|NORTH PACIFIC RESEARCH BOARD PROJECT FINAL REPORT
Estimating movement rates of Pacific cod (Gadus macrocephalus) in the Bering Sea and the Gulf of Alaska using mark-recapture methods.
NPRB Project 620 Final Report
Yunbing Shi 1, Donald R. Gunderson 1, Peter Munro 2, Joseph D. Urban 3
1 University of Washington, School of Aquatic & Fishery Sciences, 1122 NE Boat St., Box 355020, Seattle, WA 98195. (206) 364-6508, email@example.com
2 National Oceanic & Atmospheric Administration, National Marine Fisheries Service, Alaska Fisheries Science Center, Resource Ecology & Fishery Management Div. Sand Point Way NE, Seattle, WA 98115
3 Alaska Department of Fish & Game, 211 Mission Road Kodiak, AK 99615-6399
Understanding Pacific cod movements and tempo-spatial distribution is critical to successful management of Pacific cod stocks and protection of marine mammal populations. We compiled four Pacific cod tagging datasets and attempted to quantitatively model cod movement in eastern Bering Sea and Gulf of Alaska. Tag recovery indicates that Pacific cod exhibit great site fidelity with about 70% of the tags recovered less than 50 miles from their release site. Nevertheless, some individuals undertook extensive migrations of up to 675 miles.
We applied a Brownie model to tagging data to estimate Pacific cod survival, and exploitation rates. Estimated annual survival rates of Pacific cod in the eastern Bering Sea ranged from 0.36176 to 0.5384, exploitation rates from 0.1612 to 0.3224, instantaneous natural mortality rates from 0.4029 to 0.5033, and instantaneous fishing mortality rates from 0.2162 to 0.5136.
Tag recovery rates by size group were used to quantify gear selectivity, and trawl, pot, and longline selectivity curves each had a characteristic dome shape. Peak selection occurred at 55 to 70 cm for pot gear, 55cm to 75 cm for trawls and 65 cm to 80 cm for longlines.
Tagging data were fit to a Von Bertalanffy growth model, and estimated growth parameters were in good agreement with those from age determination.
The reliability of many of our estimates was compromised due to the opportunistic nature of tag releases. We recommend that more controlled and well-designed tagging experiment be carried out in order to quantitatively model Pacific cod movement and reliably estimate Pacific cod population parameters
Key Words: Pacific cod, tagging, statistical model, movement, survival, exploitation rate, growth, selectivity, seasonal, mark-recapture
Citation: Shi, Y., D.R. Gunderson, P. Munro, and J.D. Urban. 2007. Estimating movement rates of Pacific cod (Gadus macrocephalus) in the Bering Sea and the Gulf of Alaska using mark-recapture methods. North Pacific Research Board Final Report 620, ??p
Table of Contents
January 15, 2007. First progress report was submitted.
August 27, 2007. Second progress report was submitted.
September 30, 2007. Final report was submitted.
Pacific cod, Gadus macrocephalus, is a transoceanic species, occurring at depths from the shoreline to 500 m extending from about 34° N latitude (Santa Monica Bay, California on North American coast and south end of Korean Peninsula on Asian coast) to about 63° N (Bakkala, et al 1984, Zhang 1984). Pacific cod are known to make seasonal long distance migrations in the eastern Bering Sea (Shimada & Kimura 1994).
Pacific cod is one of the most important species in the eastern Bering Sea, Gulf of Alaska, and adjacent waters off Aleutian Islands. Pacific cod catches rank second among groundfish resources in Alaska waters following walleye Pollock, Theragra chalcogramma. Fishery catch has steadily increased from about 51,650 mt in 1980 to 206,130 mt in 1992, and was sustained at about 200,000 mt for the next five years. The record catch was 240,590 mt in 1996. Since 1996, it declined. The most recent annual catches have been about 170,000 mt. Recent resource survey results indicate a continued decline of exploitable biomass (Witherell 2000).
One of the obstacles to accurate stock assessment of Pacific cod is stock delineation. Successful management of exploited species requires the identification of self-recruiting populations, or stocks, as differences in recruitment, growth or mortality may necessitate separate management and conservation strategies. Pacific cod has been an important target fishery in U.S. waters since the mid-1980s, second only to walleye Pollock (Theragra chalcogramma) in commercial landings, yet very little is known about population subdivision within and between managed areas. In Alaskan waters two stocks are identified for state and federal management purposes: the Gulf of Alaska (GOA) and Bering Sea/Aleutian Island (BSAI) stocks. Genetic studies (Kathryn Cunningham, abstract of 16th SAFS Annual Graduate Student Symposium, 2006) indicate that little differentiation exists within Alaska stocks or between Alaska and Washington stocks.
In this study we analyzed four sets of Pacific cod mark-recapture data to depict exchange between large ecosystems, and seasonal movement within these ecosystems. The first data set, presented by Shimada and Kimura (1994), comes from tags that had been released as part of standardized trawl surveys conducted by the Resource Assessment and Conservation Engineering (RACE) division at Alaska Fisheries Science Center (AFSC). From now on it will be referred to as RACE I data set. The second data set has resulted from tags that were released on an opportunistic basis as part of research cruises conducted by the Alaska Department of Fish and Game (Urban, D., ADF&G, unpublished data). From now on it will be referred to as the ADF&G data set. The third data set comes from tags released during cruises for localized depletion studies conducted by the Fisheries Interaction Team (FIT) at AFSC. From now on it will be referred to as the FIT data set. The fourth data set is from archival tags released on a number research cruises carried out by AFSC RACE (Nichol and Chilton, 2006), and will be referred to as the RACE II data set. All recaptures were from commercial fisheries.
The original proposal of this study was to quantitatively model Pacific cod movement in eastern Bering Sea. However, the data are too disjointed in time and place to allow estimation of movement rates among regions of the Bering Sea or between EBS and GOA, due to the opportunistic nature of tag releases and dependence on commercial fisheries for tag recoveries.
After studying the four sets of data, we present a summary of this study in this report, to accomplish following goals:
Characterize Pacific cod movement between Eastern Bering Sea (EBS), Aleutian Islands (AI), and Gulf of Alaska (GOA) and within EBS, AI, and GOA.
Estimate survival and exploitation rate when there is sufficient data available to fit a Brownie Model.
Estimate von Bertalanffy growth parameters.
Summarize size specific recovery rate and discuss its use as an approximation for selectivity curves.
Materials and Methods
The first (RACE I) data set was generated by NMFS during AFSC chartered fishing vessels engaged in summer bottom trawl surveys off Alaska from 1982 through 1990. Pacific cod were tagged throughout their eastern Bering Sea distribution. In addition, there were tag releases from cooperating Japanese, Korean, and U.S. research vessels operating in the Aleutian Islands and Gulf of Alaska. Capture gear included bottom trawl, pot, and hook-and-line. Two types of tag were used in this study: 3.5-inch anchor tags and 8-inch lock-on spaghetti tags. The majority of releases (69%) were made with the lock-on spaghetti tag (Shimada & Kimura, 1994).
Pacific cod were tagged across the entire size range available to the capture gears, although priority was placed on the release of fish less than 55 cm. Most of the tags were released during summer months (June, July, August, and September).
There were 12,396 tags released between 1982 and 1990. Of these, 375 tags were recovered and reported by commercial fisheries between 1982 and 1992. Table 1 presents number of tags released by year and area (NMFS statistical area), number of tags recovered and recovery rate (%) by release year and release area.
The second set (ADF&G) of Pacific cod tagging data was provided by Alaska Department of Fish and Game. ADF&G has been tagging Pacific cod since 1997. A total of 13,858 tags have been released, mostly during the annual trawl survey conducted by the department. Most tags (10,334 out of 13,858 tags) were released in state waters (<= 3 miles from shoreline). Tags have been released around Kodiak Island, the south side of the Alaska Peninsula, and the eastern Aleutian Islands (Table 2). All tags were released by experienced ADF&G staff. Released fish were observed from the vessel to assess their condition. If a tagged fish is a “floater”, it is noted as such. Most tagged fish (12,164) were caught by survey trawls. A small portion of the fish for tagging (1694) was captured by pots. Tags were recovered by commercial fishermen using a variety of gear types. Over 800 tags have been recovered as of March 2007 (Table 2).
The third set (FIT) of Pacific cod tagging data was from AFSC Fisheries Interaction Team (FIT). FIT scientists released a total of 6,871 tags. Most (6,393) of the tags were released directly from tagging table. 478 of these were released after being held for a mortality study or monitoring in a portable live tank or fish hold supplied with continuously flowing fresh sea water (Table 3). All live specimens were captured using scientific pots designed for Pacific cod research. There were 683 tagged fish in mortality study/monitoring. Release date was recorded for 478 of these. It is assumed that those that did not have a release date were dead at or before evaluation. Some of the specimens with release dates were categorized as dead. Tags were pulled from dead specimens before the carcasses were discarded. Only the tags released directly from the tagging table were used in this movement and survival analysis. As of end of 2006, there were 2,487 tags recovered and reported from tags released directly. The average recovery rate was 38.9%.
The last data set (RACE II) was provided by the AFSC Resource Assessment and Conservation Engineering Division (RACE). RACE scientists along with FIT scientists released a total of 634 archival tags in the Gulf of Alaska and eastern Bering Sea between 2002 and 2005. There were 329 tags released around Kodiak Islands and 305 in Unimak Pass waters. Live specimens were captured by pot (529) and jig (105). As of end of 2006, there were 287 recoveries reported. The average recovery rate was 45.3% (Table 4).
Tags reported without location information (statistical area or latitude and longitude) were not included in movement analyses. However, those tags were included in tag recovery rate analyses. Tags recovered and reported with size information were included in size specific recovery rate analysis, regardless of availability of location information.
The movement between strata can be modeled by an expanded Brownie Model (Brownie et al., 1993). We proposed a model based on a Halibut movement model described in Anganuzzi et al. (1994):
= number of fish tagged and released in area l (l = 1,2,…,L) during time period t (t = 1,2,…,T);
= number of fish (tags) recovered in area k (k = 1,2,…,K) during time period i (t = 1,2,…, I) from group released in area l (l = 1,2,…,L) during time period t (t = 1,2,…,T);
= the probability of movement of a fish being tagged and released in area l (l = 1,2,…,L) and recovered in area k (k = 1,2,…,K) during time period i (i = 1,2,…, I);
= probability of a fish (tag) being recovered in area k (k = 1,2,…,K) during time period i (t = 1,2,…, I) from group released in area l (l = 1,2,…,L) during time period t (t = 1,2,…,T);
= utilization rate in area k (k = 1,2,…,K) during time period i (i = 1,2,…, I), given a fish survived natural causes to time i;
= reporting rate in area k (k = 1,2,…,K) during time period i (i = 1,2,…, I), given a fish is harvested;
= probability of a fish surviving all sources of mortality during time period i (i = 1,2,…, I);
= sum of the group fish released in area l (l = 1,2,…,L) during time period t (t = 1,2,…,T) and consequently recovered:
The parameter we wish to estimate is , the probability of movement. The data that we have are represented by, and. There are three critical parameters for which we must either assume or estimate values: , the utilization rate by area and time period, , the reporting rate by area and time, and , overall survival rate by time period. The last parameter,, can be estimated by fitting a Brownie model to the mark-recapture data, which we will discuss in next section.
After diligently examining the four sets of tagging data, we concluded that due to lack of key input information, such as area and time specific exploitation rates and reporting rates, it is not practical to fit existing data sets to our proposed movement model. Instead, we applied the following quantitative estimator to describe tagged fish movement between strata.
Where, Mij = movement rate of tagged fish from strata j to strata i.
Rij = number of tagged fish recovered in strata i, that were released in strata j.
This is a rough qualitative measure of fish migration between strata. However, Mij would be a good indicator of movement rate between areas, under the following assumptions:
Tagged fish are fully mixed (intermingled) with the untagged population before tagged fish were captured by fishery in both receiving system and releasing system.
Exploitation or utilization rates are in all areas at all times, i.e. there is no spatial or temporal variation in exploitation rate;
Natural mortality is constant, i.e. there is no spatial or temporal variation in natural mortality;
Recovery and reporting rates are constant, i.e. there is no spatial or temporal variation in recovery and reporting rates.
When these assumptions are violated, independent information concerning the assumptions is necessary to overcome the assumption, in order to reliably model Pacific cod movement.
Estimates of survival and exploitation rate when there is sufficient data available to fit a Brownie Model.
The primary goal of the FIT tagging program was aimed at ascertaining localized short-term movement during a before-and-after study designed to evaluate local depletion impact on Steller sea lion prey availability. Nevertheless, the tag recovery information generated interest and sometimes anxiety among fisheries professionals due to the high exploitation rate implied for eastern Bering Sea cod.
In responding to this concern, we used the same set of data to fit a mark-recapture model (Brownie Model I) to estimate Pacific cod survival and exploitation rates in the eastern Bering Sea. We also estimated instantaneous natural and fishing mortality.
Since the tagging studies were designed to qualitatively describe short-term localized movement, some of the assumptions for the Brownie Model I were not met. A detailed discussion and suggestion for further studies is presented.
In this work, the Brownie Model I (Brownie, et al, 1985) for estimation of survival and exploitation rates, and the basic fishery catch equation will be adapted to estimate Pacific cod natural and fishing mortality rates. Software program MARK (Cooch & White, 2006) developed for the analysis of data from mark-recapture studies will be used fitting the Brownie model with the FIT data set.
= Number of fish marked and released in year t;
= number of fish recovered in year j that were released in year t;
, total number of tags recovered from release group (year) t.
= exploitation rate in year j;
= tagging induced mortality at the time of release in year t; is estimated outside the model;
= tag reporting rate, estimated outside model by comparing recovery rates of high reward tags, archival tags and assumed to be constant.
= survival rate in year j including survival from natural and fishing mortality.
For simplicity, we assume that tagging induced mortality at release, , is known. We also adjust the number of tags released during each cruise by a factor of () to estimate the effective releases, i.e. . We also assume that the reporting rate is 100%. Equation 2 then becomes:
and Equation 1 becomes:
The FIT study had three years of tag release (T =3) and fours year of tag recovery data (J = 4). Therefore, the likelihood Equation 3 can be re-written as:
Where, for t = 1, 2, 3; J = 4.
To obtain maximum likelihood estimates for and , We take the derivative of log[L(…)] with respect to s and s, and solve the derivative equations (Brownie et al 1985) to obtain:
In Brownie Model, it is assumed that both recovery rate and survival rate are year-specific, but independent of the year of tagging and age of the animal tagged. Here we summarize the assumptions pertaining to this study:
The tagged fish are representative of the population, i.e. the tagged fish are mixed thoroughly with the untagged ones. Ideally, the mark-recapture study would be designed to let the tagged fish disperse widely over the study areas before fishing starts, avoiding their being subject to heavy fishing pressure immediately after releasing.
There is no tag loss. There are generally two types of tag loss. One is initial tag loss. When initial tag loss occurs, the number of tagged fish released will be effectively reduced. The second type of tag loss is chronic tag loss. When there is a chronic tag loss, mortality rate estimates will be positively biased. That is, the estimated mortality rates will be higher than the actual mortality rates.
Survival rates are not affected by tagging, i.e. there is no tagging induced mortality. Like tag loss, there are two types of tagging induced mortality, the initial short-term mortality and chronic mortality. When there is substantial initial short-term mortality, exploitation rate estimates will be negatively biased, while survival estimates may be biased positively. However, if the initial short term mortality is consistent among all release batches, the total survival rate estimates will not be biased, fishing mortality estimates will be biased negatively and natural mortality estimates will be positively biased. When there is chronic mortality due to tagging, the survival estimates will be negatively biased and the mortality estimates will be positively biased. The exploitation estimates should not be biased.