Biomass duration in growth models

To gain a better understanding of growth curve, biomass duration in several growth models, such as the exponential, linear, Gompertz, Mitscherlich, logistic, Richards and Bertalanffy, is formulated. Generally, biomass duration in these models can be given in two ways; thet- andw-representations. The latter representation, which can be defined as the summed value of reciprocal of relative growth rate with respect to biomass, gives a new significance to biomass duration. The utility of both representations is exemplified by the observed data of a fir. The idea of biomass duration is extended to get total amounts of anabolism and catabolism in the Bertalanffy model.     

Extreme longevity in freshwater mussels revisited: sources of bias in age estimates derived from mark–recapture experiments

1. There may be bias associated with mark–recapture experiments used to estimate age and growth of freshwater mussels. Using subsets of a mark–recapture dataset for Quadrula pustulosa, I examined how age and growth parameter estimates are affected by (i) the range and skew of the data and (ii) growth reduction due to handling. I compared predictions from von Bertalanffy growth models based on mark–recapture data with direct observation of mussel age and growth inferred from validated shell rings. 2. Growth models based on a dataset that included observations from a wide range of length classes (spanning ≥ the upper 50% of the population length range) produced only slightly biased age estimates for small and medium‐sized individuals (overestimated by 1–2 years relative to estimates from validated shell rings) but estimates became increasingly biased for larger individuals. Growth models using data that included only observations of larger animals (< the upper 50% of length range) overestimated age for all length classes, and estimated maximum age was two to six times greater than the maximum age observed in the population (47 years). Similarly, growth models using a left‐skewed dataset overestimated age. 3. Reductions of growth due to repeated handling also resulted in overestimates of age. The estimated age of mussels that were handled in two consecutive years was as much as twice that of mussels that were handled only once over the same period. Assuming a constant reduction in the annual rate of growth, handling an individual for five consecutive years could result in an estimated age that is five times too high. 4. These findings show that mark–recapture methods have serious limitations for estimating mussel age and growth. A previous paper (Freshwater Biology, 46, 2001, 1349) presented longevity estimates for three mussel species that were an order of magnitude higher than estimates inferred from shell rings. Because those estimates of extreme longevity were based on mark–recapture methods and subject to multiple, additive sources of bias, they cannot be considered accurate representations of life span and cannot be used to conclude that traditional methods of bivalve ageing by interpretation of shell rings are flawed.     

Preliminary observations on the life history of the white-streaked grouper, <Emphasis Type="Italic">Epinephelus ongus</Emphasis>, from Okinawa,Japan

A preliminary analysis of 175 specimens of the white-streaked grouper, Epinephelus ongus (Serranidae), was undertaken to determine life history characteristics of the species. Sagittal otoliths, stomachs, and a subsample of gonads were removed to determine age at length, diet, and reproductive strategy. The von Bertalanffy growth equation was used to describe growth in this species and yielded the growth parameters L^∞ = 438.3, K = 0.04334, and t₀ = −8.752. Fish ranged in age from 1 to 20 years. Diet was consistent with other serranid species and included crabs, shrimps, octopi, and fishes. Based on a very limited number of specimens (n = 12), the larger size and older age of males compared to females suggests that E. ongus may be a protogynous hermaphrodite.     

The clam sipho as indicator for growth indices in the soft-shell clam <Emphasis Type="Italic">Mya arenaria</Emphasis>

Due to the species’ deep burrowing behaviour, growth parameters of the soft-shell clam Mya arenaria L. 1758 are difficult to estimate, especially in deeper habitats which are not directly accessible. In this study, we analysed 192 specimens of M. arenaria and found, contrary to results of most other studies that the sigmoid Gompertz growth model (GGM) is appropriate to describe the growth. Predictions from this model confirm the finding of a life span up to 8 years and as a consequence of this, a maximum shell-length of 60 mm. Individual growth rates calculated from the first deviation indicate a nearly exponential growth in young individuals. The relationship between the clam sipho-width and age, shell-length and biomass conform to the GGM. This is a new approach to assess growth of M. arenaria and to solve practical problems that arise in field studies.     

Age and growth of mangrove red snapper Lutjanus argentimaculatus at its cool‐water‐range limits

This study investigates the age and growth of Lutjanus argentimaculatus at its southern (cooler) range limits in eastern Australia. Specimens were collected from New South Wales and southern Queensland between November 2011 and December 2013. Fork lengths (L_F) ranged from 190 to 1019 mm, and ages ranged from 2+ to 57+ years. Growth was described by the von Bertalanffy growth function with coefficients L_∞ = 874·92 mm, K = 0·087 year^?1 and t₀ = ?2·76 years. Estimates of the instantaneous natural mortality rate (M) ranged from 0·072 to 0·25. The L_F (mm) and mass (W; g) relationship was represented by the equation: . The maximum age of 57+ years is the oldest reported for any lutjanid and comparisons with tropical studies suggest that the age‐based demography of L. argentimaculatus follows a latitudinal gradient. High maximum ages and low natural mortality rates indicate considerable vulnerability to overexploitation at the species' cool‐water‐range limits. These results demonstrate the need to identify underlying processes driving latitudinal gradients in fish demography.     

Effects of density dependence,zooplankton and temperature on blue whiting Micromesistius poutassou growth

Blue whiting Micromesistius poutassou mean total length at age in the north‐east Atlantic Ocean was found to vary by around ±6% during the period 2004–2011 and mean mass at age by ±22% during the years 1981–2013. Linear modelling provided strong evidence that these phenotypic growth variations can be explained by trophic conditions, mainly negative density dependence and also food availability, and a negative long‐term temperature effect on asymptotic size.     

The importance of juveniles in modelling growth: butterflyfish at Lizard Island

Synopsis I established and fitted von Bertalanffy growth functions to size-at-age data for four species of chaetodontids at Lizard Island. Special emphasis on juveniles provided detailed information of the early growth period. All four species demonstrated rapid initial growth achieving an average of 92% of maximum theoretical size in the first 2years. I used various constraints of the theoretical age at length zero (t₀) in an analysis of both complete data sets and data sets using only adult fish. An unconstrained value of t₀ resulted in the best-fit (maximum r²) curve when juveniles were included. When excluding juveniles, it was necessary to constrain t₀ to an approximate settling size to most closely represent the growth of the species.     

Modelling the ontogeny of ectotherms exhibiting indeterminate growth

Numerous growth functions exist to describe the ontogeny of animals. Such functions (e.g., von Bertalanffy's equation, thermal-unit growth coefficient) are currently applied to ectotherms even though they fail to provide analytical expressions that adapt to a wide range of fluctuating temperatures. The underlying mechanisms responsible for the ontogeny of ectotherms exhibiting indeterminate growth have not yet been summarised in terms of a simple but meaningful mathematical equation. Here, a growth function is developed, with parameters having physical or biological interpretation that accommodates indeterminate growth under fluctuating temperatures assuming the latter vary seasonally. The equation is derived as a special case of von Bertalanffy's equation providing realistic growth trajectories throughout the ontogeny of several groups of ectotherms (R²>0.90). The results suggest that the effect of temperature on growth trajectory supersedes that of reproduction in an environment with fluctuating temperature. Furthermore, values of the allometric weight exponent (0<b<0.75) indicate that the rules of body surface and body weight do not apply under certain circumstances. Finally, the growth function circumvents problems associated with models based on thermodynamic and chemical kinetic principles (e.g., inability to predict growth of organisms in which ontogeny exceeds 3 months) and on rule of thermal summation (e.g., reliable only in a certain range of temperature). The growth function can handle a wide range of temperature fluctuations, encompass life stages and apply to key organisms in ecology, fisheries and agriculture.     

Individualism in plant populations: using stochastic differential equations to model individual neighbourhood-dependent plant growth

We study individual plant growth and size hierarchy formation in an experimental population of Arabidopsis thaliana, within an integrated analysis that explicitly accounts for size-dependent growth, size- and space-dependent competition, and environmental stochasticity. It is shown that a Gompertz-type stochastic differential equation (SDE) model, involving asymmetric competition kernels and a stochastic term which decreases with the logarithm of plant weight, efficiently describes individual plant growth, competition, and variability in the studied population. The model is evaluated within a Bayesian framework and compared to its deterministic counterpart, and to several simplified stochastic models, using distributional validation. We show that stochasticity is an important determinant of size hierarchy and that SDE models outperform the deterministic model if and only if structural components of competition (asymmetry; size- and space-dependence) are accounted for. Implications of these results are discussed in the context of plant ecology and in more general modelling situations.