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Here is its usage.
"there is sufﬁcient genetic control to make nonmetric traits useful in anthropological work, and such variables have successfully assigned individuals from distinct geographic regions to their correct groups (for example,… As such, nonmetric traits are an appropriate means for studying biological distances"
Biological distance is pretty much what you'd guess: how closely related are x and y based on genetic (phenotype or genotype) studies?
There is zero biological distance between identical twins. There is extremely little biological distance between family members (for most intents and purposes, none, no matter where they live). It goes on and on in this manner.
Biological distance, or degree of genetic relatedness, will be assessed by a comparison of dental nonmetric trait frequencies.1
The phrase has been used in Theoretical Population Biology for decades. Back then, they had phenotypes to measure the degree of biological distance.2 Today, actual genetic determination of kinship is possible.
Biological distance, or biodistance, is the measure of biological relatedness (or divergence) between and within human groups, living and past, based on human skeletal and dental variation.3
1 Dental Variation of Prehistoric Amerindian Populations from Eastern Tennessee
2 Kinship, information and biological distance
3 Biological Distance in Bioarchaeology and Human Osteology
I think this is more of a Biological Anthropology question, and my guess is the question could be rephrased as "What do anthropologists mean when they use the term “biological distance?”
The Anthropology This Site is still under construction so that is a dead end for now.
Pietrusewsky (2014) gives the following definition, and I quote:
Biological distance, or biodistance, is a measure of relatedness or divergence among groups separated by time and/or geography based on morphological variation (Buikstra et al. 1990).
Pietrusewsky continues with elaborating on Biodistance research:
Biological distance studies, which are undertaken to reconstruct population history and to assess ancestry, dominated bioarchaeological research during the 19th and early 20th centuries. [… ] These early attempts were flawed due to limitations of the approach, which included the mistaken belief that humanity could be divided into a finite number of pure races, and the lack of adequate quantitative methods. Advances in evolutionary theory, including quantitative and population genetics, and improvements in computing and statistical procedures in the early 20th century provided a much sounder basis for measuring and interpreting morphological variation within and between human groups.
These elaborations may explain the rather defensive stature the authors take in your cited article to back up their methods, and I quote:
In any case, there is sufficient genetic control to make nonmetric traits useful in anthropological work, and such variables have successfully assigned individuals from distinct geographic regions to their correct groups (for example, Winder, 1981; Prowse and Lovell, 1995; Blom et al., 1998; Christensen, 1998; Donlon, 2000; Hanihara et al., 2003). As such, nonmetric traits are an appropriate means for studying biological distances among North African populations and the implications of the patterning of these distances in assessing the relative role of the Sahara Desert as a barrier to gene flow.