Potential for production of ‘mini-mussels’ in Great Belt (Denmark) evaluated on basis of actual and modeled growth of young mussels Mytilus edulis

Abstract

The present study is a first step towards evaluation of the potential for line-mussel production in the Great Belt region between the Kattegat and Baltic Sea, Denmark. We present experimental results for actual growth rates of juvenile/adult mussels Mytilus edulis in suspended net bags in terms of shell length and dry weight of soft parts during extended periods (27–80 days) in the productive season in the first 6 series of field experiments, including 4 sites in Great Belt and 2 sites in Limfjorden, Denmark. Data were correlated and interpreted in terms of specific growth rate (μ, % day⁻¹) as a function of dry weight of soft parts (W, g) by a previously developed simple bioenergetic growth model μ = aW ^−0.34. Results were generally in good agreement with the model which assumes the prevailing average chlorophyll a concentration at field sites to essentially account for the nutrition. Our studies have shown that M. edulis can grow from settlement in spring to 30 mm in shell length in November. We therefore suggest line farming of 30 mm ‘mini-mussels’ during one growth season, recovering all equipment at the time of harvest and re-establishing it with a new population of settled mussel larvae at the beginning of the next season, thus protecting the equipment from the damaging weather of the Danish winter season. The growth behavior during the fall–winter season was recorded in an additional 7th series of mussel growth experiments on farm-ropes to show the disadvantage of this period.

Appendix: Note on experimental time series

If an extended time series of data W(t) is available, it is possible to obtain more detail in terms of how μ varies with increasing size W. The first data point in an experimental time series is normally assigned the arbitrary value of t = 0 at size W ₀, but on a true time scale of mussel life this should be some time t _s > 0. We therefore shift the time series W(t) by t _s to W(t _s + t) and examine the R ² value of a power law regression to the time-shifted data to find the shift t _s that produces the maximal value of R². Denoting the power law fit

$$ W = c\left( {t_{\text{s}} + t} \right)^{d} , $$

(9)

and using the definition μ = (1/W) dW/dt, we obtain the estimate of μ(W) as

$$ \mu = \left( {1/W} \right)dc\left( {t_{\text{s}} + t} \right)^{{d{-}1}} = d\left( {W/c} \right)^{{{-}1/d}} = a^{\prime } W^{{b^{\prime } }} . $$

(10)

Comparing Eqs. (10)–(3) shows that growth follows the model provided $a^{\prime } \equiv dc^{1/d} = a\;{\rm and} \,b^{\prime } \equiv {-}1/d = b$.

The time (τ ₂) for doubling the dry weight of soft parts of any given size of mussel may be estimated by integrating Eq. (5) from W to 2W, assuming a constant mean value of μ, which yields τ ₂ = ln2/μ, but this expression gives an underestimate for dry weight W since μ decreases with increasing size. The correct value is obtained by use of Eq. (3) in the definition (μ = (1/W) dW/dt) which integrates to

$$ \tau_{2} = \left( {2^{ - b} {-}1} \right) \, \left( { - baW^{b} } \right)^{ - 1} = 0.782/\mu , $$

(11)

where μ is now the model value at W. Similarly, for experimental data correlated by the power law of Eq. (10) integration yields

$$ \tau_{2} = \, \left( {2^{1/d} {-}1} \right) \, \left( {W/c} \right)^{1/d} . $$

(12)

Also, the time (τ _n ) to increase dry weight by an n-factor is obtained by replacing the number 2 by n in Eqs. (11) and (12).

Weight-specific growth rates and doubling times from assembled time series

Noting the degree over overlap in dry weight among the 4 groups of data at each site, it is possible to construct one continuous time series covering the full range of sizes at each site. As explained for the data from Series #1 in Fig. 9, the procedure consists of first separating the 4 size groups by arbitrary time shifts to facilitate subsequent shifts for optimal overlap and finally shift the assembled time series to maximize the R ² value of a power law regression Eq. (9) through the data. Then, the weight-specific growth rate as a function of dry weight μ(W) is calculated from Eq. (10). Such results are presented in Fig. 10 for the data of Series #1 to #6. The time (τ ₂) to double the dry weight (W) of a given mussel size calculated from Eq. (12) and based on the analytic equations for regression lines to time series of experimental data from Series #1 to #6 are shown in Fig. 11 and compared to the growth model (dashed lines) obtained from Eqs. (11) and (3) corresponding to constant levels of chl a (from 2 to 4 μg l⁻¹). As a result of the procedure, the data points fall exactly on the straight lines of the analytic solution but they are nevertheless shown to indicate the experimental size range corresponding to that of the data in Fig. 10.

Fig. 9

Mytilus edulis (Series #1). a 4 size groups separated by arbitrary shifts t _s = 10, 30, 60, and 100 days, respectively; b optimal overlap for shifts t _s = 10, 12, 25, and 45 days; c assembled time series shifted 30 days to start at t _s = 45 days, giving maximal R ² (insert); d resulting relation μ(W) calculated from Eq. (10) and compared to growth model at chl a of 3 μg l⁻¹ (dashed)

Fig. 10

Mytilus edulis (Series #1 to #6). Weight-specific growth rates calculated from assembled and time-shifted data as explained in Fig. 9. See also legend to Fig. 5

Fig. 11

Mytilus edulis (Series #1 to #6). Doubling time (τ ₂) versus dry weight of soft parts of mussels (W) from Eq. (12) based on regression lines to time series of experimental data with indicated chl a concentrations (solid lines) and growth model (dashed lines) calculated according to Eqs. (3) and (11) at constant levels of chl a (from 2 to 4 μg l⁻¹)

Comparing the variation of slopes of regression lines of the size class data μ(W _avg) presented in Fig. 5 to those of the assembled time series μ(W) in Fig. 10 suggests a beneficial smoothing effect of the latter procedure of data reduction. The experimental design of studying several (4) size groups simultaneously over a limited period of time to ensure overlapping size ranges is novel to our knowledge and is an efficient approach to obtain growth histories covering a large size range at the same relatively uniform environmental conditions.