Biodiversity is when there is a large variety of populations which leads to a healthier ecosystem. However, once one of the species begins to overpopulate, this can be disasterous. For example, if there is a huge number of deer in the ecosystem due to the lack of predators--wolves for example, the deer population will increase exponentially. The habitat where they reside will not grow any larger and must now support too many deer which are herbivores. They will wreak havoc on the producers because there will be too many deer feeding on an amount of leaves unable to possibly support them all. The producers will be in danger, but so too will other herbivores that feed on the same leaves. In fact, increased competition will occur among the excess deer leading to a struggle for existence, survival of the fittest, and a large amount of deaths in the deer herd. Overpopulation affects every level of the food web, can lead to extinctions of certain species and negatively affects the health of the ecosystem.
The ecosystem of a certain area exists and survives in a state of dynamic equilibrium, where each species in the food web can only grow in population upto a point defined by the "food" available in the ecosystem. Therefore, "food" is the limiting factor which determines how many are able to survive.
It is a given that the bigger the biodiversity (number of species), the "healthier, i.e. steadier" is the ecosystem. Consider how many different options on food each individual gets... Should overpopulation occur (the reason why is another matter), the demand for food will increase,so food availability will be limited, not only for the overpopulated species, but also for other species who are fed by the same source of food. We know that within food webs the flow of energy via food is the crucial factor that determines the survival and thriving of all involved species. One can understand that not sufficient food will mean extermination of a number of (starving) individuals, who used to be themselves prey for other animals and so forth. This process will cause a temporary imbalance in the food chain. Species that are too vulnerable may disappear leaving room for the rest of their competitors. This means reduction in biodiversity,so there will be fewer food options for the rest, which is actually bad for the ecosystem as a whole.