Billy thinks evolution is slow and continuous. he believes in gradualism, punctuated equilibrium, or convergent evolution.

Option A, Gradualism

Explanation:

As per James Hutton and Charles Lyell, gradualism is the process of evolution that lead to small changes at a gradual rate over a period of time. Some scientists relate gradualism with geological process, as the slow evolution of several species through different eras of life on earth has been established through the advent of geological findings.  

Thus it is the gradualism form of evolution in which a species evolve slowly and  gradually.  

While in punctuated evolution, there are certain period where no change occurs and there some period where there is an out-bursting of speciation.  

And convergent evolution refer to the development of analogous structure.  

Thus, Gradualism is the correct answer