72
Herbivores and Algae: Food Utilization, Growth and Reproduction ...
1.0
r:::
0
•
.... 0.8
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....
•
u
::l
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'"d
•
0
....
•
fr 0.6
....
S
'"d
d)
....
~
0.4
u
0
- -;
d
0
0.2
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u
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U-t
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20
40
60
Body size (Ilg C)
Fig. 4.3. Fraction of net assimilate allocated to reproduction (estimated from Eq. (A2.2») as a
function of body size in Daphnia pulex (pooled data from food levels> 1 (mg C) (-I, from
Lynch 1989). Solid line is the model given by Eq. (4.8)
where the operator ( ). is zero whenever the expression inside the parenthesis is ~ O. With R' = 0.8 and B' = 7.5 ~g C, Eq. (4.8) gives an acceptable fit
(Fig. 4.3). B' is then interpreted as the size of first investment to reproduction and R' is the asymptotic level of reproductive investment. The discontinuity at B' is an unavoidable consequence of the life history pattern in
Daphnia. The decrease in reproductive investment in very large animals
might be a real phenomenon caused by increasing molt costs, but it is
probably not worthwhile to introduce an additional parameter to model
this.
Equations (4.3)-(4.6) constitute a model of body growth and reproduction between instar transitions in Daphnia pulex. In Fig. 4.4 the differential
equations (4.3) and (4.4) were solved numerically (using the methods
described in Appendix A9), with initial conditions B = B J and E=O, where
B J is the body mass of a newly hatched neonate (Table 4.1). At the end of
each instar, molting and egg laying were simulated as B .- B - M and E +- 0,
where M is the molt weight at the start of the previous instar (v .- S means
that the variable v is overwritten by the result of the expression S).