Comparing Parameters in Growth Models

Parameters are of significant importance when using non-linearized models. A small shift in one parameter could change an accurate model to an inaccurate one. But to what extent can these parameters change and not affect the accuracy of the model? This question can be answered by setting a specific value in the model to reach and then output the time it took each model to arrive at that value holding all else equal. In these simulations the value used was K/2, which is the half the max population. The initial population and growth rate were the two parameters that were altered over the different simulations of the model. The models had to analytically be solved for time in order to generate the correct output. After running these simulations the relationships the parameters have to the time it takes to reach K/2 is shown. The Gompertz model has steeper contour lines, and seemed to depend less on the initial population and more on the growth rate, whereas the logarithmic model seemed to have a more balanced dependence on both parameters.