My original question was not "How likely is it that the various human races would homogenize here on Earth over the next 3000 years". It was (slightly paraphrased) "Assuming the various human races homogenize over the next 3000 years, what would the end result look like?
.
.
.
I'll amend the original question by adding an 'average'. What would the average end result look like? I'm not suggesting that every single member of the Terran population would look like that.
I think I would start by analyzing what we know of the history of Terrans from the Interstellar Wars period down to the 57th Century, according to Traveller Canon, keeping in mind that homogenization tends to occur in areas that are more "cosmopolitan" in nature (e.g. centers of trade/commerce and political centers).
During the Interstellar Wars era, the seat of government is still the United Nations, in New York City. From this I will extrapolate that in this period the center of civilization is an outgrowth of the political realities of present day (21st Century) Earth, and that Europe, and North America are still principal players. Asian power is on the rise, and contributes significantly to the major "players" of the period (being 20% of the world population), with perhaps Latin America close behind (since they seem to have a significant presence among various off-world colonies, and in terms of population dominate most of the Western Hemisphere). During the United Nations/Terran Confederation era presumably these groups would most likely be the ones "mixing", though in their home-regions they would still tend toward their modern 21st Century phenotypes. I would presume most Asians would still look "Asian" (due to simple population size), and Europeans and Western Hemisphere types would increasingly "blend together" regionally. North Americans would have a greater mix of Latin and Asian subtypes (due to migration resulting from the global economy), with increasing intermarriage between African-American and non-African groups, the general result tending to a slightly more brown-complexioned Latin/Afro-Amerasian mix. Europeans would perhaps be more "Euro-Asian/Middle Eastern" in appearance. As Vilani come into the mix, their phenotype will also have an increasing representation as the RoM progresses.
That being said,
sometime during the Long Night/Old Earth Union/Third Imperium period, the population and political centers shift to the Southern Hemisphere (cf
GT: Rim of Fire and
DGP: Solomani & Aslan). The economic center of Terra moves to Johannesburg in southern Africa, and the political center moves to Brazil (Rio de Janeiro). These become the new "cosmopolitan" regions of the Earth during this period, where the bulk of the population dwells.
Likely during this (potentially) long period, significant "Latinization" and "Africanization" of the common Terran phenotype may occur. With southern Africa becoming the economic center of the planet, it is quite likely that many residents of the African continent of the 57th century would be somewhat lighter (or lighter-brown) skinned as people migrate to the African region from across the globe (with a significant number of immigrants originating from the political center of Latin/South America, and perhaps Asia as well) and mix with indigenous peoples of the continent. The DGP material (IIRC) also mentioned that the Asians (particularly Chinese), tended to cultural conservatism and maintained elements of their culture and language to a slightly higher degree than much of the rest of Terra.
So in short, the olive/light-brown complected, dark-eyed, dark-haired phenotype would most likely be fairly common (especially in the centers of population in the southern hemisphere), with a slightly more "Asian" cast in Eastern Asia.
