Trend analysis in two standard growth models

This paper analyzes the trend processes characterized by two standard growth models using simple econometrics. The first model is the basic neoclassical growth model that postulates a deterministic trend for output. The second model is the Uzawa-Lucas model that postulates a stochastic trend for output. The aim is to understand how the different trend processes for output assumed by these two standard growth models determine the ability of each model to explain the observed trend processes of other macroeconomic variables such as consumption and investment. The results show that the two models reproduce the output trend process. Moreover, the results show that the basic growth model captures properly the consumption trend process, but fails in characterizing the investment trend process. The reverse is true for the Uzawa-Lucas model.

Discontinuous growth mechanisms of mode II crack under high-speed impact conditions

A recoverable plate impact testing technology has been used for studying the growth mechanisms of mode II crack. The results show that interactions of microcracks ahead of a crack tip cause the crack growth unsteadily. Failure mode transitions of materials were observed. Based on the observations, a discontinuous crack growth model was established. Analysis shows that the shear crack grows unsteady as the growth speed is between the Rayleigh wave speed c(R) and the shear wave speed c(s); however, when the growth speed approaches root 2c(s), the crack grows steadily. The transient microcrack growth makes the main crack speed to jump from subsonic to intersonic and the steady growth of all the sub-cracks leads the main crack to grow stably at an intersonic speed.

Early postnatal growth of the spotted dolphin, Stenella attenuata, in the offshore Eastern Tropical Pacific.

Estimates of length at birth and early postnatal growth are made for the northern and southern populations of the offshore spotted dolphin in the offshore eastern tropical Pacific. Length at birth is estimated to be 85.4 cm for the northern population and 83.2 cm for the southern population. Analyses of series of monthly distributions of length revealed two cohorts born each year in the northern population, at least in the northern inshore part of its geographic range, but only one cohort born each year in the southern population. Growth curves fitted to the means of the monthly distributions of length gave estimates of length at 1 year of 126.2 and 132.6 cm and length at 2 years of 154.3 and 154.9 cm for the two cohorts in the northern population. and length at 1 year of 127.9 cm for the southern population. A growth curve fitted to lengths and ages (in dental growth layer groups) from the northern population gave estimates of lengths at 1 and 2 years of 123.0 and 143.0 cm, respectively.

Stock assessment of the gulf menhaden, Brevoortia patronus, fishery

A stock assessment of the gulf menhaden. Brevoortia patronus, fishery was conducted with data on purse-seine landings from 1946 to 1985 and port sampling data from 1964 to 1985. These data were analyzed to determine growth rates, yield-per-recruit, spawner-recruit relationships, and maximum sustainable yield (MSY). Virtual population analysis was used to estimate stock size, year-class size, and fishing mortality rates. During the period studied, an average of 27% of age-l fish and 55% of age-2 and age-3 fish were taken by the fishery, and 54% for age-I and 38% for age-2 and -3 fish were lost annually to natural causes. Annual yield-per-recruit estimates ranged from 6.9 to 19.3 g, with recent mean conditions averaging 12.2 g since 1978. Surplus production models produced estimates of MSY from 620 to 700 kilometric tons. Recruits to age-I ranged from 8.3 to 41.8 billion fish for 1964-82. Although there was substantial scatter about the fitted curves, Ricker·type spawner-recruit relationships were found suitable for use in a population simulation model. Estimates of MSY from population simulation model runs ranged from 705 to 825 kilometric tons with F -multiples of the mean rate of fishing ranging from 1.0 to 1.5. Recent harvests in excess of the historical MSY may not be detrimental to the gulf menhaden stock. However, one should not expect long-term harvesting above the historical MSY because of the short life span of gulf menhaden and possible changes from currently favorable environmental conditions supporting high recruitment.(PDF file contains 24 pages.)

Local and Global Externalities, Environmental Policies and Growth

33 p.

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.

From organism to population: the role of life-history theory

The role of life-history theory in population and evolutionary analyses is outlined. In both cases general life histories can be analysed, but simpler life histories need fewer parameters for their description. The simplest case, of semelparous (breed-once-then-die) organisms, needs only three parameters: somatic growth rate, mortality rate and fecundity. This case is analysed in detail. If fecundity is fixed, population growth rate can be calculated direct from mortality rate and somatic growth rate, and isoclines on which population growth rate is constant can be drawn in a ”state space” with axes for mortality rate and somatic growth rate. In this space density-dependence is likely to result in a population trajectory from low density, when mortality rate is low and somatic growth rate is high and the population increases (positive population growth rate) to high density, after which the process reverses to return to low density. Possible effects of pollution on this system are discussed. The state-space approach allows direct population analysis of the twin effects of pollution and density on population growth rate. Evolutionary analysis uses related methods to identify likely evolutionary outcomes when an organism's genetic options are subject to trade-offs. The trade-off considered here is between somatic growth rate and mortality rate. Such a trade-off could arise because of an energy allocation trade-off if resources spent on personal defence (reducing mortality rate) are not available for somatic growth rate. The evolutionary implications of pollution acting on such a trade-off are outlined.

Simulation of growth process of thin film on non-planar substrate

In (2 + 1) dimension, growth process of thin film on non-planar substrate in Kuramoto-Sivashinsky model is studied with numerical simulation approach. 15 x 15 semi-ellipsoids arranged orderly on the surface of substrate are used to represent initial rough surface. The results show that at the initial stage of growth process, the surface morphology of thin film appears to be grid-structure, and the interface width constantly decreases with the growth time, then reaches minimum. However, the grid-structure becomes ambiguous, and granules of different sizes distribute evenly on the surface of thin film with the increase of growth time. Thereafter, the average size of granules and the interface width gradually increase, and the surface morphology of thin film presents fractal properties. The numerical results of height-height correlation functions of thin film verify the surface morphology of thin film to be fractal for a longer growth time. By fitting of the height-height correlation functions of thin film with different growth times, the growth process is described quantitatively. (c) 2004 Elsevier B.V. All rights reserved.

Integrating methods for determining length-at-age to improve growth estimates for two large scombrids

Fish growth is commonly estimated from length-at-age data obtained from otoliths. There are several techniques for estimating length-at-age from otoliths including 1) direct observed counts of annual increments; 2) age adjustment based on a categorization of otolith margins; 3) age adjustment based on known periods of spawning and annuli formation; 4) back-calculation to all annuli, and 5) back-calculation to the last annulus only. In this study we compared growth estimates (von Bertalanffy growth functions) obtained from the above five methods for estimating length-at-age from otoliths for two large scombrids: narrow-barred Spanish mackerel (Scomberomorus commerson) and broad-barred king mackerel (Scomberomorus semifasciatus). Likelihood ratio tests revealed that the largest differences in growth occurred between the back-calculation methods and the observed and adjusted methods for both species of mackerel. The pattern, however, was more pronounced for S. commerson than for S. semifasciatus, because of the pronounced effect of gear selectivity demonstrated for S. commerson. We propose a method of substituting length-at-age data from observed or adjusted methods with back-calculated length-at-age data to provide more appropriate estimates of population growth than those obtained with the individual methods alone, particularly when faster growing young fish are disproportionately selected for. Substitution of observed or adjusted length-at-age data with back-calculated length-at-age data provided more realistic estimates of length for younger ages than observed or adjusted methods as well as more realistic estimates of mean maximum length than those derived from backcalculation methods alone.

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.

Defining plausible migration rates based on historical tagging data: a Bayesian mark-recapture model applied to English sole (Parophrys vetulus)

A generalized Bayesian population dynamics model was developed for analysis of historical mark-recapture studies. The Bayesian approach builds upon existing maximum likelihood methods and is useful when substantial uncertainties exist in the data or little information is available about auxiliary parameters such as tag loss and reporting rates. Movement rates are obtained through Markov-chain Monte-Carlo (MCMC) simulation, which are suitable for use as input in subsequent stock assessment analysis. The mark-recapture model was applied to English sole (Parophrys vetulus) off the west coast of the United States and Canada and migration rates were estimated to be 2% per month to the north and 4% per month to the south. These posterior parameter distributions and the Bayesian framework for comparing hypotheses can guide fishery scientists in structuring the spatial and temporal complexity of future analyses of this kind. This approach could be easily generalized for application to other species and more data-rich fishery analyses.

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

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.

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.