Environmental Engineering Reference
In-Depth Information
where
B
i
and
g
i
are the standing biomass and instantaneous growth rates of the
i
th size-
class, respectively. For exponential growth,
g
i
5 ð
1
=
D
i
Þ
ln
ð
m
b1
1
=
m
b
Þ
ð
3
:
6
Þ
where
D
i
is the development time (the length of time the animal spends in the
i
th size-
class), and
m
b1
1
and
m
b
are the body masses of the animals entering and leaving the
i
th
size-class. Here, we need to know the biomass of each size-class in the field and the
amount of time the animal takes to develop through each size-class. Both of these variables
generally vary over the year. Thus, data requirements for estimating production are high.
Care must be taken that the conditions under which the
D
i
are measured mimic field con-
ditions. Because field estimates of
B
i
usually are burdened with large errors, estimates of
production using this method typically have large errors.
For animals with distinct cohorts, production may be estimated by summing the prod-
uct of mass gain and population size over the life of the cohort:
X
t
ðð
P
5
m
t1
1
2
m
t
Þð
N
t1
1
1
N
t
Þ=
2
Þ
ð
3
:
7
Þ
where
N
t
is the mean population density at time
t
and
m
t
and
m
t1
1
are the mean body
masses at two successive sampling times. This method requires good estimates of
population size and body mass in the field over the life of the cohort, and is therefore
data-intensive and subject to large errors. The size-frequency method uses an entirely
different method to estimate production, but also requires data on body mass and abun-
dance, so it also requires good estimates of population size and body mass in the field
over the year.
Finally, production may be estimated by empirical models, usually of the form
P
5 ð
P
=
B
Þ
B
ð
3
:
8
Þ
where
B
is the mean annual biomass and
P/B
is the annual turnover ratio. Estimates of
P
/
B
are now readily available for many animals from empirical models base
d
on body
mass and temperature. These empirical models still require good estimates of
B
;
and are
subject to large errors, but can be applied to a wide range of circumstances.
Further technical details on methods to estimate secondary production measurements
are available in the works of
Downing and Rigler (1984)
,
Kemp et al. (1993)
,
Benke (1984,
1993)
,
Suberkropp and Weyers (1996)
, and
Benke and Huryn (2006)
.
CONTROLS AND PREDICTION OF
SECONDARY PRODUCTION
Ecologists have devoted a lot of effort to understand what controls primary production
(see Chapter 2), and most beginning ecology students know that primary production
