Data approximation using Lotka-Volterra models and a software minimization function

In recent years, a lot of effort has been put into finding suitable mathematical models that fit historical data set. Such models often include coefficients and the accuracy of data approximation depends on them. So the goal is to choose the unknown coefficients to achieve the best possible approximation of data by the corresponding solution of the model. One of the standard methods for coefficient estimation is the least square method. This can provide us data approximation but it can also serve as a starting method for further minimizations such as Matlab function fminsearch.