*Ecological Archives* E094-258-A2

Emily V. Moran, Sharon Bewick, Christina A. Cobbold. 2013. Effects of plant genotype and insect dispersal rate on the population dynamics of a forest pest. *Ecology* 94:2792–2802. http://dx.doi.org/10.1890/12-1708.1

Appendix B. Further details on parameter estimation.

__Alpha:__

The value of *α _{i}* depends on what life stage the caterpillar is in when the parasitoid emerges. A variety of host-specific parasitoids affect forest tent caterpillars, including

We use aspen clone 271 as the reference clone, as it has the intermediate development time; average FTC development times ranged from 43 days on clone 259 to 48.4 days on clone 216. Whenever time to FTC pupation is lengthened or shortened relative to the reference clone, we assume that each FTC lifestage is lengthened or shortened proportionally. We partition the FTC development time on this clone into the average times spent in each caterpillar lifestage, denoted by the vector . FTC go through 5 larval instars. We assume that the time spent in each of the first two instars is roughly half the time spent in each of the subsequent instars (Hwang and Lindroth 1997, Verdinelli and Sanna-Passino 2003). Density-dependent mortality occurs in the 4th and 5th instars, when caterpillars are large enough and have consumed enough of the initial leaf mass to compete strongly for food. The last few days of the 5th instar are alternately categorized as the “pre-pupal” stage. After that time, the individual is a pupa, and no density-dependent mortality occurs. Thus, we assume that on clone 271:

(B.1)

where we have explicitly divided the 5th instar into an initial 10-day stage in which density-dependent mortality occurs and a 1.4-day “pre-pupal” stage.

We estimate strength of density-dependent competition for each FTC lifestage *j*, *K ^{j}*,using data from Fig. 6 of Cobbold et al. (2009). The slopes of the lines in the figure provide estimates of

(B.2)

where *T _{i}* is the total time to pupation on clone

The parameter α_{i} is defined as follows for aspen clone *i*:

(B.3)

where *L* is the FTC developmental stage at which the parasitoid emerges, and *p _{j}* is the proportion of stage

__Intrinsic rate of growth, r: __

In order to calculate *r _{i}* for each clone, we first used the mean values for female pupal mass and the linear relationship between pupal mass and egg number identified by Parry et al. (2001). Because there is a geographical cline in this relationship (southern populations produce a larger number of smaller eggs for a given female mass) we used the equation for Michigan, the population nearest the Wisconsin FACE site. For this Midwestern population:

(B.4)

where* E _{i}* is the number of eggs and

(B.5)

Average female pupal masses ranged from 0.267 g on clone 216 to 0.316 g on clone 259. The resulting *r _{i}* values are shown in Table 1 of the paper. These values are relatively small, because the pupal masses observed in the Aspen FACE experiments were at the low end of the potential weight range of 0.1 to 0.8 grams observed in wild populations (Parry et al. 2001).

__Parameters independent of aspen clone__:

Values for the remaining parameters, searching efficiency *a* and the degree of clumping of parasitoid searching *k*, were based on Cobbold et al. (2009) and references therein, giving *k=100, *close to random searchingand *a *ranging from 0.0085 to 0.03 in units of 1/(cocoons/area). However, because host and parasitoid density are expressed in number per leaf cluster in the data used to determine *α* and *K *we must first change the units of *a*. Cobbold et al. (2009) give *K* in terms of cocoons per area as 266.7 and we have *K *= 1.5897 in number per leaf cluster. These values should be equivalent; hence we can use this information to express *a* in units of 1/(number per leaf-cluster) by multiplying by 266.7/1.5897. In the non-dimensional model parasitoids are scale by *K*, hence the parameter *a* in Eq. (2) becomes non-dimensional via multiplication by *K*. We obtain the non-dimensional parameter *a *= 266.7(0.022) = 6.

Fig. B1. FTC population oscillations on isolated aspen clones, PET = 37.

Literature cited

Cobbold, C. A., J. Roland, and M. A. Lewis. 2009. The impact of parasitoid emergence time on host-parasitoid population dynamics. Theoretical Population Biology 75:201–215.

Hwang, S. Y., and R. L. Lindroth. 1997. Clonal variation in foliar chemistry of aspen: effects on gypsy moths and forest tent caterpillars. Oecologia 111:99–108.

Parry, D. 1994. The impact of predators and parasitoids on natural and experimentally created populations of forest tent caterpillar, Malacosoma

disstria Hubner (Lepidoptera: Lasiocampidae). University of Alberta, Edmonton, Alberta.

Parry, D., R. A. Goyer, and G. J. Lenhard. 2001. Macrogeographic clines in fecundity, reproductive allocation, and offspring size of the forest tent caterpillar, *Malacosoma disstria*. Ecological Entomology 26:281–291.

Sippell, W. L. 1957. A study of the forest tent caterpillar Malacosoma disstria Hbn., and its parasite complex in Ontario. University of Michigan.

Verdinelli, M., and G. Sanna-Passino. 2003. Development and feeding efficiency of *Malacosoma neustrium* larvae reared with *Quercus* spp. leaves. Ann. ap. Biol. 143:161–167.