Branching Method

Zygotic Array

If we know the probability of each type of gamete from the probability of each alleleomorph, we can calculate the probability of each zygote genotype.

An F1 zygote of genotype Bb will
produce 1/2B and 1/2b gametes. An
individual gamete must contain either
B or b alleles, but cannot contain
both alleles as a haploid gamete.
The events of a gamete containing
a B and a gamete containing a b
gamete are mutually exclusive.
    Sample Space    1/2 + 1/2 = 1

We can multiply the probability of independent events to find the probability of each type of zygote. The probability that a male gamete contains a B allele does not influence the probability that a female gamete contains a B allele. The probability of a male gamete with the B allele is independent of the probability of a female gamete with a B allele.

P (BB) zygote = P (B) x P (B) = 1/2 x 1/2 = 1/4
P (bb) zygote = P (b) x P (b) = 1/2 x 1/2 = 1/4

Heterozygotes can occur in two mutually exclusive combinations. A
male gamete with the B genotype
can unite with a female gamete with
the b gamete. Another event would
be that a male gamete with the b
genotype would unite with a female
gamete with the B genotype. Either
    Sample Space    event produces a Bb zygote.

P (B from male) P (b from female) = 1/2 x 1/2 = 1/4
[P (b from female) P (B from male)]/[P (Bb)zygote] = 1/2 x 1/2
= (1/4)/(1/2) = 1/2

We can use shorthand to describe this array:

Let p = the probability of B allele in a gamete;
Let q = the probability of b allele in a gamete;

The probability of the different types of zygotes is:
p²+pq+qp+q²= p²+2pq+q²=(p+q)²

p(event) = P (zygotes)

two = # of trials

	p2	q
p	p2	pq
q	pq	q2