 Catchability noise for seine 0.02 Area 7 mortality Treaty Indian 0.03 Area 13 gillnet mortality 0.0310 Area 12 gillnet mortality 0.04 Area 29 gillnet mortality u/s P.Mann 0.05 Area 13 seine mortality 0.039 Sport mortality 0.05 Area 29 gillnet mortality d/s P.Mann 0.05 Area 29 gillnet mortality u/s P.Mann 0.058 Aborig. driftnet mortality d/s P.Mann 0.06 Area 12 gillnet mortality 0.06 Marine migration rate -0.067 Area 7a mortality Treaty Indian 0.06 Aborig. driftnet mortality d/s P.Mann 0.06 Area 12 gillnet mortality 0.076 Area 13 seine mortality 0.07 Sport mortality 0.12 Area 12 seine mortality 0.075 Area 29 mortality d/s P.Mann 0.07 Area 12 seine mortality 0.13 Peak migration date 0.104 Diversion rate 0.10 Area 13 seine mortality 0.15 Diversion rate -0.143 Area 12 seine mortality 0.13 Marine migration rate -0.20 Sport mortality 0.152 Peak migration date -0.45 Diversion rate -0.21 Area 29 gillnet mortality d/s P.Mann 0.161 Spread of the run -0.69 Peak migration date 0.84 Spread of run -0.90

47

Table 14. Relative influence of the major determinants of overall exploitation for the 2004-2006.

Baseline values correspond to most likely parameter value implied. Figures under the

label ‘Δ Expl. Rate’ correspond to the relative change ((adjusted – likely) / likely)). All

figures based on a 50% diversion rate.

Season Factor Adjustment Value Expl. Rate Δ Expl. Rate2004 Spread of the run x 0.9 7.38 24.1% 4.3%

x 1.0 8.20 23.1% 0.0%x 1.1 9.02 22.2% -3.9%

Peak date 1 wk earlier 20-Sep 19.2% -16.9%Peak 27-Sep 23.1% 0.0%

1 wk later 04-Oct 20.4% -11.7%

Area 12 purse seine mortality x 0.9 0.18 22.9% -0.9%x 1.0 0.20 23.1% 0.0%x 1.1 0.22 23.3% 0.9%

2005 Peak date 1 wk earlier 01-Sep 10.5% -21.8%Peak 08-Sep 13.5% 0.0%

1 wk later 15-Sep 17.5% 29.7%

Diversion rate x 0.9 0.45 13.6% 0.5%x 1.0 0.50 13.5% 0.0%x 1.1 0.55 13.4% -0.4%

Marine migration rate x 0.9 15.30 15.4% 14.5%x 1.0 17.00 13.5% 0.0%x 1.1 18.70 11.9% -11.6%

2006 Spread of the run x 0.9 18.90 16.4% 5.8%x 1.0 21.00 15.5% 0.0%x 1.1 23.10 14.7% -5.2%

Area 29 comm. GN mortality d/s P.Mann x 0.9 0.540 15.0% -3.2%x 1.0 0.600 15.5% 0.0%x 1.1 0.660 15.9% 2.6%

Sport mortality x 0.9 0.027 15.2% -1.9%x 1.0 0.030 15.5% 0.0%x 1.1 0.033 15.7% 1.3%

48

11. FIGURES

49

Figure 1. Map of fishery management regions where steelhead and salmon species are caught.

50

Set initial population size (No = 1, or use hypothesized value)↓

Determine numbers entering through northern and southern routes N'o = No*diversion rate, N"o = No - N'o

↓ Determine start run time at Albion

↓ Determine dates of arrival of N'o to Area_11, and N"o to Area_21 x days earlier = Albion date - (distance*migration speed)

↓ Given normal distribution (mean, SD), split N'o and N"o into blocks i.e., determine series of N'fdk and N"fdk

↓ Start loop, block =1, day = 1

↓↑ → Update block number and/or day number↑ ↓↑ Move blocks sequentially upstream towards upper Thompson River ↑ Adjust migration rate using FW temperature if in Fraser R.↑ ↓↑ Derive q or u; set corresponding h and F↑ ↓↑ Determine numbers in each block intercepted in each fishery↑ ↓↑ Determine incidental kill due to fishery f, on block k, day d↑ ↓↑ Reduce abundance of each block impacted given incidental kill↑ ↓↑ Accumulate incidental kill by fishery↑ ↓↑ Finished moving all K blocks through all fisheries day d ?↑ ↓ ↓↑ ← ← ← ← No Yes↑ ↓↑ day = D ?↑ ↓ ↓↑ ← ← ← ← No Yes

↓ Determine overall fishery-specific impact (i.e., Sum fishery-specific incidental kills over initial population size)

↓ Determine overall fishing impact (i.e., Sum incidental kills for all fisheries over initial population size)

Figure 2. Pseudo-code used by the simulator to distribute the initial population specified, move

and deplete the initial population and compute fishery impacts.

51

0

100

200

300

400

500

600

24-Aug 13-Sep 3-Oct 23-Oct 12-Nov 2-Dec 22-Dec

Date

Cat

ch

Chum salmon

0

2

4

6

8

10

12

14

24-Aug 13-Sep 3-Oct 23-Oct 12-Nov 2-Dec 22-Dec

Date

Cat

ch

Steelhead

Figure 3. Observed (dots) and predicted (lines) test fishery catches of chum salmon and steelhead

during 2000. Predictions based on escapements figures considered to be accurate, using a

normal observation error, as described by Bison and Ahrens (2003).

52

Figure 4. Hypothesized probability distribution of peak arrival date at the northern tip of

Vancouver Island. Peak date here is Sept. 13th, with the lower and upper bounds being

Sept. 1st and Oct. 5th respectively.

Figure 5. Hypothesized probability distribution of steelhead diversion rates. There is a zero

probability of observing extreme diversion rates (0.0 or 1.0).

53

Figure 6. Hypothesized probability distribution of the average migration rate of steelhead as they

move through marine fisheries.

Figure 7. Hypothesized probability distribution of the mortality rates of steelhead released after

capture for the Area 12 GN fishery.

54

Frequency Chart

Exploitation Rate

.000

.006

.011

.017

.023

0

56.5

113

169.5

226

12% 16% 21% 25% 30%

10,000 Trials 69 Outliers

Forecast: Overall Exploitation

Frequency Chart

Exploitation Rate

.000

.006

.012

.017

.023

0

57.5

115

172.5

230

8.66% 11.81% 14.95% 18.09% 21.23%

10,000 Trials 89 Outliers

Forecast: Overall Exploitation

Frequency Chart

Exploitation Rate

.000

.006

.012

.018

.024

0

60.75

121.5

182.2

243

9.64% 14.62% 19.59% 24.56% 29.53%

10,000 Trials 90 Outliers

Forecast: Overall Exploitation

Figure 8. Monte Carlo simulation results for the 2004-2006 fishing seasons (in chronological

order from top to bottom). Scales differ across plots to facilitate viewing.

55

0%

5%

10%

15%

20%

25%

30%

35%

40%

45%

50%

1992 1994 1996 1998 2000 2002 2004 2006

% Expl. Poly. (% Expl.)

0

500

1000

1500

2000

2500

3000

3500

4000

1992 1994 1996 1998 2000 2002 2004 2006

Spawners Poly. (Spawners)

Figure 9. Time series of exploitation rate indices and corresponding escapements (year indicates

fishing season) for the Thompson River steelhead population. All figures computed

deterministically using a fixed diversion rate of 50%. The smooth black lines are third

degree polynomial fitted to each data series. No escapement figures are available for

1997 due to flood conditions that prevented field surveys to be conducted.

56

12. APPENDIX

Unless specified otherwise in one of the following sections, the symbols and notation

used in this Appendix conform to those described in Section 2 of this manuscript. Only in the

odd case (for simplification and descriptive purposes only), is a superscript or subscript modified

to help the reader understand the basic principle.

Section 1:

The following clarifications are made to the equations reported by Cave and Gazey

(1994) following a discussions with the co-author during June 2005. Consider a case where two

block are subject to exploitation for one day by one fishery (so no need for subscripts f,d)

Starting with the corrected form of their Eq. 7, with the denominator changed, the combined

catch of fully exposed block (NC) and partially exposed block (NE) blocks in a 24 h opening can

be obtained using the average abundance for the two blocks combined

(1.1) xhhNC

)1(1 −+=

Substituting N in Eq (1.1) by Cave and Gazey’s paper Eq. (4) and Eq. (6), translates into

(1.2) xC

xC

xC

xC

xEC

hNhhhN

hNhNh

hNNhC

)1(1)1(

)1(1))1((

)1(1)(

−+−+

=−+−+

=−++

=

Which after elimination of NC and NE, and substitution of NC by N reduces to

(1.3) hNh

hhNC x

x

=−+−+

=)1(1

))1(1(

57

Section 2:

Cave and Gazey (1994) consider the harvest rate on a partially exposed (or vulnerable)

block (u) is about half of that acting a fully exposed block (h), and model the relation between

both variables using a contrast coefficient (x) of 0.5 (chosen in an ad hoc fashion)

(2.1) hhhu x −−=−−=−−= 11)1(1)1(1 5.0

(2.2) hu −=− 11

(2.3) hu −=− 1)1( 2

(2.4) huu −=++ 1122

(2.5) huu =− 22

Section 3:

The following illustration describes the procedure used to account for the exploitation

and survival of partially and fully exposed blocks of fish

Block Day Fishery Size Harvest Survival Survival

k 1 of 1 Area_A 1 day after 1 d after 2 d1 u 1-u0 u 1-u

1 of 2 Area_A Area_B2 u 1-u 1-u1 2u -u ^2 (1-u )^2 (1-u )^20 u 1-u 1-u

2 of 23 u 1-u 1-u2 2u -u ^2 (1-u )^2 (1-u)^31 u (1-u )^2 (1-u)^3

The arrows indicate the direction of movement for each block during a 24 h interval.

Shaded areas are those occupied by a ‘fully exposed block’ when fishing began. The top diagram

concerns a fishery that requires 1 d to travel through. Block 0 occupies Area A when the fishery

opens, and has moved out of it 24 h later. Block 1 moves into Area A during this period. Both

58

blocks are partially exposed to fishing when entering or leaving the area, and are subject to

elementary harvest rate u, with a (1-u) survival rate after 1 d of exploitation.

The two lower diagrams concerns a fishery requiring 2 d to travel through, and is split

into two areas (A, B), each requiring 1 d to travel through. When the fishery opens, blocks 0 and

1 occupy adjacent areas. During the first day, block 0 moves out of Area B, and is subject to

harvest rate u. Block 1 moves out of Area A to replace block 0. It is fully exposed to fishing, is

subject to harvest rate h = 2u-u2, with a survival rate after 1 d of exploitation of 1-h (or 1-(2u-u2)

= 1-2u+u2 = (1-u)2). Block 2 enters Area A to replace block 1, and is subject to harvest rate u.

On day 2, all blocks move again, but block 0 is no longer subject to exploitation, and a

new one (block 3) moves into Area A. After 2 d of fishing, block 2 has been subject to an overall

rate of u + ((1-u).(2u-u2)), or 3u–3u2+u3, because the harvest rate on the second day (2u-u2)

applies only to the portion of the block that survives the first day of exploitation (1-u). This

translates into an overall survival rate of (1-u)3. Same for block 1, except that the magnitude of

the impacts on each day is reversed. So during a two day fishery, 4 blocks are involved, but only

3 are simultaneously subject to exploitation each day. Note that by the end of day 2, block 2 still

occupies Area B, so if fishing was to continue in that area the next day, block 2 would be

harvested again at rate u while it moves out, for a total survival rate of (1-u)4. Therefore, survival

over a period depends on the block location with regards to that of the fishery when exploitation

begins, the migration time through the fishery, and the fishery opening schedule.

Section 4:

As illustrated by Haddon (2001, p.43), translating annual harvest rates into instantaneous

harvest rates allows for rounding errors whose magnitude depends on the stratification level

used. For protracted fishing periods (≤ 1d), one can omit subscript d for purposes of clarity, so

the relation C=Nh=NEq is used here for illustrative purposes. If 10 fish are alive at beginning of

a ≤1 d fishery, a 20% harvest rate translates into two deaths and eight survivors by the end of the

fishing period. To use the instantaneous form of the catch equation, h or Eq are usually

transformed to produce an equivalent estimate of instantaneous fishing mortality

59

(4.1) )1()1( EqLnhLnF −−=−−=

After accounting for the above equivalencies and natural mortality that may occur during

the exploitation period, one obtains the instantaneous form of the catch equation

(4.2) ( ))(1 MFeNC +−−=

or alternatively

(4.3) ( )FeNC −−= 1 when M = 0

As a simple example, let E=1, so q=Eq and h=q. Converting h with Eq. 4.1 gives F =

0.223, which translates into the correct catch of 2.0 fish based on Eq. 4.3.

Section 5:

Let subscripts 1 and 2 denote two species subject to the same overall harvest rate in a

fishery. If so, both survival rates should be the same after passing through the fishery. For a one

day fishery impacting a ‘fully exposed’ block, survival is (1-u)2. But if the second species travels

at half the speed, its survival rate should be (1-u)4, since it is fully exposed twice. Substitute

exponents 2 and 4 by a and ab to represent the travel times in relative terms, such that for b=2,

sockeye move twice as fast a steelhead (as in this case). Elementary harvest rates for steelhead

are then derived from those of sockeye as follows

(5.1) aab uu )1()1( 12 −=−

(5.2) )1()1( 12 uLnauLnab −=−

(5.3) )1()1( 12 uLnuLnb −=−

(5.4) ( )( )buLnuLn /1exp)1(exp( 12 −=−

(5.5) ( )( )buLnu /1exp1 12 −=−

(5.6) ( )( )buLnu /1exp1 12 −−=

(5.7) bb uLn ueu 1)1(

2 111 1 −−=−= −

60