Aquaculture 271 (2007) 216 – 226 www.elsevier.com/locate/aqua-online

Growth model for Atlantic cod (Gadus morhua): Effects of temperature and body weight on growth rate Björn Björnsson a,⁎, Agnar Steinarsson b , Tómas Árnason c a

Marine Research Institute, Skúlagata 4, P.O. Box 1390, 121 Reykjavík, Iceland b Marine Research Institute, P.O. Box 42, 240 Grindavík, Iceland c University of Akureyri, Borgir v/Nordurslód, 600 Akureyri, Iceland

Received 10 April 2007; received in revised form 20 June 2007; accepted 20 June 2007

Abstract Results from several laboratory experiments showed that at each temperature there was a linear relationship between the logarithms of specific growth rate (G%/day) and body weight (W g) of Atlantic cod fed to satiation: lnG = α + βlnW. Both α and β were found to be a function of temperature (T °C): α = a + bT + cT2; β = d + eT; a = −0.7620, b = 0.3982, c = − 0.0128, d = − 0.1500, e = −0.0239. The e-parameter was altered by 10% from the laboratory value (to e = − 0.0215) to tune the model in accordance with growth rate of large cod reared in sea cages in Norway. The model predicts that the optimal temperature for growth (Topt.G) declines with body weight: Topt.G = 15.57–0.8426lnW, i.e. 15.0, 13.0, 11.1 and 9.2 °C for 2, 20, 200 and 2000 g fish, respectively. The predicted growth rates at optimal temperature (Gmax) were 7.41, 2.62, 1.02 and 0.44%/day for 2, 20, 200 and 2000 g fish, respectively. Model calculations show that 30 g cod juveniles stocked in sea cages on 15 May have reached 1.6 and 2.1 kg by the end of the second year and 4.6 and 6.3 kg by the end of the third year, in Northwest Iceland and West Norway, respectively. © 2007 Elsevier B.V. All rights reserved. Keywords: Atlantic cod; Cod farming; Growth experiments; Growth model; Optimal temperature

1. Introduction In recent years, interest in farming of cod (Gadus morhua) has been growing, especially in Norway, Iceland, Scotland, Faroe Islands and Canada. Juveniles are being produced year-round in hatcheries, selective breeding is underway and vaccines are being developed (Björnsson, in press). There is a large demand for farmed cod to fill the gap between increasing demand and diminishing supply from the cod fishery. It has been predicted that the production of farmed cod will reach a ⁎ Corresponding author. Tel.: +354 575 2045; fax: +354 575 2001. E-mail address: [email protected] (B. Björnsson). 0044-8486/$ - see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.aquaculture.2007.06.026

similar level as that of Atlantic salmon (Salmo salar) within the next 15–20 years (Rosenlund and Skretting, 2006). The price of cod is only moderate and therefore it is crucial to minimize the production costs in cod farming. Temperature is one of the most important environmental parameters determining the growth potential of cod (Jobling, 1988; Brander, 1994; Björnsson et al., 2001) and the optimal temperature for growth has been found to decrease with increasing weight of cod (Björnsson et al., 2001). Up to a certain size the juveniles must be reared in land-based farms where optimal temperatures can be maintained but for the rest of the life-cycle cod have to be reared in sea pens at ambient temperature.

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Considering the large investments needed for the ongrowing phase it is important to be able to predict the growth potential of cod in different geographical locations. The temperature profile on each location may in the long run determine to a large extent the competitiveness of the cod farm. It is therefore important to have a reliable model to predict the potential growth of cod reared at different geographic locations. A few years ago, two of the authors developed a growth model for cod (Björnsson and Steinarsson, 2002). The model appeared to be accurate at the time but lately it has become apparent that it tends to underestimate actual growth rates of cod in commercial farms. One obvious shortcoming of that model is that it can not accurately predict how optimal temperature for growth (Topt.G) varies with weight of cod, particularly for juvenile fish. This called for a complete revision of the model. The old data set was revisited and expanded with a series of new experiments to strengthen the foundation of the model. 2. Materials and methods 2.1. Experiments The methodology applied in the old data set has been described in earlier publications (Björnsson et al., 2001; Björnsson and Steinarsson, 2002) and thus only the new data set will be dealt with here. The experiments were carried out at the Mariculture Laboratory of the Marine Research Institute at Grindavík in Southwest Iceland. The seawater supply of the laboratory, obtained from a 50-m-deep well, has a constant temperature (7 °C) and salinity (32‰). Cod in the largest size-class (Experiment G) were hatched in April 2004 whereas cod from all other sizeclasses were hatched in April 2005 from eggs collected from fish caught off the southwest coast of Iceland, fertilized onboard and brought to the laboratory. The larvae were fed on rotifers and Artemia until weaned on dry feed. During the larval period the temperature was gradually increased from 8 to 12 °C. The initial mean weights of the experimental fish were 1, 4, 9, 37, 96, 301

Fig. 1. Relationship between specific growth rate (G) and temperature for seven size-classes of cod W = 2, 7 and 14 g (A); W = 57, 143, 373 and 1050 g (B). Data fitted with a third order polynomial (see Table 2).

and 769 g. The cod were reared in groups of 100 fish per tank, except 75–88 for the largest fish. The three smallest size-classes were reared at six temperatures (0, 4, 8, 12,

Table 1 The proximate composition of the dry feed according to the manufacturer's specifications (Danafeed Ltd. and Fódurblandan Ltd.) Experiment

Feed type

A B C D E F G

Dan-Ex 0.5/1.0 mm Dan-Ex 1.3 mm FB 15/53 2 mm FB 15/53 3 mm FB 15/53 4 mm FB 15/53 8 mm FB 18/50 12 mm

Protein

Fat

62 62 53 53 53 53 53

13 13 15 15 15 15 15

Carbohydrates 7.0 7.0 11.5 11.5 11.5 11.5 11.5

Fibre

Ash

Water

0.8 0.8 1.0 1.0 1.0 1.0 1.0

11.6 11.6 12.0 12.0 12.0 12.0 12.0

N/A N/A 9.0 9.0 9.0 9.0 9.0

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16 and 20 °C), the 37 g fish at five temperatures (4, 8, 12, 16 and 20 °C) and the three largest size-classes at four temperatures (4, 8, 12 and 16 °C), using two tanks at each temperature (Appendix A). Temperature which was measured daily had a mean standard deviation of 0.4 °C. The experimental fish were obtained from a large group of fish which was maintained in the laboratory at intermediate temperatures (8–10 °C) and excess feeding. The day before the initial weighing, the fish were randomly selected, moved to the experimental tanks and gradually adapted over one day to the selected temperatures (the 1 g fish were adapted over two days). The duration of the experiments varied from 17 to 154 days depending on the size of fish (Appendix A) to keep the relative weight increase of similar magnitude in all the experiments. The fish were weighed individually without anaesthesia at the start and termination of each experiment. A bucket with seawater was placed on an electronic balance and one by one the fish were dropped into the bucket from a nylon strainer after wiping it with a moist cloth to remove excess water. The three smallest size-classes were reared in grey rectangular tanks (90 × 90 × 30 cm), the two intermediate size-classes in green rectangular tanks (2.0 × 2.0 × 0.8 m) and the two largest size-classes in grey circular tanks (2.9 m diameter × 0.9 m). Heat exchangers were used to warm or chill the seawater in a flow-through system and the incoming water was degassed and aerated before entering the tanks. The water flow ( N 0.5 l/min/kg) was adjusted to keep ammonia concentration well below a critical level (Björnsson and Ólafsdóttir, 2006) and pure oxygen added to each tank to maintain oxygen saturation close to 100%. All the tanks were illuminated 24 h a day with incandescent lamps (50–200 lx at the surface) in an attempt to remove seasonal effects and prevent the largest fish from becoming sexually mature. At the end of the experiment with the largest fish (Experiment G) all the fish were sacrificed to measure the weight of the gonads. No sexual maturation was detected at any temperature, except 4 °C where 12% of the males and

Fig. 2. Linear regression between lnG and lnW at 4.1 °C (A), 8.0 °C (B), 12.0 °C (C), 16.0 °C (D) and 19.7 °C (E).

2% of the females had ripening gonads (gonadosomatic index N 5%). All the experimental fish were hand-fed 3– 5 times each day during the working hours (8:00–16:00)

Table 2 The relationship between specific growth rate (G) and temperature in °C (T) estimated by a third order polynomial (G = a + bT + cT2 + dT3) for different geometric mean weights of cod in g (W) in experiments A–G (see Fig. 1) Experiment A B C D E F G

W

a

b

c

d

r2

n

Topt.G

Gmax

1.98 6.74 13.7 56.9 143.4 373 1050

− 0.4970 − 0.2425 − 0.1596 0.0034 0.4316 0.2631 0.0698

0.1656 0.1519 0.1498 0.1702 0.0788 0.0230 0.0819

0.08588 0.05520 0.02442 0.00769 0.00281 0.00631 − 0.00605

−0.004266 −0.002931 −0.001515 −0.000813 −0.000356 −0.000465 0.000110

0.995 0.999 0.976 0.992 0.995 0.989 0.962

12 12 10 10 8 8 8

14.3 13.8 13.2 12.1 11.6 10.6 9.0

6.96 4.66 2.59 1.75 1.17 0.66 0.40

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with commercial dry feed from Danafeed Ltd. and Fódurblandan Ltd. In experiments A–C automatic beltfeeders were used additionally during the rest of the 24 h period to ensure that the fish were fed to satiation. The feeders were stocked with equal amounts of feed as had been given earlier that day. It was not possible to measure with sufficient accuracy the amount of leftovers in the experiments and therefore the actual food intake or feed conversion ratios are not presented here. The protein/fat ratio in the diet was highest for the smallest fish (62/13) and lowest for the largest fish (50/18) (Table 1). One Icelandic and five Norwegian growth studies with large cod reared at ambient temperatures were used as a comparison with the model calculations as well as to finetune the model. The Norwegian studies (Fig. 4A–E) were carried out in sea cages which were illuminated 24 h a day and stocked with juveniles produced in hatcheries or sea lagoons. In the Icelandic study (Fig. 4F), immature wild cod captured near the southwest coast in late summer 1993 were tagged and reared at 7 °C and natural photoperiod in two 8 m circular tanks from 9 February 1994 to 8 February 1995 and fed to satiation on frozen capelin (Mallotus villosus) and shrimp (Pandalus borealis). Sea temperature profiles for Northwest Iceland were copied from the web site of the Marine Research Institute, Iceland (www.hafro.is/sjora/) and the profiles for West Norway were kindly provided by the Institute of Marine Research, Austevoll, Norway.

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Fig. 3. Intercept (α) and slope (β) as a function of temperature (T) with 95% confidence interval. Diamonds are data from Fig. 2 and squares are data from Björnsson and Steinarsson, 2002 (see Table 3). α =a +bT+ cT2, r2 = 0.985; β =d +eT, r2 = 0.971.

2.2. Data analysis All the growth rate estimates in our study refer to food-unlimited growth rate, i.e. the experimental fish were in all cases fed to satiation. Specific growth rate (G) was calculated according to the formula G = 100 (lnW2 − lnW1) / (t2 − t1), where W1 and W2 are the weights of the fish measured at times t1 and t2. Geometric mean weight (W) was calculated as: W = (W1 ⁎ W2)1/2. A linear

relationship was found between natural logarithm of G and natural logarithm of W: lnG = α + βln(W). The intercept (α) and slope (β) were found to change with temperature (T): α = a + bT + cT2 and β = d + eT. The regression analysis was carried out in S-plus 7 (Insightful Corporation, Seattle, USA), estimating the parameters by the method of least squares with 95% confidence limits.

Table 3 Parameters (standard error in parentheses) from the lnG vs. lnW linear regressions in Fig. 2 and from Björnsson and Steinarsson, 2002 T (°C)

α

β

r2

n

W range (g)

Data

4.1 8.0 12.0 16.0 2.1 4.1 7.3 10.0 13.0

0.4306 (0.1008) 1.6503 (0.0704) 2.2296 (0.0678) 2.3304 (0.0661) 0.0260 (0.0477) 0.8347 (0.1534) 1.5028 (0.0746) 1.8482 (0.0573) 2.2255 (0.0767)

− 0.2043 (0.0224) − 0.3534 (0.0161) − 0.4479 (0.0154) − 0.5092 (0.0164) − 0.1884 (0.0137) − 0.2772 (0.0282) − 0.3508 (0.0152) − 0.3810 (0.0135) − 0.4680 (0.0201)

0.893 0.976 0.986 0.990 0.979 0.906 0.953 0.974 0.968

12 14 14 12 6 12 28 23 20

1.1–996 1.6–1057 1.9–1041 2.0–944 1.2–250 11.5–2224 2.2–6628 2.8–2177 3.9–2065

Fig. 2 Fig. 2 Fig. 2 Fig. 2 B&S B&S B&S B&S B&S

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Table 4 Standard error, t-values and P-values for the model parameters in Fig. 3 Parameters a b c d e

Mean

SE

t-values

P-values

− 0.7620 0.3982 − 0.0128 − 0.1500 − 0.0239

0.1767 0.0458 0.0025 0.0185 0.0019

− 4.31 8.70 − 5.05 − 8.10 − 12.35

0.0050 0.0001 0.0023 0.0001 0.0000

In the new data set, α and β could be estimated accurately for four temperatures (Table 3). Data for 20 °C were omitted due to limited weight range and in-

▪

sufficient adaptation time. Two abnormally low measurements in experiment C (4.1 °C, W = 9.2 g) and two in experiment F (16.4 °C, W = 319 g) were omitted. In the old data set (Appendix A in Björnsson and Steinarsson, 2002), α and β could be estimated accurately for five temperatures (Table 3). Data for 16 °C were omitted due to high mortality of the largest fish. Experiments carried out 6–27 August 1996 for W = 1.5 g and 6 January–12 March 1997 for W = 109 g were omitted from the analysis as they generated much lower growth rates than fish of similar size in the new data set. The main reason for poor growth rate in these

Fig. 4. Modelled weight ( ) compared with measured weight (•) in six growth studies of large cod: Villa Cod Farm, Norway, year-class 2002 (A), Villa Cod Farm year-class 2003 (www.leppefisk.no/no/torsk/forskning/) (B); Storfjord Torsk, Norway (Sørensen et al., 2005) (C); Tveit Fish Farm, Norway, Taranger et al. 2006, experiment 1 (D); Taranger et al. 2006, experiment 2 (E); Björn Björnsson, unpublished results for Icelandic cod reared in large tanks at 7 °C (F). The temperature profile for Austevoll (see Fig. 6A) was used in the model calculation for the five Norwegian studies.

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two experiments may have been insufficient feeding frequency and short daylength during winter. Experiments carried out 28 July–7 September 1995 for W = 7.5 g at 4.2 °C were also omitted since these two groups clearly had not adapted to the low temperature as seen by the increased growth rate during the following period, 7 September–19 October 1995. Finally, one typing error in Appendix A (Björnsson and Steinarsson, 2002) was corrected; in the experiment starting 3 May 1993 and performed at 5.1 °C the correct value of W2 is 3191 g (instead of 2421 g). The following recursion formula was used to calculate the growth of cod with time: W2 = e^(0.01 ⁎ e^(α + βlnW1) + lnW1). It was developed from: 100 (lnW2 − lnW1) / t2 − t1 = e^(α + βlnW) and by performing the calculation for one day at a time t2 −t1 = 1 and approximating W with W1. This assumption was tested by calculating W2 in steps of 1/10 of a day instead of once a day (W2 = e^(0.001 ⁎ e^(α + βlnW1) +lnW1)) starting with the initial weight of 2 g. The resulting body weight at one and two years of age at optimal temperature differed by less than 1% suggesting that calculations for whole days are sufficiently accurate in most cases. It is easy to use Excel for this task, making columns for days (t), daily temperatures (T), α, β and W. The initial cell in the W column is W1 and the second cell is W2 as calculated by the recursion formula above. This cell can then be copied down the column.

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as a linear function of temperature (Fig. 3) between 2– 16 °C. The results for 20 °C were omitted because the weight range was limited and because this temperature is near the lethal limit of cod and special adaptation prior to the experiment may have been required. All five parameters of the growth model were highly significant (Table 4). The model calculations with the parameters obtained from Figs. 2–3 showed an excellent fit to available data for juvenile cod but appeared to underestimate the growth rates of large cod in sea cages in Norway. In order to minimize this apparent discrepancy and to increase the practical value of the model, it was decided to finetune the model in accordance with the Norwegian data. Adjustment to these data has a tendency to decrease the slopes (β) shown in Fig. 2, especially at higher temperatures, without changing the intercept (α) and

3. Results Changes in growth rate with temperature, as measured in experiments, could be adequately described with a third degree polynomial for seven different sizeclasses of cod (Fig. 1, Table 2). The growth rate of each size-class reaches maximum (Gmax) at the optimal temperature (Topt.G). Topt.G as estimated by these polynomials decreased from 14.3 °C for 2 g fish to 9.0 °C for 1050 g fish and Gmax decreased from 7.0%/day for 2 g fish to 0.40%/day for 1050 g fish. The curves are slightly asymmetrical with a rapid decline in growth rate above Topt.G. The curves flatten with increased fish size. However, the growth rates at the highest (20 °C) and lowest temperatures (0 and 4 °C) may have been underestimated due to insufficient adaptation time for those temperatures. There was a linear relationship between lnG and lnW for the five selected temperatures (Fig. 2, Table 3). A linear relationship was also found for five temperatures in the old data set. The intercept (α) in the above relationship was found to change with temperature according to a second order polynomial and the slope (β)

Fig. 5. Model calculations of specific growth rate of cod for fish weights 2, 5, 10, 20, 50 and 100 g (A) and 200, 500, 1000, 2000 and 5000 g (B).

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thus have largest effects on the e-parameter (β = b + eT). Therefore, the model was tuned to better fit the data for large cod by slightly adjusting the e-parameter from − 0.0239 to − 0.0215. This change, which is within the 95% confidence limit (Fig. 3B), had negligible effects on the model calculations for juvenile cod (Fig. 5A) but increased the growth rate of large cod at high temperatures (Fig. 5B) enough to fit reasonably well with five growth studies of cod in Norway and one in Iceland (Fig. 4). All the following model calculations were made with this modification of the e-parameter. The model results show that with increasing temperature the growth rate of juvenile cod first goes through a phase of acceleration and then deceleration before maximum growth rate is reached at optimal temperature (Fig. 5). The model results also show that the growth rates at each temperature decline with increased fish weight. The model outcome (Fig. 5) is thus in good agreement with the measured results (Fig. 1). The model also predicts that Topt.G declines with increasing fish weight (W) in accordance with the following equation: Topt.G = 15.57 − 0.8426lnW. The largest difference between the present (Fig. 5) and former model (Fig. 3 in Björnsson and Steinarsson, 2002) is the shape of the curves and the shift in optimal temperature.

There was a good agreement between the model calculations (y), using the modified e-parameter (−0.0215), and measurements (x) of G (y= 0.063+ 1.0691x, r2 =0.960, n = 160), Topt.G (y = 3.567+ 0.7139x, r2 = 0.878, n = 12) and Gmax (y= 0.040+ 1.023x, r2 =0.987, n = 12). The model calculations were very similar to the measurements for G and Gmax. The discrepancy seen for Topt.G may be partially due to insufficient temperature range used to estimate Topt.G in some of the old experiments (Björnsson et al., 2001) and insufficient adaptation time for the groups reared at the highest temperatures in the new experiments (Fig. 1). Furthermore, it is difficult to estimate Topt.G accurately with data from individual experiments, because the curves of growth rate vs. temperature are relatively flat near the peak. The model can be used to predict growth curves at different locations where sea temperatures have been measured. As an example, the sea surface temperature profiles for West Norway and Northwest Iceland (Fig. 6A) were used as an input into the model to predict the growth rate of 30 g cod juveniles stocked in sea cages 15 May 2003 (Fig. 6B). Clearly, the low winter temperatures in Iceland and the high summer temperatures in Norway reduce the growth rate of cod. The model predicts that by the end of the first, second and third year

Fig. 6. Near sea-surface temperature in Northwest Iceland (Aedey 66°06′N, 22°40′W, 1.5–4.7 m depth, black line) and West Norway (Austevoll 60°05′N, 5°14'E, 5 m depth, grey line) (A). Growth curves in Northwest Iceland (black line) and West Norway (grey line) as predicted by the model for 30 g juveniles stocked in 15 May 2003 (B).

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the mean weights are 344 vs. 388 g, 1624 vs. 2122 g and 4640 vs. 6320 g in Northwest Iceland and West Norway, respectively. 4. Discussion There was some variation in the level of dietary protein and fat in the commercial feeds used for the different fish sizes. However, the ratio of macronutrients has been found to have relatively minor effects on the growth rate of cod (Rosenlund et al., 2004; Hamre and Mangor-Jensen, 2006). In the new data set all the fish were reared at constant illumination, whereas a natural photoperiod (at 64 °N) was used in the old data set, resulting in some growth reduction in experiments carried out mainly during the winter months. It seems sufficient to feed 200–800 g cod at 8 °C once every two days (Rosenlund et al., 2004) and 1–2 g cod at 10 °C four times per day from 8:00–15:00 h (Folkvord and Otterå, 1993). In the old data set the daily feeding time was restricted to eight hours whereas in the new data set an extra night feeding was added for the small juveniles. Faster growth rates of small juvenile cod (1–10 g) in the new experiments compared to the old experiments suggest the importance of high feeding frequency for small juvenile cod when reared at high temperatures. The new data set also suggested that there was insufficient adaptation time for the fish reared at extreme temperatures and therefore in future experiments longer adaptation times should be adopted. Accordingly, all measurements suspected to suffer from short day length, insufficient feeding frequency or inadequate adaptation time were excluded. The model parameters could only be estimated for four temperatures in the new data set and therefore the old data set, after careful screening, was also used to parameterize the model. There was no significant difference between the growth parameters estimated from the two data sets (Fig. 3). The model parameters were estimated from 160 growth rate measurements, 108 measurements from the old data set (Björnsson and Steinarsson, 2002) and 52 measurements from the new data set, after critically excluding 36 abnormally low measurements. In the new data set, special care was made to ensure optimal growth conditions by maintaining near 100% oxygen saturation, continuous light to delay sexual maturation and automatic night-feeding of juveniles to ensure sufficient food supply. Fish hatched in the same month in the laboratory were used in all new experiments, whereas in the old experiments the juveniles were hatched in the laboratory but the larger fish captured at sea.

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The five parameter growth model presented here is a significant improvement from the earlier three parameter power model (G = αWβ) developed by Björnsson and Steinarsson (2002). The earlier model could not predict accurately changes in Topt.G with weight of juvenile cod. That model was based on a linear regression of G and W on a log–log scale. The five parameter model which was developed from the linear relationship between lnG and lnW (i.e. G = e(α+βlnW)) is mathematically more flexible and can simulate the data more closely. The new model predicts more accurately changes in Topt.G and Gmax with weight of fish and the bell-shaped form of the G vs. T curves is more in line with the observed curves. The model is most reliable for a certain temperature range (2–16 °C). At very low temperatures where measured growth was negative, the results could not be used to estimate α and β. In our laboratory it was only possible to carry out experiments at 0 °C in small tanks, suitable for juvenile cod. However, these experiments were probably too short (17, 27 and 39 days) and the adjustment time not long enough (1–2 days) to give reliable estimates of growth rate. In one earlier experiment, 1.2 g cod were reared at 2.0 °C for 53 days (Björnsson and Steinarsson, 2002) resulting in G = 1.0%/day which is a much higher value than according to the polynomial regression in Fig. 1A but similar to the model predictions in Fig. 5A. Growth experiments at 20 °C were only carried out for four size-classes of fish (W = 1.3, 5.0, 10.4 and 37.3 g). Mortalities for the three smallest size-classes ranged between 4–26% but 58–65% for the largest sizeclass. High mortality may thus have affected these estimates. A longer adaptation time at these extreme temperatures might have produced more reliable results. Fish are more prone to diseases at high temperatures and to ensure maximum growth under these conditions it may be beneficial to add antibiotics to the feed (which was not done in the present study). The model was developed from experiments with fish ranging in weight from 2 to 2000 g as the facilities at the laboratory did not allow to study wider size range. It is clear that the model does not apply to the larval and early juvenile phase, since specific growth rate increases with age of larvae (Steinarsson and Björnsson, 1999), reaches a maximum at a mean weight of approximately 0.01 g wet weight (Folkvord, 2005) and from that point on it declines continuously with body weight. The model works well for juveniles down to about 2 g but it is unknown if or how far it can be extrapolated to smaller sizes before the results become unreliable (too high). Our largest experimental tanks with temperature

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control (2.9 m diameter) were considered too small to work with larger fish than about 2 kg. In the present study, mortality of cod larger than 1 kg was quite high at 16 °C and thus it is likely that the growth rates under these conditions may have been underestimated. As it is of considerable interest to predict growth rates for cod up to about 5 kg the model results were tuned in accordance with growth rate results reported for cod reared in sea cages in Norway where the fish had ample space, high water quality and continuous light to prevent or delay sexual maturation (Karlsen et al., 2006; Taranger et al., 2006). Weight measurements of large Icelandic cod reared in large tanks at 7 °C do not suggest that the growth potential of Icelandic cod is any less than that of Norwegian cod. It is not advisable to use the model for larger cod than about 5 kg since it can only describe the accelerating part of the general growth curve. In the s-shaped von Bertalanffy growth model the inflection point is at W = 0.296W∞ ≅ 6 kg for North sea cod (Beverton and Holt, 1957). Genetic differences in growth performance between different cod stocks cannot be ruled out although the available results do not suggest much difference in food-unlimited growth rate between stocks (Svåsand et al., 1996; Purchase and Brown, 2001; Kolstad et al., 2006). In two out of five growth studies of large cod (Fig. 4B, C) there was almost a perfect match with the model results and a reasonably good agreement in four studies (Fig. 4A, D–F). This modest difference between the model and the measurements is acceptable considering the uncertainty in estimating the actual rearing temperatures and the possible effects of other factors, such as origin of fish, size-grading, sub-sampling bias, quality of the juveniles, as well as influence of diet and rearing conditions during the larval phase on growth performance. For example, at Villa Cod Farm the faster growing juveniles of the year-class 2002 (Fig. 4A) were produced in sea lagoons on natural zooplankton (Parisvatnet) whereas the slower growing juveniles of the year-class 2003 (Fig. 4B) were produced intensively on rotifers and Artemia (Troms Marin Yngel), a factor which has been found to explain long-term differences in growth rates (Imsland et al., 2006). The authors believe that the model can be useful for other scientists studying growth rate of cod. The model may, for example, be useful in assessing inherent differences in growth parameters between different cod stocks and to monitor the progress of selective breeding (Kolstad et al., 2006). The model may also be helpful in assessing the feasibility of cod farming in areas with different temperature profiles and to predict the length of time it will take for cod to reach

harvestable size. Finally, the model can be used to estimate the food requirement in a cod farm, assuming a given feed conversion factor (Björnsson et al., 2001). Sea surface temperature profiles largely dictate the feasible locations for cod farming. In the five countries where cod farming is being developed the lowest and the highest monthly mean temperatures range between about 1 to 10 °C (Aedey, Northwest Iceland), 2 to 9 °C (Vardø, North Norway), − 1 to 13 °C (Station 27, Newfoundland), 6 to 10 °C (Mykines, Faroe Islands), 5 to 14 °C (Stad, West Norway) and 7 to 14 °C (Milport, West Scotland)(Jónsson, 2004). The model calculations were done for two of these areas, Northwest Iceland and West Norway, where cod farming is under rapid development. Higher temperatures for cod farming are not available elsewhere in Iceland since the south coast, where higher temperatures are found, is too exposed for sea cages. However, cod farming can probably be carried out along most of the Norwegian coast from Stavanger in the southwest (59 °N) all the way to North Norway (71 °N) where the temperature profiles are more similar to the ones in Northwest Iceland. The model predicts that cod will grow faster to market size in West Norway than in Northwest Iceland when 30 g juveniles are stocked in sea cages. Assuming no genetic differences in growth performance between Norwegian and Icelandic cod, the model predicts that juvenile cod will initially grow much faster in West Norway than in Northwest Iceland due to higher sea temperatures. However, with increasing fish size and lower optimal temperature the relative differences in growth rate become smaller and smaller and during their third summer the large cod are expected to grow faster in Northwest Iceland than in West Norway. Mortality of cod increases with increasing temperature above optimal temperatures (Björnsson et al., 2001). Therefore, it is likely that the risk of mortality of large and valuable cod is higher in West Norway than in Northwest Iceland during the summer months, especially in unusually warm summers. Thus, it is likely that the optimal slaughtering size of cod is larger in Northwest Iceland (perhaps 4–5 kg) than in West Norway (perhaps 3–4 kg). In Iceland it may be feasible to grow cod juveniles hatched in spring in land-based facilities until the following spring both due to the low winter temperatures and the availability of inexpensive geothermal water. By growing the juveniles at optimal temperatures for a year from hatching they can be stocked in May at an average weight of 250 g which will able them to grow to 3434 and 3684 g at the end of the second year in Northwest Iceland and West Norway, respectively. In this scenario of stocking sea cages with 250 g juveniles

B. Björnsson et al. / Aquaculture 271 (2007) 216–226

the mean weight at the end of the second year is only 7% lower in Iceland than Norway whereas the difference is 24% when stocked with 30 g juveniles. Although our model predicts that overall the temperature conditions for farming cod are somewhat better in Norway than in Iceland it is premature to conclude about their relative competitiveness as several other factors than sea temperature determine the feasibility of cod farming. Acknowledgements Mr. Njáll Jónsson and Mr. Kristján Sigurdsson, Marine Research Institute, Grindavík, took good care of the fish in the experiments and Dr. Ørjan Karlsen, Institute of Marine Research, Austevoll, provided sea temperature data for West Norway. Dr. Lorna Taylor and Dr. Gudmundur Thórdarson, Marine Research Institute, Reykjavík, critically read the manuscript and Mr. Sigurdur Jónsson, Marine Research Institute, helped with the statistical analysis. Three anonymous reviewers made several suggestions which improved the quality of the paper. Appendix A Table A1 Growth data of cod (new data set) in seven laboratory experiments. Mean temperature (T), initial and final number of fish (n1, n2), initial and final mean weight (w1, w2) in each tank. Initial and final dates in the experiments: A. 1–18 July 2005, B. 20 July–16 August 2005, C. 18 August–26 September 2005, D. 19 October– 12 December 2005, E. 12 January–22 March 2006, F. 3 May–3 July 2006, G. 20 October 2005–23 March 2006. Experiment T n1 n2 (°C) A A A A A A B B B B B B C C C C C C D

0.4 4.1 8.1 12.0 15.7 20.0 0.0 4.1 7.9 11.9 16.0 19.3 0.1 4.0 7.9 12.0 16.0 19.7 4.1

100 101 100 104 101 101 101 101 100 100 100 100 100 100 101 100 100 100 100

w1

93 0.98 100 1.02 98 1.11 104 1.10 100 1.12 89 0.95 100 3.81 101 3.72 99 3.67 99 3.62 97 3.75 96 3.78 90 8.98 96 8.97 101 9.19 96 8.59 96 9.19 74 9.28 100 37.0

w2 0.93 1.28 2.28 3.29 3.57 1.70 3.58 4.91 8.38 12.17 11.99 6.66 8.66 9.50 19.05 23.22 22.84 12.21 56.3

T n1 (°C)

n2

w1

0.5 4.2 8.1 12.0 15.8 20.0 0.1 4.2 7.9 11.9 16.0 19.4 0.2 4.2 7.9 12.0 16.0 19.7 4.1

94 101 101 99 102 84 98 100 100 99 100 95 98 100 98 94 94 76 100

1.08 1.05 1.10 1.14 1.10 1.08 3.59 3.66 3.73 3.80 3.63 3.73 9.30 8.81 9.01 8.29 9.07 9.07 38.2

100 101 102 100 104 102 100 100 100 100 100 100 100 100 102 100 100 100 100

w2 0.98 1.33 2.20 3.38 3.48 1.67 3.39 5.00 8.20 12.35 11.69 6.61 8.63 9.58 18.05 21.30 22.45 11.54 57.3

225

(continued) Table A1 (continued) Experiment T n1 n2 (°C)

w1

w2

T n1 (°C)

n2

w1

w2

D D D D E E E E F F F F G G G G

37.4 35.4 37.0 36.6 96.0 98.3 96.3 96.1 304.8 303.3 309.5 293.8 754.6 777.7 774.4 756.0

83.6 88.0 80.5 38.1 163.1 204.7 214.9 188.4 392.8 447.0 453.3 347.6 1245.0 1436.9 1349.1 1178.3

8.0 12.2 15.9 19.6 4.3 8.0 11.9 15.8 4.0 8.0 12.1 16.3 4.2 7.9 12.0 15.9

100 93 90 50 100 99 98 92 100 97 100 69 74 68 44 30

37.0 37.1 37.3 35.7 97.1 94.7 95.4 93.0 292.7 310.9 304.1 290.9 788.8 773.5 775.9 747.1

83.9 90.5 82.0 39.1 169.9 196.3 213.9 181.9 381.6 445.8 454.9 350.3 1258.2 1408.5 1397.6 1146.2

8.1 12.2 15.9 19.7 4.2 8.0 12.0 15.8 3.9 8.0 12.0 16.4 4.2 8.0 12.1 16.1

100 100 100 92 100 80 100 35 100 100 100 98 100 96 100 92 100 100 101 98 100 93 100 77 75 72 75 61 75 48 88 58

100 100 100 120 100 100 100 100 100 100 100 100 76 75 76 62

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