Environmental Engineering Reference
In-Depth Information
methods for defining density-dependent responses in these demographic rates,
and touch on the estimation of physical growth and transition between size classes.
Given two population totals
N
, counted
t
years apart, the annual
finite rate of
population change
can be estimated by:
1
t
N
t
N
0
can be understood as a multiplication rate. For example, if a
population of 100 grows by 10% in a year,
The parameter
1.1, and the population in the next
year will be 100
110. While this approach quantifies the net change
between two points in time, it is more often necessary to estimate the average rate
of change over longer periods. In this case, the appropriate method is to regress the
natural logarithm of a series of regularly estimated population sizes against time.
The slope of this regression gives us the
instantaneous rate of change
,
r
, which is
related to the finite rate of change by:
1.1
r
ln(
)
The abundance values used in this approach will usually be estimated using one
of the closed population methods described in Section 2.3. However, it is also pos-
sible to estimate abundance, and hence growth rate, over time using the open pop-
ulation mark-recapture methods described below in Section 2.4.2.2. An appealing
feature of these methods is that the estimation of growth rate is an integral part of
the model fitting procedure, and software implementations (Section 2.7) therefore
provide estimates of growth rate and its associated precision.
A key parameter in simple population models is the
intrinsic rate of increase
,
r
max
, which is the maximum instantaneous rate of population growth at very low
density (see Sections 1.3.11, 4.2 and 4.3.3 for more details on the meaning and use
of this parameter). There are several ways in which
r
max
can be estimated:
●
From a series of abundance measures of a small but growing population;
●
From maximal survival and productivity rates;
●
From a time-series of catch and effort data;
●
From comparisons with other species.
The approach based on a series of abundance measures makes the strong
assumption that the population is well below carrying capacity and showing its
maximal possible growth. If this assumption can be justified, the
regression
method
described above might be used to estimate the growth rate, hence
r
max
.
The second option measures
survival and productivity rates
, again making the
assumption that the sampled population is well below carrying capacity, so that the
individuals observed are free from competition. Growth rate can then be derived
from these maximal rates (Box 2.8). Individuals from a very small population may
