The model of evolutionary change in which different species slowly develop in a step-by-step fashion is called

The answer is gradualism.

Gradualism describes the rates of speciation. It means that evolutionary changes in species are slow, gradual and continuous process. 
For example, size changes of elephants' ears. Elephants use their ears as a protection from the sun and to keep them cool. Over many years, a population of elephants will develop larger ears. These larger ears will become a characteristic trait in the population after many years.

That would be a working theory.