[...]... that the analysis did not divide the results both according to the four-model types and the two-dynamical behaviors Benton and Grant (2000) considered the following “surrogate” measure of fitness: r, R0, and a estimated both with and without density-dependence effects and the average (both arithmetic and geometric) population size, K First, Benton and Grant simulated constant environments and found,... variable cannot be measured, then it is not useful and an alternate approach should be sought 5 As much as possible, write the model incrementally and as a series of modules that can be examined and debugged separately To illustrate these points the next section constructs a model of the evolution of migration in a spatially and temporally heterogeneous environment 1.4 An introduction to modeling in R and... as an integral part of the explanation, has guided the writing of this book The present book is designed to outline how evolutionary questions are formulated and how, in practice, they can be resolved by analytical and numerical methods (the emphasis being on the latter) The general structure of each chapter consists of an introduction, in which the general approach and methods are described, followed... major advantages over MATLAB: first it is free, and second it is a highly sophisticated statistical package Thus a student who learns R can use it to do modeling and to address the statistical questions that will arise following experiments to test such models MATLAB appears to be generally faster than R, except perhaps in the complex statistical analyses On the other hand, MATLAB is not cheap and although... Step 4: Creating space to store the output: c( ), vectors, matrices, etc For any model there will be information that is generated by the program that we will want to analyze at the end of the simulation While it is possible to dynamically allocate space, a better method is to preassign the space at the start of the simulation Information can be stored in a matrix, a vector, an array, a data frame,... information of the same type (e.g., only numerical information) A vector is simply a matrix with a single column or row Examples of a vector and a matrix are as follows: 2 3 1 A:vector ¼4 3 5 5 2 1 6 A:matrix ¼4 2 4 4 8 3 0 25 1 To assign 1, 3, 5 to the vector A.vector we can use the concatenate code c( ) in R and square brackets in MATLAB R CODE: A.vector .