nato asi, october 2003william silvert the fish model developed by william silvert and peter strain

NATO ASI, October 2003William Silvert

The FISH Model

Developed byWilliam Silvert

and Peter Strain

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.


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.


Module Heirarchy

FISH

FARM

BCL Nutrients O2

The modules on the lower level show what the environmental impacts are.


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).


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.O2 consumption can lead to hypoxic

conditions.


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.


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”.


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FORTRAN is no longer widely used in ecological modelling, and FORTRAN has been superseded by other languages and programming environments.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.


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.


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 thereforeGrowth = a·Wb·ec·T

where a, b and c are constants, W is weight, and T is temperature.


About Growth

The growth model,Growth = a·Wb·ec·T

has some interesting features:Allometry (Wb) 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.


Allometry

The allometric expressionRate ~ (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.


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 ~ ec·T where c is a constant and T is the temperature.


Q10

Conventionally the parameter c in the exponent ec·T is represented by Q10, which refers to the change in rate associated with a temperature change of 10C (so c = Q10/10).

For enzymatic processes the value of Q10 is usually very close to 2.2.

For salmon we find the value is much larger, currently we are using 6.4.


Why is Q10 so large?

The discrepancy between the expected value of Q10, 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.


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.


A More General Model

If we take photoperiod into account, perhaps the model we want is of the form

Growth = a·Wb·ec·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.


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.


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 Q10 is

unexpected and raises questions.If photoperiod is indeed important, then

the value of Q10 depends on latitude.So if we want to use the model

somewhere else, we have to modify it.


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 asgrate = g0 * exp(Q10*temp/10)* W^xp;

Even if you are not accustomed to programming, the code is easy to read and understand.


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.


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.


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.


Fancy Functions

If we plot the MatLab code for stress we get a plot like this:

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

The code is simple, but it looks awfully artificial! – and note the section under the arrow.

We overlooked an extreme case.


Defining f(O2)

We can construct a function that looks like this:

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

This is a much more arbitrary function, but it makes more sense and is probably more realistic.


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.

nato asi, october 2003william silvert the fish model developed by william silvert and peter strain

Documents

fish module

fish model

fish growth

young fish

old fish

reinventing fish

single fish

nato asi