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Jan Sapp reviews the evidence in two new books on the topic:

[N]ot only are the differences between the classically defined "races" very superficial, they are also of surprisingly recent origin; the variety of human populations seems to have both accumulated and begun to reintegrate within the past 50,000 to 60,000 years. The diversity among us has arisen in a blink of evolution’s eye. The process of relative geographic isolation of local populations into what might have been true races (genetically differentiated populations) during the last Ice Age began to reverse as formerly isolated human groups came back into contact and interbred. That reintegration, which has occurred intermittently throughout human history, is sped up today because of great migration and widespread mating of individuals from disparate geographic origins. The result is that individuals identified as belonging to one “race,” based on the small number of visible characters used in historical race definitions, are likely to have diverse ancestry. 

Jerry Coyne responds that "if that's the consensus, then I am an outlier":

In my own field of evolutionary biology, races of animals (also called "subspecies" or "ecotypes") are morphologically distinguishable populations that live in allopatry (i.e. are geographically separated).  There is no firm criterion on how much morphological difference it takes to delimit a race.  Races of mice, for example, are described solely on the basis of difference in coat color, which could involve only one or two genes. … As we all know, there are morphologically different groups of people who live in different areas.

Kenan Malik stakes a middle ground:

There is no such thing as a ‘natural’ human population. Yet, many of the ways in which we customarily group people socially – by race, ethnicity, nationality, religious affiliation, geographic locality and so on – are not arbitrary from a biological point of view. Members of such groups often show greater biologically relatedness than two randomly chosen individuals. Such groups have often been ghettoized by a coercive external authority, or have chosen to self-segregate from other groups. Hence they are inbred to a certain degree and can act as surrogates, however imperfectly, for biological relatedness. Categories such as ‘African American’, ‘people of Asian descent’ and ‘Ashkenazi Jew’ can be important in medical research not because they are natural races but because they are social representations of certain aspects of genetic variation. They can become means of addressing questions about human genetic differences and human genetic commonalities.

It seems to me pretty obvious that superficial racial differences are a function of relatively recent evolutionary adaptation – and have no core essence or "natural" permanence. Miscegenation and travel scrambles them, making race an increasingly complex phenomenon. But the notion that there are no "human genetic commonalities" that are related to differing populations we crudely assign to something we "socially represent" as "race" is indisputable.

(Photo from Tumblr user Taiga)