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.     

Reproductive resilience or sweepstakes recruitment? Assessing drivers of lifetime reproductive success in exploited marine fish

Understanding the processes that drive reproductive success in marine fish stocks is critical to effective fisheries management. These processes can be difficult to investigate, especially in age-structured populations, because they occur at transgenerational scales. Reproductive success is often attributed to a small portion of the adult population (<0.01%) and thought to be driven primarily by random external factors, consistent with the concept of sweepstake reproductive success (SRS). A competing concept, the reproductive resilience paradigm, posits that fishes have evolved complex spawner-recruit systems to achieve lifetime reproductive success and maintain population stability within highly variable environments. Here, we examine these two concepts. First, we analyse the popular sport fish red drum (Sciaenops ocellatus, Sciaenidae), drawing on genetic and reproductive data to estimate a plausible range for the ratio of effective population size ($N_e$) to adult abundance ($N_A$) and to infer variance in lifetime reproductive success ($V_k^{*}$). Then, we synthesize available data and infer $V_k^{*}$ for two other fishes that have $N_e/N_A$ ratios reportedly >0.10, the southern bluefin tuna (Thunnus maccoyii, Scombridae) and the silver seabream (Chrysophrys auratus, Sparidae). Although commonly regarded as an SRS species, red drum did not meet the SRS criterion. Overdispersed $V_k^{*}$ values were inferred for all three species, with those for red drum and silver seabream being dependent upon population-closure assumptions. Results are presented within the conceptual framework of reproductive resilience, considering the roles of random extrinsic forces versus evolved traits to achieve lifetime reproductive success and population stability in high and variable mortality environments.     

The effects of thermal amplitude on the growth of Chinese shrimp Fenneropenaeus chinensis (Osbeck, 1765)

Effects of thermal amplitude of diel fluctuating temperature on the growth, food consumption, food conversion efficiency and apparent digestibility coefficient of Chinese shrimp, Fenneropenaeus chinensis (Osbeck), with initial body weight of 0.36 ± 0.04 g were studied at average temperature 25, 28 and 31 °C from May to July, 2000. Among four diel different fluctuation amplitudes of ± 1, ± 2, ± 3 and ± 4°C, the growth rate of shrimp at 25 ± 2, 25 ± 3, 28 ± 2 and 31 ± 1 °C were significantly higher than those at corresponding constant temperatures of 25, 28 and 31 °C, respectively, while growth rate at 31 ± 4 °C was significantly lower than at 31 °C. There is a trend that the optimal thermal amplitude for shrimp growth decreased with the increase of average temperature in the present study. The growth rate of Chinese shrimp was a quadratic function of the thermal amplitude at the same average temperature. Such a growth model may be described by$G={\beta }_0+{\beta }_1\left(\mathrm{TA}\right)+{\beta }_2{\left(\mathrm{TA}\right)}^2$where G represents the specific growth rate on a 33-day basis, TA is thermal amplitude in degree Celsius, β₀ is intercept on G axis, and β₁ and β₂ are the regression coefficients. The optimal thermal amplitude for the growth of shrimp at sizes of this experiment at average temperature of 25, 28 and 31 °C was estimated to be ± 2.0, ± 2.2 and ± 1.4 °C, respectively. The changes of food conversion efficiency were similar to the growth rate, while the trends of food consumption of shrimp between fluctuating temperature and constant temperature were variable at different average temperatures. There was no significant difference in apparent digestibility coefficient between diel fluctuating temperatures and corresponding constant temperatures. Therefore, more food consumption, high food conversion efficiency and more energy partitioned into growth might account for the enhancement in the growth of shrimp at the diel fluctuating temperatures in the present study.     

Feeding of the short-spined sea urchin <Emphasis Type="Italic">Strongylocentrotus intermedius</Emphasis> on macroalgae and benthic animals

To examine the feeding ecology of the sea urchin Strongylocentrotus intermedius, two types of macroalgal diet (kelp Saccharina longissima and red alga Ptilota filicina) and four types of benthic animal diet [barnacle Balanus glandula, limpet Lottia cassis, free-living Perinereis aibuhitensis and P. aibuhitensis attached to a stainless steel wire (wired polychaete)], were separately or simultaneously provided for urchins of 5- to 60-mm test diameter (TD). Sea urchins of even 3-mm TD could graze the kelp, and began to graze the red alga, the wired polychaete and limpet by 5-mm TD, the barnacle by 8-mm TD and the free-living polychaete by 15-mm TD, respectively. These results suggest that the variety of macroalgae and benthic animals which the urchin can graze increases with the ontogeny of their feeding organs, motility and ability to catch animals. Both juvenile and adult sea urchins preferred to eat the polychaete as well as the kelp fronds. Feed conversion efficiency and daily growth rate of the small sea urchins fed benthic animals like the polychaete were higher than those fed macroalgae. The sea urchins are likely to grow better when feeding on animals than on macroalgae, even in habitats where they can access adequate quantities of kelp.     

Hydrodynamic characteristics of a full-scale kelp model for aquaculture applications

Hydrodynamic characteristics are needed to optimize the design of kelp aquaculture systems. To support this need, the objective of this study was to resolve both the normal and tangential drag forces acting on a dense aggregate of kelp blades using full-scale physical model tests. The physical model was designed to match the exposed length, individual blade flexural rigidity, the number of blades per unit width, the mass/length of biomass, and the aggregate mass density of kelp cultured at the University of New England experimental aquaculture lease site in Saco Bay, Maine USA. Tow tests were conducted at the United States Naval Academy in a tank with the dimensions of 116m × 7.9m × 4.9 m. The large tank size enabled the use of the full-scale physical model, minimizing dynamic similarity issues. In a series of tests, the model was towed in orientations both aligned and perpendicular to the tow direction. Horizontal and vertical reaction forces were measured for five tow speeds, along with the deflection of the dense kelp aggregate. With these datasets and the wet weight biomass per length of the model, normal and tangential drag forces were calculated. Drag components were processed into corresponding normal and tangential drag-area values. The drag-area representation was chosen since reference areas were ambiguous for both the actual kelp and model. At the higher speeds, the total horizontal drag in the aligned configuration were slightly lower than for the perpendicular orientation. Normal drag-areas as a function of tow speed ranged from 2.36 m²/m to 1.39 m²/m for the aligned case and from 2.49 to 1.88 m²/m for the perpendicular case. Tangential drag-areas as a function of tow speed ranged from 0.264 m²/m to 0.0325 m²/m for the aligned case and from 0.213 to 0.0415 m²/m for the perpendicular case. A transition from a bluff body to a streamlined body occurred as the tow speeds increased. To investigate this transition, horizontal components of the normal and tangential drag forces were reconstructed with the results of the tow tests. The reconstructed forces were obtained using a force balance system of equations with drag-area values for tow speeds less than 0.25 m/s extrapolated from the experimental datasets. For both aligned and perpendicular orientations, the model-aggregate reconfigured at a threshold of 0.25 m/s. We defined the threshold for reconfiguration as the tow speed at which the horizontal component of tangential drag equaled or exceeded the horizontal component of the normal drag. The drag-area results from this study can be incorporated into a dynamic fluid-structure interaction model representing kelp aggregates as a finite element beam prescribed with in-situ values of length, volume, mass density and flexural-rigidity of kelp material.     

Epiphytism on Blades of the Edible Kelps Undaria pinnatifida and Saccharina latissima Farmed under Different Abiotic Conditions

The kelps Undaria pinnatifida and Saccharina latissima are economically valuable edible seaweeds. Although epiphytism is a major problem affecting the productivity and quality of farmed seaweeds, studies of its effects on kelp aquaculture are scarce. We investigated the effects of epiphytism in two U. pinnatifida and S. latissima culture grounds located in two different parts (exposed and sheltered) of a bay (ría) in Galicia (NW Spain). Epiphytic organisms on blades were identified and their abundance was documented. The percentage of the total blade covered with epiphytes was measured for both kelp species in order to estimate the blade biomass that must be discarded during processing for human consumption. Algae, hydroids, and crustaceans were the most common epiphytic organism on kelp blades; colonies of the hydroid Obelia geniculata and harpacticoid copepods were the most abundant epiphytes. Abundance of epiphytes on the blades of both kelps was significantly higher for fronds growing in the sheltered area of the bay compared to those farmed at the exposed location. Different environmental conditions and other factors, such as the proximity of mussel cultures to kelp cultures, may be important contributors to epiphytism. The results presented here can be used to devise better ways for kelp aquaculture facilities to diminish the negative effects of epiphytism.     

Phenology of the kelp <Emphasis Type="Italic">Saccharina japonica</Emphasis> and its effect on the gonad index of the sea urchin <Emphasis Type="Italic">Mesocentrotus nudus</Emphasis> across a depth gradient off the Sanriku coast,northeastern Japan

The kelp Saccharina japonica is a dominant seaweed along the Sanriku coast where fisheries for sea urchin and abalone are among the most prosperous in Japan. We investigated the phenology of the kelp at depths of 6, 9 and 12 m from March 2015 to March 2016. The sea urchin Mesocentrotus nudus, a dominant herbivore off the coast, was also monitored with respect to its gonads for fishery use. Juvenile kelp appeared in March and rapidly elongated until May. Weight of the kelp significantly increased from April to July. Sori formation commenced from September and ceased in December. Density and biomass of the kelp were higher in the shallower sites than in the deeper one throughout the year. The highest biomasses recorded between July and October were 3773, 1939 and 501 g dry weight m^?2 at depths of 6, 9 and 12 m, respectively. No regrowth of kelp blades was observed, indicating that S. japonica in this region has an annual life cycle. The gonad index of the sea urchin in the 12-m site was lower than that in the 6- and 9-m sites, indicating the close relation of the gonad index with the biomass of the kelp.