Assumptions

To develop a model, we need to make some assumptions about the spotted knapweed. Assumptions are needed to simplify biological systems, so that we can translate them into problems that we can work with. This means that we won't be modeling our exact system, but a simplified version of the system. However, studying these simplified systems can provide insight into many different problems.

Since the spotted knapweed can be described by its life cycle stages, we say that this plant population exhibits stage structure. We would like to take advantage of this structure, and so we will use what is called a stage structured model to mathematically describe the spotted knapweed system. The stage structured model is one of many different types of models that can be used to describe a system which changes over time.

Definition: A stage structured model is one in which individuals can be classified according to different stages, where each stage has its own survival and reproductive characteristics.

To be able to use a stage structured model, we need to make several key assumptions. We assume that: