Ishii, K.; Matsuda, H.; Ogita, N., 1982: A mathematical model of biological evolution. Journal of Mathematical Biology 14(3): 327-353

In order to understand how the biological evolution rate depends on relevant parameters such as mutation rate, intensity of selection pressure and its persistence time, the following mathematical model is proposed: dNn(t)/dt = (mn(t) - mu )Nn(t) + mu Nn-1(t) (n = 0, 1, 2, 3..), where Nn(t) and mn(t) are respectively the number and Malthusian parameter of replicons with step number n in a population at time t, and mu is the mutation rate, assumed to be a positive constant.