The simplest behaviour one can hope for when studying a mathematical model of evolution by natural selection is when evolution always maximises the value of some function of the trait under consideration, thus providing an absolute measure of fitness for the model. We survey the role of such models, known as optimisation models in the literature, and give some general results concerning the question of when a model turns out to be an optimisation model. The results presented vary from more abstract results with a game-theoretical flavour to more detailed considerations of life history models. We also give a number of concrete examples and discuss the role of optimisation models in the wider framework of adaptive dynamics.
Gyllenberg, M., Metz, J. A. J. H., & Service, R. (2011). When Do Optimisation Arguments Make Evolutionary Sense? In The Mathematics of Darwin’s Legacy (pp. 233–268). Springer Basel. https://doi.org/10.1007/978-3-0348-0122-5_12