Knights: always tell the truth;
Liars: always tell lies;
Knaves: each of a knave's statements strictly alternate truth and lies;
Transposers: a transposer's statements are always of opposite truth-value to the
  previous statement most recently made by anyone, including himself or herself.
  If no one has made a statement yet, a transposer will speak truth or a lie
  randomly for the first statement.

Scientists have discovered that in Kivelians, veracity is an inherited characteristic based on blood type. Any individual has one of six possible genotypes (KK, KO, LL, LO, KL, and OO) that produce one of four possible phenotypes:

Knight (produced by KK homozygous and KO heterozygous genotypes),
Liar (produced by LL homozygous and LO heterozygous genotypes),
Knave (produced by the KL heterozygous genotype), and
Transposer (produced by the OO homozygous genotype).

If April, Baxter, Celeste, and Douglass, are a knight, a liar, a knave, and a transposer, in some order; and if each one is a parent or child to at least one other person in the group, can you determine each person's type, and relation to the others, given the statements below?

April: I am heterozygous.
Baxter: I am a knight.
Celeste: Douglass is April's father.
Douglass: I am heterozygous.

Baxter: Douglass is not my father.
April: Baxter is a knave.
Baxter: Celeste is April's mother.
Celeste: The liar among us is homozygous.

Douglass: Baxter is my son.
Celeste: Baxter is my son.
April: There are exactly two heterozygous and two homozygous among us.
Baxter: The liar among us is heterozygous.

Celeste: April is heterozygous.
Douglass: I am related by blood to exactly two of the others here.
April: Douglass is heterozygous.
Douglass: The knight among us is homozygous.

Notes: You may find it helpful to use Punnett Squares to test which types of parents can produce which types of children. Here's an example of a Punnett Square using blood types.

Also, the spacing is given only for readability. You may assume the comments are all said in order, with no breaks between them.