Growth with seasonally varying temperatures: an expansion of the von Bertalanffy growth model

The von Bertalanffy growth function has limitations for describing the growth of fishes in seasonal climates. In the present work, a new equation is proposed where the growth parameter k is substituted by a function related to monthly water temperatures. The computer program GROWTHS was developed to fit and simulate the growth for seasonally varying temperatures. Examples for natural populations of Barbatula barbatula and Cottus gobio are presented.     

A diffusion process to model generalized von Bertalanffy growth patterns: Fitting to real data

The von Bertalanffy growth curve has been commonly used for modeling animal growth (particularly fish). Both deterministic and stochastic models exist in association with this curve, the latter allowing for the inclusion of fluctuations or disturbances that might exist in the system under consideration which are not always quantifiable or may even be unknown. This curve is mainly used for modeling the length variable whereas a generalized version, including a new parameter b≥1, allows for modeling both length and weight for some animal species in both isometric (b=3) and allometric (b≠3) situations.In this paper a stochastic model related to the generalized von Bertalanffy growth curve is proposed. This model allows to investigate the time evolution of growth variables associated both with individual behaviors and mean population behavior. Also, with the purpose of fitting the above-mentioned model to real data and so be able to forecast and analyze particular characteristics, we study the maximum likelihood estimation of the parameters of the model. In addition, and regarding the numerical problems posed by solving the likelihood equations, a strategy is developed for obtaining initial solutions for the usual numerical procedures. Such strategy is validated by means of simulated examples. Finally, an application to real data of mean weight of swordfish is presented.     

Neuroendocrine regulation of somatic growth in fishes

Growth is a polygenic trait that is under the influence of multiple physiological pathways regulating energy metabolism and muscle growth.Among the possible growth-regulating pathways in vertebrates,components of the somatotropic axis are thought to have the greatest influence.There is growing body of literature focusing on the somatotropic axis and its role regulating growth in fish.This includes research into growth hormone,upstream hypothalamic hormones,insulin-like growth factors,and downstream signaling molecules.Many of these signals have both somatic effects stimulating the growth of tissues and metabolic effects that play a role in nutrient metabolism.Signals of other endocrine axes exhibit profound effects on the function of the somatotropic axis in vivo.In this review we highlight recent advances in our understanding of the teleost fish endocrine somatotropic axis,including emerging research using genetic modified models.These studies have revealed new aspects and challenges associated with regulation of the important steps of somatic growth.     

The von Bertalanffy growth model fitted to Planigale tenuirostris (Marsupialia: Dasyuridae) post-weaning data

Growth of head length in P. tenuirostris from the end of weaning throughout life was studied in the laboratory. The growth curves for males and females followed the von Bertalanffy model. Growth continued throughout life and in each age class males were larger than females, resulting in a range of head lengths among mature planigales. This range in sizes has potentially important implications with respect to population niche breadth, resource partitioning and species diversity in dasyurid communities.     

Two Bayesian methods for estimating parameters of the von Bertalanffy growth equation

The von Bertalanffy growth equation (VBGE) is commonly used in ecology and fisheries management to model individual growth of an organism. Generally, a nonlinear regression is used with length-at-age data to recover key life history parameters: L _∞ (asymptotic size), k (the growth coefficient), and t ₀ (a time used to calculate size at age 0). However, age data are often unavailable for many species of interest, which makes the regression impossible. To confront this problem, we have developed a Bayesian model to find L _∞ using only length data. We use length-at-age data for female blue shark, Prionace glauca, to test our hypothesis. Preliminary comparisons of the model output and the results of a nonlinear regression using the VBGE show similar estimates of L _∞ . We also developed a full Bayesian model that fits the VBGE to the same data used in the classical regression and the length-based Bayesian model. Classical regression methods are highly sensitive to missing data points, and our analysis shows that fitting the VBGE in a Bayesian framework is more robust. We investigate the assumptions made with the traditional curve fitting methods, and argue that either the full Bayesian or the length-based Bayesian models are preferable to classical nonlinear regressions. These methods clarify and address assumptions␣made in classical regressions using von Bertalanffy growth and facilitate more detailed stock assessments of species for which data are sparse.     

Patterns and propensities in reproduction and growth of marine fishes

A number of strong regularities characterize certain very basic biological parameters in marine fishes. For example, the ovulated eggs of fish usually measure approximately 1 mm in diameter. The small, relatively uniform size of the eggs means that almost all fish larvae experience environmental variability at very similar scales, which itself establishes strong constraints for, and links between reproduction and recruitment. Additional constraints emerge from seawater being a poor medium for respiration, which establishes further linkages between growth and mortality. These constraints have produced strongly convergent features, and thence the patterns in reproduction and growth of marine fishes that are presented.     

Measuring the cost of reproduction

Gravid and barren Daphnia pulex were exposed to a variety of predators in laboratory aquaria. Small fish (guppies, sticklebacks and shiner fry) consistently preferred the gravid females, establishing the existence of a behavioural cost of reproduction. However, no such cost was associated with predation by more efficient visual predators (sunfish) or by nonvisual predators (hydras), and the excess of gravid females eaten by backswimmers was found to be attributable to their distribution in the water column. Moreover, the cost associated with predation by small fish was observed only when the Daphnia were presented against a light background, and was abolished when a dark background was substituted. In a further series of experiments with guppies we attempted to show that each egg added to the brood caused a decrease in survival; in two such experiments survival rate was related to body size but not to fecundity, while in a third the effect of body size did not appear, and a negative correlation between survival and fecundity could be demonstrated. Although these experiments unambiguously demonstrate a cost of reproduction they also illustrate the elusiveness of the phenomenom and emphasize the need to develop theories which specify the type and magnitude of costs generated by different ways of life.     

Measuring the cost of reproduction

Summary The timing of the first two broods and the number and size of offspring in each was measured in a series of three experiments for monoclonal cultures of the cladoceran Daphnia pulex reared under standard conditions of ration, temperature and photoperiod. The pattern of total correlations between pairs of life-history variables did not in general support predictions made by hypotheses of reproductive cost. A partial correlation analysis, involving initial size and subsequent growth as well as the life history variables themselves, was performed in an attempt to avoid potential fallacies introduced by the use of total correlations. The only consistent effect found was a positive relationship between the age at reproductive maturity and the mean size of offspring in the first brood. The structure of this segment of the life history is strongly influenced by interactions between size and reproduction, to an extent that precludes the use of simple optimality models.     

The cost of reproduction: the devil in the details

The cost of reproduction is of fundamental importance in life-history evolution. However, our understanding of its mechanistic basis has been limited by a lack of detailed functional information at all biological levels. Here, we identify, evaluate and integrate recent studies in five areas examining the proximate mechanisms underlying the cost of reproduction. Rather than being alternate explanations, hormonal regulation and intermediary metabolism act in concert and have an overarching influence in shaping the cost of reproduction. Immune function is compromised by reproduction, as is resistance to environmental stress. These studies not only provide new information about mechanisms that comprise 'the cost', but also hint at an underlying evolutionarily conserved causal mechanism.     

Description of the individual growth of Daphnia magna (Crustacea: Cladocera) through the von Bertalanffy growth equation. Effect of photoperiod and temperature

Daphnia magna is a cladoceran used as a model organism in aquatic ecology and ecotoxicology studies. Because growth is a critical parameter to study the effect of environmental conditions on the development of zooplankters, the somatic growth of D. magna was measured here and described by the von Bertalanffy growth equation (VBGE), a mathematical model widely used in fisheries management. For this purpose, the effect of two temperatures (20 and 25°C) and two photoperiod conditions (12:12 and 16:8, light:dark) was assayed. Experiments began with neonate females and were finished when parthenogenetic females reached the age of 41 days; they were fed the microalga Ankistrodesmus falcatus (400,000 cell ml⁻¹, 12 mg l⁻¹, dry weight). According to the VBGE, maximal length (L _max) was inversely correlated with the growth rate (K). The highest L _max (6.45 mm) was for the females grown at 20°C with the 12:12 photoperiod, whereas the maximum growth rate (K = 0.182 ± 0.010) was for individuals grown at 25°C with the 12:12 photoperiod. The number of clutches during the studied period was significantly higher for females grown at 25°C, 12:12. Temperature affected the growth rate and the maximum size in D. magna; interaction of temperature with photoperiod was also noteworthy. The VBGE was a nifty way to assess the effects of the tested environmental factors.     

Asexual reproduction and somatic growth of the fissiparous sea star Allostichaster polyplax in New Zealand

Allostichaster polyplax is a fissiparous (capable of reproducing asexually by fission) sea star found in intertidal and shallow subtidal habitats in New Zealand and Australia. A localized population of A. polyplax occurred at a density of 2.7?individuals?m^?2 in an intertidal boulder field at Otago Harbour, South Island, New Zealand. The percentage of sea stars undergoing fission, recorded from January 2010 to March 2011, peaked in January (midsummer) in both years. The frequency of fission decreased for larger sea stars (mean arm length, R?>?25?mm), suggesting an ontogenic shift from asexual to sexual reproduction. Effects of fission (i.e. arm regeneration) and food availability (small gastropods) on growth, storage and sexual reproduction were examined in a factorial laboratory experiment. There was no effect of arm regeneration or food on total arm growth. Storage capacity, measured as pyloric caeca index (PCI), was greater in full-armed than regenerating sea stars, and greater in fed than starved individuals. Fed individuals had a similar PCI as field-collected ones. Gonads were observed in two individuals (males) in the full-armed and fed treatment. Fission did not occur during the experiment. Feeding rate on snails was greater for full-armed than regenerating sea stars. Water temperature had a weak positive effect on the feeding rate of regenerating sea stars. Our findings suggest that fission and subsequent growth of ramets can sustain demographically stable and geographically isolated populations of A. polyplax. The role of sexual reproduction in population dynamics and connectivity of this species (and fissiparous sea stars in general) remains equivocal and requires further research on genetic differentiation within and among populations.     

Long‐term patterns in growth of Oneida Lake walleye: a multivariate and stage‐explicit approach for applying the von Bertalanffy growth function

Total length ( L _T) and its inter annual variation of walleye Sander vitreus from Oneida Lake, New York, based on 51 years (1950–2000) of data for ages 1 to 7 years were analysed. Growth increased over time at young ages, did not change at intermediate ages and decreased at old ages. Total length at age increased over time to age 4 or 5 years, but was stable at older ages. Principle component analysis was used to study the pattern of variations in annual L _T increments among years. More than 92 and 91% of inter annual variability in growth was described by the first three principal components for males and females, respectively. The first principal component was a general indicator of annual growth at all ages, but was dominated by annual growth at intermediate ages. The second and third principal components represented contrasts among yearling L _T, yearling growth and growth at older ages. Therefore, changes in the three stage‐specific parameters, yearling L _T, yearling growth and asymptotic L _T, explained most of the variance in observed growth. Using these three stage‐specific parameters for the von Bertalanffy growth function facilitated interpretations of growth comparisons.     

A preliminary study on quantitative relations among growth,reproduction and mortality in fishes

As a quantitative approach to the life histories of fishes, the present paper attempted to predict a relation among reproduction, growth and mortality numerically with a technique of control theory, the discrete maximum principle. A method for predicting the relation was derived on the postulate that natural selection maximized the net reproductive rate subject to a few constraints. The derived method was applied to Atlantic cod and Atlantic herring populations in the Southern Gulf of St. Lawrence as numerical examples. The examples demonstrated that the theoretical reproductive effort and body weight were well consistent with the observed ones every age but the theoretical survival rates were slightly different from the observed ones. For the reasons mentioned below, however, it should be interpreted that the examples rather support the adopted postulate to a certain degree. First, in general, it is very difficult to obtain good estimates of the rates with traditional methods. Second, intense fishing pressure possibly changes the life history parameters to some extent in fish populations. Moreover, the examples also suggested that, to examine the postulate in further detail, similar analyses had to be made with the data of many fish populations on which intense fishing pressure had not been exerted.     

Resource allocation to growth,reproduction and survival in Gladiolus : The cost of male function

Theoretical models of life-history evolution assume trade-offs between present and future reproduction and/or survival. Models of the evolution of sex assume trade-offs between male function and female function. Generally, experiments designed to evaluate the cost of reproduction on other functions tend to ignore male function. The present work on Gladiolus takes into account simultaneously the different primary functions of the plant and separates sexual reproduction into one male component (pollen production) and one female component (seed production). The study of environmental (within-clone), between-clone and genetic correlations using strains of Gladiolus and principal component analysis show that trade-offs exist between male function, female function and survival, including both characters of plant vigour, perennation (corm production) and vegetative propagation (cormel production). Phenotypic correlations, using different species and species-hybrids, have been obtained which confirm these results. In particular, these results underline the importance of the impact of pollen production on the other functions.     

Equivalence of three allocation currencies as estimates of reproductive allocation and somatic cost of reproduction in Pinguicula vulgaris

Which is the most appropriate currency (biomass, energy, water, or some mineral nutrient) for expressing resource allocation in plants has been repeatedly discussed. Researchers need to assess to which extent interindividual, interpopulational, or interspecific comparisons of resource allocation could be affected by the allocation currency chosen. The "currency issue" is relevant to at least three related aspects of resource allocation to reproduction: (a) reproductive allocation (RA), (b) size-dependence of reproductive allocation, and (c) somatic cost of reproduction (SCR). Empirical tests have mostly dealt with the first aspect only. We examined the equivalence of estimates for the three aspects above across three different allocation currencies (dry mass, N, P) in 11 populations of PINGUICULA VULGARIS. For RA we studied the equivalence of allocation currencies at three scales: among individuals of the same population, between populations of the same species, and among species. Equivalence of currencies in the ranking of RA for individuals within populations was high ( RS >/= 0.43) and did not strongly decrease when comparing populations or species. Excepting for size-dependence of RA, ranking of RA, or SCR between populations was equivalent for biomass and N, but not for P. Our study gives two positive guidelines for empirical plant reproductive ecologists facing the "currency issue": (1) become increasingly concerned about the "currency issue" as you increase the scale of your comparison from individuals to populations to species, and (2) avoid estimating allocation in redundant currencies (biomass and N in our case) and choose preferentially "complementary" currencies that provide a broader view of allocation patterns (biomass and P in our case).     

The cost of reproduction in the glaucous-winged gull

Summary Experimental enlargement of brood size in the glaucous-winged gull (Larus glaucescens) resulted in increased adult foraging time, decreased adult body weight at the end of the breeding season, and decreased over-winter adult survival. The decreased survival of breeding adults was associated with reduced body condition at the end of breeding (resulting from physiological costs of reproduction). Decreased survival was not due to an increased risk of injury or predation during the breeding season. Brood size did not directly affect the fecundity of surviving birds in the subsequent year. However, brood size may have an indirect effect on subsequent fecundity because the probability of mate loss increased among birds with large broods and the reproductive performance of birds with new mates was reduced. Based on estimates of life-time fitness calculated from fecundity and survivorship, birds with two- or three-chick broods (the normal brood size) have higher fitness than birds with one- or four-chick broods. However, the decreased fitness of birds with four-chick broods was slight, and probably not a sufficient explanation for the absence of natural four-chick broods in the glaucouswinged gull.     

Nonlinear multivariate models of successional change in community structure using the von Bertalanffy curve

von Bertalanffy curves were used to describe the nonlinear relationship between assemblages inhabiting holdfasts of the kelp Ecklonia radiata and the volume of the holdfast. This was done using nonlinear canonical analyses of principal coordinates (NCAP). The volume of the holdfast is a proxy for the age of the plant and, thus, the canonical axis is a proxy for succession in the marine invertebrate community inhabiting the holdfast. Analyses were done at several different taxonomic resolutions on the basis of various dissimilarity measures. Assemblages in relatively large holdfasts demonstrated ongoing variation in community structure with increasing volume when the dissimilarity used was independent of sample size. Smaller holdfasts had proportionately greater abundances of ophiuroids and encrusting organisms (bryozoans, sponges, ascidians), while larger holdfasts were characterised by proportionately greater abundances of crustaceans, polychaetes and molluscs. Such linear and nonlinear multivariate models may be applied to analyse system-level responses to the growth of many habitat-forming organisms, such as sponges, coral reefs, coralline algal turf or forest canopies.