  We investigate the dose and dose-rate dependence of the mutation frequency
caused by artificial radiations with Whack-A-Mole (WAM) model which we have
recently proposed. In particular, we pay special attention to the case of
long-term and low dose-rate exposure. The results indicate that the dose-rate
dependence is successfully described with WAM model and it may replace the
so-called DDREF, the concept of which has long been adopted to take account of
the difference between the high dose-rate data and the low dose-rate ones.
Basic properties of WAM model are discussed emphasizing the dose-rate
dependence to demonstrate how the explicit dose-rate dependence built in the
model plays a key role. By adopting the parameters that are determined to fit
the mega mouse experiments, biological effects of long-term exposure to
extremely low dose-rate radiation are discussed. In WAM model, the effects of
the long-term exposure show a saturation property, which makes a clear
distinction from the LNT hypothesis which predicts a linear increase of the
effects with time.
