This is one of a series of questions centered around how an isolated group of people would survive. Each question focuses on a single aspect of survival. Details about the peoples' situation are below:
In a novel I am developing, an undefined number of people is living on a peninsula. The isthmus connecting the peninsula to the mainland is very narrow, and spanned by a wall, which prevents the people from leaving (there are deterrents preventing them from climbing the wall or otherwise circumventing it). They also cannot swim around the wall. This also means that no land-based animals can cross onto the peninsual from the mainland. The inhabitants have to live with what they have. For the sake of details, assume the peninusla is roughly the size, shape, and location of Mahia Peninsula.
My question is about the population. I want to know how many people I can have on the peninsula (all living together in one village) and still maintain the ecosystem.
I want to avoid such things as deforestation and hunting animals to extinction (remember that the animals are stuck there too), as well as depleting the peninsula's natural resources. Taking into account the size of Mahia Peninsula, how small does my population need to be to avoid these things?
A very important detail is that there are novel-related events which keep the population at the same number. Overpopulation through reproduction is not an issue.