L 111 - 2016-17 - Endeligt svar på spørgsmål 126: Spm., om ministeren vil fremsende de nævnte rapporter Miljømuslinger og muslinger som supplerende virkemidler fra 2013 og Combiopdræt 2015 samt artiklerne fra Aquaculture International 2014 og Open Journal, til miljø- fødevareministeren

Miljø- og Fødevareudvalget 2016-17
L 111
Offentligt

Aquacult Int (2014) 22:859–885

DOI 10.1007/s10499-013-9713-y

Potential for production of ‘mini-mussels’ in Great Belt

(Denmark) evaluated on basis of actual and modeled

growth of young mussels

Mytilus edulis

Hans Ulrik Riisgard

•

Kim Lundgreen

•

Poul S. Larsen

Received: 28 June 2013 / Accepted: 17 October 2013 / Published online: 27 October 2013

Springer Science+Business Media Dordrecht 2013

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 (l, % day

-1

) as a function of dry

weight of soft parts (W, g) by a previously developed simple bioenergetic growth model

-0.34

. Results were generally in good agreement with the model which assumes the

prevailing average chlorophyll

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.

Keywords

Energy budget

Bioenergetic growth model

Speciﬁc growth rate

Doubling time

Chl

Pelagic biomass

Line-mussels

Electronic supplementary material

The online version of this article (doi:10.1007/s10499-013-9713-y)

contains supplementary material, which is available to authorized users.

H. U. Riisgard (&)

K. Lundgreen

Marine Biological Research Centre, University of Southern Denmark, Hindsholmvej 11,

5300 Kerteminde, Denmark

e-mail: [email protected]

P. S. Larsen

DTU Mechanical Engineering, Fluid Mechanics, Technical University of Denmark, Building 403,

2800 Kongens Lyngby, Denmark

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L 111 - 2016-17 - Endeligt svar på spørgsmål 126: Spm., om ministeren vil fremsende de nævnte rapporter Miljømuslinger og muslinger som supplerende virkemidler fra 2013 og Combiopdræt 2015 samt artiklerne fra Aquaculture International 2014 og Open Journal, til miljø- fødevareministeren

860

Aquacult Int (2014) 22:859–885

Introduction

Bivalve aquaculture is of increasingly economic importance, and about 50 % of the annual

worldwide harvest of mussels comes from Europe where the main yields of the Atlantic

blue mussel (Mytilus

edulis)

and the Mediterranean mussel

M. galloprovinciales

are from

Spain, France, The Netherlands, and Denmark (Smaal

2002;

Buck et al.

2010).

In Den-

mark, the mussel production mainly comes from ﬁshery on wild stocks of

M. edulis

Limfjorden with annual landings of 80,000–100,000 t in the 1990’s (Kristensen

1997;

Dolmer and Frandsen

2002),

resulting in overﬁshing and a subsequent reduction of the

mussel stock (Kristensen and Hoffmann

2004;

Dolmer and Geitner

2004),

and in

2006–2008, the mussel ﬁshery declined to about 30,000 tons per year (Dinesen et al.

2011)

which led to restrictions and a national policy that aims at developing a sustainable

production of cultured mussels in balance with the extensive ﬁshery of mussels (Dinesen

et al.

2011).

In recent years, the total annual Danish mussel harvest has been around 35,000

tons, with 70 % coming from Limfjorden (data available at

http://naturerhverv.fvm.dk/

landings-_og_fangststatistik.aspx?ID=24363).

Because eutrophication and seasonal oxy-

gen depletion cause high mortality of bottom-living wild mussels during late summer,

especially in the central parts of Limfjorden, line-mussel farming has recently been

introduced to increase the production of mussels and to mitigate the temporary habit

disturbance of mussel dredging (Dolmer et al.

1999;

Ahsan and Roth

2010;

Dinesen et al.

2011).

An alternative solution to the problems with mussel dredging and farming in the

eutrophicated Limfjorden and other shallow Danish fjords may be the use of more open

and deeper marine areas for cultivation of mussels. Thus, the aim for the MarBioShell

project (2008–2012) has been to evaluate the potential of the Great Belt region between the

Kattegat and the Baltic Sea as a new line-mussel cultivation site to relieve some of the

pressure on the vulnerable Limfjorden and to cover an increasing demand for blue mussels.

Deeper water and faster current speeds in the Great Belt are likely to prevent the envi-

ronmental problems encountered in Limfjorden, although a mean salinity in the Great Belt,

being approximately half of that in Limfjorden, may reduce the growth of mussels. The

wild blue mussels in the Great Belt have never been commercially exploited (no ofﬁcial

landing statistics) and the mussel stocks have not been assessed. The present study is a ﬁrst

step towards evaluation of the potential for mussel production in the Great Belt region

based on ﬁeld experiments analyzed and interpreted by a bioenergetic growth model

(BEG) introduced by Clausen and Riisgard (1996) and further developed by Riisgard et al.

(2012a,

2013a)

and Larsen et al. (2013). In addition an important by-product of the present

study has been the consequent further testing of the bioenergetic growth model because it

could assist in evaluating the growth potentials at different locations in the Great Belt and

other Danish waters. Further, because the growth model assumes that the prevailing

average chlorophyll

(chl

concentration accounts for the nutrition, the possible role of

heterotrophic plankton (without chl

as supplementary diet has been evaluated.

Methods

Bioenergetic growth model

The growth (production) of a mussel may be predicted from the difference between

assimilated food energy and metabolic energy expenses, here limited to the seasonal

growth ignoring energy loss due to spawning. Thus, equating the rate of net intake of

123

Aquacult Int (2014) 22:859–885

861

nutritional energy to the sum of various rates of consumption, the energy balance for the

growing organism may be written as (see earlier development by Clausen and Riisgard

1996;

Riisgard et al.

2012a, 2013a;

Larsen et al.

2013),

¼ �½ðF Â

AEÞ

ð1Þ

where

is the ﬁltration rate (= clearance, assuming 100 % retention),

the algal con-

centration, AE the assimilation efﬁciency (AE

excretion/ingestion, excretion:

feces

urine, e.g. Jørgensen

1990),

the maintenance respiratory rate. The constant

(=1.12) follows from the experience that the metabolic cost of growth (i.e., synthesis of

new biomass) constitutes an amount of energy equivalent to 12 % of the growth (biomass

production) (Clausen and Riisgard

1996).

Because the ﬁltration rate (F, l h

-1

) of

Mytilus

edulis

can be estimated from the dry weight of soft parts (W, g) according to

7.45;

0.66, Møhlenberg and Riisgard

1979)

and the maintenance respiratory

-1

rate (R

, ml O

h ) can be estimated according to

, (a

0.475;

0.663,

Hamburger et al.

1983),

the growth rate may now be expressed as,

¼ ðC Â

ÞW

;

ð2Þ

where

0.66 has been used. Thus, the resulting semi-empirical BEG for weight-

speciﬁc growth rate (l

G=W

) may now be expressed as

;

ða ¼

0:871

CÀ0:986; b

¼ À0:34Þ;

ð3Þ

where units are

in % day

-1

in g dry weight of soft parts, and

chl

-1

The constants in Eq. (3) are obtained from use of the cited formulas above for ﬁltration

and respiration, assuming the value of AE

80 % (although 75 % has been suggested by

Rosland et al.

2009,

Table

therein), and use of the following conversion factors: (a) 1 ml

19.88 J; (b) energy of

Rhodomonas salina,

equivalent to 1.75

cell

-1

(Kiørboe

et al.

1985);

M. edulis

20.51 J (Dare and Edwards

1975);

(d) 1

chl

-1

1/(1.251

-3

)

799

Rhodomonas salina

cells ml

-1

(Clausen and Riisgard

1996).

Equations of data analysis

The condition index (CI) of the mussels at given times during growth was calculated from

the dry weight of soft parts (W, mg) and the shell length (L, cm) according to the formula:

W=L

ð4Þ

According to the deﬁnition, dW/dt

lW,

this may be integrated assuming a constant

average value

(day

-1

) of weight-speciﬁc growth rate,

exp

Þ;

¼ ð

lnW

Þ=t

ð6Þ

ð5Þ

Therefore, considering a particular size group of mussels, the mean value of

for

growth from

during period

0 equals the slope of the linear regression

line to a plot of lnW versus

or according to Eq. (5), as the coefﬁcient in the exponent of

an exponential regression to a plot of

versus

for

constant over the time period. Given

123

862

123

Coordinates

Monitoring station

Coordinates

Depth

Distance,

direction

32 m

53°03.96N, 10°48.12E

55°06.87N, 11°41.16E

56°57.24N, 09°03.75E

56°44.56N, 08°50.58E

56°36.05N, 08°24.89E

8.8 m

9.0 m

7.1 m

5.5 m

6.2 m

12.0 km, NE

12.3 km, W

10.3 km, NE

13.0 km, E

28.2 km, N

1.4 km, SW

32.0 km, SW

55°25.56N, 10°44.20E

55°28.74N, 11°03.12E

55°00.31N, 10°40.83E

55°07.36N, 11°29.13E

56°42.63N, 09°12.15E

56°45.03N, 08°51.60E

Løgstør Bredning (St. 4)

Salling Sund (temp./sal.) (St. 5)

Nissum Bredning (chl

(St. 6)

Karrebæksminde Bugt (St. 3)

Langelandssundet (St. 2)

ST53, close to Romsø (St. 1)

55°30.46N, 10°51.72 E

55°30.46N, 10°51.72E

Table 1

Coordinates of mussel growth sites, Danish national environmental monitoring stations, water depth, and distance/direction of monitoring stations relative to growth

sites for mussels in net bags (Series #1 to #6) or on farm-ropes (Series #7)

Series

Growth site

Abbreviation

#1, #7

Kerteminde Bugt

GB-K

Musholm Bugt

GB-M

Svendborg Sund

GB-S

GB-B

Karrebæksminde Bugt (Bisserup)

Risgarde Bredning (Hvalpsund)

L-H

Salling Sund (Glyngøre)

L-G

Aquacult Int (2014) 22:859–885

Aquacult Int (2014) 22:859–885

863

several size classes of mussels at a given site, such

l-values

referred to corresponding

average sizes

avg

)

1/2

leads to an experimentally determined relation of

form:

avg

ð7Þ

which may be compared to Eq. (3) for growth according to the model. Finally, given

the

time to double the size in terms of dry weight is obtained from Eqs. (5) or (6) for

ln2=l

Study areas

Main focus of the present study was on ﬁeld growth experiments with mussels in net bags

in the Great Belt (Denmark), but in order to evaluate the bioenergetic growth model and

the potential for line-mussel farming in this area, it was found useful to conduct similar

growth experiments in Limfjorden where the environmental conditions are rather different

with regard to levels and changes in salinity, water current speeds, and chl

concentrations

as it appears from the following two sections.

Great Belt

is one of the Danish Straits that form the transition between the tidal North

Sea and the non-tidal Baltic Sea (Fig.

1).

The prevailing depths are 10–25 m along the

sides of the deep (up to 70 m) winding main channel. The water exchange between the

Baltic Sea and the open sea is driven both by the river run off and by the meteorological

conditions over the North Sea–Baltic Sea area (Kullenberg and Jacobsen

1981).

The

freshwater supply to the Baltic Sea generates an outgoing brackish water surface current of

less density than the more saline water from the Kattegat, and therefore, the Straits are

permanently stratiﬁed. Thus, the surface salinity in the southeast Kattegat is low, less than

20 psu, whereas the salinity beneath the halocline at about 15 m depth is high, about

30–34 psu. Due to shifting winds, the water level difference between Kattegat and the

western Baltic Sea is highly variable causing an oscillating ﬂow through the Straits (Møller

1996).

In the Great Belt, the salinity therefore varies according to changing ﬂow situations.

Outﬂow of water from the Baltic Sea gives salinities down to less than 10 psu, whereas

inﬂow to the Baltic Sea gives salinities up to 27 psu in the upper layer of the Great Belt

(Jurgensen

1995).

The tides cause current speed in the surface layer on the order of

20–40 cm s

-1

and sea level ﬂuctuations of about

±10–30

cm within a 12-h period. A

combination of tides, wind, and atmospheric pressure causes the currents in the Great Belt

which can be described as pulsating movements of the same body of water which does not,

over a period of days or weeks, result a net transportation of water through the Great Belt.

Normally, the actual current speed through the Great Belt is about 50 cm s

-1

(Funen

1991,

p. 132 therein). The annual mean (±SD) chl

concentration measured in the period 2000

to 2010 at 1 m depth in the northern Great Belt was 2.8

2.4

-1

. For the same area

from April to November (without including spring peaks and winter periods) the mean

annual concentration was 2.5

1.2

chl

-1

. There were between 35 and 50 sampling

days distributed throughout the years. (Data supplied by Environmental Centre Odense,

Danish Ministry of the Environment).

Limfjorden

is a shallow water system that connects the North Sea in the west with the

Kattegat in the east (Fig.

1).

The mean water depth is about 4.5 m, the tidal amplitude is

10–20 cm, and vertical mixing is mainly wind driven. Westerly wind causes inﬂow of

North Sea water in the west, whereas easterly wind results in inﬂow of Kattegat in the east.

ð8Þ

123

864

Aquacult Int (2014) 22:859–885

Fig. 1

Map of Denmark showing the locations for ﬁeld growth experiments with

Mytilus edulis

hung up in

net bags at different localities in Great Belt (Kerteminde Bugt

GB-K, Musholm Bugt

GB-M,

Svendborg Sund

GB-S, Karrebæksminde Bugt

GB-B), and in Limfjorden (Risgarde Bredning

(Hvalpsund)

L-H, Salling Sund (Glyngøre)

L-G). Coordinates for mussels growth sites (closed

symbol)

and environmental monitoring stations (open

symbols,

St. 1–6) are presented in Table

Between the west and east boundaries, there is a permanent horizontal salinity gradient

having a salinity of 32–34 psu at the connection to the North Sea and 19–25 psu at the

connection to the Kattegat (Wiles et al.

2006;

Hofmeister et al.

2009).

Limfjorden is

eutrophic, receiving nutrient from the catchment area which is dominated by agriculture.

The western part of Limfjorden is less eutrophicated and less stratiﬁed than the central

northern part with intermediate stratiﬁed and eutrophic conditions, while the inner central

southern part is strongly stratiﬁed and eutrophic which frequently results in oxygen

depletion in the near-bottom water. The key factor determining the extent of oxygen

depletion is the weather conditions during the summer months July through September

where high temperatures coupled with low wind cause severe oxygen depletion, especially

in areas with dense mussel beds (Jørgensen

1980;

Dolmer et al.

1999;

Møhlenberg

1999;

Møhlenberg et al.

2007;

Møller and Riisgard

2007;

Maar et al.

2010,

Dinesen et al.

2011).

The water currents in Limfjorden are driven by horizontal water density gradients and the

wind. The water current velocity 1 m above the bottom varies typically between

and

6 cm s

-1

, but near the surface, current velocities may be up to 10 cm s

-1

(Dolmer

2000a,

Maar et al.

2007).

The annual mean (±SD) chl

concentration in the period 1982–2006

in the central northern part of Limfjorden (Løgstør Bredning) was 7.5

12.1

chl

-1

Measurements were taken at 2–3 different depths on the location each day of sampling.

There were between 9 and 29 sampling days distributed throughout the years. Maximum

123

Aquacult Int (2014) 22:859–885

865

depth on station was 7.3 m. (Data supplied by Environmental Centre Ringkøbing, Danish

Ministry of the Environment).

Experimental mussels and growth sites

Blue mussels,

M. edulis,

were collected in Limfjorden (Skive Fjord) and in the Great Belt

(Kerteminde Bugt) (Fig.

about 2 weeks before the onset of 6 (Series #1 to #6) ﬁeld

growth experiments with different size groups of mussels in net bags transferred to various

localities with different chl

concentration levels. In Great Belt, 4 locations: Kerteminde

Bugt (Series #1), Musholm Bugt (Series #2), Svendborg Sund (Series #3), and Kar-

rebæksminde Bugt (Series #4) (Fig.

were chosen for growth experiments with mussels

from Kerteminde Bugt between slightly variable periods from 20 July to 8 October

depending on location (Table

1).

In Limfjorden, Risgarde Bredning and Salling Sund

(Fig.

were chosen, and on these locations, growth experiments with locally collected

mussels were carried out during two periods: (Series #5) July 29 to August 25, 2010 and

(Series #6) July 29 to September 21, 2010 (Table

1).

Before sorting of mussels in size groups, these were kept in aerated 1000-l tanks with

running seawater from the inlet to Kerteminde Fjord (18–22 psu). Mussels were then

cleaned, total shell length measured with a vernier gauge, sorted into 4 size groups (each

with near identical shell length

±0.4–1.3

mm), and put into net bags (Go Deep Interna-

tional Inc.) before they were transferred to the ﬁeld location and hung up in a buoy system

(Fig.

2).

The net bags were made of polypropylene ﬁbers and cotton strings that rot away

after about 1 week which result in an increase in mask width. This system enables mussels

to settle ﬁrmly, and the subsequent disappearance of cotton strings ensure that the shell

opening of the mussels does not become restricted. The widths of the masks for small

mussels (20.8–31.0 mm shell length) were 10

10 mm, and for larger mussels

([40.0 mm shell length) were 10

15 mm. The net bags were 50 cm long and placed

approximately 1 m apart to avoid entanglement. Subsamples were subsequently collected

with about 14 days interval from the buoy systems and transported to the Marine Bio-

logical Research Centre, Kerteminde, for analysis. Shell length was measured with a

vernier gauge, soft parts removed from the shells, wet weight measured, and then drying

Fig. 2

Buoy system with mussels (Series #1 to #6) in net bags used at 4 locations in Great Belt and 2

locations in Limfjorden (see Fig.

123

866

Table 2

Mytilus edulis

(Series #1 to #6)

Temp. (°C)

16.0

3.5

25.8

30.8

39.1

16.0

3.5

26.0

30.8

39.0

123

Salinity (psu)

14.2

3.4

0.116

0.104

0.067

0.123

0.070

0.060

0.040

0.183

0.135

0.129

0.095

0.125

0.063

0.060

-0.003

0.266

0.215

0.174

0.100

105.1

194.2

42.9

69.2

102.3

203.2

41.2

74.9

108.6

199.8

75.4

41.2

233.7

1.3

3.6

2.8

2.9

2.5

2.4

1.8

1.1

5.2

4.0

3.7

2.8

115.6

1.7

69.2

2.0

41.7

2.9

242.5

2.0

465

152

230

352

111

160

234

368

108

168

259

129

180

292

91.6

2.6

231

79.9

2.5

182

20.8

0.149

41.2

3.3

138

21.0

27.7

26.7

34.7

23.9

34.7

40.8

53.3

19.3

24.8

23.9

27.7

28.9

38.5

63.0

13.3

17.3

18.7

24.8

(mm)

(mm day

-1

)

(mg)

avg

(mg)

(%day

-1

)

(day)

14.2

3.4

21.0

17.5

3.5

25.9

31.0

39.2

17.1

3.9

25.9

30.6

40.0

18.8

1.5

25.9

30.8

39.4

26.9

0.8

21.1

10.7

1.1

21.3

15.4

1.8

21.2

Series location period

(day)

Chl

(lg l

-1

)

Series #1, GB-K

Kerteminde Bugt

28 Jul to 7 Oct 2010

3.1

0.7

Series #2, GB-M

Musholm Bugt

20 Jul to 8 Oct 2010

3.1

0.7

Series #3, GB-S

Svendborg Sund

26 Jul to 13 Sep 2010

3.0

2.8

Series #4, GB-B

Karrebæksminde Bugt (Bisserup)

24 Jul to 7 Oct 2010

2.8

2.1

Series #5, L-H

Risgarde Bredning (Hvalpsund)

29 Jul to 25 Aug 2010

3.6

1.6

Aquacult Int (2014) 22:859–885

Table 2

continued

Temp. (°C)

19.0

1.9

25.9

30.9

39.3

0.122

173.2

2.1

310

0.185

99.9

2.2

200

0.221

79.6

2.5

163

29.4

1.0

20.8

0.225

49.7

3.1

121

22.4

27.7

31.5

33.0

Salinity (psu)

(mm)

(mm day

-1

)

(mg)

avg

(mg)

(%day

-1

)

(day)

Series location period

(day)

Chl

(lg l

-1

)

Series #6, L-G

Salling Sund (Glyngøre)

29 Jul to 21 Sep 2010

3.2

1.7

Data are mean (±SD) concentration of chl

in the period 2000–2009 as no chl

data from this location were available for 2010

Aquacult Int (2014) 22:859–885

chl

data are from Nissum Bredning because no chl

data from Salling Sund exist for this period

Overview of locations, periods, and duration (Dt) of mussel growth in Great Belt (GB-K, GB-M, GB-S, GB-B) and Limfjorden (L-H, L-G) in 2010. Mean (±SD) values of

chlorophyll

(chl

a),

temperature, salinity, initial shell length (L

) and body dry weight (W

), average daily increase in shell length (L

), average body dry weight (W

avg

average weight-speciﬁc growth rate (l, slopes in Fig.

3),

and doubling time (s

). Chlorophyll

data were supplied by Environmental Centre, Ringkøbing, Danish Ministry of

the Environment. Mean

SD are based on data collected on the locations at a depth of 1 m between 5 and 11 times distributed throughout the experimental periods

867

123

868

Aquacult Int (2014) 22:859–885

(a)

(b)

lnW

39.06 mm

30.82 mm

25.78 mm

20.82 mm

(µ = 2.0)

(µ = 2.6)

(µ = 2.5)

(µ = 3.3)

39.04 mm

30.80 mm

26.01 mm

21.00 mm

(µ = 1.3)

(µ = 1.7)

(µ = 2.0)

(µ = 2.9)

(c)

(d)

lnW

39.17 mm

30.97 mm

25.89 mm

21.16 mm

(µ = 2.9)

(µ = 3.3)

(µ = 3.1)

(µ = 4.0)

40.02 mm (µ = 1.1)

30.63 mm (µ = 1.8)

25.93 mm (µ = 1.8)

21.25 mm (µ = 2.4)

(e)

(f)

lnW

39.39mm

30.79 mm

25.88 mm

21.07 mm

(µ = 2.8)

(µ = 3.7)

(µ = 4.0)

(µ = 5.2)

39.30 mm

30.85mm

25.92 mm

20.78 mm

(µ = 2.2)

(µ = 2.5)

(µ = 3.1)

Time (d)

Fig. 3

Mytilus edulis

(Series #1 to #6: ﬁgures

a–f,

see Table

1).

Natural logarithm (ln) of dry weight of soft

parts (W, mg) as a function of time (days) of 4 size classes of mussels. The slope

(% day

-1

) denotes the

weight-speciﬁc growth over the period

both shells and soft parts on pieces of tin foil in an oven for 24 h at 90

°C

to obtain also the

dry tissue weight.

Environmental data

Data on chl

salinity, and temperature for the actual mussel growth periods were obtained

from 6 stations monitored by Environmental Centre Ringkøbing (Limfjorden), Environ-

mental Centre Odense, and Environmental Centre Roskilde (Great Belt). Temperature and

123

Aquacult Int (2014) 22:859–885

869

salinity were measured with a CTD at heights spaced 0.2 m apart, from 0.8 m below the

surface down to about 0.3 m above the bottom. Oxygen concentrations were measured in

the top and bottom layers using the Winkler method. Chl

was determined from water

samples taken from a depth of 1 m and subsequently analyzed at an authorized laboratory

according to Danish national standards. The water depths at the 6 monitoring stations and

distance to the mussel growth sites are summarized in Table

Current velocity data were

supplied by DHI.

Growth of mussels on farm-ropes (Series #7)

From September 2010 to March 2011, 7 samples of 1-m-long pieces of rope with mussels

were collected 1 m below the water surface at the experimental mussel farm run by the

MarBioShell project in Kerteminde Bugt (Fig.

location GB-K). The farm-ropes were

made of long 15-cm-width bands cut out of ﬁshing net (3 mm nylon, 5

5 cm mesh;

Hvalpsund Net A/S). The rope samples were transported to the nearby Marine Biological

Research Centre, Kerteminde, and stored in a freezer until analysis could take place. For

analysis, the rope samples were allowed to defreeze and representative segments of 5 cm

(small mussels) or 10 cm (larger mussels) from the middle of the ropes were cut out with a

scalpel, the mussels removed, counted, and thoroughly mixed in a container where after

about 100 mussels were randomly sampled with a spoon. The density (number of mussels

per cm rope), mean shell length, and wet and dry weight of soft parts were subsequently

determined.

Pelagic biomass in Limfjorden and the Great Belt

Data on pelagic biomass of autotrophic and heterotrophic plankton in the Great Belt and

Limfjorden were obtained from the Danish National Environmental Research Institute

(http://www.dmu.dk/en/water/marinemonitoring/mads/plankton/) and the Danish Ministry

of the Environment, Nature Agency, respectively.

Results

The ﬁeld studies involve 6 sites (Series #1 to #4 in Great Belt, and Series #5 & #6 in

Limfjorden) with measurement of growth of mussels in net bags in the productive summer

season (Tables

1, 2;

Figs.

3, 4, 5, 6),

and one site (Series #7, close to that of Series #1) with

growth measurement of mussels settled on farm-rope, covering fall and winter seasons

(Tables

3, 4;

Figs.

7, 8).

Actual growth and average weight-speciﬁc growth rates (Series #1 to #6)

The recorded data on ﬁeld growth of 4 size classes of mussels at each of the 6 sites are

presented in Fig.

in terms of the natural logarithm of dry weight (lnW) versus time with

the slope of linear regression lines giving the average weight-speciﬁc growth rate (l) over

the period, according to Eq. (5). These

l-values,

for 4 size groups at each site, are shown in

Fig.

versus the corresponding values of average dry weight (W

avg

) along with power law

regression lines approximations of form Eq. (7),

avg

. For comparison, model

predictions from Eq. (3) for indicated values of chl

concentrations are shown as dashed

123

870

Aquacult Int (2014) 22:859–885

(mg cm

-3

)

(mg cm

-3

)

20.82 mm

25.78 mm

30.82 mm

39.06 mm

(a)

21.00 mm

26.01 mm

30.80 mm

39.04 mm

(b)

Time (d)

21.16 mm

25.89 mm

30.97 mm

39.17 mm

Time (d)

(c)

(mg cm

-3

)

(mg cm

-3

)

21.25 mm

25.93 mm

30.63 mm

40.02 mm

(d)

Time (d)

21.07 mm

25.88 mm

30.79 mm

39.39mm

Time (d)

(e)

(mg cm

-3

)

(mg cm

-3

)

20.78 mm

25.92 mm

30.85 mm

39.30 mm

(f)

Time (d)

Fig. 4

Mytilus edulis

(Series #1 to #6: ﬁgures

a–f).

Condition index (CI, mg cm

-3

, mean

SD) as a

function of time (days) of 4 size classes of mussels

lines in Fig.

Growth data in terms of the condition index (CI) are presented in Fig.

showing generally increasing CI for almost all classes during the period.

Mussels on farm-ropes (Series #7)

The growth as a function of time of the biggest 5-mm-size group of mussels (1–5 mm

longer than the other mussels) on farm-rope samples collected during the period September

1, 2010 to March 2, 2011 has been shown in Figs.

and

along with data for chl

temperature, and salinity in the same period. The growth period can be divided into two:

Period I

September 1, 2010 to November 16, 2010, where the increase in shell length is

123

Aquacult Int (2014) 22:859–885

Fig. 5

Mytilus edulis

(Series #1

to #6). Experimental data for

average weight-speciﬁc growth

rate (l

avg

, cf. Eq.

7),

derived from slope of regression

lines in Fig.

as a function of

average body dry weight (W

avg

)

of all size classes of mussels

(GB

Great Belt,

Limfjorden. Constants

a’

and

b’

equal coefﬁcient and

exponent in power law regression

lines shown, and chl

from

Table

Predictions (dashed

lines,

slope

–0.34) from

growth model at different

constant levels of chl

(from 1.5

to 4.0

-1

) calculated

according to Eq. (3). *Mean

concentration at 1 m depth for

the period 2000–2009, because

chl

was not measured on this

location (GB-S, see Table

2010

100.0

Series

chl

(µg l

-1

)

#1 1.49 -0.36

3.1 ±0.7

871

0.69 -0.60

2.33 -0.22

0.58 -0.54

1.60 -0.47

1.25 -0.40

3.1 ±0.7

3.0 ±2.8*

2.8 ±2.1

3.6 ±1.6

3.2 ±1.7

10.0

µ (% d

-1

)

4.0

1.0

3.0

2.0

1.5

0.1

0.01

0.10

1.00

10.00

avg

(g)

0.277 mm day

-1

, and Period II

November 16, 2010 to March 2, 2011 with loss of

weight (Fig.

but essentially without increase in shell length (Fig.

7b;

Table

3).

Further

details on weight loss during Period II are given Table

Pelagic biomass

The biomass of autotrophic and heterotrophic plankton in the Great Belt in 1997 and in

Limfjorden in 2010 when also mixotrophic species were quantiﬁed are shown in Tables

and

It appears that the heterotrophic biomass in the Great Belt in 1997 was 3.4

3.3 %

of the total pelagic biomass, whereas the heterotrophic and mixotrophic biomass were

23.7

24.5 % of the total in Løgstør Bredning and 5.9

6.7 % in Skive Fjord, respec-

tively. Although the heterotrophic fraction of the total plankton biomass available for ﬁlter-

feeding mussels may at times be relatively high, it seems safe to conclude that the auto-

trophic plankton, which can be quantiﬁed by measurement of the chl

concentration,

generally dominates the pelagic microplankton.

Discussion

In the present work, we ﬁrst present experimental data on the growth of mussels during the

productive summer season and also test to what degree the observed weight-speciﬁc

123

872

Aquacult Int (2014) 22:859–885

Salinity/Temperature/Chl.

series#1

series#2

Salinity/Temperature/Chl.

Salinity/Temperature

series#3

series#4

Salinity/Temperature/Chl.

series#5

series#6

Fig. 6

Chlorophyll

(C,

-1

), temperature (T,

°C),

and salinity (S, psu) in Kerteminde Bugt (Series#1),

Musholm Bugt (Series#2; same as for Series #1), Svendborg Sund (Series#3), Karrebæksminde Bugt

(Series#4), Risgarde Bredning (Series#5), and Salling Sund (Series#6) during growth periods.

Dashed

vertical lines

mark the beginning and end of mussel growth period. No chl

data are available for

Svendborg Sund (Series#3) in 2010. Data supplied by Environmental Centre Odense, Danish Ministry of the

Environment

growth rate as a function of mussel dry weight can be related to the model expressed by

Eq. (3). We suggest that deviations from either the expected exponent of

= -0.34

or the

constant

expressing the magnitude of growth for the prevailing chl

concentration level

indicate suboptimal growth conditions, although more precise interpretations may not be

possible without supplementary studies.

Figure

shows that ﬁeld data from 6 different sites fall in the general area of prediction

according to the bioenergetic growth model. But in regard to predicted levels of growth

rates for the theoretical and the measured chl

concentrations near the growth sites, there

are some differences. Series #1, #5, and #6 appear close to the model, Series #2 and #4

appear suboptimal, while Series #3 appears to grow faster than predicted by the theory for

the measured chl

concentration near the site.

The reasons for suboptimal growth in Series # 2 and #4 despite high chl

levels may be

suggested by examination of Eq. (1)–(3). Thus, if the

b-exponent

is essentially that of the

model, this implies

- and

-exponents to be near identical (& 0.66), and this leaves the

constants

, AE, and

as sources of suboptimality (or deviations from prerequisites

123

Aquacult Int (2014) 22:859–885

Table 3

Mytilus edulis

(Series #7)

(mm)

big

Date

big 5

(mm)

(mg)

3.3

2.7

11.1

3.6

53.4

26.3

197.3

21.6

171.9

28.6

146.9

37.9

7.0

0.6

6.6

1.4

5.1

1.3

8.7

1.4

7.7

1.4

7.3

1.5

(mg cm

-3

)

shell

(mg)

7.4

1.5

11.2

0.9

18.1

2.4

28.1

2.1

27.9

2.6

29.1

2.4

Day

Rope

(cm)

4.4

1.6

7.0

3.2

11.6

4.7

14.4

6.8

13.0

7.1

11.6

6.5

tot

Density

(ind. cm

-1

)

(%)

67.7

7.6

76.2

3.0

(%day

-1

)

01-09-2010

5.0

1123

225

162

16.1

11.1

40.8

11.0

185.2

78.5

700.0

69.8

884.5

110.9

896.9

132.8

18-09-2010

4.5

831

185

7.1

78.1

2.0

79.8

1.3

81.4

1.3

84.2

1.3

8.3

3.3

-0.3

07-10-2010

10.0

1683

16-11-2010

10.0

1145

115

155

05-01-2011

126

9.7

1066

110

124

02-03-2011

182

10.5

1468

140

198

Overview of growth parameters for farm-rope mussels collected in the period September 1, 2010 to March 2, 2011.

tot

total number of mussels on rope segment sample;

number of randomly collected mussels in sample for shell length measurement;

big 5

number of mussels from biggest 5-mm-size group in

;

shell length of

mussels in

;

big 5

shell length of mussels in

big 5

;

dry weight of soft parts; CI

condition index;

shell

dry weight of shells; WC

water content

% water

in body soft parts. Mean

SD are shown. Weight-speciﬁc growth rate (l) calculated from Eq. (6) for each speciﬁc subsample of farm-rope mussels (see also Fig.

873

123

874

Table 4

Mytilus edulis

(Series #7)

Date

Time

(day)

106

(mg)

197.3

171.9

146.9

-25.4

-25.0

-0.508

-0.446

period

(mg)

act

(mg day

-1

)

Aquacult Int (2014) 22:859–885

(ml O

-1

)

0.162

0.148

0.133

est

(mg day

-1

)

-3.8

-3.4

-3.1

16-11-2010

05-01-2011

02-03-2011

est

(mg day

-1

)

24 h day

-1

19.88 J h

-1

)/(20.51 J mg

-1

)

Mean dry weight of soft parts (W) of mussels in the biggest 5-mm-size group of mussels sampled from farm-

ropes in the winter-starvation period, November 11, 2010 to March 2, 2011 (Fig.

8).

Loss of dry weight in

period between sampling (DW

period

) and actual daily weight loss (DW

act

) is shown along with estimated

weight loss (DW

est

) calculated from the maintenance respiratory rate (R

, see text)

Fig. 7 a

Chlorophyll

(C,

chl

-1

), temperature (T,

°C),

and salinity (S, psu) from

September 1, 2010 to March 2,

2011.

Mytilus edulis

(Series

#7). Mean (±SD) shell length (L,

mm) as a function of time (t, d) of

the biggest 5-mm-size group of

mussels (1–5 mm longer than the

other mussels) on farm-rope

samples collected during this

period. The growth period is

divided into two: Period

September 1, 2010 to

November 16, 2010, Period

November 16, 2010 to

March 2, 2011 (see Table

100

120

140

160

180

200

(a)

Period I:

T = 12.4±2.9

C = 3.1±0.8

Salinity/Temperature/chl

Period II:

T = 3.2±2.6

C = 3.3±3.1

(b)

Period II:

= 0.0101t + 27.071

R² = 0.607

Period I:

= 0.277t + 7.255

R² = 0.994

(mm)

for the growth model) associated with the level of growth. The most obvious candidate for

low level of growth is some degree of reduced ﬁltration rate for the full size range (i.e.,

smaller

) or increased respiration rate due to, e.g., stress caused by varying salinity (i.e.,

larger

) (e.g., Strickle and Sabourin

1979;

Riisgard et al.

2012b).

The case of Series #3, showing higher growth rates than predicted for the chl

con-

centration measured nearby, could be explained by the rather large experimental uncer-

tainty of data, notably 3.0

2.8

-1

, or by the availability of other sources of nutrition

123

Aquacult Int (2014) 22:859–885

Fig. 8

Mytilus edulis

(Series

#7). Mean (±SD) dry weight of

soft parts (W, mg) as a function

of time of farm-rope samples

collected in the period September

1, 2010 to March 2, 2011

(Table

3).

The weight-speciﬁc

growth rate (l, % day

-1

) during

the period September 1, 2010 to

November 16, 2010 (76 days)

was 5.3 % day

-1

250

200

875

= -0.475t + 232.82

R² = 0.999

(mg)

150

100

= 4.454e

0.053t

R² = 0.950

Table 5

Total pelagic biomass (lg C l

-1

) of autotrophic plankton (phytoplankton), heterotrophic plankton

(microzooplankton), and percentage heterotrophic biomass of total biomass of plankton in the Great Belt

during 1997

Date 1997

1 Jan

13 Jan

27 Jan

10 Feb

24 Feb

10 Mar

24 Mar

7 Apr

21 Apr

6 May

26 May

9 Jun

24 Jun

3 Jul

21 Jul

4 Aug

18 Aug

2 Sep

16 Sep

22 Sep

6 Oct

20 Oct

3 Nov

17 Nov

1 Dec

15 Dec

Mean

±SD

Autotrophic

13.7

11.6

10.4

1115.5

95.1

219.1

59.7

16.6

12.5

21.4

35.5

295.7

50.7

35.4

28.7

302.4

159.9

339.8

134.8

164.8

143.7

181.1

516.8

63.6

18.8

76.2

158.6

232.7

Heterotrophic

0.6

0.3

0.2

15.2

1.7

4.1

14.3

3.7

0.2

0.5

2.6

1.9

9.4

3.3

3.2

3.6

1.6

9.4

35.5

9.7

13.4

6.3

2.5

0.1

0.4

1.5

5.6

7.7

Total

14.3

11.9

10.6

1130.7

96.7

223.2

74.0

20.2

12.7

21.9

38.1

297.6

60.1

38.7

31.9

306.0

161.4

349.3

170.3

174.5

157.0

187.4

519.3

63.7

19.2

77.6

164.2

235.0

% Heterotrophic

4.1

2.4

2.0

1.3

1.7

1.8

19.4

18.1

1.8

2.3

6.8

0.6

15.6

8.6

10.1

1.2

1.0

2.7

20.8

5.6

8.5

3.3

0.5

0.2

2.2

1.9

3.4

3.3

123

876

123

May

4.8

0.4

58.3

12.6

Jun

58.4

0.4

2.8

5.2

10.1

10.6

5.1

1.0

0.8

6.4

19.9

4.0

61.4

24.9

3.7

5.0

0.0

3.8

40.0

96.0

373.2

379.0

197.0

1150.7

2.5

8.9

1.0

Jun

Jul

Aug

Sep

15.8

0.1

1.3

17.6

18.0

22.9

45.6

12.3

15.1

20.1

46.5 53.5

Oct

66.5

0.4

7.8

11.0

54.5

59.7

75.6

129.3

61.6

38.9

31.7

340.1 95.5

2.2

18.8

0.4

0.0

3.6

4.2

6.6

9.0

9.8

11.8

82.6

46.2

61.8

120.0 208.8

36.2 421.0 201.6

130.9

136.4 81.2

96.7

17.4

1.7

61.7

75.1

Nov

5.9

0.0

2.7

31.4

May

Jun

Jul

Aug

Sep

Oct

Nov

21.8

0.2

44.2

60.2

Nov

13.6

3.1

28.1

39.3

Mean

146.0

152.7

4.9

5.5

68.9

71.4

23.7

24.5

Mean

252.8

322.0

3.0

6.5

13.0

16.6

5.9

6.7

Table 6

Total biomass of autotrophic (Nostocophyceae, Chrysophyseae, Euglenophyceae, Prasinophyceae, Cryptophyceae, Diatomophyceae, Dinophyceae, and other

undetermined species), mixotrophic (Dinophyceae, Crysophyceae, and Prymnesiophyceae), and heterotrophic (Dinophyceae, Cryptophyceae, ciliates, pelagic bacteria,

ﬂagellates other microzooplankton species, but not including copepods, and other mesozooplankton species) plankton in Løgstør Bredning and Skive Fjord in 2010

Løgstør

bredning

Mar

Apr

Autotrophic

548.7

1.1

375.8

198.2 98.4

Mixotrophic

0.4

0.2

4.0

2.0 14.8

Heterotrophic

18.2 14.3

32.1

47.9 35.5

% mixo

hetero

3.3 92.9

8.1

12.9 18.7

Skive Fjord

May

Apr

May

Autotrophic

690.4

503.5

78.6

64.7

72.4

Mixotrophic

0.5

0.0

3.1

25.5

0.0

Heterotrophic

1.2

15.8

30.5

3.8

28.6

Aquacult Int (2014) 22:859–885

% mixo

hetero

0.2

3.0

29.9

31.2

28.3

Aquacult Int (2014) 22:859–885

Table 7

Maximum, minimum, and mean (±SD) current speeds at the 4 mussel growth sites in the Great Belt during the growth periods (Fig.

Table

Location

0.20

0.14

0.27

0.20

0.04

0.02

0.04

0.03

46.2

15.5

34.2

3.6

Max speed (cm s

-1

) Minimum speed (cm s

-1

) Mean speed (cm s

-1

) %

[25

cm s

-1

[50

cm s

-1

(2010) (psu)

(2008–2010) (psu)

15.4

3.8

15.4

3.8

15.4

3.2

11.6

1.7

16.5

4.2

16.5

4.2

16.7

3.9

11.9

1.8

Kerteminde Bugt

0.66

Musholm Bugt

0.87

Svendborg Sund

0.12

Karrebæksminde Bugt 0.12

No data available for 2009 (mean of 2008 and 2010)

Additionally, the current speed above 25 and 50 cm s

-1

in % of total time is shown. Mean current speeds at the two northernmost stations (Kerteminde Bugt and Musholm

Bugt) and two southernmost stations (Svendborg Sund and Karrebæksminde Bugt) were 0.77 and 0.12 cm s

-1

, respectively. Mean

SD salinities (S, psu) in 2010 and in the

3-year period (2008–2010) for the 4 mussel growth locations in Great Belt

877

123

878

Table 8

Mean chlorophyll

(chl

a),

minimum, maximum, and average temperature (T), and salinity (S) in the northern part of Great Belt (Fig.

St #1) in 2000–2010.

Additionally, the frequency of salinity changes of more than 9 psu are shown along with the corresponding changing rate expressed as psu day

-1

and psu h

-1

min

(psu)

10.98

12.42

10.20

9.57

9.93

11.01

12.49

9.90

10.26

11.60

10.20

10.66

11.89

10.50

10.41

10.06

24.10

16.65

10.83

10.47

9.49

10.80

9.38

25.22

16.80

23.18

16.44

12.31

10.46

13.41

11.97

9.38

10.01

25.34

15.99

12.63

24.15

17.41

10.01

0.28

0.73

0.41

0.73

0.42

0.31

0.37

0.43

0.30

0.75

0.33

0.46

0.19

0.26

0.35

0.55

0.48

0.89

0.26

25.59

17.15

10.52

0.53

24.76

16.09

9.95

1.00

22.57

16.30

–

0.89

0.04

0.00

0.04

0.02

0.01

0.04

0.01

0.03

0.02

0.03

0.02

0.01

0.02

0.01

0.03

0.01

0.02

0.01

0.02

27.14

17.16

13.41

0.64

0.03

max

(psu)

avg

(psu)

Freq

psu

Amplitude (psu)

(day)

Change (psu day

-1

)

Change (psu h

-1

)

123

Year

Chl

(lg l

-1

)

min

(°C)

max

(°C)

avg

(°C)

2000

2.6

2.43

17.11

9.77

2001

2.3

2.15

19.80

9.76

2002

2.4

2.41

20.17

10.08

2003

2.4

0.66

19.13

9.21

2004

2.8

1.72

18.79

10.06

2005

2.7

1.02

18.29

10.42

2006

3.8

0.84

19.57

11.06

2007

3.5

3.01

18.50

10.94

Aquacult Int (2014) 22:859–885

2008

2.3

3.36

18.29

10.22

Table 8

continued

min

(psu)

10.48

10.62

11.07

10.23

9.04

9.42

0.25

1.29

22.44

15.42

9.70

0.33

0.53

0.02

0.01

0.05

0.01

0.17

0.01

24.36

17.60

10.55

0.46

0.02

max

(psu)

avg

(psu)

Freq

psu

Amplitude (psu)

(day)

Change (psu day

-1

)

Change (psu h

-1

)

Year

Chl

(lg l

-1

)

min

(°C)

max

(°C)

avg

(°C)

2009

3.1

2.15

19.05

11.12

Aquacult Int (2014) 22:859–885

2010

2.7

-0.48

20.98

8.23

879

123

880

Aquacult Int (2014) 22:859–885

than phytoplankton, e.g., heterotrophic ﬂagellates, ciliates, and other microzooplankton

that may form part of the in situ diet of mussels (Nielsen and Maar

2007),

and further that

mesozooplankton in turbulent water may be ingested by ﬁlter-feeding mussels (Davenport

et al.

2000).

Thus, growth rates higher than estimated from an energy budget based solely

on chl

may express a possible supplementary ingestion of heterotrophic food.

In case of Series #6, showing growth rates somewhat lower than predicted for the

growth model, a probable explanation is the generally high current speeds at this growth

site in Great Belt (Musholm Bugt). Here, the current speed was higher than 0.25 and

5 cm s

-1

for 46.2 and 15.5 % of the time, respectively (Table

7),

and according to Wildish

and Miyares (1990) ﬂow-induced inhibition of the ﬁltration rate of blue mussels takes

place in ﬂume ﬂows above 6 cm s

-1

, and at ﬂows between 25 and 38 cm s

-1

, the ﬁltration

rate was reduced to only about 12 % of that measured at 6 cm s

-1

Secondly, we study mussel growth during the fall–winter season. Here, the growth of

mussels on farm-ropes (Series #7) shows that the weight-speciﬁc growth rate (about

5 % day

-1

at about 3–4

chl

-1

, Fig.

followed model prediction during Period I,

thus suggesting density independent growth of the biggest 5-mm-size group of mussels, but

in Period II when both the chl

concentration and temperature became very low (Fig.

7a),

the mussels were losing weight (Fig.

8),

a scenario which is beyond the parameter range

covered by the model. As it appears from Table

the actual daily weight loss is signif-

icantly lower (about 7 times) than the estimated weight loss calculated from the mainte-

nance respiration rate assuming this were at the normal level of a fully open mussel. This

indicates that the mussels during Period II may have been partially closed and thus saving

energy by the reduced respiration rate (Jørgensen et al.

1986).

As to the general potential for mussel farming in Danish waters, it is noted that the

variation in chl

temperature, and salinity in the northern and southern part of Great Belt

during a 10-year period, from beginning of 2000 to end of 2010, have been monitored by

the Danish Nature Agency (Table

8),

and the mean salinities in the study period

2008–2010 for the 4 mussel growth locations in Great Belt has been shown in Table

Based on the present study of actual growth of mussels in net bags and on farm-ropes in the

ﬁeld, it seems reasonable here to make a provisional evaluation of the potential for line-

mussel farming in the Great Belt. The speciﬁc growth rates observed in Great Belt compare

quite well with the growth in Limfjorden, although frequently high current speeds at

certain sites in Great Belt may induce inhibition of feeding and thus growth. The observed

variations in salinities, however, are not likely to inﬂuence the growth rate of mussels in

Great Belt (Riisgard et al.

2012b, 2013b).

Thus, based on the present bioenergetic growth model and experimental approach, it is

possible to evaluate the potential for optimal line-mussel growth in selected areas of

special interest, especially if supplementary local ﬁeld measurements of chl

heterotro-

phic plankton, and current speeds were to be made to ﬁne-adjust the growth model, all

without the need for elaborate growth experiments. Regarding future mussel farming, our

studies have shown that

M. edulis

can grow from settlement in spring to 30 mm in shell

length in November. However, to reach the traditional consumer size of at least 45 mm, it

will probably take about 18 months, as suggested by Dolmer and Frandsen (2002) for long

line-mussels in Limfjorden, because of the winter period with weight loss and subsequent

re-growth during the next season. It may therefore be suggested to consider a new approach

of line farming of 30-mm mini-mussels during one growth season, from early spring to

November, recovering all equipment at the time of harvest and re-establishing it at the

beginning of the next season for a new population and thus protecting the equipment from

the often damaging weather of the Danish winter season. The new, smaller-sized consumer

123

Aquacult Int (2014) 22:859–885

1000

900

800

700

600

500

400

300

200

100

1000

900

800

700

600

500

400

300

200

100

881

(mg)

39.06 mm

30.82 mm

25.78 mm

20.82 mm

(a)

(mg)

20 40 60 80 100 120 140 160 180 200

1000

900

800

700

600

500

400

300

200

100

39.06 mm

30.82 mm

25.78 mm

20.82 mm

(b)

20 40 60 80 100 120 140 160 180 200

Time,

(d)

0.97

0.96

-1

Time,

(d)

(c)

µ (% d )

3.0 µg chl

-1

(d)

(mg)

0.95

0.94

40 60

(d)

= 0.011t

2.228

R² = 0.969

39.06 mm

30.82 mm

25.78 mm

20.82 mm

Power (All data)

µ = 1.345

-0.435

R² = 0.969

0.01

0.10

1.00

20 40 60 80 100 120 140 160 180 200

Time,

(d)

(g)

Fig. 9

Mytilus edulis

(Series #1).

4 size groups separated by arbitrary shifts

10, 30, 60, and

100 days, respectively;

optimal overlap for shifts

10, 12, 25, and 45 days;

assembled time series

shifted 30 days to start at

45 days, giving maximal

(insert);

resulting relation

l(W)

calculated

from Eq. (10) and compared to growth model at chl

of 3

-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.

See also

legend to Fig.

100.0

Series

1.34

0.89

1.88

0.80

1.96

1.37

-0.44

-0.40

-0.33

-0.38

-0.42

chl

(µg l

-1

)

3.1±0.7

3.0±2.8*

2.8±2.1

3.6±1.6

3.2±1.7

4.0 µg chl

-1

10.0

3.0

2.0

µ (% d

-1

)

1.5

1.0

0.1

0.01

0.10

1.00

(g)

123

882

Fig. 11

Mytilus edulis

(Series

#1 to #6). Doubling time (s

)

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

concentrations

(solid

lines)

and growth model

(dashed

lines)

calculated

according to Eqs. (3) and (11) at

constant levels of chl

(from 2 to

-1

)

100

Aquacult Int (2014) 22:859–885

Series chl

(µg l

-1

)

3.1±0.7

3.0±2.8*

2.8±2.1

3.6±1.6

3.2±1.7

(d)

2.0 µg chl

-1

0.01

3.0

4.0

0.10

1.00

(g)

product should be attractive in its own right—like the small French 40-mm ‘bouchot’

mussels for which there is a market (Prou and Goulletquer

2002).

Acknowledgments

This work formed part of the MarBioShell project supported by the Danish Agency for

Science, Technology and Innovation for the period January 2008 to December 2012. Thanks are due to

Mads Anker van Deurs and Isabel B. Saavedra for technical assistance, to Lars Birger Nielsen for practical

assistance, to Mads Joakim Birkeland and Flemming Møhlenberg, DHI, for providing current velocity data,

and to the Danish Nature Agency, Danish Ministry of the Environment, for providing hydrographical data,

and for excellent co-operation, especially with Benny Ludvigsen Bruhn, Bent Jensen, and Flemming

Nørgaard. Two anonymous reviewers provided many constructive comments on the manuscript.

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

varies with increasing size

The ﬁrst data point in an experimental time

series is normally assigned the arbitrary value of

0 at size

, but on a true time scale

of mussel life this should be some time

[

0. We therefore shift the time series

W(t)

W(t

and examine the

value of a power law regression to the time-shifted data to

ﬁnd the shift

that produces the maximal value of R

. Denoting the power law ﬁt

;

and using the deﬁnition

(1/W) dW/dt, we obtain the estimate of

l(W)

¼ ð

1=W

Þdcð

dÀ1

W=c

À1=d

ð9Þ

ð10Þ

Comparing Eqs. (10)–(3) shows that growth follows the model provided

1=d

and

À1=d ¼

The time (s

) for doubling the dry weight of soft parts of any given size of mussel may

be estimated by integrating Eq. (5) from

to 2W, assuming a constant mean value of

which yields

ln2/l, but this expression gives an underestimate for dry weight

since

decreases with increasing size. The correct value is obtained by use of Eq. (3) in the

deﬁnition (l

(1/W) dW/dt) which integrates to

123

Aquacult Int (2014) 22:859–885

883

À1

ÁÀ

Àb

À1 ÀbaW

0:782=l;

ð11Þ

where

is now the model value at

Similarly, for experimental data correlated by the

power law of Eq. (10) integration yields

1=d

ð12Þ

À1 ð

W=c

1=d

Also, the time (s

) to increase dry weight by an

n-factor

is obtained by replacing the

number 2 by

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.

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

value of a power law

regression Eq. (9) through the data. Then, the weight-speciﬁc growth rate as a function of

dry weight

l(W)

is calculated from Eq. (10). Such results are presented in Fig.

for the

data of Series #1 to #6. The time (s

) 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.

and compared to the

growth model (dashed lines) obtained from Eqs. (11) and (3) corresponding to constant

levels of chl

(from 2 to 4

-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.

Comparing the variation of slopes of regression lines of the size class data

l(W

avg

)

presented in Fig.

to those of the assembled time series

l(W)

in Fig.

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 envi-

ronmental conditions.

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