Final answer:
In favorable conditions for a low-density population, growth is typically exponential, occurring rapidly when resources are plentiful. It follows a 'J-shaped' curve. Over time, as resources become limited, growth transitions to a logistic pattern, leveling off at the carrying capacity.
Step-by-step explanation:
When the conditions are favorable for a population at low density, such as when a species colonizes a new environment, population growth is typically exponential. This type of growth occurs under ideal conditions when unlimited resources are available, enabling the population to grow larger at a rapid rate, which is shown as a "J-shaped" curve.
It is characterized by an accelerating growth rate as the size of the population increases. However, in the real world, resources are not unlimited, and populations eventually face limiting factors that slow down and regulate growth, leading to a pattern described by the logistic growth model. This model includes factors that become limiting as the population grows, such as availability of food, the buildup of wastes, and space for living and breeding. Logistic growth is represented by an "S-shaped" curve that levels off when the carrying capacity of the environment is reached.