Production efficiency in the von Liebig model

The objective of this paper is to revisit the von Liebig hypothesis by reexamining five samples of experimental data and by applying to it recent advances in Bayesian techniques. The samples were published by Hexem and Heady as described in a further section. Prior to outlining the estimation strategy, we discuss the intuition underlying our approach and, briefly, the literature on which it is based. We present an algorithm for the basic von Liebig formulation and demonstrate its application using simulated data (table 1). We then discuss the modifications needed to the basic model that facilitate estimation of a von Liebig frontier and we demonstrate the extended algorithm using simulated data (table 2). We then explore, empirically, the relationships between limiting water and nitrogen in the Hexem and Heady corn samples and compare the results between the two formulations (table 3). Finally, some conclusions and suggestions for further research are offered.

Growth of the tambaqui Colossoma macropomum (Cuvier) (Characiformes: Characidae): which is the best model?

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Ciclo de vida pós-marsupial e crescimento de Metamysidopsis elongata atlantica (Crustacea, Mysidacea, Mysidae) em cultivo de laboratório

Metamysidopsis elongata atlantica (Bacescu, 1968) was reared in the laboratory for 45 days at 20±1°C and salinity of 30ppt. Growth curves (von Bertalanffy model) were calculated for both sexes and for each sex. The daily rate of carapace growth was significantly different between females and males (F test, p <0.05). Before the sexual maturity (14 days), the growth rate of females was higher than that of males (females, 0.0457 mm day-1; males, 0.0448 mm day-1). After the maturity (15 to 45 days), these rates decreased similarly for both sexes (females, 0.0203 mm day-1; males, 0.0174mm day-1). The average growth rate was 0.0207mm day-1 over the 45 days. Twelve molts were observed in a period of 60 days. The first five molts occurred up to 14 days old (age of the sexual differentiation), with a mean intermolt period of 2.9 days. From the 6th molt it increased to 5.6 days. The results suggest that the use of the carapace length is a good measure to calculate the growth and longevity of the organisms.

Age and growth parameters of cachara Pseudoplastystoma reticulatum (Siluriformes, Pimelodidae) from the Cuiabá River, Brazil

Age and growth parameters of cachara Pseudoplatystoma reticulatum (Eigenmann & Eigenmann, 1889) (Siluriformes, Pimelodidae) (males and females) were estimated through the analysis of growth rings in spines of pectoral fins. Fish were collected from January to December 2007, in the area directly influenced by the Aproveitamento Múltiplo de Manso (APM Manso) and in the Cuiabá River (upper parts of the Pantanal). The maximum number of growth rings was seven for males, and eight, for females. The analysis of temporal variations in mean marginal increment showed that rings found in the spines were formed annually, in December. Growth rings were associated to spawning (in the study region from November to March) of the species. The growth curve in length was obtained by the von Bertalanffy model adjusted by the Ford-Walford transformation. The equations are: Ls = 72.7*[1-e-0.44(t+1.5974)] for males, and Ls = 84.5*[1-e-0.33(t+2.0943)] for females. The equations that describe the growth curve in weight are: Wt = 4991.61*[1-e-0.44 (t+1.5974] 2.70 for males and Wt = 7503.17*[1-e-0.33 (t+2.0943] 2.99 for females.

Aging and growth parameter from the Piaractus mesopotamicus (pacu) from the Cuiabá river, Mato Grosso, Brazil

This study has aims to determine the age and to estimate the growth parameters using scales of the species. Individuals of Piaractus mesopotamicus (Holmberg, 1887) used in this study were captured in the commercial fishery conducted in the region, along the year 2006. The model selected to express the growth of the species was the von Bertalanffy Sl= Sl∞*[1-exp-k(t-to)]. To determine if scales are suitable for studying the growth of pacu, we analyzed the relation between standard length (Sl) and the radius of the scales through linear regression. The period of annuli formation was determined analyzing the variations in the marginal increment and evaluating the consistency of the readings through the analysis of the coefficient of variations (CVs) for the average standard lengths of each age (number of rings) observed in the scales. The relationship between Ls of the fish and the radius of the scales showed that scales can be used to study the age and growth of P. mesopotamicus (R= 0.79). CVs were always below 20%, demonstrating the consistency of the readings. Annuli formation occurred in February, probably related to trophic migration that occurs in this month in the region. Equations that represents the growth in length obtained for P. mesopotamicus are Sl=50.00*[1-exp-0.18(t-(-3.00)] for males and Sl=59.23*[1-exp-0.14(t-(-3.36)] for females. The growth parameters obtained in this study were lower compared to other studies previously conducted for the same species and can related to overexploitation that species is submitted by fishing in the region. These values show also that females of pacu attain greater asymptotic length than males that growth faster.

Life-time growth patterns of pumpkinseed Lepomis gibbosus introduced to Europe, relative to North American populations

The pumpkinseed Lepomis gibbosus, an omnivorous, nest guarding North American sunfish, was introduced into European waters about 100 years ago. To assess growth performance following introduction, we reviewed the available data for North American and European populations of pumpkinseed and compared the back-calculated age-specific growth for juveniles (standard length, SL, at age two) and adults (age two to five increment) as well as adult body size (SL at age five), von Bertalanffy growth model parameters and the index of growth (in length) performance (φ′). For continental comparisons of growth trajectory, mean growth curves for North American and Europe were calculated with the von Bertalanffy model using pooled data sets for each continent. Juvenile growth rate did not differ between European and North American pumpkinseed, but mean adult body size and adult growth rate were both significantly greater in North American than European populations. Adult body size decreased with increasing latitude (ANOVA) in North American populations, but this was not observed with adult growth rate. In contrast, adult body size tended to increase with latitude in European populations. Adult body size correlated significantly with φ′. The von Bertalanffy model described the overall growth patterns of North American and European populations reasonably well, but on the individual population level, length asymptotes were unrealistic (estimates that were > 20 % of the mean back-calculated size for the oldest age class) for a third of European populations and 80% of the North American populations. In contrast to North American pumpkinseed populations, somatic growth in European populations appears to be compromised by limited, but adequate, food resources, probably due to strong intraspecific interactions. This appears to be especially acute in adults, having potential ramifications for life span and reproductive allocation

Growth of the speckled swimming crab, Arenaeus cribrarius (Lamarck, 1818) (Crustacea, Brachyura, Portunidae), in Ubatuba (SP), Brazil

A total of 2629 individuals of Arenaeus cribrarius (1293 males and 1336 females) were captured in Ubatuba (SP), from August 1996 to July 1997. Individuals were distributed in 5 mm size class carapace width (CW), to verify sex-specific growth-age equations. The Von Bertalanffy model was chosen to determine the growth rate and expressed by CW=120.52[1-e(-1.80t)] for males and CW=100.81[1-e(-1.60t)] for females. The age estimated for the first juvenile stage (t(o)) was 6.1 and 8.3 days for males and females, respectively. The maximum age determined was 1.8 years for males and 2 years for females, which correspond to a maximum size of 115.8 and 96.7 mm, respectively. The maximum size (CWmax) estimated using 95% of asymptotic size was 114.5 mm for males and 95.8 mm for females. Males have a precocious sexual maturity (5 months) when compared to females (6.8 months). The growth rate and size of A. cribrarius are higher than other portunid species, with great interest for aquaculture.

Non-linear growth models for bullfrog tadpoles

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Herdabilidades e Correlações Genéticas para Peso e Perímetro Escrotal de Machos e Características Reprodutivas e de Crescimento de Fêmeas, na Raça Canchim

The objective of this study was to estimate heritabilities of and genetic correlations among male body weight (BW12) and scrotal circumference (SC12) at 12 months of age, and female body weights at first (BWFC) and second (BWSC) calvings, age at first (AFC) and second (ASC) calvings, adult weight (AW), and mature weight (A) and maturation rate (k) obtained by the use of the Von Bertalanffy model. The restricted maximum likelihood method with an animal model that included the fixed effects of contemporary group and the random effects of animals, was used to estimate the variance and covariance components. The heritability estimates were equal to: 0.37 (BW12),0.30 (SC12),0.38 (A), 0.35 (k), 0.12 (AFC), 0.33 (BWFC), 0.04 (ASC), 0.39 (BWSC), and 0.38 (AW). The genetic correlations among BW12 and the female traits were: 0.19 (parameter A), 0.62 (parameter k), -0.58 (AFC), 0.69 (BWFC), -0.56 (ASC), 0.61 (BWSC), and 0.60 (AW). The genetic correlations among SC12 and the female traits were: -0.24 (A), 0.27 (k), -0.47 (AFC), 0.09 (BWFC), -0.67 (ASC), 0.07 (BWSC), and -0.17 (AW). These results indicate that male body weight and scrotal circumference and female weights (BWFC, BWSC and AW) and growth curve parameters A and k have enough additive genetic variation to respond to mass selection. Selection to increase male body weight at 12 months of age should result on favorable correlated changes in AFC, ASC and parameter k of females, but with increases in female body weights (BWFC, BWSC and AW). Selection to increase SC12 should result on desirable correlated responses in AFC, ASC and k, without any considerable change in female adult body weights.

Population dynamics of the seabob shrimp Xiphopenaeus kroyeri (Dendrobranchiata, Penaeidae) in south-eastern Brazil

The population dynamics, including the sex ratio, reproductive period, individual growth and longevity, and population structure of the shrimp Xiphopenaeus kroyeri, are described. The shrimps were collected monthly from July 2005 to June 2007 at four sites in Ubatuba Bay, Brazil. The salinity, temperature, depth, organic matter content and sediment grain size were measured at each site. Specimens were quantified and sexed, their carapace length measured and their gonads were classified according to the stage of maturation. A von Bertalanffy model was used to estimate the individual growth, and longevity was calculated using its inverted formula. In total, 6 470 individuals were examined and the number of males and females differed significantly in favour of females. During some periods, the segregation could be related to the reproductive period. Reproductive females were captured throughout the sampled period, and there were biannual peaks that were followed by peaks of juveniles. Carapace growth was less for males than for females, which is likely related to oocyte production and the higher fecundity of the females. The higher probability of female capture can be related to their longer foraging to sustain the enhanced food requirement during the ovarian maturation period. © 2013 Copyright NISC (Pty) Ltd.

Dinâmica populacional de Lepidophthalmus siriboia Felder & Rodrigues, 1993 (Decapoda: Callianassidae) da Ilha de Maiandeua-PA

Os Thalassinidea são invertebrados marinhos de grande importância na ecologia de ambientes de fundos moles, especialmente dado sua influência nos fluxos de oxigênio, energia e nutrientes e, atividades bioturbadoras. Estes organismos vivem em galerias das quais dependem para diversas necessidades, como proteção, reprodução e alimentação. Em alguns lugares do mundo este grupo tem sido explorado para utilização como isca. A espécie Lepidophthalmus siriboia Felder & Rodrigues, 1993 (Crustacea: Callianassidae) ocorre desde a Flórida até o Brasil. Este estudo tem como objetivo avaliar a dinâmica e a estrutura populacional de L. siriboia na ilha de Maiandeua (PA), associando os processos observados com características ambientais ligadas ao sedimento e à água. As coletas ocorreram mensalmente entre junho de 2007 e maio de 2008, sendo os organismos capturados utilizando bomba de sucção. Em laboratório, os animais foram sexados, medidos e pesados. Nas fêmeas ovígeras foi contado o número de ovos aderidos aos pleópodos. O crescimento foi estimado através da equação de crescimento de Von Bertalanffy que estabelece a relação entre o comprimento total (CT) e a idade (t). Foi capturado um total de 1268 indivíduos (753 machos e 515 fêmeas), cujos comprimentos variaram de 0,3 a 1,85 cm e o peso de 0,01 a 3,09 g. Os comprimentos médios mensais das fêmeas foram significantemente maiores do que dos machos (p<0.05) em quase todos os meses do ano. O comprimento da carapaça e o comprimento do propódio para os machos tiveram alta e significante correlação, com crescimento alométrico positivo para ambos os sexos. O tamanho de primeira maturação obtido foi de 0,7 cm para as fêmeas e 0,6 cm para os machos. Os machos foram proporcionalmente mais abundantes, totalizando 59,4% de todos os organismos capturados (proporção sexual de 1,46 machos: 1 fêmea). Houve predomínio significativo de machos nas classes de comprimento entre 0,2 e 1,2 cm e de fêmeas nas classes de comprimento maior/igual a 1,2 cm. Foram registradas 139 fêmeas ovígeras, na qual a maioria (48,2% do total) ocorreu no intervalo de classe 1,1 a 1,2 cm de comprimento da carapaça. A fecundidade absoluta variou de 0 a 1546 ovos/fêmea, com valor médio de 826,25 ovos/fêmea. Observou-se correlação significativa entre o número de ovos, peso e comprimento da carapaça. As fêmeas tiveram crescimento maior que dos machos, sendo observados valores para machos de L_: 1,63 , K: 1, C: 0,2, WP: 0,18 e para fêmeas; L_: 1,68, K: 0,8, C: 0,2 e WP: 0,09. As estimativas de mortalidade dos machos foram maiores que para as fêmeas em todos os métodos utilizados: curva de captura (Z=1,67 e Z=0,11 para machos e fêmeas), Beverton e Holt (Z=1,9 e Z= 1,76 para machos e fêmeas) e Powell–Wetherall (Z/K=3,98 e Z/K= 2,25 para machos e fêmeas). Foram registrados três pulsos principais, sendo um pulso registrado em novembro, um em fevereiro e outro em maio. Os resultados obtidos permitem concluir: 1. comprimento médio dos machos é inferior ao das fêmeas ao longo do ano; 2. fêmeas são dominantes nas classes de comprimento superiores (_1,2 cm); 3. a reprodução é contínua com a ocorrência de fêmeas ovígeras ao longo do ano; 4. parâmetros de crescimento estimados foram maiores para as fêmeas do que para machos; 5. Fêmeas tiveram redução da taxa de crescimento em janeiro (WP: 0,09) e machos em fevereiro (WP: 0,18); 6. a mortalidade é maior para os machos; 7. Recrutamento ocorre ao longo do ano com três picos pronunciados em novembro, fevereiro e maio.

Growth of the speckled swimming crab, Arenaeus cribrarius (Lamarck, 1818) (Crustacea, Brachyura, Portunidae), in Ubatuba (SP), Brazil

A total of 2629 individuals of Arenaeus cribrarius (1293 males and 1336 females) were captured in Ubatuba (SP), from August 1996 to July 1997. Individuals were distributed in 5 mm size class carapace width (CW), to verify sex-specific growth-age equations. The Von Bertalanffy model was chosen to determine the growth rate and expressed by CW=120.52[1-e(-1.80t)] for males and CW=100.81[1-e(-1.60t)] for females. The age estimated for the first juvenile stage (t(o)) was 6.1 and 8.3 days for males and females, respectively. The maximum age determined was 1.8 years for males and 2 years for females, which correspond to a maximum size of 115.8 and 96.7 mm, respectively. The maximum size (CWmax) estimated using 95% of asymptotic size was 114.5 mm for males and 95.8 mm for females. Males have a precocious sexual maturity (5 months) when compared to females (6.8 months). The growth rate and size of A. cribrarius are higher than other portunid species, with great interest for aquaculture.