Review of mark-recapture sampling program
to estimate abundance of Burbot in Moyie Lake, British Columbia
Carl James Schwarz, P.Stat.
Department of Statistics and Actuarial Science
Simon Fraser University
cschwarz@stat.sfu.ca
2011-01-28
1. Introduction
This report will review the proposed mark-recapture sampling program to estimate the
abundance (and other population parameters such as survival) on Moyie Lake, British
Columbia. This review is based on information provided in Neufeld (2010), Neufeld and
Spence (2009), Neufeld (2008) and Westover (2007).
Briefly, burbot are captured as part the gamete collection and spawning surveys
conducted typically in February of each year. Fish are captured using angling at spawning
locations on the north basin. They are measured for length and weight, assessed for sex
and maturity, tagged with a single Floy tag, and released. For example, Neufeld (2010)
reported that in the 2010 survey was conducted from 8-18 February 2010. During this
time, 542 fish were captured; 514 were unmarked and so were tagged, measured, and
released; 28 were recaptures of fish tagged in previous years, and so were released.
Sampling occurs primarily at the Cotton Creek area of the north basin.
The proposed program is a standard capture-recapture experiment. Because individually
numbered tags are used, a capture-history (a sequence of 1’s and 0’s indicating if a fish
was captured or not-captured) will be constructed. This will serve as the input to the
standard analysis programs such as MARK or RMark if all assumptions specific to the
various models are met.
In this review, I will examine the current sampling protocol to see what level of precison
could be expected in the future; indicate how violations of the standard assumptions
could lead to biases in the estimates of abundance; and suggest improvements to the
design to isolate potential problems.
2. What is the study population?
The population of interest for which an abundance estimate is required was not defined in
the reviewed documents. All captures occur on the spawning grounds and Figure 5 of
1
Neufeld (2010) shows that the captured burbot are all about 400 mm or larger. This
suggests that the population of interest will be sexually mature burbot about 400 mm (or
about 0.75 kg) or larger that use the sample spawning area. The latter restriction may be
problematic if fish exhibit high fidelity to spawning areas so that fish at other spawning
areas are not subject to sampling and so are “invisible” (refer to the discussion of the
mixing assumption later in the report).
The north basin of Moyie Lake is not a closed system and there is a connection with the
south basin. If fish from the two basins do not mix, then, the population sampled will be
the fish only in north basin. If fish from the two basins mix completely, then the
population sampled will be fish from both basins. If there is partial mixing, then the
population sampled is a weighted “average” of the populations in the two basins, and the
estimated population size can refer to different components depending on the sampling
design.
Consequently, it is recommended that a careful definition of the target population be
created and the sampling methodology be reviewed carefully to ensure that the target
population is being sampled (refer to details below).
3. Projected precision of the study design assuming no
violations of assumptions.
The proposed sampling scheme is a example of Jolly-Seber (Jolly, 1965; Seber, 1965)
sampling experiment. Each year, samples of fish are taken on the spawning grounds,
examined for marks, unmarked fish are marked, and marked fish are then released.
The methods of Devineau et al (2006) were used to estimate the approximate precision of
the estimates in this experiment. Briefly, a population is defined with known parameter
values for abundance, survival, recruitment, and catchability. These are used to generate
the expected counts for each possible capture history. These expected counts are used as
“data” in a capture-recapture analysis and the resulting estimates and standard errors will
provide estimates of the likely precision under these conditions.
Neufeld (2008) estimated the population size in the north basis as between 1500 and 2500
adults with an annual survival rate of around 0.70 to 0.80. Neufeld and Spence (2009)
indicated that a harvest of 360 fish in 2008 represented 14-24% of the population
indicating a population size of around 1900 fish; a reported harvest of 147 fish in 2009
represented between 6-10% of the population indicating a population size again around
1900 fish.
We used a population size of 2000 in our simulation exercise with an annual survival rate
of .80 (which includes harvest and natural mortality). To keep the population at steady
state, we assumed a recruitment of 0.20 new fish per adult fish in the population.
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We examined a number of scenarios (Table 1) where all of the typical mark-recapture
assumptions held (see next section) varying the total fish captured per year and the length
of the study. Note that in a standard Jolly-Seber experiment, estimates are not available
for the first year of the study and only available in the last year of the study if one is
willing to assume that survival rate is approximately constant over time. The relative 95%
confidence interval (2se/N) is less than the 25% (i.e. the relative standard error is less
than 12%) as recommended by Seber (1982) for management purposes, if the sampling
effort captures about 400 fish per year for at least 5 years.
Table 1. Approximate precision of estimates of abundance
from a Jolly-Seber experiment with an initial population
size of 2000 fish, annual survival of 0.80, recruitment to
keep the population at steady state when a model with
constant survival rates over time, but time varying capture
rates and recruitment rates. Note that estimates are not
available for first year of study and se report are an
“average” of the se for the middle years.
Fish captured per
Length of
Typical se of
year
Experiment (years) estimates of N
(rse)
133
3
1200 (60%)
5
700 (35%)
7
530 (26%)
266
3
586 (29%)
5
320 (16%)
7
275 (13%)
400
3
360 (18%)
5
200 (10%)
7
175 ( 9%)
533
3
250 (12%)
5
150 ( 7%)
7
120 ( 6%)
Of course, the actual precision may differ from the results in Table 1 because of unequal
sampling effort or violations of assumptions as outlined below.
As part of the planning process, it is important to specify the precision required for
management purposes so that adequate sampling can be done to meet the target.
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4. Standard assumptions and the effects of their
violations.
Standard capture-recapture models to estimate abundance (e.g. the Jolly-Seber model)
make some basic assumptions about the study design and biology of the population of
interest:
 no effect of marking on survival and catchability;
 marks are not lost;
 emigration from the study area is permanent (and not distinguishable from
mortality);
 homogeneous survival over all fish;
 homogeneous catchability over all fish;
 marked and unmarked fish mix in the population.
Violations of these assumptions may lead to biases in the estimates of abundance,
recruitment, and survival.
4.1 No effect of marking on survival and catchability.
Unfortunately, there is no way to study the effect of marking on survival as it is
impossible to monitor an unmarked group for survival rates in a natural setting unless the
animals can be individual identified (e.g. natural marks). The reviewed documents
indicate that great care is taken to reduce the trauma inflicted by angling on the fish.
Immediate handling mortality could potentially be studied using cages where newly
tagged animals are held to monitor mortality rates. This may be impractical given
sampling occurs in the winter.
There is some evidence from trap studies conducted in past years that burbot which were
captured in traps shows trap avoidance for later recaptures in the same year. It is unclear
if angling will have the same effect.
4.2 Marks are not lost.
All fish are currently tagged with a single Floy tag. Tag loss is often an important
problem in long-term monitoring. Homogeneous tag-loss (tag loss occurs at the same rate
for newly tagged and previously tagged fish) has been shown to lead to unbiased
estimates of abundance (Arnason and Mills, 1981), but still leads to bias in estimates of
survival and recruitment. However, tag loss may not homogeneous because newly
applied tags may be more prone to loss than older tags which have scar tissue to hold the
tag more securely. Heterogeneous tag loss is known to lead to bias in estimate of
abundance as well (McDonald et al. 2003) especially if tag loss rates are high.
McDonald et al. (2003) found that the relative bias in estimated population sizes when
newly tagged animals have an initial tag loss can be approximated as

(1 p)
1 
4
where p is the capture rate and  is the initial tag-loss rate. Neufeld (2009) reported an
estimate tag loss rate within a single year of around 5%. Based on a population size of
around 2000 fish with 300 fish being captured each year, the capture rate is around 15%,
the relative bias in the estimates of abundance will be around 5% which is much smaller
than the expected relative standard errors reported in Table 1 for all but the high
effort/long-term studies.
It is recommended that some (or all) fish be double tagged so that the initial and
cumulative long-term tag loss rate can be estimated using the methods of Seber and
Felton (1981). Adjustment can be made to the estimates of abundance using the methods
of Cowen and Schwarz (2006). In many wildlife studies, the cost of applying a second
tag to an animal in-hand is small relative to the cost of actually capturing each animal and
often all fish are double tagged. It is not necessary to double tag fish in all years (e.g.
double tag every second year), but in order to get reasonable estimates of tag loss, it is
important to have sufficient double tagged fish in the population so that at least 20 are
returned in subsequent capture events. This would imply that with a 10-20% recapture
rate, about 100-200 double tagged fish should be in the population under ideal conditions.
A secondary batch mark can also be used (e.g. fin clip), but then a fish captured with a
secondary clip and no tag provides no information on when the tag is lost. Use of batch
marks for long-term studies is not recommended.
4.3 No temporary emigration (I).
The north basis on Moyie Lake is not geographically closed with some evidence that fish
can move to/from the south basin.
If emigration to/from from the north basin to the south basin was permanent (i.e. oneway), then this is indistinguishable from mortality. Estimates of mortality then will
include a component for this permanent emigration. Estimates of abundance in the north
basin will not be biased and reflect the population in the north basin at the time of
sampling. Estimates of recruitment will reflect a combination of recruitment from the fish
in the north basis and movement from the south basin.
If movement among basins is “random”, i.e. the probability that a fish will be in the north
basin in year i is the same regardless if it was in the north or south basin in year i-1, then
estimates of abundance refer to the ENTIRE population of both the north and south
basins! Under these conditions, the catchability of a fish is simply the product of the
probability of being present in the north basin and the probability of being captured on
the spawning ground. Random movement is equivalent to complete mixing of the fish in
the two basins between sampling events.
If movement among basins is “sticky” (i.e. non-random), then the probability of being in
the north basin in year i is typically higher if the fish was in the north basin in year i-1
compared to a fish in the south basin in year i-1. Under these conditions, it is not clear
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what the estimates of abundance refer to – typically some combination of actual
abundance in the north basin at the time of sampling plus some fraction of the fish in the
south basin.
The methods of Devineau et al (2006) can be used to estimate the bias in the estimates of
abundance under non-random movement. Neufeld (2009) reported that of about 200
tagged in the north basin in 2006 one was recaptured in the south basin. Assuming a
recapture rate in the south basis of about 10% (based on an assumed population size of
around 1500 fish), this corresponds to 10/200 = 5% movement per year of tagged fish
from the north to the south basin. Similarly, Neufeld (2009) reported that of about 200
fish tagged in the south basin, 3 were recaptured in the north basin. Assuming a recapture
rate in the north basis of 25% in the north basin over the two years, this corresponds to
12/200 tags that moved from the south to the north, or again about a 5% movement per
year. Estimates of the bias to be expected are presented in Table 2. Notice that the bias in
the estimates of abundance does NOT depend on the sample size and increases with the
length of the study. The bias appears to be small relative to the uncertainty in the
estimates (refer to Table 1) except for the high effort/long term scenarios.
Table 2. Approximate bias of estimates of abundance in
the North basin from a Jolly-Seber experiment with an
initial population size of 2000 fish in the north basin, 1500
fish in the south basin, annual survival of 0.80 in both
basins, recruitment to keep the population at steady state,
a 0.95 probability that a fish in north basin stays in north
basin and a 0.05 chance that a fish in the south basin
moves to the north basin between years.
A model with constant survival rates over time, but time
varying capture rates and recruitment rates was fit. Note
that estimates are not available for first year of study and
se report are an “average” of the se for the middle years.
Fish captured per
Length of
% bias in N
year
Experiment (years) by end of
study
133/266/400/533
3
-3%
5
-4%
7
-5%
If temporary emigration between the two basins is a concern, then a modified sampling
design should be considered called the Robust Design (Pollock, 1982; Kendall et al.
1997, 1995). Under the robust design, the sampling protocol is modified to sample on
two temporal scales. At the primary level, sampling takes place every year as currently
proposed. The population is assumed to be open to mortality and emigration between
primary periods. Within each primary periods, two or more closely spaced sampling
passes are conducted during which the population is assumed to be closed (Figure 1).
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Figure 1. A diagram of the robust design.
A diagram of the model for this type of sampling is presented in Figure 2.
Figure 2. The structural model for this robust design. The secondary samples within the
primary period are conducted on the segment of the population on the study area (small
circles). During the secondary samples, the population is assumed to be closed. Between
primary periods, animals may stay in the study area, or temporarily migrate outside of the
study area (larger circle). The  ' and  '' parameters measure the migration rates.
Intuitively, the multiple secondary sessions estimate the size of the population on the
study area (population in the small circle in Figure 2). However, when you consider the
capture histories across the primary periods, the Jolly-Seber model estimates the size of
the population on the study area and outside the study area (larger circle). The difference
in these two populations provides information on the migration rates.
In the context of Moyie Lake, such a robust design could be implemented by doing two
(or more) passes over the spawning areas assuming that fish remained on the spawning
grounds for both passes. [If fish spawned and then left after spending only a short time on
the spawning ground, the robust design above would not be feasible, but there is a more
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complicated model called the Open Robust Design (Kendall and Bjorkland, 2001) that
has been developed but requires quite extensive data.]
There are several alternatives to using the robust design if the degree of mixing is a
concern.
A program where fish were tagged in both basins would be analyzed using the multistratum Jolly-Seber model (Dupuis and Schwarz, 2007) and would provide estimates of
abundance for both basins.
Or a telemetry component could be added where some fish are tagged in the north and
south basins and tracked over time (following Powell et al, 2000). They recommend that
a minimum 25 animals be radio tagged in each time period and geographic stratum of
interest. If you were willing to assume that movement rates were constant over time, then
a one-year study may be adequate with fish marked in both basins. This would provide
high quality information on the exchange rates which could be used to adjust for any bias
in the estimates of abundance due to exchanges between basins.
Finally, a monitoring program of tagged fish could be established in the south basin to
estimate what fraction of fish in the south basin have tags from the north basin. For
example, an automated camera system could photograph fish and if the mark is readily
detectable (e.g. a white tag on a black fish, even if the id number was not readable), then
the marked fraction of fish in the south basin with tags from the north basin provides
information on the mixing rate. I’m am not aware of any previous work that has taken
this approach, but it is justified theoretically and not difficult to implement.
4.4 No temporary emigration (II).
The Jolly-Seber model assumes that all fish are equally catchable in each year regardless
if it was on the spawning ground or not on the spawning ground in the previous year.
This assumption would be violated if fish are less likely to spawn next year if they spawn
in this year. An extreme form of this is skip spawning where fish spawn every second
year.
The effect of the temporary emigration is similar to that discussed in the previous section,
i.e. leads to a negative bias in estimates of abundance. I could not find any information on
the life-history with respect to spawning to generate any sensible simulation.
The Robust Design can again be used for this scenario. Kendall and Nichols (2002) have
also developed a model for skip-spawning if this is a concern.
4.5 Homogeneity of survival.
The Jolly-Seber model assumes that all fish have the same probability of survival.
Neufeld (2010, Figure 6) showed that captured fish ranged in age from 5 to 16 years but
8
there was little variation in length over these ages. In many species of fish, survival rates
tend to increase with age/size. Fortunately, heterogeneity in survival rates among
members of the population do not lead to bias in estimates of survival as long as survival
is independent of catchability. In this case, the estimates of survival refer to the average
survival rate over all fish. Reported estimates of the standard error need to be adjusted for
this heterogeneity (i.e. using the over-dispersion parameter commonly determined by
capture-recapture software) but the increase in the standard error are usually small unless
heterogeneity is large.
One way in which this assumption of independence between catchability and survival
would be violated is if larger fish which higher survival rates had lower capture rates than
smaller fish with lower survival rates.
With modern capture-recapture software, models can be fit to assess if survival is a
function of observable covariates such as weight or length (Bonner and Schwarz, 2010).
4.6 Homogeneity of catchability.
Heterogeneity in catchability can occur for many reasons, but the two most important
reasons from a capture-recapture perspective are behavioural and animal effects.
Examples of behavioural effects are trap happiness and trap-shyness. In these cases, the
estimates of catchability are biased upwards/downwards with biases in estimates of
abundance in the opposite direction. With long-term datasets, these effects can estimated
(assuming that trap responses diminish over time). Given that sampling takes place a year
apart, it is hoped that any behavioural effects are minimal.
Animal-based heterogeneityin catchability is typically related to size in fisheries. For
example, gill nets have a well defined selectively curve. Hook sizes can also have an
effect on the size of fish that can be selected. Males and females may also show
differential catchability.
Carothers (1973) showed that the relative bias of estimates of abundance is a function of
the coefficient of variation (standard deviation/mean) in the capture-probabilities among
animals (  ):
E  N̂  
N
1  2
For example, if half of the population has a catchability of 0.15 and half of the population
has a catchability of 0.25 (for an average catchability of .20), then the cv of the
catchabilities is 1.12 and the approximate bias in the estimates of abundance is -20%.
This result can be used to approximate the bias if some estimates of the difference in
catchability are available.
For fixed attributes, such as sex, or attributes that change very slowly (e.g. length of older
fish) the common methodology to deal with heterogeneity in catchability is to stratify the
population by sex, compute estimates of abundance separately for each sex, and then sum
9
these two values. While the standard error of the estimates of abundance for each sex will
be larger than desired, the combined estimate will have comparable precision to a pooled
sample (assuming that the catchabilities are not extremely different.]
This procedure assumes that every captured fish can be correctly assigned to each sex.
Neufeld (2009) reported that only 8% of captures could not be sexed [Of course, if the
sex is determined on a subsequent recapture, this information can be brought
backwards.]. Challenger and Schwarz (2009) have also developed models to deal with
uncertainty in classification that can be used if not all animals can be sexed.
For attributes that change dramatically over the course of the experiment, there are two
common methods of dealing with this. First, the attribute is broken into classes (e.g.
length classes) where the catchability varies among classes, and use multi-state models
(e.g. Nichols et al, 1992) where animals are allowed to move among states. For slow
growing fish such as burbot this may not be necessary. The multi-state Jolly-Seber
model (Dupuis and Schwarz, 2007) can be used when catchability depends on geographic
locations (e.g. different spawning areas) and all spawning areas are sampled.
In this case, the attribute can be used as a continuous covariate to model the catchability
as a function of the attribute (e.g. as a function of length) and then this is used to estimate
the population size using a Horvitz-Thompson estimator (Bonner and Schwarz, 2010).
In this study, Neufeld (2009, Figure 5) showed the distribution of length of captured fish.
The histogram of lengths is a convolution of the distribution of lengths in the population
and the selectively of the gear used to capture fish. I did not find any information about
the selectivity of the gear used in the study and recommend that future sampling efforts
use a variety of gear (e.g. different hook sizes) to try and determine if there is a difference
in catchability by length/weight.
4.7 Mixing of tagged and untagged fish.
Capture-recapture methods that estimate abundance assume that tagged and untagged fish
mix between sampling occasions. Unequal mixing leads to potential biases in both
direction.
There are two common cases of non-mixing. First is when subsequent samples after
marking take place very quickly after marking. In this study, capture events take place a
year apart, so unless the fish stay in well defined schools for the entire year, mixing
should occur.
The second case occurs when fish are “faithful” to their sampling areas. Neufeld (2010)
noted that all of the fish captured in 2010 came from spawning areas around Cotton
Creek. If fish are completely faithful to their spawning locations across years, the marked
fish will not mix with fish that spawned at other spawning areas, and the estimate of
abundance will refer only to the spawners at the sampled sites. In this case, changes in the
10
sampled area (e.g. adding more spawning areas) will look like an increase in the
population size but will be an artefact of the sampling protocol.
If fish are partially faithful to their spawning area, then we are back at the case of
temporary emigration discussed earlier.
The only way to determine the degree of fidelity to spawning areas is to sample at several
sampling areas and estimate the degree of interchange among the different spawning
areas. The selected areas should be reasonably far apart so that observed movement is a
good indicator of general mixing. If all spawning areas are sampled, then the multi-state
Jolly-Seber model can be used directly (Dupuis and Schwarz, 2007).
If not all spawning areas are sampled, then a robust design sampling protocol will be
needed as outlined earlier.
5. Estimating population growth vs. absolute
abundance.
A common meta-analysis once estimates of abundance have been obtained is to estimate
the population growth rate over time. It turns out that population growth can be estimated
directly from the Jolly-Seber protocol and is more robust to violations of assumptions
than the estimates of abundance (Schwarz, 2001).
For example, heterogeneity in catchability is roughly constant over time, and so the
relative biases in estimates of abundance are approximately equal over time. This implies
that in the estimates of population growth (the ratio of subsequent abundances), the bias
factor ( 1  2 ) will tend to cancel, and the estimates of population growth will be
relatively unaffected by heterogeneity.
Similarly, if there is temporary emigration, the biases again will tend to be constant over
time.
Lastly, if fish are completely faithful to the spawning grounds, the estimates of
abundance will refer only to the population using the sample grounds. As long as the
spawning resource is not limiting and that the population trajectory of the sample
spawning population matches the general population, estimates of population growth will
be unbiased.
6. Collection and incorporation of auxiliary information.
Classical capture-recapture models only use the information provided by the experiment
to estimate the parameters of interest. However, if additional information is easily
collected, this can be incorporated into the estimation procedure.
11
6.1 Information on the marked fraction.
The marked fraction in the population is the key to estimating abundance. So outside
information on the marked-fraction provides additional information to estimate
abundance. For example, if tags are readily visible (but not necessarily readable) from a
stationary camera, then as long as tagged and untagged fish mix, the marked-ratio from
this stationary camera is useful. At the moment, standard software cannot incorporate this
information, but bespoke software can be readily written.
6.2 Information on an index of abundance.
In some cases, information that is proportional to abundance (but the constant of
proportionality is unknown) is available. For example, if angler efficiency remains
relatively constant over time, the CPUE provides additional information on trends in
abundance. The incorporation of this auxillary information with capture-recapture data is
termed integrated population modeling. An example of such a model is found in Besbeas
et al (2003).
7. Recommendations
(a) Carefully define the target population for this study and ensure that
tagging/recapture methods sample the relevant population. For example, are you
interested only in the abundance of mature, spawning fish above a certain length?
(b) Review the life-history of the species for information on fidelity to spawning
ground and the two basins. Sampling may have to done a more than one spawning
location (to estimate the mixing rates), or at more than one temporal scale (to
estimate temporary emigration among basins or because of skip spawning). For the
latter, a robust design is preferred if feasible and biologically sensible.
(b) Apply double tags to at least 200 fish to estimate the cumulative tag loss rate. In
many cases, the extra cost of double tagging once a fish is in-hand is small relative to
the cost of obtaining the fish and so all fish are often double-tagged.
(c) Continue to record attributes such as location of capture, sex, maturity,
length/weight on all handled fish so that models with stratification can be fit to
account for heterogeneity in catchability.
(d) Vary the sampling gear (e.g. different hook sizes) to determine the selectivity
curve for the current gear.
(e) Losses on capture (e.g. fish removed for brood stock) should be recorded. If
information on harvests is available this can be incorporated into the modeling of
abundance.
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(f) If auxiliary information on the mark-ratio or indices that are proportion to
abundance are easily collected, these should be integrated with the analysis.
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