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Hierarchical structure of bivalve culture systems and optimal stocking density

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Abstract

Bivalve culture systems are hierarchical, with culture units being nested within culture gear, which are nested within farms, and so on. The possibility that processes acting at the scale of individual culture units may interact with high-level processes has been overlooked in carrying capacity models, although basin-scale patterns are generated at the scale of culture units. Here I study the effect of increasing basin-scale loading on unit-scale optimal stocking density (OSD). I find a curvilinear relationship, with OSD decreasing with basin-scale loading. Clearly basin-scale models should incorporate culture-unit effects. This may be achieved by using experimental studies of the clearance rate of whole culture units to complement estimates of ecophysiological processes of individuals. Such culture-unit information, along with knowledge of associated local phytoplankton depletion at various current speeds and culture-unit stocking levels, may be used to generate submodels to be included in basin-scale models. To facilitate experimental testing of across-scale effects, I develop a simple food-regulated growth model combining density dependence at the scale of individual culture units and at the scale of basins.

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Abbreviations

OSD:

Culture unit optimal stocking density

BN curve:

Biomass-density curve

N* model:

Body size-density model with hierarchical effect of number of culture units only

mN model:

Body size-density model

mNN* model:

Body size-density model with hierarchical effect of body size, culture unit population density and number of culture units combined

RMS:

Residual mean square

PEI:

Prince Edward Island

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Acknowledgments

G. Daigle (Université Laval, Québec) provided the methods used in Appendix B. I thank J.-F. Dumais, D. Lefaivre, and C.W. McKindsey for stimulating discussions and comments.

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Authors and Affiliations

  1. Institut Maurice-Lamontagne, Ministère des Pêches et des Océans, C.P. 1000, Mont-Joli, QC, Canada, G5H 3Z4

    Marcel Fréchette

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Correspondence to Marcel Fréchette.

Appendices

Appendix A: List of model parameters and variables of the simulation model

Parameter

Symbol

Value

Units

Source

Volume of hypothetical reservoirs

V

100

l

 

Water flow rate in the hypothetical reservoirs

ν

864

l day−1

 

Volume of basin

V *

1,000

l

 

Water flow rate in the basin

ν *

4,320

l day−1

 

Water temperature

T

14.0

°C

Alunno-Bruscia et al. (2000)

Phytoplankton energy density entering the basin

ρ *

10.4

J l−1

 

Phytoplankton energy density entering the hypothetical reservoirs and exiting the basin

ρ in

 

J l−1

 

Phytoplankton energy density exiting the hypothetical reservoirs

ρ

 

J l−1

 

Initial mussel soft tissue mass

m 0

0.029

g

 

Filtering coefficient

a f

50.88

l day−1

Fréchette and Bacher (1998)

Filtering exponent

λ

0.408

 

Fréchette and Bacher (1998)

Assimilation efficiency

e a

0.85

 

Fréchette and Bacher (1998)

Respiration exponent for mass

β

0.844

 

Fréchette and Bacher (1998)

Respiration exponent for temperature

γ

1.358

 

Fréchette and Bacher (1998)

Respiration coefficient

a r

13.584

J day−1

Fréchette and Bacher (1998)

Population density

N

 

Mussels reservoir−1

 

Number of culture units

N *

 

Units per basin

 

Individual mussel soft tissue mass

m

 

g

 

Appendix B: Estimation of OSD

To estimate OSD, use the derivative of B = q 1 N/(1 + q 2 N q), which is

$$ \partial B/\partial N = \left[ {\frac{{q_1 }}{{1 + q_2 N^q }}} \right] \cdot \left[ {1 - \frac{{qq_2 N^q }}{{1 + q_2 N^q }}} \right] $$
(1A)

and solve Eq. 1A for N 0 with the condition \( \partial B/\partial N = 0.029 \). The solution is

$$ N_0 = \left( {\frac{{q_1 (1 - q) - 0.058 + \sqrt {(q_1 - qq_1 - 0.058)^2 + 0.116(q_1 - 0.029)} }}{{0.058q_2 }}} \right)^{(1/q)}. $$
(2A)

N 0 is an estimate of OSD.

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Fréchette, M. Hierarchical structure of bivalve culture systems and optimal stocking density. Aquacult Int 18, 99–114 (2010). https://doi.org/10.1007/s10499-008-9198-2

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