Darwin uses a variety of evidence to support three main arguments. The first is the principle of gradation in which a species make gradual changes over time instead of suddenly coming into being in the geological record. The main support for this principle lies in the sterility of hybrids. The first cross-species has organs that are still functional but the hybrids are sterile. Any radical change to the variations of a species usually results in sterility. The second supporting argument claims the specific incitement for variation would be the climate. The glacial period being referenced as a radical period of variation for species. He states that it is illogical to expect to see the links between species because they are usually supplanted and surpassed by their more adapted counterparts. The support for this argument is limited due to the lack of geological records. “The noble science of Geology loses glory from the extreme imperfections of the record” (Darwin pg510) There is also the human issue of classifying every addition to the geological record as a new species. His third supporting argument is the domestication of certain plants and animals. He argues that if people can select for certain favorable traits to aid in survival then it is not a leap in logic to see the same selection in nature. The species most able of producing offspring that has favorable traits for their living conditions will thrive over their competitors. The climate and conditions will naturally select the most successful traits for that area.
The most convincing argument is the sterility of species who have undergone dramatic changes. This is an experiment that anyone could do in their backyard with a few species of plants or just a couple ant terrariums. In my opinion, the most easily replicable argument is the most effective. It is really hard to convince people of ideological principles because it takes a basis of common understanding. You can give anybody an easy science project and tell them to come to their own conclusions. Granted, it takes longer than just blindly accepting the results of those before you, but it gives a more concrete understanding of the principals at work.