If you think about your family tree, you have two parents (strictly biologically speaking), four grandparents, eight great-grandparents, and so on. Going back n generations, you had 2n ancestors in that generation. Considering your lineage from the other direction, however, it quickly becomes clear that there were not 2n unique individuals alive if you go far enough back. For example, if you suppose there have been thirty generations between 1000 AD and today (allowing for a bit over thirty years per generation), that would give you over 1 billion ancestor positions at that time but estimates of the entire population alive at that time range from 250-310 million.
This seeming difficulty is resolved once you realize that not all the ancestor slots on your family tree were unique. Some of your ancestors partnered with people they were related to, whether closely (such as a first cousin) or more distantly. The next conclusion that you can draw from this line of thought is that at some point in the past everyone who was alive at that time is the ancestor of everyone who is alive today.
Rutherford’s clear explanation of this fact is one of the book’s strongest passages:
Our family trees coalesce and collapse in on themselves as we go back in time. You certainly must have a trillion positions on your family tree, but the further you go back, the more frequently these positions will be occupied by the same individuals multiple times. It is quite possible that although I had sixty-four ancestral positions at the same tier as Mary Huntley, they may have been occupied by fewer than sixty-four women. Family trees coalesce with startling speed. The last common ancestors of all people with long-standing European ancestries lived only six hundred years ago—meaning that if we could draw a perfect complete family tree for every European, at least one branch on each tree would pass through a single person who lived around 1400 CE. This person would appear on all our family trees, as would all their ancestors. The fact that multiple positions are occupied by the same people indicates that the notion of a tree is again not the most accurate metaphor for describing genealogy: Trees only ever branch, but family trees contain loops. Your own pedigree rises from you like a tree, but sooner or later two of those branches will collide in a person from whom you are descended twice. These people sit atop genealogical loops. …
Go back a few centuries further and we reach a mathematical certainty referred to as the genetic isopoint. This is the time in history when the entire population is the ancestor of the entire contemporary population today. For the people of Europe, the isopoint occurs in the tenth century. In other words, if you were alive in the tenth century in Europe, and you have European descendants alive today, then you are the ancestor of all Europeans alive today (we estimate that up to 80 percent of the population of tenth-century Europe has living descendants). Another way to think of it is like this: One branch of a family tree of two first cousins crosses in a shared grandparent; one branch of all European family trees cross through one individual in 1400 CE; at the isopoint, all branches of all family trees cross through all people for that population. (p. 82-84)
This argument for how closely humans are related makes it clear that racist claims are not supported by genetic science. Even if there were multiple origins of human ancestry, there are genetic isopoints for large swathes of the global population within recorded history.
Where the book comes up somewhat short is in regards to its subtitle: what genes can or cannot tell us about human difference. Rutherford spends substantial time on sports performance and whether certain groups are better suited to athletic activities such as running. In this section of the book he could have marshalled stronger evidence from existing research, and tackled other claims regarding additional aspects of human behavior.
This book’s title is evidently intended to cash in on current dialogue regarding race and racism, but its overall evidence for human similarity and introduction to population genetics is valuable beyond the present moment.