Definitions Recap

• Alpha (α) Diversity: The diversity within a single host, habitat, or community—essentially, the average number of species per unit (e.g., per host).

• Beta (β) Diversity: The diversity between two hosts or habitats, representing the difference or turnover in species composition from one to another.

• Gamma (γ) Diversity: The total diversity across all hosts or habitats in the study area—the overall species richness at the landscape or regional scale47.

The Mathematical Relationship

In ecology, these diversity measures are mathematically related. A common formulation is:

β=γαβ=αγ

This means that beta diversity is the ratio of the total diversity (gamma) to the average local diversity (alpha).

What Happens When Alpha Diversity Increases and Gamma Diversity Is Constant?

If gamma diversity (the total number of unique pathogens across all hosts) is held constant, but alpha diversity (the number of pathogens per host) increases, the equation above shows that beta diversity must decrease. This is because as each host contains more of the total pathogen species, the difference in species composition between hosts becomes smaller.

Example

• Suppose gamma diversity is 100 (total unique pathogens across all hosts).

• If alpha diversity increases from 10 to 20 (each host has more pathogens on average), then:

  • When α = 10: β = 100/10 = 10

  • When α = 20: β = 100/20 = 5

As alpha diversity increases, beta diversity decreases, provided gamma diversity does not change.

Ecological Interpretation

• Higher alpha diversity means individual hosts share more species, reducing the uniqueness or turnover between hosts (lower beta diversity).

• Constant gamma diversity ensures the total species pool does not change, so any increase in local diversity must come at the expense of differences between hosts.

Conclusion

If gamma diversity is constant and alpha diversity increases, beta diversity will decrease. This relationship is foundational in biodiversity studies and helps explain patterns of species distribution across landscapes and hosts.

Correct answer:
(2) β-diversity will decrease