Benthic Fauna of Lakes
191
It is assumed that the population(s) is univoltine, that individuals remain in each
of the length classes for the same amount of time, and that they all can grow to the
maximum length in this length-frequency table. Consequently, an animal growing
through 10 length classes would be expected to remain in each of the length classes
for 1/10 of the year, assuming its life expectancy is one year. The mean number in
each length class then is multiplied by 10, in this case, to obtain an estimate of the
number of individuals that grew to the mean length of that length class during the
course of the year [cf. Hamilton (1969b)]. Thus, i of column 8 is the number oflength
classes that a population grows through to reach its maximum length. The production
in volume units (column 9) then is the product of columns 7 and 8.
It is important to note that the last column is the algebraic sum of both positive
and negative results, as production losses are summed between size classes. The total
for all of the size groups yields a reasonable estimate of the annual production rate
for the population. Where production rates of a given species have been determined
comparatively by all four techniques, the size-frequency method compares well with
the others (A. Benke, personal communication).
In natural heterogeneous populations, the size-frequency distribution can be
regarded as a first estimate of an "average cohort" when the number of average
cohorts equals the number of size classes through which the organisms grow
(Hamilton, 1969b). Growth is assumed to be linear within the size classes. Under
these conditions, numerical differences can be attributed to mortality. When all size
classes are considered together, the effect of nonlinear growth on the estimate of
annual production is small. When most of the organisms are not univoltine, however,
a serious error is introduced.
Estimates of rates of annual production of multivoltine inverterbrates by the
size-frequency method sometimes are made by multiplying the production value by
the average number of generations per year (Hamilton, 1969b). When egg, pupal, or
adult stages of aquatic insects constitute a significant portion of the total generation
time, this procedure underestimates productivity (Benke, 1979). If reproduction were
to occur before the final size class was attained, as in crustaceans, this procedure
would overestimate productivity. These errors can be reduced by determining the
average development time for the aquatic stages, the cohort production interval (CPI),
which applies only to the aquatic stages throughout which growth and production
are occurring (Benke, 1979). The production value from the size-frequency table
should be multiplied by 365/CPI, which yields annual production. Thus the average
time from hatching to pupation or final size must be known, and this average time
can be obtained from temporal patterns of size frequencies or growth studies.
It should be noted that weight units also can be used directly in construction of
the size-frequency table. The mean weight for each size group replaces volume
(columns 4 and 6) and production is calculated directly in g/m 2 over the year. When
volume calculations are used, conversion to weight can be estimated by assuming
that average organisms are cylinders five times as long as broad with a specific gravity
of 1.05 (Hamilton, 1969b). Then, using a formula, n'r 2 'L'p each I-mm unit of these
cylinders weights, in grams wet weight:
n(0.1)2 (L)(1.05)
1000
A coversion factor is needed to correct the values from wet to dry weight, a more
meaningful value. This factor is variable and should be determined (about 80% water
or a factor of 0.2).
191
It is assumed that the population(s) is univoltine, that individuals remain in each
of the length classes for the same amount of time, and that they all can grow to the
maximum length in this length-frequency table. Consequently, an animal growing
through 10 length classes would be expected to remain in each of the length classes
for 1/10 of the year, assuming its life expectancy is one year. The mean number in
each length class then is multiplied by 10, in this case, to obtain an estimate of the
number of individuals that grew to the mean length of that length class during the
course of the year [cf. Hamilton (1969b)]. Thus, i of column 8 is the number oflength
classes that a population grows through to reach its maximum length. The production
in volume units (column 9) then is the product of columns 7 and 8.
It is important to note that the last column is the algebraic sum of both positive
and negative results, as production losses are summed between size classes. The total
for all of the size groups yields a reasonable estimate of the annual production rate
for the population. Where production rates of a given species have been determined
comparatively by all four techniques, the size-frequency method compares well with
the others (A. Benke, personal communication).
In natural heterogeneous populations, the size-frequency distribution can be
regarded as a first estimate of an "average cohort" when the number of average
cohorts equals the number of size classes through which the organisms grow
(Hamilton, 1969b). Growth is assumed to be linear within the size classes. Under
these conditions, numerical differences can be attributed to mortality. When all size
classes are considered together, the effect of nonlinear growth on the estimate of
annual production is small. When most of the organisms are not univoltine, however,
a serious error is introduced.
Estimates of rates of annual production of multivoltine inverterbrates by the
size-frequency method sometimes are made by multiplying the production value by
the average number of generations per year (Hamilton, 1969b). When egg, pupal, or
adult stages of aquatic insects constitute a significant portion of the total generation
time, this procedure underestimates productivity (Benke, 1979). If reproduction were
to occur before the final size class was attained, as in crustaceans, this procedure
would overestimate productivity. These errors can be reduced by determining the
average development time for the aquatic stages, the cohort production interval (CPI),
which applies only to the aquatic stages throughout which growth and production
are occurring (Benke, 1979). The production value from the size-frequency table
should be multiplied by 365/CPI, which yields annual production. Thus the average
time from hatching to pupation or final size must be known, and this average time
can be obtained from temporal patterns of size frequencies or growth studies.
It should be noted that weight units also can be used directly in construction of
the size-frequency table. The mean weight for each size group replaces volume
(columns 4 and 6) and production is calculated directly in g/m 2 over the year. When
volume calculations are used, conversion to weight can be estimated by assuming
that average organisms are cylinders five times as long as broad with a specific gravity
of 1.05 (Hamilton, 1969b). Then, using a formula, n'r 2 'L'p each I-mm unit of these
cylinders weights, in grams wet weight:
n(0.1)2 (L)(1.05)
1000
A coversion factor is needed to correct the values from wet to dry weight, a more
meaningful value. This factor is variable and should be determined (about 80% water
or a factor of 0.2).