Boundary compression model

Fig. 1. Inter-boundary distance is proportional to the rate of population spread, v, if the rate of population growth, r=ln[N(t+1)/N(t)], is constant.

The main assumption of this model is that the rate of poulation growth, r, outside of the barrier zone is independent from the rate of population front expansion. We believe that this assumption is true for gypsy moth because it spreads mainly due to transportation of egg masses and other life stages by human vehicles. After isolated colony is established, its growth no longer depends on immigration because a very small proportion of the entire population is transported.

This assumption may not be always true with other spreading species. For example, the model of Skellam (1951) predicts that in populations where all individuals have equal migration activity, only a half of population increase is caused by local reproduction, whereas the other half is caused by immigration.

Fig. 2. Dynamics of boundary "compression" after barrier zone establishment. D1 and D2 are inter-boundary distances.

Alexei Sharov 06/16/95