Final answer:
The most likely effect of accelerated logging is deforestation, leading to the loss of the forest and its resources as the population size decreases and cannot recover fast enough.
Step-by-step explanation:
The most likely effect of people logging a forest faster than it can grow back is a decrease in the forest's population size until it eventually disappears, leading to a depletion of the resources it provides. Forests are a renewable resource, but their regeneration is limited by their growth rates and the availability of space, nutrients, and other ecological factors. When trees are removed more quickly than they can grow back, a process known as deforestation occurs, which can result in the loss of habitat, decreases in biodiversity, and disruption of ecological balance. Furthermore, when the carrying capacity of the environment is surpassed due to excessive resource use, the population growth of the forest species follows a logistic growth pattern, slowing down as resources become scarce and eventually leveling off at a point where the environment can no longer support additional growth.