A threshold model for punctuated gradualism.

A model for continuous and discontinuous evolutionary change is proposed that accommodates both punctuated equilibrium and phyletic gradualism. Natural selection operating on a gaussian distribution of phenotypes subjected to severe stress will result in a skewing of the normal distribution in the direction of the favoured phenotype. If a reproductive isolation threshold is imposed upon this model, rapid crossing of the threshold by large numbers of individuals within the skewed distribution will result in the sudden achievement of a critical descendant population mass. Mild directional selection however, will result in gentle shifts of the gaussian mean thus leading us to suggest that stasis and incipient speciatior are extremes of the same spectrum, defined by the rates of mean-shift in response to varying severities of selection pressure. Both punctuated and gradualistic evolution as accommodated in our model may further be described within Thom's cusp catastrophe theory.