Members of large-animal species must consume enormous amounts of food to survive  When climatic conditions in their environment deteriorate, such animals are often unable to find enough food
This fact helps make large-animal species more vulnerable to extinction than small-animal species, which can maintain greater populations on smaller amounts of food
Whenever climatic conditions in a given environment are bad enough to threaten large-animal species with extinction, small-animal species are able to find enough food to survive.