NEETZoologyOrganisms and Populations
In a population exhibiting Verhulst-Pearl logistic growth, a small number of individuals are introduced into a new habitat with abundant resources. When the population density (N) is very small compared to the carrying capacity (K), what does the value of the term ( K-N K ) approach, and what is the resulting growth pattern?
Options
- AIt approaches 0, and the population growth is nearly zero.
- BIt approaches 1, and the population growth is nearly exponential.
- CIt approaches K, and the population growth is nearly zero.
- DIt approaches 1, and the population growth stops completely.
Correct answer
B. It approaches 1, and the population growth is nearly exponential.
Step-by-step solution
The Verhulst-Pearl logistic growth is described by the equation dN dt = rN ( K-N K ) . When the population density (N) is very small compared to the carrying capacity (K), the value of N is negligible relative to K. Therefore, the term ( K-N K ) approaches K K , which is equal to 1. Substituting this back into the equation gives dN dt rN(1) = rN . This indicates that when resources are abundant and population density is low, the population grows in a nearly exponential manner. As N increases and approaches K, the t