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Field validation of growth models used in Atlantic salmon farming
Field validation of growth models used in Atlantic salmon farming Arnfinn Aunsmo, Randi Krontveit, Paul Steinar Valle, Jon Bohlin PII: DOI: Reference:
S0044-8486(14)00110-0 doi: 10.1016/j.aquaculture.2014.03.007 AQUA 631072
To appear in:
Aquaculture
Received date: Revised date: Accepted date:
5 May 2013 9 March 2014 10 March 2014
Please cite this article as: Aunsmo, Arnfinn, Krontveit, Randi, Valle, Paul Steinar, Bohlin, Jon, Field validation of growth models used in Atlantic salmon farming, Aquaculture (2014), doi: 10.1016/j.aquaculture.2014.03.007
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Field validation of growth models used in Atlantic salmon farming
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Arnfinn Aunsmo1, Randi Krontveit1, Paul Steinar Valle2, Jon Bohlin1,3
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Norwegian University of Life Sciences, Campus Adamstuen, Department of Food Safety and Infection Biology, PO Box 8146 Dep, 0033 Oslo, Norway Kontali Analyse AS, Industriveien 18, 6517 Kristiansund N
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Norwegian Institute of Public Health, Division of Epidemiology, Marcus Thranes gate 6,
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Corresponding author. Tel.: +47 48083021
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P.O. Box 4404, 0403 Oslo, Norway
E-mail address: [email protected]
Keywords: Aquaculture, Atlantic salmon, growth, growth models, validation
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ACCEPTED MANUSCRIPT Abstract Several models for description of fish growth are commonly used in Atlantic salmon
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farming, including the specific growth rate (SGR), the thermal growth coefficient (TGC),
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the Ewos growth index (EGI), and average daily weight gain (ADG). In the present study, a subset of a commercial database containing information from 827 fish groups from the
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year-classes 2000-2005, produced along the Norwegian coastline, was used to validate
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these four growth models. A number of biotic and abiotic factors were fitted to the models of interest in order to evaluate model strengths and weaknesses and to identify
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additional factors whose inclusion may improve model performance. Preliminary analysis indicated non-linear relations; to account for this we applied Generalized Additive
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Models (GAM) in regression analysis. Our findings indicate that ADG was strongly associated with harvest weight and was thus
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deemed unsuitable for describing growth in Atlantic salmon. SGR was also associated with fish size and biased towards small fish when fish of uneven stocking size were compared. The TGC, SGR and the EGI models were all moderately associated with harvest weight, and the same three models were more strongly associated with mean temperature and mean day-length. These models might therefore present bias when used to compare growth in varying environmental conditions. The EGI was considered the most robust model overall for predicting growth at different sizes exposed to variable abiotic exposure such as temperature and light. Finally, the study suggests that the robustness of growth models can be improved by accounting for non-linear effects on growth and including abiotic factors such as temperature, light, and latitude.
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ACCEPTED MANUSCRIPT 1. Introduction Growth is a production parameter of central interest in farmed Atlantic salmon
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operations. Important areas in improving and managing fish growth includes:
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identification of causal factors, quantifying effects, predicting fish growth, as well as benchmarking growth between cages, sites, genetic strains, and companies. Growth in
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fish is regulated by abiotic factors such as time, temperature and light (Austreng et al.,
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1987; Duston and Saunders, 1995; Forsberg, 1995; Smith et al., 1993), as well as such biotic factors as body size (Brett, 1979; Jobling, 1983; Talbot, 1993). Local factors
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related to environment, management, nutrition, and diseases have also been found to
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Pratoomyot et al., 2008).
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affect growth (Breck et al., 2003; Fivelstad et al., 2007; Midtlyng and Lillehaug, 1998;
Models that convert feed given to fish into increased biomass or growth are
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commonly used for monitoring the increase in fish biomass over time on salmon farms (Aunsmo et al., 2013; Brett, 1979). However, these models cannot be used to make predictions of growth, and comparing levels of feeding have limited value when studying growth in fish groups of uneven size or subjected to varying abiotic exposures. Several models are available for the prediction and comparison of growth in farmed Atlantic salmon; the specific growth rate (SGR) (Austreng et al., 1987), the thermal growth coefficient (TGC) (Cho, 1992; Iwama and Tautz, 1981), and the Ewos growth index (EGI)1. Average daily weight gain (ADG) is commonly used in studies of growth in terrestrial livestock (Johansen et al., 2013), and has also been applied in aquaculture (Garber et al., 1995). These growth models are primarily used for describing growth between a start-weight (w0 - often at time of sea transfer) and an end-weight (we – 1
Ewos AS, http://www.ewos.com/wps/wcm/connect/ewos-content-group/ewos-group
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ACCEPTED MANUSCRIPT often at time of harvest) or to predict growth from a start-weight at time=t0 to an endweight at time=te. For instance, SGR is based on the natural logarithm of body weight
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between t0 and te (Bureau et al., 2000). The TGC model combines the cubic root of fish
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weight with a linear function of temperature, and is based on data from controlled growth studies (Iwama and Tautz, 1981). Abiotic factors such as light and temperature are
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included in some models, thus with the potential of controlling for varying physical
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exposure. The EGI model, as such, is a linear regression model based on estimated parameters from field data. Growth trajectories, i.e. repeated weight measurements, are
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not included in any of the models.
In order to objectively investigate latent effects related to disease, feed, local
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environment, and management practices, etc. over a time interval, the models should principally be independent of w0 and we. Similarly, to compare growth in varying
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environmental settings, the models should also be independent of, or account for, variables such as temperature and light. Correlations between harvest weight, latitude, temperature and the growth models have been described for Atlantic salmon, suggesting that the models reflect different properties (Iversen and Kosmo, 2004). Non-linear effects are described for temperature (Jobling, 1983), and are further indicated by the use of squared, quadratic and third root variables in the EGI model. The objectives of this study were to validate four growth models used in Atlantic salmon farming, exploring the effects of biotic and abiotic factors on the models through the use of field data. Preliminary analyses revealed non-linear relationships, and validation was thus also performed using Generalized Additive Models (GAM) (Hastie and Tibshirani, 1986).
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2. Materials and methods
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2.1 Commercial Field Data - the MonAqua database
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The benchmarking company MonAqua has since the year-class of 1998 collected biological information from the Norwegian salmon industry, based on a voluntarily
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contribution by companies (Anonymous, 2007). Information is registered at the fish
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group level (Table 1), where a fish group is defined as fish of common year-class, genetic origin (strain), smolt plant, vaccine, and sea site of initial transfer. Fish groups stocked
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between 2000 and 2005 had the most complete observations and were included in the present study; more recent data were unfortunately not available. These 935 fish groups
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came from 28 companies and were located on 225 sites from 58.1° to 70.7° degrees north, constituting a north-south range of approximately 1400 km (Table 1). The
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statistical unit in the dataset was the fish group with an average of 165 000 salmon stocked per group (Table 1). The dataset contained no information about grading and mixing, which usually takes place within the fish group. Each site had a registered mean number of 624 000 stocked fish per year-class, each site commonly taking on a new yearclass every second year.
Estimates of growth, as expressed by the four growth models SGR, TGC, EGI and ADG, were calculated in the period from sea transfer until harvest. As the sea transfer period of a fish group usually is limited to a few days, mean date of sea transfer was used. Time of harvest was estimated (by the MonAqua database) as the biomass-weighted time of slaughter, giving both a date of harvest and a harvest weight for each fish group. Harvest period per fish group was not available in the dataset. Total production time
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ACCEPTED MANUSCRIPT (days) was calculated as time between sea transfer and the estimated harvest date. The participating fish farmers supplied temperatures to the MonAqua database as monthly
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total degree-days, which were then summed and divided by days at sea, giving the mean
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temperature for each production period (Table 2).
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2.2 Calculation of growth variables for individual fish groups
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Estimates of growth were calculated for individual fish groups in the MonAqua database by each of the four growth models: ADG, SGR, TGC and EGI.
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For all models, w0 and we designate stocking and harvest weight, respectively. Days d are summed from d=1 until slaughter at d=n, and daily temperature Td for each
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day from d=1 until d=n. Average daily weight gain (ADG) was calculated as: ADG
( we w0 ) n
d d 1
Daily specific growth rate (SGR) was calculated according to Brett and Grover (1979) as: SGR
(ln(we ) ln( w0 )) n
d d 1
Thermal growth coefficient (TGC) was calculated and multiplied by 1000 according to Iwama and Tautz (1981) as: TGC
1000(3 we 3 w0 ) n
T d 1
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d
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(x1i), change in day length (x2i), third root of weight (wi1/3), day length times third root of
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weight (x1i ∙ wi1/3), and the third root of squared weight (wi2/3). ei~N(µ=0, =1) designates
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the normally distributed errors, with mean µ=0 and standard deviation =1, for each observation i:
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YiEGI=a0+a1Ti2+a2Ti4+a3x1i+a4x2i+a5wi1/3+a6x1iwi1/3+a7wi2/3+ei
The estimated parameters for the intercept (a0) and each variable (a1-a7) were not
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released, but were calculated by the MonAqua database using an Ewos-developed
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application.
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2.3 Calculation of day-length and civil twilight Hours of daylight (i.e. sun above the horizon) and civil twilight (i.e. sun between the horizon and 6° below horizon) were calculated on a daily basis using Microsoft® Excel (Microsoft Corporation, Redmond, WA, USA) for each 0.1° latitude in the period the fish groups were at sea (Glarner, 2007).
m 1 tan(l ) tan( a cos( jd ))
h cos(l )
Where l is latitude, a is the angle of the equatorial plane to the ecliptic plane (23.439º), j = π /182,625° in radians, h is the angle in degrees of the sun below the horizon and d is day of the year starting on December 22. The outcome m was further normalized to be in
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ACCEPTED MANUSCRIPT the interval [0, 2], where values below zero were set equal to 0 (the polar night) and values above 2 were set equal to 2 (midnight sun).
arccos(1 m) 180
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b
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The formula:
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is the proportion in radians of the day where the sun is above a given angle h. Total hours
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of light (in hours) were calculated as b∙24 for h=0 and h=6º. The hours of light were further summed for individual fish groups from stocking until harvest (total light-hours)
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and split into day-length (h=0°) and civil twilight (hours of light at sun h=6º below
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horizon subtracted day-length) (Table 2).
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2.3 Data management and statistical analysis
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The MonAqua database was converted into STATA 12.0 (StataCorp LP, College Station, TE, USA) and R (Development Core Team 2011) where data for light were merged using fish group number as an ID. Only fish groups with complete observations were used in final analysis, excluding 96 groups. The variables were quality controlled for extreme values (minimum and maximum), and an observation with maximum mean temperature of 14.4°C at 62.7° degrees North over 581 production days was considered erroneous and omitted. Observations with EGI above 150 were considered erroneous and as a consequence five observations were excluded (John H. Pettersen, EWOS pers. com.). Six fish groups were further omitted based on extreme values of harvest weight, day length or stocking size, leaving 827 fish groups for final analysis (Table 2).
2.4 Statistical modelling
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ACCEPTED MANUSCRIPT Literature and preliminary analysis (graphical plots) indicated the presence of nonlinear relationships. Consequently, Generalized Additive Models (GAM), using the
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'mgcv' package in R (R Core Team, 2013; Wood, 2001), which uses cross-validation to
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determine the degree of smoothing, were fitted to explore biotic and abiotic variables (Table 2) potentially associated with the growth models (Hastie and Tibshirani, 1986).
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zi=f(yi)=a0+s1(x1i)+a1x2i+s2(x3i)+ s3(x4i)+s4(x5i)+s5(x6i) +s6(x7i)+ei
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zi, designates the f() -transformed response variable yi representing the growth models (TGC, SGR, EGI and ADG), while sl (1l6) are the spline functions (see (Hastie and
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Tibshirani, 1986; Wood, 2006; Wood and Augustin, 2002) for details regarding transform of response and selection of smoothing splines) for the included explanatory variables
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(Table 2): stocking weight (x1i), mean temp (x3i), mean light (x4i), mean civil twilight (x5i), latitude (x6i), and harvest weight (x7i) respectively, with ei~N(µ=0, =1)
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representing the residual errors. The residual distributions from the GAM models used to validate the growth models can be observed in Figure 1. Stocking year (x2i) was considered as a categorical factor with associated parameter estimates designated by the vector a1. All models were run with default assumptions on splines, and convergence criteria and model fit were described as the percentage of deviance explained (% dev exp) and adjusted coefficient of determination (R2 adj) with successive inclusion of variables. Increase in % dev exp. (Δ % dev exp) was used to quantify model improvement associated with individual variables, using p < 0.05 as criteria for reporting significant Δ % dev exp values. Possible site and management specific effects were investigated with site and company added as hierarchical random effects to the GAM models described above, using Generalized Additive mixed Models (GAMM) (Wood, 2006).
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3. Results
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The mean and standard deviation (sd) of the four growth models for the 827 fish groups
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used in final analysis were as followed; TGC 2.5 (0.37), SGR 0.7 (0.09), EGI 92.1 (12.2),
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and ADG 8.5 (1.5).
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3.1 The association between mean hours of day-length, twilight and latitude Plots displayed a minor increase in mean hours of day-length (sun above the
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horizon) with increased latitude (Figure 2A). The variance was found to largely increase with latitude, suggesting greater differences in day-lengths in fish groups located in
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northern areas (Figure 2A). Mean hours of twilight demonstrated a somewhat different pattern with respect to latitude; a sharp linear increase towards the Polar circle (66.7°N),
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after which it plateaued (Figure 2B). A trend of increase in twilight variance with latitude, similarly to mean day-length was observed.
3.2 Influence of inclusion of biotic and abiotic factors on the growth models We tested the influence of a set of predictors on the TGC, SGR, EGI and ADG growth models using GAM regression (Table 3 and Figures 3-6). From Table 3, it can be seen that stocking weight had little influence on all models except the SGR model, on which effect was substantial (Figure 4) with 20.7 units change in % dev exp compared with less than 5.6 units change for all other models. Stocking year increased % dev exp by approximately 5-7 units in the TGC, EGI and SGR models, and 10.8 units in the ADG model. The effects of the different categories of stocking year on the models are
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ACCEPTED MANUSCRIPT described in detail in Table 4 using year-class 2000 as baseline. Three of the models (TGC, SGR and ADG) showed significant reduced growth of the 2002 year-class, EGI
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showed significant improved growth for the 2004 year-class, and growth were
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significantly improved in all models for the year-class 2005 (Table 4). The inclusion of mean temperature resulted in substantial increase in % dev exp for all models, from 16.2
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units in the ADG model to 49 units in the TGC model (Table 3 and Figure 3). The
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addition of mean day-length increased the % dev exp substantially in all models, the greatest increase occurring in the SGR model (14.2 Δ% dev exp) (Table 3). Mean day-
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length exhibited a similar non-linear trend in all models (Figure 3-6). Latitude increased % dev exp in the EGI and ADG models with 4.9 units and 4.2 units, respectively, while
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remaining largely unchanged for the SGR and TGC models. The addition of mean civil twilight resulted in a minor but significant increase in % dev exp in the TGC, EGI and
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ADG models. This factor was found to correlate with temperature, light and latitude, but resulted nevertheless in slightly improved models. All models were, to varying degrees, also associated with harvest weight. This was especially noticeable with the ADG model (Figure 6), which increased 39.5 units % dev exp from 44.6% to 84.1%, compared with 5, 7 and 9 units in the SGR, TGC, and EGI models respectively. Including site and company as random effects did not improve model fit with respect to R2 adj (% dev exp is not available for mixed effects GAMs) when latitude was included as an explanatory factor. Leaving out site and company as random effects and adding latitude as a fixed effect resulted in significantly improved models, indicating weak or negligible site and/or company specific effects (Table 5), possibly due to correlation with the other explanatory variables.
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ACCEPTED MANUSCRIPT All models improved (i.e. % dev exp and R2 adj increased) with spline representation for the predictors, except stocking year x2i, implying a non-linear
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relationship with the remaining explanatory factors for models TGC, SGR, EGI and
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ADG. The goodness-of-fit of the final GAM models can, in addition to Figures 3-6, be
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assessed from Figure 1, the included density plots based on the model residuals.
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4. Discussion
4.1 Current growth models – limitations and areas of use
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A growth model may serve many purposes and should ideally be able to compare and predict growth in fish of different sizes, stocked at different geographic locations,
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during all seasons of the year, and under different temperature conditions. ADG was, as expected, found to be largely influenced by fish size (Table 3 and Figure 6).
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Harvest weight had a particularly large influence, explained by the increased absolute daily weight gain with increased fish size. The ADG model is thus considered an inappropriate model for describing growth in salmon. It can be seen from Table 3 and Figure 4 that SGR is strongly associated with stocking weight, which is explained by the larger percentage (relative) daily weight gain in smaller fish. Therefore the SGR model is also considered inappropriate for predicting growth in fish, as was suggested by Bureau et al., 2000. The TGC and EGI models (Figures 3 and 5, respectively) appeared to be largely independent of stocking weight, while the TGC, SGR and EGI models were all moderately positively associated with harvest weight (Figure 3-5). The latter may partly be explained by the effect of slaughtering salmon on a planned harvest date, leading to a
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ACCEPTED MANUSCRIPT greater final harvest weight of faster growing salmon when compared to the harvesting of slower growing salmon. The moderate effect of harvest weight does not therefore
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necessarily suggest that the models are biased with respect to harvest weight; this bias
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will rather apply in situations where harvest date is prescheduled and not random. The TGC, SGR and EGI models were all associated with the abiotic variables
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mean temperature and mean day-length (Table 3 and Figures 3-5, respectively).
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Comparison of growth in fish exposed to different temperature and light conditions using these models may thus give biased results. TGC has been reported to produce poor
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growth predictions when used outside normal temperature ranges and in fish groups with marked changes in body condition, measured as condition score (Jobling, 1983; Jobling,
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2003). Mean day-length displayed a pattern of u-shaped associations with all the four growth models. This suggests that growth of the fish groups included in the study was
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different if light was predominantly at summer (mean day-length > 12 hrs) or predominantly at winter (mean day-length < 12 hrs) compared to mean day-length of approximately 12hrs.
Appropriate use of models depends on the specific study design and data available
for comparing growth. Individual fish in single units may be compared using TGC if all fish are exposed to the same environmental conditions (Aunsmo et al., 2008; Thodesen et al., 2001). For benchmarking purposes, growth models that account for different biotic and abiotic variables are the most reliable. In this context the EGI model was considered most robust, including more abiotic variables.
4.2 Potential for improved models
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ACCEPTED MANUSCRIPT The large effects of mean day-length and mean temperature on the models suggest that these abiotic factors need to be included, or better quantified, in future growth
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models. The study further indicates that the growth models may be slightly improved by
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the inclusion of the abiotic factors latitude and twilight. Latitude had slight but significant effects on all the models, although this is unlikely to be a causal mechanism. The figures
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(3-6) display an undulating effect of latitude which may be due to varying environmental-
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or possibly management- related effects along the coast.
All the models displayed similar u-shaped non-linear associations with mean day-
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length. This finding suggests that associations of abiotic variables can be non-linear, and using models capable of handling non-linear associations may be important in fitting field
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data in similar studies.
Twilight is not included in any of the existing growth models, while day-length is
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included in the EGI model. The properties of twilight versus latitude are quite different from day-length, and are explained by the reduced angle the sun descend and ascend the horizon at increasing latitudes (Figure 2). North of the Polar circle (66.7°N) this linear effect plateaus as the midnight sun will be above the horizon 24 hours per day during summer. Inclusion of twilight improved three of the models slightly but significantly, suggesting that twilight may influence growth in farmed fish. For estimation of new growth coefficients, refinement of the existing, or development of new growth models or, datasets with individual net pens instead of fish group as the statistical unit should be used for estimation purposes, thus improving data resolution. Further incorporation of repeated measures data (i.e. growth trajectories) will also benefit the further refinement of such models. Growth stanzas have been
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ACCEPTED MANUSCRIPT documented in rainbow trout (Dumas et al., 2007) and should be similarly investigated in farmed salmon.
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In the present study, inclusion of latitude as a fixed effect resulted in a better
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model fit with respect to R2 adj than identical models without latitude but with company and site included as hierarchical random effects. Both site and company are variables
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associated with geographical location and the lack of improved model fit when included
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in the models may be due to overlapping effects with the other explanatory factors in addition to latitude. Traits such as growth are likely to be associated with management
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and also site-specific environmental effects, and should therefore be investigated in studies of this nature. The results indicated increased growth over the study period
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demonstrated by the use of stocking year as a predictor in the models, but with variation between year-classes. Improved growth may be due to a range of factors such as
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improved genetics, improved feed and feeding management, improved general management, reduced disease impacts etc. Stocking year will to a certain extent control for these changes, allowing for comparison over years. The modified models described variation in growth between the year-classes fairly similarly, suggesting consistency in predictions across the modified models.
4.4 Validity The dataset used in the present study is designed for benchmarking production data. Fish group is the unit of concern and registrations through the production period from sea transfer to harvest is aggregated into single figures for the fish group. This will reduce information and consequently the precision of the analyses. Fish groups are
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ACCEPTED MANUSCRIPT stocked throughout the year and over a wide range of latitudes that may give varying accumulated effects of temperature and light. Furthermore, the database is based on
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production data supplied by commercial companies that might have different registration
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systems or procedures, adding to the risk of varying and idiosyncratic datasets. Missing data is a challenge in all such datasets and can (if not missing by random) introduce bias
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to the results. If data are missing by random the effect will result in reduced power, which
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may, in a worst-case scenario, result in undetected significant associations. Finally, it can be seen from Figures 2-6 that most explanatory variables exhibited substantial non-linear
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behaviours implying that validation of growth models using linear methods can at best give misleading results. Nevertheless, results from the present study should not be
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considered to be final estimates of future growth models, but rather to describe limitations
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of current models and to make suggestions as to how future models may be improved.
Conclusion
The growth models currently used in Atlantic salmon farming describe growth according to different models or modes of expression. Some of these models might be biased with respect to biotic factors such as size, while others might be biased with respect to abiotic factors such as temperature and light. Of the four models evaluated in the present study, the EGI model, incorporating both biotic and abiotic factors, are considered most robust for use in epidemiological studies and for use on benchmarking production data (i.e. growth). This study suggests that models can be improved by including abiotic factors such as temperature and day-light, and to some degree latitude and twilight related to the individual fish group. The study revealed non-linear
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ACCEPTED MANUSCRIPT associations that need to be represented in analysis. Combined with other factors influencing growth (diseases, genetics, feed and feeding, management etc.), there is
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substantial potential for better understanding fish growth in industrial salmon farming.
Acknowledgements
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MonAqua with Jan Petter Kosmo (currently Kontali Analyse AS) are acknowledged for
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facilitating the database for analysis and valuable input during the work. Ewos is
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acknowledged for providing information about the Ewos growth index.
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Jobling, M., 2003. The thermal growth coefficient (TGC) model of fish growth: a cautionary note. Aquaculture Research 34, 581-584.
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Midtlyng, P.J., Lillehaug, A., 1998. Growth of Atlantic salmon Salmo salar after intraperitoneal administration of vaccines containing adjuvants. Diseases of Aquatic Organisms 32, 91-97. Pratoomyot, J., Bendiksen, E.Å., Bell, J.G., Tocher, D.R., 2008. Comparison of effects of vegetable oils blended with southern hemisphere fish oil and decontaminated northern hemisphere fish oil on growth perfomance, compositiona nd gene expression in Atlantic salmon (Salmo salar L.). Aquaculture 280, 170-178. R Core Team, 2013. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria.URL http://www.R-project.org/ Smith, I.P., Metcalfe, N.B., Huntingford, F.A., Kadri, S., 1993. Daily and seasonal patterns in the feeding-behavior of Atlantic salmon (Salmo-Salar L) in a sea cage. Aquaculture 117, 165178. Talbot, C., 1993. Some aspects of the biology of feeding and growth in fish. Proceedings of the Nutrition Society 52, 403-416. Thodesen, J., Gjerde, B., Grisdale-Helland, B., Storebakken, T., 2001. Genetic variation in feed intake, growth and feed utilization in Atlantic salmon (Salmo salar). Aquaculture 194, 273281. Wood, S.N., 2001. mgvc: GAMs and Generalized Ridge Regression for R. R News 1, 20-25.
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ACCEPTED MANUSCRIPT Wood, S.N., 2006. Generalized Additive Models: An Introduction with R. Chapman & Hall/ CRC, Boca Raton.
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Wood, S.N., Augustin, N.H., 2002. GAMs with integrated model selection using penalized regression splines and applications to environmental modelling. Ecological Modelling 157, 157177.
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Figure 1 Density plots of the residual distributions from GAM models with the four growth models used in the study as responses: the thermal growth coefficient (TGC), the specific growth rate (SGR), the Ewos growth index (EGI), and average daily weight gain (ADG).
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Figure 2
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The two panels show latitude (horizontal axis) plotted against mean hours of day-light (Figure 2A), and mean hours of civil twilight per day (Figure 2B). Each point represents the mean hours of day-light and civil twilight per fish group in the dataset.
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Figure 3
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The transformed growth model f(tgc) (vertical axis) plotted against explanatory variables (horizontal axis) from GAM regression. Shaded area represents confidence bands for the smoothing splines with width equal to two standard errors. At the bottom of each graph a rugplot is included that indicates the density of the points with respect to the explanatory variable.
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Figure 4
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The transformed growth model f(sgr) (vertical axis) plotted against explanatory variables (horizontal axis) from GAM regression. Shaded area represents confidence bands for the smoothing splines with width equal to two standard errors. At the bottom of each graph a rugplot is included that indicates the density of the points with respect to the explanatory variable.
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Figure 5
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The transformed growth model f(egi) (vertical axis) plotted against explanatory variables (horizontal axis) from GAM regression. Shaded area represents confidence bands for the smoothing splines with width equal to two standard errors. At the bottom of each graph a rugplot is included that indicates the density of the points with respect to the explanatory variable.
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Figure 6
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The transformed growth model f(adg) (vertical axis) plotted against explanatory variables (horizontal axis) from GAM regression. Shaded area represents confidence bands for the smoothing splines with width equal to two standard errors. At the bottom of each graph a rugplot is included that indicates the density of the points with respect to the explanatory variable.
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ACCEPTED MANUSCRIPT Table 1 Description of the MonAqua dataset with year classes 2000 – 2005 used in this study. The
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material comprised of 935 fish groups from 28 companies stocked on 224 sites located on the
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Norwegian coast from 58.1 to 70.7 degrees north.
Number of fish groups
157
153
222
77
153
935
Mean no of stocked fish per fish group
119
137
204
187
208
141
165
173
522
576
666
632
633
666
66.4
65.8
64.0
64.1
63.3
64.8
(in 1000) Mean number of stocked fish per site (in 1000)
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Mean latitude (°N) of fish groups
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2000 2001 2002 2003 2004 2005 Dataset
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Year class
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64.8
ACCEPTED MANUSCRIPT Table 2 Description of variables used in the analyses with mean, standard deviation (sd), minimum, and
Mean (sd)
min
Stocking weight (grams)1
96.0 (44.3) 25
Harvest weight (grams)2
5034 (870) 1362 8661
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363
2000 2005 8.8 (1.3)
6.0
Mean day-length (hours)4
12.2 (1.0)
9.8
Mean civil twilight (hours) 2.6 (0.3)
14.5
1.8
3.1
58.2
70.7
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65.1 (3.4)
11.91
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Mean temperature (°C)3
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Stocking year (year-class)
Latitude (°N)
max
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Variable
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maximum values. The total number of observations used in final analysis was n = 827.
Two fish groups with stocking weight over 400 grams were excluded, being extreme values
2
Three fish groups with harvest over 10 kg were excluded presumably being brood fish
3
The maximum mean temperature of 14.4°C at 62.7°N over 581 production days in one fish
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group was considered erroneous and excluded 4
One fish group with a mean day-length of 8.6 hours were excluded, considered erroneous
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ACCEPTED MANUSCRIPT Table 3 Results from Generalized Additive Models (GAM) of growth model estimates fitted with biotic
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and abiotic variables. Percentage deviance explained (% dev. exp.) and adjusted coefficient of
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determination (R2 adj.) were used to describe model fit. Delta percentage deviance explained (Δ % dev. exp) quantifies model improvement by successive inclusion of variables. Only significant
TGC1
dev
dev
exp
exp
0
R2 adj
%
Δ%
R2 adj
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Δ%
0
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%
SGR2
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Model
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values (p < 0.05) are reported. The total number of observations was n = 827 for all models.
EGI3 %
Δ%
ADG4 R2 adj
%
Δ%
R2 adj
dev
dev
dev
dev
dev
dev
exp
exp
exp
exp
exp
exp
0
0
0
0
0
0
3.2
3.2
0.03
20.7
20.7
0.20
3.7
3.7
0.03
5.6
5.6
0.05
Stocking year
9.0
5.8
0.08
27.3
6.6
0.27
11.1
7.4
0.10
16.4
10.8
0.16
Mean temp
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Stocking weight
58.1
49.1
0.57
46.1
18.9
0.45
30.5
19.4
0.29
32.6
16.2
0.31
Mean day-length
67.5
9.4
0.67
60.3
14.2
0.59
42.8
12.3
0.41
39.9
7.3
0.38
Latitude
68.6
1.1
0.67
60.5
0.2
0.59
47.7
4.9
0.46
44.1
4.2
0.42
Mean civil twilight
68.6
1.1
0.67
60.5
0
0.59
48.9
1.2
0.47
44.6
0.5
0.42
Harvest weight
73.8
5.1
0.73
67.5
7.0
0.66
58.1
9.2
0.56
84.1
39.5
0.83
Full model
73.8
0.73
67.5
0.66
58.1
0.56
84.1
1
Thermal growth coefficient
2
Specific growth rate
3
Ewos growth index
4
Average daily weight gain
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growth models, using the year-class 2000 as baseline, analysed using Generalized Additive
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Models (GAM). Only significant effects (p<0.05) are included in the table and significant levels are indicated by asterisks. The same fixed effects are used in all the models; stocking weight,
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stocking year, mean temperature, mean day-light, latitude, mean civil twilight, and harvest
SGR
EGI
2001 ns
ns
ns
ADG
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Year TGC
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weight. The total number of observations was n = 827 for all models.
ns -0.2 (0.08)**
2003 ns
ns
ns
ns
2004 ns
ns
3.3 (1.4)*
ns
2005 0.1 (0.03)***
0.02 (0.007)**
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2002 -0.07 (0.02)** -0.02 (0.007)** ns
5.3 (1.2)*** 0.3 (0.09)**
ns not significant * p < 0.05 ** p < 0.01 *** p < 0.001
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ACCEPTED MANUSCRIPT Table 5 The table shows adjusted coefficients of determination (R2 adj.) resulting from comparison of
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Generalized Additive Models (GAM) with site and company added as random effects (both
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individually and combined), making the GAM models effectively Generalized Additive Mixedeffects Models (GAMM). The same fixed effects are used in all the models; stocking weight,
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stocking year, mean temperature, mean day-light, latitude, mean civil twilight, and harvest
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weight. The total number of observations was n = 827 for all models.
0.73
0.66
0.56
0.83
Site
0.69
0.62
0.50
0.81
Company
0.71
0.63
0.53
0.82
Site and company
0.69
0.61
0.50
0.81
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No random effects
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TGC1 SGR2 EGI3 ADG4
1
Thermal growth coefficient
2
Specific growth rate
3
Ewos growth index
4
Average daily weight gain
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Highlights We validated 4 growth models using data from 827 fish groups produced over a 1400 km north-south distance Models are influenced by different biotic and abiotic factors, which, if unaccounted for, could result in biased results Abiotic variables showed non-linear associations with the growth models The industry growth model “Ewos growth index” was considered to be the most robust model for epidemiological studies and benchmarking production data
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S0044-8486(14)00110-0 doi: 10.1016/j.aquaculture.2014.03.007 AQUA 631072
To appear in:
Aquaculture
Received date: Revised date: Accepted date:
5 May 2013 9 March 2014 10 March 2014
Please cite this article as: Aunsmo, Arnfinn, Krontveit, Randi, Valle, Paul Steinar, Bohlin, Jon, Field validation of growth models used in Atlantic salmon farming, Aquaculture (2014), doi: 10.1016/j.aquaculture.2014.03.007
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Field validation of growth models used in Atlantic salmon farming
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Arnfinn Aunsmo1, Randi Krontveit1, Paul Steinar Valle2, Jon Bohlin1,3
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Norwegian University of Life Sciences, Campus Adamstuen, Department of Food Safety and Infection Biology, PO Box 8146 Dep, 0033 Oslo, Norway Kontali Analyse AS, Industriveien 18, 6517 Kristiansund N
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Norwegian Institute of Public Health, Division of Epidemiology, Marcus Thranes gate 6,
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Corresponding author. Tel.: +47 48083021
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P.O. Box 4404, 0403 Oslo, Norway
E-mail address: [email protected]
Keywords: Aquaculture, Atlantic salmon, growth, growth models, validation
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ACCEPTED MANUSCRIPT Abstract Several models for description of fish growth are commonly used in Atlantic salmon
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farming, including the specific growth rate (SGR), the thermal growth coefficient (TGC),
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the Ewos growth index (EGI), and average daily weight gain (ADG). In the present study, a subset of a commercial database containing information from 827 fish groups from the
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year-classes 2000-2005, produced along the Norwegian coastline, was used to validate
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these four growth models. A number of biotic and abiotic factors were fitted to the models of interest in order to evaluate model strengths and weaknesses and to identify
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additional factors whose inclusion may improve model performance. Preliminary analysis indicated non-linear relations; to account for this we applied Generalized Additive
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Models (GAM) in regression analysis. Our findings indicate that ADG was strongly associated with harvest weight and was thus
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deemed unsuitable for describing growth in Atlantic salmon. SGR was also associated with fish size and biased towards small fish when fish of uneven stocking size were compared. The TGC, SGR and the EGI models were all moderately associated with harvest weight, and the same three models were more strongly associated with mean temperature and mean day-length. These models might therefore present bias when used to compare growth in varying environmental conditions. The EGI was considered the most robust model overall for predicting growth at different sizes exposed to variable abiotic exposure such as temperature and light. Finally, the study suggests that the robustness of growth models can be improved by accounting for non-linear effects on growth and including abiotic factors such as temperature, light, and latitude.
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ACCEPTED MANUSCRIPT 1. Introduction Growth is a production parameter of central interest in farmed Atlantic salmon
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operations. Important areas in improving and managing fish growth includes:
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identification of causal factors, quantifying effects, predicting fish growth, as well as benchmarking growth between cages, sites, genetic strains, and companies. Growth in
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fish is regulated by abiotic factors such as time, temperature and light (Austreng et al.,
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1987; Duston and Saunders, 1995; Forsberg, 1995; Smith et al., 1993), as well as such biotic factors as body size (Brett, 1979; Jobling, 1983; Talbot, 1993). Local factors
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related to environment, management, nutrition, and diseases have also been found to
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Pratoomyot et al., 2008).
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affect growth (Breck et al., 2003; Fivelstad et al., 2007; Midtlyng and Lillehaug, 1998;
Models that convert feed given to fish into increased biomass or growth are
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commonly used for monitoring the increase in fish biomass over time on salmon farms (Aunsmo et al., 2013; Brett, 1979). However, these models cannot be used to make predictions of growth, and comparing levels of feeding have limited value when studying growth in fish groups of uneven size or subjected to varying abiotic exposures. Several models are available for the prediction and comparison of growth in farmed Atlantic salmon; the specific growth rate (SGR) (Austreng et al., 1987), the thermal growth coefficient (TGC) (Cho, 1992; Iwama and Tautz, 1981), and the Ewos growth index (EGI)1. Average daily weight gain (ADG) is commonly used in studies of growth in terrestrial livestock (Johansen et al., 2013), and has also been applied in aquaculture (Garber et al., 1995). These growth models are primarily used for describing growth between a start-weight (w0 - often at time of sea transfer) and an end-weight (we – 1
Ewos AS, http://www.ewos.com/wps/wcm/connect/ewos-content-group/ewos-group
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ACCEPTED MANUSCRIPT often at time of harvest) or to predict growth from a start-weight at time=t0 to an endweight at time=te. For instance, SGR is based on the natural logarithm of body weight
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between t0 and te (Bureau et al., 2000). The TGC model combines the cubic root of fish
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weight with a linear function of temperature, and is based on data from controlled growth studies (Iwama and Tautz, 1981). Abiotic factors such as light and temperature are
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included in some models, thus with the potential of controlling for varying physical
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exposure. The EGI model, as such, is a linear regression model based on estimated parameters from field data. Growth trajectories, i.e. repeated weight measurements, are
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not included in any of the models.
In order to objectively investigate latent effects related to disease, feed, local
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environment, and management practices, etc. over a time interval, the models should principally be independent of w0 and we. Similarly, to compare growth in varying
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environmental settings, the models should also be independent of, or account for, variables such as temperature and light. Correlations between harvest weight, latitude, temperature and the growth models have been described for Atlantic salmon, suggesting that the models reflect different properties (Iversen and Kosmo, 2004). Non-linear effects are described for temperature (Jobling, 1983), and are further indicated by the use of squared, quadratic and third root variables in the EGI model. The objectives of this study were to validate four growth models used in Atlantic salmon farming, exploring the effects of biotic and abiotic factors on the models through the use of field data. Preliminary analyses revealed non-linear relationships, and validation was thus also performed using Generalized Additive Models (GAM) (Hastie and Tibshirani, 1986).
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2. Materials and methods
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2.1 Commercial Field Data - the MonAqua database
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The benchmarking company MonAqua has since the year-class of 1998 collected biological information from the Norwegian salmon industry, based on a voluntarily
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contribution by companies (Anonymous, 2007). Information is registered at the fish
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group level (Table 1), where a fish group is defined as fish of common year-class, genetic origin (strain), smolt plant, vaccine, and sea site of initial transfer. Fish groups stocked
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between 2000 and 2005 had the most complete observations and were included in the present study; more recent data were unfortunately not available. These 935 fish groups
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came from 28 companies and were located on 225 sites from 58.1° to 70.7° degrees north, constituting a north-south range of approximately 1400 km (Table 1). The
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statistical unit in the dataset was the fish group with an average of 165 000 salmon stocked per group (Table 1). The dataset contained no information about grading and mixing, which usually takes place within the fish group. Each site had a registered mean number of 624 000 stocked fish per year-class, each site commonly taking on a new yearclass every second year.
Estimates of growth, as expressed by the four growth models SGR, TGC, EGI and ADG, were calculated in the period from sea transfer until harvest. As the sea transfer period of a fish group usually is limited to a few days, mean date of sea transfer was used. Time of harvest was estimated (by the MonAqua database) as the biomass-weighted time of slaughter, giving both a date of harvest and a harvest weight for each fish group. Harvest period per fish group was not available in the dataset. Total production time
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total degree-days, which were then summed and divided by days at sea, giving the mean
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temperature for each production period (Table 2).
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2.2 Calculation of growth variables for individual fish groups
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Estimates of growth were calculated for individual fish groups in the MonAqua database by each of the four growth models: ADG, SGR, TGC and EGI.
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For all models, w0 and we designate stocking and harvest weight, respectively. Days d are summed from d=1 until slaughter at d=n, and daily temperature Td for each
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day from d=1 until d=n. Average daily weight gain (ADG) was calculated as: ADG
( we w0 ) n
d d 1
Daily specific growth rate (SGR) was calculated according to Brett and Grover (1979) as: SGR
(ln(we ) ln( w0 )) n
d d 1
Thermal growth coefficient (TGC) was calculated and multiplied by 1000 according to Iwama and Tautz (1981) as: TGC
1000(3 we 3 w0 ) n
T d 1
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(x1i), change in day length (x2i), third root of weight (wi1/3), day length times third root of
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weight (x1i ∙ wi1/3), and the third root of squared weight (wi2/3). ei~N(µ=0, =1) designates
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the normally distributed errors, with mean µ=0 and standard deviation =1, for each observation i:
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YiEGI=a0+a1Ti2+a2Ti4+a3x1i+a4x2i+a5wi1/3+a6x1iwi1/3+a7wi2/3+ei
The estimated parameters for the intercept (a0) and each variable (a1-a7) were not
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released, but were calculated by the MonAqua database using an Ewos-developed
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2.3 Calculation of day-length and civil twilight Hours of daylight (i.e. sun above the horizon) and civil twilight (i.e. sun between the horizon and 6° below horizon) were calculated on a daily basis using Microsoft® Excel (Microsoft Corporation, Redmond, WA, USA) for each 0.1° latitude in the period the fish groups were at sea (Glarner, 2007).
m 1 tan(l ) tan( a cos( jd ))
h cos(l )
Where l is latitude, a is the angle of the equatorial plane to the ecliptic plane (23.439º), j = π /182,625° in radians, h is the angle in degrees of the sun below the horizon and d is day of the year starting on December 22. The outcome m was further normalized to be in
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arccos(1 m) 180
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b
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The formula:
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is the proportion in radians of the day where the sun is above a given angle h. Total hours
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of light (in hours) were calculated as b∙24 for h=0 and h=6º. The hours of light were further summed for individual fish groups from stocking until harvest (total light-hours)
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and split into day-length (h=0°) and civil twilight (hours of light at sun h=6º below
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horizon subtracted day-length) (Table 2).
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2.3 Data management and statistical analysis
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The MonAqua database was converted into STATA 12.0 (StataCorp LP, College Station, TE, USA) and R (Development Core Team 2011) where data for light were merged using fish group number as an ID. Only fish groups with complete observations were used in final analysis, excluding 96 groups. The variables were quality controlled for extreme values (minimum and maximum), and an observation with maximum mean temperature of 14.4°C at 62.7° degrees North over 581 production days was considered erroneous and omitted. Observations with EGI above 150 were considered erroneous and as a consequence five observations were excluded (John H. Pettersen, EWOS pers. com.). Six fish groups were further omitted based on extreme values of harvest weight, day length or stocking size, leaving 827 fish groups for final analysis (Table 2).
2.4 Statistical modelling
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'mgcv' package in R (R Core Team, 2013; Wood, 2001), which uses cross-validation to
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determine the degree of smoothing, were fitted to explore biotic and abiotic variables (Table 2) potentially associated with the growth models (Hastie and Tibshirani, 1986).
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zi=f(yi)=a0+s1(x1i)+a1x2i+s2(x3i)+ s3(x4i)+s4(x5i)+s5(x6i) +s6(x7i)+ei
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zi, designates the f() -transformed response variable yi representing the growth models (TGC, SGR, EGI and ADG), while sl (1l6) are the spline functions (see (Hastie and
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Tibshirani, 1986; Wood, 2006; Wood and Augustin, 2002) for details regarding transform of response and selection of smoothing splines) for the included explanatory variables
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(Table 2): stocking weight (x1i), mean temp (x3i), mean light (x4i), mean civil twilight (x5i), latitude (x6i), and harvest weight (x7i) respectively, with ei~N(µ=0, =1)
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representing the residual errors. The residual distributions from the GAM models used to validate the growth models can be observed in Figure 1. Stocking year (x2i) was considered as a categorical factor with associated parameter estimates designated by the vector a1. All models were run with default assumptions on splines, and convergence criteria and model fit were described as the percentage of deviance explained (% dev exp) and adjusted coefficient of determination (R2 adj) with successive inclusion of variables. Increase in % dev exp. (Δ % dev exp) was used to quantify model improvement associated with individual variables, using p < 0.05 as criteria for reporting significant Δ % dev exp values. Possible site and management specific effects were investigated with site and company added as hierarchical random effects to the GAM models described above, using Generalized Additive mixed Models (GAMM) (Wood, 2006).
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3. Results
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The mean and standard deviation (sd) of the four growth models for the 827 fish groups
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used in final analysis were as followed; TGC 2.5 (0.37), SGR 0.7 (0.09), EGI 92.1 (12.2),
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and ADG 8.5 (1.5).
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3.1 The association between mean hours of day-length, twilight and latitude Plots displayed a minor increase in mean hours of day-length (sun above the
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horizon) with increased latitude (Figure 2A). The variance was found to largely increase with latitude, suggesting greater differences in day-lengths in fish groups located in
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northern areas (Figure 2A). Mean hours of twilight demonstrated a somewhat different pattern with respect to latitude; a sharp linear increase towards the Polar circle (66.7°N),
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after which it plateaued (Figure 2B). A trend of increase in twilight variance with latitude, similarly to mean day-length was observed.
3.2 Influence of inclusion of biotic and abiotic factors on the growth models We tested the influence of a set of predictors on the TGC, SGR, EGI and ADG growth models using GAM regression (Table 3 and Figures 3-6). From Table 3, it can be seen that stocking weight had little influence on all models except the SGR model, on which effect was substantial (Figure 4) with 20.7 units change in % dev exp compared with less than 5.6 units change for all other models. Stocking year increased % dev exp by approximately 5-7 units in the TGC, EGI and SGR models, and 10.8 units in the ADG model. The effects of the different categories of stocking year on the models are
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ACCEPTED MANUSCRIPT described in detail in Table 4 using year-class 2000 as baseline. Three of the models (TGC, SGR and ADG) showed significant reduced growth of the 2002 year-class, EGI
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showed significant improved growth for the 2004 year-class, and growth were
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significantly improved in all models for the year-class 2005 (Table 4). The inclusion of mean temperature resulted in substantial increase in % dev exp for all models, from 16.2
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units in the ADG model to 49 units in the TGC model (Table 3 and Figure 3). The
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addition of mean day-length increased the % dev exp substantially in all models, the greatest increase occurring in the SGR model (14.2 Δ% dev exp) (Table 3). Mean day-
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length exhibited a similar non-linear trend in all models (Figure 3-6). Latitude increased % dev exp in the EGI and ADG models with 4.9 units and 4.2 units, respectively, while
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remaining largely unchanged for the SGR and TGC models. The addition of mean civil twilight resulted in a minor but significant increase in % dev exp in the TGC, EGI and
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ADG models. This factor was found to correlate with temperature, light and latitude, but resulted nevertheless in slightly improved models. All models were, to varying degrees, also associated with harvest weight. This was especially noticeable with the ADG model (Figure 6), which increased 39.5 units % dev exp from 44.6% to 84.1%, compared with 5, 7 and 9 units in the SGR, TGC, and EGI models respectively. Including site and company as random effects did not improve model fit with respect to R2 adj (% dev exp is not available for mixed effects GAMs) when latitude was included as an explanatory factor. Leaving out site and company as random effects and adding latitude as a fixed effect resulted in significantly improved models, indicating weak or negligible site and/or company specific effects (Table 5), possibly due to correlation with the other explanatory variables.
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ACCEPTED MANUSCRIPT All models improved (i.e. % dev exp and R2 adj increased) with spline representation for the predictors, except stocking year x2i, implying a non-linear
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relationship with the remaining explanatory factors for models TGC, SGR, EGI and
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ADG. The goodness-of-fit of the final GAM models can, in addition to Figures 3-6, be
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assessed from Figure 1, the included density plots based on the model residuals.
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4. Discussion
4.1 Current growth models – limitations and areas of use
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A growth model may serve many purposes and should ideally be able to compare and predict growth in fish of different sizes, stocked at different geographic locations,
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during all seasons of the year, and under different temperature conditions. ADG was, as expected, found to be largely influenced by fish size (Table 3 and Figure 6).
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Harvest weight had a particularly large influence, explained by the increased absolute daily weight gain with increased fish size. The ADG model is thus considered an inappropriate model for describing growth in salmon. It can be seen from Table 3 and Figure 4 that SGR is strongly associated with stocking weight, which is explained by the larger percentage (relative) daily weight gain in smaller fish. Therefore the SGR model is also considered inappropriate for predicting growth in fish, as was suggested by Bureau et al., 2000. The TGC and EGI models (Figures 3 and 5, respectively) appeared to be largely independent of stocking weight, while the TGC, SGR and EGI models were all moderately positively associated with harvest weight (Figure 3-5). The latter may partly be explained by the effect of slaughtering salmon on a planned harvest date, leading to a
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ACCEPTED MANUSCRIPT greater final harvest weight of faster growing salmon when compared to the harvesting of slower growing salmon. The moderate effect of harvest weight does not therefore
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necessarily suggest that the models are biased with respect to harvest weight; this bias
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will rather apply in situations where harvest date is prescheduled and not random. The TGC, SGR and EGI models were all associated with the abiotic variables
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mean temperature and mean day-length (Table 3 and Figures 3-5, respectively).
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Comparison of growth in fish exposed to different temperature and light conditions using these models may thus give biased results. TGC has been reported to produce poor
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growth predictions when used outside normal temperature ranges and in fish groups with marked changes in body condition, measured as condition score (Jobling, 1983; Jobling,
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2003). Mean day-length displayed a pattern of u-shaped associations with all the four growth models. This suggests that growth of the fish groups included in the study was
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different if light was predominantly at summer (mean day-length > 12 hrs) or predominantly at winter (mean day-length < 12 hrs) compared to mean day-length of approximately 12hrs.
Appropriate use of models depends on the specific study design and data available
for comparing growth. Individual fish in single units may be compared using TGC if all fish are exposed to the same environmental conditions (Aunsmo et al., 2008; Thodesen et al., 2001). For benchmarking purposes, growth models that account for different biotic and abiotic variables are the most reliable. In this context the EGI model was considered most robust, including more abiotic variables.
4.2 Potential for improved models
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ACCEPTED MANUSCRIPT The large effects of mean day-length and mean temperature on the models suggest that these abiotic factors need to be included, or better quantified, in future growth
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models. The study further indicates that the growth models may be slightly improved by
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the inclusion of the abiotic factors latitude and twilight. Latitude had slight but significant effects on all the models, although this is unlikely to be a causal mechanism. The figures
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(3-6) display an undulating effect of latitude which may be due to varying environmental-
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or possibly management- related effects along the coast.
All the models displayed similar u-shaped non-linear associations with mean day-
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length. This finding suggests that associations of abiotic variables can be non-linear, and using models capable of handling non-linear associations may be important in fitting field
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data in similar studies.
Twilight is not included in any of the existing growth models, while day-length is
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included in the EGI model. The properties of twilight versus latitude are quite different from day-length, and are explained by the reduced angle the sun descend and ascend the horizon at increasing latitudes (Figure 2). North of the Polar circle (66.7°N) this linear effect plateaus as the midnight sun will be above the horizon 24 hours per day during summer. Inclusion of twilight improved three of the models slightly but significantly, suggesting that twilight may influence growth in farmed fish. For estimation of new growth coefficients, refinement of the existing, or development of new growth models or, datasets with individual net pens instead of fish group as the statistical unit should be used for estimation purposes, thus improving data resolution. Further incorporation of repeated measures data (i.e. growth trajectories) will also benefit the further refinement of such models. Growth stanzas have been
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ACCEPTED MANUSCRIPT documented in rainbow trout (Dumas et al., 2007) and should be similarly investigated in farmed salmon.
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In the present study, inclusion of latitude as a fixed effect resulted in a better
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model fit with respect to R2 adj than identical models without latitude but with company and site included as hierarchical random effects. Both site and company are variables
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associated with geographical location and the lack of improved model fit when included
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in the models may be due to overlapping effects with the other explanatory factors in addition to latitude. Traits such as growth are likely to be associated with management
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and also site-specific environmental effects, and should therefore be investigated in studies of this nature. The results indicated increased growth over the study period
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demonstrated by the use of stocking year as a predictor in the models, but with variation between year-classes. Improved growth may be due to a range of factors such as
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improved genetics, improved feed and feeding management, improved general management, reduced disease impacts etc. Stocking year will to a certain extent control for these changes, allowing for comparison over years. The modified models described variation in growth between the year-classes fairly similarly, suggesting consistency in predictions across the modified models.
4.4 Validity The dataset used in the present study is designed for benchmarking production data. Fish group is the unit of concern and registrations through the production period from sea transfer to harvest is aggregated into single figures for the fish group. This will reduce information and consequently the precision of the analyses. Fish groups are
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ACCEPTED MANUSCRIPT stocked throughout the year and over a wide range of latitudes that may give varying accumulated effects of temperature and light. Furthermore, the database is based on
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production data supplied by commercial companies that might have different registration
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systems or procedures, adding to the risk of varying and idiosyncratic datasets. Missing data is a challenge in all such datasets and can (if not missing by random) introduce bias
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to the results. If data are missing by random the effect will result in reduced power, which
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may, in a worst-case scenario, result in undetected significant associations. Finally, it can be seen from Figures 2-6 that most explanatory variables exhibited substantial non-linear
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behaviours implying that validation of growth models using linear methods can at best give misleading results. Nevertheless, results from the present study should not be
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considered to be final estimates of future growth models, but rather to describe limitations
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of current models and to make suggestions as to how future models may be improved.
Conclusion
The growth models currently used in Atlantic salmon farming describe growth according to different models or modes of expression. Some of these models might be biased with respect to biotic factors such as size, while others might be biased with respect to abiotic factors such as temperature and light. Of the four models evaluated in the present study, the EGI model, incorporating both biotic and abiotic factors, are considered most robust for use in epidemiological studies and for use on benchmarking production data (i.e. growth). This study suggests that models can be improved by including abiotic factors such as temperature and day-light, and to some degree latitude and twilight related to the individual fish group. The study revealed non-linear
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ACCEPTED MANUSCRIPT associations that need to be represented in analysis. Combined with other factors influencing growth (diseases, genetics, feed and feeding, management etc.), there is
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substantial potential for better understanding fish growth in industrial salmon farming.
Acknowledgements
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MonAqua with Jan Petter Kosmo (currently Kontali Analyse AS) are acknowledged for
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facilitating the database for analysis and valuable input during the work. Ewos is
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acknowledged for providing information about the Ewos growth index.
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ACCEPTED MANUSCRIPT References Anonymous, 2007. MonAqua database. Accessed 21. August 2007. MonAqua AS, Industriveien 18, 6517 Kristiansund N, Norway.
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Aunsmo, A., Larssen, R.B., Valle, P.S., Sandberg, M., Evensen, Ø., Midtlyng, P.J., Østvik, A., Skjerve, E., 2008. Improved field trial methodology for quantifying vaccination side-effects in farmed Atlantic salmon (Salmo salar L.). Aquaculture 284, 19-24.
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Aunsmo, A., Skjerve, E., Midtlyng, P.J., 2013. Accuracy and precision of harvest stock estimation in Atlantic salmon farming. Aquaculture 396-399, 113-118.
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Austreng, E., Storebakken, T., Asgard, T., 1987. Growth rate estimates for cultured Atlantic salmon and rainbow trout. Aquaculture 60, 157-160.
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Breck, O., Bjerkas, E., Campbell, P., Arnesen, P., Haldorsen, P., Waagbo, R., 2003. Cataract preventative role of mammalian blood meal, histidine, iron and zinc in diets for Atlantic salmon (Salmo salar L.) of different strains. Aquaculture Nutrition 9, 341-350.
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Brett, J.R., 1979. Environmental factors and growth. In: Hoar, W.S., Randall, D.J., Brett, J.R. (Eds.), Fish physiology. Academic press, London, pp. 599-675.
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Brett, J.R., Grover, T.D.D., 1979. Physiological energetics and growth. In: Hoar, W.S., Randall, D.J., Brett, J.R. (Eds.), Fish pysiology. Academic Press, New York, pp. 279-352.
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Bureau, D.P., Azevedo, P.A., Tapia-Salazar, M., Cuzon, G., 2000. Pattern and cost of growth and nutrient deposition in fish and shrimp: Potential implications and applications. In: CruzSuàrez, L.E., Ricque-Marie, D., Tapia-Salazar, M., Olvera-Novoa, M.A., Civera-Cerecedo, R. (Eds.), Avances en nutricion acuicola V. Memorias del V simposium internacional de nutricion acuicola., Marida, pp. 111-140. Cho, C.Y., 1992. Feeding systems for rainbow trout and other salmonids with reference to current estimates of energy and protein requirements. Aquaculture 100, 107-123. Dumas, A., France, J., Bureau, D.P., 2007. Evidence of three growth stanzas in rainbow trout (Oncorhynchus mykiss) across life stages and adaptation of the thermal-unit growth coefficient. Aquaculture 267, 139-146. Duston, J., Saunders, R.L., 1995. Advancing smolting to autumn in age 0+ Atlantic salmon by photoperiod, and long-term performance in sea water. Aquaculture 135, 295-309. Fivelstad, S., Waagbo, R., Stefansson, S., Olsen, A.B., 2007. Impacts of elevated water carbon dioxide partial pressure at two temperatures on Atlantic salmon (Salmo salar L.) parr growth and haematology. Aquaculture 269, 241-249. Forsberg, O.I., 1995. Empirical investigations on growth of post-smolt Atlantic salmon (Salmo-salar L) in land-based farms - evidence of a photoperiodic influence. Aquaculture 133, 235-248.
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ACCEPTED MANUSCRIPT Garber, M.J., DeYonge, K.G., Byatt, J.C., Lellis, W.A., Honeyfield, D.C., Bull, R.C., Schelling, G.T., Roeder, R.A., 1995. Dose-response effects of recombinant bovine somatotropin (Posilac) on growth performance and body composition of two-year-old rainbow trout (Oncorhynchus mykiss). Journal of Animal Science 73, 3216-3222.
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Glarner, H., 2007. Length of day and twilight. http://www.gandraxa.com/length_of_day.xml. Accessed 21. August 2007.
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Hastie, T., Tibshirani, R., 1986. Generalized additive models. Statistical Science Vol. 1 No. 3, 297-318.
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Iversen, A., Kosmo, J.P., 2004. Kan vekstindeksene sammenlignes (in Norwegian). Norsk fiskeoppdrett 4, 62-64. Iwama, G.K., Tautz, A., 1981. A simple growth model for salmonids in hatcheries. Canadian Journal of Fisheries and Aquatic Sciences 38, 649-656.
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Jobling, M., 1983. Growth studies with fish - overcoming the problems of size variation. Journal of Fish Biology 22, 153-157.
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Jobling, M., 2003. The thermal growth coefficient (TGC) model of fish growth: a cautionary note. Aquaculture Research 34, 581-584.
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Midtlyng, P.J., Lillehaug, A., 1998. Growth of Atlantic salmon Salmo salar after intraperitoneal administration of vaccines containing adjuvants. Diseases of Aquatic Organisms 32, 91-97. Pratoomyot, J., Bendiksen, E.Å., Bell, J.G., Tocher, D.R., 2008. Comparison of effects of vegetable oils blended with southern hemisphere fish oil and decontaminated northern hemisphere fish oil on growth perfomance, compositiona nd gene expression in Atlantic salmon (Salmo salar L.). Aquaculture 280, 170-178. R Core Team, 2013. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria.URL http://www.R-project.org/ Smith, I.P., Metcalfe, N.B., Huntingford, F.A., Kadri, S., 1993. Daily and seasonal patterns in the feeding-behavior of Atlantic salmon (Salmo-Salar L) in a sea cage. Aquaculture 117, 165178. Talbot, C., 1993. Some aspects of the biology of feeding and growth in fish. Proceedings of the Nutrition Society 52, 403-416. Thodesen, J., Gjerde, B., Grisdale-Helland, B., Storebakken, T., 2001. Genetic variation in feed intake, growth and feed utilization in Atlantic salmon (Salmo salar). Aquaculture 194, 273281. Wood, S.N., 2001. mgvc: GAMs and Generalized Ridge Regression for R. R News 1, 20-25.
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ACCEPTED MANUSCRIPT Wood, S.N., 2006. Generalized Additive Models: An Introduction with R. Chapman & Hall/ CRC, Boca Raton.
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Wood, S.N., Augustin, N.H., 2002. GAMs with integrated model selection using penalized regression splines and applications to environmental modelling. Ecological Modelling 157, 157177.
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Figure 1 Density plots of the residual distributions from GAM models with the four growth models used in the study as responses: the thermal growth coefficient (TGC), the specific growth rate (SGR), the Ewos growth index (EGI), and average daily weight gain (ADG).
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Figure 2
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The two panels show latitude (horizontal axis) plotted against mean hours of day-light (Figure 2A), and mean hours of civil twilight per day (Figure 2B). Each point represents the mean hours of day-light and civil twilight per fish group in the dataset.
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Figure 3
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The transformed growth model f(tgc) (vertical axis) plotted against explanatory variables (horizontal axis) from GAM regression. Shaded area represents confidence bands for the smoothing splines with width equal to two standard errors. At the bottom of each graph a rugplot is included that indicates the density of the points with respect to the explanatory variable.
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Figure 4
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The transformed growth model f(sgr) (vertical axis) plotted against explanatory variables (horizontal axis) from GAM regression. Shaded area represents confidence bands for the smoothing splines with width equal to two standard errors. At the bottom of each graph a rugplot is included that indicates the density of the points with respect to the explanatory variable.
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Figure 5
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The transformed growth model f(egi) (vertical axis) plotted against explanatory variables (horizontal axis) from GAM regression. Shaded area represents confidence bands for the smoothing splines with width equal to two standard errors. At the bottom of each graph a rugplot is included that indicates the density of the points with respect to the explanatory variable.
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Figure 6
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The transformed growth model f(adg) (vertical axis) plotted against explanatory variables (horizontal axis) from GAM regression. Shaded area represents confidence bands for the smoothing splines with width equal to two standard errors. At the bottom of each graph a rugplot is included that indicates the density of the points with respect to the explanatory variable.
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ACCEPTED MANUSCRIPT Table 1 Description of the MonAqua dataset with year classes 2000 – 2005 used in this study. The
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material comprised of 935 fish groups from 28 companies stocked on 224 sites located on the
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Norwegian coast from 58.1 to 70.7 degrees north.
Number of fish groups
157
153
222
77
153
935
Mean no of stocked fish per fish group
119
137
204
187
208
141
165
173
522
576
666
632
633
666
66.4
65.8
64.0
64.1
63.3
64.8
(in 1000) Mean number of stocked fish per site (in 1000)
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Mean latitude (°N) of fish groups
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2000 2001 2002 2003 2004 2005 Dataset
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Year class
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64.8
ACCEPTED MANUSCRIPT Table 2 Description of variables used in the analyses with mean, standard deviation (sd), minimum, and
Mean (sd)
min
Stocking weight (grams)1
96.0 (44.3) 25
Harvest weight (grams)2
5034 (870) 1362 8661
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363
2000 2005 8.8 (1.3)
6.0
Mean day-length (hours)4
12.2 (1.0)
9.8
Mean civil twilight (hours) 2.6 (0.3)
14.5
1.8
3.1
58.2
70.7
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65.1 (3.4)
11.91
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Mean temperature (°C)3
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Stocking year (year-class)
Latitude (°N)
max
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Variable
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maximum values. The total number of observations used in final analysis was n = 827.
Two fish groups with stocking weight over 400 grams were excluded, being extreme values
2
Three fish groups with harvest over 10 kg were excluded presumably being brood fish
3
The maximum mean temperature of 14.4°C at 62.7°N over 581 production days in one fish
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group was considered erroneous and excluded 4
One fish group with a mean day-length of 8.6 hours were excluded, considered erroneous
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ACCEPTED MANUSCRIPT Table 3 Results from Generalized Additive Models (GAM) of growth model estimates fitted with biotic
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and abiotic variables. Percentage deviance explained (% dev. exp.) and adjusted coefficient of
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determination (R2 adj.) were used to describe model fit. Delta percentage deviance explained (Δ % dev. exp) quantifies model improvement by successive inclusion of variables. Only significant
TGC1
dev
dev
exp
exp
0
R2 adj
%
Δ%
R2 adj
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Δ%
0
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Empty model
%
SGR2
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Model
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values (p < 0.05) are reported. The total number of observations was n = 827 for all models.
EGI3 %
Δ%
ADG4 R2 adj
%
Δ%
R2 adj
dev
dev
dev
dev
dev
dev
exp
exp
exp
exp
exp
exp
0
0
0
0
0
0
3.2
3.2
0.03
20.7
20.7
0.20
3.7
3.7
0.03
5.6
5.6
0.05
Stocking year
9.0
5.8
0.08
27.3
6.6
0.27
11.1
7.4
0.10
16.4
10.8
0.16
Mean temp
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Stocking weight
58.1
49.1
0.57
46.1
18.9
0.45
30.5
19.4
0.29
32.6
16.2
0.31
Mean day-length
67.5
9.4
0.67
60.3
14.2
0.59
42.8
12.3
0.41
39.9
7.3
0.38
Latitude
68.6
1.1
0.67
60.5
0.2
0.59
47.7
4.9
0.46
44.1
4.2
0.42
Mean civil twilight
68.6
1.1
0.67
60.5
0
0.59
48.9
1.2
0.47
44.6
0.5
0.42
Harvest weight
73.8
5.1
0.73
67.5
7.0
0.66
58.1
9.2
0.56
84.1
39.5
0.83
Full model
73.8
0.73
67.5
0.66
58.1
0.56
84.1
1
Thermal growth coefficient
2
Specific growth rate
3
Ewos growth index
4
Average daily weight gain
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0.83
ACCEPTED MANUSCRIPT Table 4 The table shows the effect (coefficients and standard error (s.e.)) of stocking year on the four
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growth models, using the year-class 2000 as baseline, analysed using Generalized Additive
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Models (GAM). Only significant effects (p<0.05) are included in the table and significant levels are indicated by asterisks. The same fixed effects are used in all the models; stocking weight,
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stocking year, mean temperature, mean day-light, latitude, mean civil twilight, and harvest
SGR
EGI
2001 ns
ns
ns
ADG
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Year TGC
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weight. The total number of observations was n = 827 for all models.
ns -0.2 (0.08)**
2003 ns
ns
ns
ns
2004 ns
ns
3.3 (1.4)*
ns
2005 0.1 (0.03)***
0.02 (0.007)**
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2002 -0.07 (0.02)** -0.02 (0.007)** ns
5.3 (1.2)*** 0.3 (0.09)**
ns not significant * p < 0.05 ** p < 0.01 *** p < 0.001
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ACCEPTED MANUSCRIPT Table 5 The table shows adjusted coefficients of determination (R2 adj.) resulting from comparison of
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Generalized Additive Models (GAM) with site and company added as random effects (both
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individually and combined), making the GAM models effectively Generalized Additive Mixedeffects Models (GAMM). The same fixed effects are used in all the models; stocking weight,
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stocking year, mean temperature, mean day-light, latitude, mean civil twilight, and harvest
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weight. The total number of observations was n = 827 for all models.
0.73
0.66
0.56
0.83
Site
0.69
0.62
0.50
0.81
Company
0.71
0.63
0.53
0.82
Site and company
0.69
0.61
0.50
0.81
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No random effects
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TGC1 SGR2 EGI3 ADG4
1
Thermal growth coefficient
2
Specific growth rate
3
Ewos growth index
4
Average daily weight gain
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Highlights We validated 4 growth models using data from 827 fish groups produced over a 1400 km north-south distance Models are influenced by different biotic and abiotic factors, which, if unaccounted for, could result in biased results Abiotic variables showed non-linear associations with the growth models The industry growth model “Ewos growth index” was considered to be the most robust model for epidemiological studies and benchmarking production data
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