See the previous entries on this thread: (Part 2) or (Part 1).
Dolichocephalic (long headed) skulls are those which are rather narrow in comparison to their length (breadth - length ratio of about 75%), shorter skulls (ratio of around 80%) are known as Brachycephalic (broad headed), and those in between, Mesocephalic.
These ratios or cephalic indexes were invented by Swedish scientist Anders Retzius in the early 1800s as a tool for anthropology. Of course, ignorant bigots have used them for their horrible racist or nationalist purposes, trying to prove that certain traits imply the superiority or, the inferiority of certain groups (and we all know the kind of suffering that those absurd notions can cause).
Cephalic indexes are not 100% reliable and even within one same group of people living in their own homeland, there is considerable variability. What is more, environment and other conditions modify skull shape in babies (i.e. cultures that bind and elongate their malleable toddlers heads), which in turn alters cephalic indexes.
Having said this, it is however easy to apply. Simple measurements and a division let you calculate the index in a quick and straightforward manner. It also seems to have a correlation with heredity and thus to race or ancestry. So, without digging too deeply into which "race" has which cephalic index, we can reach some interesting conclusions:
1) Some studies  have suggested that skull shape may be an adaptation to handle climate, as Brachycephalic skulls are better suited for cold climates while the longer Dolichocephalicones are best in a hot climate.
2) Most of the South American and North American Indians, are Brachycephalic, indicating a common origin. Actually there are some native Americans that are exactly the opposite, being Dolichocephalic. Which may be an indication of a different origin.
This discrepancy among native Americans has led to the theory of two different groups peopling America, which came here from the Old World in two (or perhaps more) migratory events: 
- The Palaeoamericans, or Paleoindians, who were characterized by long and narrow cranial vault (i.e. dolichocephalic morphology) and a narrow face, which are purportedly the first to have arrived in America.
- The Amerindians, from which most of modern American groups derive, and who exhibited short and wide cranial vault, along with wide faces (i.e. brachycephalic morphology). These would be the ‘newcomers’ –arriving some 10,000 years ago.
Skull shape, Patagonian natives and H. erectus
The Patagonian natives exhibit "the most robust and dolichocephalic crania" among a sample of South American natives .
Though, the authors of the above quoted statement believe that " mechanisms other than genetic drift (e.g., natural selection) could have acted to shape the pattern observed in some craniofacial structures " of these natives. It could of course have been caused by the fact that they were a small intermarrying group of "surviving" Paleoamericans whose isolation in the arid and harsh tip of Southern South America saved from being wiped out by the second wave of brachycephalic invaders.
Now, the interesting part is that: "Homo erectus developed a dolichocephalic shape of skull" , this may be due to two causes:
1) That they were “long skulled” or
2) That their prominent brows were included in the length and therefore exaggerated their length of their skulls.
Either way, and even if we take their brows into account, they have long skulls.
Now my suggestion, based on the Multiregional theory of the origin of Modern Man (in a nutshell: Homo erectus moved out of Africa, spread out around the Old World, and there as well as in Africa, continued evolving until all became modern Homo sapiens humans.
This is in conflict with the opposing Out of Africa hypothesis which states that only the African erectus kept on evolving, turning into modern men, who then left Africa and overtook the world leading our old and less brainy ancestor erectus to his demise (either by absorbing them or killing them).
An alternative explanation
My suggestion is that: erectus kept on the move, entered America a long time ago (maybe 500 to 300 thousand years ago) and evolved here into dolichocephalic modern humans along the lines of the Multiregional hypothesis.
These were the Paleoindians. So we rid ourselves of the notion of an ancient first wave of humans or Paleoamericans. These in turn, were overtaken by a wave of Old World brachicephalic humans some ten thousand years ago.
 Clare V. Merry, (2005). Mind - Primary Cause of Human Evolution, Trafford Publishing, vol. 1 pp. 327}
 S. R. Prabhu, (1992). Oral diseases in the tropics. Oxford University Press, pp. 37.
 Perez SI, Bernal V, Gonzalez PN, Sardi M, Politis GG, (2009). Discrepancy between Cranial and DNA Data of Early Americans: Implications for American Peopling. PLoS ONE 4(5): e5746. doi:10.1371/journal.pone.0005746
 Perez, S. I., Bernal, V. and Gonzalez, P. N. (2007). Morphological differentiation of aboriginal human populations from Tierra del Fuego (Patagonia): Implications for South American peopling. American Journal of Physical Anthropology, 133: 1067–1079. doi: 10.1002/ajpa.20633
Patagonian Monsters - Cryptozoology, Myths & legends in Patagonia2010 International Year of Biodiversity Copyright 2009-2010 by Austin Whittall ©