Single parasitoid models
In the absence of C. viator parasitism, the rescaled full parasitoid model has At = Nt and Nt+1 = Pt+1, so we can eliminate A and P from the model, giving|
|
Similarly, if parasitism by Dusona
is absent then Pt+1 = Lt+1
and we can eliminate L, giving
|
and the same equations hold after re-scaling if Dusona parasitism is constant.
Scaling the maternal effects model
Using Eq. 14 of the text to eliminate
Et from the 3-equation model yields
|
 |
Substituting these into Eqs. A.9–A.10 and suppressing the primes gives the final form of the model.
Oviposition preference function for food quality model
The data in Fig. 1 of Šmits et al. (2001) presumably represent the number of eggs after some eggs have dropped off the new needles. Thus we need to correct those data to reconstruct the egg laying preference. Let
be the fraction of eggs observed on mature needles (from the figure) and let 
be the fraction of eggs that fall off of new needles. Then the true fraction of
eggs laid on mature needles is
 |
We digitized the data from Fig.
1 of Šmits et al. (2001), and corrected the oviposition fraction (using
Eq. A.17) for the estimated value of
and for the extreme values observed. After some trial and error we fit the corrected
preference data with an equation of the form
 |
which appears to provide a satisfactory fit (Fig. A1). The parameter estimates are in Table A1.
|
| FIG. A1: Fits of Eq. A.18 under different egg drop assumptions. The circles are data; the lines are the fitted curves. |
TABLE A1. Estimated value of
from Eq. A.18, along with its standard error and the standard error of the residuals.
Data SE ( Residual SE Observed 1.998 0.114 0.151 1.843 0.102 0.154 1.927 0.109 0.152 1.695 0.091 0.156
LITERATURE CITED
Šmits, A., S. Larsson, and R. Hopkins. 2001. Reduced realised fecundity in the pine looper Bupalus piniarius caused by host plant defoliation. Ecological Entomology 26:417–424.