My learned lessons in mathematical biology (in progress)

• The key of modeling in biology is how to model the phenotype. 
• If both functions can be expanded into similar first few terms of Taylor series, they can approximate each other. This is very useful to exchange binomial form and the exponential form. 
• Initial values are very important for numerical fitting. 
• The gnls function in R often looks for local optima around the initial values. For poor data, gnls can even output the initial values as fitting results.