Which Population Size Is Best for Maximum Sustainable Harvesting of Resources?

Sustainable resource management is a cornerstone of modern ecology, fisheries science, and conservation. Ensuring that populations of harvested species remain healthy while providing maximum yield is a delicate balance. This article explores which population condition is most favorable for achieving maximum sustainable harvesting of resources, using the principles of population ecology and the concept of maximum sustainable yield (MSY).

Understanding Maximum Sustainable Yield (MSY)

Maximum sustainable yield (MSY) is defined as the largest yield or catch that can be taken from a species’ population over an indefinite period without causing the population to decline. MSY is a foundational concept in fisheries, forestry, and wildlife management, where the goal is to balance human use with the long-term health of the resource.

The MSY is closely tied to the logistic growth model, which describes how populations grow rapidly at first but slow as they approach the environment’s carrying capacity (the maximum population size the environment can sustain).

The Logistic Growth Model and MSY

The logistic growth equation is:

dNdt=rN(1−NK)dtdN=rN(1−KN)

where:

• $N$: current population size

• $K$: carrying capacity

• $r$: intrinsic growth rate

The growth rate is highest when the population is at half the carrying capacity ($N=K/2$). At this point, the population is said to be at the inflection point of the logistic curve, where the rate of increase is maximized. This is also the point where the maximum sustainable yield is achieved.

Why Is Harvesting at Half the Carrying Capacity Most Favorable?

When a population is at or near the carrying capacity ($N\approx K$), the growth rate is low because resources are limited and competition is high. Harvesting at this point would reduce the population, but the yield would not be maximized because the population’s ability to replace itself is limited.

Conversely, if the population is much lower than the carrying capacity ($N<K/2$), the growth rate is increasing, but the absolute number of new individuals added per unit time is less than at the inflection point.

At half the carrying capacity ($N=K/2$), the population growth rate is at its maximum. This means that the number of new individuals produced each year is highest, and thus the number that can be sustainably harvested without reducing the population size is also highest.

Evaluating the Options

Let’s examine each option in the context of sustainable harvesting:

1. Major part of population is near or around the carrying capacity

   • Analysis: At or near carrying capacity, the population growth rate is low. Harvesting at this point would not be sustainable for maximum yield, as the population’s ability to replace harvested individuals is limited.

   • Favorability for MSY: Low

2. Population is at half of the carrying capacity

   • Analysis: At half the carrying capacity, the population growth rate is at its maximum. This is the point where the maximum number of individuals can be sustainably harvested each year.

   • Favorability for MSY: Highest

3. Population is one fourth below the carrying capacity

   • Analysis: If the population is at three-fourths of the carrying capacity ($N=3K/4$), the growth rate is already declining from its maximum. If “one fourth below” is interpreted as $N=K/4$, the growth rate is still increasing but not yet at its peak.

   • Favorability for MSY: Not optimal

4. Population has slow doubling time

   • Analysis: A slow doubling time indicates a low intrinsic growth rate, which is not directly related to the population’s position relative to the carrying capacity. This does not indicate the best condition for maximum sustainable yield.

   • Favorability for MSY: Not relevant

Real-World Implications

In fisheries, for example, managing fish stocks so that the population remains at about half the carrying capacity allows for the highest sustainable catch. If the population is allowed to drop too low, the yield decreases because there are fewer individuals to reproduce. If the population is near the carrying capacity, the yield is also lower because the growth rate is reduced.

Similarly, in forestry and wildlife management, maintaining populations at the inflection point of the logistic curve ensures that the resource can be harvested sustainably over the long term.

Common Misconceptions

• Harvesting at carrying capacity is best: Many assume that the largest population will provide the highest yield, but in reality, the growth rate is lowest at this point.

• Harvesting at very low population sizes is sustainable: While populations can recover if not overharvested, the yield is not maximized at low population sizes.

• Slow doubling time means better yield: A slow doubling time simply reflects a low growth rate, not the optimal position for sustainable harvesting.

Summary Table

Conclusion

The most favorable condition for maximum sustainable harvesting of resources is when the population is at half of the carrying capacity. At this point, the population growth rate is at its maximum, allowing for the highest sustainable yield without causing the population to decline over time.

Correct answer:
(2) Population is at half of the carrying capacity