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Since you cite Rightmire as a source, I'll present more of his work. By the way, he did a lot of work using multivariate statistics, in particular multiple discriminate function analysis; I used that a lot in graduate school to study modern human skeletal material. Here is a nice simple essay for your reading pleasure:

AN EARLY UPPER PLEISTOCENE AND AFRICAN ORIGIN FOR THE NEANDERTHALS

Patrick Fleming, February 1992

Summary

This contribution to the ongoing Neanderthal debate (Graves, 1991) postulates that the species Homo sapiens originated in Africa in the early Upper Pleistocene. This population then split into two groups. One group migrated to the Near East and Europe where it developed into Neanderthal. The other group stayed in Africa and developed into anatomically modern Homo sapiens. This latter group then migrated from Africa sometime later. The article will indicate that:

i) Homo erectus was a world-wide taxon that died out in all locations except Africa where it developed into archaic Homo sapiens (AHS);
ii) All archaic Homo sapiens populations (Africa, Europe, Asia) belong to the one taxon that originated in Africa;
iii) Anatomically modern Homo sapiens (AMH) belonged to the same species as AHS and was an adaptation to the warm conditions of Africa;
iv) Neanderthal belonged to the same species as archaic Homo sapiens and was an adaptation to the icy conditions of Europe and Northern latitudes.

THE STATUS OF HOMO ERECTUS

Rightmire (1990) discusses the following questions in relation to Homo erectus:

i) whether Homo erectus is best defined as an arbitrary grade in the Homo lineage or a discrete entity;
ii) the necessity, or even utility, of recognizing characters which are unique (autapomorphic) to Homo erectus if this species is to be diagnosed adequately relative to other taxa;
iii) Evolutionary tempos and whether gradual change can be documented within Homo erectus over a long span of Pleistocene time.

He presents a case for viewing Homo erectus as a real taxon. His description of this species lists many characters which are primitive and which are not shared with modern humans. It is also possible to identify some traits which are clearly derived for Homo erectus in comparison to earlier Homo or Australopithecus. These include a heavy brow, midline keeling and parietal tori, strong flexion of the occiput and development of a prominent transverse torus, features of the cranial base and expansion of cranial capacity. Such characters serve to diagnose the species in a more precise way, and it can be argued, he states, that Homo erectus is not simply an arbitrarily defined segment of a lineage. This paleospecies had ancestors and probably left descendants, but these groups can be distinguished from one another on the basis of morphological comparisons. Regarding ancestors he states that two taxa may be present, as both large and small-brained morphs are present.

Following the emergence of Homo erectus, he continues, systematic change is not easily documented. There is a trend towards endocranial expansion, which is apparent particularly in the later assemblages at Zhoukoudian and Ngandong. The growth of brain size with time depends on the date assigned to the Ngandong crania. If these crania are included then brain volume increases at a rate of about 180 ml/my. However, there is much doubt about the age of the Ngandong hominids, and assigning them a late Middle Pleistocene date biases the analysis. If a regression line is constructed without reference to Ngandong the slope drops to about 120 ml/my. This result cannot be distinguished from zero, and there is no evidence that the trend is statistically significant. Other characters change slowly or not at all. Towards the close of the Middle Pleistocene, there are signs that some of these traits begin to change more rapidly. It is during this period that populations of Homo erectus must have given way to the first representatives of a new species.

Rightmire states that early in the Middle Pleistocene, Homo erectus can be documented from fossils found in the South, Eastern and Northwestern parts of Africa, in the Far Eastern tropics and in the cooler reaches of Northern China. Populations inhabiting these far-flung regions of the Old World are anatomically similar, and the morphology of the species seems to have changed little over more than a million years. However, differences in behaviour are apparent. In Africa, Middle Pleistocene humans utilized an Acheulian technology, while at Zhoukoudian the chopping tools associated with Homo erectus do not include hand axes. In Java, few stone tools of any sort are found in the deposits yielding ancient hominids. This suggests that Homo erectus groups were adapting differently to local circumstances.

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