238
WILLIdM STREIFER
contains four unknown constants do, d,, d, and a,. These could be
determined by regression analysis of data or, in the case of the predator
term, by working from detailed submodels such as those of Holling
(1959a, b, 1966) or Watt (1959). Equation (81) is meant only as one
example of a vast number of possible functional forms. I should
emphasize that fitting data within a submodel and then utilizing that
and other submodels in an overall model to predict the populational
dynamics, is quite different to fitting a total population model to total
population data.
VII. APPLICATIONS O F AGE-SIZE SPECIFIC M O D E L S
The single-species density function model of section IV,
has been applied to two species. These are described in detail in this
section. Other applications of age and age-size specific models are
discussed in the following section.
A. D A P H N I A P U L E X
Daphnia pulex is a species widely used in laboratory experiments.
These animals normally reproduce parthenogenetically and laboratory
populations show pronounced oscillations in number without apparent
environmental variations. The oscillation mechanisms have been described by Pratt (1943), Slobodkin (1954) and Frank (1960), and the
results of Frank’s algebraic model C’, which include considerations of
biomass, are in good agreement with experiment. The discussion here
closely follows the paper of Sinko and Streifer (1969), in which an
experimental population of Slobodkin and Richman (1956) was modeled.
Although Daphnia has been extensively studied, sufficient data are not
available to specify all the required information in our submodels. Thus
a number of assumptions are made and the model is tested for sensitivity
to these assumptions.
1. Growth function and birth rate
The growth function Y and the birth rate are treated together because
they are both closely related to the consumed food. Each individual
assimilates an equivalent food energy, ea, each day. That energy less the
maintenance energy, em, is the excess assimilated energy, A , which is
partitioned between growth and reproduction, i.e.
A = ea-em = A g + A r
(83)
WILLIdM STREIFER
contains four unknown constants do, d,, d, and a,. These could be
determined by regression analysis of data or, in the case of the predator
term, by working from detailed submodels such as those of Holling
(1959a, b, 1966) or Watt (1959). Equation (81) is meant only as one
example of a vast number of possible functional forms. I should
emphasize that fitting data within a submodel and then utilizing that
and other submodels in an overall model to predict the populational
dynamics, is quite different to fitting a total population model to total
population data.
VII. APPLICATIONS O F AGE-SIZE SPECIFIC M O D E L S
The single-species density function model of section IV,
has been applied to two species. These are described in detail in this
section. Other applications of age and age-size specific models are
discussed in the following section.
A. D A P H N I A P U L E X
Daphnia pulex is a species widely used in laboratory experiments.
These animals normally reproduce parthenogenetically and laboratory
populations show pronounced oscillations in number without apparent
environmental variations. The oscillation mechanisms have been described by Pratt (1943), Slobodkin (1954) and Frank (1960), and the
results of Frank’s algebraic model C’, which include considerations of
biomass, are in good agreement with experiment. The discussion here
closely follows the paper of Sinko and Streifer (1969), in which an
experimental population of Slobodkin and Richman (1956) was modeled.
Although Daphnia has been extensively studied, sufficient data are not
available to specify all the required information in our submodels. Thus
a number of assumptions are made and the model is tested for sensitivity
to these assumptions.
1. Growth function and birth rate
The growth function Y and the birth rate are treated together because
they are both closely related to the consumed food. Each individual
assimilates an equivalent food energy, ea, each day. That energy less the
maintenance energy, em, is the excess assimilated energy, A , which is
partitioned between growth and reproduction, i.e.
A = ea-em = A g + A r
(83)