86
Herbivores and Algae: Food Utilization, Growth and Reproduction ••.
The resulting allocation scheme for ingested food carbon as a function of
body size can be summarized by Fig. 4.10. As material lost by molting is
taken from the investment in somatic growth, the net effect will be much
less in juveniles, which invest all net assimilate in somatic growth, than in
adults, where the major fraction of net assimilate is invested in reproduction. The combined effects of decreasing energy input and the increasing
relative costs of metabolic and structural maintenance with body size,
create the characteristic sigmoidal growth curve in Daphnia. The retardation of body growth rate makes body size change very slowly with age in
adults, which again leads to the nearly constant net production rate in
adult Daphnia, as reported by Lynch et a1. (1986).
Comparison with Other Daphnia Growth Models. Although the assumption
of competitive superiority of large-bodied animals forms the basis of both
the competition part of the size-efficiency hypothesis (Brooks and Dodson
1965) and several other more general zooplankton growth models (Hall et
a1. 1976; Lynch 1977), it seems not to be given strong support by recent
investigations (DeMott 1989). Both the present and several other Daphnia
models (e.g., Kooijman 1986; Gurney et al. 1990; McCauley et al. 1990)
predict that juveniles should be competitively superior to adults under food
limitation. The model of Paloheimo et al. (1982), with which the present
model otherwise shares important structural similarities, predicts the
opposite, mainly due to an assumption of increasing assimilation efficiency
with body size.
Kooijman (1986) presented a model of Daphnia growth and reproduction under food limitation, where the discontinuities associated with
molting, maturation, brood production, and starvation in Daphnia are
deliberately neglected. Even the allocation to reproduction is represented
as a smooth function of size under the assumption that juveniles allocate a
fraction of their assimilate in preparation of adulthood. As noticed by
McCauleyet a1. (1990), maintaining a continuous dependence of reproduction on assimilation implies that the animals continue to reproduce them
selves to death when their overall carbon balance goes negative. On the
other hand, constructing a model that is analytical everywhere also offers
advantages in the sense that the model is considerably more wellbehaved
from a mathematical point of view, allowing analytical treatment to an
extent which is most likely unattainable in more realistic models.
Gurney et al. (1990) and McCauley et al. (1990) formulated a Daphnia
model that gives full attention to the discreteness of Daphnia life-history
events. By choosing to represent the state of an individual in terms of both
carapace length (which changes only at molt) and body weight (which
changes continuously between molts), they also obtained the advantage of
representing short-term starvation in a simple way as the weight-for-length
index: an animal is defined as starving if its current body weight is less than
would be expected from its carapace length. By defining the onset of
Herbivores and Algae: Food Utilization, Growth and Reproduction ••.
The resulting allocation scheme for ingested food carbon as a function of
body size can be summarized by Fig. 4.10. As material lost by molting is
taken from the investment in somatic growth, the net effect will be much
less in juveniles, which invest all net assimilate in somatic growth, than in
adults, where the major fraction of net assimilate is invested in reproduction. The combined effects of decreasing energy input and the increasing
relative costs of metabolic and structural maintenance with body size,
create the characteristic sigmoidal growth curve in Daphnia. The retardation of body growth rate makes body size change very slowly with age in
adults, which again leads to the nearly constant net production rate in
adult Daphnia, as reported by Lynch et a1. (1986).
Comparison with Other Daphnia Growth Models. Although the assumption
of competitive superiority of large-bodied animals forms the basis of both
the competition part of the size-efficiency hypothesis (Brooks and Dodson
1965) and several other more general zooplankton growth models (Hall et
a1. 1976; Lynch 1977), it seems not to be given strong support by recent
investigations (DeMott 1989). Both the present and several other Daphnia
models (e.g., Kooijman 1986; Gurney et al. 1990; McCauley et al. 1990)
predict that juveniles should be competitively superior to adults under food
limitation. The model of Paloheimo et al. (1982), with which the present
model otherwise shares important structural similarities, predicts the
opposite, mainly due to an assumption of increasing assimilation efficiency
with body size.
Kooijman (1986) presented a model of Daphnia growth and reproduction under food limitation, where the discontinuities associated with
molting, maturation, brood production, and starvation in Daphnia are
deliberately neglected. Even the allocation to reproduction is represented
as a smooth function of size under the assumption that juveniles allocate a
fraction of their assimilate in preparation of adulthood. As noticed by
McCauleyet a1. (1990), maintaining a continuous dependence of reproduction on assimilation implies that the animals continue to reproduce them
selves to death when their overall carbon balance goes negative. On the
other hand, constructing a model that is analytical everywhere also offers
advantages in the sense that the model is considerably more wellbehaved
from a mathematical point of view, allowing analytical treatment to an
extent which is most likely unattainable in more realistic models.
Gurney et al. (1990) and McCauley et al. (1990) formulated a Daphnia
model that gives full attention to the discreteness of Daphnia life-history
events. By choosing to represent the state of an individual in terms of both
carapace length (which changes only at molt) and body weight (which
changes continuously between molts), they also obtained the advantage of
representing short-term starvation in a simple way as the weight-for-length
index: an animal is defined as starving if its current body weight is less than
would be expected from its carapace length. By defining the onset of