There are three mathematical ideas that one needs to come to terms with in order to get the full flavor of how natural selection works.
- One is the rate at which favorable mutations occur in organisms. These do occur by chance and the question is whether the frequency of such occurrences is sufficient to explain evolution.
- The second is the rate at which favorable mutations become more numerous in the population. It is not enough to produce a single favorable organism. The population of varieties with advantageous properties has to eventually grow to sufficiently high numbers that it dominates the population and can form the basis for yet further mutations.
- The third is whether the rate at which repeated small and favorable mutations build on each other is sufficient to produce major changes in complex systems (the eye, ear, and other organs for example) and even entirely new species.