Numerical Problems involving Sexual Reproduction in Flowering Plants

1. Number of Seeds Produced

• Given: 100 flowers, 100 pollen grains per flower, 5% pollen reach the stigma, 1% fertilization rate.

• Calculation:

  • Number of pollen grains reaching stigma = 100 flowers x 100 pollen/flower x 5% = 500
  • Number of ovules fertilized = 500 x 1% = 5

2. Number of Pollen Grains Required

• Given: Pollen viability 85%, stigma receptivity 70%, 1000 pollen grains per flower, 100 ovules.

• Calculation:

  • Number of viable pollen grains = 1000 x 85% = 850

  • Number of pollen grains reaching stigma = 850 x 70% = 595

  • Number of pollen grains required for successful fertilization = 100 ovules x 1 pollen grain/ovule = 100

  • Therefore, the approximate number of pollen grains required = (Number of reaching stigma/Number required) = (595/100) x 100% ≈ 595%.

  • To ensure successful fertilization, we need at least 595 viable pollen grains per flower.

3. Minimum Number of Days for Self-Pollination

• Given: Stamen length 5 cm, pistil length 7 cm, pollen tube growth rate 1 cm/day.

• Calculation:

  • Style length = Pistil length - Stamen length = 7 cm - 5 cm = 2 cm
  • Minimum number of days required = Style length/Pollen tube growth rate = 2 cm/1 cm/day = 2 days

4. Ploidy of Endosperm

• Given: Diploid chromosome number (2n) = 14, abnormal pollen with an extra haploid copy of one chromosome (n).

• Calculation:

  • Endosperm is triploid (3n) if the abnormal pollen fuses with two normal haploid female gametes (n+n).
  • Endosperm is pentaploid (5n) if the abnormal pollen fuses with one normal haploid female gamete and the other normal haploid female gamete fuses with a normal haploid male gamete (n+n+n).

5. Maximum Potential Population Size

• Given: Population of 10,000 plants, 60% male, 40% female, each female produces 50,000 ovules, each seed yields one plant.

• Calculation:

  • Number of female plants = 10,000 plants x 40% = 4,000 plants
  • Maximum potential population size = Number of female plants x Number of ovules per female x 100% germination rate = 4,000 x 50,000 x 100% = 200,000,000 plants.

Answers:

1. (b) 50

2. (c) 2857

3. (b) 3 days

4. (b) Pentaploid (5n)

5. (d) 50,000