Dealing with possible "outliers" first...
All the specimens used in the Zakrzewski study clearly display tropical proportion indexes, with the Badarian male being the only outlier in this regard, particularly where the crural index is concerned. The mean crural index for the Badarian females, of sample size 4, was harder to determine with accuracy because the sample sizes that Zakrzewski reports for the mean maximum femoral length and the mean maximum tibial length respectively were inconsistent, like for example, the sample size involved in the determination of the mean femoral length was the full sample size of 4 when that involved in the determination of the mean tibial length was only 3 specimens. On the other hand, the Badarian males of sample size 6 was consistently used in the determination of the mean values of both the maximum femoral length and the maximum tibial length, so that it was possible to determine the mean crural index—which comes out as 82%, thus putting the Badarian male series within the reach of sub-tropical and temperate-climate indexes. For the record, in line with male samples of other time frames, the Badarian male samples generally reported relatively higher mean values for both the stature and stature-variation (Coefficient of Variation—denoted by V*) than the Badarian female counterparts. To verify the stated values, one will need to refer to Zakrzewski's Table 3.
At basic, the higher variation of the male stature suggests that sexual selection was of little consequence in male stature. However, as an alternative idea, it might be said that the male sample, as small as it was, might have been suggestive of a male population that emerged from two distinct ancestral populations, with some originating from a tropically situated source, and with others deriving from a non-tropically situated source. This idea though, suffers from one problem, when cranial data is called on. In many of the groups suspected to have such ancestry, the cranial patterns comprise of trends that are generally at least bimodal in nature. Take for instance, the late Bronze Age to Iron Age Maghrebi specimens or the Iron Age Lachish samples.
Some have sought out a connection between the Badarians and the Natufians, on the account of Zakrzewski's report on the male femoral and tibial lengths. According to this mindset, the Badarians are supposed to have originated in the Levant and subsequently situated themselves in the Nile River valley. This is supposedly then further qualified by the presence of some "Near Eastern" material item in Badarian stratigraphical layers, but in fact, the core culture of the Badarians is said to be very much African, and it is as follows: Neolithic settlements of the Badari culture in the Nile valley recall African livestock enclosures and suggest a rather mobile existence (33). The practice of cattle burials is a presumably religious custom that has been recorded in the Egyptian Sahara from the fifth millennium B.C.E. (4). Saharan traditions of cattle pastoralism have thus become an essential component of Neolithic life in the Nile valley. - Rudolph Kuper and Stefan Kropelin, Climate-Controlled Holocene Occupation in the Sahara: Motor of Africa’s Evolution, 2006.
While possible Badarian ancestry in the Natufian samples have been suggested before [see: Larry Angel, 1972], there is one fundamental distinction between studied Badarian samples and Natufian samples: In the cranial patterns! Multivariate analysis, such as those done earlier on by S.O.Y. Keita, have demonstrated that none of the Badarian samples misclassified into Eurasian samples, whereas tests on Natufian specimens [Brace et al. 2005] suggested that there was a "sub-Saharan element of equal importance as the Eurasian element" in the cranial trends; it is of importance to note that Brace et al. (2005) use "sub-Saharan" only in the context of the idealized "True Negro" type. This bimodal contrast means that the Natufian samples exhibited a characteristic that one can attribute to genetic exchange between two populations that were formerly isolated geographically.
It should also be pointed out that when the Lachish crania (sample size of 61) were run as unknowns [see: Keita (1988)], the Badarian series (sample size of 22) received the least amount of misclassified Lachish crania [but tied with the Maghrebi series (sample size of 49)] after the pre-colonial recent Teita series (sample size of 30); this is when the Lachish series were not included in the analysis. However, when the Lachish series were included in the analysis, the Badarian series received an even less amount of Lachish crania that can be classified into the Badarian series, having the least amount of misclassified crania. The only other series to match the Badarians in this regard, with regards to misclassified Lachish crania, was the Teita series. What does all this mean? Well, it is highly likely that the core Badarian population was an African population that maintained a long enough presence in the sub-tropical regions of the Sahara, such that it was a population undergoing micro-adaptive evolution to that environment, as reflected in the mean crural index of Zakrzewski's male samples. One will have to otherwise explain why specimens from the pre-mid to mid early Holocene "Near East" or Levant often have greater affinity, however small or what not, with Eurasian specimens than the Badarians generally do, which is often fairly little to none.
If one assumed that the Badarian were direct remnants of either the earliest modern humans or else Upper Paleothic modern humans of the "Near East", who have a so-called "generalized" modern cranial pattern—often said to be closest to patterns seen in recent Australians, Melanesians and Africans, then it is useful to note that even the Upper Paleothic ancestors of Europeans retained tropical limb proportions, which should be cause to ask why the same wouldn't have applied to the Badarians. To this end, the only logical explanation left to consider, is either that the Badarian samples were way too small to account for a more general pattern, thereby leaving only a snapshot of internal variation which is then misleadingly interpreted as the characteristic variation of the Badarian male sample, when the actual variation would have otherwise had a relatively less coefficient of variation than what we were led to believe; this explanation suggests that the fairly small sample size had the effect of exaggerating the internal variation of the Badarian male crural index values, and possibly the stature values, OR yet, that there may have been some unclear pathological factor involved that had the effect of bringing the mean crural index of that small Badarian male series down from the expected mean [i.e. given the generally tropical means of the Nile Valley specimens], but one which less afflicted the Badarian female series. The former of these last two explanations is the more logically attractive, i.e. if sexual bias is ruled out as a factor. It should be noted that sexual selection does not appear to have prevented the analyzed post-Badarian Nile Valley specimens from reporting tropical mean crural indexes. To quote Zakrzewski, it would have to be concluded that there is little sexual dimorphism between the Badarian male series and that of the female counterpart:
The Badarian sample clearly has greater similarities in computed statures than all the other time periods. The most sexual dimorphism is seen during the LPD, with high levels also found during the MK.
The female Badarian population is the tallest relative to its male counterpart (at 95% of the male stature), and hence the Badarian sample exhibits the least sexual dimorphism of the Egyptian groups studied...The low dimorphism of the Badarian was predicted, as archeological evidence suggests it to be the most egalitarian of the groups studied (Midant-Reynes, 2000b), and therefore reasonably likely to have equal access to food and other resources.
...but Zakrzewski goes onto say this, which might play into the aforementioned "affliction by some unexplained pathological reason" vis-a-vis the Badarian male sample:
Females were initially better buffered than males against the growth-inhibiting effects of disease and malnutrition in childhood. This would mean that they were already closer to reaching their genetically predisposed height during the Badarian period, and so could only increase slightly in stature with better food and health provision.
If it is assumed that the Badarian female series was less afflicted by "growth-inhibiting effects of disease and malnutrition in childhood", then it appears that any such affliction in the Badarian male series did not seem to have occurred again in the post-Badarian time frames through to the Middle Kingdom, since all the other specimens reported higher limb proportions. If there were any "growth-inhibiting effects of disease and malnutrition in childhood", then they must not have been acute enough to alter the generally tropical mean crural indexes of the post-Badarian Nile Valley samples.
Zakrzewski, for her part, sought to explain the Badarian stature in the following manner, a portion of which will be revisited again, but it still doesn't account for the anomalous Badarian male mean crural index:
Mean calculated stature increased through the Predynastic periods, to reach a maximum in the Early Dynastic period, and then declined to the MK. Stature increased over the period of change in subsistence strategy, from pastoralism with gathering and cultivation during the Badarian period to agriculture in the Early Dynastic period, while stature declined over the phase of agricultural intensification and formation of social hierarchies (see Fig. 3). The same bow-shape pattern is also seen in all long bone lengths (e.g., Fig. 5). This pattern suggests that the Badarian sample may have suffered from some degree of growth inhibition. The increase in stature over the Predynastic periods supports the model that as agriculture became more reliable, growth stunting was reduced. The later reduction in stature is harder to explain from this model, and is more likely to be related to changes in social ranking and how well the samples represent and cross-cut the social hierarchy of the period.
Whatever may be said of the Badarian male samples, it is worth noting that:
The nature of the body plan was also investigated by comparing the intermembral, brachial, and crural indices for these samples with values obtained from the literature. No significant differences were found in either index through time for either sex. The raw values in Table 6 suggest that Egyptians had the “super-Negroid” body plan described by Robins (1983)...
This pattern is supported by Figure 7 (a plot of population mean femoral and tibial lengths; data from Ruff, 1994), which indicates that the Egyptians generally have tropical body plans.
Of the Egyptian samples, only the Badarian and Early Dynastic period populations have shorter tibiae than predicted from femoral length. Despite these differences, all samples lie relatively clustered together as compared to the other populations.
Hence, the differences were not great enough to cause the ancient Egyptian samples to lie too far apart from one another, or deviate from their general trend of being "tropically adapted", despite their residency in a sub-tropical region of Africa. This "super-Negroid" body plan that Zakrzewski mentions is not some superficial connection to "sub-Saharan" Africans, as some Eurocentric ideologues like to spin it, because only sensible results were obtained when computational parameters used for "tropical Africans" were also applied to the ancient Egyptian specimens; European parameters were not able to provide sensible results [e.g. see Robins 1986]. As such, we get:
their physical proportions were more like modern negroes than those of modern whites, with limbs that were relatively long compared with the trunk, and distal segments that were long compared with the proximal segments. - Robins, regarding both predynastic and Dynastic Egyptian specimens.
And now, let's take a look at other cases in Zakrzewski's analysis, as well as to determine when specimens should not be considered an outlier...
There have been questions surrounding the usage and consideration of the Middle Kingdom (MK) sample in the results reported by Zakrzewski. It can positively be said that Zakrzewski did not exclude the Middle Kingdom sample. It is precisely because the Middle Kingdom sample was included, that Zakrzewski was able to describe the temporal changes in the long bone lengths, except for the fibula—the measurements of which is said to have no correlation to the change in the time frames under study.
Zakrzewski makes a link between the Middle Kingdom specimens and the so-called "Nubian" mercenaries presumably part of the ancient Egyptian army. It should be pointed out that Zakrzewki provides no concrete biological evidence, or on-site [cemetery] funerary scripture confirmation of the Middle Kingdom graves supposedly containing the remains of "Nubian" mercenaries other than to say that Middle Kingdom-era Stele(s) tell us about their presence in the region at that time, and that coefficient of variance reverts back to the trend of the male samples having larger variance than the female counterparts of the same time frame. Emphasis is made here on "reverts back to", because the Middle Kingdom samples' coefficient of variance recall the trend seen in specimens prior to the Early Dynastic and Old Kingdom. So, in this regard, the Middle Kingdom sample is really NOT an outlier, as some observers figure, but rather, it has precedences! The only question here, is why we see this "boomerang-like" (bow-like) change in variance.
Let's examine what the measurements tell us, according to Zakrzewski:
1) Reduction in humerus length accompanies increase in ulna length, through the time frames under study...
The ratio of maximum humerus length to maximum ulna length (XLH/XLU) shows a reduction through time. Plotting each of the lengths separately by time period shows that maximum humerus length (XLH) follows the same bow-like pattern seen in Figures 3 and 5, while maximum ulna length (XLU) increases in length through time, especially in males.
The Effect—of the above, when a Cartesian schematic is used to plot the said limb variables, is as follows: There is yet another reversion back to a trend seen in specimens preceding the Early Dynastic and Old Kingdom specimens!
2) Aforementioned coefficient of variance...
The coefficients of variation for the computed statures for each time period are plotted in Figure 4. Figure 4 indicates that over the start of the Dynastic period, greater variation is found in the computed statures of females than males, and that the reverse is true by the MK.
Effect—of the above: Reversion back to pre-Early Dynastic trend. Emphasis is made on "reversion", because the trend is not an entirely new one that is different from all preceding periods, but rather, that the trend seen in the Middle Kingdom samples was also seen in samples preceding the Early Dynastic samples.
3) Reduction in tibial length after the Early Dynastic sample...
See fig. 5 for details (see below). We are told that this reduction is the general trend...
A reduction in stature and long bone lengths was found through the Dynastic periods, although the decrease occurred most in the MK sample.
We are not clued in on the precise magnitude of reduction in the humerus reduction, except that it follows the pattern [the values through time produce the so-called "bow-like" trajectory] seen in stature and tibial length respective reductions.
Effect of the above: Another reversion to pre-Early Dynastic era trend!
In light of the above-mentioned, it would NOT be accurate to say that the Middle Kingdom is an outlier, but rather, it would be more reasonable to ask why there is a reversion of trends. This is what Zakrzewski sought to disentangle, as she acknowledges in the following:
The same bow-shape pattern is also seen in all long bone lengths (e.g., Fig. 5). This pattern suggests that the Badarian sample may have suffered from some degree of growth inhibition. The increase in stature over the Predynastic periods supports the model that as agriculture became more reliable, growth stunting was reduced. The later reduction in stature is harder to explain from this model, and is more likely to be related to changes in social ranking and how well the samples represent and cross-cut the social hierarchy of the period.
It is against this backdrop, the "harder to explain" situation that Zakrzewski implicates either a "Nubian" presence, and/or invokes "changes in social ranking". There is a caveat to the second/latter possibility, which is this: only if it is assumed that the specimens from the Old Kingdom and Early Dynastic period represented socially "high-ranking" personalities with better access to resources. Should this be so, then "Nubian presence" justification would not be necessary. In other words, the Middle Kingdom represented less well-off individuals than those of the Old Kingdom and Early Dynastic period, and hence, the reason for the reduction trend in long bone lengths and stature. If push comes to shove, just based on objective assessment of trends in specimens before and after the Early Dynastic specimens, this would be the more likely scenario than the invocation of "Nubian presence". Otherwise, one would have to assume that "Nubian presence" was also there in pretty much all the specimens preceding the Early Dynastic specimens, because what we see is essentially a reversion of trends, as opposed to a totally new trend. It should be kept in mind that a segment of Early pre-Dynastic specimens too had been sourced from a Gebelein site, and they show more or less similar trends in stature and tibial lengths to those seen in the Middle Kingdom specimens.
Short of specifying the names on the burial sites pointing specifically to "Nubian" personalities, Zakrzewski's assessment is largely circumstantial and conjectural, as pointed out earlier. Zakrzewski did not actually measure any independent "Nubian" series and compare it against the MK series, which would allow readers to determine whether the MK produces the very same internal variations as the would-be "Nubian" counterpart. Nor has Zakrzewski specified what particular "Nubians" we are supposed to be dealing with, although one can perhaps guess that the said "Nubians" would likely have been what some of us have come to recognize as the "Medjay" or "Mdw", presumably brought in from "lower Nubia", who reportedly made up part of Egyptian mercenaries during the Middle Kingdom Dynastic epoches. "Nubian" or "Nubia" as a term has never actually been used by the ancients of the Nile Valley to describe any polity or ethnic group, and so, judging by its frequent Eurocentric usage, the term could refer to just about any of the diverse ethnic and geographically-distinct Nile Valley inhabitants south of ancient Egypt's border. And even if one were to take Zakrzewski's words at face value, "Nubian" presence doesn't account for "tropical-body" proportions in preceding specimens, presumably with "little to no Nubian presence"!
The specifics discussed here, when taken as a whole, demonstrate that while social and dietary pressures may affect stature, these elements generally have little to no effect on the body and limb proportion indexes that characterize tropical and non-tropical climes respectively. The bulk of the ancient Egyptian samples studied had reported "tropical" body and limb proportions, which is interesting, since the ancient Egyptians lived in a largely sub-tropical part of Africa. They pretty much retained this general body plan through to the Dynastic period. The only sensible explanation for this phenomenon, is that the ancient Egyptians had recent ancestry in tropical Africa at that point in time, and since the annual mean temperature of their sub-tropical habitat would not have been too drastically distinct from those of the tropics, there were no considerable temporal or spatial alterations, brought to bear by environmental pressures, to their generally tropical body and limb proportions. There is therefore a genealogical component to the ancient Egyptians' retention of tropical body proportions, rather than a matter of social hierarchy and dietary pressures. The latter (social and dietary pressures) are generally inclined to affect stature more readily so than they do body and limb proportions, for if they did affect the body & limb proportions as well, then there would not be clear contrasting patterns between body and limb proportions of populations in "high latitudes" and those in the tropics, as reflected in the results of study after study, and time after time.
*Last updated on July 15th, 2011. Look for possible future updates.
— Sonia Zakrzewski, Variation in Ancient Egyptian Stature and Body Proportions, 2003.
— Rudolph Kuper and Stefan Kropelin, Climate-Controlled Holocene Occupation in the Sahara: Motor of Africa’s Evolution, 2006.
— Robins, Predynastic Egyptian stature and physical proportions, 1986.
— Larry Angel, Biological Relations of Egyptians and Eastern Mediterranean Populations during pre-dynastic and Dynastic Times, 1972.
— Brace et al., The questionable contribution of the Neolithic and the Bronze Age to European craniofacial form, 2005.
— S.O.Y. Keita, An Analysis of Crania From Tell-Duweir Using Multiple Discriminant Functions, 1988.
— Personal notes from 2009 & 2011.