would it be reasonable to predict that several species living naturally in a natural community would have a high degree of niche overlap?
Actually, there is usually niche diversification rather than niche overlap in a community where species are living in close proximity. As seen in the famous experiment by Gause in the early 1900's, when two species live in the same environment with the same niche, one lives and thrives and the other dies off. This is the competitive exclusion principle. He worked with two species of Paramecium--P. Aurelia and P.Caudatum. They were in the same test tube with one food supply. The more successful species P.Aurelia lived and the other one died. In nature, organisms generally have their own unique niches, rather than overlapping those niches with other species. This leads to a more successful survival rate. For example, Darwin's finches in the Galapagos show that within a single tree(habitat)due to niche diversification, species may feed on the ground, at the top of the tree, or in the middle of the tree. Some may feed on insects, some on small, medium or large seeds. Their beaks too, reflect how evolution shaped these variations so that their niches rarely overlap when feeding.