The term (K−N)/K
a. Is the carrying capacity for a population.
b. Is greatest when K is very large.
c. Is zero when population size equals carrying capacity.
d. Increases in value as N approaches K.

Verified step by step guidance

1. Step 1: Begin by identifying the components of the term (K−N)/K. Here, K represents the carrying capacity of a population, and N represents the current population size.
2. Step 2: Understand the biological significance of the term (K−N). This represents the difference between the carrying capacity (K) and the current population size (N). When N is equal to K, the difference becomes zero, indicating that the population has reached its carrying capacity.
3. Step 3: Divide (K−N) by K to normalize the difference relative to the carrying capacity. This term essentially measures how far the population is from reaching its carrying capacity as a proportion of K.
4. Step 4: Analyze the behavior of the term (K−N)/K under different conditions: (a) When N equals K, the term becomes zero, indicating no growth potential. (b) When N is much smaller than K, the term approaches 1, indicating high growth potential. (c) As N approaches K, the term decreases in value, reflecting reduced growth potential.
5. Step 5: Use the above analysis to evaluate the options provided in the problem. For example, option (c) aligns with the observation that (K−N)/K equals zero when N equals K, and option (d) contradicts the fact that the term decreases as N approaches K.

Key Concepts

Carrying Capacity (K)

Carrying capacity (K) refers to the maximum number of individuals of a species that an environment can sustainably support. It is determined by factors such as resource availability, habitat space, and environmental conditions. Understanding K is crucial for analyzing population dynamics and predicting how populations grow or decline over time.

Population Size (N)

Population size (N) is the current number of individuals in a population. It fluctuates due to births, deaths, immigration, and emigration. The relationship between N and K is vital for understanding population growth; as N approaches K, the growth rate slows, reflecting the limitations imposed by the environment.

Logistic Growth Model

The logistic growth model describes how populations grow in an environment with limited resources. It is characterized by an initial exponential growth phase, followed by a slowdown as the population reaches its carrying capacity (K). The formula (K−N)/K represents the fraction of resources available for growth, which decreases as N approaches K, indicating that growth becomes limited.