Said another way, he posited that populations increased by a fixed proportion over a given period of time and that, absent constraints, this proportion was not affected by the size of the population. By way of example, according to Malthus, if a population of 100 individuals increased to a population 135 individuals over the course of, say, five years, then a population of 1000 individuals would increase to 1350 individuals over the same period of time. Malthus's model is an example of a model with one variable and one parameter. A variable is the quantity we are interested in observing. They usually change over time.
Parameters are quantities which are known to the modeler before the model is constructed.
Often they are constants, although it is possible for a parameter to change over time. In the Malthusian model the variable is the population and the parameter is the population growth rate. A model in this form, where the population at the next time period is determined by the population at the previous time period, is said to be a difference equation model. If we have a difference equation model and know the population at the beginning of a time period, we can use the model to determine population sizes at any point in the future by applying the equation repeatedly until we reach the desired point in time. The Stella II software we will use to analyze these models requires the model to be in a slightly different form.