Benthic Fauna of Lakes
187
Removal-Summation Method. A simple life history of a single-species population is
determined and a series of density and biomass estimates is made throughout the
life of a single cohort or generation. The mortality, in terms of biomass, can be
calculated between successive samples of the series, taking into account the size of
the organisms during the period of loss. The sum of the observed mortalities over
the entire life cycle then is equivalent to the total production of the cohort. When
the species is univoltine, i.e., has only one reproductive generation per year, the cohort
production then is equivalent to the annual production for this species [see Waters
(1977), Benke (1984), and Rigler and Downing (1984)].
The removal- (=mortality) summation method evaluates production (P) as the
sum of mean individual weight (w, as dry weight in mg/individual) times the change
in numbers (N) for each sample interval or cohort interval (P = Iw~N). This
removal-summation method essentially is identical to the growth increment
summation method, based on the same population statistics, where production is
equal to the sum of mean numbers times the change in mean individual biomass
(weight) for each sample interval (P = IN ~w).
Instantaneous Growth Method. The production rate for a given interval of time is
estimated by the product of the instantaneous rate of growth and the mean biomass
(standing stock) during the time interval:
P=G(B)
where P = production in biomass/area (e.g., g/m2) over a given interval of time;
G = instantaneous rate of growth during this period, computed as the naturallogarithm of the ratio of the mean individual weight at the end of the time interval to the
mean weight at the beginning of the interval; and B = mean biomass/area (e.g., g/m2)
during the time interval, computed as the average of the biomass at the beginning
and end of the time period.
It should be emphasized that this simple exponential growth model assumes
continuous growth. Many organisms usually exhibit discontinuous growth in which
birth, death, immigration, and emigration vary and cause differing discrete changes
in the population size and growth. It is important that sampling frequency take these
factors into consideration in relation to rate of growth. While monthly sampling may
be quite adequate for many benthic animals, much more frequent sampling may be
needed for some forms. In general, the shorter the sampling interval, the better will
be the estimations of rates of production. See Edmondson and Winberg (1971),
Winberg (1971), Waters (1977), Benke (1984), and Rigler and Downing (1984) for
detailed analyses.
The instantaneous growth method can be used for production estimates of
asynchronous populations also when independent estimates of G from growth studies
can be obtained. Furthermore, if there were size-specific differences in growth rates
for a population, the best estimate of production would be obtained by
P = G1Bl + G2B2 + ... + (all sizes).
Allen Curve Method. The Allen curve method extends the instantaneous growth
method and the removal-summation method to a graphical treatment, in which a
curve is constructed from the numbers/weight relationship of a cohort over its life
cycle (Gillespie and Benke, 1979). The method is basically a comparison of the
survivorship of a cohort and the weights of individuals at selected points along the
survivorship curve. Density in numbers per unit area is plotted against mean individual
187
Removal-Summation Method. A simple life history of a single-species population is
determined and a series of density and biomass estimates is made throughout the
life of a single cohort or generation. The mortality, in terms of biomass, can be
calculated between successive samples of the series, taking into account the size of
the organisms during the period of loss. The sum of the observed mortalities over
the entire life cycle then is equivalent to the total production of the cohort. When
the species is univoltine, i.e., has only one reproductive generation per year, the cohort
production then is equivalent to the annual production for this species [see Waters
(1977), Benke (1984), and Rigler and Downing (1984)].
The removal- (=mortality) summation method evaluates production (P) as the
sum of mean individual weight (w, as dry weight in mg/individual) times the change
in numbers (N) for each sample interval or cohort interval (P = Iw~N). This
removal-summation method essentially is identical to the growth increment
summation method, based on the same population statistics, where production is
equal to the sum of mean numbers times the change in mean individual biomass
(weight) for each sample interval (P = IN ~w).
Instantaneous Growth Method. The production rate for a given interval of time is
estimated by the product of the instantaneous rate of growth and the mean biomass
(standing stock) during the time interval:
P=G(B)
where P = production in biomass/area (e.g., g/m2) over a given interval of time;
G = instantaneous rate of growth during this period, computed as the naturallogarithm of the ratio of the mean individual weight at the end of the time interval to the
mean weight at the beginning of the interval; and B = mean biomass/area (e.g., g/m2)
during the time interval, computed as the average of the biomass at the beginning
and end of the time period.
It should be emphasized that this simple exponential growth model assumes
continuous growth. Many organisms usually exhibit discontinuous growth in which
birth, death, immigration, and emigration vary and cause differing discrete changes
in the population size and growth. It is important that sampling frequency take these
factors into consideration in relation to rate of growth. While monthly sampling may
be quite adequate for many benthic animals, much more frequent sampling may be
needed for some forms. In general, the shorter the sampling interval, the better will
be the estimations of rates of production. See Edmondson and Winberg (1971),
Winberg (1971), Waters (1977), Benke (1984), and Rigler and Downing (1984) for
detailed analyses.
The instantaneous growth method can be used for production estimates of
asynchronous populations also when independent estimates of G from growth studies
can be obtained. Furthermore, if there were size-specific differences in growth rates
for a population, the best estimate of production would be obtained by
P = G1Bl + G2B2 + ... + (all sizes).
Allen Curve Method. The Allen curve method extends the instantaneous growth
method and the removal-summation method to a graphical treatment, in which a
curve is constructed from the numbers/weight relationship of a cohort over its life
cycle (Gillespie and Benke, 1979). The method is basically a comparison of the
survivorship of a cohort and the weights of individuals at selected points along the
survivorship curve. Density in numbers per unit area is plotted against mean individual