Number of Progenics Required to Establish the Genotype
of a Phenotype
Suppose we want to determine whether an A_ phenotype
is the AA or Aa genotype. We self-fertilize A_. How
many progeny of the A_ plant must be evaluated to determine
the genotype of this A_ plant with a specified probability
of erroneously rejecting Ho(Type I error).
Ho:plant is Aa
HA:plant is AA
a = 0.05
We can identify the genotype of the A_ phenotype by
observing a single aa offspring.
Let q = failure to observe a homozygous recessive offspring
of A_.
Example:
How many progeny must be evaluated to determine whether
A_ is in fact the Aa genotype with a
= 0.05 probability of erroneously concluding that an
Aa plant has the AA genotype?
q = failure to observe homozygous recessive offspring
due to sampling = 3/4.
q = 3/4 because each time we observe either an AA or
Aa progeny we fail to observe aa progeny.
The probability of n failures to observe an aa offspring
is P = a, when plant is actually
Aa genotype.
P = qn
log(P) = n log(q)
because:
n! (q)n(P)n
= qn when r = 0
(n-r)!r!
n = log(P) = log(0.05)
= -1.301
log(q) log(0.75) -0.1249
n = 10.4 
10
If we want to be 99% certain of identifying a homozygous
recessive progeny when the parent is heterozygous, we
set P = 0.01.
P = qn
n = log(P) = log(0.01)
= -2
n = log(q) =
log(0.75) = -0.1249
= 16
