A geneticist crossed two corn plants, creating a heterozygous decahybrid (ten traits). This decahybrid was then self-fertilized. How many different kinds of gametes were produced? What portion of the offspring were homozygous recessive? How many different kinds of genotypes and phenotypes were generated in the offspring? What would your answer be if the decahybrid were test crossed instead?

1 answer

If you try to work this problem by diagraming the cross, it will be intractable because the Punnett Square would be 1024 rows by 1024 columns. The chart given below with the answers inserted in the appropriate place (2^n means 2 raised to the nth power; 2^3 = 2x2x2 = 8). Remember that a decahybrid is heterozygous at 10 loci (AaBbCcDdEeFfGgHhIiJj).

mono tri deca
# of gametes 2 8 2^10=1024

prop. of
recessive homozygotes in the F2 generation
1/4 1/64 (1/(2^10))^2= 1/1048576


# of genotypes in
the F2 generation 3 27 3^10 = 59049

# of phenotypes in
the F2 generation 2 8 2^10 = 1024

If the decahybrid was testcrossed the only numbers that would change would be the prop. of recessive homozygotes [(1/(2^10)) = 1/1024] and the number of genotypes in the F2 generation [(2^10) = 1024].
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