Critical points on growth curves in autoregressive and mixed models

Adjusting autoregressive and mixed models to growth data fits discontinuous functions, which makes it difficult to determine critical points. In this study we propose a new approach to determine the critical stability point of cattle growth using a first-order autoregressive model and a mixed model with random asymptote, using the deterministic portion of the models. Three functions were compared: logistic, Gompertz, and Richards. The Richards autoregressive model yielded the best fit, but the critical growth values were adjusted very early, and for this purpose the Gompertz model was more appropriate.

Phenological cycles, thermal time and growth curves of mango fruit cultivars in subtropical conditions

There are many mango cultivars available in different regions. It is about time we analysed their productive behavior in these areas, as well as their phenological performance. This study aimed to evaluate: phenological cycles, thermal time and growth curves of mango fruit cultivars in subtropical conditions. For this study we used the following cultivars: Espada Vermelha, Keitt and Palmer. All the experiments were done at UNESP experimental farm in Sao Manuel (SP), during the agricultural cycle from 2012 to 2013. It was selected 15 branches in each plant, which provided 150 per cultivar. It was determined the number of days of phenological cycles of flowering to fruit ripening, as well as the total number of days to flowering and harvesting. The thermal time was evaluated to each phenological cycle and expressed in accumulation of degree-days. The measurement of the longitudinal diameters (LD) and transverse diameters (TD) of the fruitwere performed in a 12 day’s intervals, from the tenth day after the flowers anthesis, to evaluate the growth curve. Based on the data, it was found that Keitt cultivar requires more days for the fruit to reach physiological maturity and greater accumulation of degree-days to complete its production cycle. The growth curves of the three varieties of fruits have a simple sigmoidal model in function of the days after anthesis.

Growth curves for cardio-metabolic risk factors in children and adolescents

OBJECTIVE: This study developed percentile curves for anthropometric (waist circumference) and cardiovascular (lipid profile) risk factors for US children and adolescents. STUDY DESIGN: A representative sample of US children and adolescents from the National Health and Nutrition Examination Survey from 1988 to 1994 (NHANES III) and the current national series (NHANES 1999-2006) were combined. Percentile curves were constructed, nationally weighted, and smoothed using the Lambda, Mu, and Sigma method. The percentile curves included age- and sex-specific percentile values that correspond with and transition into the adult abnormal cut-off values for each of these anthropometric and cardiovascular components. To increase the sample size, a second series of percentile curves was also created from the combination of the 2 NHANES databases, along with cross-sectional data from the Bogalusa Heart Study, the Muscatine Study, the Fels Longitudinal Study and the Princeton Lipid Research Clinics Study. RESULTS: These analyses resulted in a series of growth curves for waist circumference, total cholesterol, LDL cholesterol, triglycerides, and HDL cholesterol from a combination of pediatric data sets. The cut-off for abnormal waist circumference in adult males (102 cm) was equivalent to the 94(th) percentile line in 18-year-olds, and the cut-off in adult females (88 cm) was equivalent to the 84(th) percentile line in 18-year-olds. Triglycerides were found to have a bimodal pattern among females, with an initial peak at age 11 and a second at age 20; the curve for males increased steadily with age. The HDL curve for females was relatively flat, but the male curve declined starting at age 9 years. Similar curves for total and LDL cholesterol were constructed for both males and females. When data from the additional child studies were added to the national data, there was little difference in their patterns or rates of change from year to year. CONCLUSIONS: These curves represent waist and lipid percentiles for US children and adolescents, with identification of values that transition to adult abnormalities. They could be used conditionally for both epidemiological and possibly clinical applications, although they need to be validated against longitudinal data.

Growth curves of four crustose lichens

The growth curves of four common species of crustose lichens, viz., Buellia aethalea (Ach.) Th. Fr., Lecidea tumida Massai., Rhizocarpon geographicum (L.) DC., and Rhizocarpon reductum Th. Fr. were studied at a site in south Gwynedd, north Wales, UK. Radial growth rates (RGR, mm 1.5 yr-1) were greatest in thalli of R. reductum and least in R. geographicum. Variation in RGR between thalli was greater in B. aethalea and L. tumida than in the species of Rhizocarpon. The relationship between growth rate and thallus diameter was not asymptotic; RGR increasing in smaller thalli to a maximum and then declining in larger diameter thalli. A polynomial curve was fitted to the data; the growth curves being fitted best by a second-order (quadratic) curve, the best fit to this model being shown by B. aethalea. A significant linear regression with a negative slope was also fitted to the growth of the larger thalli of each species. The data suggest that the growth curves of the four crustose lichens differ significantly from the asymptotic curves of foliose lichen species. A phase of declining RGR in larger thalli appears to be characteristic of crustose lichens and is consistent with data from lichenometric studies.

A comparison of the growth curves of the foliose lichen Parmelia conspersa determined by a cross-sectional study and by direct measurement

Changes in the radial growth rate (RGR mm/yr) through life were studied in thalli of the foliose lichen Parmelia conspersa by two methods: (1) a cross-sectional study (Study A) in which the RGR was measured in 60 thalli from 0.2 to 13 cm in diameter, and (2) by radial growth measurements over 4.5 years of fragments, consisting of a single major lobe, which were removed from large thalli and glued to pieces of slate (Study B). Both studies suggested there was a phase of increasing RGR in small thalli followed by a more constant phase, the latter beginning at approximately a thallus radius of 6-8 mm. However, in Study B significantly increased RGR was observed during the second 6-month growth period. This phase of growth was more likely to be due to an increase in lobe width than to an effect of climate. In addition, a lobe in a large thallus with both adjacent lobes removed significantly increased in width over 1 year compared with control lobes. These results suggest that (1) mean lobe width in a thallus may be determined by the intensity of marginal competition between adjacent lobes, and (2) changes in lobe width during the life of a lichen thallus may be a factor determining the establishment of the linear phase of growth in foliose lichens. © 1992.

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.

Growth of yellowfin tuna, Thunnus albacares, in the Eastern Pacific Ocean based on otolith increments

ENGLISH: The growth of yellowfin tuna in the eastern Pacific is described in terms of several measurements taken from the fish and their otoliths (sagittae). Equations are also developed to predict age from the readily available dimensions of fork length and head length. The data for all of these relationships were obtained from a sample of 196 fish collected during 1977 through 1979 from purse seiners fishing north of the equator and east of 137°W. The fork-length range of the sample was 30-170 cm. The number of increments on a sagitta of each fish was used as a direct estimate of its age in days. The correspondence between increments and days has been validated for yellowfin in the length range of 40-110 cm. Circumstantial evidence indicates that the relationship also applies in the intervals of 0-40 cm and 110-170 cm. This circumstancial evidence was derived from: 1) literature on validated increments during early growth for other species, 2) knowledge that structures assumed to be daily increments on yellowfin otoliths have subsequently been validated in the corresponding zone on bluefin otoliths, and 3) a comparison of the growth curve based on increments to others obtained from length frequency modal analysis. Based on this information the age estimates over the entire size range of sampled fish are believed to be accurate. In addition to the general growth and age-predictive relationships, the major conclusions of the study are that: 1) Sexually dimorphic growth exists in terms of fork length, fish weight and the length of the otolith counting path for the entire data set. Examination of the data for 1977 and 1979 also revealed that the fork-length growth of each sex differed within years. 2) For combined sexes there were significant differences among the fork-length growth curves for yellowfin sampled in different years. 3) Yellowfin caught inshore (within 275 miles of the coast) were heavier than those caught offshore for fork lengths between 30 and 110 cm. The situation was reversed for lengths greater than 110 cm. 4) Back-calculated spawning months were distributed uniformly throughout the year in 1974 and 1977, but in 1975-1976 and 1978 spawning activity was apparently concentrated in the latter half of the year. SPANISH: El crecimiento del atún aleta amarilla en el Pacífico oriental se describe en términos de varias medidas obtenidas de peces y otolitos (sagita). Se formularon también ecuaciones para pronosticar la edad, según las dimensiones fácilmente disponibles de la longitud horquilla y longitud de la cabeza. Los datos de todas estas relaciones fueron obtenidos mediante una muestra de 196 peces recolectados desde 1977hasta 1979, en barcos cerqueros que estaban pescando al norte de la línea ecuatorial y al este de los 137°W. El intervalo de la longitud horquilla de la muestra fue de 30-170 cm. Se empleó el número de incrementos en la sagita de cada pez como un estimado directo de la edad en días. Se ha comprobado la relación entre los incrementos y los días en el intervalo de longitud de 40-110 cm del aleta amarilla. La evidencia circunstancial indica que se aplica también la relación a los intervalos de 0-40 cm y 110-170 cm. Esta evidencia circunstancial se dedujo: 1) de las publicaciones sobre incrementos comprobados de otras especies durante el primer crecimiento, 2) del conocimientoque las estructuras que se supone son incrementos diarios en los otolitos del aleta amarilla han sido comprobadas luego en la parte correspondiente de otolitos del aleta azul y 3) por una comparación de la curva de crecimiento, basada en incrementos relacionados a otras curvas obtenidas según el análisis modal frecuencia-talla. Se cree, basados en esta información, que las estimaciones de la edad sobre toda la amplitud de talla de los peces muestreados, es acertada. Además de la relación del crecimiento general y del pronóstico de la edad, las principales conclusiones de este estudio son: 1) En toda la serie de datos existe el crecimiento sexualmente dimórfico en términos de longitud horquilla, peso del pez y longitud del plano de conteo del otolito. El examen de los datos de 1977 y 1979, revelan también que el crecimiento longitud horquilla de cada sexo es diferente en los años. 2) En los sexos combinados hubo diferencias significativas entre las curvas de crecimiento longitud horquilla del aleta amarilla muestreado en diferentes años. 3) El aleta amarilla capturado cerca a la costa (en las primeras 275 millas) fue más pesado que el capturado en las aguas mar afuera, correspondiente a la longitud horquilla entre 30 y 110 cm. La situación fue inversa para tallas de más de 110 cm. 4) En 1974 y 1977, los meses retrocalculados del desove se distribuyeron uniformemente durante el año, pero en 1975-1976 y 1978, la actividad del desove se concentró aparentemente en el último semestre del año. (PDF contains 62 pages.)

Estimation of the growth curve parameters in Macrobrachium rosenbergii

Growth is one of the most important characteristics of cultured species. The objective of this study was to determine the fitness of linear, log linear, polynomial, exponential and Logistic functions to the growth curves of Macrobrachium rosenbergii obtained by using weekly records of live weight, total length, head length, claw length, and last segment length from 20 to 192 days of age. The models were evaluated according to the coefficient of determination (R2), and error sum off square (ESS) and helps in formulating breeders in selective breeding programs. Twenty full-sib families consisting 400 PLs each were stocked in 20 different hapas and reared till 8 weeks after which a total of 1200 animals were transferred to earthen ponds and reared up to 192 days. The R2 values of the models ranged from 56 – 96 in case of overall body weight with logistic model being the highest. The R2 value for total length ranged from 62 to 90 with logistic model being the highest. In case of head length, the R2 value ranged between 55 and 95 with logistic model being the highest. The R2 value for claw length ranged from 44 to 94 with logistic model being the highest. For last segment length, R2 value ranged from 55 – 80 with polynomial model being the highest. However, the log linear model registered low ESS value followed by linear model for overall body weight while exponential model showed low ESS value followed by log linear model in case of head length. For total length the low ESS value was given by log linear model followed by logistic model and for claw length exponential model showed low ESS value followed by log linear model. In case of last segment length, linear model showed lowest ESS value followed by log linear model. Since, the model that shows highest R2 value with low ESS value is generally considered as the best fit model. Among the five models tested, logistic model, log linear model and linear models were found to be the best models for overall body weight, total length and head length respectively. For claw length and last segment length, log linear model was found to be the best model. These models can be used to predict growth rates in M. rosenbergii. However, further studies need to be conducted with more growth traits taken into consideration

Growth, recruitment, and abundance of juvenile striped mullet (Mugil cephalus) in South Carolina estuaries

Growth, recruitment, and abundance of young-of-the-year (YOY) striped mullet (Mugil cephalus L.) in estuarine habitats in South Carolina from 1998 to 2000 were examined and compared to historical data (1986–91) of growth, recruitment, and abundance. Daily growth increments from the sagittal otoliths of juvenile striped mullet were validated by using fish immersed in oxytetracycline hydrochloride (OTC) for five hours from the Charleston Harbor Estuary system. The distribution of back-calculated birthdates indicated that striped mullet spawn from October to late April and estuarine recruitment occurs from January through May. Juveniles were more abundant in mesohaline and polyhaline salinity regimes but were found throughout the estuary. Juvenile growth after recruitment into the estuary can be described by the relationship Total length (mm) = 0.341 (Age)1.04 (r2=0.741, P=0.001). Growth of juveniles according to the analysis of size-frequency data from historical surveys (1986 to 1991) in the same estuaries gave the relationship Total length (mm) = 8.77 (month)1.12 (r2=0.950, P=0.001). The similarity in the growth curves for both groups of fish suggests that juvenile striped mullet in South Carolina have consistent annual growth during the first year of life.

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 size composition, growth rate, reproductive biology, and habitats of the West Australian dhufish (Glaucosoma hebraicum) and their relevance to the management of this species

Samples of the commercially and recreationally important West Australian dhufish (Glaucosoma hebraicum) were obtained from the lower west coast of Australia by a variety of methods. Fish <300 mm TL were caught over flat, hard substrata and low-lying limestone reefs, whereas larger fish were caught over larger limestone and coral reef formations. Maximum total lengths, weights, and ages were 981 mm, 15.3 kg, and 39 years, respectively, for females and 1120 mm, 23.2 kg, and 41 years, respectively, for males. The von Bertalanffy growth curves for females and males were significantly different. The values for L∞, k, and t0 in the von Bertalanffy growth equations were 929 mm, 0.111/year, and –0.141 years, respectively, for females, and 1025 mm, 0.111/year, and –0.052 years, respectively, for males. Preliminary estimates of total mortality indicated that G. hebraicum is now subjected to a level of fishing pressure that must be of concern to fishery managers. Glaucosoma hebraicum, which spawns between November and April and predominantly between December and March, breeds at a wide range of depths and is a multiple spawner. The L50’s for females and males at first maturity, i.e. 301 and 320 mm, respectively, were attained by about the end of the third year of life and are well below the minimum legal length (MLL) of 500 mm. Because females and males did not reach the MLL until the end of their seventh and sixth years of life, respectively, they would have had, on average, the opportunity of spawning during four and three spawning seasons, respectively, before they reached the MLL. However, because G. hebraicum caught in water depths >40 m typically die upon release, a MLL is of limited use for conserving this species. Alternative approaches, such as restricting fishing activity in highly fished areas, reducing daily bag limits for recreational fishermen, introducing quotas or revising specific details of certain commercial hand-line licences (or doing both) are more likely to provide effective conservation measures.

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.