  We introduce a model of biological evolution where species evolve in response
to biotic interactions and a fluctuating environmental stress. The species may
either become extinct or mutate to acquire a new fitness value when the
effective stress level is greater than their individual fitness. The model
exhibits a phase transition to a completely extinct phase as the environmental
stress or the mutation rate is varied. We discuss the generic conditions for
which this transition is continuous. The model is exactly solvable and the
critical behavior is characterized by an unusual dynamic exponent z=1/3. Apart
from predicting large scale evolution, the model can be applied to understand
the trends in the available fossil data.
