The Effect of Migration on a Similarity Index

Abstract

Fewster and Buckland (2001) defined a similarity index between two communities by allowing changes between sites to reduce the influence of local discrepancies. The similarity index of Fewster and Buckland is calculated to attain the maximum similarity between two communities in the presence of migration. Instead of maximizing similarity, we propose random migration to measure the similarity of two communities with two types of stochastic migration. The similarity values based on the proposed methods can be treated as the expected value of similarity under migration. We use computer simulation and empirical examples to demonstrate our approach.

Keywords:

• Jaccard's index
• Migration
• Similarity index
• Spatial randomness

Mathematics Subject Classification:

• 62P10
• 62P12

Acknowledgment

The authors are grateful for the funding from National Science Council in Taiwan, NSC Project 92-2118-M-004-004, and insightful comments from the anonymous reviewer, which helped us to clarify the context of our work.

Notes

Note: The results are from 1,000 simulation runs

Note: The AN and unrestricted cases are from 10,000 simulation runs.

Note: 10,000 simulation runs.

Note: The AN and unrestricted cases are from 10,000 simulation runs.

Note: 10,000 simulation runs.

Note: AN and unrestricted cases are from 10,000 simulation runs.