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.

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.

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.

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

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.

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.

Age and growth of the estuarine dolphin (Sotalia guianensis) (Cetacea, Delphinidae) on the Paraná Coast, southern Brazil

Teeth of 71 estuarine dolphins (Sotalia guianensis) incidentally caught on the coast of Paraná State, southern Brazil, were used to estimate age. The oldest male and female dolphins were 29 and 30 years, respectively. The mean distance from the neonatal line to the end of the first growth layer group (GLG) was 622.4 ±19.1 μm (n=48). One or two accessory layers were observed between the neonatal line and the end of the first GLG. One of the accessory layers, which was not always present, was located at a mean of 248.9 ±32.6 μm (n=25) from the neonatal line, and its interpretation remains uncertain.The other layer, located at a mean of 419.6 ±44.6 μm (n=54) from the neonatal line, was always present and was first observed between 6.7 and 10.3 months of age. This accessory layer could be a record of weaning in this dolphin. Although no differences in age estimates were observed between teeth sectioned in the anterior-posterior and buccal-lingual planes, we recommend sectioning the teeth in the buccal-lingual plane in order to obtain on-center sections more easily. We also recommend not using teeth from the most anterior part of the mandibles for age estimation. The number of GLGs counted in those teeth was 50% less than the number of GLGs counted in the teeth from the median part of the mandible of the same animal. Although no significant difference (P>0.05) was found between the total lengths of adult male and female estuarine dolphins, we observed that males exhibited a second growth spurt around five years of age. This growth spurt would require that separate growth curves be calculated for the sexes. The asymptotic length (TL∞), k, and t0 obtained by the von Bertalanffy growth model were 177.3 cm, 0.66, and –1.23, respectively, for females and 159.6 cm, 2.02, and –0.38, respectively, for males up to five years, and 186.4 cm, 0.53 and –1.40, respectively, for males older than five years. The total weight (TW)/total length (TL) equations obtained for male and female estuarine dolphins were TW = 3.156 × 10−6 × TL 3.2836 (r=0.96), and TW = 8.974 × 10−5 × TL 2.6182 (r=0.95), respectively.

Age and growth of blue rockfish (Sebastes mystinus) from central and northern California

Otoliths from blue rockfish (Sebastes mystinus), were aged by using a combination of surface and break-and-burn methods. The samples were collected between 1978 and 1998 off central and northern California. Annual growth increments in the otoliths were validated by using edge analysis for females up to age 23 and for males to age 25.The first annual growth increment was identified by comparing the diameter of the otolith from fish known to be one year old collected in May (when translucent zone formation was completed) to the mean diameter of the first translucent zone in the otoliths from older fish. Our estimated maxi-mum ages of 44 years for males and 41 years for females were much older than those reported in previous studies. Von Bertalanffy growth models were developed for each sex. Females grew faster and reached larger maximum length than males. The growth models were similar to those generated in other studies of this species in southern and central California. Fish from northern and central California had similar maximum sizes, maximum ages, and growth model parameters.

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.