Synchronization in Von Bertalanffy’s models

Many data have been useful to describe the growth of marine mammals, invertebrates and reptiles, seabirds, sea turtles and fishes, using the logistic, the Gom-pertz and von Bertalanffy's growth models. A generalized family of von Bertalanffy's maps, which is proportional to the right hand side of von Bertalanffy's growth equation, is studied and its dynamical approach is proposed. The system complexity is measured using Lyapunov exponents, which depend on two biological parameters: von Bertalanffy's growth rate constant and the asymptotic weight. Applications of synchronization in real world is of current interest. The behavior of birds ocks, schools of fish and other animals is an important phenomenon characterized by synchronized motion of individuals. In this work, we consider networks having in each node a von Bertalanffy's model and we study the synchronization interval of these networks, as a function of those two biological parameters. Numerical simulation are also presented to support our approaches.

Big bang bifurcations in von Bertalanffy’s dynamics with strong and weak Allee effects

The main purpose of this work was to study population dynamic discrete models in which the growth of the population is described by generalized von Bertalanffy's functions, with an adjustment or correction factor of polynomial type. The consideration of this correction factor is made with the aim to introduce the Allee effect. To the class of generalized von Bertalanffy's functions is identified and characterized subclasses of strong and weak Allee's functions and functions with no Allee effect. This classification is founded on the concepts of strong and weak Allee's effects to population growth rates associated. A complete description of the dynamic behavior is given, where we provide necessary conditions for the occurrence of unconditional and essential extinction types. The bifurcation structures of the parameter plane are analyzed regarding the evolution of the Allee limit with the aim to understand how the transition from strong Allee effect to no Allee effect, passing through the weak Allee effect, is realized. To generalized von Bertalanffy's functions with strong and weak Allee effects is identified an Allee's effect region, to which is associated the concepts of chaotic semistability curve and Allee's bifurcation point. We verified that under some sufficient conditions, generalized von Bertalanffy's functions have a particular bifurcation structure: the big bang bifurcations of the so-called box-within-a-box type. To this family of maps, the Allee bifurcation points and the big bang bifurcation points are characterized by the symmetric of Allee's limit and by a null intrinsic growth rate. The present paper is also a significant contribution in the framework of the big bang bifurcation analysis for continuous 1D maps and unveil their relationship with the explosion birth and the extinction phenomena.

LIFE CYCLE AND POPULATION STRUCTURE OF AEGLA PAULENSIS (DECAPODA: ANOMURA: AEGLIDAE)

We describe growth, longevity, sex ratio, reproductive period, and recruitment of Aegla paulensis from Jaragua Stale Park, Sao Paulo, Brazil (23 degrees 27'27.9 '' S; 46 degrees 45'32.3 '' W). The population was sampled monthly (September 2007 through August 2009) with the aid of traps. Over five thousand individuals were captured, sexed, measured (carapace length = CL) and inspected for reproductive traits (females only), and then released back to the sampling site. The pattern of the reproductive cycle was strongly seasonal (austral mid autumn through late winter), with a single recruitment pulse per year. The obtained von Bertalanffy growth equations were CL = 21.25[1-e(-0.041(t + 1.250))] and CL = 16.52[1-e(-0.049(t + 1.823))] for males and females, respectively. Males (mean CL +/- SD = 11.86 +/- 2.79 mm) attain larger sizes than females (mean CL +/- SD = 10.84 +/- 2.36 mm). Aegla paulensis reproduces twice during an estimated life span of 40.2 months for females and 33.9 months for males. Temporal variation of sex ratio showed a distinctive pattern characterized by a sequence of three distinct periods that repeated from one year to another, and which suggested that a behavioral component influence the proportion of sex in adult specimens sampled with traps during reproductive and non-reproductive periods.

Comparison of different nonlinear functions to describe Nelore cattle growth

This work aims to compare different nonlinear functions for describing the growth curves of Nelore females. The growth curve parameters, their (co) variance components, and environmental and genetic effects were estimated jointly through a Bayesian hierarchical model. In the first stage of the hierarchy, 4 nonlinear functions were compared: Brody, Von Bertalanffy, Gompertz, and logistic. The analyses were carried out using 3 different data sets to check goodness of fit while having animals with few records. Three different assumptions about SD of fitting errors were considered: constancy throughout the trajectory, linear increasing until 3 yr of age and constancy thereafter, and variation following the nonlinear function applied in the first stage of the hierarchy. Comparisons of the overall goodness of fit were based on Akaike information criterion, the Bayesian information criterion, and the deviance information criterion. Goodness of fit at different points of the growth curve was compared applying the Gelfand`s check function. The posterior means of adult BW ranged from 531.78 to 586.89 kg. Greater estimates of adult BW were observed when the fitting error variance was considered constant along the trajectory. The models were not suitable to describe the SD of fitting errors at the beginning of the growth curve. All functions provided less accurate predictions at the beginning of growth, and predictions were more accurate after 48 mo of age. The prediction of adult BW using nonlinear functions can be accurate when growth curve parameters and their (co) variance components are estimated jointly. The hierarchical model used in the present study can be applied to the prediction of mature BW in herds in which a portion of the animals are culled before adult age. Gompertz, Von Bertalanffy, and Brody functions were adequate to establish mean growth patterns and to predict the adult BW of Nelore females. The Brody model was more accurate in predicting the birth weight of these animals and presented the best overall goodness of fit.

Idades e crescimento da cioba, Ocyururs chrysurus, da Costa Central do Brasil

A idade e o crescimento da cioba da costa central do Brasil foram estudados a partir de leituras de otólitos obtidos em amostragens mensais de desembarques comerciais, realizados nas cidades de Vitória e Vila Velha, entre os anos de 1998 e 1999. Através da análise do incremento marginal, foi verificada a formação anual de uma zona translúcida a partir do final do outono e durante o inverno. Foram observadas ciobas de 2 a 19 anos. Os comprimentos furcais (CF) médios retrocalculados variaram de 108 mm para idade 1 a 524 mm para idade 19. A equação de Von Bertalanffy ajustada aos CF médios retrocalculados foi CFt = 567,1 (1 - e -0.130 (t + 0.773)). A relação comprimento peso foi P = 2,68x10-5CF2.914, onde P = peso total em gramas. O crescimento é lento, com os incrementos anuais em peso aumentando gradativamente até atingir o máximo de 164 g entre as idades 7 e 8 anos. Os resultados deste trabalho indicam que a cioba tem longa expectativa de vida e baixas taxas de crescimento somático, características das espécies mais sensíveis à exploração pesqueira.

Biologia (idade e crescimento), reprodução e caracterização da pesca do peixe-espada branco, Lepidopus caudatus (Euphrasen, 1788) no arquipélago dos Açores

Dissertação de Mestrado, Estudos Integrados dos Oceanos, 3 de Maio 2012, Universidade dos Açores.

ESTIMACION DE EDAD Y CRECIMIENTO EN LA "PACORA" (PLAGIOSCION SURINAMENSIS BLEECKER, 1873) POR MEDIO DE LA COMPARACION DE LOS METODOS DE ANALISIS DE DISTRIBUCION DE FRECUENCIAS Y LAS MARCAS EN ESCAMAS Y OTOLITOS

En la presente investigación se estima la edad y creecimiento de la pacora (Plagiosclon surinamensis), por medio de la comparación de los métodoe de distribución de frecuencias, marcas en las escamas y marcae en los otolitos; de esta comparación se concluye que la pacora forma tres anillos en las escamas por año y con base en este método, estableciendo los grupos de edad anuales, se calcula la ecuación de crecimiento de Von Bertalanffy, la cual se expressa de la siguiente manera:Lt (ram) = 775.1 * {1 - e -0.362 * (t - 0.0978)}. La relación talla-peso se calculó ordenando las tallas en intervalos de 10 ram y corresponde a la ecuación:Peso (gr) = 1.1 * 10-5 * L. E.(3.08), no encontrándose diferencias significativas entre el crecimiento de hembras y el de machos. Se complementa la investigación con información sobre tallas mínimas y medias de madurez sexual y espectro trófico de la especie en la parte baja de la cuenca del Río Magdalena y su plano inundable.

Age, growth and population dynamics of lemon sole Microstomus kitt (Walbaum 1792) sampled off the West Coast of Ireland

The age, growth, maturity and population dynamics of lemon sole (Microstomus kitt), captured off the west coast of Ireland (ICES division Vllb), were determined for the period November 2000 to February 2002. The maximum age recorded was 14 years. Males of the population were dominated by 4 year olds, while females were dominated by 5 year olds. Females dominated the sex ratio in the overall sample, each month sampled, at each age and from 22cm in total length onwards (when N > 20). Possible reasons for the dominance of females in the sex ratio are discussed. Three models were used to obtain the parameters of the von Bertalanfly growth equation. These were the Ford-Walford plot (Beverton and Holt 1957), the Gulland and Holt plot (1959) and the Rafail (1973) method. Results of the fitted von Bertalanffy growth curves showed that female lemon sole o f f the west coast of Ireland grew faster than males and attained a greater size. Male and female lemon sole mature from 2 years of age onwards. There is evidence in the population o f a smaller asymptotic length (L«, = 34.47cm), faster growth rate (K = 0.1955) and younger age at first maturity, all of which are indicative o f a decrease in population size, when present results are compared to data collected in the same area 22 years earlier. Results of the yield per recruit curve indicate that lemon sole are currently being over-fished o f f the west coast of Ireland. Problems of selectivity within the sampling method, particularly at the discarding stage, may have influenced the outcome of results of the models used in the assessment of this stock. Therefore, additional/future work on this species should include catch data which incorporates discards and not landings data alone.

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.

Crescimento de Chasmagnathus granulatus (Crustacea, Decapoda, Varunidae) na Lagoa do Peixe, Rio Grande do Sul, Brasil

O estudo do crescimento em largura da carapaça de Chasmagnathus granulatus Dana, 1851 foi baseado em dados de 1940 exemplares coletados na Lagoa do Peixe, Estado do Rio Grande do Sul, Brasil. As coletas foram realizadas de julho/1994 a junho/1995. Os caranguejos foram coletados manualmente nas margens da lagoa e em laboratório foram separados por sexo e a largura da carapaça mensurada. O modelo de von Bertalanffy foi utilizado para a descrição do crescimento. As curvas de crescimento em largura (mm), para dados obtidos através da progressão modal, são descritas pelas equações: Lt= 44,69 [1- e -0.0066(t+20,45)] e Lt= 37,63 [1- e -0.0072(t+21,92)], resultando em idades máximas estimadas de 2 anos para ambos os sexos.

Crescimento de Callinectes sapidus (Crustacea, Decapoda, Portunidae) no estuário da laguna dos Patos, RS, Brasil

Utilizando o método de deslocamento modal para a identificação das idades, estimou-se o crescimento do siri-azul Callinectes sapidus Rathbun, 1896 em duas áreas de pesca no estuário da Lagoa dos Patos. Os indivíduos foram coletados entre fevereiro de 2005 e março de 2006 no Saco da Mangueira e Saco do Arraial por meio de arrasto de rede de portas da pesca artesanal. Coletou-se um total de 2.609 animais, sendo 1.193 machos e 1.416 fêmeas. Para obtenção das curvas de crescimento utilizou-se o modelo de von Bertalanffy. As curvas foram validadas pela sua adequação ao ciclo de vida e aspectos biológicos da espécie. O tamanho máximo de largura de carapaça (LCmáx) utilizado foi mantido fixo em todas as análises (LCmáx=162,71mm; ± d.p.=3,10 para machos e LCmáx=157,78mm; ± d.p.=5,45 para fêmeas), sendo esses valores médios das maiores medidas obtidas em mais de 20 anos de coletas no estuário. Os parâmetros de crescimento e longevidade foram estimados para machos (Saco da Mangueira, K=0,0039/dia; t o=-6.07; 1.195 dias; Saco do Arraial, K=0,0041/dia; t o=-5,84; 1.102 dias) e fêmeas (Saco da Mangueira, K=0,0040/dia; t o=-6,22; 1.153 dias; Saco do Arraial, K=0,0039/dia; t o=-5.91; 1.181 dias). As curvas de crescimento estimadas nesse trabalho denotam que a espécie atinge o tamanho mínimo de captura praticamente no primeiro ano de vida (120mm).

Differences on allocation of available resources, in growth, reproduction, and survival, in an exotic gastropod of Physidae compared to an endemic one

Physa acuta Draparnaud, 1805 is an invasive gastropod that can affect local species. In Argentina, it is widespread and abundant, even in environments inhabited by the native species Stenophysa marmorata Guilding, 1828. Its predominance raises the question whether this could be explained by a more successful energy allocation in functional requirements (growth, reproduction and survival) compared to S. marmorata. This study was aimed at comparing growth rates, as well as survival and fecundity, between both species under laboratory conditions. Individuals born on the same day were grouped in four per aquaria and kept under controlled conditions of food, light, and temperature. Snails were weekly measured (maximum shell length), and growth rates were calculated using the Von Bertalanffy's equation. The number of eggs and survivors were grouped by week. Stenophysa marmorata was larger at birth than Physa acuta and invested more energy in growth, delaying sexual maturity. This resulted in a disadvantage in fecundity and survival compared to P. acuta, which had a lower growth rate but matured earlier and survived longer. Furthermore, the growth of P. acuta was not affected by reproduction, its reproductive period was longer, consequently with more eggs laid than S. marmorata.

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.

Crescimento de Aegla manuinflata (Decapoda, Anomura, Aeglidae) em ambiente natural

O presente trabalho teve como objetivo avaliar o crescimento de Aegla manuinflata Bond-Buckup & Santos, 2009 em ambiente natural. Para isso foram realizadas coletas mensais de abril de 2006 a maio de 2007 no arroio Passo Taquara, no município de São Pedro do Sul, Rio Grande do Sul, Brasil. Os organismos foram coletados utilizando armadilhas plásticas e puçá. Os espécimes foram sexados e tiveram mensurado o comprimento do cefalotórax (CC), em seguida foram devolvidos ao córrego. O crescimento foi avaliado utilizando o modelo de von Bertalanffy. As curvas de crescimento do cefalotórax, estimadas para machos e fêmeas, são descritas pelas seguintes equações Ct = 28,00 [1 - e-0,0047(t+10,63)] e Ct = 25,16 [1 - e-0,0051(t+17,65)], respectivamente. Os machos atingem tamanhos maiores que as fêmeas. A longevidade foi estimada em três anos para os machos e dois anos e meio para as fêmeas.