ABSTRACT
Most biological systems can be described on some scale in terms of continuous change over time, whether it is the gradual accumulation of algae on the edges of a stagnant pond or the rapid ebb and flow of species such as the mayfly Dolania americana, the females of which generally live less than five minutes as adults (Figure 3.1). For populations which do not reproduce in distinct, synchronized generations, or for which frequent data is available, considering changes to occur continuously in time may allow a model to capture important features of growth. Although populations of discrete individuals should increase or decrease by discrete numbers, rather than continuous amounts, for large populations the inaccuracies incurred by treating the population size as a continuous quantity are small. In cases where changes are continuous in time, we can describe those changes by describing the rate of change in terms of the time-derivative of the quantity, typically a population, rather than in terms of the difference between population sizes in two consecutive generations, as is done for discrete-time models. Doing so results in models composed of differential equations, rather than difference equations.
