E N E R G Y I N ANIMAL ECOLOGY
a5
The final term is superfluous, regardless of the definition of turnover
time.
It is not safe t o salvage any of the values from Lindeman’s data due
t o his sequential procedure of evaluation. The same remarks apply t o
the data of Dineen (1953) and t o Lindeman’s analysis of the data of
Juday (1940).
It is of interest that Clarke (1946) does not commit the error of
Lindeman but does not point it out explicitly.
The questions raised by Lindeman remain valid and t o a large degree
unanswered.
V. D A P H N ~ A
ENERGETICS
Perhaps the most complete study of ecological energetics has been
made with Daphnia populations in the laboratory. Pratt (1943)
demonstrated that Daphnia magna populations in the laboratory will
fluctuate in even a constant environment. Slobodkin (1954) confirmed
this result of Pratt’s and showed that size of Daphnia obtusa populations
in the laboratory is linearly dependent on food supply. The population
fluctuations were considered to arise because of age and size-specific
differences between the individual Daphnia composing the population.
A population composed primarily of small, young animals will have a
lower feeding rate than a population of the same number of large animals. Growth and reproduction in Daphnia are closely dependent on
food supply. Under starvation conditions reproduction and growth
effectively cease. Mortality is not severely altered by changes in nutrition (Frank, 1960). Given appropriate age and size distribution, mortality
reduces competition for food just sufficiently to enhance the reproductive and growth rates of the survivors and this permits the population to return to its initial age structure. It can be shown in theory
(Slobodkin, 1961b) that for a species with an essentially rectangular
survivorship curve the number of animals of a given age in this stable
age-structure is proportional to the inverse of the growth rate at that
age. Age-structure change combined with the maintenance of severe
starvation and the fact that different sized animals have different food
consumption rates requires numerical fluctuations in the population
even if the environment is kept as constant as possible.
If animals are removed from Daphnia populations by the experimenter at some fixed rate, the size of the residual population is reduced
while the linear dependence on food supply persists. When small animals are preferentially removed (see Fig. 3) the relation between population size P, and removal ra.te F (expressed as number of animals
removed per unit time divided by the births during that time) is given
by the simple equation
a5
The final term is superfluous, regardless of the definition of turnover
time.
It is not safe t o salvage any of the values from Lindeman’s data due
t o his sequential procedure of evaluation. The same remarks apply t o
the data of Dineen (1953) and t o Lindeman’s analysis of the data of
Juday (1940).
It is of interest that Clarke (1946) does not commit the error of
Lindeman but does not point it out explicitly.
The questions raised by Lindeman remain valid and t o a large degree
unanswered.
V. D A P H N ~ A
ENERGETICS
Perhaps the most complete study of ecological energetics has been
made with Daphnia populations in the laboratory. Pratt (1943)
demonstrated that Daphnia magna populations in the laboratory will
fluctuate in even a constant environment. Slobodkin (1954) confirmed
this result of Pratt’s and showed that size of Daphnia obtusa populations
in the laboratory is linearly dependent on food supply. The population
fluctuations were considered to arise because of age and size-specific
differences between the individual Daphnia composing the population.
A population composed primarily of small, young animals will have a
lower feeding rate than a population of the same number of large animals. Growth and reproduction in Daphnia are closely dependent on
food supply. Under starvation conditions reproduction and growth
effectively cease. Mortality is not severely altered by changes in nutrition (Frank, 1960). Given appropriate age and size distribution, mortality
reduces competition for food just sufficiently to enhance the reproductive and growth rates of the survivors and this permits the population to return to its initial age structure. It can be shown in theory
(Slobodkin, 1961b) that for a species with an essentially rectangular
survivorship curve the number of animals of a given age in this stable
age-structure is proportional to the inverse of the growth rate at that
age. Age-structure change combined with the maintenance of severe
starvation and the fact that different sized animals have different food
consumption rates requires numerical fluctuations in the population
even if the environment is kept as constant as possible.
If animals are removed from Daphnia populations by the experimenter at some fixed rate, the size of the residual population is reduced
while the linear dependence on food supply persists. When small animals are preferentially removed (see Fig. 3) the relation between population size P, and removal ra.te F (expressed as number of animals
removed per unit time divided by the births during that time) is given
by the simple equation