The reproductive cycles of two populations (X and Y) of the silk cotton tree (Ceiba pentandra) were monitored for one year. A census was carried out and all plants were tagged and counted throughout this period and is reflected in the data sheet given below:

Parameter	Population X	Population Y
Initial number of plants (N₀)	500	300
Number of new seedlings (B)	200	210
Number of initial plants that died (D)	20	27

Given that there is no seedling mortality, which one of the options correctly depicts the per capita rate of increase (r) for the two populations?

Correct option is A

The correct answer is: (1) X: 0.16, Y: 0.61

Explanation:

The per capita rate of increase $r$ for a population is calculated using the formula:

$$r = \frac{B - D}{N_0}$$​​$$r = \frac{B - D}{N_0}$$

Where:

• $B$ is the number of new seedlings established,

• $D$ is the number of plants that died,

• N0N_0N0​ is the initial number of plants.

For Population X:

• Initial number of plants N0=500N_0 = 500N0​=500

• Number of new seedlings $B=100$

• Number of plants that died $D=20$

  The per capita rate of increase rrr for Population X:

  ​$$r = \frac{100 - 20}{500} = \frac{80}{500} = 0.16$$

  For Population Y:​

  • Initial number of plants N0=300N_0 = 300N0​=300

  • Number of new seedlings $B=210$

  • Number of plants that died $D=27$

  ​

  The per capita rate of increase $r$ for Population Y:

  ​$$r = \frac{210 - 27}{300} = \frac{183}{300} = 0.61$$

  
  

  Thus, the correct per capita rates are X: 0.16 and Y: 0.61.