Population density at time $t+1$ is typically expressed as:

$Nt+1=Nt+(\{B+I\}-\{D+E\})$, where $B+I$ is,

Inversely proportional to D + E

The correct answer is Option (2) → Inversely proportional to D + E 

We are given the population growth equation:

N_t+1 = N_t+ (B + I - D - E)

Where:

• N_t= population size at time t
• B= births
• I = immigration
• D = deaths
• E = emigration

Here, (B + I) represents the inputs to the population (factors that increase population size).

• More births and immigration → population increases
• These are directly proportional to the population growth

Similarly, (D + E) represents the losses (factors that decrease population size).

Other options:

• Inversely proportional to B + I →  makes no sense (B + I can’t be inversely proportional to itself).
•  Directly proportional to E →  E (emigration) reduces population, not increases.
•  Directly proportional to D →  D (deaths) reduces population too.

The correct interpretation: B + I is directly proportional to the increase in population size, but none of the given options say this exactly.
However, if population increases with B + I, it opposes D + E.
Hence, the only reasonable relation is: It is inversely proportional to D + E — when deaths and emigration increase, the relative effect of B+I decreases, and vice versa.

Correct Answer: Inversely proportional to D + E