Growth-Prediction Model for Blue Mussels (Mytilus edulis) on Future Optimally Thinned Farm-Ropes in Great Belt (Denmark)
Abstract
:1. Introduction
2. Materials and Methods
2.1. Model for Calculating Mussel-Growth History
2.2. Field Data and Data Analysis
3. Results
3.1. Actual and Predicted Growth of Mussels, from Newly Settled to Mini-Mussel
3.2. Predicted Influence of chl a and Temperature on Growth
3.3. Sensitivity to Change of Model Exponents
4. Discussion
4.1. Prediction Estimates
4.2. Importance of Thinning for Optimal Growth
Acknowledgments
Author Contributions
Conflicts of Interest
Abbreviations
BEG | BioEnergetic Growth model |
Appendix A
- Veliger larvae
- Young post-metamorphic mussels
- Juvenile and adult mussels
- Allometry, W(L)
- Filtration rate, F(W)
- Respiration, R(W)
- F = filtration rate (clearance)
- L = shell length
- Rm = maintenance respiration
- W = dry weight of soft parts
- a0 = 1.12 (factor accounting for cost of growth, assumed = 0.12 × G)
- AE = assimilation efficiency
- C = algal concentration expressed as chlorophyll (chl a)
- G = dW/dt = growth rate
- NGE = net growth efficiency
- t = time
- µ = W−1dW/dt = specific growth rate.
Eq. | Correlation | Correlation (Alternative Units) | °C | Reference |
---|---|---|---|---|
I. Veliger larvae (10−8–10−6 g) | ||||
1 | W(µg) = 2.53 × 10−9 L(µm)3.49 | W(mg) = 0.0747 × L(mm)3.49 | 12 | [23] |
2 | F(µL·h−1) = 1.25 × 10−5 L(µm)2.85 | F(µL h−1) = 132 × W(µg)0.817 | 17–19 | [23] |
3 | F(L h−1) = 10.5 × W(g)0.817 | |||
4 | Rm(nL O2 h−1) = 3.10 × W(µg)0.902 | Rm(mL O2 h−1) = 0.801 × W(g)0.903 | 15 | Figure 3 of [8] |
Potential BEG-model based on Equations (3) and (4) | ||||
5 | G = dW/dt = (C × AE × F − Rm)/1.12 | |||
6 | G(%g·d−1) = 1.228 × C × (AE/0.8) × W(g)0.817 − 1.664 × W(g)0.902 | |||
7 | µ(% d−1) = 1.228 × C × (AE/0.8) × W(g)−0.183 − 1.664 × W(g)−0.098 | |||
Estimate based on NGE = 2/3 and Equation (4); (NGE ~ 43%–73%) | ||||
8 | µ = NGE × R/[(1-NGE) × W] | [7] | ||
9 | µ(d−1) = 0.0388 × W(g)−0.097 G(d−1) = 0.0388 × W(g)0.903 | cf. [24] | ||
Estimate based on measured shell length L versus time t and Equation (1) | 15 | Figure 7 of [23] | ||
10 | L(mm) = 0.0634 + 0.0087 × t(d) G(g·d−1) = 0.01254 × W(g)0.713 | |||
11 | µL(d−1) = 0.0087 × L(mm)−1 µ(d−1) = 0.01254 × W(g)−0.287 | |||
Other relations: | ||||
F(µL·h−1) = 220 × W(µg)0.846 | F(L·h−1) = 26.2 × W(g)0.846 | 15 | Figure 2 of [8] | |
II. Young post-metamorphic mussels (10−6–10−2 g) | ||||
12 | W(mg) = 0.0247 × L(mm)2.42 | see also [5] (Figure 8) | 12 | [23] |
13 | F(mL·h−1) = 0.025 × W(µg)1.03 | F(L h−1) = 37.84 × W(g)1.03 | 12–14 | Figure 4 of [6] |
14 | Rm(nL O2 h−1) = 0.287 W(µg)1.14 | Rm(mL O2 h−1) = 0.1986 × W(g)1.14 | 12–14 | Figure 6 of [6] |
Potential BEG-model based on Equations (13) and (14) | ||||
15 | G = dW/dt = (C × AE × F − Rm)/1.12 | |||
16 | G(%g·d−1) = 4.424 × C × (AE/0.8) × W(g)1.03 − 0.413 × W(g)1.14 | |||
17 | µ(% d−1) = 4.424 × C × (AE/0.8) × W(g)0.03 − 0.413 × W(g)0.14 | |||
18 | Rm(µL O2 h−1) = 315 × W(g)0.887 | Rm(mL O2 h−1) = 0.315 × W(g)0.887 | 12 | Figure 1 of [7] |
Extended BEG-model | Based on field data | Figure 5 of [5] | ||
19 | G(mg·d−1) = 4.248 × W(mg)0.866 | µ(% d−1) = 4.248 × W(g)−0.134 | Present | |
Ad hoc BEG-model based on Equations (18) and (19) and scaling of Equation (25) | ||||
20 | G(%g·d−1) = [4.89 × C × (AE/0.8) − 5.54] × W(g)0.887 | Present | ||
III. Juvenile and adult mussels (10−2–1 g) | ||||
21 | W(mg) = 0.00215 L(mm)3.40 | Figure 8 of [5] | ||
22 | F(L h−1) = 7.45 × W(g)0.66 | 10–13 | Equation (8) of [3] | |
23 | Rm(µL O2 h−1) = 475 × W(g)0.663 | Rm(mL O2 h−1) = 0.475 × W(g)0.663 | 14 | Figure 1 of [7] |
Basic BEG-model based on Equations (23) and (24) | ||||
24 | G = dW/dt = (C × AE × F − Rm)/1.12 | [25] | ||
25 | G(%g·d−1) = 0.871 × C × (AE/0.8) × W(g)0.663 − 0.986 × W(g)0.66 | [3] | ||
26 | µ(% d−1) = 0.871 × C × (AE/0.8) × W(g)−0.34 − 0.986 × W(g)−0.34 | |||
27 | Modified BEG-model: G(mg·d−1) = C1 × W(mg)0.66 | Equation (5) of [4] | ||
28 | C1 = 0.1047 × m1 × (0.871 × m2 × n2 × C × AE/0.80 − 0.986 × m3 × n3) | |||
29 | m1 = 1.12/[1 + (a0 − 1)n3 (1 − E)]; m2 = 1 − E; m3 = 1 − 0.9(1 + C/C0)E; | |||
30 | E = exp(−C/C0); C0 = 0.4 µg chl a l−1; n2 = [1 + 0.0251(T − TF)]; | |||
31 | n3 = 1.54(T−TQ)/10; TF = 11.5 °C; TQ = 14 °C |
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m1 = 1.12/[1 + (a0 − 1)n3 (1 − E)] |
m2 = 1 − E |
m3 = 1 − 0.9(1 + C/C0)E |
E = exp(−C/C0) |
C0 = 0.4 µg chl a L−1 |
n2 = [1 + 0.0251(T − TF)] |
n3 = 1.54(T−TQ)/10 |
TF = 11.5 °C; TQ = 14 °C |
T = 15 °C | |||
C (µg chl a L−1) | 2 | 2.5 | 3 |
t30 (d) | 155 | 105 | 80 |
t45 (d) | 249 | 170 | 129 |
C = 2.5 µg chl a L−1 | |||
T (°C) | 5 | 10 | 15 |
t30 (d) | 115 | 109 | 105 |
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Larsen, P.S.; Riisgård, H.U. Growth-Prediction Model for Blue Mussels (Mytilus edulis) on Future Optimally Thinned Farm-Ropes in Great Belt (Denmark). J. Mar. Sci. Eng. 2016, 4, 42. https://doi.org/10.3390/jmse4030042
Larsen PS, Riisgård HU. Growth-Prediction Model for Blue Mussels (Mytilus edulis) on Future Optimally Thinned Farm-Ropes in Great Belt (Denmark). Journal of Marine Science and Engineering. 2016; 4(3):42. https://doi.org/10.3390/jmse4030042
Chicago/Turabian StyleLarsen, Poul S., and Hans Ulrik Riisgård. 2016. "Growth-Prediction Model for Blue Mussels (Mytilus edulis) on Future Optimally Thinned Farm-Ropes in Great Belt (Denmark)" Journal of Marine Science and Engineering 4, no. 3: 42. https://doi.org/10.3390/jmse4030042
APA StyleLarsen, P. S., & Riisgård, H. U. (2016). Growth-Prediction Model for Blue Mussels (Mytilus edulis) on Future Optimally Thinned Farm-Ropes in Great Belt (Denmark). Journal of Marine Science and Engineering, 4(3), 42. https://doi.org/10.3390/jmse4030042