Environmental Engineering Reference
In-Depth Information
to explore the consequences of assumptions about the values of given parameters
or shapes of functional forms, and to highlight areas of greatest uncertainty where
research effort should be targetted. Models are a logical expression of the conse-
quences of our assumptions about system dynamics; we all have implicit models of
the system in our heads anyway, and formalising them allows transparency in
discussing conservation options. Some ways of obtaining an estimate for a
parameter on which the data are poor or unavailable are:
Use the literature , both to obtain estimates for closely related species and to
get a priori expectations from theory. For example, adult survival can be hard
to measure (Section 2.4.2), but we would expect adult female survival in
ungulates to be around 0.8-0.9 (Eberhardt 2002).
Allometry is a useful tool for obtaining estimates for parameters which are linked
to body size, such as carrying capacity and the intrinsic rate of increase (Peters
1983, Section 2.4.1, Figure 2.10). Although allometric relationships are not
always particularly strong, and the differences between a species' predicted and
actual values may be biologically important, they at least give a ball-park figure.
Use your model to test out the implications of a particular assumption. This
is particularly useful if we have data on all but one parameter. For example, if
we have estimates for everything except adult survival and we put in a value of
0.8, what do the age structure, longevity and equilibrium population size turn
out to be? Are they realistic values, and are they in line with observations in
your population and/or others?
If your model is still parameterised using highly uncertain data and using default
functional forms (such as linear density dependence), you may rightly be uncom-
fortable about using it for management purposes. But it can still be worth building
the model, because the exercise itself exposes our ignorance about the system. Here
are some useful things to do with a model such as this:
Vary the parameter values over the full range of possibilities, and look for
qualitative shifts in model behaviour. Under which circumstances does the
population decline to extinction? In which areas of parameter space is model
behaviour stable rather than fluctuating or cycling? You can then look to see if
your best guess parameter values place the system in a 'safe' area of parameter
space, or near a boundary with an unsafe area. For example, how precaution-
ary should a harvest strategy be to ensure that, given our best understanding
of the system, we keep population size within safe limits?
Invert the questions you ask. Instead of asking what level of hunting morta-
lity is safe given the fecundity rate you assume, you could ask how high
the population's fecundity rate needs to be in order to support sustainable
hunting with a given quota. What is the minimum level of spillover of har-
vestable fish from a Marine Protected Area that will provide a sustainable
livelihood for local fishers? And then you can ask how likely it is that the fish
dispersal parameter is at this level.
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