68
Herbivores and Algae: Food Utilization, Growth and Reproduction ...
normal distribution (which implies that rates are non-negative, as they
should be), the compound distribution of g resulting from Eq. (4.2) will not
be lognormal, and will contain both negative and positive values. In other
words, taking the difference of lognormal variables tends to amplify the
uncertainty in the individual variables to an extent that the result can be
nearly meaningless.
Another, and perhaps more serious objection to describing growth from
submodels of assimilation and respiration comes from a study by Lynch et
al. (1986), who compared Daphnia net growth estimates based on two
essentially different methods: long-term lifetable studies and short-term
physiological measurements. The disparity in experimental time scales
apparently created some striking inconsistencies between the two methods;
while correspondence was good for juvenile Daphnia, life tables gave constant production [as (Ilg C) ind: 1 datI] in adults, while tracer studies
predicted production proportional to animal size throughout their lifespan
(Lynch et al. 1986). Assimilation measurements by tracer methods on the
time scale of 1-3 h, as used by Lampert and coworkers (Lampert 1977;
Lynch et al. 1986), are based on quite a few assumptions that are necessary
to correct for respirationallosses of fresh assimilate. As direct growth measured in life table experiments contains fundamentally fewer assumptions
than tracer-based methods, it is reasonable that one should put more confidence in life table data under conditions where the two approaches diverge.
The modeling strategy chosen here will therefore be first to formulate a
model of the allocation of net assimilate (i.e. assimilation less respiration)
into growth and reproduction, using life table data as input. In the next
section this model will be expanded to include the overheads of egestion
and respiration, so that assimilation will be given as the carbon input
necessary to support observed growth and maintenance costs.
Net Assimilate Allocation ModeL As the molt cycle appears to be a fundamental rhythm in cladoceran growth and reproduction, the instar duration
is a natural time scale for an energy-allocation model. At 20°C, the intermolt period is 1-3 days in Daphnia, with the adult instars being approximately twice as long as the juvenile ones. At this time scale there is probably no reason explicitly to model the dynamics of the fast pool identified
with the contents of the hemocoel in Fig. 4.1. If we consider the carapace
and the eggs carried in the brood pouch as passive components of an adult
Daphnia, we need to take into account only two carbon pools to describe
growth from one instar to the next; body mass (B) and accumulated ovary
material that will be extruded as eggs at next molt (E) (both as Ilg C):
B = (1 - R) g B
(4.3)
E=RgB,
(4.4)
Herbivores and Algae: Food Utilization, Growth and Reproduction ...
normal distribution (which implies that rates are non-negative, as they
should be), the compound distribution of g resulting from Eq. (4.2) will not
be lognormal, and will contain both negative and positive values. In other
words, taking the difference of lognormal variables tends to amplify the
uncertainty in the individual variables to an extent that the result can be
nearly meaningless.
Another, and perhaps more serious objection to describing growth from
submodels of assimilation and respiration comes from a study by Lynch et
al. (1986), who compared Daphnia net growth estimates based on two
essentially different methods: long-term lifetable studies and short-term
physiological measurements. The disparity in experimental time scales
apparently created some striking inconsistencies between the two methods;
while correspondence was good for juvenile Daphnia, life tables gave constant production [as (Ilg C) ind: 1 datI] in adults, while tracer studies
predicted production proportional to animal size throughout their lifespan
(Lynch et al. 1986). Assimilation measurements by tracer methods on the
time scale of 1-3 h, as used by Lampert and coworkers (Lampert 1977;
Lynch et al. 1986), are based on quite a few assumptions that are necessary
to correct for respirationallosses of fresh assimilate. As direct growth measured in life table experiments contains fundamentally fewer assumptions
than tracer-based methods, it is reasonable that one should put more confidence in life table data under conditions where the two approaches diverge.
The modeling strategy chosen here will therefore be first to formulate a
model of the allocation of net assimilate (i.e. assimilation less respiration)
into growth and reproduction, using life table data as input. In the next
section this model will be expanded to include the overheads of egestion
and respiration, so that assimilation will be given as the carbon input
necessary to support observed growth and maintenance costs.
Net Assimilate Allocation ModeL As the molt cycle appears to be a fundamental rhythm in cladoceran growth and reproduction, the instar duration
is a natural time scale for an energy-allocation model. At 20°C, the intermolt period is 1-3 days in Daphnia, with the adult instars being approximately twice as long as the juvenile ones. At this time scale there is probably no reason explicitly to model the dynamics of the fast pool identified
with the contents of the hemocoel in Fig. 4.1. If we consider the carapace
and the eggs carried in the brood pouch as passive components of an adult
Daphnia, we need to take into account only two carbon pools to describe
growth from one instar to the next; body mass (B) and accumulated ovary
material that will be extruded as eggs at next molt (E) (both as Ilg C):
B = (1 - R) g B
(4.3)
E=RgB,
(4.4)