Crawfish are shelled organisms that live in shallow freshwater rivers. They can have antennae of different lengths. Two parents with medium length antennae have offspring. One of their offspring has short antennae, and one has long antennae. How did the offspring end up with traits that are different from the traits of their parents? How did the gene combinations result in these traits?

Assuming a single, diallelic gene, coding for antennae length, the offspring end up with traits that are different from the traits of their parents because the mode of inheritance is by  incomplete dominance.

Available data:

We will assume that this trait is coded by a single, autosomic, diallelic gene.

The expression of three phenotypes suggests that the mode of inheritance is by incomplete dominance.

Incomplete dominance refers to the cases in which the heter0zyg0us individual expresses an intermediate phenotype between the h0m0zyg0us dominant and the recessive phenotypes. Neither of the involved alleles completely dominates over the other one.

In this example the expression of the trait would be as follows,

Genotype                         Phenotype

AA                                  Long anteannae

Aa                            Medium length antennae

aa                                    Short antennae

According to this information, the cross would be

Cross: Between two medium length antennae individuals

Parentals)   Aa     x     Aa

Gametes)  A    a        A     a

Punnett square)     A        a

                   A       AA      Aa

                    a       Aa      aa

F1)  1/4 = 25% of the progeny is expected to be h0m0zyg0us dominant expressing long antennae

      2/4 = 1/2 = 50% of the progeny is expected to be heter0zyg0us expressing the medium length phenotype

      1/4 = 25% of the progeny is expected to be h0m0zyg0us recessive expressing short antennae.

So, while the parents were heter0zyg0us for the trait, Aa, one of the offspring was h0m0zyg0us dominant, AA, and the other one h0m0zyg0us recessive, aa.

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Genes are the hereditary units, which carry information from the parent to offspring. The variant form of the gene, an allele codes for different traits, but is present at the same locus of the chromosome.

Given that:

The phenotypes of crawfish are long, medium, and short.

Parents have medium antennae.

The progeny have long and short antennae.

Let us assume the genotype as:

Let allele A be dominant that codes for long antennae.

Allele a is recessive and codes for short antennae.

The expression of three phenotypes suggests that the alleles are inherited through incomplete dominance.

Incomplete dominance is the phenomenon in which both the alleles will be expressed incompletely. The alleles for long and short will not be expressed properly, leading to medium-length antennae.

The expression can be given as:

AA - Long antennae

Aa - Medium Length antennae

aa - Short Length antennae

The cross for the given alleles is given in the attachment below.

Thus, F1 progeny will have 25 % purebred dominant for long antennae, 50% of the progeny will have heterozygous medium antennae, and 25% of the progeny will have purebred recessive short antennae.

To know more about the cross, refer to the following link:

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you did not attach the discourse, but i assume it to be the discourse on the origin and basis of inequality among men (the original titile in french is: "discours sur l'origine et les fondements de l'inégalité parmi les hommes"), also know as "second discourse". in this discourse, jean-jacques rousseau emphasizes that private property is the basis of all inequalities.

therefore, what enabled the old regime to maintain as long as it did was private property.