An environmentally based growth model that uses finite difference calculus with maximum likelihood method: its application to the brackish water bivalve Corbicula japonica in Lake Abashiri, Japan

We present a growth analysis model that combines large amounts of environmental data with limited amounts of biological data and apply it to Corbicula japonica. The model uses the maximum-likelihood method with the Akaike information criterion, which provides an objective criterion for model selection. An adequate distribution for describing a single cohort is selected from available probability density functions, which are expressed by location and scale parameters. Daily relative increase rates of the location parameter are expressed by a multivariate logistic function with environmental factors for each day and categorical variables indicating animal ages as independent variables. Daily relative increase rates of the scale parameter are expressed by an equation describing the relationship with the daily relative increase rate of the location parameter. Corbicula japonica grows to a modal shell length of 0.7 mm during the first year in Lake Abashiri. Compared with the attain-able maximum size of about 30 mm, the growth of juveniles is extremely slow because their growth is less susceptible to environmental factors until the second winter. The extremely slow growth in Lake Abashiri could be a geographical genetic variation within C. japonica.

A new growth model for red drum (Sciaenops ocellatus) that accommodates seasonal and ontogenic changes in growth rates

The red drum (Sciaenops ocellatus) is a popular gamefish found throughout the coastal waters of the Gulf of Mexico and along the eastern seaboard as far north as Massachusetts. Juvenile red drum grow extremely rapidly, especially during the warmer months, but adults grow very little. In fact, the change in growth with age is so abrupt that the standard von Bertalanffy curve has proven inadequate— the predicted lengths of younger fish are generally too large and the predicted lengths of older fish too small (see Beckman et al., 1988; Murphy and Taylor, 1990).

A catch-free stock assessment model with application to goliath grouper (Epinephelus itajara) off southern Florida

Many modern stock assessment methods provide the machinery for determining the status of a stock in relation to certain reference points and for estimating how quickly a stock can be rebuilt. However, these methods typically require catch data, which are not always available. We introduce a model-based framework for estimating reference points, stock status, and recovery times in situations where catch data and other measures of absolute abundance are unavailable. The specif ic estimator developed is essentially an age-structured production model recast in terms relative to pre-exploitation levels. A Bayesian estimation scheme is adopted to allow the incorporation of pertinent auxiliary information such as might be obtained from meta-analyses of similar stocks or anecdotal observations. The approach is applied to the population of goliath grouper (Epinephelus itajara) off southern Florida, for which there are three indices of relative abundance but no reliable catch data. The results confirm anecdotal accounts of a marked decline in abundance during the 1980s followed by a substantial increase after the harvest of goliath grouper was banned in 1990. The ban appears to have reduced fishing pressure to between 10% and 50% of the levels observed during the 1980s. Nevertheless, the predicted fishing mortality rate under the ban appears to remain substantial, perhaps owing to illegal harvest and depth-related release mortality. As a result, the base model predicts that there is less than a 40% chance that the spawning biomass will recover to a level that would produce a 50% spawning potential ratio.

Growth dynamics of the spinner shark (Carcharhinus brevipinna) off the United States southeast and Gulf of Mexico coasts: a comparison of methods

The age and growth dynamics of the spinner shark (Carcharhinus brevipinna) in the northwest Atlantic Ocean off the southeast United States and in the Gulf of Mexico were examined and four growth models were used to examine variation in the ability to fit size-at-age data. The von Bertalanffy growth model, an alternative equation of the von Bertalanffy growth model with a size-at-birth intercept, the Gompertz growth model, and a logistic model were fitted to sex-specific observed size-at-age data. Considering the statistical criteria (e.g., lowest mean square error [MSE], high coefficient-of-determination, and greatest level of significance) we desired for this study, the logistic model provided the best overall fit to the size-at-age data, whereas the von Bertalanffy growth model gave the worst. For “biological validity,” the von Bertalanffy model for female sharks provided estimates similar to those reported in other studies. However, the von Bertalanffy model was deemed inappropriate for describing the growth of male spinner sharks because estimates of theoretical maximum size (L∞) indicated a size much larger than that observed in the field. However, the growth coefficient (k= 0.14/yr) from the Gompertz model provided an estimate most similar to that reported for other large coastal species. The analysis of growth for spinner shark in the present study demonstrates the importance of fitting alternative models when standard models fit the data poorly or when growth estimates do not appear to be realistic.

The three dimensional model with the affection of stratified density (Caspian Sea)

The hydro dynamical actions in big Lakes directly influence dynamic, physical and chemical affairs. The circulation's models and temperature have something to do with the movements of fluids, and analysis for circulation in Caspian sea is because of the lack of observation through which the circulations and out comings are determined. Through the studies, three dimensional simulations (Large- Scale) are planned and performed, according to Smolakiewicz and Margolin works. This is a non- hydrostatic and Boussinesq approximation is used in its formulation is used in its formulation on the basis of Lipps (1990) theorem and curve lines, the fluid is constant adiabatic and stratified, and the wind power is considered zero. The profile of speed according to previous depth and before ridge can be drawn on the basis of density available between northern and southern ridges. The circulation field is drawn from 3 cm/s to 13 cm/s on the plate z= 5 cm , the vertical changes of speed on the plate is 0.02 m/s. Vertical profile , horizontal speed in previous on, and after the ridges on are drawn on different spaces. It changes from 0.5 cm/s to 1 cm/s before ridges.

Food conversion efficiency and the von Bertalanffy growth function. Part II and conclusion: Extension of the new model to the generalized von Bertalanffy growth function

The simple model relating food conversion efficiency (K sub(1)) to body weight derived from the theoretical concepts behind von Bertalanffy's growth model, is extended here in the context of Pauly's generalization of that model. The exponent, which was fixed to 1/3 in the simple model, is in the extended model equivalent to 1-d, with d being the weight exponent of the anabolism term in Pauly's growth model. This makes the model applicable to fish for which the assumptions of the original (special) version of von Bertalanffy's growth model are violated.

PICES-GLOBEC International Program on Climate Change and Carrying Capacity: Report of 2001 BASS/MODEL, MONITOR and REX Workshops, and the 2002 MODEL/REX Workshop

Table of Contents [pdf, 0.22 Mb] Executive Summary [pdf, 0.31 Mb] Report of the 2001 BASS/MODEL Workshop [pdf, 0.65 Mb] To review ecosystem models for the subarctic gyres Report of the 2001 MONITOR Workshop [pdf, 0.7 Mb] To review ecosystem models for the subarctic gyres Workshop presentations: Sonia D. Batten PICES Continuous Plankton Recorder pilot project Phillip R. Mundy GEM (Exxon Valdez Oil Spill Trustee Council`s "Gulf Ecosystem Monitoring" initiative) and U.S. GOOS plans in the North Pacific Ron McLaren and Brian O`Donnell A proposal for a North Pacific Action group of the international Data Buoy Cooperation Panel Gilberto Gaxiola-Castrol and Sila Najera-Martinez The Mexican oceanographic North Pacific program: IMECOCAL Sydney Levitus Building global ocean profile and plankton databases for scientific research Report of the 2001 REX Workshop [pdf, 1.73 Mb] On temporal variations in size-at-age for fish species in coastal areas around the Pacific Rim Workshop presentations: Brian J. Pyper, Randall M. Peterman, Michael F. Lapointe and Carl J. Walters [pdf, 0.33 Mb] Spatial patterns of covariation in size-at-age of British Columbia and Alaska sockeye salmon stocks and effects of abundance and ocean temperature R. Bruce MacFarlane, Steven Ralston, Chantell Royer and Elizabeth C. Norton [pdf, 0.4 Mb] Influences of the 1997-1998 El Niño and 1999 La Niña on juvenile Chinook salmon in the Gulf of the Farallones Olga S. Temnykh and Sergey L. Marchenko [pdf, 0.5 Mb] Variability of the pink salmon sizes in relation with abundance of Okhotsk Sea stocks Ludmila A. Chernoivanova, Alexander N. Vdoven and D.V. Antonenko [pdf, 0.3 Mb] The characteristic growth rate of herring in Peter the Great Bay (Japan/East Sea) Nikolay I. Naumenko [pdf, 0.5 Mb] Temporal variations in size-at-age of the western Bering Sea herring Evelyn D. Brown [pdf, 0.45 Mb] Effects of climate on Pacific herring, Clupea pallasii, in the northern Gulf of Alaska and Prince William Sound, Alaska Jake Schweigert, Fritz Funk, Ken Oda and Tom Moore [pdf, 0.6 Mb] Herring size-at-age variation in the North Pacific Ron W. Tanasichuk [pdf, 0.3 Mb] Implications of variation in euphausiid productivity for the growth, production and resilience of Pacific herring (Clupea pallasi) from the southwest coast of Vancouver Island Chikako Watanabe, Ahihiko Yatsu and Yoshiro Watanabe [pdf, 0.3 Mb] Changes in growth with fluctuation of chub mackerel abundance in the Pacific waters off central Japan from 1970 to 1997 Yoshiro Watanabe, Yoshiaki Hiyama, Chikako Watanabe and Shiro Takayana [pdf, 0.35 Mb] Inter-decadal fluctuations in length-at-age of Hokkaido-Sakhalin herring and Japanese sardine in the Sea of Japan Pavel A. Balykin and Alexander V. Buslov [pdf, 0.4 Mb] Long-term variability in length of walley pollock in the western Bering Sea and east Kamchtka Alexander A. Bonk [pdf, 0.4 Mb] Effect of population abundance increase on herring distribution in the western Bering Sea Sergey N. Tarasyuk [pdf, 0.4 Mb] Survival of yellowfin sole (Limanda aspera Pallas) in the northern part of the Tatar Strait (Sea of Japan) during the second half of the 20th century Report of the 2002 MODEL/REX Workshop [pdf, 1.2 Mb] To develop a marine ecosystem model of the North Pacific Ocean including pelagic fishes Summary and Overview [pdf, 0.4 Mb] Workshop presentations: Bernard A. Megrey, Kenny Rose, Francisco E. Werner, Robert A. Klumb and Douglas E. Hay [pdf, 0.47 Mb] A generalized fish bioenergetics/biomass model with an application to Pacific herring Robert A. Klumb [pdf, 0.34 Mb] Review of Clupeid biology with emphasis on energetics Douglas E. Hay [pdf, 0.47 Mb] Reflections of factors affecting size-at-age and strong year classes of herring in the North Pacific Shin-ichi Ito, Yutaka Kurita, Yoshioki Oozeki, Satoshi Suyama, Hiroya Sugisaki and Yongjin Tian [pdf, 0.34 Mb] Review for Pacific saury (Cololabis saira) study under the VENFISH project lexander V. Leonov and Gennady A. Kantakov [pdf, 0.34 Mb] Formalization of interactions between chemical and biological compartments in the mathematical model describing the transformation of nitrogen, phosphorus, silicon and carbon compounds Herring group report and model results [pdf, 0.34 Mb] Saury group report and model results [pdf, 0.46 Mb] Model experiments and hypotheses Recommendations [pdf, 0.4 Mb] Achievements and future steps Acknowledgements [pdf, 0.29 Mb] References [pdf, 0.32 Mb] Appendix 1. List of Participants [pdf, 0.32 Mb] Appendices 2-5. FORTRAN codes [pdf, 0.4 Mb] (Document pdf contains 182 pages)

Reference-growth rate – a simple and handy parameter summarizing the influence of environmental conditions

Abstract Environmental changes may have an impact on life conditions of the fish, e.g. food supply for the fish. The prevailing environmental conditions apply evenly to all age groups of one stock. Small fish have high growth rates, whereas large fish grow with low rates. But, it can be shown on the basis of the von Bertalanffy-growth model that it is sufficient to know only the growth rate of one single age group to compute the growth rates of all other age groups. The growth rate of a reference fish GRF (e.g. a fish with a body mass of 1 kg) was introduced as a reference growth describing the current food condition of all age groups of the stock. As an example a time series of the reference-growth rate of the northern cod stock (NAFO, 3K) was computed for the time span 1979 to 1999. For the northern cod stock it can be observed that environmental conditions caused growth rates below the long-term mean for seven years in a row. After a prolonged hunger period the fish stock collapsed in 1992 also by the impact of fisheries - and this was probably not a coincidence. Now, with the reference-growth rate GRF a simple and handy parameter was found to summarize the influence of the environmental conditions on growth and other derived models and therefore makes it easier to compute the influence of environmental changes within stock assessment. Zusammenfassung Veränderungen der Umwelt können Auswirkungen auf die Lebensbedingungen der Fische haben, z. B. auf das Nahrungsangebot der Fische. Die vorherrschenden Umgebungsbedingungen wirken gleichmäßig auf alle Altersgruppen eines Bestandes, wobei typischer Weise kleineFische hohe Wachstumsraten haben, während die großen Fische mit niedrigen Raten wachsen. Auf der Grundlage des von Bertalanffy-Wachstumsmodells kann gezeigt werden, dass es ausreicht, nur die Wachstumsrate von einer einzigen Altersgruppe zu kennen, um die Wachstumsraten von allen anderen Altersgruppen berechnen zu können. Die Wachstumsrate eines Referenz-Fisches (z.B. eines Fisches mit einer Körpermasse von 1 kg) wurde als Referenz-Wachstum GRF eingeführt, die den aktuellen Zustand des Nahrungsangebots füralle Altersgruppen des Bestandes beschreibt. Als Beispiel wurde einer Zeitreihe der Referenz-Wachstumsraten des nördlichen Kabeljaubestandes (NAFO, 3K) für die Zeitsraum 1979 bis 1999 berechnet. Für diesen Kabeljaubestand war zu beobachten, dass Umgebungsbedingungen für sieben Jahre in Folge Wachstumsraten unter dem langjährigen Mittelwert verursachten. Nach einer längeren Hungerperiode kollabierte dieser Fischbestand im Jahr 1992 auch durch den Einfluß der Fischerei - und dies war sicher kein Zufall. Jetzt, mit der Referenz-Wachstumsrate GRF, ist ein einfacher und handlicher Parameter gefunden, der es gestattet den Einfluss der Umweltbedingungen auf die Wachstumsbedingungen und andere davon abgeleitete Modelle zusammenzufassen. Dies macht es einfach, den Einfluss von Umweltveränderungen innerhalb der Bestandsabschätzungen zu berechnen.

Age validation, growth, mortality, and demographic modeling of spotted gully shark (Triakis megalopterus) from the southeast coast of South Africa

This study documents validation of vertebral band-pair formation in spotted gully shark (Triakis megalopterus) with the use of fluorochrome injection and tagging of captive and wild sharks over a 21-year period. Growth and mortality rates of T. megalopterus were also estimated and a demographic analysis of the species was conducted. Of the 23 OTC (oxytetracycline) -marked vertebrae examined (12 from captive and 11 from wild sharks), seven vertebrae (three from captive and four from wild sharks) exhibited chelation of the OTC and fluoresced under ultraviolet light. It was concluded that a single opaque and translucent band pair was deposited annually up to at least 25 years of age, the maximum age recorded. Reader precision was assessed by using an index of average percent error calculated at 5%. No significant differences were found between male and female growth patterns (P>0.05), and von Bertalanffy growth model parameters for combined sexes were estimated to be L∞=1711.07 mm TL, k=0.11/yr and t0=–2.43 yr (n=86). Natural mortality was estimated at 0.17/yr. Age at maturity was estimated at 11 years for males and 15 years for females. Results of the demographic analysis showed that the population, in the absence of fishing mortality, was stable and not significantly different from zero and particularly sensitive to overfishing. At the current age at first capture and natural mortality rate, the fishing mortality rate required to result in negative population growth was low at F>0.004/ yr. Elasticity analysis revealed that juvenile survival was the principal factor in explaining variability in population growth rate.

Age and growth of spiny dogfish (Squalus acanthias) in the Gulf of Alaska: analysis of alternative growth models

Ten growth models were fitted to age and growth data for spiny dogfish (Squalus acanthias) in the Gulf of Alaska. Previous studies of spiny dogfish growth have all fitted the t0 formulation of the von Bertalanffy model without examination of alternative models. Among the alternatives, we present a new two-phase von Bertalanffy growth model formulation with a logistically scaled k parameter and which estimates L0. A total of 1602 dogfish were aged from opportunistic collections with longline, rod and reel, set net, and trawling gear in the eastern and central Gulf of Alaska between 2004 and 2007. Ages were estimated from the median band count of three independent readings of the second dorsal spine plus the estimated number of worn bands for worn spines. Owing to a lack of small dogfish in the samples, lengths at age of small individuals were back-calculated from a subsample of 153 dogfish with unworn spines. The von Bertalanffy, two-parameter von Bertalanffy, two-phase von Bertalanffy, Gompertz, two-parameter Gompertz, and logistic models were fitted to length-at-age data for each sex separately, both with and without back-calculated lengths at age. The two-phase von Bertalanffy growth model produced the statistically best fit for both sexes of Gulf of Alaska spiny dogfish, resulting in L∞ = 87.2 and 102.5 cm and k= 0.106 and 0.058 for males and females, respectively.

Age and growth of swordfish (Xiphias gladius) caught by the Hawaii-based pelagic longline fishery

We verified the age and growth of swordfish (Xiphias gla-dius) by comparing ages determined from annuli in fin ray sections with daily growth increments in otoliths. Growth of swordfish of exploitable sizes is described on the basis of annuli present in cross sections of the second ray of the first anal fins of 1292 specimens (60−260 cm eye-to-fork length, EFL) caught in the region of the Hawaii-based pelagic longline fishery. The position of the initial fin ray annulus of swordfish was verified for the first time with the use of scanning electron micrographs of presumed daily growth increments present in the otoliths of juveniles. Fish growth through age 7 was validated by marginal increment analysis. Faster growth of females was confirmed, and the standard von Bertalanffy growth model was identified as the most parsimonious for describing growth in length for fish greater than 60 cm EFL. The observed growth of three fish, a year-old in size when first caught and then recaptured from 364 to1490 days later, is consistent with modeled growth for fish of this size range. Our novel approach to verifying age and growth should increase confidence in conducting an age-structured stock assessment for swordfish in the North Pacific Ocean.

Modification of the biological intercept model to account for ontogenetic effects in laboratory-reared delta smelt (Hypomesus transpacificus)*

We investigated age, growth, and ontogenetic effects on the proportionality of otolith size to fish size in laboratory-reared delta smelt (Hypomesus transpacificus) from the San Francisco Bay estuary. Delta smelt larvae were reared from hatching in laboratory mesocosms for 100 days. Otolith increments from known-age fish were enumerated to validate that growth increments were deposited daily and to validate the age of fish at first ring formation. Delta smelt were found to lay down daily ring increments; however, the first increment did not form until six days after hatching. The relationship between otolith size and fish size was not biased by age or growth-rate effects but did exhibit an interruption in linear growth owing to an ontogenetic shift at the postflexon stage. To back-calculate the size-at-age of individual fish, we modified the biological intercept (BI) model to account for ontogenetic changes in the otolith-size−fish-size relationship and compared the results to the time-varying growth model, as well as the modified Fry model. We found the modified BI model estimated more accurately the size-at-age from hatching to 100 days after hatching. Before back-calculating size-at-age with existing models, we recommend a critical evaluation of the effects that age, growth, and ontogeny can have on the otolith-size−fish-size relations

Interdecadal change in growth of sablefish (Anoplopoma fimbria) in the northeast Pacific Ocean

Errors in growth estimates can affect drastically the spawner-perrecruit threshold used to recommend quotas for commercial fish catches. Growth parameters for sablefish (Anoplopoma fimbria) in Alaska have not been updated for stock assessment purposes for more than 20 years, although aging of sablefish has continued. In this study, length-stratified data (1981–93 data from the annual longline survey conducted cooperatively by the Fisheries Agency of Japan and the Alaska Fisheries Science Center of the National Marine Fisheries Service) were updated and corrected for discovered sampling bias. In addition, more recent, randomly collected samples (1996–2004 data from the annual longline survey conducted by the Alaska Fisheries Science Center) were analyzed and new length-at-age and weight-at-age parameters were estimated. Results were similar between this analysis with length-at-age data from 1981 to 2004 and analysis with updated longline survey data through 2010; therefore, we used our initial results from analysis done with data through 2004. We found that, because of a stratified sampling scheme, growth estimates of sablefish were overestimated with the older data (1981–93), and growth parameters used in the Alaskan sablefish assessment model were, thus, too large. In addition, a comparison of the bias-corrected 1981–93 data and the 1996–2004 data showed that, in more recent years, sablefish grew larger and growth differed among regions. The updated growth information improves the fit of the data to the sablefish stock assessment model with biologically reasonable results. These findings indicate that when the updated growth data (1996–2004) are used in the existing sablefish assessment model, estimates of fishing mortality increase slightly and estimates of female spawning biomass decrease slightly. This study provides evidence of the importance of periodically revisiting biological parameter estimates, especially as data accumulate, because the addition of more recent data often will be more biologically realistic. In addition, it exemplifies the importance of correcting biases from sampling that may contribute to erroneous parameter estimates.

Reproductive biology, spawning season, and growth of female rex sole (Glyptocephalus zachirus) in the Gulf of Alaska

Rex sole (Glyptocephalus zachirus) have a wide distribution throughout the North Pacific, ranging from central Baja California to the western Bering Sea. Although rex sole are an important species in the commercial trawl fisheries off the U.S. West Coast, knowledge of their reproductive biology is limited to one study off the Oregon coast where ovaries were analyzed with gross anatomical methods. This study was initiated to determine reproductive and growth parameters specific to rex sole in the Gulf of Alaska (GOA) stock. Female rex sole (n=594) ranging in total length from 166 to 552 mm were collected opportunistically around Kodiak Island, Alaska, from February 2000 to October 2001. All ovaries were analyzed by using standard histological criteria to determine the maturity stage. Year-round sampling of rex sole ovaries confirmed that rex sole are batch spawners and have a protracted spawning season in the GOA that lasts at least eight months, from October to May; the duration of the spawning season and the months of spawning activity are different from those previously estimated. Female rex sole in the GOA had an estimated length at 50% maturity (ML50) of 352 mm, which is greater than the previously estimated ML50 at southern latitudes. The maximum age of collected female rex sole was 29 years, and the estimated age at 50% maturity (MA50) in the GOA was 5.1 years. The von Bertalanffy growth model for rex sole in the GOA was significantly different from the previously estimated model for rex sole off the Oregon coast. This study indicated that there are higher growth rates for rex sole in the GOA than off the Oregon coast and that there are differences in length at maturity and similarity in age at maturity between the two regions.

Age validation of juvenile Shortfin Mako (Isurus oxyrinchus) tagged and marked with oxytetracycline off southern California

The purpose of this study was to validate aging results of juvenile Shortfin Mako (Isurus oxyrinchus) by vertebral band counts. Vertebrae of 29 juvenile Shortfin Mako marked with oxytetracycline (OTC) were obtained from tag-recapture activities to determine centrum growth-band deposition. Tagging occurred off southern California from 1996 to 2010, and time at liberty of the 29 sharks ranged from 4 months to 4.4 years (mean=1.3 years). Growth information also was obtained from length-frequency modal analyses (MULTIFAN and MIXDIST) by using a 29-year data set of commercial and research catch data, in addition to a tag-recapture growth model (e.g, the GROTAG model). For vertebrae samples used for age validation, shark size at time of release ranged from 79 to 142 cm fork length (FL) and from 98 to 200 cm FL at recapture. Results from band counts of vertebrae distal to OTC marks indicate 2 band pairs (2 translucent and 2 opaque) are formed each year for Shortfin Mako of the size range examined. Length-frequency analyses identified 3 age class modes. Growth rate estimates from 26.5 to 35.5 cm/year were calculated for the first age-class mode (85 cm FL) and from 22.4 to 28.6 cm/year for the second age-class mode (130 cm FL). Results from the tag-recapture growth model revealed fast growth during time at liberty for tagged fish of the 2 youngest age classes. Collectively, these methods suggest rapid growth of juvenile Shortfin Mako in the southern California study area and indicate biannual deposition of growth bands in vertebrae for the first 5 years.