Stock Production Models of Blue Marlin and White Marlin in the Atlantic Ocean: A Case History

Fishery Stock Assessment Models 99 Alaska Sea Grant College Program AK-SG-98-01, 1998 Stock Production Models of Blue Marlin and White Marlin in the Atlantic Ocean: A Case History Christopher D. Jones University of Miami, Rosenstiel School of Marine and Atmospheric Science, Miami, Florida Eric D. Prince, Gerald P. Scott, and Mark I. Farber National Marine Fisheries Service, Southeast Fisheries Science Center, Miami, Florida Abstract Historically, stock assessments of Atlantic blue marlin (Makaira nigricans) and white marlin (Tetrapturus albidus), conducted under the auspices of the International Commission for the Conservation of Atlantic Tunas (ICCAT), have been restricted to production modeling approaches. Production models are used due to the unique fisheries and biological aspects of the species which result in a paucity of detailed information on the size or age structure of the catch. These analyses have evolved from single index equilibrium, to multiple index non-equilibrium models, as the ICCAT Enhanced Research Program for Billfish improved the Atlanticwide data and new non-equilibrium multifishery production models became available. Analyses of these fisheries data have been conducted over the last two decades through a series of intersessional billfish workshops held by ICCAT, under various stock structure hypotheses, to provide estimates of historical relative biomass, fishing mortalities, and maximum sustainable yield. Among the difficulties in modeling stock biomass, there have been conflicting indices of abundance for several fisheries, difficulties in modeling the dynamics of precipitous drops in CPUE through non age structured approaches, and typically flat solution surfaces which cause difficulty in searches for optimal, unconstrained model solutions. However, in each case various assumptions were made, or certain parameters Current address for C.D. Jones is National Marine Fisheries Service, Southwest Fisheries Science Center, 8604 La Jolla Shores Dr., La Jolla, CA 92038

100 Jones et al. Stock Production Models of Atlantic Marlin fixed, generally based on working group consensus, and solutions were achieved. A case history of multi-fishery Atlantic billfish assessments is presented, along with approaches that enabled specific problems to be addressed in the model fitting. Introduction International management of Atlantic blue marlin (Makaira nigricans) and white marlin (Tetrapturus albidus) falls under the auspices of the International Commission for the Conservation of Atlantic Tunas (ICCAT), which currently has 25 member countries and is headquartered in Madrid, Spain. The commission was originally formed in 1966 to maintain the populations of tunas and tunalike fishes (including billfishes, Istiophoridae, and swordfish, Xiiphidae) at levels that permit the maximum sustainable catch for food and other purposes. Assessing the population status of Atlantic blue marlin and white marlin, as well as other istiophorids, has historically been difficult because of the unique aspects of the fisheries (Furman 1989) and biology (Boggs 1989) of these species which hinder acquisition of information to assess the status of the stocks. In general, billfishes are large highly mobile species, long-lived, and sparsely distributed predators with an extensive geographical range. The historical delineation of Atlantic billfish stock structure has had considerable uncertainties. Although there have been numerous instances of trans- Atlantic movements of both blue and white marlin (Jones and Prince 1996), and at least one documented trans-oceanic movement of a blue marlin to the Indian Ocean (NMFS 1994), tag recovery data provides limited insight into ocean-wide structure of the populations and questions on stock structure have not been fully resolved. As a result, in most assessments three possible scenarios have been contemplated: a North Atlantic stock, a South Atlantic stock, and a total Atlantic stock. Recognizing that gains in scientific advice about the status of these resources could be realized if more detailed and comprehensive information was available, ICCAT initiated the Enhanced Research Program for Billfish (ERPB) in 1986. The ERPB elevated billfish research priorities to the international level and made funds (primarily from private recreational interests in the United States) available to reduce deficiencies in the ICCAT billfish database. The major objectives of the ERPB included: (1) Improve catch, effort, and landings statistics; (2) develop an Atlantic-wide tagging program for billfish; and (3) promote the advancement of age and growth studies. This data collection and research program continues in 1998. Atlantic-wide estimates of billfish nominal landings and catch-perunit-effort (CPUE) have undergone extensive revision since statistics were first compiled, as a result of research activities of ERPB and through a series of intersessional billfish workshops held by ICCAT (ICCAT 1981, 1994, 1996). The changes in data collection and estimation of abundance indices have been addressed in four billfish workshops, three of which

Symposium on Fishery Stock Assessment Models 101 were held under the auspices of ICCAT. The results of these workshops, along with the evolution of billfish stock assessment techniques from single to multi-fishery production models, is the primary focus of this paper. Approaches to Population Assessment Data Collection Collection of data for stock assessments of blue and white marlin are difficult, due to several factors related to the fishery. In any given year, 70-90% of the Atlantic-wide billfish landings (representing about 1% of the total Atlantic-wide landings of tuna and tuna-like species) reported to ICCAT come from longline fisheries that target tuna and swordfish, in which billfish are incidentally caught. Billfishes caught in this manner are normally dressed at sea, with heads, spines, fins, tails, and viscera removed to permit efficient onboard storage. The carcasses are then frozen for long periods before they are off-loaded at transshipment ports. This method of processing may lead to species mis-identification, non-reporting of landings, and lumping two or more billfish species into unclassified billfish category. In addition, this can lead to increased difficulties in acquisition of size frequency data, determination of sex ratios, and collection of other landings statistics. These problems are not unique to Atlantic fisheries (Alverson et al. 1994), since non-target species are generally not accounted for in as much detail in terms of landing statistics. Estimating dead discards and incidental mortality is difficult for both commercial and recreational fisheries. In the recreational fishery, the majority of catches are released. Not only is the estimation of the total recreational landings (actual landings plus dead discards from fish released) extremely difficult due to few adequate surveys, but the proportion of released fish that die from the stress of capture and subsequent release is poorly understood in both commercial and recreational catches. The collection of nominal landings data is further complicated because as many as four dozen nations (many not members of ICCAT) catch Atlantic billfishes but do not routinely report billfish landings directly to ICCAT, although catch reports are obtained through other international organizations (e.g., FAO). Prior to 1986, billfish had a lower research priority than tunas or swordfish for many ICCAT countries due to the incidental nature of most of the Atlantic billfish landings. Recognition of a large but generally unquantified socioeconomic value (Meyer 1989) for the recreational component of Atlantic billfish fisheries has elevated the priority somewhat. Atlantic-wide blue marlin and white marlin nominal landings reported to ICCAT have shown great fluctuations over time (Fig. 1). The longline fishery in the Atlantic was established in the late 1950s, and very high landings occurred for both species into the 1960s. The landings peaked in

102 Jones et al. Stock Production Models of Atlantic Marlin Figure 1. Historical total catch (t) of total Atlantic blue marlin and white marlin, 1960-1995. the mid-1960s and have since remained well below those levels for both species. Trends in landings have generally followed longline fishing effort, particularly by the Japanese fleet. However, estimated landings have increased for blue marlin in the last decade, while remaining at fairly constant levels since the early 1970s for white marlin. Population Production Models The difficulties in compilation of landing statistics coupled with the lack of detailed information on biology of these species makes information very limited or unavailable. As a result, these restrictions hinder attempts to apply a range of age or size based stock assessment analyses. Because lumped biomass stock production models require only a time series of catch and index of abundance (i.e., CPUE) these models have been the quantitative method of choice for billfish stock assessments. The simplest production models assume a logistic increase in the rate of change of a stock due to production, and often include an equilibrium assumption (Graham 1935, Schaefer 1954). Several variations on the simple stock production approach have been developed. One of the most

Symposium on Fishery Stock Assessment Models 103 flexible approaches was the generalized production model (Pella and Tomlinson 1969). This model adds an additional parameter to the logistic equation that allows various shapes in the production function, and does not require the equilibrium assumption. Though this model has increased flexibility, most implementations only allow fitting of a single index of abundance. The introduction of ASPIC (a stock-production model incorporating covariates, Prager 1992) also extended the simple logistic population production model approaches by allowing for simultaneous analysis of multiple data series, and not requiring equilibrium assumptions. These characteristics allowed for a more extensive use of the ICCAT Atlanticwide multi-fishery database. The detailed theory and mechanics of ASPIC are fully described in Prager (1992, 1995). The parameters estimated in the ASPIC model formulation are: K, the biological carrying capacity; i.e., maximum equilibrium stock size (t); B 1 R, the ratio of biomass in the first year to K; r, the biological yearly intrinsic rate of increase of the stock; and q(i), the catchability coefficients for each of the individual i data series. For the purposes of ICCAT, the derived quantities of most interest were: MSY, the maximum sustainable yield (t) per year (= Kr/4); B MSY, the stock biomass (t) at MSY (= K/2); and F MSY, the fishing mortality rate at MSY (= r/2), as well as the time trajectories of the relative statistics B/B MSY and F/F MSY, which provide information on the status of the resource over time. Because the quantities estimated most precisely by production models are MSY, effort at MSY, and biomass and fishing mortality levels relative to MSY (Prager 1992), estimates of biomass and fishing mortality trajectories presented are in terms of relative biomass (B/B MSY ) and relative fishing mortality (F/F MSY ). Overview of Past Assessment Results Early Assessments Little modeling of Atlantic billfish population dynamics was attempted prior to 1977, due to limited catch and effort data and a poor understanding of the fishery and biology of the species. The billfish stock assessment workshop held in Hawaii in 1977 (NMFS 1978) was the first important forum that addressed data needs and direction of research efforts to better understand the world s populations of billfish. Conser and Beardsley (1979) built upon the work of Kikawa and Honma (1978), and assessed the status of stocks of blue marlin and white marlin in the Atlantic Ocean. Following the recommendations of the 1977 workshop, available data were analyzed under the two stock structure assumptions: separate North Atlantic and South Atlantic stocks; and a single total Atlantic-wide stock. In that assessment, Japanese longline data and estimates of Atlantic-wide catches were analyzed using the generalized stock production model (Pella and Thomlinson 1969). Although model fits to the data were generally

104 Jones et al. Stock Production Models of Atlantic Marlin Table 1. Historical estimates of maximum sustainable yield (t) for blue marlin and white marlin under the north, south, and total Atlantic Ocean stock assumption. Stock assumption Source Blue marlin White marlin North Atlantic Kikawa & Honma 1978 2,300 1,700 Conser & Beardsley 1979 2,884-3,136 1,877-2,042 Farber & Conser 1983 2,232-2,623 2,092-3,776 Cramer & Prager 1994 1,718-1,864 Farber & Jones 1994 388-921 ICCAT 1996 1,741-2,133 85-771 South Atlantic Conser & Beardsley 1979 2,516-2,871 Farber & Conser 1983 2,074-2,353 2,579-2,672 Cramer & Prager 1994 704-1,278 Farber & Jones 1994 739-2,282 Jones & Farber 1996 1,193-1,224 1,000 Total Atlantic Conser & Beardsley 1979 4,768-5,333 Farber & Conser 1983 3,807-5,040 6,230-6,286 Cramer & Prager 1994 3,517-3,623 Farber & Jones 1994 1,502-1,741 ICCAT 1996 4,096-4,787 2,102-2,228 poor, some of the earliest estimates of maximum sustainable yield were developed as a result of the 1977 workshop (Table 1). Although the report by the Standing Committee on Research and Statistics (SCRS) (ICCAT 1980) concluded that it was not clear as to whether the apparent over-fishing of the North Atlantic stock of marlin is growth overfishing or recruitment overfishing, the analyses indicated that the stock was probably below the level which could produce MSY. Soon after this workshop, Beardsley and Conser (1981) examined catch and effort data from the U.S. recreational fishery for billfishes to evaluate their usefulness in determining trends in abundance. Using a power model (Robson 1966), they were able to develop an index of relative abundance over the period 1971-1978. However, the usefulness of this series for Atlantic wide population assessment was limited, given that there were no analytical tools at the time for modeling multiple fishery data series simultaneously. However, the importance of accounting for separate CPUE series for the overall stock was recognized as a means of improving assessment advice. During the First ICCAT Inter-Sessional Billfish Workshop (ICCAT 1981), blue marlin and white marlin catch statistics by country, compiled prima-

Symposium on Fishery Stock Assessment Models 105 rily from the ICCAT Statistical Bulletins, were reviewed, refined, and reestimated for the period 1957-1979. The only extensive standardized time series of CPUE was collected from the Japanese longline fishery. Farber and Conser (1981) followed the methodology of Conser and Beardsley (1979) and applied the generalized stock production model with equilibrium assumptions, fitting an index of abundance and a weighted average of effective fishing intensity using the PRODFIT program (Fox 1975). Farber and Conser (1981) found that under the North Atlantic stock assumption, the models fit the data fairly well. Although there were still problems and uncertainties with the assessment, they concluded that the assumed north, south, and total Atlantic stock of blue marlin appeared to have been overexploited in the early 1970s and that if the most recent (i.e., 1977-1978) indices were reliable, the North Atlantic stock of white marlin may be seriously overfished. Relatively uncertain results were found for the South Atlantic and for the total Atlantic stock assumptions. However, despite the uncertainties, they concluded that the total Atlantic stock was at least fully exploited since 1970 and probably overexploited by 1977 and 1978. Farber (1982) followed the methodology of Conser and Beardsley (1979) and Farber and Conser (1981) and attempted to assess the status of marlin stocks based on revised data. However, an inconsistency between CPUE and fishing effort was found. Concern was expressed that the Japanese longline fishery, used in the past to index abundance for all Atlantic marlins, represented a decreasingly smaller percentage of the total billfish catch down to roughly 10% in 1979, compared to 95% over the period 1960-1964, possibly reflecting changes in the fishing strategies over time by the Japanese fleet. It was concluded that it could not be determined if exploitation levels were above optimum, but that high levels of effort and yield had been followed by declining yields, with a decline in CPUE over time. Farber and Conser (1983) updated the marlin assessments of Farber (1982) using the catch and effort data through 1980 and followed the same methodology and assumptions as previous assessments. In that analysis, the generalized production model did not fit the data well under either stock structure assumption. Nevertheless, separate estimates of maximum sustainable yield for the north, south, and total Atlantic Ocean were again provided (Table 1) for blue and white marlin. Assessments in the 1990s Available Indices of Abundance for Blue and White Marlin The Second ICCAT Billfish Workshop, held in Miami in 1992 (ICCAT 1994), was significant in that existing indices of abundance were refined and newly standardized CPUE series were developed for several countries that catch significant amounts of blue and white marlin (Fig. 2). For example, a major problem hindering improved stock assessments for all billfish species was accounting for changes in fishing strategy for the Japanese Atlan-

106 Jones et al. Stock Production Models of Atlantic Marlin Figure 2. Standardized relative indices of abundance, including composite series, for fisheries used in the 1996 analysis. Fig. 4A contains the blue marlin North Atlantic longline CPUE trajectories; Fig. 4B is the blue marlin South Atlantic longline series; Fig. 4C is the blue marlin North Atlantic recreational series; Fig. 4D is the white marlin North Atlantic longline CPUE series; Fig. 4E is the white marlin South Atlantic longline series; Fig. 4F is the white marlin North Atlantic recreational series.

Symposium on Fishery Stock Assessment Models 107 tic longline fleet in the mid- to late-1970s (ICCAT 1991). The historical Japanese longline data series was considered to represent two distinct fisheries due to changes in the tuna target species: the earlier 1961-1979 period using regular longline techniques, and the more recent 1980-1990 period using deep longline techniques. The differences between methods are detailed in Uozumi and Nakano (1994) and basically refer to the gear configuration and deployment that corresponded to changes in target species and spatial changes in effort. The changes were addressed for blue marlin by Nakano et al. (1994a) and for white marlin by Nakano et al. (1994b) by standardizing marlin CPUEs from the Japanese Atlantic longline fishery using a general linear model (GLM) and the Honma (1974) method. This permitted standardized CPUE indices to be presented for the entire historical time-series, 1960-1989, while accounting for shifts in fleet effort and deployment patterns. Supplementary CPUE series in most cases were standardized to account for gear and geographical effects. These included the blue and white marlin U.S. recreational fishery in the North Atlantic for 1973-1991 (Farber et al. 1994), and the Venezuelan recreational fishery in the North Atlantic for 1961-1990 (Gaertner and Alio 1994). In addition to these series, standardized CPUE series were developed at the workshop for the Brazilian longline fishery in the South Atlantic (Amorim et al. 1994, Antero-Silva et al. 1994) and the Taiwanese longline fishery (ICCAT 1994). The Brazilian series was, however, based on limited data, and continued development was recommended at the time. The Taiwanese series was developed at the workshop without the advice of Taiwanese scientists (who were not present), and was therefore considered a tentative, and potentially unreliable, data series. The Third ICCAT Billfish Workshop, held in Miami in 1996 (ICCAT 1996), provided greater opportunities for global cooperation in advancing the state of billfish assessments. This workshop marked the first time representatives from all major Asian longline fleets fishing the Atlantic attended an ICCAT Billfish intersessional meeting. Here, five countries submitted standardized indices of abundance for blue marlin and white marlin fisheries (Fig. 2). The standardized blue marlin and white marlin CPUEs from the Japanese Atlantic longline fishery for 1960 to 1995 were presented by Uosaki (1996) and Uozumi (1996), respectively. Taiwanese scientists attended the billfish workshop for the first time and provided corrected and updated standardized CPUE estimates for the Taiwanese longline fishery from 1967 to 1994 (Hsu 1996). A scientist from Korea also attended the billfish workshop for the first time and provided revisions for the Korean nominal billfish landings data. The U.S. longline standardized CPUE for the years 1987-1995 (Cramer 1996) was presented and the Brazilian longline data for 1971 to 1995 (Amorim et al. 1996) was substantially revised and updated at the workshop. In addition, the Venezuelan (Gaertner and Alio 1996) and U.S. (Jones et al. 1996) recreational CPUE data were revised and updated through 1995.

108 Jones et al. Stock Production Models of Atlantic Marlin Blue Marlin The 1992 Assessment. Cramer and Prager (1994) presented the first multifishery exploratory stock assessment analysis for blue marlin using the ASPIC approach. Total catches from 1960 to 1990 (Fig. 1), were compiled from ICCAT statistical tables. Longline catches were matched with their respective longline CPUE series, recreational catches with the recreational series, and any additional unallocated longline catches were indexed by the Japanese longline series. Because questions of stock delineation were still unresolved at this time, the assessment was analyzed using North Atlantic, South Atlantic, and total Atlantic stock structure assumptions. In the North Atlantic runs, weighted and unweighted (inverse variance weighting) models were fitted with and without the Taiwanese data series. Where the Taiwanese series was not used, all Taiwanese catch was indexed by the Japanese CPUE. It was quickly determined that this series was needed to estimate model parameters, as fits without this index resulted in unrealistically large estimates of stock biomass. Hence, the Taiwanese data series was used in this assessment. The resulting estimates of MSY (Table 1) were lower than those estimated from previous assessments. The relative biomass trajectory (Fig. 3A) demonstrated a precipitous drop in the mid-1960s, with an upward trend in the late 1980s, but at levels below historical highs. The relative fishing mortality (Fig. 3A) had much greater fluctuations, at times greater than twice the optimum fishing mortality, though there was a slight decline in the late 1980s. The addition of the Taiwanese data series had little effect on the estimated parameters in the South Atlantic. However, the weighted and unweighted model gave different results, with the unweighted model estimating a higher MSY and slightly less optimistic relative biomass. Nevertheless, both estimates resulted in relative biomass ratios less than half of that required to produce MSY in the terminal year (Fig. 3B). Estimates of model parameters for the total Atlantic stock assumption were generated using all available data series. The computed MSY estimate (Table 1) was also lower than any previous assessment, though higher than most annual catches in the two decades prior to the assessment. The relative biomass (Fig. 3C) was very low throughout most of the time series. It was concluded that the stock could not support such a high level of harvest, and that relative fishing mortality well exceeded the optimum level for the total Atlantic (Cramer and Prager 1994). The 1996 Assessment. The question of north/south blue marlin stock delineation was explored in much greater detail at the 1996 ICCAT Billfish workshop. One of the major advances in the 1996 assessment was that progress in genetic and tagging studies allowed the scientific working group to conclude that a total Atlantic stock structure assumption for both blue marlin and white marlin was most appropriate for stock assessment. However, the working group also concluded that biological evidence concerning stock structure was not totally definitive and therefore recom-

Symposium on Fishery Stock Assessment Models 109 Figure 3. Annual relative biomass and relative fishing mortality trajectories from 1992 and 1996 assessments for blue marlin under the North Atlantic (A), South Atlantic (B) and total Atlantic stock assumption (C).

110 Jones et al. Stock Production Models of Atlantic Marlin mended that north and South Atlantic runs also be done as a prudent approach to the assessments. The initial fits of the North Atlantic model incorporated five available standardized CPUE series for the North Atlantic (Japanese longline, Taiwanese longline, U.S. longline, Venezuelan recreational, and U.S. recreational; Figs. 2A and 2C) for the entire time series (ICCAT 1996). These fits were unsuccessful, due to negative correlations among the longline CPUE series, as well as between the recreational and longline series. Although these negative correlation problems were not severe in terms of the trends across entire time series (Fig. 2), resolving this problem prior to model fitting presented a considerable challenge to the working group. Several alternative models were proposed, including using Japanese, or Taiwanese, CPUEs only to index all longline catches, and fitting models with separate catchability coefficients for the longline fisheries in the 1960s. Finally, composite CPUE indices were constructed for the longline and recreational series. This provided a way of incorporating all information, and confronting the negative correlation problem. The longline and recreational composite CPUE indices were constructed by first dividing all CPUEs for each series by the mean CPUE of the overlapping years. In years where there was only one CPUE available (e.g., Japanese longline 1960-1968, and Venezuelan recreational 1961-1972), only that estimate was used. In years with overlapping indices, averages of the adjusted CPUE estimates were used. The result was a separate composite CPUE for the longline fishery and for the recreational fishery (Figs. 2A and 2C). These composite indices were fairly well correlated (r = 0.76). The longline composite indices were matched to all longline catches and the recreational composite index was matched to all recreational catches. Both longline and recreational composite indices of abundance in the North Atlantic for the 1960s exhibited initial rapid declines, and model runs using catch data from 1960 to 1995 failed to capture the dynamics of this stock response. The working group extensively discussed the issue of whether the rapid declines in CPUE and landings were real or an artifact of data collection. The working group concluded that because the peak in fishing effort during the mid-1960s was at about twice the level of MSY (as calculated in 1996), the rapid declines were likely accurate reflections of population responses to such high rates of fishing mortality. The group felt that such steep declines might well be expected from any fish populations exposed to such heavy fishing pressure. The solution to this problem was to use catches for blue marlin dating back to 1956, when the stock was believed relatively unexploited, fix the B 1 R parameter to 2.0 (the equilibrium level for an unexploited stock), and estimate the populations rate of growth, r, and the separate catchabilities, q(i), for the longline and recreational composite series. In addition, a 5% two-sided tail trim was applied to the residual distribution to mitigate the effects of possible statistical outliers during the fitting.

Symposium on Fishery Stock Assessment Models 111 The resulting model fits for the North Atlantic stock assumption generated MSY estimates (Table 1) similar to the estimates of Cramer and Prager (1994), though with a slightly greater range. The relative biomass trajectory (Fig. 3A) was also very similar to that of Cramer and Prager (1994), for overlapping years, though this appears to be scaled down slightly. The relative fishing mortality (Fig. 3A) also tracked well with the 1992 assessment. As with previous assessments, the greatest impact on the stock biomass appears in the early 1960s. Jones and Farber (1996) conducted the South Atlantic blue marlin assessment separately from the other 1996 assessments. The available CPUE series for this analysis included the Japanese, Taiwanese, and Brazilian longline data sets (Fig. 2B). Initially, models were attempted using all data sets, because attempting to fit models with a single composite CPUE series was unsuccessful. Due to difficulties finding minima during the model s search routine, it was necessary to fix the initial biomass, B 1 R, similar to the North Atlantic model. The resulting model produced levels of MSY (Table 1) similar to that of Cramer and Prager (1994). However, biomass trajectories (Fig. 3B) for blue marlin were scaled considerably higher than that of any other trajectory for the mid-1980s. Nevertheless, models indicate there was a downturn of biomass through the 1990s, and the results suggest that the blue marlin stock is heavily overexploited under a South Atlantic stock assumption. This downturn in biomass corresponds to very high estimated relative fishing mortality levels in the 1990s (Fig. 3B). The assessment for blue marlin under a total Atlantic stock assumption, considered the superior approach by the working group, combined all available information for Atlantic blue marlin. Along with freely estimated B 1 R and r parameters, three separate q estimates were derived: a North Atlantic composite longline (Japanese, Taiwanese, U.S.); South Atlantic composite longline (Japanese, Taiwanese, Brazilian); and a North Atlantic composite recreational (Venezuelan, U.S.). The estimates of MSY from these model parameters were slightly higher than those of the 1992 assessment (Table 1). The relative biomass ratio (Fig. 3C) shows a similar drop, as has been the case with all models, in the 1960s, a general increase in the 1980s, followed by a decline from 1989 to 1996. White Marlin The 1992 Assessment. In preparation for the ASPIC production models for white marlin, Farber and Jones (1994) indexed white marlin abundance from 1961 to 1990 (Fig. 1) using standardized CPUE series for the Japanese and Taiwanese longline and the U.S. and Venezuelan recreational data series for the North Atlantic (Fig. 2D), and the Japanese and Brazilian longline for the South Atlantic (Fig. 2E). The total Atlantic analysis used all series (Fig. 2F). In the analysis, all ASPIC models were fits using yield (t) and fishing effort by fleet, f. Initially, models were fitted using calculated fishing effort, f, as catch/cpue. This methodology proved inappropriate

112 Jones et al. Stock Production Models of Atlantic Marlin with these data, with the model either not converging to any solution or the fit being extremely poor with unreasonable parameter estimates. A plot of the average weight of individual fish (i.e., catch in weight/catch in number), for both the North Atlantic and South Atlantic data exhibited great variability and was unrealistically high for several years. An alternative method of estimating f, based on catch in weight (=catch [t]/cpue [number/unit effort]) was assumed a more reliable statistic than the catch in number, given that the average weight of white marlin was presumed reasonably constant over the period considered. The values of f for all longline fisheries were derived using the CPUE series from the Japanese fleet. For the North Atlantic model, large fluctuations were evident in these CPUE series from 1961 through 1965. This resulted in difficulties in model fitting (large residuals), and an inability to capture the dynamics of the large catch and effort fluctuations during this period. Beginning the longline series in 1966, along with U.S. recreational data for 1973-1990 and Venezuelan recreational data for 1966-1990, mitigated this problem. As a result, the models were successfully fit, with effort residuals reasonably balanced with no apparent trends or extreme values. The computed estimates of MSY (Table 1) were well below estimates from previous assessments. The North Atlantic relative biomass was less than 1.0 for all years after 1974 (Fig. 4A), and was estimated at the start of 1991 to be about 57% of the biomass that could produce MSY. The relative annual fishing mortality (Fig. 4A) showed considerable annual variability, and was estimated well above the optimum level for most years except during 1978-1980 and 1989-1990, when it was below optimum. The South Atlantic white marlin analysis included the Brazilian longline CPUE series for the period 1971 to 1990 (Fig. 2E). Because there was considerably less fluctuation in the South Atlantic Japanese longline CPUE series for the years 1961 to 1965, this data series was retained. Estimates of MSY from this analysis were less than that of the previous assessment (Table 1), though not nearly as dramatic as the North Atlantic. The estimated relative biomass was less than that which could produce MSY for the entire time series and exhibits a declining trend to extremely low levels (Fig. 4B), with the estimated biomass at the start of 1991 only 3% of that which could produce MSY. Estimates of relative fishing mortality (Fig. 4B) were greater than 1.0, exhibiting variability without trend over the period 1962-1982, and then increasing sharply from 1.0 to very high levels over the period 1983-1990. Farber and Jones (1994) noted that during the mid-1970s, the Japanese longline catches of white marlin in the South Atlantic were extremely low, and questioned if the CPUEs for those years (used to calculate effort) were representative of the total South Atlantic longline catch. For the total Atlantic analysis, all annual yields (t) were the arithmetic sums of the North Atlantic and South Atlantic data series. The point estimate of MSY (Table 1) was, like the north and south, well below the previous

Symposium on Fishery Stock Assessment Models 113 Figure 4. Annual relative biomass and relative fishing mortality trajectories from 1992 and 1996 assessments for white marlin under the North Atlantic (A), South Atlantic (B) and total Atlantic stock assumption (C).

114 Jones et al. Stock Production Models of Atlantic Marlin assessment estimate. The relative biomass trajectory indicates a declining stock over the period 1966-1977, followed by an increase through the mid- 1980s, and then decreasing again through 1991 (Fig. 4C). The estimated relative biomass was less than optimum for all years after 1972, with the estimated biomass at the start of 1991 at 25% of that which could produce MSY. The estimates of relative fishing mortality were greater than 1.0 for all years after 1969, with variability and periods of both increasing and decreasing trend (Fig. 4C). The conclusion for the total Atlantic from this assessment was that white marlin were at least fully exploited with a strong possibility of substantial overexploitation during the last 17 to 20 years. The 1996 Assessment. Catch and effort data available for white marlin were similar to blue marlin. Available CPUE series were from the Japanese, Taiwanese, and Brazilian longline fisheries, and the Venezuelan and U.S. recreational fishery (Figs. 2D,2E,2F). Similar to the blue marlin runs, the initial models were not fitted due to a lack of correlation between indices of abundance. Separate series of composite indices for the North Atlantic longline, the South Atlantic longline, and the North Atlantic recreational CPUE series were estimated to mitigate this problem. The procedures for constructing the combined CPUE series were identical to those used for the blue marlin. Further, an approximate 5% two-sided tail trim was applied to the composite indices to allay the potential effects of statistical outliers. As with blue marlin, the longline composite indices were matched to all longline catches and the recreational composite index was matched to all recreational catches. The resulting MSY estimates from these model fits for the North Atlantic stock assumption (Table 1) were among the lowest of any previous assessment. However, relative biomass (Fig. 4A) and relative fishing mortality levels were very similar to that of the 1992 assessment, and demonstrate a continuous downward trend across the entire time series. For the South Atlantic model, Jones and Farber (1996) were unable to fit models with single composite indices for Japanese, Taiwanese, and Brazilian fisheries due to problems with model convergence. They found it was necessary to fix the B 1 R parameter, as well as the population intrinsic rate of increase, r to facilitate model convergence. Although there were several problems with the South Atlantic analysis, results were consistent with previous assessments, both in terms of MSY estimates (Table 1), and relative trajectories (Fig. 4B). Data preparation for the total Atlantic analysis was similar to that of blue marlin, except the rod and reel (i.e., recreational) composite index was not used. Although rod and reel catches for white marlin represent a very low (about 5%) proportion of the total white marlin landings, the model could not capture the catch rate pattern observed in the earliest period, unless initial biomass was set at a biologically unrealistic low level (ICCAT 1996). The working group recommended that this series therefore be excluded. The resulting estimates of MSY from the fitted model were

Symposium on Fishery Stock Assessment Models 115 higher than the 1992 assessment for the total stock assumption (Table 1), though substantially less than the Farber and Conser (1983) estimate. Relative biomass levels (Fig. 4C) have declined since the mid-1980s, after a slight period of recovery in the early 1980s (ICCAT 1996). Relative fishing mortality (Fig. 4C) appears to be about twice the optimal level necessary to produce MSY. Discussion The early production model assessments of blue and white marlin relied exclusively on the Japanese longline CPUE to index abundance and did not adequately represent the complexity and dynamics of multiple countries fishing a widely distributed stock with different gear types, representing both directed and incidental bycatch fisheries. Nevertheless, both single and multiple fishery-based assessment approaches indicate levels of biomass for Atlantic blue marlin and white marlin have greatly declined over the time series. Assessments suggest that blue marlin and white marlin have been fully exploited since the 1960s, and are likely currently heavily overexploited. One of the recommendations resulting from the workshop was to evaluate whether critical model assumptions were met. There was particular concern that the landings data was incomplete or systematically underreported. This is a difficult problem to detect and address, since evaluating the implications of errors in annual landings by a constant percentage of under-reporting only adjusts absolute levels of maximum sustainable yield and biomass levels. Thus, there remains much uncertainty about these absolute levels, though less so for relative trends. Conclusion The evolution of assessment approaches represents substantial progress in analyzing the status of the blue marlin and white marlin stocks in the Atlantic Ocean. Increased representation of fishing nations at workshops, as well as the working group approach, has been instrumental in advancing the state of billfish stock assessments. The application of the ASPIC model permits the incorporation of all available data, giving a more comprehensive representation of the stocks than previous assessments that relied exclusively on Japanese longline CPUE data. This is particularly important because the Japanese longline data represents an increasingly smaller percentage of white marlin landings during the most recent years (though Japanese longline landings for blue marlin have increased in the most recent years). The trends in the 1996 assessment for the total Atlantic are similar to those described in the 1992 assessment, and although there remains considerable uncertainty in absolute trends of abundance and fishing mortality, relative levels appear to be more precisely estimated. Most important, all assessments, using both single and multiple index

116 Jones et al. Stock Production Models of Atlantic Marlin approaches, indicate that Atlantic blue marlin and white marlin stocks are overexploited, and possibly severely so. The strength of using production model techniques to examine trends in stock abundance depends on many factors, including degree of density-dependence on recruitment, recruitment variability, and possible agestructured lags in the population s response to fishing pressure. Further improvements in billfish assessment will also be needed, if we are to provide advice on the expected dynamics of these stocks under potentially heavier exploitation. Evaluations of alternative underlying production functions, relating to overexploited stock productivity may provide a basis for better understanding low biomass dynamics of these stocks. This could be accomplished by implementing a generalized stock production model that would allow fitting of multiple indices of abundance. Methods for better incorporation of mixed unit abundance indices (e.g., in numbers and in biomass) need to be applied as well. Finally, incorporation of information now being developed on the size structure of the catches could also be used to improve assessments, possibly to better accommodate the initial declines in catch rate indices observed in these fisheries. This paper is Miami Laboratory Contribution MIA-97/98-01. References Alverson, D.L., M.H. Freeburg, S.A. Murawski, and J.G. Pope. 1994. A global assessment of fisheries bycatch and discards. FAO Fish. Tech. Pap. 339. 233 pp. Amorim, A.F., C.A. Arfelli, J.N. Antero-Silva, L. Fagundes, F.E.S. Costa, and R. Assumpcao. 1996. Blue marlin (Makaira nigricans) and white marlin (Tetrapturus albidus) caught off the Brazilian Coast. Int. Com. Cons. Atl. Tunas, Coll. Vol. Sci. Pap. SCRS/96/101. Amorim, A.F., C.A. Arfelli, F.H.V. Hazzin, J.N., Antero-Silva, R.P.T. Lessa, and R.R. Areas. 1994. Blue marlin (Makaira nigricans) fisheries off Brazilian coast from national and leased longliners (1971-91). Int. Comm. Cons. Atl. Tunas, Coll. Vol. Sci. Pap. 41:208-213. Antero-Silva, J.N., A.F. Amorim, R.P.T. Lessa, F.H.V. Hazzin, and C.A. Arfelli. 1994. White marlin (Tetrapturus albidus) fisheries off Brazilian coast from national and leased longliner fleet. Int. Comm. Cons. Atl. Tunas, Coll. Vol. Sci. Pap. 41:189-198. Beardsley, G.L., and R.J. Conser. 1981. An analysis of catch and effort data from the U.S. recreational fishery for billfishes (Istiophoridae) in the western North Atlantic Ocean and Gulf of Mexico, 1971-1978. Fish Bull. U.S. 79(1):49-68. Boggs, C.H. 1989. Vital rate statistics for billfish stock assessment. Marine Recreational Fisheries 13:225-234. Conser, R.J. 1989. Assessing the status of stock of Atlantic blue marlin and white marlin. Marine Recreational Fisheries 13:153-164.

Symposium on Fishery Stock Assessment Models 117 Conser, R.J., and G.L. Beardsley. 1979. An assessment of the status of stocks of blue marlin (Makaira nigricans) and white marlin (Tetrapturus albidus) in the Atlantic Ocean. Int. Comm. Cons. Atl. Tunas, Coll. Vol. Sci. Pap. 8(2):461-489. Cramer, J.L. 1996. Large pelagic logbook catch rates indices for billfish. Int. Comm. Cons. Atl. Tunas, Coll. Vol. Sci. Pap. SCRS/96/110. Cramer, J.L., and M.H. Prager. 1994. Refinements in exploratory surplus-production analyses of Atlantic blue marlin. Int. Comm. Cons. Atl. Tunas, Coll. Vol. Sci. Pap. 41:565-571. Farber, M.I. 1982. An assessment of the status of stocks of blue marlin (Makaira nigricans) and white marlin (Tetrapturus albidus) in the Atlantic Ocean through 1979. Int. Comm. Cons. Atl. Tunas, Coll. Vol. Sci. Pap. 17(2):395-414. Farber, M.I., and R.J. Conser. 1981. An assessment of the status of stocks of blue marlin (Makaira nigricans) and white marlin (Tetrapturus albidus) in the Atlantic Ocean. Int. Comm. Consv. Atl. Tunas, Coll. Vol. Sci. Pap. 15(2):387-406. Farber, M.I., and R.J. Conser. 1983. An update on the status of stocks of blue marlin and white marlin in the Atlantic Ocean. Int. Comm. Cons. Atl. Tunas, Coll. Vol. Sci. Pap. 18(3):674-692. Farber, M.I., and C.D. Jones. 1994. An exploratory stock-production model analysis of white marlin (Tetrapturus albidus) in the Atlantic Ocean. Int. Comm. Cons. Atl. Tunas, Coll. Vol. Sci. Pap. 41:572-587. Farber, M.I., J.A. Browder, and J.P. Contillo. 1994. Standardization of recreational fishing success for marlin in the western North Atlantic Ocean, 1973-1991, using generalized linear model techniques. Int. Comm. Cons. Atl. Tunas, Coll. Vol. Sci. Pap. 41:363-392. Fox Jr., W.W., 1975. Fitting the generalized stock production model by least-squares and equilibrium approximation. Fish. Bull. U.S. 73:23-37. Furman, R.S. 1989. The adequacy of current billfish fisheries statistics for stock assessment and management purposes. Marine Recreational Fisheries 13: 215-224. Gaertner, D., and J. Alio. 1994. Changes in the apparent abundance indices of billfishes in the Venezuelan recreational fishery off Playa Grande (1961-1990), Central Venezuelan coast. Int. Comm. Cons. Atl. Tunas, Coll. Vol. Sci. Pap. 41:473-489. Gaertner, D., and J. Alio. 1996. Trends in the recreational billfish fishery CPUE off Playa Grande (1961-1995), Central Venezuelan coast. Int. Comm. Cons. Atl. Tunas, Coll. Vol. Sci. Pap. SCRS/96/109. Graham, M. 1935. Modern theory of exploiting a fishery, and application to North Sea trawling. J. Cons. Cons. Int. Explor. Mer 37:199-204. Honma, M. 1974. Estimation of overall effective fishing intensity of tuna longline fishery. Bull. 10, Far Seas Fish. Res. Lab. Shimizu 424, Japan, pp. 63-86. Hsu, C.C. 1996. A review of catches, fishing efforts and catch per unit effort of the Taiwanese longline fishery for billfishes in the Atlantic. Int. Comm. Cons. Atl. Tunas, Coll. Vol. Sci. Pap. SCRS/96/100.

118 Jones et al. Stock Production Models of Atlantic Marlin ICCAT. 1980. Report for biennial period, 1978-79. Int. Comm. Cons. Atl. Tunas. 280 pp. ICCAT. 1981. Report of the ICCAT inter-sessional workshop on billfish. Int. Comm. Cons. Atl. Tunas, Coll. Vol. Sci. Pap. 16. 375 pp. ICCAT. 1991. Report for biennial period, 1990-91. Int. Comm. Cons. Atl. Tunas. 445 pp. ICCAT. 1994. Report of the Second ICCAT Billfish Workshop. Int. Comm. Cons. Atl. Tunas, Coll. Vol. Sci. Pap. 41. 587 pp. ICCAT. 1996. Report of the Third ICCAT Billfish Workshop. Int. Comm. Cons. Atl. Tunas, Coll. Vol. Sci. Pap. COM-SCRS/96/19. Jones, C.D., and M.I. Farber. 1996. Exploratory stock-production model analysis of blue marlin and white marlin in the South Atlantic Ocean. Int. Comm. Cons. Atl. Tunas, Coll. Vol. Sci. Pap. SCRS/96/159. Jones, C.D., and E.D. Prince. 1996. The Cooperative Tagging Center mark recapture database for istiophoridae (1954-1995), with an analysis of the West Atlantic ICCAT billfish tagging program. Int. Comm. Cons. Atl. Tunas, Coll. Vol. Sci. Pap. SCRS/96/96. Jones, C.D., M.T. Judge, and M. Ortiz. 1996. Standardization of recreational CPUE for blue and white marlin in the western North Atlantic Ocean 1973-1995. Int. Comm. Cons. Atl. Tunas, Coll. Vol. Sci. Pap. SCRS/96/104. Kikawa, S., and M. Honma. 1978. Status of the white and blue marlins caught by the longline fisheries in the North Atlantic Ocean, 1956-76. Int. Comm. Cons. Atl. Tunas, Coll. Vol. Sci. Pap. SCRS/78/100. Meyer, P.A. 1989. Socio-economic trends in recreational billfish fisheries. Marine Recreational Fisheries 13:103-108. Nakano, H., Y. Uozumi, and M. Honma. 1994a. The CPUE trend for Atlantic blue marlin caught by Japanese longline fishery. Int. Comm. Cons. Atl. Tunas, Coll. Vol. Sci. Pap. 41:408-424. Nakano, H., Y. Uozumi, and M. Honma. 1994b. The CPUE trend for Atlantic white marlin caught by Japanese longline fishery. Int. Comm. Cons. Atl. Tunas, Coll. Vol. Sci. Pap. 41:393-407. NMFS. 1978. Report of the Billfish Stock Assessment Workshop, Atlantic Session. Dec. 1977, Honolulu, HI. NOAA/NMFS, SEFC, Miami, FL 33149. 47 pp. NMFS. 1994. Cooperative game fish tagging program annual newsletter: 1992. NOAA Tech. Memo. NMFS/SEFSC-346. 23 pp. Pella, J.J., and P.K. Tomlinson. 1969. A generalized stock production model. Bull. Inter-Amer. Trop. Tuna Comm. 13:419-496. Prager, M.H. 1992. ASPIC: A surplus-production model incorporating covariates. Inter. Comm. Conserv. Atl. Tunas, Coll. Vol. Sci. Pap. 37:218-229. Prager, M.H. 1995. A suite of extensions to a nonequilibrium surplus-production model. Fish. Bull. U.S. 92:374-389.

Symposium on Fishery Stock Assessment Models 119 Schaefer, M.B. 1954. Some aspects of the dynamics of populations important to the management of the commercial marine fisheries. Inter-Am. Trop. Tuna Comm. Bull. 1(2):27-56. Robson, D.S. 1966. Estimation of the relative fishing power of individual ships. Int. Comm. Northwest Atl. Fish. Res. Bull. 3:5-14. Uosaki, K. 1996. The CPUE trend for Atlantic blue marlin caught by the Japanese longline fishery. Int. Comm. Cons. Atl. Tunas, Coll. Vol. Sci. Pap. SCRS/96/93. Uozumi, Y.H. 1996. Standardization of CPUE for white marlin caught by the Japanese longline fishery in the Atlantic. Int. Comm. Cons. Atl. Tunas, Coll. Vol. Sci. Pap. SCRS/96/94. Uozumi, Y.H., and H.J. Nakano. 1994. A historical review of Japanese longline fishery and billfish catches in the Atlantic Ocean. Int. Comm. Cons. Atl. Tunas, Coll. Vol. Sci. Pap. 41:233-243.