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?

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].

To determine the number of different kinds of gametes produced by the heterozygous decahybrid, we need to understand the concept of independent assortment and the number of traits involved in the cross.

For independent assortment, Mendel's second law states that during gamete formation, different pairs of alleles segregate independently of one another. In this case, since there are ten traits involved (decahybrid), each with two alleles, we calculate the number of possible combinations using the formula 2^n, where n is the number of traits.

So, 2^10 = 1024 different kinds of gametes were produced by the decahybrid.

To determine the portion of the offspring that were homozygous recessive, we need to know the specific genotype of the parents. However, since the decahybrid was self-fertilized, we can assume that both alleles for each trait segregate independently during gamete formation.

If we assume random segregation and disregard any lethal or deleterious alleles, we can use the probability that offspring will be homozygous recessive for a particular trait.

For each trait, the probability of offspring being homozygous recessive is 1/4 (1/2 * 1/2). Since there are ten traits, the probability of offspring being homozygous recessive for all ten traits would be (1/4)^10 = 1/1,048,576.

However, it is essential to note that this calculation assumes independent assortment, random segregation, and the absence of any modifying factors such as lethal or deleterious alleles.

To determine the number of different kinds of genotypes and phenotypes generated in the offspring, we can use the formula 3^n, where n represents the number of traits. This formula assumes complete dominance, meaning that the dominant allele masks the effect of the recessive allele, resulting in three possible genotypes (homozygous dominant, heterozygous, and homozygous recessive) for each trait.

So, 3^10 = 59,049 different kinds of genotypes and phenotypes were generated in the offspring.

If the decahybrid were test crossed instead, the answers would differ. A test cross involves crossing the individual with an individual that is homozygous recessive for all traits.

In this case, the number of different kinds of gametes produced would remain the same, i.e., 1024.

However, the portion of the offspring that would be homozygous recessive would vary. Since the test cross involves crossing with an individual that is homozygous recessive for all traits, all the offspring would be heterozygous for all the traits. None of the offspring would be homozygous recessive.

Furthermore, since all offspring would be heterozygous for all traits, the number of different kinds of genotypes and phenotypes generated would be reduced to 1, as all individuals would have the same genotype and phenotype.

It's crucial to note that these calculations are based on simplified assumptions and ideal scenarios. In real-life situations, genetic crosses can involve more complexities and variations.