Modelling fish growth: Model selection,multi-model inference and model selection uncertainty

Model selection based on information theory is a relatively new paradigm in biological sciences with several advantages over the classical approaches. The aim of the present study was to apply information theory in the area of modelling fish growth and to show how model selection uncertainty may be taken into account when estimating growth parameters. The methodology was applied for length–age data of four species of fish, taken from the literature. Five-candidate models were fitted to each dataset: von Bertalanffy growth model (VBGM), generalized VBGM, Gompertz growth model, Schnute–Richards growth model, and logistic. In each case, the ‘best’ model was selected by minimizing the small-sample, bias-corrected form of the Akaike information criterion (AIC). To quantify the plausibility of each model, given the data and the set of five models, the ‘Akaike weight’ $w_i$ of each model was calculated. The average model was estimated for each case based on $w_i$. Following a multi-model inference (MMI) approach, the model-averaged asymptotic length ${\overline{L}}_{\infty }$ for each species was estimated, using all five models, by model-averaging estimations of L_∞ and weighting the prediction of each model by $w_i$. In the examples of this study, model selection uncertainty caused a magnification of the standard error of the asymptotic length of the best model (up to 3.9 times) and thus in all four cases estimating L_∞ from just the best model would have caused overestimation of precision of the asymptotic length. The VBGM, when used for inference, without being the best model, could cause biased point estimation and false evaluation of precision. Model selection uncertainty should not be ignored even if VBGM is the best model. Multi-model inference by model-averaging, based on Akaike weights, is recommended for making robust parameter estimations and for dealing with uncertainty in model selection.     

Effects of temperature and water calcium concentration on growth,survival and moulting of freshwater crayfish,Paranephrops zealandicus

Two 3-month experiments were conducted to investigate the effects of temperature and water calcium concentrations on growth, survival and moulting of freshwater crayfish (Paranephrops zealandicus). Both experiments were conducted using three replicates of five treatments (water temperatures of 14, 16, 18, 20 and 22 °C for Experiment 1 and water calcium concentrations of 0, 5, 10, 30 and 80 mg/L for Experiment 2). Growth rates increased with water temperature (maximum specific growth rate = 0.57) but were unchanged with increased water calcium concentration. Variability in growth rates decreased with increased water calcium concentrations. Survival decreased as water temperatures exceeded 16 °C and increased with water calcium concentrations above 10 mg/L. Inter-moult period decreased from > 90 ± 20 days at water temperatures of 14 °C to ∼ 40 ± 10 days at water temperatures > 20 °C. Moult increment of the crayfish was unaltered by either water temperature or water calcium concentrations. The optimum water temperature for productivity under conditions employed was 16 °C.     

Use of artificial substrates in the culture of Litopenaeus vannamei (Biofloc System) at different stocking densities: Effects on microbial activity,water quality and production rates

Although the use of artificial substrates can favor shrimp culture, some studies indicate that their presence in growth tanks does not improve water quality or the performance of the animals. One objective of this study was to evaluate whether the presence of artificial substrates modifies the microbial activity and the water quality of the culture of Litopenaeus vannamei with bioflocs. The substrate effects on the shrimp performance and the relationship between these effects and the stocking density/biomass of shrimp were also evaluated. The experiment consisted of four treatments: D238: 238 shrimp m⁻³; D238 + S: 238 shrimp m⁻³ + substrates; D473: 473 shrimp m⁻³; D473 + S: 473 shrimp m⁻³ + substrates. Twelve experimental units of 850 L were stocked with juvenile L. vannamei (2.6 g) that were grown for 34 days. The substrates did not appear to affect water quality since the concentrations of orthophosphate, ammonia and nitrite were not significantly different in tanks with or without substrates. The periphyton biomass was low and the biological activity on the substrates was not significant, indicating that the water quality variables were mainly controlled by the microbial community associated with the suspended bioflocs. The shrimp grown in the presence of the substrate exhibited greater weight gain (D238 + S = 1.40 ± 0.05 and D473 + S = 1.20 ± 0.04 g week⁻¹) than those grown without substrates (D238 = 0.73 ± 0.04 and D473 = 0.44 ± 0.13 g week⁻¹). The final biomass was 314% greater in the tanks with substrates. The shrimp survival was significantly higher in the tanks with substrates (93.9 ± 2.4%) than in the tanks without substrates (42.5 ± 35.9%). The results indicate that the substrates served to increase the surface area of the tank and to reduce the relative stocking density, which appears to reduce the stress levels of shrimp, indicated by higher shrimp performance. In tanks with higher biomass, where the negative effects of intensification were most severe, the presence of the substrates had a positive effect on the production indices.     

Quantification by fluorescent in situ hybridization of bacteria associated with Litopenaeus vannamei larvae in Mexican shrimp hatchery

The bacterial composition in the hatchery at Unidad Experimental Peñasco (UEP) of the Sonora University, Mexico, was studied by using Fluorescent In Situ Hybridization (FISH) with rRNA-specific oligonucleotide probes. We applied fluorochrome-labeled polyribonucleotide probes to identify and enumerate marine shrimp culture hatchery related bacteria. Quantitative whole-cell hybridization experiments using α-, γ- and δ-Proteobacteria, and high and low G + C Gram-positive bacteria accounted for 20.8 ± 3.4% to 69.3 ± 3.3% of the total 4′,6-diamidino-2-phenylindole (DAPI)-stained cells in most samples. As predicted in a previous study, marine high G + C and γ-Proteobacteria predominated in different shrimp life sub-stages. The elevated percent of high G + C and γ-Proteobacteria, extending from nauplii to mysis stages, suggest that they represent a large and significant fraction of the total picoplankton biomass in Litopenaeus vannamei larval culture.     

Availability of essential amino acids,nutrient utilisation and growth in juvenile black tiger shrimp,Penaeus monodon,following fishmeal replacement by plant protein

Two trials with juvenile black tiger shrimp (Penaeus monodon) were undertaken to study the effects of replacing fishmeal by different levels of plant proteins on growth performances and nutrient utilisation of shrimp in semi-intensive conditions (Expt. 1) and on the availability of dietary nitrogen (N) and amino acids (Expt. 2). Five isoproteic diets (on crude protein basis) were formulated to contain 34, 24, 16, 8, or 0% fishmeal, with fishmeal being replaced by a mixture of plant protein (corn gluten meal, wheat gluten, and rapeseed meal). In Expt. 1, the shrimp (initial body weight, IBW 1.5 ± 0.1 g) were reared in earthen ponds for 144 days and fed one of the experimental diets. Apparent digestibility of nutrients and AA were assessed in Expt. 2, using 150 L tanks and shrimp of 12.8 ± 0.4 g IBW. After 144 days in grow-out ponds, shrimp fed the diet with 24% of fishmeal had similar growth as those fed the control diet containing 34% fishmeal (0% replacement). When 50% or more of the fishmeal were replaced, weight gain as well as N and energy gains significantly decreased. Digestibility of dry matter, protein and energy was also significantly lower in all fishmeal-replaced diets. In particular, leucine digestibility decreased by 26% at 100% replacement, which was significantly correlated to an increased incorporation of corn gluten meal. Our data confirm the need to improve our knowledge on AA availability and raw material quality in order to improve fishmeal replacement in P. monodon diets.     

The effects of food and the sum of effective temperature on the embryonic development of the seahorse,Hippocampus kuda Bleeker

The effect of different food (live Acetes spp., live Mysis spp., frozen Mysis spp., and mixed food of 50% live Acetes spp. and 50% frozen Mysis spp.) on gonad development of seahorses, Hippocampus kuda Bleeker, was evaluated in this experiment. The developmental durations of testes and ovary of seahorses were significantly different among the four experimental treatments. The live Acetes spp. treatment presented the shortest developmental durations to stage V, which were 87.6 ± 3.84 days and 89.2 ± 3.71 days, respectively, for ovary and testes. The frozen Mysis spp. treatment had the longest developmental durations (F_3,15 = 13.284, P < 0.05). The relationship between developmental duration of the ovary and gonad developmental stages could be formulated: Y₁ = 12.04x + 24.36 (r² = 0.9722, n = 16, P < 0.05). The gonadosomatic index (GSI) of parent seahorses among the four treatments differed significantly (F_3,15 = 18.364, P < 0.05). The standard GSI of seahorses fed live Acetes spp. was 15.64 ± 1.65%, which was the highest. Feeding live food had a significant effect on the fecundity and spawning of seahorses. The fecundity and spawning number of the live Acetes spp. treatment were 598 ± 45.49 and 552 ± 49.19 individuals, respectively, which were dramatically higher than those of frozen treatment (F_3,19 = 34.152, P < 0.05). Live food also had a similar effect on the fertilization and hatching rate during the embryonic development of seahorses (F_3,19 = 11.386, P < 0.05). Food treatment could also induce an indirect effect on survival rate of juveniles through gonadal and embryonic development of the parents (F_3,15 = 14.519, P < 0.05). In this experiment, the mortality within parent seahorses in the frozen Mysis spp. treatment was the highest (15.1 ± 6.55%), and the survival of juveniles was the highest in the live Acetes spp. treatment (90.4 ± 2.26% at 10 days). In conclusion, feeding live Acetes spp. significantly benefited the gonadal and embryonic development of H. kuda.The effect of temperature (22 °C, 24 °C, 26 °C, 28 °C, 30 °C and 32 °C) on the hatching time of H. kuda was also studied. We demonstrated that the higher the temperature, the shorter the hatching time, as well as the higher the hatching speed. The relationship between hatching time and temperature could be expressed: T = − 39.337 t + 677.75 (r² = 0.9755, n = 30, P < 0.05). In this finding, we provided the sum of effective temperature (SET) and threshold temperature of embryonic development of H. kuda (14066.9 °C h^− 1 and 13.7 °C, respectively). This new information on the effect of feeding type and culture temperature is beneficial for the commercial rearing and breeding industry of this species.     

Effects of storage duration and storage media on initial and post-eyeing mortality of stored ova of rainbow trout Oncorhynchus mykiss

The effects of storage duration and storage media on the viability of unfertilized eggs of rainbow trout from fertilization to hatching stage was studied. The unfertilized eggs were stored in coelomic fluid and Cortland artificial media buffered with Tris–HCl (C₄H₁₁NO₃–HCl) and Hepes (C₈H₁₈N₂O₄S) at 2–3 °C. These eggs were fertilized after 0 (i.e. control eggs fertilized prior to storage), 2 and 9 days post-stripping using fresh, pooled sperm obtained from 4 to 5 males. According to the results of present study, after 2 days of storage, no significant (p > 0.05) change in survival to eyeing and hatching of eggs stored in coelomic fluid (85.5 ± 4.8%, 80.2 ± 6.3%) and Cortland medium buffered with Hepes (73.3 ± 4.1%,68.1 ± 4%) was observed in comparison to the control (82.6 ± 8%,78.7 ± 7.8%). However, eyeing and hatching survival rates of eggs stored for the same period in Cortland medium buffered with Tris–HCl (44.5 ± 7%,34.2 ± 8.2%) decreased significantly (p < 0.05) in comparison with the control. Also, eggs stored for 2 days in Cortland medium buffered with Tris–HCl (25 ± 6.7%) had significantly (p < 0.05) greater eyed egg mortality compared to the control (4.7 ± 0.6%), while no significant (p > 0.05) differences were observed between eyed egg mortality rates of eggs stored in coelomic fluid (6.7 ± 2.1%) and Cortland medium buffered with Hepes (7.3 ± 0.9%) compared to control. After 9 days of storage, the eggs that were stored in coelomic fluid showed no significant (p > 0.05) differences in eyeing (77.5 ± 7.2%) and hatching (67 ± 8.1%) rates in comparison with control, while both Cortland storage media exhibited significant (p < 0.05) loss in eyeing (44.4 ± 11.5%, 24.7 ± 13.8% for Hepes and Tris–HCl, respectively), and hatching (24.5 ± 5.9%, 19.2 ± 14.4% for Hepes and Tris–HCl, respectively) in comparison with control. Furthermore, eyed egg mortality increased significantly (p < 0.05) in coelomic fluid (14 ± 2.9%), media buffered with Hepes (43 ± 6.2%) and Tris–HCl (49.3 ± 26.9%) compared to control. Based on this study, unfertilized eggs of rainbow trout can be successfully stored in coelomic fluid for 9 days at (2–3 °C) without significant loss of fertility. However, storage within a similar period in artificial media showed lower fertilization rates and higher eyed egg mortality compared to coelomic fluid.     

Growth,survival and feed efficiency for post-metamorphosed Atlantic cod (Gadus morhua) reared at different temperatures

Two growth trials were completed on post-metamorphosed Atlantic cod (Gadus morhua) for a period of four weeks to determine the optimal temperature for best growth and feed efficiency. The same experiment was repeated twice under similar conditions to determine the effect of four temperature regimes (10, 12, 14 and 16 °C) on randomly selected juvenile cod with an initial weight ranging from 0.34 to 0.51 g. Post-metamorphosed cod grown at 14 and 16 °C were significantly larger at the end of the experiments than the fish grown at 10 or 12 °C, with specific growth rates following a similar trend (p < 0.05). Fish held at 16 °C utilized feed less efficiently than those held at the lower temperatures in experiment II and the highest feed efficiency was observed in fish held at 10 °C (p < 0.05). The results of the feed efficiency and the maximum growth per degree (dG / dT_max) in experiment II suggest that the feed efficiency was likely maximized at a lower temperature than those used in this study. By using data collected from sub-samples of fish in experiment II, maximum growth (G_max) was estimated at 14.5 °C using a growth temperature model. Cannibalism was a problem in the first experiment but was greatly reduced in experiment II by feeding a larger size feed pellet (2 mm).     

Combined effects of feeding enriched rotifers and antibiotic addition on performance of striped trumpeter (Latris lineata) larvae

Striped trumpeter have a complex and extended larval phase and are difficult to culture. Two experiments were conducted in replicated, 300-l hemispherical tanks to determine if larval survival, growth, bacterial or fatty acid profile were improved by feeding non-enriched rotifers or rotifers enriched with algae or commercially available products, as well as the effect of an antibiotic, oxytetracycline (OTC). Larvae were stocked at 25 l^− 1 and 15 l^− 1 and reared until Day 16 and Day 19 in Experiments 1 and 2, respectively. In Experiment 1, the feeding treatments were non-enriched rotifers, or rotifers enriched on algae, DHA Selco (a fish oil based emulsion) or RotiMac (dried Schizochytrium). There were no significant differences in mean survival (± SD) across treatments, which were generally low at 14.6 ± 5.2%. Larvae reared on rotifers fed DHA Selco and RotiMac, had significantly higher proportions of incorporated DHA but no significant increase in growth. In Experiment 2, larvae were fed rotifers enriched on DHA Selco or AlgaMac 2000 and reared with or without the daily addition of 25 mg l^− 1 OTC. At Day 19, there was significantly higher survival for larvae reared on AlgaMac 2000 and OTC, (37.4 ± 5.6%), than DHA Selco and OTC, (16.0 ± 7.4%), AlgaMac 2000 without OTC (7.0 ± 8.0) and DHA Selco without OTC (3.3 ± 1.2). Larvae reared with OTC were larger (279 ± 58 μg and 7.4 ± 0.2 mm) than without OTC (177 ± 40 μg and 6.3 ± 0.2 mm). The addition of antibiotics did not significantly influence fatty acid profiles of larvae. There were no significant differences in the percentage of DHA, 27.6 ± 2.8%, EPA 4.6 ± 1.0% or ARA 4.9 ± 0.4%. Larvae reared with OTC had significantly less ‘grey gut’ (a measure of intestinal dysfunction). The results indicated that bacterial infection was a major source of mortality in striped trumpeter larvae and compromised larval growth. Assessment of the bacterial flora indicated that antibiotic use reduced the bacterial load, but did not eliminate potential pathogens. Our study suggests that microbial control has a greater influence than lipid nutrition on the survival and growth of larvae during the rotifer feeding stage.     

Effect of different total suspended solids concentrations on the growth performance of Litopenaeus vannamei in a BFT system

Decreased Litopenaeus vannamei performance resulting from excess total suspended solids (TSS) has been highlighted in previous studies. Therefore, the aim of this study was to evaluate the effect of different TSS concentrations on the L. vannamei growth performance in a BFT system for 42 days. Five TSS concentrations were used—250, 500, 1000, 2000, and 4000 mg L⁻¹—in three replicates identified as T250, T500, T1000, T2000, and T4000, respectively, in 200 L-tanks each. Dissolved oxygen concentration (DO) was maintained above 5 mg L⁻¹. Shrimp with an initial average weight of 4.57 ± 1.07 g were stocked at a density of 277 shrimp m⁻². The physical and chemical parameters were monitored. Water quality parameters and animal performance were subjected to analysis of variance (ANOVA − one way). The physical and chemical parameters were within the recommended range for L. vannamei. Weekly weight gain, feed conversion rate, survival, and productivity showed no significant differences (p > 0.05). The high TSS concentrations did not seem to affect the performance of this species when DO concentrations were maintained above 5 mg L⁻¹.     

Nutrient discharge,sludge quantity and characteristics in biofloc shrimp culture using two methods of carbohydrate fertilization

The aim of this study was to evaluate the effect of two methodologies of carbohydrate fertilization on the volume and characteristics of effluent from intensive biofloc shrimp cultivation. Six fiberglass circular tanks (50 m² each) were divided into two treatments. In the treatment called continuous (CONT), the tanks received daily molasses fertilization throughout the entire rearing period. In the treatment named initial (INI), molasses was used only in the early weeks of cultivation. Juvenile Litopenaeus vannamei (0.87 ± 0.10 g) were stocked at a density of 180 animals m⁻² and cultured during 12 weeks until they reached an average weight of 12 g. The tanks were operated with no water exchange and the total suspended solids concentration were kept between 300 and 400 mg L⁻¹ using settling chambers. The sludge produced and the wastewater at harvest were quantified and their characteristics were determined. The production of TSS in the CONT treatment was higher (0.25 kg of solids per kg of applied feed) than in the INI treatment (0.16 kg kg⁻¹) (P < 0.05). The analysis of the sludge revealed a high amount of volatile solids in both treatments, between 636 and 702 g kg⁻¹. However, due to the elevated sludge nitrogen content, the carbon to nitrogen (C:N) ratio was low, with values of 6.4 ± 1.4 and 7.5 ± 1.6 for INI and CONT respectively. The BOD:TSS ratio was also low in both treatments, but the INI showed lower values (10.3 ± 0.6%) than the CONT (14.9 ± 0.0%) (P < 0.05). Both fertilization strategies were able to modify the characteristics of sludge produced during cultivation. Moreover, the high nitrogen and sulfate content of the sludge in both treatments indicated that it may be difficult to use an anaerobic digestion process to treat sludge. In the INI treatment tanks, the sludge is partially stabilized, while in the CONT there was a greater need for stabilization.     

Study of sex ratio in progeny of a complex Oreochromis hybrid,the Florida red tilapia

This paper reports a study on the progeny sex-ratio distribution in the Florida red tilapia. This hybrid originated as a cross between O. mossambicus male and O. urolepis hornorum female, which was then crossed with O. niloticus and O. aureus in order to improve its growth rate and its resistance to low temperature. We have studied the sex-ratio of 111 progenies from 46 females and 12 males, where the male percentage varied between 5% to 89%. The analysis of distribution showed three groups characterised by a mean male percentage of 26.7 ± 9.8; 50.0 ± 8.9 and 70.3 ± 5.5%. The stability of sex ratios in repeated single pair matings and the parental influence on progeny sex ratios obtained are in agreement with a polygenic basis of sex determination in this complex hybrid.     

Dietary phosphorus requirement of large yellow croaker,Pseudosciaena crocea R

A study was conducted to estimate the optimum requirement of dietary phosphorus for large yellow croaker in floating sea cages (1.0 × 1.0 × 1.5 m). Five practical diets were formulated to contain graded levels (0.30%, 0.55%, 0.69%, 0.91% and 1.16%) of available phosphorus from dietary ingredients and monocalcium phosphate (MCP). Each diet was randomly assigned to triplicate groups of 180 juvenile fish (initial body weight, 1.88 ± 0.02 g). Fish were fed twice daily (5:00 and 17:00) to satiation for 8 weeks. During the experimental period, the water temperature fluctuated from 26.5 to 32.5 °C, salinity from 32‰ to 36‰ and dissolved oxygen was more than 7 mg l^− 1. Specific growth rate (SGR) significantly increased with increasing available phosphorus from 0.30% to 0.69% of diet (P < 0.05), and then leveled off. The body composition analysis showed that the whole-body ash and lipid, as well as phosphorus content in the whole body, vertebrae and scales were significantly affected by dietary available phosphorus level (P < 0.05). Broken-line analysis based on SGR indicated the minimum available phosphorus requirement for the optimal growth of large yellow croaker was 0.70%. Based on the phosphorus content in either vertebrae or whole body, the requirements were 0.89% and 0.91%, respectively.