For the Darwinists “evolution” by natural selection is what created all the species. Since they are used to say that evolution is well scientifically established as gravity, and given that Newton’s mechanics and Einstein’s relativity theory, which deal with gravitation, are plenty of mathematical equations whose calculations pretty well match with the data, one could wonder how many equations there are in evolutionary theory, and how well they compute the biological data related to the Darwinian creation.
As known, Darwin introduced no math whatsoever in his theory of origin of species. Darwin hated math (not by chance). Therefore one had to wait for few XX century mathematicians before seeing some math in evolutionary theory. It is specifically in population genetics that one finally encounters some applications of probability theory and statistics. They consist basically in two main equations: the Hardy-Weinberg law and the Price equation. Here is not the case to examine in detail those equations, however something can be said about.
The Hardy-Weinberg law mathematically describes how a population is in equilibrium both for the frequency of alleles and for the frequency of genotypes. Indeed because this law is a fundamental principle of genetic equilibrium, it doesn’t support Darwinism, which means exactly the contrary, the breaking of equilibrium toward the increase of organization and creation of entirely new organisms. To claim that the Hardy-Weinberg law explains evolution is as to say that in mechanics a principle of statics (immobility) explains dynamics (movement and the forces causing it).
The Price equation is more complicated than the former because reformulates what is called Fisher’s theorem. Given this theorem is considered even the “fundamental theorem of natural selection” we could believe to be finally on target. For a detailed critic of Price’s analysis by serious statisticians see here. After having read such critic we are disenchanted. In fact, they, after having considered various possible examples of real application of Price’s theory, say that it is a model somehow circular, because:
“the data explain the data” […] “for doing statistics the Price equation did not help” […] “can’t think of anything remotely useful about the Price equation” […] “some of us remember a feeling of doubt when first confronted with the Price equation, it may be a relief to hear John Maynard Smith [the famous evolutionist] say ‘I’m not going to tell you what Price’s theorem is, because I don’t actually understand it’ …”
The Price equation tries to deal with the transitions between generations. But it is a statistical description of an evolutionary process considered a priori capable of increasing complex characteristics (related to fitness) in a population. These characteristics are thought never decreasing from the parent to the child population. In these conditions it is obvious the Price equation could be used to model any evolution and to prove any improvement, if one presupposes them. No wonder some evolutionists used it to prove the evolution of altruism, of sight, of sickle cell anemia, of … anything.
The final point to take is that, also to be very generous, the Price equation does not explain at all how new systems arise in the species in the first place. It gets them as input systems already created by an unknown organizational cause. But the Darwinist claim is that evolution does create biological systems, and the Price equation, like the Hardy-Weinberg law, helps exactly zero to explain such creation.
So the initial question, how well math support Darwinian evolution, has the short answer: it doesn’t support evolution at all. Despite of the pretension of evolution to be a scientific theory with the mathematical certitude of the hard sciences, properly the equations of evolution do not exist.