Darwin's scheme embodies three principles (Lewontin 1):
These three principles embody the principle of evolution by natural selection. While they hold, a population will undergo evolutionary change. It is important to note a certain generality in the principles. No particular mechanism of inheritance is specified, but only a correlation in fitness between parent and offspring. The population would evolve whether the correlation between parent and offspring arose from Mendelian, cytoplasmic, or cultural inheritance.
- Different individuals in a population have different morphologies, physiologies, and behaviors (phenotypic variation).
- Different phenotypes have different rates of survival and reproduction in different environments (differential fitness).
- There is a correlation between parents and offspring in the contribution of each to future generations (fitness is heritable).
Lewontin's principles boil down to variation, selection and heredity.
Lewontin offers a description of evolution by natural selection. However, other types of evolution don't require fitness to be heritable - namely genetic drift. In some respects, it would be better to have a characterization of evolution, rather than just one mechanism of evolution.
Note that Lewontin's principles don't guarantee that adaptations will accumulate. The conditions required for cumulative adaptive evolution are much more demanding. Lewontin's principles cover devolution and the loss of adaptations as much as adaptive evolution.
Lastly, Lewontin's principles tend to lead to a kind-of distorted neo-Darwinian perspective. They are a bit vague about what counts as a "parent" and what counts as an "offspring" - but they clearly include splitting, but make no reference to "joining". Merging is very important in evolution - and should be classified as a form of evolutionary change. Merging includes symbiosis and sex. The most common forms of merging involve parasitism by viruses - which are ubiquitous.
Merging has been systematically neglected by evolutionary theorists in the past. It still needs more emphasis.