Environmental Engineering Reference
In-Depth Information
SE(
M
ˆ
)
M
ˆ
CV (
N
before
)
2
CV (
N
after
)
2
When natural and harvest mortality operate simultaneously: using dead recovery data.
Given recovery rate,
v
(the probability of dying and being reported), estimated from
harvest returns alone, and reporting rate,
p
, the harvest mortality rate is given by:
v
p
M
ˆ
SE(
M
ˆ
)
M
ˆ
CV(
v
)
2
CV(
p
)
2
Care may be needed with this approach where harvesters kill significant numbers
without recovering them. If this happens and the estimated reporting rate does
not take this into account, effective harvest mortality will be underestimated.
While survival describes the rate at which individuals leave a population through
death, productivity defines the rate at which new individuals enter through repro-
duction (birth, seed set, etc.). Along with survival, productivity is thus a key deter-
minant of population growth and response to exploitation (Jennings
et al
. 1998).
Productivity can be expressed in a number of related ways, depending on the data
available and the question one is attempting to answer. Here we define it as the
number of young produced per adult per unit time
. Another common formula-
tion for dioecious species is
fecundity
, the number of young females produced per
female. Fecundity is frequently used in population models when it can be assumed
that access to males does not constrain reproduction (see Milner-Gulland
et al
.
2003, for an example of the limits to this assumption). The general methods for
productivity described below apply equally to the estimation of fecundity, simply
requiring data to be restricted to females.
Another important concept in the measurement of productivity is
recruitment
,
defined as the age at which individuals functionally enter the population. In popu-
lation dynamic studies, this is frequently defined as the age at first breeding, while
in exploited species it may be defined as the age at which individuals first become
vulnerable to capture. For the discussion of methods here, we define recruitment
more generally as the point at which reproductive output is measured and used,
which will vary from one study to the next. In some cases, offspring may be
counted when they are a year or more old, while in others observations may take
place at a very early developmental stage (e.g. eggs, embryos or seeds). In this case,
in order to obtain a productivity estimate that can be used in the modelling
approaches described in Chapter 5, it may be necessary to multiply early stage prod-
uctivity by the rate of survival to the point of recruitment as defined in the model.
However, early survival rates are usually difficult to measure, and add another level
of sampling error, so it is best to estimate productivity directly if possible.
