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Revision as of 11:15, 31 January 2015
, 11:15, 31 January 2015→Derivation for counting the number of genotypes
= Derivation for counting the number of genotypes =
= Derivation for counting the number of genotypes =
For the case where A < P, there must always be P observed alleles and there can only be at most A alleles. This can be modeled by P+A-1 points where you choose A-1 points to be dividers to define the alleles.
Thus the number of ways you can observe this is <math> \binom{P+A-1}{A-1} </math>.
For the case where A >= P,
<math>
\begin{align}
\binom{P+A-1}{A-1} &, A < P \\
\sum_{i=1}^{P-1} \binom{A}{i}\binom{P-1}{i-1} + \binom{A}{P} &, A \ge P
\end{align}
</math>
where P is the ploidy number and A is the number of alleles.
