Maximum likelihood estimation of mortality and growth with individual variability from multiple length-frequency data

We consider estimation of mortality rates and growth parameters from length-frequency data of a fish stock and derive the underlying length distribution of the population and the catch when there is individual variability in the von Bertalanffy growth parameter L∞. The model is flexible enough to accommodate 1) any recruitment pattern as a function of both time and length, 2) length-specific selectivity, and 3) varying fishing effort over time. The maximum likelihood method gives consistent estimates, provided the underlying distribution for individual variation in growth is correctly specified. Simulation results indicate that our method is reasonably robust to violations in the assumptions. The method is applied to tiger prawn data (Penaeus semisulcatus) to obtain estimates of natural and fishing mortality.

Effects of fishing on growth traits: a simulation analysis

Abstract—Fisheries often target individuals based on size. Size-selective fishing can create selection differentials on life-history traits and, when those traits have a genetic basis, may cause evolution. The evolution of life history traits affects potential yield and sustainability of fishing, and it is therefore an issue for fishery management. Yet fishery managers usually disregard the possibility of evolution, because little guidance is available to predict evolutionary consequences of management strategies. We attempt to provide some generic guidance. We develop an individual-based model of a population with overlapping generations and continuous reproduction. We simulate model populations under size-selective fishing to generate and quantify selection differentials on growth. The analysis comprises a variety of common life-history and fishery characteristics: variability in growth, correlation between von Bertalanffy growth parameters (K and L∞), maturity rate, natural mortality rate (M), M/K ratio, duration of spawning season, fishing mortality rate (F), maximum size limit, slope of selectivity curve, age at 50% selectivity, and duration of fishing season. We found that each characteristic affected the magnitude of selection differentials. The most vulnerable stocks were those with a short spawning or fishing season. Under almost all life-history and fishery characteristics examined, selection differentials created by realistic fishing mortality rates are considerable.

Age and growth estimates of the thorny skate (Amblyraja radiata) in the western Gulf of Maine

The northwest Atlantic population of thorny skates (Amblyraja radiata) inhabits an area that ranges from Greenland and Hudson Bay, Canada, to South Carolina. Despite such a wide range, very little is known about most aspects of the biology of this species. Recent stock assessment studies in the northeast United States indicate that the biomass of the thorny skate is below the threshold levels mandated by the Sustainable Fisheries Act. In order to gain insight into the life history of this skate, we estimated age and growth for thorny skates, using vertebral band counts from 224 individuals ranging in size from 29 to 105 cm total length (TL). Age bias plots and the coefficient of variation indicated that our aging method represents a nonbiased and precise approach for the age assessment of A. radiata. Marginal increments were significantly different between months (Kruskal-Wallis P<0.001); a distinct trend of increasing monthly increment growth began in August. Age-at-length data were used to determine the von Bertalanffy growth parameters for this population: L∞ = 127 cm (TL) and k= 0.11 for males; L∞ = 120 cm (TL) and k= 0.13 for females. The oldest age estimates obtained for the thorny skate were 16 years for both males and females, which corresponded to total lengths of 103 cm and 105 cm, respectively.

Age, Growth, Life History, and Fisheries of the Sand Sole, Psettichthys melanostictus

Sand sole, Psettichthys melanostictus, is a small but important part of the west coast groundfish fishery. It has never been assessed and there is a limited amount of biological data for the species. We provide the first estimates of age and growth for California populations and compare them with studies from other areas. We found that sand sole is a rapidly growing species which may show a strong latitudinal gradient in growth rate. We also found evidence of a recent, strong cohortrelated shift in the sex ratio of the population towards fewer females. In addition we examined data from the Washington, Oregon, and California commercial fishery to make an initial determination of population status. We found that catch per unit of effort in commercial trawls experienced a decline over time but has rebounded in recent years, except central California (the southern part of its commercial range), where the decline has not reversed.

Combining stable isotopes and skeletal growth marks to detect habitat shifts in juvenile loggerhead sea turtles Caretta caretta

Understanding the phase and timing of ontogenetic habitat shifts underlies the study of a species’ life history and population dynamics. This information is especially critical to the conservation and management of threatened and endangered species, such as the loggerhead sea turtle Caretta caretta. The early life of loggerheads consists of a terrestrial egg and hatchling stage, a posthatchling and juvenile oceanic, pelagic feeding stage, and a juvenile neritic, primarily benthic feeding stage. In the present study, novel approaches were applied to explore the timing of the loggerhead ontogenetic shift from pelagic to benthic habitats. The most recent years of somatic growth are recorded as annual marks in humerus cross sections. A consistent growth mark pattern in benthic juvenile loggerheads was identified, with narrow growth marks in the interior of the bone transitioning to wider growth marks at the exterior, indicative of a sharp increase in growth rates at the transitional growth mark. This increase in annual growth is hypothesized to correlate with the ontogenetic shift from pelagic to benthic habitats. Stable isotopes of carbon and nitrogen just interior and exterior to the transitional growth mark, as well as stable isotopes from pelagic and benthic flora, fauna and loggerhead stomach contents, were analyzed to determine whether this transition related to a diet shift. The results clearly indicate that a dietary shift from oceanic/pelagic to neritic/benthic feeding corresponds to a transitional growth mark. The combination of stable isotope analysis with skeletochronology can elucidate the ecology of cryptic life history stages during loggerhead ontogeny.

Description and growth of larval and pelagic juvenile pygmy rockfish (Sebastes wilsoni) (family Sebastidae)

A developmental series of larval and pelagic juvenile pygmy rockfish (Sebastes wilsoni) from central California is illustrated and described. Sebastes wilsoni is a non- commercially, but ecologically, important rockfish, and the ability to differentiate its young stages will aid researchers in population abundance studies. Pigment patterns, meristic characters, morphometric measurements, and head spination were recorded from specimens that ranged from 8.1 to 34.4 mm in standard length. Larvae were identified initially by meristic characters and the absence of ventral and lateral midline pigment. Pelagic juveniles developed a prominent pigment pattern of three body bars that did not extend to the ventral surface. Species identification was confirmed subsequently by using mitochondrial sequence data of four representative specimens of various sizes. As determined from the examination of otoliths, the growth rate of larval and pelagic juvenile pygmy rockfish was 0.28 mm/day, which is relatively slow in comparison to the growth rate of other species of Sebastes. These data will aid researchers in determining species abundance.

Estimating long-term growth-rate changes of southern bluefin tuna (Thunnus maccoyii) from two periods of tag-return data

Southern bluefin tuna (SBT) (Thunnus maccoyii) growth rates are estimated from tag-return data associated with two time periods, the 1960s and 1980s. The traditional von Bertalanffy growth model (VBG) and a two-phase VBG model were fitted to the data by maximum likelihood. The traditional VBG model did not provide an adequate representation of growth in SBT, and the two-phase VBG yielded a significantly better fit. The results indicated that significant change occurs in the pattern of growth in relation to a VBG curve during the juvenile stages of the SBT life cycle, which may be related to the transition from a tightly schooling fish that spends substantial time in near and surface shore waters to one that is found primarily in more offshore and deeper waters. The results suggest that more complex growth models should be considered for other tunas and for other species that show a marked change in habitat use with age. The likelihood surface for the two-phase VBG model was found to be bimodal and some implications of this are investigated. Significant and substantial differences were found in the growth for fish spawned in the 1960s and in the 1980s, such that after age four there is a difference of about one year in the expected age of a fish of similar length which persists over the size range for which meaningful recapture data are available. This difference may be a density-dependent response as a consequence of the marked reduction in the SBT population. Given the key role that estimates of growth have in most stock assessments, the results indicate that there is a need both for the regular monitoring of growth rates and for provisions for changes in growth over time (possibly related to changes in abundance) in the stock assessment models used for SBT and other species.

Biology and population dynamics of cowcod (Sebastes levis) in the southern California Bight

Cowcod (Sebastes levis) is a large (100-cm-FL), long-lived (maximum observed age 55 yr) demersal rockfish taken in multispecies commercial and recreational fisheries off southern and central California. It lives at 20–500 m depth: adults (>44 cm TL) inhabit rocky areas at 90–300 m and juveniles inhabit fine sand and clay at 40–100 m. Both sexes have similar growth and maturity. Both sexes recruit to the fishery before reaching full maturity. Based on age and growth data, the natural mortality rate is about M =0.055/yr, but the estimate is uncertain. Biomass, recruitment, and mortality during 1951–98 were estimated in a delay-difference model with catch data and abundance indices. The same model gave less precise estimates for 1916–50 based on catch data and assumptions about virgin biomass and recruitment such as used in stock reduction analysis. Abundance indices, based on rare event data, included a habitat-area–weighted index of recreational catch per unit of fishing effort (CPUE index values were 0.003–0.07 fish per angler hour), a standardized index of proportion of positive tows in CalCOFI ichthyoplankton survey data (binomial errors, 0–13% positive tows/yr), and proportion of positive tows for juveniles in bottom trawl surveys (binomial errors, 0–30% positive tows/yr). Cowcod are overfished in the southern California Bight; biomass during the 1998 season was about 7% of the virgin level and recent catches have been near 20 metric tons (t)/yr. Projections based on recent recruitment levels indicate that biomass will decline at catch levels > 5 t/yr. Trend data indicate that recruitment will be poor in the near future. Recreational fishing effort in deep water has increased and has become more effective for catching cowcod. Areas with relatively high catch rates for cowcod are fewer and are farther offshore. Cowcod die after capture and cannot be released alive. Two areas recently closed to bottom fishing will help rebuild the cowcod stock.

Life history and population dynamics of the finetooth shark (Carcharhinus isodon) in the northeastern Gulf of Mexico

The life history and population dynamics of the finetooth shark (Carcharhinus isodon) in the north-eastern Gulf of Mexico were studied by determining age, growth, size-at-maturity, natural mortality, productivity, and elasticity of vital rates of the population. The von Bertalanffy growth model was estimated as Lt=1559 mm TL (1–e–0.24 (t+2.07)) for females and Lt = 1337 mm TL (1–e–0.41 (t+1.39)) for males. For comparison, the Fabens growth equation was also fitted separately to observed size-at-age data, and the fits to the data were found to be similar. The oldest aged specimens were 8.0 and 8.1 yr, and theoretical longevity estimates were 14.4 and 8.5 yr for females and males, respectively. Median length at maturity was 1187 and 1230 mm TL, equivalent to 3.9 and 4.3 yr for males and females, respectively. Two scenarios, based on the results of the two equations used to describe growth, were considered for population modeling and the results were similar. Annual rates of survivorship estimated through five methods ranged from 0.850/yr to 0.607/yr for scenario 1 and from 0.840/yr to 0.590/yr for scenario 2. Productivities were 0.041/yr for scenario 1 and 0.038/yr for scenario 2 when the population level that produces maximum sustain-able yield is assumed to occur at an instantaneous total mortality rate (Z) equaling 1.5 M, and were 0.071/yr and 0.067/yr, when Z=2 M for scenario 1 and 2, respectively. Mean generation time was 6.96 yr and 6.34 yr for scenarios 1 and 2, respectively. Elasticities calculated through simulation of Leslie matrices averaged 12.6% (12.1% for scenario 2) for fertility, 47.7% (46.2% for scenario 2) for juvenile survival, and 39.7% (41.6% for scenario 2) for adult survival. In all, the finetooth shark exhibits life-history and population characteristics intermediate to those of sharks in the small coastal complex and those from some large coastal species, such as the blacktip shark (Carcharhinus limbatus).

Developing a growth-transition matrix for the stock assessment of the green sea urchin (Strongylocentrotus droebachiensis) off Maine

The green sea urchin (Strongylocentrotus droebachiensis) is important to the economy of Maine. It is the state’s fourth largest fishery by value. The fishery has experienced a continuous decline in landings since 1992 because of decreasing stock abundance. Because determining the age of sea urchins is often difficult, a formal stock assessment demands the development of a size-structured population dynamic model. One of the most important components in a size-structured model is a growth-transition matrix. We developed an approach for estimating the growth-transition matrix using von Bertalanffy growth parameters estimated in previous studies of the green sea urchin off Maine. This approach explicitly considers size-specific variations associated with yearly growth increments for these urchins. The proposed growth-transition matrix can be updated readily with new information on growth, which is important because changes in stock abundance and the ecosystem will likely result in changes in sea urchin key life history parameters including growth. This growth-transition matrix can be readily incorporated into the size-structured stock assessment model that has been developed for assessing the green sea urchin stock off Maine.

Age, growth, and reproduction of permit (Trachinotus falcatus) in Florida waters

We examined 536 permit (Trachinotus falcatus, 65–916 mm FL) collected from the waters of Florida Keys and from the Tampa Bay area on Florida’s Gulf coast to describe their growth and reproduction.Among permit that we sexed, females ranged from 266 to 916 mm in length (mean=617) and males ranged from 274 to 855 mm (mean=601). Ages of 297 permit ranging from 102 to 900 mm FL were estimated from thin-sectioned otoliths (sagittae). The large proportion of otoliths with an annulus on the margin and an otolith from an OTC-injected fish suggested that a single annulus was formed each year during late spring or early summer.Permit reach a maximum age of at least 23 years.Permit grew rapidly until an age of about five years, and then growth slowed considerably. Male and female von Bertalanffy growth models were not significantly different, and the sexes-combined growth model was FL=753.1(1–e –0.348(Age+0.585)). Gonad development was seasonal, and spawning occurred during late spring and summer over artificial and natural reefs at depths of 10–30 m. Ovaries that contained oocytes in the final stages of oocyte maturation or postovulatory follicles were found during May–July. We estimated that 50% of the females in the population had reached sexual maturity by 547 mm and an age of 3.1 years and that 50% of the males in the population had reached sexual maturity by 486 mm and an age of 2.3 years. Because Florida regulations restrict the maximum size of permit caught in recreational and commercial fisheries to 20-inch (508-mm), most fish harvested are sexually immature. With the current size selectivity of the fishery, the spawning stock biomass of permit could decrease quickly in response to moderate levels of fishing mortality; thus, the regulations in place in Florida to restrict harvest levels appear to be justified.

Validated age and growth of the porbeagle shark (Lamna nasus) in the western North Atlantic Ocean

Growth parameters were estimated for porbeagle shark (Lamna nasus) in the northwest Atlantic Ocean on the basis of vertebral annuli. A total of 578 vertebrae was analyzed. Annuli were validated up to an age of 11 years by using vertebrae from recaptured oxytetracycline-injected and known-age sharks. Males and females grew at similar rates until the size of male sexual maturity, after which the relative growth of the males declined. The growth rate of the females declined in a similar manner at the onset of maturity. Growth curves were consistent with those derived from tag-recapture analyses (GROTAG) of 76 recaptured fish and those based on length-frequency methods with measurements from 13,589 individuals. Von Bertalanffy growth curve parameters (combined sexes) were L∞ = 289.4 cm fork length, K = 0.07 and t0 = –6.06. Maximum age, based on vertebral band pair counts, was 25 and 24 years for males and females, respectively. Longevity calculations, however, indicated a maximum age of 45 to 46 years in an unfished population.

Do fluctuations in the somatic growth rate of rock lobster (Jasus lalandii) encompass all size classes? A re-assessment of juvenile growth

Catch rates in the South African rock lobster (Jasus lalandii) fishery declined after 1989 in response to reduced adult somatic growth rates and a consequent reduction in recruitment to the fishable population. Although spatial and temporal trends in adult growth are well described, little is known about how juvenile growth rates have been affected. In our study, growth rates of juvenile rock lobster on Cape Town harbor wall were compared with those recorded at the same site more than 25 years prior to our study, and with those on a nearby natural nursery reef. We found that indices of somatic growth measured during 1996–97 at the harbor wall had declined significantly since 1971–72. Furthermore, growth was slower among juvenile J. lalandii at the harbor wall than those at the natural nursery reef. These results suggest that growth rates of juvenile and adult J. lalandii exhibit similar types of spatiotemporal patterns. Thus, the recent coastwide decline in adult somatic growth rates might also encompass smaller size classes.

Age and growth of the smooth dogfish (Mustelus canis) in the northwest Atlantic Ocean

The northwest Atlantic population of smooth dogfish (Mustelus canis) ranges from Cape Cod, Massachusetts, to South Carolina. Although M. canis is seasonally abundant in this region, very little is known about important aspects of its biology, such as growth and reproductive rates. In the early 1990s, commercial fishery landings of smooth dogfish dramatically increased on the east coast of the United States. This study investigated growth rates of the east coast M. canis population through analysis of growth patterns in vertebral centra. Marginal increment analysis, estimates of precision, and patterns in seasonal growth supported the use of vertebrae to age these sharks. Growth bands in vertebral samples were used to estimate ages for 894 smooth dogfish. Age-length data were used to determine von Bertalanffy growth parameters for this population: K = 0.292/yr, L∞ = 123.57 cm, and t0 = –1.94 years for females, and K = 0.440/yr, L∞ = 105.17 cm, and t0 = –1.52 years for males. Males matured at two or three years of age and females matured between four and seven years of age. The oldest age estimate for male and female samples was ten and sixteen years, respectively.

Morphometry and population dynamics of Sepia aculeata, (Orbigny - 1848) along the Bombay coast

Cephalopods gained importance in the fishing industry when they emerged as one of the leading sea food products exclusively for international market in the mid seventies. Cephalopods fishery in India is still in an infant stage with vast scope for exploitation. The present work on the cephalopods fishery along the Bombay coast is an effort to quantify the resource potential of Sepia acculeata. The morphometry, growth parameters, mortality (total, natural and fishing) rates, the yield per recruit and standing stock were studied.