Types of nonlinear models

Growth models are typically mechanistic rather than empirical. Mechanistic models are developed based on some assumptions about the specific situation or environment. Based on these theoretical considerations equations are written. Thus, we do not need as much data to create a reliable model.

In empirical models, the mechanistic relationship is unknown, so we need a lot of data to show that the model is consistent.

In this post we discuss a few of these growth models based on theoretical considerations:

Monomolecular:

Properties:

When t → 0, then:     

When t → ∞, then the β term approaches 0 and W= α

There are no inflection points

Logistic:

Properties:

When t → 0, then: 

When t → ∞, then W= α

The curve is always positive.

Mitcherlich growth:

Properties:

Similar to the monomolecular growth it is used in chemical processes.