Environmental Engineering Reference
In-Depth Information
equilibrium the population growth rate is zero. This means that growth rate on its
own doesn't tell the whole story when our focus is sustainability.
Population size
is
also useful, particularly when it's related to a biological reference point like MSY
(Section 4.2.1). But in a bio-economic system there may be other parameters that
are relevant to sustainability; perhaps the number of hunters, their catch per unit
effort, the profits made, or the number of animals killed.
5.3.4.1 Carrying out elasticity analyses
An elasticity analysis in a simulation model involves varying each parameter in
turn by a small amount (typically 1-10%) above and below its baseline value and
recording the percentage change in the output parameter of interest. For example,
we may look at the percentage change in the population size at equilibrium with
a 1% change in each of the survival rates in the deer model. This tells us which
parameters have the biggest proportional impact on our output parameter.
Elasticities can be calculated analytically if the model is simple enough, which can
be very useful (Caswell 2001). They are also scale-independent, so they can be
compared between different vital rates and between species.
There has been much debate about how useful elasticity analysis is in conserva-
tion and ecology (e.g. Benton and Grant 1999; Mills
et al
. 1999). The general
message is that elasticity analysis is a useful component of model exploration, but
is not adequate alone. Instead we also have to carry out sensitivity analyses across
the range of values that is observed in nature—this gives us a better feel for the
likely effects of realistic conservation interventions, and of variation in the envi-
ronment. For example, elasticity analysis for many age-structured populations
shows that the population growth rate is most sensitive to adult survival and not
particularly sensitive to juvenile survival. But in ungulates, adult survival varies
very little, while juvenile survival is often highly dependent on environmental
conditions. These observations are linked, because natural selection favours
canalisation of traits for which variation has a strong effect on population growth
rate (Eberhardt 2002; Gaillard and Yoccoz 2003). In practical terms, this means
that if adult survival is already 98%, then even though increasing it to 99% might
substantially improve a population's chances of not going extinct, it may be impos-
sible to achieve. Even if variation in turtle egg survival is not a major contributor to
population growth rate or size because it is naturally low, it may still be of conser-
vation relevance to explore the effect of a 20% increase in collecting pressure on the
population. These kinds of issues can be addressed by sensitivity analysis.
5.3.4.2 Carrying out sensitivity analyses
Sensitivity analyses are particularly appropriate for simulation models, where the
strengths of elasticity analyses (scale-independence and analytical tractability)
are not so relevant. The first set of tests to do is in turn to vary each of the input param-
eters across a
range of values
, keeping the other values the same. This range will be
based on 'reasonable' values from the literature, but should also include extreme
