You could look at other factors which can be seen in an individual which are clearly deleterious and which could reasonably be expected to eventually reduce populations. For example, the effect on a long-lived mammal such as the elephant could reduce fertility or overall health and vigor and, over several generations/a few hundred years lead to noticeable population declines.
Work Step by Step
Think about a human disease such as cancer. If it were a slow growing cancer, you might not die for years, but there would be obvious signs of trouble. These are analogous with what you would look for in a long-lived species or unwieldy-to-work-with species to understand the effects of competition.