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NATO ASI, October 2003William Silvert The FISH Model Developed by William Silvert and Peter Strain

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NATO ASI, October 2003 Modular Modelling Models should be developed in a modular fashion. Not only does this simplify the modelling, but it also makes it easier to maintain and update the model. Modelling of aquaculture impact especially calls for a modular approach.

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NATO ASI, October 2003 Modelling Heirarchy Start with a model of a single fish, represented by a module called FISH. Outputs of the FISH module are integrated in a module representing all stocks in a fish farm, called FARM. The outputs of FARM are inputs to a suite of separate modules describing environmental impact.

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NATO ASI, October 2003 Module Heirarchy FISH FARM BCLNutrientsO2 The modules on the lower level show what the environmental impacts are.

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NATO ASI, October 2003 Trivial Example Suppose that the FISH module shows that young fish excrete 1 g-N/d and old fish excrete 2 g-N/d. Suppose that a farm has 4 000 young fish and 3 000 old fish. Then the FARM module would generate total nitrogen loading of 10 000 g-N/d (4 000 x 1 + 3 000 x 2).

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NATO ASI, October 2003 Use of Model Outputs The FISH and FARM modules generate different types of output which feed into different types of environmental impact: N, P and other soluble nutrients contribute to eutrophication. C and faecal wastes enrich the benthos, often to excessive levels. O 2 consumption can lead to hypoxic conditions.

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NATO ASI, October 2003 The FISH Module The FISH module was first developed by William Silvert in the early 1990’s. It was written in FORTRAN and was based on fish farming practices that were common at the time. Many of the features of the model quickly became obsolete. For example, the type of feed used changed drastically in a short period of time.

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NATO ASI, October 2003 Module Maintenance Despite ongoing changes in feed type and farming practices, our models of aquaculture impact are relatively easy to maintain. There are two main reasons for this: The modular design means that only the FISH module needs to be changed. Feed characteristics are defined in a parameter block and are not “hard-wired”.

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NATO ASI, October 2003 Reinventing FISH Originally the FISH and other modules were written in FORTRAN-77 and ran within the BSIM software framework. FORTRAN is no longer widely used in ecological modelling, and FORTRAN has been superseded by other languages and programming environments. Several alternate programming approaches have been implemented.

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NATO ASI, October 2003 The MatLab Version Recently the FISH module has been updated and rewritten in MatLab by Peter Strain at the Bedford Institute of Oceanography. The code shown is derived from his MatLab version. It is similar to the original FORTRAN code, and some changes have been made for clarity.

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NATO ASI, October 2003 Fish Growth The basic assumption of the FISH model is that growth can be represented as allometric with a temperature-dependent rate factor. The underlying equation is therefore Growth = a·W b ·e c·T where a, b and c are constants, W is weight, and T is temperature.

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NATO ASI, October 2003 About Growth The growth model, Growth = a·W b ·e c·T has some interesting features: Allometry ( W b ) is widely found in biological systems and is a good basis for modelling in the absence of more detailed physiological information. The value of c is abnormally high, and is probably not due only to temperature.

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NATO ASI, October 2003 Allometry The allometric expression Rate ~ (Weight) xp where xp is some constant exponent, is widely used in modelling size-dependent metabolic rates when detailed physiological data are not available. Most rates – growth, respiration, even mortality – are reasonably well described by allometry.

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NATO ASI, October 2003 Temperature Effects The effects of temperature on living organisms are complex, but over the temperature range in which the organisms are not stressed it is common for metabolic rates to vary according to an expression of the form Rate ~ e c·T where c is a constant and T is the temperature.

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NATO ASI, October 2003 Q 10 Conventionally the parameter c in the exponent e c·T is represented by Q 10, which refers to the change in rate associated with a temperature change of 10 C (so c = Q 10 /10). For enzymatic processes the value of Q 10 is usually very close to 2.2. For salmon we find the value is much larger, currently we are using 6.4.

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NATO ASI, October 2003 Why is Q 10 so large? The discrepancy between the expected value of Q 10, 2.2, and the much higher value of 6.4 obtained by fitting salmon growth data, reflects the difficulty in fitting models to restricted sets of data which do not allow for independent assessment of all the possible factors involved.

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NATO ASI, October 2003 Is it the Photoperiod? The growth rate of fish is known to depend on how much sunlight they get, and in natural systems this depends on the photoperiod. Temperature is a proxy for the photoperiod, since it is highest when the photoperiod is longest and vice versa. They are highly correlated.

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NATO ASI, October 2003 A More General Model If we take photoperiod into account, perhaps the model we want is of the form Growth = a·W b ·e c·T ·f(P) where c is now a true temperature effect and f(P) is some function of photoperiod, the form of which remains to be determined.

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NATO ASI, October 2003 But why Generalise? If the simple model that includes only weight and temperature gives good results, why do we have to complicate matters by including photoperiod? When we apply a model we have to make sure that it is really applicable. Models developed in one location may not be valid in some other place.

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NATO ASI, October 2003 The Reasoning Process It is important to understand why we should introduce photoperiod. The model with just W and T works very well in the area where it was developed, But the very high value of Q 10 is unexpected and raises questions. If photoperiod is indeed important, then the value of Q 10 depends on latitude. So if we want to use the model somewhere else, we have to modify it.

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NATO ASI, October 2003 Code Samples Here is some typical model code: temp = tm + tr*cos(day*2*pi/365); (fits annual water temp to a sinusoid). Specific growth (%/d) is modelled as grate = g0 * exp(Q10*temp/10)* W^xp; Even if you are not accustomed to programming, the code is easy to read and understand.

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NATO ASI, October 2003 Other Generalisations There are other aspects of the model which can be improved by taking additional factors into account. Stress affects growth and other metabolic processes. Stress can be caused by many factors, such as low oxygen levels.

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NATO ASI, October 2003 Modelling Stress Here is some of Peter Strain’s initial MatLab code for the effects of stress: stress = min(oxygen/O2crit,1); if (stress < 0.5) ans = 'Dangerously low O2 levels' stress = 0.1; elseif (stress < 0.9) ans = 'Stress inhibits growth‘ end grate = grate * stress; This is a reasonable first try at taking oxygen stress into account.

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NATO ASI, October 2003 Generalised Stress A more general approach to modelling oxygen stress would be to write: grate = grate * f(oxygen/O2crit); where f() is some general function of oxygen level. This requires much more data. Even in the absence of data it is more realistic, but then it can be subject to criticism.

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NATO ASI, October 2003 Fancy Functions If we plot the MatLab code for stress we get a plot like this: The code is simple, but it looks awfully artificial! – and note the section under the arrow. We overlooked an extreme case.

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NATO ASI, October 2003 Defining f(O 2 ) We can construct a function that looks like this: This is a much more arbitrary function, but it makes more sense and is probably more realistic.

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NATO ASI, October 2003 Be Brave! Building models that are realistic may involve guessing at mathematical forms that are not based on solid data. People show misplaced confidence in simple models with few parameters. It is more important to be realistic than to come up with “bullet-proof” mathematical equations.

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