A Nutritional Bioenergetic Model for Farmed Fish: Effects of Food Composition on Growth, Oxygen Consumption and Waste Production

Abstract

The study of flow and transformation of energy and nutrients via mathematical modelling provides an in silico tool approach for designing scientific experiments, improving precision in aquaculture production and reducing the need for experimental animals. The proposed nutritional bioenergetics model is based on the dynamic energy budget (DEB) theory, a mechanistic framework to study individual metabolism. The model is an extension of the typical DEB models in that it includes a digestion module where the protein and non-protein food components contribute to assimilation via the concept of a synthesising unit (SU). The model allows predictions for measurable quantities of interest for aquaculture, including feeding rate, oxygen consumption, carbon dioxide, ammonia and solid waste production, under various temperatures and feeding conditions, both in terms of quantity and macronutrient composition. The feeding schedule's effects, such as the diurnal variation in waste production in response to feeding frequency, are also captured. The model quantifies the effects of the dietary protein-to-energy ratio on food intake and assimilation; energy-rich diets or those with excessive or poor amounts of protein show reduced intake. The model has been parametrised and validated for rainbow trout (Oncorhynchus mykiss) to demonstrate its capabilities. Testing the model with diverse datasets has shown that it predicts weight gain well, and to a lesser extent, oxygen consumption and total ammonia production. The proposed model could be a useful in silico tool for fish researchers, technicians and farm operators.

Keywords: DEB theory; Oncorhynchus mykiss; digestion; nutritional model; oxygen consumption; protein-to-energy ratio; total ammonia production.

Figure 1

Conceptual representation of the metabolic processes. Food is partitioned into protein and non-protein components. Energy assimilated from food is added into reserves and subsequently allocated to fuel the metabolic processes: a fixed fraction κ of the mobilised flux is allocated to somatic maintenance and growth and the remaining (1−κ) to increase and maintain maturity or to reproduction. This representation is an extension of the standard DEB conceptualisation in that it includes the digestion of food in the gut and the partitioning of food into protein and non-protein components.

Figure 2

Stomach content in % of the initial amount as a function of time at three temperatures. Fish were fed ad libitum and t = 0 is the time feeding ceased. Points indicate observations and lines model predictions. Data on gastric evacuation obtained from From and Rasmussen [52]. The different colors indicate different fish sizes, with the light red to correspond to small fish and the dark teal to larger size.

Figure 3

Relationship between stomach volume and fish weight (a), water in stomach content and dry mass of stomach content (b), and dry mass of stomach content and stomach volume (c). Points indicate observations and lines model predictions. Data from Pirhonen and Koskela [49] (red dots) and Ruohonen and Grove [53] (blue dots).

Figure 4

Weight increase of rainbow trout during a 85 day digestibility trial (points) compared to model predictions (line). Data from Zhu et al. [55].

Figure 5

Comparison of DEB model predictions for trial observations of wet weight (a), O₂ consumption and CO₂ production (b) and total ammonia nitrogen (TAN) excretion (c) using as input trial rearing conditions (temperature, trial duration, initial fish size, feed composition, ration size and feeding schedule). Different colors indicate different literature datasets and varying marker sizes indicate different feeding conditions: satiation (large), restricted (medium) and starvation (small). The equality line serves as a reference, denoting perfect agreement between observed and predicted values.

Figure 6

Simulations of fish weight, O₂ consumption, and total ammonia nitrogen (TAN) production over a 30-day experiment under different feeding conditions. Effects of feeding level (top row): 1.2% (red) and 0.8% (blue) of body weight per day, feed composition is 45% protein, 22% fat, 19% carbohydrates and feeding frequency once per day. Effects of feed composition (middle row): 45% protein, 22% fat, 19% carbohydrates (red) and 30% protein, 38% fat, 19% carbohydrates (blue), for a feeding level of 1.2% of bodyweight and feeding frequency once per day. Effects of feeding frequency (bottom row): once (red) and three times per day (blue), (feeding level 1.2% of body weight and feed composition is 45% protein, 22% fat and 19% carbohydrates. Simulations are performed at T = 15°C and for a group of fish N = 100.

Figure 7

Effects of diet composition on food intake and assimilation rates. (a) Heatmaps for a range of fractions of protein in the food and fractions of fat in the non-protein component of food. (b) Food intake and assimilation rates (expressed in ash-free dry mass, g/d) as a function of the fraction of protein in the food at two constant fractions of fat and carbohydrate contents for the non-protein component of the food (fractions of 0.7 fat (red) and 0.3 fat (blue) for the remaining food once protein is accounted for). Simulations were done for 150 g trout, at 14°C and for ADC of protein, fat and carbohydrates being 0.9, 0.9 and 0.7, respectively.

Figure 8

(a) Simulated effects of nutrient composition (protein, fat and carbohydrates) on the gross energy content of the diet for a range of protein fractions in the food and fat fractions in the non-protein component (as calculated from eq. A7). (b) Food intake (expressed in ash-free dry mass, g/d) as function of gross energy at two protein fraction levels: 60% (red) and 30% (blue) and fat fractions in the non-protein component in the range of 20%–80%.