Environmental Engineering Reference
In-Depth Information
on the species. For example, patterns of tooth wear and eruption (Hewison
et al
.
1999; Gipson
et al
. 2000) or annual rings in teeth (Bodkin
et al
. 1997; Costello
et al
. 2004) may be used in many mammals, plumage characteristics are used in
many birds (Prince
et al
. 1997), annual rings in scales or ear bones (otoliths) are
used in some fish (Buckmeier and Howells 2003; Rifflart
et al
. 2006), and annual
rings in woody plants in seasonal environments. A picture of age structure may be
taken as a single snapshot in time, or accumulated over time if this is necessary to
provide a sufficiently large sample.
The analytical framework for data of this kind is the static life table. The under-
lying concept here is the same as that behind the calculations for full population
estimates outlined in Box 2.9; in essence, you just need to substitute sample
counts,
n
a
, for complete population estimates
N
a
(Box 2.10). Skalski
et al
. (2005b)
provide a comprehensive set of statistical methods for static life tables. The key
assumptions of this approach are that:
●
Population size is stable;
●
The age structure is stable;
●
Ages are accurately estimated;
●
Individuals of all age classes are equally likely to be sampled.
The
stable population
assumption can be relaxed if the rate of change has been
constant in the recent past and is known. Given finite rate of change
(Section
2.4.1), the survival rate can be calculated as:
n
a
1
n
a
S
a
While this allows for trends in population size, it still assumes that the
age struc-
ture
is stable. Unfortunately this will often not be the case in exploited species. If
harvest has just begun, has recently been substantially reduced, or is highly vari-
able, age structure may show strong fluctuations. This will also occur in popula-
tions that fluctuate naturally, for example because of highly variable recruitment
patterns. In any of these cases, variable age structure leads to biased age-specific
survival rate estimates. When faced with this problem, age samples pooled over an
extended period, rather than taken from a single snapshot, can help to smooth out
fluctuations and reveal the underlying survival patterns. A more robust approach
has been developed by Udevitz and Ballachey (1998), using data from both the liv-
ing population and the harvest sampled over time, and allowing age structure to
fluctuate, so long as the population growth rate is independently known.
The third and fourth assumptions (
accurate aging
and
equal detectability
) are
necessary to ensure that the age sample faithfully reflects the actual age structure in
the population. In practice, this is frequently very difficult to achieve. Apart from
the obvious difficulties in obtaining accurate ages in many species, different age
classes are likely to have different detectabilities. In the case of visual samples,
this might be controlled for by using one of the census methods in Section 2.3 to
quantify and control for the variation in detectability. However, when sampling
