Infer gene frequency within a species over time
There are really two ways to infer past genetics.


Sample the past. 


Only really works if you have well-preserved uncontaminated archaeological samples, but works surprisingly well, considering. The accuracy and completeness goes down fairly quickly as you go back in time but thousands of years to hundreds of thousands of years is roughly possible. You won't have many samples so it's hard to say anything about population genetics. Don't do this. It doesn't work very well and it's very hard.


Molecular clocks. 


Same-sense mutations that affect nothing accumulate in genes over time as they're passed down. Genes that have a distant common ancestor are more different than genes that are just a generation or two apart. This is essentially how phylogenetics works as a whole, but you can use age differences between nearby genes to detect selection in this way. If gene A is nearly identical in every individual in a population, but gene B has thousands of pretty distinct variations, it's clear gene A does something important and has been powerfully selected for. Don't just count the number of kinds of alleles for gene A, calculate the average relatedness between all the alleles you find. If the relatedness for gene A is much lower than for other genes, gene A is being selected on. This is what the text means by 'reduction in genetic diversity', bringing down the average relatedness.

You can't work out allele frequencies at arbitrary times in the past without a time machine(even ancient sampling, you can't really be sure you're getting an accurate sample of the historical population), but phylogenetics can hint at what happened by detecting the signatures of evolution.