Modelling fish growth: multi-model inference as a better alternative to a priori using von Bertalanffy equation

The common practice among researchers who study fish growth is to a priori adopt the von Bertalanffy growth model (VBGM), which is the most used and ubiquitous equation in the fisheries literature. However, in many cases VBGM is not supported by the data and many species seem to follow different growth trajectories. The information theory approach frees the researcher from the limiting concept that a ‘true’ growth model exists. Multi‐model inference (MMI) based on information theory is proposed as a more robust alternative to study fish growth. The proposed methodology was applied to 133 sets of length‐at‐age data. Four candidate models were fitted to each data set: von Bertalanffy growth model (VBGM), Gompertz model, Logistic and the Power model; the three former assume asymptotic and the latter non‐asymptotic growth. In each case, the ‘best’ model was selected by minimizing the small‐sample, bias‐corrected form of the Akaike information criterion (AIC_c). To quantify the plausibility of each model, the ‘Akaike weight’w_i of each model was calculated. Following a MMI approach, the model averaged asymptotic length for each case was estimated, by model averaging estimations of interpreting Akaike weights as a posterior probability distribution over the set of candidate models. The VBGM was not selected as the best model in 65.4% of the cases. Most often VBGM was either strongly supported by the data (with no other substantially supported model) or had very low or no support by the data. The estimation of asymptotic length was greatly model dependent; as estimated by VBGM was in every case greater than that estimated by the Gompertz model, which in turn was always greater than that estimated by the Logistic model. The percentage underestimation of the standard error of , when ignoring model selection uncertainty, was on average 18% with values as high as 91%. Ignoring model selection uncertainty may have serious implications, e.g. when comparing the growth parameters of different fish populations. Multi‐model inference by model averaging, based on Akaike weights, is recommended as a simple and easy to implement method to model fish growth, for making robust parameter estimations and dealing with model selection uncertainty.     

基于生长和死亡参数变化的官井洋大黄鱼资源现状分析

依据2010—2011年福建官井洋水域渔业资源监测调查资料,对2 098尾大黄鱼的体长、体质量、生长、性腺进行测定。据此,利用von Bertalanffy生长方程和死亡参数分析官井洋大黄鱼资源现状,并讨论了拐点年龄,临界年龄等渔业生物学特征。结果表明,目前官井洋大黄鱼平均体长132.6 mm,优势体长组为110～150 mm,占55.96%;平均体质量45.1 g,优势体质量组为10～50 g,占61.77%,大黄鱼幼鱼和补充群体已成为渔业生产的主要捕捞对象。大黄鱼体长—体质量间的关系式为W=2.001×10-5L3.006。用ELEFAN技术拟合的von Bertalanffy生长方程参数分别为L∞=385.4 mm、k=0.43及t0=-0.32a,拐点年龄为2.2龄。对照20世纪80年代福建近海海域大黄鱼群体L∞值从555.4 mm下降到现在的385.4 mm,拐点年龄由2.97下降到2.2,均表明当今大黄鱼群体小型化且低龄化严重。生长系数k由0.36增长到0.43表明大黄鱼的生长速度加快。总死亡系数(Z)为3.12,自然死亡系数(M)为0.45,捕捞死亡系数(F)为2.67,资源开发率(E)为0.856。大黄鱼M值出现上升,可能与福建近海环境质量下降有关,而高强度的捕捞促使大黄鱼捕捞死亡系数由0.84上升到2.67,说明大黄鱼资源已经处于过度开发状态。在官井洋大黄鱼现行资源状态下,应努力降低捕捞死亡水平,保护大黄鱼生存环境,而对目前以小型化和低龄化为主的大黄鱼群体,建议以控制大黄鱼的开捕年龄(t0)为主。     

Single nucleotide polymorphisms in the growth hormone gene of Oreochromis niloticus and their association with growth performance

Polymorphisms in the growth hormone (GH) gene that is associated with the growth rate of farmed fish have been the target of many breeding programmes. The present study aimed to identify single nucleotide polymorphisms (SNPs) in GH gene regions to evaluate the association of SNP variations with the growth rate of two Nile tilapia: Oreochromis niloticus (Linnaeus, 1758) strains. The targeted regions were amplified, sequenced, aligned and screened for the presence of SNPs; thereafter, performance tests were used to check for the association between SNPs and weight. Allele and genotype frequencies were estimated for each SNP and genotype. Genotype blocks or sets of SNP genotypes and frequencies were also estimated. Association between SNPs and growth rate was statistically evaluated using a univariate linear mixed model that included both fixed and random effects. A total of 10 SNPs were identified, nine in the proximal promoter and one located in the 5′ UTR, forming 10 genotype blocks. In all weight recordings, five genotype blocks were significantly associated with the highest weights. Single nucleotide polymorphisms 6‐10 were also found to be significantly associated with growth (p‐value < .05). Genotypes with higher additive genetic values for weight were identified in the Chitralada strain, suggesting a possible impact of these additive effects of the GH SNP genotype on the growth rate of Nile tilapia. These findings may be used as part of marker‐assisted selection in tilapia breeding programmes.     

Age and growth rates of the critically endangered fish Garra ghorensis can inform their conservation management

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Multimodel approaches in shark and ray growth studies: strengths,weaknesses and the future

Multimodel frameworks are common in contemporary elasmobranch growth literature. These techniques offer a proposed improvement over individual growth functions by incorporating additional candidate models with alternative characteristics. Sigmoid functions (e.g. Gompertz and logistic) are a popular alternative to the commonly used von Bertalanffy growth function (VBGF) as they are hypothesized to better suit certain taxa based on body shape (such as batoids) or reproductive mode (such as egg‐layers). However, this hypothesis has never been tested. This study examined 74 elasmobranch multimodel growth studies by comparing the growth curves of their respective candidate models. Hypotheses regarding model performances were rejected as the VBGF was equally likely to fit best for all taxa and reproductive modes. Subsequently, no individual model was suited to be used a priori. Differences between candidate model fits were greatest at age zero with Gompertz and logistic functions providing estimates that were 15% and 23% larger on average than the VBGF, respectively. However, length‐at‐age estimates of the different models became negligible at older ages. Differences between candidate models were mostly small (≤5%), and the multimodel framework only marginally affected length‐at‐age estimates. However, there were cases where some candidate models provided inappropriate fits that contrasted considerably to the best fitting model. In some of these instances, a single‐model framework could have yielded biologically unrealistic growth estimates. Therefore, no study could pre‐empt whether or not it required a multimodel framework. A framework was subsequently recommended to maximize the accuracy of model fits for elasmobranch length‐at‐age estimates using multimodel approaches.     

Spatial variability in the somatic growth of pikeperch Sander lucioperca,an invasive piscivorous fish

Introduced fishes can develop invasive populations that impact native species and ecosystems. Understanding the population ecology of introduced species in their extended ranges and how this compares to their native ranges is therefore important for informing their management. Here, the age and somatic growth rates of the piscivorous freshwater fish pikeperch Sander lucioperca were analysed across their invasive and native ranges to determine their spatial patterns and drivers. Analyses were initially completed in their invaded range in central and western England. Populations varied spatially in their growth rates; being slowest for a population in a narrow and shallow canal and fastest in a large, impounded lowland river. A meta‐analysis of parameters of the von Bertalanffy growth model then revealed that across their native and invasive ranges, their theoretical ultimate lengths (L_∞) and growth coefficients (K) were significantly related to latitude, but not longitude. Their relationships with latitude were nonlinear, with higher values of L_∞ and lower values of K being evident towards their northerly and southerly range limits. Faster growth rates were evident in the middle of their range (45 to 55°N), suggesting temperatures here were most optimal for growth, but were in a trade‐off with reduced ultimate lengths. These spatial patterns suggest that whilst introduced S. lucioperca can colonise new waters across a wide area, the expression of their life‐history traits will vary spatially, with potential implications for how invasive populations establish and integrate into native fish communities.     

Stepwise function of natural growth for Scylla serrata in East Africa: a valuable tool for assessing growth of mud crabs in aquaculture

Predicting growth is critical in aquaculture, but models of growth are largely missing for mud crab species. Here, we present the first model of natural growth in juvenile and adult mud crabs Scylla serrata from East Africa using a stepwise growth function based on data on intermoult periods and growth at moult from field mark‐recapture, pond and laboratory studies. The results showed a sigmoid growth pattern in carapace width and suggest that S. serrata in East Africa will reach 300 g and sexual maturity ~9.9 months after settlement, and a commercial size of 500 g after 12.4 months. Analyses of the literature identified several issues with the common praxis to compare standard growth measures between aquaculture studies with different initial size or growing periods. Using the new growth function to estimate the proportional difference between modelled and obtained growth as an alternative method, we show that growth rates of S. serrata cultured in cage systems, which are dominant in East Africa, was <40% of the estimated natural growth and growth obtained in pond systems. The analysis also indicated that growth rates of S. serrata in Southeast Asia was over 50% higher compared with similar culture systems in East Africa, and that different species of mud crabs had large differences in growth rates. This study shows that growth in the present mud crab aquaculture systems in East Africa is below their expected potential. Further work is needed to identify the factors behind this observation.     

Revisiting a central prediction of the Gill Oxygen Limitation Theory: Gill area index and growth performance

The Gill Oxygen Limitation Theory (GOLT) posits that a mismatch in oxygen supply and demand stemming from geometric constraints on gill surface area limits metabolic rate and energy available for biological processes. This theory has been suggested to explain numerous phenomena observed with warming yet is based upon a relationship among maximum size, growth, and gill surface area established over 40 years ago. However, the metric used in this relationship to characterize gill surface area, gill area index, fails to capture the known variability in the scaling of gill surface area and is biased by the sizes at which gills were measured. Here, we revisit a central prediction of the GOLT, asking four key questions that examine limitations in the original relationship. We find that gill area index does indeed explain variation in growth performance across 132 species of fish and this relationship is strikingly similar to the original relationship across 42 species. Yet, we argue that gill area index is not an adequate measure of gill surface area because (1) gill surface area has a non-linear relationship with size and, thus, changes ontogenetically as an individual grows over time and (2) because it is based on mean estimates of both gill surface area and body mass. Indeed, we show that the value of gill area index for a given species is variable depending on how it is calculated. We therefore suggest a pathway forward for assessing whether gill surface area is an important factor in explaining variation in growth performance.     

Growth of common carp Cyprinus carpio in Anatolia (Turkey), with a comparison to native and invasive areas worldwide

Common carp Cyprinus carpio occurs in several non‐native areas worldwide, where it is generally regarded as either naturalised or invasive. Anatolia (Turkey) represents a unique region for evaluating common carp growth, due both to its location at the southernmost range of expansion of the species' wild form and to most of its water bodies having been stocked with domesticated strains. Based on a review of length‐at‐age data for common carp stocks from 45 water bodies sampled between 1953 and 2007, regional patterns in growth across climates, water body types, scalation variants and sexes, along with altitudinal gradients in growth performance and mortality, were investigated. Growth rates were lower in cold and arid relative to temperate climates, and also under hot or dry summers; this was true also of the mirror relative to the scale variant, males to females, but not of water body types (i.e., man‐made reservoirs, natural lakes, water courses). Growth performance and mortality decreased with increasing altitude and decreasing temperature, likely due to optimisation of resource allocation between growth and reproduction. Growth rate of common carp from Anatolia was consistently lower compared to its native (Eurasian) and, especially, invasive (North American) counterparts, which reflected an opportunistic life‐history strategy. Lower growth rates in Anatolia were ascribed to lower resilience of the widespread mirror variant together with limited habitat for spawning in man‐made reservoirs. Better knowledge of common carp growth in Anatolia will improve stock management and conservation efforts. Further studies will help clarify the mechanisms responsible for evolutionary genotype–phenotype inter‐relationships.     

碳源添加方式对循环水养殖系统中微生物悬浮生长反应器水处理的影响

采用中试规模的循环水养殖系统,对比研究碳源连续添加的微生物悬浮生长反应器(SGR-Con)和碳源分次添加反应器(SGR-Sev)的水处理效果。典型反应周期内的溶解性有机碳浓度变化,SGR-Con反应区处于较高的稳定水平,SGR-Sev在反应周期的第0小时至碳源瞬时添加时快速上升至SGR-Con的水平,并且在反应周期的第4小时以后降至较低的稳定水平。实验期间,SGR-Sev反应区和沉淀区的溶解氧含量分别显著高于SGRCon的反应区和沉淀区;2个反应器的反应区pH无显著差异,沉淀区pH在2个反应器之间亦无显著差异。碳源分次添加的方式显著提高了反应器的脱氮效果,SGR-Sev对硝氮和总氮的去除率、出水碱度分别可达63.91%±14.31%、64.07%±12.11%和(278.18±80.33)mg/L。相较于SGR-Con,SGR-Sev的出水总氨氮和亚硝氮浓度较高。反应器采用碳源分次添加的方式可使絮团具有良好的沉降性能。研究表明,微生物悬浮生长反应器宜采用碳源分次添加的方式。     

Growth variations within a farm of mussel (Mytilus galloprovincialis) held near fish cages: importance for the implementation of integrated aquaculture

Fish farming releases extensive amounts of particulate organic waste that can be exploited by bivalves in integrated culture. We tested if mussels Mytilus galloprovincialis cultured at two depths (1 and 6 m) in a raft, moored 170 m from a fish farm had greater growth than bivalves held 550 m from the fish cages. Mussel growth was monitored monthly, covering the second phase of the culture, from thinning‐out to harvest (March to November 2011). We also studied if fish solid and dissolved nutrients increased the organic content of the seston and chlorophyll‐a levels near the fish cages through weekly samples. Results showed no differences in seston, chlorophyll and physiochemical characteristics of the water among rafts. Maximum growth and Condition Index (CI) occurred during spring–summer (April–August), when mussels had access to greater food quality and quantity. Mussels cultivated close to the cages showed similar shell length, weight and CI compared with mussels distant from the fish farm. Average shell length, meat dry weight and CI at harvest were 76.31 mm, 2.51 g and 23%. Bivalves cultured distant from the fish cages displayed 26% higher biomass than the other raft at the end of the experiment. Differences in biomass were explained by the significantly higher recruitment of mussel seed observed at the raft distant from the fish cages from June to November. The lack of a significant enhancement in growth of the bivalves cultured next to finfish is discussed.     

On the drivers of cost changes in the Norwegian salmon aquaculture sector: a decomposition of a flexible cost function from 2001 to 2014

Abstract

Since 2005, Norwegian salmon farmers have experienced increasing unit costs, contrasting pre-2005 trends characterized by innovations, rapid productivity growth, and diminishing unit costs. This article investigates these cost changes using a panel of salmon producers. The drivers behind cost changes in the industry are identified for the period of 2001–2014 using a flexible cost function. In particular, it is explored how cost changes can be attributable to scale economies, negative productivity shocks, production expansion, and input prices. The results indicate that cost increases in the sector are affected by external factors out of the control of individual firms such as input prices and environmental conditions like sea lice.     

Lion's paw scallop (Nodipecten subnodosus, Sowerby 1835) aquaculture in Bahía Magdalena, Mexico: effects of population density and season on juvenile growth and mortality

This study examined the effects of density and growing season on growth and survival of juvenile lion's paw scallops (Nodipecten subnodosus) in Estero San Buto, a mangrove channel in Bahía Magdalena, Mexico. Scallops were kept in plastic mesh bags in oyster trays at three population densities (500, 1000 and 2000 organisms per tray, or low medium and high density respectively) over a period of 2 months from October to December 2001 and from February to April 2002. Growth (shell height increment) was measured every 7–12 days and mortality was evaluated at the end of the experiment (dead shell count). Overall growth was fast (0.24–0.38 mm day^?1) in comparison with other pectinids. Significant differences were found for both, density and season, with faster growth occurring at lower densities and during the fall season when the water temperature was higher. Mortality was low (0.5–3.0% 60 day^?1) except for the high‐density treatment in the fall (44% 60 day^?1). Crowding together with high water temperatures and increased metabolic oxygen demand of the scallops and possibly competition for food were the probable reasons for this high mortality. Overall, mortality was lower in the spring, when temperatures were lower, O₂ values were higher and food was more abundant.     

Development of a microsatellite multiplex genotyping tool for the fish Gilthead seabream (Sparus aurata): applicability in population genetics and pedigree analysis

In spite of the numerous studies performed in the aquacultured fish gilthead seabream, the overall structure of wild and cultivated stocks is rather confusing. In this study, we developed a 10 microsatellite genotyping tool SaGT(6+4), conformed by two polymerase chain reaction‐multiplex reactions (SaGT6 and SaGT4), which can be simultaneously combined in automatic sequencers. The utility of this tool was proven through the following applications: (i) characterization and differentiation of wild and cultivated populations; (ii) pedigree reconstruction and estimation of the effective size in a cultivated stock; (iii) ability for pedigree reconstruction under different simulated situations; and (iv) determination of genetic relationships in the absence of data from parents. Based on our results, some recommendations have been provided on the management of the screened stocks. Our results also support the use of this tool in a standardized way, to understand the actual status of gilthead seabream from both wild and cultivated populations.     

Otolith–fish size relationship in juvenile gag (Mycteroperca microlepis) of the eastern Gulf of Mexico: a comparison of growth rates between laboratory and field populations

In this study, we conducted experiments on wild-caught juvenile gag Mycteroperca microlepis from the eastern Gulf of Mexico to evaluate the effect of food availability on somatic growth and otolith growth. Juveniles were fed at two different food levels until all fish attained similar sizes. We found that food availability significantly affected growth rates. However, we also found that this manifested itself in differential otolith size. That is, slower-growing gag had larger, heavier otoliths than equal-sized faster-growing gag; an experimental result that has been observed previously among various fish species. We wanted to apply these experimental results to field-caught gag because our initial observations indicated that gag from more southern latitudes along Florida’s west coast were larger than gag from more northern latitudes, at least during the early juvenile period. Applying these relationships to regional field populations, we found that juvenile gag from the more northern latitudes appeared to grow faster than those from southern latitudes, using an otolith–fish size proxy for growth. However, examination of fish length–age relationships revealed that juvenile gag growth rates were not significantly different between regions. These results are contrary to the expectation that larger-sized gag from southern latitudes are growing faster, and suggests that other factors, such as spawning time and habitat quality may explain regional size differences.     

Identification of a heparin-binding,mesoderm-inducing peptide in the swim-bladder of the red seabream,Pagrus major: a probable fish fibroblast growth factor

The brain, pituitary, liver, ovary and swim-bladder of the red seabream (Pagrus major) were screened for the presence of a growth factor capable of stimulating the proliferation of BHK-21 cells, and the swimbladder extract was found to exert the most powerful activity. Swim-bladder derived growth factor (SBDGF) with heparin-binding ability was isolated by heparin-affinity and size-exclusion chromatography using heparin-Sepharose CL-6B and Superose 12, respectively. The relative molecular mass of SBDGF was 22,500 and the isoelectric point was 9.4. The growth of mammalian fibroblasts (BALB/3c 3T3, BHK-21) and endothelial cells (CPAE) was markedly stimulated by SBDGF. Its growth-promoting activity was also effective in fish fibroblasts (BF-2 and RTG-2), and was heat- and acid-labile. In the mesoderm-induction assay, explants of presumptive ectoderm dissected from Xenopus laevis blastulae (stage 9) were incubated with SBDGF. SBDGF induced ventral mesoderm in the explants, including hemocyte-like cells, mesenchyme and coelomic epithelium. These properties suggest that SBDGF is a fish fibroblast growth factor and that the swim-bladder is the source.     

缢蛏IGFBP基因结构及生长性状相关SNP筛选

类胰岛素生长因子结合蛋白(IGFBP)是IGF系统的一部分,主要参与IGF的运输、定位和生物活性调节。本研究采用RACE技术和长PCR技术,克隆了缢蛏IGFBP基因的cDNA和DNA全长序列,应用荧光定量PCR技术分析了缢蛏不同发育时期和不同组织中IGFBP mRNA的表达特征,并进一步筛选了IGFBP基因与生长性状相关的SNP位点。序列分析表明,缢蛏IGFBP cDNA序列全长631 bp,包括5'端非编码区60 bp,3'端非编码区136 bp和开放阅读框435 bp,编码144个氨基酸。该基因含有保守的IGFBP-N端,包含12个半胱氨酸残基,其中1～18个氨基酸为信号肽,属于分泌型蛋白。IGFBP DNA全长3 122 bp,其中包含1个内含子(2 687 bp)和2个外显子(200和235 bp)。荧光定量PCR结果显示,IGFBP mRNA在消化腺组织中表达量最高;在缢蛏的稚贝期,IGFBP mRNA呈现高表达,而在其他发育时期表达量低。在IGFBP基因中筛选到4个SNP位点,其中1个SNP位点与缢蛏的壳长和体质量呈显著相关。     

The growth of larval cod and haddock in the Irish Sea: a model with temperature,prey size and turbulence forcing

We applied a physiological individual‐based model for the foraging and growth of cod (Gadus morhua) and haddock (Melanogrammus aeglefinus) larvae, using observed temperature and prey fields data from the Irish Sea, collected during the 2006 spawning season. We used the model to estimate larval growth and survival and explore the different productivities of the cod and haddock stocks encountered in the Irish Sea. The larvae of both species showed similar responses to changes in environmental conditions (temperature, wind, prey availability, daylight hours) and better survival was predicted in the western Irish Sea, covering the spawning ground for haddock and about half of that for cod. Larval growth was predicted to be mostly prey‐limited, but exploration of stock recruitment data suggests that other factors are important to ensure successful recruitment. We suggest that the presence of a cyclonic gyre in the western Irish Sea, influencing the retention and/or dispersal of larvae from their spawning grounds, and the increasing abundance of clupeids adding predatory pressure on the eggs and larvae; both may play a key role. These two processes deserve more attention if we want to understand the mechanisms behind the recruitment of cod and haddock in the Irish Sea. For the ecosystem‐based management approach, there is a need to achieve a greater understanding of the interactions between species on the scale a fish stock is managed, and to work toward integrated fisheries management in particular when considering the effects of advection from spawning grounds and prey–predator reversal on the recovery of depleted stocks.