Individual Variation In Growth Research Articles

The effects of applying mis-specified age- and size-structured models

Stock assessments estimate biomass and fishing mortality in absolute terms and relative to reference points. Most of the world’s stock assessments are based on age- or size-structured population dynamics models, with few stock assessments directly accounting for both age and size dynamics. However, the life history parameters of fish and invertebrate populations are often functions of both age and size. An operating model that is based on an age- and size-structured population dynamics model is used to evaluate the performance of assessment methods based on age-, size- and age- and size-structured population dynamics models. Variants of the operating model and the assessment methods, which include ‘platoons’ to better represent individual variation in growth, are considered to explore the impact of this source of uncertainty on the performance of stock assessment methods. Simulation experiments based conceptually on the assessment for Pacific cod in the Eastern Bering Sea are used to explore the consequences of applying assessment methods that are mis-specified in terms of the population dynamics model and the way variation in growth is modelled. The age-structured assessment methods perform poorest, most likely because they mis-represent how mortality, due to fishing, is removed from the population in the operating model, but also because of mis-specification of the growth curve. The assessment methods with platoons can outperform those that ignore platoon structure when this is present, but their performance when there are no platoons is such that, overall, simpler assessment methods based on size-structured, or age- and size-structured population dynamics models, appear best. Conducting assessments using multiple model types and selecting the best model based on the lowest AIC was, however, the best approach overall.

Modelling individual variability in growth of bull trout in the Walla Walla River Basin using a hierarchical von Bertalanffy growth model

AbstractWe examined growth in length of fluvial bull trout (Salvelinus confluentus) in the Walla Walla River Basin, Washington and Oregon. Our objectives were to quantify individual variability in growth; examine growth within and among years, life history forms, life stages and sexes; and estimate von Bertalanffy growth parameters. Individual variability was evaluated by modelling asymptotic length (L∞) and the growth coefficient (k) as random variables. All models were fit with Bayesian methods and were evaluated for fit by the deviance information criterion. By incorporating individual variability, population‐level estimates of L∞ and k appeared appropriate and estimated growth trajectories for specific bull trout fit individual observed patterns in growth. Growth trajectories and positive correlation between individual estimates of L∞ and k suggest that some individuals grow at a faster rate and reach a larger maximum size than other individuals and those differences are maintained throughout life. Selected models suggest that fluvial migrants have higher estimates of L∞ and k than residents, but there were only slight differences in parameter estimates among migrants from two adjacent spawning populations in the Walla Walla River Basin, as well as between males and females. Growth rates increased for fluvial migrants after subadult emigration. Individual variability in growth is consistent with the life history diversity assumed essential for bull trout population persistence. Quantifying this variability is important for modelling population dynamics and viability to conserve this threatened species.

Sex, growth rate, rank order after brood reduction, and hatching date affect first-year survival of long-lived Herring Gulls

Among most species of birds, survival from hatching throughout the first year of life is generally lower than subsequent survival rates. Survival of young birds during their first year may depend on a combination of selection, learning, unpredictable resources, and environmental events (i.e., post-fledging factors). However, knowledge about post-fledging development in long-lived species is usually limited due to a lengthy immature stage when individuals are generally unobservable. Therefore, pre-fledging characteristics are often used to predict the survival of young birds. We assessed effects of nestling growth rates, hatching date, hatching asynchrony, brood size and rank order after brood reduction, and sex on first-year survival of 137 fledglings using a mark-resighting analysis. We found that the survival probability (Phi(1yr) = 0.39) of first-year Herring Gulls (Larus argentatus) in our study colony located at the outer port of Zeebrugge (Belgium) was lower than that of older individuals (Phi(>1yr) = 0.75). All 10 models best supported by our data included nestling growth rate, suggesting that variability in first-year survival may be linked primarily to individual variation in growth. First-year survival was negatively correlated with hatching date and rank order after brood reduction. Hence, carry-over effects of breeding season events such as timing of breeding, early development, and social status had an influence on survival of Herring Gulls after fledging. Furthermore, we found sex-biased mortality in first-year Herring Gulls, with females (Phi(1yr) = 0.45) surviving better than males (Phi(1yr) = 0.38). Although adult survival is generally regarded as the key parameter driving population trajectories in long-lived species, juvenile survival has recently been acknowledged as an important source of variability in population growth rates. Thus, increasing our knowledge of factors affecting age-specific survival rates is necessary to improve our understanding of population dynamics and ultimately life-history variation.

Trade-offs between accuracy and interpretability in von Bertalanffy random-effects models of growth.

Better understanding of variation in growth will always be an important problem in ecology. Individual variation in growth can arise from a variety of processes; for example, individuals within a population vary in their intrinsic metabolic rates and behavioral traits, which may influence their foraging dynamics and access to resources. However, when adopting a growth model, we face trade-offs between model complexity, biological interpretability of parameters, and goodness of fit. We explore how different formulations of the von Bertalanffy growth function (vBGF) with individual random effects and environmental predictors affect these trade-offs. In the vBGF, the growth of an organism results from a dynamic balance between anabolic and catabolic processes. We start from a formulation of the vBGF that models the anabolic coefficient (q) as a function of the catabolic coefficient (k), a coefficient related to the properties of the environment (γ) and a parameter that determines the relative importance of behavior and environment in determining growth (ψ). We treat the vBGF parameters as a function of individual random effects and environmental variables. We use simulations to show how different functional forms and individual or group variability in the growth function's parameters provide a very flexible description of growth trajectories. We then consider a case study of two fish populations of Salmo marmoratus and Salmo trutta to test the goodness of fit and predictive power of the models, along with the biological interpretability of vBGF's parameters when using different model formulations. The best models, according to AIC, included individual variability in both k and γ and cohort as predictor of growth trajectories, and are consistent with the hypothesis that habitat selection is more important than behavioral and metabolic traits in determining lifetime growth trajectories of the two fish species. Model predictions of individual growth trajectories were largely more accurate than predictions based on mean size-at-age of fish. Our method shares information across individuals, and thus, for both fish populations investigated, allows using a single measurement early in the life of individual fish or cohort to obtain accurate predictions of lifetime individual or cohort size-at-age.

Acclimation temperature alters the relationship between growth and swimming performance among juvenile common carp (Cyprinus carpio)

Individual variation in growth, metabolism and swimming performance, their possible interrelationships, and the effects of temperature were investigated in 30 juvenile common carp (Cyprinus carpio) at two acclimation temperatures (15 and 25°C). We measured body mass, critical swimming speed (Ucrit), resting metabolic rate (RMR), active metabolic rate (AMR) and metabolic scope (MS) twice (28days apart) in both temperature groups. Fish acclimated to 25°C showed a 204% higher specific growth rate (SGR) than those acclimated to 15°C due to a 97% higher feeding rate (FR) and a 46% higher feed efficiency (FE). Among individuals, SGR was positively correlated with the FR and FE at both low and high temperatures. All measured variables (Ucrit, RMR and AMR) related to swimming except MS showed a high repeatability after adjusting for body mass (mass-independent). Fish acclimated to 25°C had a 40% higher Ucrit compared with 15°C acclimated fish, which was at least partially due to an improved metabolic capacity. AMR showed a 97% increase, and MS showed a 104% parallel increase with the higher acclimation temperature. Residual (mass-independent) Ucrit was positively correlated with residual RMR, AMR and MS, except for the residual RMR at high temperature. When acclimated to the lower temperature, both the residual and absolute Ucrit were negatively correlated with FR and FE and, hence, with SGR, suggesting a functional trade-off between growth and locomotion in fish acclimated to low temperatures. However, when acclimated to the higher temperature, this trade-off no longer existed; absolute Ucrit was positively correlated with SGR because individuals with rapid growth exhibited greatly increased body mass. The higher metabolic capacity at 25°C showed a positive effect on both swimming performance and growth rate (because of improved digestive efficiency) under the high-temperature condition, which we did not anticipate. Overall, these results indicate that temperature alters the relationship between growth and swimming performance of juvenile common carp. This change may be an adaptive strategy to seasonal temperature variation during their life history.

Divergent reproductive allocation trade‐offs with canopy exposure across tree species in temperate forests

AbstractVariation in tree reproduction can alter forest community dynamics, especially if reproductive output is costly for other functions like growth. However, empirical studies reach conflicting conclusions about the constraints on reproductive allocation relative to growth and how they vary through time, across species, and between environments. Here, we test the hypothesis that a critical resource, canopy exposure to light availability, limits reproductive allocation by comparing long‐term relationships between reproduction and growth for trees from 21 species in forests throughout the Southeastern United States. We found that species have divergent responses to light availability, with shade‐intolerant species experiencing an alleviation of trade‐offs at high light‐ and shade‐tolerant species showing no changes in reproductive output across light environments. Correlations between temporal variation in individual growth and reproduction were weak and generally insensitive to canopy exposure, but changed when considering time lags. The diversity of responses across species indicates that reproductive allocation for trees in these forests is strongly influenced by both species’ life history and environmental heterogeneity in space and time.

Maximum Growth Potential and Periods of Resource Limitation in Apple Tree.

Knowledge of seasonal maximum potential growth rates are important for assessing periods of resource limitations in fruit tree species. In this study we assessed the periods of resource limitation for vegetative (current year stems, and woody biomass) and reproductive (fruit) organs of a major agricultural crop: the apple tree. This was done by comparing relative growth rates (RGRs) of individual organs in trees with reduced competition for resources to trees grown under standard field conditions. Special attention was dedicated to disentangling patterns and values of maximum potential growth for each organ type. The period of resource limitation for vegetative growth was much longer than in another fruit tree species (peach): from late May until harvest. Two periods of resource limitation were highlighted for fruit: from the beginning of the season until mid-June, and about 1 month prior to harvest. By investigating the variability in individual organs growth we identified substantial differences in RGRs among different shoot categories (proleptic and epicormic) and within each group of monitored organs. Qualitatively different and more accurate values of growth rates for vegetative organs, compared to the use of the simple compartmental means, were estimated. Detailed, source-sink based tree growth models, commonly in need of fine parameter tuning, are expected to benefit from the results produced by these analyses.

Growth Asymmetry, Head Circumference, and Neurodevelopmental Outcomes in Infants with Single Ventricles

To assess the variability in asymmetric growth and its association with neurodevelopment in infants with single ventricle (SV). We analyzed weight-for-age z-score minus head circumference-for-age z-score (HCAZ), relative head growth (cm/kg), along with individual growth variables in subjects prospectively enrolled in the Infant Single Ventricle Trial. Associations between growth indices and scores on the Psychomotor Developmental Index (PDI) and Mental Developmental Index (MDI) of the Bayley Scales of Infant Development-II (BSID-II) at 14months were assessed. Of the 230 subjects enrolled in the Infant Single Ventricle trial, complete growth data and BSID-II scores were available in 168 (73%). Across the cohort, indices of asymmetric growth varied widely at enrollment and before superior cavopulmonary connection (SCPC) surgery. BSID-II scores were not associated with these asymmetry indices. In bivariate analyses, greater pre-SCPC HCAZ correlated with higher MDI (r=0.21; P=.006) and PDI (r=0.38; P<.001) and a greater HCAZ increase from enrollment to pre-SCPC with higher PDI (r=0.15; P=.049). In multivariable modeling, pre-SCPC HCAZ was an independent predictor of PDI (P=.03), but not MDI. In infants with SV, growth asymmetry was not associated with neurodevelopment at 14months, but pre-SCPC HCAZ was associated with PDI. Asymmetric growth, important in other high-risk infants, is not a brain-sparing adaptation in infants with SV. Clinicaltrials.gov: NCT00113087.

Estimating individual growth variability in albacore (Thunnus alalunga) from the North Atlantic stock: Aging for assessment purposes

Length-frequency data and derived catch at age matrices are used in north Atlantic albacore (Thunnus alalunga) stock assessment conducted within the International Commission for the Conservation of Atlantic Tunas (ICCAT). Growth is assumed to follow the von Bertalanffy model with the assumption that growth parameters are constant over time and the same for all fish. However, individual growth variability is an important factor not considered and affecting the input into the modelling of the population. This study describes a Bayesian hierarchical model applied to model the individual variability in the parameters asymptotic length (L∞) and growth rate (K) of the von Bertalanffy growth model for North Atlantic albacore. The method assumes that the L∞ and K values for each individual fish are drawn from a random distribution centered on the population mean values, with estimated variances. Multiple observations of spine diameter at age for individual fish were obtained by direct reading of spine sections collected in 2011 and 2012. A suite of back calculation methods were then applied to the measurements of annuli diameters in the aged individuals observed to back-calculate lengths at each age. The von Bertalanffy model was fitted to the measured and back-calculated lengths. Models with and without individual growth variability were compared using the deviance information criterion (DIC) to find the best model. Normal and log-normal error distribution models were used to analyse the data. Additionally, subsamples of the data were used to evaluate whether an unbalanced age-distribution in the data affects estimates of growth parameters. It was found that North Atlantic albacore asymptotic length (L∞) varies significantly between individual fish but not individual rate growth (K), for all back-calculation methods. Furthermore, negatively correlated relationships between von Bertalanffy growth parameters of asymptotic mean (L∞) and growth rate (K) were estimated for North Atlantic albacore with the array of models explored. The overall estimated values of K and population mean L∞ parameters were similar to values estimates in previous north Atlantic albacore growth studies.

Modelling growth in tuna RFMO stock assessments: Current approaches and challenges

We review the approaches used to model growth in recent tuna Regional Fisheries Management Organization (tRFMO) stock assessments, and the challenges encountered. The tRFMO fisheries span vast areas, with multinational fleets operating a diverse range of gear types, and are assessed with a range of modelling methods. Despite the high volume and/or value nature of many tuna and billfish fisheries, there remain substantial data input challenges, including biased size composition sampling, conflicting age estimates from hard parts (and inconclusive validation studies), and very high error rates in some large-scale tagging programmes. There is evidence for spatial and temporal variability in growth rates, but sampling is rarely adequate to quantify this variability, and it is not described in most tRFMO assessments. Sophisticated statistical methods have been developed to combine catch length frequency distributions, age-length data and tag growth increment observations into a single estimation framework (though the data are generally not sufficient to allow the variances to be objectively partitioned). Modelling individual growth variability with random effects has the potential to greatly reduce biases from tag growth increment analyses, but this is computationally prohibitive when the growth curve is estimated within the assessment model. In contrast, the effects of size-based selectivity may not be adequately described if growth is estimated outside of the assessment model. Different species are affected by these problems to different and largely unknown degrees. We discuss options for mitigating some of these problems, but doubt that entirely satisfactory solutions can be achieved in most cases. Accordingly, we recommend that i) greater emphasis should be placed on representing the plausible growth uncertainty in the assessments (i.e. using a model ensemble approach), and ii) management strategy evaluation should be used to develop harvest strategies that are robust to the growth (and other, potentially more urgent) uncertainties, and to prioritize research investment in the context of achieving management objectives.

Individual-based approach as a useful tool to disentangle the relative importance of tree age, size and inter-tree competition in dendroclimatic studies

In this work, an individual-based approach was used to assess the relative importance of tree age, size, and competition in modulating the individual dendroclimatic response of Quercus robur L. This was performed in a multi-aged forest in northwestern Spain under a wet Atlantic climate. All trees in five replicated forest stands with homogeneous soil conditions were mapped and inter-tree competition was quantified with a distance-dependent competition index. Tree rings of cored trees were crossdated and total age was estimated on individuals where the pith was missed. The climatic response was evaluated by bootstrapped correlations of individual tree-ring chronologies with climatic records. Inter-annual growth variation, i.e., mean sensitivity, was independent of tree age and bole diameter, but modulated by competition. Water excess in previous summer-autumn and spring negatively affected growth, while warmer September conditions favored growth. Individual response to climate was independent of tree age, but related to the joint effect of tree bole diameter and competition. Larger oaks in less competitive environments responded more plastically to climatic stress, while smaller trees under high competition levels were less responsive to climate. Strong inter-tree competition reduced growth plasticity but amplified the vulnerability of smaller oaks to the particularly rainy conditions of the study area. These findings suggest that inter-tree competition is a relevant size-mediated extrinsic factor that can potentially modulate individual radial growth variation and its response to limiting climatic conditions in temperate deciduous forests. This study highlights the value of individual-based approach as a useful tool that informs about the relative contribution of factors modulating the climatic response of tree-ring growth.

Effects of prompt versus stepwise relocation to a novel environment on foals' responses to weaning in domestic horses (Equus caballus)

Abstract Artificial weaning is often highly stressful for both mother and offspring. We investigated the effect of 2 different weaning and schedules on growth rate and saliva cortisol concentrations in a group of loose-housed domestic horses. We predicted higher acute stress (cortisol concentrations), but a lower long-term effect on weight gain, which would indicate lower chronic stress in foals, if the foals were moved to the new environment immediately after separation from the mothers (prompt relocation [PR]) compared with that was adjourned for a week (stepwise relocation [SWR]). Within 2 seasons, 56 foals weaned at age of 165-250 days were regularly weighed up to 140 days after weaning. Growth rate significantly differed between SWR and PR foals. The PR weanlings revealed relatively stable increase in their weights, whereas SWR foals experienced a significant drop in growth during the first 3 weeks after weaning. The weight differences were still apparent 5 months after weaning (predicted weight, least squares means ± standard error: 374.40 ± 1.75 kg in PR vs. 362.71 ± 1.66 kg in SWR foals). Cortisol concentrations changed significantly between and within different weaning procedures and were highest in PR foals after weaning and relocation. Compared with pre-weaning values, cortisol levels increased in PR but not in SWR foals, either after weaning or deferred moving. We found large individual variability in foals' growth and in cortisol concentrations for both weaning procedures. There was also a year effect in SWR foals. Stepwise changes of the physical and social environment (deferred removal to the remote facility) within a short period after abrupt weaning resulted in lower acute stress but induced long-term negative effects on foals' growth rate compared with joint weaning and relocation. Our results support rather prompt moving of the weanlings to the new facility, rather than to a stepwise location on horse breeding farms.

The Impact of Taxation on Economic Growth: Case Study of OECD Countries

Abstract The aim of this paper is to evaluate the impact of individual types of taxes on the economic growth by utilizing regression analysis on the OECD countries for the period of 2000–2011. The impact of taxation is integrated into growth models by its impact on the individual growth variables, which are capital accumulation and investment, human capital and technology. The analysis in this paper is based on extended neoclassical growth model of Mankiw, Romer and Weil (1992), and for the verification of relation between taxation and economic growth the panel regression method is used. The taxation rate itself is not approximated only by traditional tax quota, which is characteristic by many insufficiencies, but also by the alternative World Tax Index which combines hard and soft data. It is evident from the results of both analyses that corporate taxation followed by personal income taxes and social security contribution are the most harmful for economic growth. Concurrently, in case of the value added tax approximated by tax quota, the negative impact on economic growth was not confirmed, from which it can be concluded that tax quota, in this case as the indicator of taxation, fails. When utilizing World Tax Index, a negative relation between these two variables was confirmed, however, it was the least quantifiable. The impact of property taxes was statistically insignificant. Based on the analysis results it is evident that in effort to stimulate economic growth in OECD countries, economic-politic authorities should lower the corporate taxation and personal income taxes, and the loss of income tax revenues should be compensated by the growth of indirect tax revenues.

Canopy Layers Stratified Volume Equations for Pinus caribaea Stands in South West Nigeria using Linear Mixed Models

Background and Purpose: Efficient forest stand management requires reliable estimates of growing stock. The reliability of stem volume estimates depends on the range and extent of available sample data. The potentials of canopy layers stratification in pure plantations as a means of improving the accuracy of stem volume equations have not been fully explored. Linear Mixed Model (LMM) approach is a statistical technique capable of yielding a more efficient prediction under clustered data structure. This study investigates the existence and potentials of canopy stratifications for improving the reliability of stem volume prediction equations under pure plantations using linear mixed model approach. Materials and Methods: Pinus caribaea Morelet plantations in Oluwa Forest Reserve, Ondo State, Nigeria were investigated. Individual tree growth variables, including diameters, heights and crown measurements were obtained in 2010 on twenty-five 0.04 ha plots representing five different stands planted between 1979 and 1991. Visual assessment of the trees within each plot was also done to classify them into four canopy strata (i.e. dominant, co-dominant, intermediate and suppressed). Linear mixed model approach was used to analyze the tree growth data using SAS Proc Mixed. Two variants of volume equations; simple linear and exponential were investigated. Results: Results show that simple linear mixed model consistently give better fit criteria (e.g. AIC) of 135.8, 18.9, -214.7 and -174.6 under dominant, co-dominant, intermediate and suppressed canopy layers, respectively. The covariance parameter estimate for dominant canopy (0.2219) is about 370 as large as that of suppressed (0.0006). This implies that canopy layers not only influence stem volume prediction but also reduce within-stand variance as well.

Density‐dependent and density‐independent growth in a population of juvenile sea‐trout,Salmo trutta, assessed using long‐term data from a small stream in Northwest England

SummaryThe objectives were to check the validity of a growth model and to examine the relationship between population density and (i) the overall mean length of the trout (ii) the difference between each model‐estimated mean length and the observed mean lengths for the highest and lowest 10% of measurements in each sample and (iii) the individual variation in trout lengths (measured by coefficient of variation:CV%).First (0+)‐ and second (1+)‐year‐old juvenile sea‐trout were sampled by electrofishing at the beginning and at the end of the summer from 1967 to 2000. The trout left the stream as pre‐smolts in May, soon after their second birthday, so that few 2+ trout were taken. Length, rather than mass, was used in this study because all fish were measured, but only a subsample was weighed.Mean length was not related to population density and, therefore, mean growth was density independent. A growth model (Elliott, Hurley &amp; Fryer, 1995) estimated the mean mass of the trout over the two years spent in fresh water. These estimates were converted to mean length, using length–mass regression equations. There was good agreement in most year‐classes between the model‐estimated value and the observed mean length for all trout taken in each sample. Exceptions were that the mean length of 0+ trout after two summer droughts was lower than expected, although compensatory growth followed, so that observed and expected values were similar for 1+ trout.Mean lengths for the highest and lowest 10% of measurements in each sample were significantly higher or lower, respectively, than the estimated mean value. The difference between the latter and the higher or lower mean values was related negatively to population density. Therefore, mean lengths of the fastest and slowest growing trout were density dependent. There was also a negative relationship between population density and theCV% for 0+ and 1+ trout. Therefore, although growth in terms of overall mean length was density independent, individual variation in trout growth was density dependent, being highest at low density and lowest at high density of trout.

Once upon a larva: revisiting the relationship between feeding success and growth in fish larvae

AbstractVariations in larval fish growth rates are largely the result of variability in biotic and abiotic characteristics of the feeding environment experienced by each individual. An assessment of an individual's overall feeding success (i.e. accumulation of utilizable organic matter) can best be achieved at the time of capture when the relationships among environment, short-term feeding success as defined by gut content and long-term feeding success as defined by accumulated growth can be contrasted. Here, we investigated the relationships between average growth, feeding success, and variability in individual growth and feeding rates across a range of taxa based on a synthesis of studies in which stomach content and otolith growth were measured in the same individuals. Instantaneous measures of feeding success were highly variable and demonstrated a positive yet somewhat limited association with growth rates across all taxa. The strength of the feeding-growth relationships among taxa, and cohorts within taxa, was reflected in the autocorrelation of individual growth rates, suggesting that stable growth was achieved through consistent feeding success. However, when viewed at the individual level, faster growth was achieved in individuals with more variable growth rates, and by inference more variable past feeding success. The dichotomy in these underlying relationships may point to the importance of stochastic events in the development of exceptional individuals in a population, and may be linked to how surplus energy is allocated to individual growth rates. The positive correlation found between feeding success and growth in all taxa is consistent with the growth-survival paradigm for the larval stage of fish. However, both the correlation between feeding success and growth and the serial correlation of growth time-series was greatest in fast-growing species, suggesting that the potential for an early “critical period” regulating survival varies among species, reaching a maximum in fast-growing fish.

Maturation shifts in a temperate marine fish population cannot be explained by simulated changes in temperature-dependent growth and maturity

To disentangle genetic and environmental influences on phenotypic traits that influence maturation of fish, it would be useful to predict the expected change due to environment alone to compare with observations. This requires a realistically scaled, species-specific life history model of environmentally determined variation in individual growth and maturation. In this study, inter-annual variability in the proportion of mature haddock in the west North Sea was predicted using a stochastic, individual-based simulation model incorporating a temperature-dependent maturation threshold. This species and region are particularly relevant to the debate about the relative importance of genetic and climate change because North Sea haddock have experienced both high fishing mortality and substantial warming in recent decades. Using observed temperatures in combination with temperature-dependent models for growth and maturation, the simulation model predicted year-to-year variation in length and maturity at age expected for cohorts produced from 1979 to 2006. The simulated proportions mature at age 2 were then compared to the observed proportions in an annual bottom trawl survey. Although the model explained much of the high-frequency variation in maturation, the simulated time trend under-represented the rate of increase in the observed trend in proportions mature. This inability of the temperature-dependent life history model to predict the magnitude of change appears consistent with a long-term decline in the maturation threshold. This result provides indirect support for a genetic change in a key life history trait.

Determining individual variation in growth and its implication for life-history and population processes using the empirical Bayes method.

The differences in demographic and life-history processes between organisms living in the same population have important consequences for ecological and evolutionary dynamics. Modern statistical and computational methods allow the investigation of individual and shared (among homogeneous groups) determinants of the observed variation in growth. We use an Empirical Bayes approach to estimate individual and shared variation in somatic growth using a von Bertalanffy growth model with random effects. To illustrate the power and generality of the method, we consider two populations of marble trout Salmo marmoratus living in Slovenian streams, where individually tagged fish have been sampled for more than 15 years. We use year-of-birth cohort, population density during the first year of life, and individual random effects as potential predictors of the von Bertalanffy growth function's parameters k (rate of growth) and (asymptotic size). Our results showed that size ranks were largely maintained throughout marble trout lifetime in both populations. According to the Akaike Information Criterion (AIC), the best models showed different growth patterns for year-of-birth cohorts as well as the existence of substantial individual variation in growth trajectories after accounting for the cohort effect. For both populations, models including density during the first year of life showed that growth tended to decrease with increasing population density early in life. Model validation showed that predictions of individual growth trajectories using the random-effects model were more accurate than predictions based on mean size-at-age of fish.

Effect of culture methods on individual variation in the growth of sea cucumber Apostichopus japonicus within a cohort and family

There is substantial individual variation in the growth rates of sea cucumber Apostichopus japonicus individuals. This necessitates additional work to grade the seed stock and lengthens the production period. We evaluated the influence of three culture methods (free-mixed, isolated-mixed, isolated-alone) on individual variation in growth and assessed the relationship between feeding, energy conversion efficiency, and individual growth variation in individually cultured sea cucumbers. Of the different culture methods, animals grew best when reared in the isolated-mixed treatment (i.e., size classes were held separately), though there was no difference in individual variation in growth between rearing treatment groups. The individual variation in growth was primarily attributed to genetic factors. The difference in food conversion efficiency caused by genetic differences among individuals was thought to be the origin of the variance. The level of individual growth variation may be altered by interactions among individuals and environmental heterogeneity. Our results suggest that, in addition to traditional seed grading, design of a new kind of substrate that changes the spatial distribution of sea cucumbers would effectively enhance growth and reduce individual variation in growth of sea cucumbers in culture.

Estimating growth of tropical tunas in the Indian Ocean using tag-recapture data and otolith-based age estimates

A growth model from which the expected age of a fish can be estimated based on its length is a key component to most stock assessments. For the three tropical tuna species in the Indian Ocean – yellowfin (YFT; Thunnus albacares), bigeye (BET; T. obesus) and skipjack (SKJ; Katsuwonus pelamis) – information about growth has been very limited until recently, when data from a large-scale Indian Ocean tuna tagging program became available. In this paper, parametric growth models were fit to tag-recapture data for all three species using a maximum likelihood method that models the joint density of release and recapture lengths as a function of age by treating age at tagging as a random variable. The method allows for individual variability in growth by modelling the asymptotic length parameter as a random effect. Direct age and length data from otolith readings were also included in the analysis for YFT and BET. The results support two-stanza growth models for all three species; however, the growth patterns for YFT and BET differ from SKJ. YFT and BET exhibit a transition in growth between age 2 and 3, with faster growth in the second stanza than the first, whereas SKJ exhibit a transition in growth around age 1, with much faster growth in the first stanza than the second. Most likely, YFT and BET also experience a phase of rapid growth directly following hatching, but lack of data for fish less than 50cm for these species precludes its estimation. Differences in growth between sexes were found for YFT and BET, with males growing to a larger size; information on sex was not available for SKJ.