Heredity give a continuity so physical and genetic traits can be passed on to offspring. The environment determines the traits that are fit. Good traits with survival capacity are passed on to the next generation. Traits that yield weakness tend to give organisms that do not survive to reproduce so those traits are eliminated. This is accomplished by mutation which changes the order of bases in a gene or by sexual reproduction where genes from a male and female are combined to give a new genetic diversity.
Evolution is usually slow with few new species.
Punctuated equilibrium represents a situation in which there is a sudden change, perhaps induced by mass extinction. This opens up many new opportunities to fit into the biosphere and can result in a suddden rapid growth in the number of new species.