Appendix B. Spatially explicit, individual-based simulation (SEIS) of gypsy moth populations.
The SEIS ran on a 160 × 160 raster landscape of 4-m2 pixels. Local mouse density (m) varied among pixels in the range 10–30 mice/ha, based on a typical plot-level (1–3 ha) mouse density of 20 mice/ha (Elkinton et al. 1996, Wolff 1996, Ostfeld et al. 2001). These landscapes of risk were generated (algorithm detailed in Goodwin et al. 2005) with positive spatial autocorrelation on the scale of 20–30 m, which is approximately the size of a mouse home range (Wolff 1985) and similar to the observed scale of spatial autocorrelation in predation by mice on gypsy moth pupae and tree seeds (Manson 2000, Connors et al. 2005). The landscape pattern was temporally static in each simulation. After a landscape was generated, the simulation began by assigning a female pupa to each of 100 randomly selected pixels. Survival of each pupa over the 13-day pupal period (Campbell 1978) was stochastic with probability e-13ma, where a is the daily attack rate by mice. In each simulation run, a was held constant at a value between 0.016 and 0.020 (based on field data, Schauber et al. 2004). The contribution of each surviving pupa to the next generation of female pupae was a Poisson random variable with mean = 37 (750 eggs × 33% hatch × 30% survival to pupation × 50% female) (Gould et al. 1990, Williams et al. 1990, Moore and Jones 1992). Thus, landscape mean suitability varied among simulations depending on the value of a. Each offspring dispersed a random direction (circular uniform) and distance (x, based on an exponential dispersal kernel, ) from its natal pixel before pupating. If this put the offspring outside the simulated landscape, a new random direction and distance from the natal pixel were selected until the offspring remained on the landscape. In each simulation run, was held constant at a value between 0.005 and 0.035 (median dispersal distance 20–139 m, Weseloh 1997). For each combination of a and , we ran 1000 simulations on each of 10 replicate landscapes. Each simulation stopped when no pupae survived, 10 generations had elapsed, or the number of pupae exceeded 30,000. The spatial autocorrelation function ((x)) of survival probability was calculated for each simulated landscape, and the realized dispersal kernel (k(x)) was determined by simulating dispersal of 100,000 offspring from random points within the simulated landscape. The realized dispersal kernel differed from the theoretical exponential distribution (especially when median dispersal distance was long) because dispersal outside the simulated landscape was not permitted. Therefore, we calculated heritability as
which is a discrete-space version of Eq. 5 over distances up to the maximum distance across the simulated landscape
Campbell, R. W. 1978. Some effects of gypsy moth density on rate of development, pupation time, and fecundity. Annals of the Entomological Society of America 71:442–448.
Connors, M. J., E. M. Schauber, A. Forbes, C. G. Jones, B. J. Goodwin, and R. S. Ostfeld. 2005. Use of track plates to quantify predation risk at small spatial scales. Journal of Mammalogy 86:991–996.
Elkinton, J. S., W. M. Healy, J. P. Buonaccorsi, G. H. Boettner, A. M. Hazzard, H. R. Smith, and A. M. Liebhold. 1996. Interactions among gypsy moths, white-footed mice, and acorns. Ecology 77:2332–2342.
Goodwin, B. J., C. G. Jones, E. M. Schauber, and R. S. Ostfeld. 2005. Limited dispersal and heterogeneous predation risk synergistically enhance persistence of rare prey. Ecology 86:3139–3148.
Gould, J. R., J. S. Elkinton, and W. E. Wallner. 1990. Density-dependent suppression of experimentally created gypsy moth, Lymantria dispar (Lepidoptera: Lymantriidae), populations by natural enemies. Journal of Animal Ecology 59:213–233.
Manson, R. H. 2000. Spatial autocorrelation and the interpretation of patterns of tree seed and seedling predation by rodents in old-fields. Oikos 91:162–174.
Moore, K. E. B., and C. G. Jones. 1992. Estimating field hatch of gypsy moth (Lepidoptera: Lymantriidae). Environmental Entomology 21:276–280.
Ostfeld, R. S., E. M. Schauber, C. D. Canham, F. Keesing, C. G. Jones, and J. O. Wolff. 2001. Effects of acorn production and mouse abundance on abundance and Borrelia burgdorferi infection prevalence of nymphal Ixodes scapularis ticks. Vector Borne and Zoonotic Diseases 1:55–63.
Schauber, E. M., R. S. Ostfeld, and C. G. Jones. 2004. Type 3 functional response of mice to gypsy moth pupae: is it stabilizing? Oikos 107:592–602.
Weseloh, R. M. 1997. Evidence for limited dispersal of larval gypsy moth, Lymantria dispar L. (Lepidoptera: Lymantriidae). The Canadian Entomologist 129:355–361.
Williams, D. W., R. W. Fuester, W. W. Metterhouse, R. J. Balaam, R. H. Bullock, R. J. Chianese, and R. C. Reardon. 1990. Density, size, and mortality of egg masses in New Jersey populations of the gypsy moth (Lepidoptera: Lymantriidae). Environmental Entomology 19:943–948.
Wolff, J. O. 1985. The effects of density, food, and interspecific interference on home range size in Peromyscus leucopus and Peromyscus maniculatus. Canadian Journal of Zoology 63:2657–2662.
Wolff, J. O. 1996. Population fluctuations of mast-eating rodents are correlated with production of acorns. Journal of Mammalogy 77:850–856.