Based on the intensity and rates of various kinds of intense ionizing radiation events such as supernovae and gamma-ray bursts, it is likely that the Earth has been subjected to one or more events of potential mass extinction level intensity during the Phanerozoic. These induce changes in atmospheric chemistry so that the level of Solar ultraviolet-B radiation reaching surface and near-surface waters may be approximately doubled for up to one decade. This UVB level is known from experiment to be more than enough to kill off many kinds of organisms, particularly phytoplankton. It could easily induce a crash of the photosynthetic-based food chain in the oceans. Certain regularities in the latitudinal distribution of damage are apparent in computational simulations of the atmospheric changes. It was previously proposed that the late Ordovician extinction is a candidate for a contribution from an ionizing radiation event, based on environmental selectivity in trilobites. We confront this hypothesis with data from a published analysis of latitudinal gradients in the Ordovician extinction. We find that the pattern of damage predicted from our simulations is consistent with the data assuming a burst approximately over the South Pole. However, the patterns are not sufficiently selective as to be said to provide strong evidence for the ionizing radiation hypothesis. We predict that any land mass (such as part of north China) which then lay substantially north of the equator should be a refugium from the UVB effects, and show a different pattern of extinction in the first strike of the end-Ordovician extinction, if it were induced by such a radiation event.