Natural Mortality Values Research Articles

The potential fish provisioning services of vegetated and unvegetated habitat in a lagoon nursery

The potential fish provisioning services of the Ria Formosa lagoon (Portugal) were calculated for single cohorts of 7 commercially fished species, based on densities of juveniles sampled with beach seines on a monthly basis over a 17-month period at 41 locations. The potential maximum yield per recruit (F0.1 criteria) was calculated for vegetated (V) and unvegetated (UV) habitat for low and high natural mortality values. Vegetated habitat enhanced yield (g m−2) of 5 of the 7 species, with the greatest enhancement for the herbivore Sarpa salpa (137 and 150 fold for low and high M). At F0.1, the calculated total potential yield of the 7 cohorts was 463 tons (low M) and 333 tons (high M), worth EUR 5,649,084 and 3,651,881, respectively. Mean annual landings of the 7 species from 1997 to 2017 ranged from 407 to 577 tons, with a mean of 495 tons (s.e. = 11.1), highlighting the importance of the lagoon nursery as a major source of recruits for local small-scale coastal fisheries. The methodology used here is the first to calculate the potential maximum yield and the corresponding fishing mortality (F0.1) for single cohorts and for different habitats within an important fish nursery. It provides more realistic values of potential fish provisioning services and economic contribution to local fisheries than studies that do not consider fishing mortality.

Estimating of the maximum life expectancy and natural mortality of the red king crab on the example of the Barents Sea population

The purpose of the study is to establish the maximum life span (tmax) and natural mortality (M) in commercial Lithodidae using the example of the red king crab Paralithodes camtschaticus.Material and methods — after the introduction of P. camtschaticus into the Barents Sea in 1969, the dynamics of the maximum carapace width (CWmax) from the first crab catches in 1974 to 2022 was considered. The data of the authors’ own observations and the results of studies from the open press were used.Results. The retrospective dynamics of the maximum size of crabs for older ages for 1974–2022 is presented. The maximum sizes were established: in males CWmax 280–312 and 298 mm was in 2002 and 2003, and in females CWmax 210–220 mm in 1995, 1998 and in a later period.New data. Based on the fifty-year dynamics of CWmax, it was suggested that after the end of the acclimatization of P. camtschaticus in 1969, the first generation of local juveniles appeared in the area of introduction in the early 1970s; in the absence of fishing, these juveniles were able to freely reach the maximum historical size and maximum age. Males caught in 2002–2003 with CWmax 280–312 mm, could have been 30–33 years old (mean 31 years), and the age of females in 1995 with CWmax 210 mm was 20–25 years (mean 23 years). This age limit of crabs allows us to establish a natural mortality according to the formula М=3/tmax for crabs with CW ≥70–90 mm, when their natural elimination is minimal. In this case, the decrease in M in males will be 10% per year, and in females 13%.Practical significance. To estimate the commercial stock of P. camtschaticus, the values of natural mortality used today are 1.8–2.3 times higher than M established by tmax for this species in the Barents Sea. The use of a double overestimated value of M in model calculations leads to a decrease in the commercial stock of crab and, as a consequence, to a decrease in its total allowable catch.

Life-history characteristics and mortality of the protogynous hermaphroditic frostback rockcod (Epinephelus bilobatus) from the eastern Indian Ocean

The frostback rockcod, Epinephelus bilobatus, is a small epinephelid (<50 cm total length) with a limited distribution in the tropical eastern Indian Ocean (i.e., north-western Australia and parts of Indonesia). Although its fishery harvest in Western Australia is low (<6 t year−1), its life history is not well known (i.e., reproductive biology, growth, and natural mortality) preventing assessment of its inherent vulnerability to overfishing. Samples of E. bilobatus were collected from ∼2000 km of the north-western Australian coast, comprising the Kimberley, Pilbara, and Gascoyne regions, between 2012 and 2022 to determine its life-history characteristics. Detailed histological analysis of gonads (n = 1460) identified that E. bilobatus is a monandric protogynous hermaphrodite. The length and age at which females matured was 278 mm LT and 2.5 years in the Pilbara region, and the lengths and ages at which they changed to males was 336 and 342 mm LT and 6.2 and 6.5 years in the Kimberley and Pilbara, respectively (i.e., less than 5% variation between regions). Based on histology, female E. bilobatus were in spawning condition in all months. However, the mean monthly gonadosomatic indices and proportions of developed/spawning females were highest (i.e., >0.95 and 40%, respectively) for 5 months of the year (i.e., January to April and September). Marginal increment analysis confirmed the annual formation of one opaque and one translucent zone in the sagittal otoliths of this species. Epinephelus bilobatus had a moderate longevity (∼20 years) and attained a larger mean length-at-age in the cooler southern Gascoyne region compared to the more northern Kimberley and Pilbara regions. Three values of natural mortality (M) were used to assess the sensitivity of fishing mortality (F) in the Kimberley and Pilbara commercial trap fisheries, with all point estimates of F < M, indicating that at the time of sampling, the harvest of this species over a long period (>20 years) was sustainable for these contemporary fisheries.

Assumptions influencing the estimation of natural mortality in a tag-integrated statistical model for western and central Pacific Ocean skipjack

The status of skipjack tuna (Katsuwonus pelamis) in the western and central Pacific Ocean is regularly assessed using the integrated catch-at-age model MULTIFAN-CL. The model utilizes catch, fishery-dependent standardized CPUE indices, unstandardized effort, mark-recapture, and length-composition data. We tested the sensitivity of natural mortality estimation to functional forms of M at age, assumptions of tag reporting rate parameters, and modeling decisions that influence the fit to the length composition and tag data. We estimated M at age internal to the tag-integrated spatially-explicit model using a range of parameterizations. Likelihood component profiles for mean natural mortality values, nodes in a cubic spline of M at age, and reporting rate parameters were conducted to determine which data were contributing to the estimation of these parameters. The functional form of M at age did not have a large influence on performance indicators (Frecent/FMSY and SBrecent/SBF=0), but cubic splines proved a parameter efficient method of estimation. Assumed functional forms of selectivity and the fixed growth curve influenced estimates of M at age and had moderate impacts on performance indicators, though the weighting of the length composition data was less influential. Some reporting rate parameters were estimated on the upper bound for all models; changes to assumptions of these parameters impacted performance indicators slightly more than length composition changes, but did not strongly influence M-at-age estimates. Assumptions that affected the amount of tagging data included in the model, such as the mixing period, had a large impact on the performance indicators and shape of M at age, but only moderate changes to mean M estimates. Likelihood profiling showed that both tagging data and length composition data strongly influenced estimates of M at age in this catch-at-length tag-integrated model, but there is conflict among the data sources and tagging programs. Standard errors of M at age were small for most ages, particularly those with numerous tag recaptures, and mean M estimates across tested sensitivity models were mostly consistent. There is some concern that estimates may be biased due to incomplete mixing of tags and other assumption violations, but simulation studies are needed to determine the severity. Research is also recommended on methods to resolve data conflict that may be causing reporting rates estimated on upper bounds and to determine appropriate mixing periods of tagging data.

Approaches for estimating natural mortality in tuna stock assessments: Application to global yellowfin tuna stocks

The values used for natural mortality (M) are very influential in stock assessment models, affecting model outcomes and management advice. Natural mortality is one of the most difficult demographic parameters to estimate, and there is often limited information about the true levels. Here, we summarise the evidence used to estimate natural mortality at age for the four main stocks of yellowfin tuna (Indian, Western and Central Pacific, Eastern Pacific, and Atlantic Oceans), including catch curves, tagging experiments, and maximum observed age. We identify important issues for estimating M such as variation with age linked to size, maturity state or senescence, and highlight information gaps. We describe the history of natural mortality values used in stock assessments by the tuna Regional Fisheries Management Organisations responsible for managing each stock and assess the evidence supporting these values. In June 2021, an online meeting was held by the Center for the Advancement of Population Assessment Methodology (CAPAM), to provide advice and guidance on practices for modelling natural mortality in fishery assessments. Based on approaches presented and discussed at the meeting, we develop a range of yellowfin tuna natural mortality estimates for each stock. We also recommend future research to improve these estimates of natural mortality.

Variation in population dynamics and abundance of the bigeye croaker Micropogonias megalops in the Northern Gulf of California

The bigeye croaker Micropogonias megalops is an endemic Sciaenidae fish species of the Gulf of California. Although it is a stock that has been exploited for nearly three decades, its biological and fishery information has been limited over time. Therefore, its recent and current population status is poorly known. This study analyzed biological and fishery data for M. megalops in the Northern Gulf of California for the period 1995–2020. Variation of species population dynamics has been analyzed for years with biological information (2000, 2010, and 2020), finding points in time with relative decreases and increases in growth and natural mortality values. An interannual abundance analysis was performed, obtaining biological reference points for the resource through two surplus production models, the Monte Carlo (CMSY+) and the Bayesian state–space Schaefer surplus production model (BSM) methods. The results for management (based on the BSM analysis) indicated that the currently relative stock biomass level is at 79% of virgin biomass (k), which means a recovery compared to the 2017 biomass level (64% k) that has been the lowest in this fishery history. According to the Kobe phase plot, the resource has been harvested in a healthy way, showing a maximum sustainable yield of 8 248.52 t and current status of sub-exploited.

English

Sardinella aurita is the main species exploited by small-scale fisheries in Senegal and represents an important source of low cost protein in the Senegalese market. The objective of this study was to determine the age, growth and mortality parameters of S. aurita obtained from the Senegalese coastal waters. Age, growth parameters and mortality rates of this species were estimated using FiSAT II (FAO–ICLARM Stock Assessment Tools) software. A total of 5104 specimens of S. aurita were collected monthly between March 2012 and February 2013 from commercial landings in three sites of Senegalese coasts (Joal, Mbour and Kayar). Mean growth parameters for the entire period were estimated as L∞= 32.82 cm, K= 1.10 year-1 and t0 = -0.14 year. Instantaneous total mortality (Z = 2.77 year-1) coefficients per year were estimated using catch curves and methods based on the mean length of the fish caught. Natural mortality (M = 1.49 year-1) was estimated using the Pauly’s empirical equation and fishing mortality (F = 1.28 year-1) by the difference between total and natural mortality values. The exploitation rate (E) of 0.46 indicated no over-i¬shing on this species. Key words: Round sardinella, age, growth, mortality, Senegalese coast.

Estimation of annual, time-varying natural mortality and survival for Eastern Bering Sea snow crab (Chionoecetes opilio) with state-space population models

Sex-specific, state-space population models with size and stage structure and fit to survey and fishery data were developed for the eastern Bering Sea (EBS) snow crab for the years 1982–2017. Motivation for model development was to estimate population dynamics by shell condition for female crabs; estimate sex-specific annual, time-varying natural morality rates; and explore in general the feasibility of state space modeling for EBS snow crab. Model fits were very good and mean natural mortality estimates agreed with previous studies but several quite high and/or quite low annual natural mortality values were estimated for both sexes. Estimated mean female natural mortality was 0.49 yr−1 (s.d. = 0.01) with annual values from 0.04 yr−1 to 3.34 yr−1. Estimated mean male natural mortality was 0.36 yr−1 (s.d. = 0.07) with annual values from 0.03 yr−1 to 0.91 yr−1. Episodic high and low annual natural mortality estimates indicate potential model overfitting which an autoregressive or random walk estimation framework for natural mortality may address. We consider the models as proof-of-concept estimation frameworks and their results preliminary. After further refinement and testing, they could be a complementary approach to ongoing stock assessment modeling or prototypes for state-space assessment models. Additional process variability, such as for growth and maturation, can be incorporated in future work. Abundance estimates by mature female shell condition makes feasible estimation of annual and biennial spawner abundances, necessary for accurate egg production estimation. State-space population dynamics models of other Chionoecetes populations with both size and stage-based data (e.g., maturity status or shell condition) can be developed utilizing this study’s modeling framework.

EDAD, CRECIMIENTO Y MORTALIDAD DE LUTJANUS PURPUREUS POEY, 1867 (PISCES: LUTJANIDAE) DE LA REGION DE GUAYANAS

Age, growth and mortality of the red snapper, Lutjanus purpureus Poey, 1867, were estimated based on lecture of 152 urohials of 1561 individuals caught in the region of Guianas, located between 06° - 10° LN and 54° - 61° LW, in 1988, by means of a research survey of the B/l "Dr. Fridtjof Nansen". Seven age groups could be distinguished within the annual zones of the urohial. The theoretical growth curves was adjusted according to the values of the von Bertalanffy growth model parameters: L„ = 91.99 cm ; K = 0.245 per year; to = - 0.499 yr. The values of natural mortality M = 0.255, were obtained using the equation of Taylor; and total mortality Z = 0.703 per year, by aplication of the linearized catch curve method.

Application of a Gnomonic Model to Estimate the Life Span and Natural Mortality inPanopea globosa

Natural mortality estimates are commonly computed from empirical methods or catch curve analysis, and their values are assumed constant for age or size in a population; however, estimates of natural mortality usually vary spatially, temporally, or by size and age. Several factors affect natural mortality rates, such as predation, disease, senescence, cannibalism, starvation, or environmental factors. Seven gnomonic time divisions (GTD) were used to estimate the natural mortality of Panopea globosa for specific portions of its life history: 1, egg to trochophore larvae (24 h); 2, early larvae (6.5 days); 3, late larvae (11 days); 4, early juvenile (35 days); 5, juvenile (3–9 mo); 6, late juvenile (1–2 y); and 7, preadult to adult (47 y). The statistical procedure based on gnomonic time divisions assumes units of time increase as a constant proportion of time elapsed from the end of the previous biological stage; in this manner, the method estimates a vector of natural mortality values by dividing the life cycle into specific time-based subunits. The results provided the following values of naturalmortality atGTD: 1 = 537.42/y; 2 = 230.32/y; 3 = 134.35/y; 4 = 33.58/y; 5 = 2.55/y; 6 = 2.21/y; and 7 = 0.046/y. The consistency of the estimates derived were compared with previous reports of mortality rates and yielded similar values. The gnomonic time method proved to be particularly effective in estimating natural mortality based on the specific life history and life span of the geoduck.

LIFE TABLE PARAMETERS OF THE COTTON LEAFWORM, Spodoptera littoralis (BOISD.)(LEPIDOPTERA:NOCTUIDAE) ON DIFFERENT HOST PLANTS.

Present work is carried out to study the effect of different hot plants on life table parameters of the cotton leafworm Spodoptera littoralis (Boisd.) under laboratory conditions. In this study, development rate, age-specific survival and age and age-specific fecundity for cotton leafworm larvae reared on six host plants: (turnip, bean , corn , castor bean , cowpea and siris ) under laboratory conditions were studied for two successive generations. Results obtained revealed that the cotton leafworm larvae survived on four host plants, but on the fifth host (cowpea), most moths died during first two days after emergence, in the same time on the sixth host (siris), young larvae failed to survive. The remaining four host plants could be arranged according to their suitability for insect development in the following descending order castor bean, bean, corn and turnip. The lowest percentage of natural mortality values occurred 6.01, 5.9, 5.54 and 0.61% when the larvae fed on castor bean leaves for AM, RM, IM and MSR% mortality respectively. Meanwhile, the highest mortality rates were 62.56, 36.1, 32.09 and 10.84% for AM, RM, IM and MSR% mortality respectively when larvae fed on turnip leaves. On the same time, castor bean leaves harbored the highest net reproductive rate (Ro) 687.97 females/female. While the shortest reproductive rate 99.36 females/female were obtained when larvae fed on turnip leaves. Also, the longest mean generation duration (Gt) was 31.92 days when larvae were fed on corn leaves, while, moderate duration was 29.94 and 28.31 days when larvae were fed on castor bean and turnip respectively. The population intrinsic rate (rm) decreases from 0.2182, 0.1792 to 0.1736 individuals/female/day and the finite rate of increase (λ) yield 1.244, 1.196, 1.91, and 1.189 individuals /female/ day when larvae fed on castor bean leaves, bean leaves, corn leaves and turnip leaves respectively. The highest intrinsic and finite rates of increase of S. littoralis were obtained when larvae fed on castor bean leaves. The population of cotton leafworm moth doubled once every 3.98, 4.85, 4.96 and 5.0 days when larvae fed on castor bean leaves, bean leaves, corn leaves and turnip leaves respectively.

Age and growth of flathead, Platycephalus indicus from the Persian Gulf (Bandar Abbas, Iran)

In a study of the age and growth of Platycephalus indicus, a total of 1106 fish were collected from May 2011 to March 2012 in the coastal waters of Iran, Persian Gulf. The ages of 279 specimens were determined by sectioned otoliths. The ages of the females were estimated to be between 0+ to 7+ , while the ages of the males were from 0+ to 4+. The von Bertalanffy growth curve was well suited to the age/total length data of males and females as follows: Lt = 43.40{1–exp[−0.45(t + 0.328)]} for males, and Lt = 63 {1–exp[−0.50(t + 0.30)]} for females. linf = 43.40, k = 0.45, t0 = −0.328 for females and linf = 63, k = 0.50, t0 = −0.30 for males. The estimated values of natural mortality (M) were M = 0.886 yr−1 for females and 0.736 yr−1 for males, and the estimated Z values were 1.43 yr−1 for females and 1.62 yr−1 for males. The mean value of the gonadosomatic index for males and females was 0.82 ± 0.25 and 2.48 ± 0.59, respectively, in each year. The mean values of the hepatosomatic index (HSI) were 0.89 ± 0.20 for males and 1.28 ± 0.16 for females. The highest HSI values for this location were observed in January, and the lowest were in April.

Assessment of the sardine (Sardina pilchardus Walbaum, 1792) fishery in the eastern Mediterranean basin (North Aegean Sea)

The aim of this study was to describe the biometric characteristics of the European sardine (Sardina pilchardus) catches and assess the current status of sardine stock in North Aegean Sea based on population characteristics and abundance trends. The stock was dominated by age groups 1 and 2, not exceeding age group 4. The sardine stock in this area was assessed through an Integrated Catch-at-Age model which implements a separable Virtual Population Analysis on catch at age data with weighted tuning indices. Sardine landings data derived from the commercial purse seine fishery over the period 2000-2008 were combined with the age structure of the stock as resulted from fisheries independent acoustic surveys. Sensitivity analysis of the impact of natural mortality values on stock assessment results was applied. Additionally forecast of the sardine population parameters and catches under different exploitation scenarios was implemented in a medium term basis. Results indicated that the North Aegean Sea sardine stock is considered fully exploited with the fishery operating close but over the empirical exploitation level for sustainability. Finally, the status of the sardine stock in N. Aegean Sea is discussed in relation to the sardine stocks from the western and the central Mediterranean basin.

Developing age-structured stock assessment models as a basis for management procedure evaluations for Namibian sardine

The Namibian sardine stock has experienced intense exploitation since 1950, with catches peaking at 1.4 million tonnes in 1968, followed by a collapse in the 1970s and 1980s. Namibia therefore inherited a severely depleted stock at Independence in 1990. The paper describes data available since Independence, which includes research survey data, and length frequencies obtained from port sampling. It also presents age-structured stock assessment models, which consider some of the main sources of uncertainty relating to values for natural mortality, and assumptions about survey bias, density-dependent effects in survey bias and variance, and the form of the stock-recruit curve. These models could be used as “operating models” to underpin the future development of management procedures for Namibian sardine. Despite reasonable fits, 95% confidence intervals for natural mortality are fairly wide and estimates of precision poor for most models considered. However, the model that assumes density-dependence in survey variance shows superior fits and improved estimates compared to the others, despite reservations about the existence of such effects. This indicates the need to explore the possibility of density-dependence in survey variance further if future management procedure performance is negatively affected by it.

Application of the sex-specific age-structured assessment method for swordfish, Xiphias gladius, in the North Pacific Ocean

Swordfish are known to be sexually dimorphic. However, previous assessments of the status of swordfish in the North Pacific Ocean have ignored this. A sex-specific age-structured assessment model was therefore constructed and fitted to catch, catch-rate and length–frequency data for the swordfish fisheries that operate in the North Pacific Ocean. Except if natural mortality is lower than its “best” estimate, the results indicate that the spawning stock biomass in 2002 was at a high fraction of its unfished level and that the fishing intensity in 2002 was less than F MSY. Therefore, the swordfish stock in the North Pacific Ocean appears to be relatively stable at the current level of exploitation. However, the results of the assessment model are sensitive to the values for natural mortality and the steepness of the stock-recruitment relationship. Forward projections based on samples from a Bayesian posterior distribution indicate that there is negligible risk of the stock dropping below 40% of the unfished spawning stock biomass if fleet-aggregated fishing intensity remains at the current level. However, the risk of population depletion is higher if natural mortality is lower than the “best” estimate.

Life history stage duration and natural mortality for the pink shrimp Farfantepenaeus duorarum (Burkenroad, 1939) in the southern Gulf of Mexico, using the gnomonic model for time division

The gnomonic model proposed by Caddy [Aquat. Living Resour. 9 (1996) 197] to estimate life history stage duration and natural mortality values ( M) is applied to the pink shrimp Farfantepenaeus duorarum of the southern Gulf of Mexico. Estimates of life history stage duration and M were consistent with other estimates in the literature. Evidence from the literature suggests that M declines with age, which is also reflected by results through the gnomonic model. If the product of natural mortality and duration for gnomonic intervals is close to constant, as assumed by the model, then age specific natural mortality rates estimated in this study may be useful in modeling and managing the fishery for pink shrimp.

The Effects of Unaccounted Discards and Misspecified Natural Mortality on Harvest Policies Based on Estimates of Spawners per Recruit

Abstract The amount of exploitation in a fishery is typically controlled by regulatory harvest policies, of which the best for maximizing total yield is F MSY, the fishing rate that provides the maximum sustainable yield. However, estimation of F MSY can be difficult for many fisheries, and for this reason proxies such as the spawning-biomass-per-recruit rate (often denoted F %) have been adopted for some fisheries. Around 1992, the Pacific Fishery Management Council adopted an F 35% harvest policy for U.S. West Coast groundfish. Recently, this policy has been questioned, along with the overall productivity of West Coast groundfish. Estimates of appropriate harvest rates and productivity are computed from stock assessment models, which often rely on poorly estimated values for natural mortality and at-sea discard levels. The effects of unaccounted discards and misspecified natural mortality on estimates of appropriate harvest rates were investigated using a basic catch-age model. A deterministic, generali...

Fisheries regulations based on yield-per-recruit analysis for the linefish silver kob Argyrosomus inodorus in Namibian waters

The most important linefish species, silver kob Argyrosomus inodorus was assessed using two yield-per-recruit approaches, Beverton and Holt and Thompson and Bell. For the Beverton and Holt model, the analysis was run using three different values of natural mortality and depletion of the stock was estimated to be between 14 and 35%. Using the Thompson and Bell method, uncertain values of parameters such as catches, natural mortality and terminal fishing mortality were modelled using Monte Carlo simulations with a pseudo-cohort analysis. For this analysis, it was estimated that the stock was depleted below F SB(40%). In addition, natural mortality versus fishing mortality per age class was investigated and it was found that natural mortality was higher for the first three age classes. Based on the analysis it was recommended that the commercial fishery should be subjected to a total allowable catch, a license system should be introduced, bag limits should be lowered and a maximum size limit be implemented.

Who eats whom in the Barents Sea?

An overview of the estimates of consumption by predators on the main fish stocks in the Barents Sea is given. The main predators are cod (Gadus morhua), harp seal (Phoca groenlandica) and minke whale (Balaenoptera acutorostrata). The results indicate that cod is the most important predator, consuming about as much food annually as harp seals and minke whales combined. The consumption estimates, together with data on the amount of fish removed by commercial fisheries, are compared to estimates of the abundance and removal through natural mortality of the various species of fish prey. The consistency between these estimates is discussed. The natural mortality values for cod and haddock used in assessments are found to be reasonably consistent with the consumption estimates. The consumption of capelin is found to be higher than what is available for predation in years of low capelin abundance, while in years of high herring abundance the consumption of herring does not explain all the mortality. The way in which the consumption estimates are and can be utilised in theassessment and management of fish stocks in the Barents Sea using multispecies models and approaches is described.

Yield-per-Recruit and Relative Mean Biomass Estimates, and their Management Consequences, to the Penaeus Indicus Fishery in the Gulf of Masirah

The von Bertalanffy growth parameters estimated based on the 1990/91 carapace length data of Penaeus indicus from the Gulf of Masirah, Oman were used to calculate total mortality, yield-per-recruit ( i.e. average weight of a shrimp from a cohort under a given fishing pattern) , and relative mean biomass ( i.e. exploited cohort biomass over un-exploited cohort biomass) for the population sampled. The instantaneous total mortality coefficient value indicated under exploitation in 1990/91. When different fishing seasons scenarios were considered with the current total mortality level but with a range of natural mortality values, high yield, per recruit and relative mean biomass values were shown for October-April and November-April fishing seasons. The fishing season is currently late August to end of April. Thus, a one to two-month delay in the fishing season appears to be beneficial to this fishery.