The relationship between the number of species encountered and the area surveyed is a fundamental concept in ecology, known as the species-area relationship. This principle is crucial for understanding patterns of biodiversity, guiding conservation efforts, and predicting species loss due to habitat destruction.

What Is the Species-Area Relationship?

The species-area relationship describes how the number of species (species richness) increases with the area sampled. As you explore progressively larger areas, you typically encounter more species, but the rate at which new species are found decreases over time.

The Mathematical Model

Ecologists often express this relationship with the equation:
S=cAzS=cAz
where:

• $S$ = number of species

• $A$ = area

• $c$ and $z$ = constants that vary with habitat and taxa

When plotted on a standard (arithmetic) scale, the curve rises quickly at first and then levels off, forming a rectangular hyperbola. This means that as you keep increasing the area, the number of new species found increases at a decreasing rate.

What Does the Graph Look Like?

• Straight line: Would indicate a constant rate of new species with area, which is not observed in nature.

• Hyperbola: Correct! The curve is steep at first (many new species in small areas), then flattens as most species have already been encountered.

• Sigmoid: Suggests an S-shaped curve, not typical for species-area relationships.

• Parabola: Indicates a quadratic relationship, which does not fit observed data.

Why Is It a Hyperbola?

• In the beginning, every new area adds several new species.

• As the area increases, the chance of finding new, previously unrecorded species decreases.

• Eventually, the curve approaches a plateau, as most species present in the region have already been found.

Ecological Significance

• Conservation planning: Helps predict how many species might be lost if a certain amount of habitat is destroyed.

• Reserve design: Informs how large protected areas need to be to conserve maximum biodiversity.

• Biodiversity studies: Provides a baseline for comparing species richness across different habitats and regions.

Conclusion

The graph depicting the number of new species encountered with progressive area covered forms a hyperbola. This classic species-area curve is a cornerstone of ecological theory and practical conservation.

Correct answer:
(2) Hyperbola