Estimation of the potential speed of range expansion of an introduced species: characteristics and applicability of the gamma model

The potential speed at which the range of an introduced species expands in its optimal environment can be predicted by using the gamma model proposed by Yamamura (Popul Ecol 46:87-101, 2004). In this paper we first clarify the difference between the gamma model and Einstein's Brownian motion model. We then apply the model to the ragweed beetle, Ophraella communa LeSage that rapidly expanded its distribution in Japan after it was first found in 1996. The parameters of the model are estimated by conducting a field experiment. The species' net reproductive rate is examined in the laboratory. By combining these estimates, we estimate the potential speed of range expansion to be 82 km per generation and 329 km per year, while the observed speed is estimated to be 77 km per year, the observed speed being considerably slower than the potential speed. This discrepancy may be due to the low reproductive rate caused by mortality in the actual field. The applicability of the gamma model to the econometric data is also briefly discussed.