Estimation of growth parameters for the exploited sea cucumber Holothuria arguinensis from South Portugal

Understanding how species grow is critical for choosing appropriate fisheries management strategies. Sea cucumbers shrink during periods of aestivation and have naturally flaccid bodies that make measuring growth difficult. In this study, we obtained length-frequency data on Holothuria arguinensis, measuring undisturbed animals in situ, because it is one of the new target species of the NE Atlantic and Southwestern Mediterranean fisheries. Growth parameters were estimated for individuals inhabiting the Ria Formosa lagoon (Portugal). Length-frequency data were collected between November 2012 and March 2014 by using a visual census augmented with random sampling in 2014. To estimate the asymptotic length (L-infinity) and growth coefficient (K), 2 different growth models were fitted to the length frequency data for 1198 sea cucumbers: the nonseasonal von Bertalanffy and Hoenig seasonal von Bertalanffy models. A L-infinity of 69.9 cm and K of 0.88 were estimated by using the Hoenig function for seasonal growth. The value of 1.0 obtained for the parameter C of this function indicates reduction in growth during winter. The relatively high growth rate (K) of this species may have important implications for its survival, mainly in environments where conditions cause biological stress and oceanic disturbances but may also increase its potential as a candidate for aquaculture.CUMFISH project - Fundacao para a Ciencia e a Tecnologia (FCT, Portugal) [PTDC/MAR/119363/2010]; "Sea cucumber as new marine resource: potential for aquaculture" (CUMARSUR) project - Fundacao para a Ciencia e a Tecnologia (FCT, Portugal) [PTDC/MAR-BIO/5948/2014]; Fundacion para el Futuro de Colombia (Colfuturo); FCT Investigator Programme-Career Development [IF/00998/2014

Evolution of size-dependent flowering in Onopordum illyricum: A quantitative assessment of the role of stochastic selection pressures

We explore the evolution of delayed, size-dependent reproduction in the monocarpic perennial Onopordum illyricum, using a range of mathematical models, parameterized with long-term field data. Analysis of the long-term data indicated that mortality, flowering, and growth were age and size dependent. Using mixed models, we estimated the variance about each of these relationships and also individual-specific effects. For the held populations, recruitment was the main density-dependent process, although there were weak effects of local density on growth and mortality Using parameterized growth models, which assume plants grow along a deterministic trajectory, we predict plants should flower at sizes approximately 50% smaller than observed in the field. We then develop a simple criterion, termed the "1-yr look-ahead criterion," based on equating seed production now with that of next year, allowing for mortality and growth, to determine at what size a plant should flower. This model allows the incorporation of variance about the growth function and individual-specific effects. The model predicts flowering at sizes approximately double that observed, indicating that variance about the growth curve selects for larger sizes at flowering. The 1-yr look-ahead approach is approximate because it ignores growth opportunities more than 1 yr ahead. To assess the accuracy of this approach, we develop a more complicated dynamic state variable model. Both models give similar results indicating the utility of the 1-yr look-ahead criterion. To allow for temporal variation in the model parameters, we used an individual-based model with a generic algorithm. This gave very accurate prediction of the observed flowering strategies. Sensitivity analysis of the model suggested that temporal variation in the parameters of the growth equation made waiting to flower more risky, so selected for smaller sizes at flowering. The models clearly indicate the need to incorporate stochastic variation in life-history analyses

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

Growth curve based on scale mixtures of skew-normal distributions to model the age-length relationship of Cardinalfish (Epigonus Crassicaudus)

Our article presents a robust and flexible statistical modeling for the growth curve associated to the age-length relationship of Cardinalfish (Epigonus Crassicaudus). Specifically, we consider a non-linear regression model, in which the error distribution allows heteroscedasticity and belongs to the family of scale mixture of the skewnormal (SMSN) distributions, thus eliminating the need to transform the dependent variable into many data sets. The SMSN is a tractable and flexible class of asymmetric heavy-tailed distributions that are useful for robust inference when the normality assumption for error distribution is questionable. Two well-known important members of this class are the proper skew-normal and skew-t distributions. In this work emphasis is given to the skew-t model. However, the proposed methodology can be adapted for each of the SMSN models with some basic changes. The present work is motivated by previous analysis about of Cardinalfish age, in which a maximum age of 15 years has been determined. Therefore, in this study we carry out the mentioned methodology over a data set that include a long-range of ages based on an otolith sample where the determined longevity is higher than 54 years.Comment: 16 pages, 6 figure

Analysis of logistic growth models

A variety of growth curves have been developed to model both unpredated, intraspecific population dynamics and more general biological growth. Most successful predictive models are shown to be based on extended forms of the classical Verhulst logistic growth equation. We further review and compare several such models and calculate and investigate properties of interest for these. We also identify and detail several previously unreported associated limitations and restrictions. A generalized form of the logistic growth curve is introduced which is shown incorporate these models as special cases. The reported limitations of the generic growth model are shown to be addressed by this new model and similarities between this and the extended growth curves are identified. Several of its properties are also presented. We furthermore show that additional growth characteristics are accommodated by this new model, enabling previously unsupported, untypical population dynamics to be modelled by judicious choice of model parameter values alone

Density-Dependence as a Size-Independent Regulatory Mechanism

The growth function of populations is central in biomathematics. The main dogma is the existence of density dependence mechanisms, which can be modelled with distinct functional forms that depend on the size of the population. One important class of regulatory functions is the $\theta$-logistic, which generalises the logistic equation. Using this model as a motivation, this paper introduces a simple dynamical reformulation that generalises many growth functions. The reformulation consists of two equations, one for population size, and one for the growth rate. Furthermore, the model shows that although population is density-dependent, the dynamics of the growth rate does not depend either on population size, nor on the carrying capacity. Actually, the growth equation is uncoupled from the population size equation, and the model has only two parameters, a Malthusian parameter $\rho$ and a competition coefficient $\theta$. Distinct sign combinations of these parameters reproduce not only the family of $\theta$-logistics, but also the van Bertalanffy, Gompertz and Potential Growth equations, among other possibilities. It is also shown that, except for two critical points, there is a general size-scaling relation that includes those appearing in the most important allometric theories, including the recently proposed Metabolic Theory of Ecology. With this model, several issues of general interest are discussed such as the growth of animal population, extinctions, cell growth and allometry, and the effect of environment over a population.Comment: 41 Pages, 5 figures Submitted to JT

Warming temperatures and smaller body sizes : synchronous changes in growth of North Sea fishes

Funded by Marine Scotland SciencePeer reviewedPostprin

A jump-growth model for predator-prey dynamics: derivation and application to marine ecosystems

This paper investigates the dynamics of biomass in a marine ecosystem. A stochastic process is defined in which organisms undergo jumps in body size as they catch and eat smaller organisms. Using a systematic expansion of the master equation, we derive a deterministic equation for the macroscopic dynamics, which we call the deterministic jump-growth equation, and a linear Fokker-Planck equation for the stochastic fluctuations. The McKendrick--von Foerster equation, used in previous studies, is shown to be a first-order approximation, appropriate in equilibrium systems where predators are much larger than their prey. The model has a power-law steady state consistent with the approximate constancy of mass density in logarithmic intervals of body mass often observed in marine ecosystems. The behaviours of the stochastic process, the deterministic jump-growth equation and the McKendrick--von Foerster equation are compared using numerical methods. The numerical analysis shows two classes of attractors: steady states and travelling waves.Comment: 27 pages, 4 figures. Final version as published. Only minor change

General state-space population dynamics model for Bayesian stock assessment

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