What happened to the tribe of Dan in Revelation? Compare the twelve tribes of Israel, according to Genesis 35:23-26 (left column) and Revelation 7:5-8 (right):


Asher : Asher
Benjamin : Benjamin
Dan : Gad
Gad : Issachar
Issachar : Joseph
Joseph : Judah
Judah : Levi
Levi : Manasseh
Naphtali : Naphtali
Reuben : Reuben
Simeon : Simeon
Zebulun : Zebulun


(Sorted into alphabetical order.)

Why is Dan replaced by Manasseh?

Background info: I know that Manasseh and Ephraim were Joseph's sons. I also know that the tribe of Joseph was split into two half-tribes: Manasseh and Ephraim.

Note on answer: I know the topic of Revelation can easily turn speculative but if at all possible I'm looking for a fact based answer (e.g. the tribe of Dan no longer exists and Manasseh is now twice as big).
This is an excellent question! Consider the following argument, posited in the seventh chapter of An Exposition of the Seven Church Ages by William Marrion Branham.

The book of Exodus tells the story of how the tribe of Levi was separated to serve the Lord.


  Exodus 32:26-29 Then Moses stood in the gate of the camp, and said,
  Who is on the LORD'S side? let him come unto me. And all the sons of
  Levi gathered themselves together unto him. And he said unto them,
  Thus saith the LORD God of Israel, Put every man his sword by his
  side, and go in and out from gate to gate throughout the camp, and
  slay every man his brother, and every man his companion, and every man
  his neighbour. And the children of Levi did according to the word of
  Moses: and there fell of the people that day about three thousand men.


Because of their stand for God, God chose the Levites to serve Him.


  NUMBERS 18:6 And I, behold, I have taken your brethren the Levites
  from among the children of Israel: to you they are given as a gift for
  the LORD, to do the service of the tabernacle of the congregation.


Numbers 10:11-28 lists the twelve tribes as Reuben, Simeon, Issachar, Judah, Zebulun, Benjamin, Dan, Naphtali, Gad, Asher, Ephraim and Manasseh. Levi ministered to the twelve tribes, and so was treated separately. When the twelve tribes encamped, they always camped three tribes to a side, surrounding the Levites and the temple.

You'll notice that Ephraim, in Revelation, is also removed from this list of tribes in Numbers. 

The answer to the question of "what happened to Dan and Ephraim?" lies in Deuteronomy 29:16-20.


  DEUTERONOMY 29:16 (For ye know how we have dwelt in the land of Egypt;
  and how we came through the nations which ye passed by; And ye have
  seen their abominations, and their idols, wood and stone, silver and
  gold, which were among them:) Lest there should be among you man, or
  woman, or family, or tribe, whose heart turneth away this day from the
  LORD our God, to go and serve the gods of these nations; lest there
  should be among you a root that beareth gall and wormwood; And it come
  to pass, when he heareth the words of this curse, that he bless
  himself in his heart, saying, I shall have peace, though I walk in the
  imagination of mine heart, to add drunkenness to thirst: The LORD will
  not spare him, but then the anger of the LORD and his jealousy shall
  smoke against that man, and all the curses that are written in this
  book shall lie upon him, and the LORD shall blot out his name from
  under heaven.


The curse of idolatry (or spiritual fornication) was to have your name blotted out.

Now, let's see how this applied to the tribe of Dan.


  I Kings 12:25-30 Then Jeroboam built Shechem in mount Ephraim, and
  dwelt therein; and went out from thence, and built Penuel. And
  Jeroboam said in his heart, Now shall the kingdom return to the house
  of David: If this people go up to do sacrifice in the house of the
  LORD at Jerusalem, then shall the heart of this people turn again unto
  their lord, even unto Rehoboam king of Judah, and they shall kill me,
  and go again to Rehoboam king of Judah. Whereupon the king took
  counsel, and made two calves of gold, and said unto them, It is too
  much for you to go up to Jerusalem: behold thy gods, O Israel, which
  brought thee up out of the land of Egypt. And he set the one in
  Bethel, and the other put he in Dan. And this thing became a sin: for
  the people went to worship before the one, even unto Dan.


And now Ephraim...


  Hosea 4:17 Ephraim is joined to idols: let him alone.


As Jesus said...


  MATTHEW 24:35 Heaven and earth shall pass away, but my words shall not
  pass away.


God remembered His Word in Deuteronomy by removing Dan and Ephraim from the final list of the tribes sealed in the 144,000 of Revelation.