There were some nice moments of clarity in the Stanford encyclopedia link:
ONE:
“3. Population-Genetic Models of Evolution
Population geneticists usually define ‘evolution’ as any change in a population’s genetic composition over time. The four factors that can bring about such a change are:
i) natural selection,
ii) mutation,
iii) random genetic drift, and
iv) migration into or out of the population.”
The 4th point can become relevant if a river that runs through a population’s territory suddenly has a shift in its course, dividing instead of containing the population in a particular area.
TWO:
Then there’s this text:
3.2 Selection-Mutation Balance
Mutation is the ultimate source of genetic variation, preventing populations from becoming genetically homogeneous in situations where they otherwise would. Once mutation is taken into account, the conclusions drawn in the previous section need to be modified. Even if one allele is selectively superior to all others at a given locus, it will not become fixed in the population; recurrent mutation will ensure that other alleles are present at low frequency, thus maintaining a degree of polymorphism. Population geneticists have long been interested in exploring what happens when selection and mutation act simultaneously.
THREE:
Deleterious vs. Beneficial Mutations
"3.2 Selection-Mutation Balance
Mutation is the ultimate source of genetic variation, preventing populations from becoming genetically homogeneous in situations where they otherwise would. Once mutation is taken into account, the conclusions drawn in the previous section need to be modified. Even if one allele is selectively superior to all others at a given locus, it will not become fixed in the population; recurrent mutation will ensure that other alleles are present at low frequency, thus maintaining a degree of polymorphism. Population geneticists have long been interested in exploring what happens when selection and mutation act simultaneously."
FOUR: Random Drift
"3.3 Random Drift
Random genetic drift refers to the chance fluctuations in gene frequency that arise in finite populations; it can be thought of as a type of ‘sampling error’. In many evolutionary models, the population is assumed to be infinite, or very large, precisely in order to abstract away from chance fluctuations. But though mathematically convenient, this assumption is often unrealistic. In real life, chance factors will invariably play a role, particularly in small populations. The term ‘random drift’ is sometimes used in broad sense, to refer to any stochastic factors that affect gene frequencies in a population, including for example chance fluctuations in survival and mating success; and sometimes in a narrower sense, to refer to the random sampling of gametes to form the offspring generation (which arises because organisms produce many more gametes than will ever make it into a fertilized zygote). "
FIVE: Population Genetics vs. Other approaches
"Population-genetic models of evolution have also been criticised on the grounds that few phenotypic traits are controlled by genotype at a single locus, or even two or three loci. (Multi-locus population-genetic models do exist, but they tend to be extremely complicated.) There is an alternative body of theory, known as quantitative genetics, which deals with so-called ‘polygenic’ or ‘continuous’ traits, such as height, which are thought to be affected by genes at many different loci in the genome, rather than just one or two; see Falconer (1995) for a good introduction. Quantitative genetics employs a quite different methodology from population genetics. The latter, as we have seen, aims to track gene and genotype frequencies across generations. By contrast, quantitative genetics does not directly deal with gene frequencies; the aim is to track the phenotype distribution, or moments of the distribution such as the mean or the variance, across generations. Though widely used by animal and plant breeders, quantitative genetics is usually regarded as a less fundamental body of theory than population genetics, given its ‘phenotypic’ orientation, and plays less of a role in evolutionary theorising. Nonetheless, the relationship between population and quantitative genetics is essentially harmonious.
A different criticism of the population-genetic approach to evolution is that it ignores embryological development; this criticism really applies to the evolutionary theory of the ‘modern synthesis’ era more generally, which had population genetics at its core. As we have seen, population-genetic reasoning assumes that an organism’s genes somehow affect its phenotype, and thus its fitness, but it is silent about the details of how genes actually build organisms, i.e. about embryology. The founders of the modern synthesis treated embryology as a ‘black box’, the details of which could be ignored for the purposes of evolutionary theory; their focus was on the transmission of genes across generations, not the process by which genes make organisms. This strategy was perfectly reasonable, given how little was understood about development at the time. In recent years, great strides have been made in molecular developmental genetics, which has renewed hopes of integrating the study of embryological development with evolutionary theory; hence the emerging new discipline of ‘evolutionary developmental biology’, or evo-devo. It is sometimes argued that evo-devo is in tension with traditional neo-Darwinism (e.g. Amundson 2007), but it is more plausible to view them as compatible theories with different emphases.
In a recent book, Sean Carroll, a leading evo-devo researcher, argues that population genetics no longer deserves pride-of-place on the evolutionary biology curriculum. He writes: “millions of biology students have been taught the view (from population genetics) that ‘evolution is change in gene frequencies’ … This view forces the explanation toward mathematics and abstract descriptions of genes, and away from butterflies and zebras, or Australopithecines and Neanderthals” (2005 p. 294). A similar argument has been made by Massimo Pigliucci (2008). Carroll argues that instead of defining evolution as ‘change in gene frequencies’, we should define it as ‘change in development’, in recognition of the fact that most morphological evolution is brought about through mutations that affect organismic development. Carroll may be right that evo-devo makes for a more accessible introduction to evolutionary biology than population genetics, and that an exclusive focus on gene frequency dynamics is not the best way to understand all evolutionary phenomena; but population genetics arguably remains indispensable to a full understanding of the evolutionary process.
Despite the criticisms levelled against it, population genetics has had a major influence on our understanding of how evolution works. For example, the well-known ‘gene’s eye’ view of evolution, developed by biologists such as G.C. Williams, W.D. Hamilton and Richard Dawkins, stems directly from population-genetic reasoning; indeed, important aspects of gene’s eye thinking were already present in Fisher’s writings (Okasha 2008). Proponents of the gene’s eye view argue that genes are the real beneficiaries of the evolutionary process; genotypes and organisms are mere temporary manifestations. Natural selection is at root a matter of competition between gene lineages for greater representation in the gene pool; creating organisms with adaptive features is a ‘strategy’ that genes have devised to secure their posterity (Dawkins 1976, 1982). Gene’s eye thinking has revolutionised many areas of evolutionary biology in the last thirty years, particularly in the field of animal behaviour; but in many ways it is simply a colourful gloss on the conception of evolution implicit in the formalisms of population genetics."