Environmental Engineering Reference
In-Depth Information
Box 2.17
Estimating size class transition rates.
The probability that an individual in a given size class will grow to the next one in
a given time unit is equal to the proportion of individuals in the class that are
within one time unit of the size threshold for transition. If it can be assumed that
survival rate,
S
, is constant across all members of the class, the transition prob-
ability for a class that lasts
t
time units is given by:
S
t
1
S
t
q
S
t
1
The average time span of a size class,
t
, can be measured directly by following the
growth of a sample of individuals. However, it will obviously take a very long time
to accumulate the necessary information in this way for long-lived, slow-growing
species. In this case, data on the sizes and ages of a cross section of individuals can
be used to plot a growth curve, and the average time span of a size class can be
estimated from this. For example, given growth rate (
g
) and maximum size (
s
max
)
estimates from a von Bertalanffy growth function (see Box 2.16), the average
duration of a class with upper and lower size thresholds of
s
u
and
s
l
is given by:
s
max
s
l
s
max
s
u
g
t
ln
Harvesters and the species they harvest exist in a spatially variable world, and analyses
of sustainability will often need to take this into account. This is particularly the
case where spatial management strategies, such as zoned use areas, have been imple-
mented or are being considered (Section 6.4.1). The main analytical approaches that
focus on spatial patterns, and which we introduce in this section, are the estimation
of
movement rates
, and the measurement of
habitat associations
.
In mobile species (including plants with widely dispersed seeds or corals with
pelagic larvae), movements in or out of a population can be an important element
of its dynamics. For example, if regular immigration boosts the growth rate of an
exploited population, the sustainability of its use might depend on maintaining
the source of the immigrants. Indeed, this process is a key determinant of the success
or otherwise of no take zones or protected areas in preserving stocks and providing
overspill for harvest (Sale
et al
. 2005).
Direct measures of movement depend on observing the locations of a sample of
known individuals
at intervals. One way to do this is by
telemetry
. Traditionally
