#note Population Genetics A Concise Guide (3)

Page 11

Problem 1.1 How many different genotypes are there at a locus with n alleles that differ by state? You already know that there is one genotype at a locus with one allele and three genotypes at a locus with two alleles. Continue this with three, four, and more alleles until you divine the general case.

Note:

Take n=4 as an example, for homozygote, there are four (n) genotypes:

   

Namely, there are n homozygotes. For heterozygote, there are (we see A_ij and A_ji are the same) three (n-1) heterozygotes start with 1 (A₁₂, A₁₃, A₁₄), two (n-2) heterozygotes start with 2 (A₂₃, A₂₄) and one heterozygote starts with 3 (A₃₄).

So for the general case there are altogether n + (n-1) + (n-2) + … + 1 genotypes with n alleles that differ by state. Namely n(n+1)/2.

Use Java Stream to print all genotypes:

import java.util.stream.IntStream;
import java.util.stream.Stream;

public class PrintGenotypes{
  
  public static void main(String[] args){
    int n = 4;
    Stream<int[]> genotypes =
            IntStream.rangeClosed(1, n).boxed()
                    .flatMap(i ->
                            IntStream.rangeClosed(i, n)
                                    .filter(j -> j>=i)
                                    .mapToObj(j ->
                                            new int[]{i, j})
                    );

    genotypes
            .forEach(t ->
                    System.out.println("A" + t[0] + "" + t[1] ));
  }
} 

Output:

A11
A12
A13
A14
A22
A23
A24
A33
A34
A44