Simulations in evolution. II. Relative fitness and the propagation of mutants

In Neo-Darwinism, variation and natural selection are the two evolutionary mechanisms which propel biological evolution. Our previous article presented a histogram model [1] consisting in populations of individuals whose number changed under the influence of variation and/or fitness, the total population remaining constant. Individuals are classified into bins, and the content of each bin is calculated generation after generation by an Excel spreadsheet. Here, we apply the histogram model to a stable population with fitness F(1)=1.00 in which one or two fitter mutants emerge. In a first scenario, a single mutant emerged in the population whose fitness was greater than 1.00. The simulations ended when the original population was reduced to a single individual. The histogram model was validated by excellent agreement between its predictions and those of a classical continuous function (Eqn. 1) which predicts the number of generations needed for a favorable mutation to spread throughout a population. But in contrast to Eqn. 1, our histogram model is adaptable to more complex scenarios, as demonstrated here. In the second and third scenarios, the original population was present at time zero together with two mutants which differed from the original population by two higher and distinct fitness values. In the fourth scenario, the large original population was present at time zero together with one fitter mutant. After a number of generations, when the mutant offspring had multiplied, a second mutant was introduced whose fitness was even greater. The histogram model also allows Shannon entropy (SE) to be monitored continuously as the information content of the total population decreases or increases. The results of these simulations illustrate, in a graphically didactic manner, the influence of natural selection, operating through relative fitness, in the emergence and dominance of a fitter mutant.