...in the light of genetics.
Theodosius Dobzhanksy famously wrote, "Nothing in biology makes sense except in the light of evolution." Dobzhansky, considered one of the foremost figures of the modern synthesis, grossly underestimated his importance to the field of biology. Given the modern state of both evolutionary biology and molecular genetics, I propose that the twenty-first century edition of Dobzhanksy's quote should be:
NOTHING IN EVOLUTION MAKES SENSE EXCEPT IN THE LIGHT OF GENETICS
The most important discovery in evolutionary biology of the twentieth century was not made by Dobzhansky, Ernst Mayr, R.A. Fisher, J.B.S Haldane, or Sewall Wright, but by G.H. Hardy and Wilhelm Weinberg. Hardy and Weinberg independently came up with what is now referred to as the Hardy-Weinberg equilibrium. Assuming no mutation, no migration into the population, no natural selection, large population size, and random mating, they showed that allele frequencies will not change and genotype frequencies will stabilize at certain equilibrium values after one to two generations of random mating. Hardy and Weinberg proved that MENDELIAN INHERITANCE DOES NOT CHANGE ALLELE FREQUENCIES.
Prior to their discovery, no one had synergized Mendel's findings with Darwin's theory. From Mendel's experiments, it appeared that genotype and allele frequencies could change over time because different crosses produced different numbers of phenotypes. However, when examining all of the mating in a population, it turns out that allele frequencies do not change. This simple theory laid the groundwork for all of the theoretical population geneticists to formulate the modern synthesis (these simple populations were later referred to as "Wright-Fisher populations").
Only by violating one or more Hardy-Weinberg assumptions can we cause allele frequencies to change. For instance, if we impose directional selection, one allele will approach fixation while the other allele will be lost (a deterministic process). On the other hand, if we have a small population, genetic drift (a stochastic process) can lead to the loss or fixation of an allele via random chance. As you can see, both of these violations of the Hardy-Weinberg assumptions lead to changes in allele frequencies and evolution.
Every theory in population genetics, from the earliest models by Wright and Fisher to modern coalescent theory, relies on the important discovery by Hardy and Weinberg: random mating does not change allele frequencies. In order for evolution to occur within a population allele frequencies must change. When evolution occurs between populations or leads new species (speciation) allele frequencies at at least one locus must change. By showing that Mendelian inheritance alone cannot lead to these changes, Hardy and Weinberg gave birth to the field of population genetics and allowed us to study evolution using molecular data (the material of heredity). Whether population structure, genetic drift or natural selection are the main forces of evolution and speciation are debatable, but you never hear any legitimate biologist say that random mating causes evolution thanks to a clever physician and a curious mathematician.