Final answer:
Option 4 is correct: Some short individuals may appear in the F2 generation because when an F1 generation plant that is heterozygous (Tt) self-pollinates, 25% of the offspring could theoretically be short (tt) according to Mendelian genetics.
Step-by-step explanation:
When considering the cross of a true-breeding tall pea plant with a tall pea plant of unknown parentage, several scenarios are possible. True-breeding organisms are those that, when crossed among themselves, produce offspring identical to the parent with respect to the trait of interest. In Mendelian terms, true-breeding plants that are tall would have a genotype of TT, where 'T' stands for the tall trait, which is considered dominant.
Given that the tall plant of unknown parentage is simply known to produce tall progeny but its precise genotype (TT or Tt) is unknown, when crossed with a true-breeding tall plant (TT), all the F1 offspring will certainly be tall. This is because they will all inherit at least one allele for the tall trait from the true-breeding parent. This rules out options 1 and 3. Over several generations, short individuals will only appear if the tall plant of unknown parentage contributes a recessive allele for shortness (t). So, if the tall plant is heterozygous (Tt), self-pollination of the F1 generation (which are all Tt) could produce some short (tt) offspring in the F2 generation. Therefore, option 4 is correct.
A Punnett square analysis can support this claim. Upon self-pollination of the F1 heterozygous plants (Tt), the F2 generation will exhibit a phenotypic ratio of 3 tall to 1 short, as a result of the genotypic combinations TT, Tt (or tT), and tt. However, if the unknown parent is also true-breeding (TT), then over several generations, no short individuals will appear, as indicated in option 2, though this is less likely given the information provided.