What evidence is there that the genealogies in the early part of Genesis refer to tribes instead of individuals? One method of interpreting the genealogies in the early parts of Genesis is as not referring to actual individuals, but rather to tribes, nations, and groups of people represented by the names of individuals.  What evidence (internal or external) do people who support this interpretation cite?
The evidence that the genealogies in the early part of Genesis refer to tribes instead of individuals is disarmingly simple. It is seen especially clearly in Genesis 10, which is commonly referred to as the Table of Nations. Here is the introductory verse of the chapter:


  This is the account of Shem, Ham, and Japheth, Noah's sons, who themselves had sons after the flood. (Genesis 10:1)


What follows is, in fact, a listing of names of races, nations, and tribes, all organized as a series of three genealogies of Noah's three sons: first of Japheth (Genesis 10:2-5), then of Ham (Genesis 10:6-20), then of Shem (Genesis 10:21-31). The chapter ends with this summary:


  These are the clans of Noah's sons, according to their lines of descent, within their nations. From these the nations spread out over the earth after the flood. (Genesis 10:32)


So although Genesis 10 is in the form of a genealogy of the descendants of Noah's three sons, the names in the genealogy are identified with the nations that repopulated the earth after the Great Flood had destroyed all of humanity except for Noah, his sons, and their wives.

So the basic evidence that the genealogies in the early part of Genesis refer to races, nations, and tribes is that the names in the main organizing genealogy in Genesis 10 are the names of races, nations, and tribes, and are associated with them in the genealogy itself.

Here is a visual representation of the Table of Nations in Genesis 10 in which the various names are placed in their most likely geographical regions on a map of the ancient Biblical world:



As graphically represented on this map:


Japheth represents the races inhabiting Asia Minor (roughly present-day Turkey) and the surrounding areas of Europe and Asia to its west, north, east, and southeast.
Ham represents the races inhabiting northeastern Africa and adjoining parts of Palestine and the Arabian Peninsula.
Shem represents the races inhabiting the northern and eastern parts of the Fertile Crescent, and the bulk of the Arabian Peninsula.


The names in these three genealogies are a catalog of all the major nations and races of the ancient Biblical world within these general racial groups. Some of them figure prominently in the Bible story, such as Egypt and Canaan in the genealogy of Ham, and Ashur (Assyria) and Eber (an ancestor of Abraham) in the genealogy of Shem. Others are mentioned only occasionally elsewhere in the Bible narrative.

The main point is that these names are the names of races, nations, and tribes, arranged in the form of a genealogy showing their origins and interrelationships with one another. This is the basic "evidence" that the genealogies in the early chapters of Genesis refer to races, nations, and tribes. They simply do refer to races, nations, and tribes.

From Genesis 10 we can project the same principles to the earlier chapters of Genesis, making it very likely that the earlier genealogies, such as the one in Genesis 5, also refer to whole races and nations of people that inhabited the earlier, pre-Flood world.

And as Dick Harfield's answer points out, some scholars believe that figures in later genealogies, including the twelve sons of Jacob, also represent tribes rather than individuals.

The Table of Nations in Genesis 10, then, provides the key to the identification of the genealogies of Genesis as being genealogies of races, nations, and tribes rather than the genealogies of individual human beings.