Sampling Methodology - Pacific Islands Region

Pacific Islands Fisheries Science Center

SAMPLING THE HAWAII DEEP-SET LONGLINE FISHERY

Marti L. McCracken

Pacific Islands Fisheries Science Center
National Marine Fisheries Service, NOAA
1845 Wasp Boulevard, Building 176
Honolulu, Hawaii 96822-2396
FOR INTERNAL USE ONLY

1. INTRODUCTION
Quantifying bycatch in the Hawaii deep-set longline fishery is required by the MagnusonStevens Fishery Conservation and Management Act (MSA), Endangered Species Act (ESA),
Marine Mammal Protection Act (MMPA), and Migratory Bird Treaty Act (MBTA) and their
implementing regulations. As over a hundred species, some of them listed as endangered or
threatened, have been recorded as being caught in the Hawaii deep-set longline fishery,
reliable estimates of each species’ total bycatch need to be computed in a relatively quick
manner on a yearly basis. A probability sample and corresponding design-based estimators
provide the framework for producing such estimates. Characteristics of the NOAA Fisheries
Pacific Islands Observer Program (PIOP), established to monitor bycatch, and the Hawaii
deep-set longline fishery require a sampling design that can adapt to fluctuating observer
coverage and does not require a complete list of deep-set trips prior to drawing the sample.
As so many of the bycatch estimates are legally mandated and used for management
purposes, a probability sample design that is expected to provide the best average efficiency
over all species seems preferable. The simple random sample (SRS) is often the sample
design that satisfies this criteria and has the advantage that data analysis is more familiar
and straightforward. This design is not practical or cost effective for sampling the DSLL
fishery, as it requires keeping enough observers on staff to cover the clumps of samples in a
brief time period that can naturally occur when drawing a SRS or when the fleet becomes
very active. This document describes the unique sampling design created to sample the
DSLL fleet in a cost effective manner while accommodating the practical constraints that
are inherit in sampling the fleet and aiming for a probability sample.
2. Sampling Design
When a trip is selected to be sampled, an observer is placed aboard the vessel for the duration of the trip and instructed to observe the complete haul back of every fishery operation.
Our problem is to determine how to select trips for observer placement, preferably using a
probability sampling design. To begin addressing this question, a sampling frame needs to
be chosen. Two lists that are readily available for use as the sampling frame are the list of
permitted vessels and the list of notifications. Notifications are recorded sequentially in the
order they are accepted, and since they are accepted prior to a trip’s departure, they can be
used as a sampling unit. Once a notification is selected, the trip linked to it is considered
selected for observation. A drawback to using the list of notifications is that the list is not
complete until the year’s end. In contrast, the list of permitted vessels is available prior
to the new year. There are disadvantageous with using this list. First, a permitted vessel
may not be active in the DSLL fishery throughout the year. Furthermore, all trips by the
selected vessels would need to be observed (likely to be perceived as unfair by the selected
vessels) or a secondary random sample of trips from each selected vessel is needed. As a list
of a vessel’s DSLL trips does not exist prior to the new year, drawing a probability sample
is difficult unless we use the list of notifications. After considering both lists, we decided to
use the list of notifications as the sampling frame.
The next problem to resolve is how to randomly select the notifications. A systematic
sample is a natural design to consider in this circumstance as it can be easily drawn using
the sequential list of notifications. Using this design, all notifications have a probability of
being sampled and this probability is positive and known. Regarding placing observers, the
benefits of this design are that the selected notifications are spread out evenly among the

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notifications and it is known when the next selected trip is approaching. There are two
characteristics of the systematic sample that do not meet our needs. First, the systematic
sample maintains a constant level of coverage. Therefore, enough observers need to be
available to cover all selected trips during the periods of higher fishing activity. Second, the
systematic sample will not accommodate the periods when there are more observers ready
for deployment than required to cover the systematic sample. For example, when an observer
training class is completed or when the fishery is not very active. To maintain the systematic
sample at the required 20% coverage level would increase the cost of the observer program
as more observers would need to be on staff and paid when they are not deployed. These
requirements typically cannot be met under the current level of funding. To reach a balance
between obtaining a probability sample and being cost effective, the sampling design used
since mid-year 2002 has a two-stage sampling protocol. This two-stage design accommodates
fluctuating coverage levels while utilizing observers efficiently.
2.1. The First Stage. For reasons stated above, the first stage of the sampling protocol is a
systematic sample. The systematic sample is drawn at approximately 5% lower coverage than
the targeted coverage level specified by the PIOP and contractor. Drawing the systematic
sample at this level balances the need to insure that observers are available to cover the
selected trips while maximizing the percent coverage by the systematic sample.
A detail to be resolved concerning the systematic sample is the number of starting points.
Once a starting point is selected, every k th unit thereafter is chosen to be sampled. A
systematic sample is a special case of a cluster sample with k clusters in the population. For
example, suppose there are a total of 100 trips and a systematic sample at 20% coverage
with 5 starting points is to be drawn. Using sets of notification numbers, the 25 clusters
that define the population are {1, 26, 51, 76}, {2, 27, 52, 77}, . . . , {25, 50, 75, 100}. To draw a
sample of 5 clusters only 5 starting points between 1 and 25 need to be drawn to define the
selected clusters. If one starting point is used only one cluster is being sampled and it is not
possible to obtain an unbiased estimate of the variance of the estimated bycatch.
When drawing a systematic sample for sampling the DSLL fishery, 5 starting points are
selected from the integers 1 to k using simple random sampling without replacement (SRSWOR). Using 5 starting points provides the benefits of multiple starting points while preventing too many randomly selected trips being clumped together by random chance. For
m denoting the number of starting points and C denoting the targeted percent coverage of
the systematic sample, k = 100m/C. As an example, for C = 15% and m = 5, k = 33.33.
Rounding k down to the integer 33 provides approximately 15.15% coverage by the systematic sample. This level of coverage has been the most commonly targeted level of coverage
by the systematic sample. Hereafter, let M denote the number of clusters, the rounded value
of k.
In summary, the systematic sample by itself constitutes a probability sample of the fleet.
The systematic sample is a one-stage cluster sample where all elements in the selected clusters
are sampled. Hereafter, the clusters defined by a systematic sample will be referred to as
the systematic clusters. Hence, the primary sample units are the systematic clusters and
the notifications are the primary elements of the systematic clusters. The primary sampling
units are selected by SRSWOR.
2.2. The Second Stage. Now, let’s consider drawing the additional samples required to
achieve the targeted coverage level. Only after all upcoming notifications selected by the

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systematic sample are assigned an observer and there are still observers ready to be deployed should additional samples be drawn. The method for drawing these samples needs
to be straightforward as they are needed quickly and with little forewarning. Drawing the
additional notifications using SRSWOR from the list of notifications still eligible for observer
placement is straightforward and the method that PIOP is instructed to use.
Because the occasions when secondary samples are drawn are not randomly selected but
determined by the need to deploy observers, the probability a notification is selected by the
secondary sample is unknown and needs to be approximated. To approximate these probabilities, the contractor’s list of notifications is used. Examination of this list reveals periods
when coverage appears to have been greater or less than the full targeted coverage. Further
details regarding approximating these probabilities are provided in Section ??. Regarding
the complete two-stage sample, notifications are selected with unequal probability as a result
of the secondary sample. For example, notifications that are in the sampling frame of the
secondary sample will have a greater probability of being selected than those not in this
sampling frame.
2.3. Systematic-Plus Sample. Hereafter, this two-stage design is called a systematic-plus
(SYSPLUS) design. The samples selected by the secondary samples are referred to as the
plus sample. The scheme used to derive the plus sample is referred to as the day scheme
(samples are drawn on days when additional samples are needed), and a day sample refers
to the occasion when a secondary sample was drawn from all eligible notifications. The plus
sample typically consists of several day samples. The SYSPLUS sample is not a traditional
two-stage sample as the term “two-stage design” typically refers to a design where primary
units are selected during the first stage and elements within the selected primary units
are selected during the second stage. The second stage of the SYSPLUS sample selects
notifications that were not selected by the first stage systematic sample.
2.4. Implementation of the Systematic-Plus Sample. Since 2013, a new systematic
sample is drawn yearly at a level of coverage that can be maintained, typically 15% coverage.
If the percent coverage of the systematic sample needs to be adjusted during the year, a new
systematic sample is drawn. This strategy encourages maintaining at least 15% observer
coverage while allowing for a quick reaction to a shortage of observers. For example, as a
consequence of having to delay an observer training course at the end of 2013, there was a
shortage of observers at the beginning of 2014, so a systematic sample was drawn at 10%
coverage. After newly trained observers passed the required exam and were ready to be
deployed, a new systematic sample was drawn at 17.25% coverage and maintained until
the 2015 systematic sample began. When more than one systematic sample is drawn in a
year, the year’s sample is stratified with SYSPLUS sampling within stratum. Hereafter, this
design is referred to as a stratified SYSPLUS design.
This current strategy differs from the original protocol. When the SYSPLUS sample was
first used in 2002 there was some interest in quarterly bycatch estimates, so a new systematic
sample was drawn quarterly. Additionally, this quarterly draw allowed the coverage to be
lower the first quarter of the year when the SSLL fishery is usually most active. During
years 2005-2009, the first quarter systematic sample was drawn at 10% coverage to ensure
observers were available to cover this sample and the SSLL fleet. The lower coverage in
the first quarter was offset using the day scheme throughout the year so that the required
annual 20% coverage was achieved. This strategy allowed for greater variability in the level

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of coverage throughout the year at the expense of precision. In an effort to increase the
precision of the annual estimates with minimal additional cost, the observer program was
encouraged to reduce the variability in observer coverage and maintain a systematic sample
at 15% coverage throughout the year.
2.5. Accommodating Research Trips. In previous years, there were trips that participate in one of several NOAA research projects. Except for a few small research projects, all
trips that participated in a project had a NOAA observer aboard performing their normal
responsibilities and tasks required by the project. Trips involved in projects with 100% observer coverage were excluded from the sampling frame. Because these trips fished within
the DSLL regulations and under the incidental take permit for the DSLL fishery, their bycatch was considered part of the bycatch for the fishery. For the years where there were
research projects with 100% coverage, the estimated bycatch was the sum of the bycatch on
the research projects and the estimated bycatch for the remaining fleet’s effort.
Most projects without observers aboard did not interfere with the normal fishing operation
and involved no more than a couple trips per year. For these projects, the participating trips
were considered part of the sampling frame and treated as if they were not selected by the
SYSPLUS sample. For the projects without observers aboard that did interfere with the
normal fishing operation, there was a NOAA scientist aboard that recorded the bycatch for
the trip. Trips with a NOAA scientist aboard recording bycatch were treated in the same
manner as those with a NOAA observer aboard. Trips involved with research projects in the
future will likely be handled in the same manner.
2.6. Exclusion Bias. On 27 August 2012 there was a change in the regulations of the
Hawaii DSLL fishery that imposed new limits on swordfish landed. The new limits are as
follows: (1) With a NMFS observer aboard, there is no limit on the number of swordfish
landed or possessed on a trip, regardless of the type of hook used; (2) With no NMFS
observer aboard, the limit is 25 swordfish landed or possessed on a trip, if the vessel uses
only circle hooks; (3) With no NMFS observer aboard, and if the vessel uses any hooks other
than circle hooks, the limit is 10 swordfish landed or possessed on a trip. In essence, this
regulation created three components of the DSLL fishery defined by the number of swordfish
a trip can keep. Regardless what design is used to select notifications, the first component
(no limit on swordfish kept) will have 100% coverage and the other two components will have
no observer coverage. Prior to the new regulations, all DSLL trips had a trip limit of 10
swordfish landed. The regulation limiting number of swordfish landed was put into place to
discourage trips from targeting swordfish, which typically implies setting the gear shallow.
The shallow setting of gear has historically resulted in different observed catch rates for the
protected species. The exclusion of part of the fleet from the sample gives rise to the potential
of exclusion bias and places limits on how much information our sample can provide about
the total effort of the DSLL fleet. Extrapolating from our sample to the population requires
making assumptions about the population that cannot be confirmed from the sample.
Although the SYSPLUS sample is still used to sample the notifications, the new regulations
changed what the sample represents. Prior to the new regulations, the sample was a random
sample of all DSLL trips fishing under a uniform set of rules and requirements. Under the
new regulations, what is being randomly drawn is a selection of trips that will have an
observer aboard and not have a trip limit on swordfish landings.