Model assumptions and limitations

Every mathematical model simplifies reality. The simplifications that define how the model represents the biological system are its assumptions. The consequences of those simplifications contribute to the model's limitations.

Assumptions

Assumptions specify what is treated as true within the model. They may concern population structure, interactions, parameter behaviour, spatial mixing, environmental conditions or which processes are included.

Example. A simple epidemic model may assume a closed population and homogeneous mixing. These assumptions make the model tractable, but they exclude migration and differences in contact patterns.

Limitations

A limitation identifies where a model may fail to represent the real system adequately or where its conclusions should be interpreted cautiously. Limitations can arise from simplifying assumptions, uncertain parameters, incomplete data, omitted mechanisms or numerical approximations.

Validity depends on purpose

A simplified model is not necessarily a poor model. A model can be useful if its assumptions are appropriate for the question being asked. Conversely, a mathematically sophisticated model can be unsuitable if it includes the wrong biological mechanisms.

Questions to ask

What biological processes are included and excluded?
Over what population, spatial region and time scale is the model intended to apply?
Which assumptions are essential to the conclusions?
How uncertain are the parameter values and observations?
Would relaxing an assumption materially change the result?

Key principle. Model conclusions are conditional on the model structure, assumptions and information used. Assumptions should therefore be stated explicitly, and limitations should be considered when interpreting biological conclusions.