While the population growth may not be in the forest areas, once the population demand for timber or cattle pastures can lead to deforestation relating population growth of other areas to deforestation, such is the case of the Amazon Rainforest.
A population dependent on agriculture may also affect forested areas, as local people and migrants settle at the forest frontier and clear land to provide more area for subsistence farming. This happens a lot in Central America, the area around the Maya Biosphere Reserve in Guatemala being an example.