A note on the von Bertalanffy growth function concerning the allocation of surplus energy to reproduction

We propose an extended form of the von Bertalanffy growth function (VBGF), where the allocation of surplus energy to reproduction is considered. Any function can be used in our model to describe the ratio of energy allocation for reproduction to that for somatic growth. As an example, two models for energy allocation were derived: a step-function and a logistic function. The extended model can jointly describe growth in adult and juvenile stages. The change in growth rate between the two stages can be either gradual or steep; the latter gives a biphasic VBGF. The results of curve fitting indicated that a consideration of reproductive energy is meaningful for model extension. By controlling parameter values, our comprehensive model gives various growth curve shapes ranging from indeterminate to determinate growth. An increase in the number of parameters is unavoidable in practical applications of this new model. Additional information on reproduction will improve the reliability of model estimates.

Using an inverse-logistic model to describe growth increments of blacklip abalone (Haliotis rubra) in Tasmania

A new description of growth in blacklip abalone (Haliotis rubra) with the use of an inverse-logistic model is introduced. The inverse-logistic model avoids the disadvantageous assumptions of either rapid or slow growth for small and juvenile individuals implied by the von Bertalanffy and Gompertz growth models, respectively, and allows for indeterminate growth where necessary. An inverse-logistic model was used to estimate the expected mean growth increment for different black-lip abalone populations around southern Tasmania, Australia. Estimates of the time needed for abalone to grow from settlement until recruitment (at 138 mm shell length) into the fishery varied from eight to nine years. The variability of the residuals about the predicted mean growth increments was described with either a second inverse-logistic relationship (standard deviation vs. initial length) or by a power relationship (standard deviation vs. predicted growth increment). The inverse-logistic model can describe linear growth of small and juvenile abalone (as observed in Tasmania), as well as a spectrum of growth possibilities, from determinate to indeterminate growth (a spectrum that would lead to a spread of maximum lengths).

The von Bertalanffy growth curve: when a good fit is not good enough

The von Bertalanffy growth function is used for length based analysis of growth and mortality patterns for management of fisheries. However, certain fish have growth patterns that the VBGF may not be able to describe adequately.e.g. the Acanthurus lineatus in Samoa. In such cases a two phase VBGF may be a useful approach.

Escapement of the Cape rock lobster (Jasus lalandii ) through the mesh and entrance of commercial traps

Metal-framed traps covered with polyethylene mesh used in the fishery for the South African Cape rock lobster (Jasus lalandii) incidentally capture large numbers of undersize (<75 mm CL) specimens. Air-exposure, handling, and release procedures affect captured rock lobsters and reduce the productivity of the stock, which is heavily fished. Optimally, traps should retain legalsize rock lobsters and allow sublegal animals to escape before traps are hauled. Escapement, based on lobster morphometric measurements, through meshes of 62 mm, 75 mm, and 100 mm was investigated theoretically under controlled conditions in an aquarium, and during field trials. SELECT models were used to model escapement, wherever appropriate. Size-selectivity curves based on the logistic model fitted the aquarium and field data better than asymmetrical Richards curves. The lobster length at 50% retention (L50) on the escapement curve for 100-mm mesh in the aquarium (75.5 mm CL) approximated the minimum legal size (75 mm CL); however estimates of L50 increased to 77.4 mm in field trials where trapentrances were sealed, and to 82.2 mm where trap-entrances were open. Therfore, rock lobsters that cannot escape through the mesh of sealed field traps do so through the trap entrance of open traps. By contrast, the wider selection range and lower L25 of field, compared to aquarium, trials (SR = 8.2 mm vs. 2.6 mm; L25 =73.4 mm vs. 74.1 mm), indicate that small lobsters that should be able to escape from 100-mm mesh traps do not always do so. Escapement from 62-mm mesh traps with open entrance funnels increased by 40−60% over sealed traps. The findings of this study with a known size distribution, are related to those of a recent indirect (comparative) study for the same species, and implications for trap surveys, commercial catch rates, and ghost fishing are discussed.

O peptídeo natriurético tipo B (BNP) como preditor de mortalidade a longo prazo em pacientes com síndrome coronariana aguda sem supradesnível do segmento ST

Fundamentos: Apesar dos conhecimentos adquiridos sobre marcadores preditores de mortalidade na síndrome coronariana aguda (SCA), a capacidade de avaliação a longo prazo permanece desconhecida. O peptídeo natriurético tipo B (BNP) tem sido extensamente utilizado, porém as evidências existentes se restringem ao seguimento de curto e médio prazos. Objetivos: Determinar se o BNP é um preditor independente de mortalidade por todas as causas a longo prazo em pacientes com síndrome coronariana aguda sem supradesnível do segmento ST (SCASSST). Métodos: No período de 1o de Janeiro de 2002 a 31 de Dezembro de 2003, foram selecionados 224 pacientes consecutivos atendidos na sala de emergência com SCASSST. A dosagem do BNP à admissão foi incorporada no protocolo diagnóstico, tendo o seu valor sido correlacionado com a mortalidade ao final do seguimento. Resultados: Os pacientes foram acompanhados por 9,34 anos (mediana), tinham 71,5 anos (intervalo IQ=60,5;79,0) e com predomínio do gênero masculino (62,9%). A hipertensão arterial esteve presente em 82,1% e o diabetes em 23,7%. A angina instável (AI) foi diagnosticada em 52,2% e o infarto agudo do miocárdio sem supradesnível do segmento ST (IAMSSST) em 47,8%. O BNP mediano foi de 81,9 pg/ml (intervalo IQ 22,2; 225). A mortalidade se correlacionou com os quartis crescentes do BNP: 14,3; 16,1; 48,2; e 73,2% (p<0,0001). A curva ROC determinou o BNP=100 pg/ml como o melhor ponto de corte, tendo apresentado área sobre a curva (AUC) de 0,79 (IC 95%=0,72-0,85) e sendo preditor de mortalidade ao final do seguimento: 17,3% vs. 65,0%, p<0,001, RR=3,76 (IC 95%=2,49-5,63). O BNP teve poder prognóstico tanto nos pacientes com (26,7 vs. 71,2%, p<0,001) como nos sem (12,9 vs. 56,8%, p<0,001) alteração da função ventricular, e também conforme o diagnóstico de AI (18,7 vs. 48,6%, p=0,001) e IAMSSST (14,9 vs. 75,0%, p<0,001). Na análise de regressão logística, a idade>72 anos (OR=3,79, IC 95%=1,62-8,86, p=0,002), o BNP≥100 pg/ml (OR=6,24, IC 95%=2,95-13,23, p<0,001) e a taxa de filtração glomerular estimada (TFGE)(OR=0,98, IC 95%=0,97-0,99, p=0.049) foram preditores independentes de mortalidade. Conclusões: O BNP dosado à admissão dos pacientes com SCASSST é um forte e independente preditor de mortalidade a longo prazo.

Design, construction and evaluation of systems to predict risk in obstetrics.

We present a systematic, practical approach to developing risk prediction systems, suitable for use with large databases of medical information. An important part of this approach is a novel feature selection algorithm which uses the area under the receiver operating characteristic (ROC) curve to measure the expected discriminative power of different sets of predictor variables. We describe this algorithm and use it to select variables to predict risk of a specific adverse pregnancy outcome: failure to progress in labour. Neural network, logistic regression and hierarchical Bayesian risk prediction models are constructed, all of which achieve close to the limit of performance attainable on this prediction task. We show that better prediction performance requires more discriminative clinical information rather than improved modelling techniques. It is also shown that better diagnostic criteria in clinical records would greatly assist the development of systems to predict risk in pregnancy.

Modeling red sea urchin (Strongylocentrotus franciscanus) growth using six growth functions

The growth of red sea urchins (Strongylocentrotus franciscanus) was modeled by using tag-recapture data from northern California. Red sea urchins (n=211) ranging in test diameter from 7 to 131 mm were examined for changes in size over one year. We used the function Jt+1 = Jt + f(Jt) to model growth, in which Jt is the jaw size (mm) at tagging, and Jt+1 is the jaw size one year later. The function f(Jt), represents one of six deterministic models: logistic dose response, Gaussian, Tanaka, Ricker, Richards, and von Bertalanffy with 3, 3, 3, 2, 3, and 2 minimization parameters, respectively. We found that three measures of goodness of fi t ranked the models similarly, in the order given. The results from these six models indicate that red sea urchins are slow growing animals (mean of 7.2 ±1.3 years to enter the fishery). We show that poor model selection or data from a limited range of urchin sizes (or both) produces erroneous growth parameter estimates and years-to-fishery estimates. Individual variation in growth dominated spatial variation at shallow and deep sites (F=0.246, n=199, P=0.62). We summarize the six models using a composite growth curve of jaw size, J, as a function of time, t: J = A(B – e–Ct) + Dt, in which each model is distinguished by the constants A, B, C, and D. We suggest that this composite model has the flexibility of the other six models and could be broadly applied. Given the robustness of our results regarding the number of years to enter the fishery, this information could be incorporated into future fishery management plans for red sea urchins in northern California.