In cucumbers, heart-shaped leaves (hl) are recessive to normal leaves (HL) and having numerous fruit spines (ns) is recessive to having few fruit spines (NS). The genes for leaf shape and for number of spines are located on the same chromosome; findings from mapping experiments indicate that they are 32.6 m. u. apart. A cucumber plant having heart-shaped leaves and numerous spines is crossed with a plant that is homozygous for normal leaves and few spines. The F1 are crossed with plants that have heart-shaped leaves and numerous spines. What percentage of the progeny would be expected to have normal leaves and numerous spines (HL, ns)?

given,

heart-shaped cucumber leaves (hl) are recessive and have numerous fruit spines (ns).

normal leaves (Hl) are dominant and have few fruit spines (Ns).

the genes for leaf shape and fruit spines are 32.6 m.u. apart from each other and situated on the same chromosome,

in other words,  32.6% of the progeny of the cross will be recombinants.

and there will be two types  of recombinants (those with heart-shaped leaves and few spines and those with normal-shaped leaves and few spines), so each recombinant phenotype will  constitute (32.6/2)= 16.3% of the progeny.

The non-recombinant progeny (those with heart shaped leaves and numerous spines and those with normal-shaped leaves and few  spines) will make up the remainder of the progeny (100% - 32.6% = 67.4%)

which will be equally divided between the two non-recombinant phenotypes (67.4/2= 33.7% each).

Heart-shaped, numerous spines will give 33.7% of  nonrecombinant cross

Normal-shaped, few spines  will give 33.7%  of nonrecombinant cross

Heart-shaped, few spines 16.3%  of recombinant cross

Normal-shaped, numerous spines 16.3% of recombinant cross

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