This model considers a population (stock) responding to a situation in which there is a continuous but limited supply of resources. For example, imagine our termite population invades a mature forest that is in what ecologists term a “mosaic steady state”. This means that old trees are falling down and creating patches in which young trees mature.
For at least some period of time there are many situations in which the growth of a population (or some other type of stock) is directly proportional to the size of the stock. For example, the initial rate of growth when an invasive species is introduced, money in the bank given a fixed interest rate and no withdrawals, etc. If material or energy are in any way necessary, unconstrained growth eventually must become constrained.