Local to Global Mariculture Modelling

Project Documentation

Author

Dr Tormey Reimer

Published

4 August 2025

1 Table of Contents

All code and processes for this project are linked below. Note that some scripts require access to raw data which is not stored on Github. While this page (the index) has code that runs prior to rendering, all code in the subsequent pages has not been run for rendering.

1.1 Main scripts

The main scripts for this project focus on setting up the model to examine the differences in total protein, carbohydrate, lipid and nitrogen losses between feeds.

Page Description
Data Tidying Initial data tidying and preparation
Extracting Production Locations Identification and processing of mariculture production site locations
Assessing Species Potential Evaluation of species suitability for different locations
Extracting Temperatures SST data extraction and processing for model inputs
Formulating Feeds Feed composition formulation for model runs
Running Atlantic Salmon Model Atlantic salmon growth model execution

1.2 Extra scripts

The extra scripts for this project involved some exploration into potential impacts of nutrient losses. These will likely not make it into the final manuscript.

Page Description
Species Layers Spatial analysis of species distribution layers, to try and acertain impacts on vulnerable species
Relative N Inputs Analysis of nitrogen input (runoff) patterns and the relative impacts of farm nutrients

2 Results

Table 1 is a summary of all the results I’ve processed so far, basically trying to acertain all the major differences in inputs between the feeds.

The NI diet was more efficient than the PD diet. When farms were fed the NI diet they had an average FCE* of 1.08, compared to the average FCE of 1.09 when farms were fed the PD diet, and feeding the NI diet resulted in 2.1% more biomass produced with the same population compared to the PD diet.

*Note that when I refer to “FCE” here I’m talking about the “PLC weight” (weight of protein + lipid + carbohydrate) of feed, which may differ from its actual weight because of the inclusion of minerals and non-digestible material.

Despite this, nutrients lost to the environment were generally highest in the NI diet and lowest in the MD diet. In terms of total waste, the NI and PD diets were very similar. I initially thought that this was because the NI and PD diets are more similar than the MD and PD diets, but this doesn’t match up with the numbers (PD and NI diets are 63.3% the same, while the PD and MD diets are 54.3% the same). The MD diet had markedly lower total waste than either the PD or NI diets.

However, the composition of waste lost to the environment was very different between the diets, particularly in terms of proteins and carbohydrates (Figure 1). The PD diet had the lowest protein waste output and the NI diet had the highest, while the MD diet had the lowest carbohydrate and lipid waste outputs and the PD diet the highest. Overall, changing from the PD diet to the NI diet would result in a 44.6% increase in protein waste but a 36.8% and 2.2% reduction in carbohydrates and lipids respectively, while changing to the MD diet would result in a 23.4% increase in protein waste but a 36.8% and 2.2% reduction in carbohydrates and lipids respectively.

Consequently, while total waste was only 0.5% higher when farms were fed the NI diet, protein waste was 44.6% higher and nitrogen waste was 54.6% higher relative to when farms were fed the PD diet.

Proteins in the NI diet were only slightly less digestible than those used in the PD diet (Table 2), but this difference, combined with the higher protein content in the NI diet, resulted in the large difference in nitrogen lost to the environment.

Table 1: Summary of all results. Unless otherwise specified, values presented are means across all farms, summed across a single production period. In the % change columns, the colour of the text indicates whether there is an increase (red) or a decrease (green). Some cells of this table are blank - sometimes that means it doesn’t make sense to fill that cell, but sometimes it means I haven’t got to it yet.
Description Plant-dominant Marine-dominant Novel-inclusive Change from PD to MD (%) Change from PD to NI (%)
Salmon biomass produced (t) 847.5 811.6 865.2 -4.3 2.1
Feed provided (t) 909.5 885.4 921.3 -2.7 1.3
Feed provided (kg/kg salmon) 1.09 1.11 1.08 1.7 -0.8
Uneaten feed (t) 25 24.2 25.3 -3.6 1
Excreted waste (t) 101.8 75.6 102.2 -25.8 0.4
Total waste (E+U, t) 126.9 99.7 127.5 -21.4 0.5
Proportion of total waste composed of excretion (%) 80.2 75.7 80.1
Total protein waste (t) 43.5 52.2 67.3 23.4 44.6
Total carbohydrate waste (t) 62 31.6 39.3 -38.9 -36.8
Total lipid waste (t) 21.4 16 20.9 -24.9 -2.2
Proportion of protein waste from excretion (%) 77.2 75.3 81.4
Proportion of carbohydrate waste from excretion (%) 90.6 86.4 90.8
Proportion of lipid waste from excretion (%) 56.1 56.2 56
Total N from uneaten feed (t) 61.8 80.4 78.1 30 26.3
Total N from excreted waste (t) 210.2 245.6 342.4 16.8 62.9
Total N inputs (E+U, t) 272 326 420.5 19.8 54.6

I accidentally used raw total waste in Figure 1 instead of waste per kg of biomass

Figure 1: Mean waste lost to the environment in a complete production cycle when farms are fed the MD (blue), PD (green) or NI (red) diet. Errorbars show SD across all farms.

3 N inputs only

4 Spatially

Figure 2: Total N inputs per unit biomass of salmon produced when farms are fed the MD feed (top), the PD feed (middle) or the NI feed (bottom).

5 Supplemental methods

5.1 Population and biomass

Each farm’s final population was calculated by dividing the production tonnage required by the average modelled individual harvest size for each farm (when feed reference feed, Figure 3). A population timeseries was then generated using the standard mortality rate (0.06 % d\(^{-1}\)).

Figure 3: Frequency distribution of harvest sizes used to create the population timeseries for each farm, as predicted by the fish-growth model.

Using this method, a farm’s ‘population’ is not a good representation of the actual number of individuals being farmed, but it ensures each farm location is producing the correct tonnage while allowing comparisons between the different feeds.

Figure 4: Example of how the overlapping cohorts combine into a single farm production curve (in this case biomass). The left plot shows the farm biomass produced by each cohort from initialisation to harvest, while the right plot shows the combined farm biomass over the course of a single production period of 548 days.

By this method, farm biomass as predicted by the model predicted farm tonnage relatively accurately. Predicted farm biomass was within -3.2% – 3% of tonnage produced.

5.2 Feed provision and feeding response to temperature

Figure 5 shows the response of food ingested to temperature, and the food provided in response.

Figure 5: Temperature changes in potential ingestion (solid line) and amount of food provided (dotted line), relative to maximum potential ingestion. The vertical dotted lines show the actual minimum and maximum daily temperatures experienced by farms represented in the model.

5.3 Modelled experimental feeds

Table 2: Feed macronutrient details (composition in feed, digestibility).
Feed Protein Lipid Carbohydrate
Plant-dominant 36% (89.4%) 34% (96%) 21% (69.7%)
Marine-dominant 48% (90.5%) 26.2% (96%) 15.9% (80.1%)
Novel-inclusive 44.8% (86.3%) 32.8% (96%) 13.1% (69.4%)

5.4 Model sensitivity to parameter changes

Parameter sensitivity was tested by varying each parameter by \(\pm 10\)% and calculating sensitivity as \(S_p = \frac{(P_{1.1} - P_{0.9})}{0.2 \times P_1}\), where \(S\) is the sensitivity of the measured variable to changes in parameter \(p\), and \(P_{1.1}\), \(P_{0.9}\), and \(P_{1}\) are the value of the measured variable when the model is run with parameter \(p\) at 110%, 90%, and 100% of its value respectively. The population-level parameters (\(\overline{W}\), \(\Delta{W}\), \(\overline{I_{max}}\), \(\Delta{I_{max}}\), \(\overline{F}\), \(\Delta{F}\)) were tested with a population of of 5000 on a random 10% of farms, while all other parameters were tested across all farms with a population of 10 (Figure 6).

Figure 6: Sensitivity of modelled individual fish weight (blue) and total farm excretion across a full production period (red) to a 10% increase in each model parameter. Bars show mean values, error bars show standard deviation between farms.

6 Code and packages used

All analysis was conducted in R version 4.4.2 “Pile of Leaves” (R Core Team 2019). Major packages used include packages aquamapsdata version 0.1.6 (Skyttner 2020), arrow version 20.0.0.2 (Richardson et al. 2024), dplyr version 1.1.4 (Wickham et al. 2023), furrr version 0.3.1 (Vaughan and Dancho 2022), future version 1.58.0 (Bengtsson 2021), ggplot2 version 3.5.2 (Wickham 2016), lubridate version 1.9.4 (Grolemund and Wickham 2011), magrittr version 2.0.3 (Bache and Wickham 2022), rnaturalearth version 1.1.0 (Massicotte and South, n.d.), sf version 1.0.21 (Pebesma 2018), stringr version 1.5.1 (Wickham 2023), targets version 1.11.3 (Landau 2021), terra version 1.8.60 (Hijmans 2024), tidyr version 1.3.1 (Wickham, Vaughan, and Girlich 2024), units version 0.8.7 (Pebesma, Mailund, and Hiebert 2016), and worrms version 0.4.3 (Chamberlain and Vanhoorne. 2025).

For a full list of R packages used see the lockfile on Github. This manuscript was written in Quarto (Allaire et al. 2024) using TinyTex (Xie 2017) and the acronyms extension (Chaput 2024).

References

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