Peter A. Hambäck and Christer Björkman. 2002. Estimating the consequences of apparent competition: a method for host-parasitoid interactions. Ecology 83:1591-1596.

Appendix A. Calculating parasitoid selectivities of Anagrus epos.

For the invasion analysis, it was necessary to extract data on the selectivity of A. epos, where selectivity = ln(S_glh)/ln(S_vlh) (Eq. 6), parasitizing variegated and grape leafhoppers. To validate the analysis, it was also necessary that is independent on leafhopper densities. The paper by Settle and Wilson (1990a) did not directly provide empirical values on , but these could be calculated for each data point in their Fig. 8 (N = 69), by using information from Fig. 7a. Values on are calculated from estimates of S_vlh[..] and S_glh[..], where S_i[..] is the proportion of unparasitized eggs, larvae and pupae as functions of initial egg densities (vlh = variegated leafhopper, glh = grape leafhopper).

Extracting the raw data: From Fig. 7a in Settle and Wilson, we extracted the parasitization frequency by A. epos on grape leafhoppers (p_glh) as a function of the relative density of variegated leafhopper (VLH_rel), i.e,

pglh = (1-Sglh[..]) = + *VLHrel,

(A.1)

where

,

(A.2)

H_vlh is the density of variegated leafhoppers, H_glh is the density of grape leafhopper, and and are constants. Both and were estimated from the data in Fig. 7a ( = 0.65 and = 0.36). From Fig. 8 in Settle and Wilson, we extracted VLH_rel (X-axis) and the relative emergence rate of A. epos from variegated leafhoppers (P_rel, Y-axis), defined as

,

(A.3)

for each data point (P_vlh and P_glh are the number of parasitoids emerging from variegated and grape leafhoppers, respectively).

Calculating S_glh and S_vlh: Values on S_glh were calculated for each data point in Fig. 8 by entering observed relative leafhopper densities (VLH_rel) into Eq. (A.1), using estimated values on and from Fig. 7a. It was not possible to use data points in Fig. 7a directly as points from Figs. 7a and 8 could not be matched. To calculate S_vlh from the data in Settle and Wilson was more complex, but was possible using the following derived function. First, rearrange Eq. (A.3), such that

.

(A.4)

Then rearrange Eq. (A.2), such that

,

(A.5)

and combine Eqs. (A.4) and (A.5), such that

.

(A.6)

This provides estimates of S_vlh that depend only on parameters extracted from Figs. 7a and 8 in Settle and Wilson. It was therefore also possible to calculate for each data point from Fig. 8. The density dependence of was tested by correlating this data with VLH_rel. This analysis indicated no density dependence (r = 0.05, P > 0.05, N = 69, Fig. A1).

Fig. A.1. Observed parasitoid selectivities ( = ln(S_glh)/ln(S_vlh)) in relation to the relative density of variegated leafhoppers (VLH_rel).

Literature Cited

Settle, W. H., and L. T. Wilson. 1990a. Invasion by the variegated leafhopper and biotic interactions: parasitism, competition, and apparent competition. Ecology 71:1461-1470.