A researcher is comparing the species diversity of two islands. Both islands are roughly equal in size; however, one island is much closer to the mainland. The researcher determines that the S value (number of species at equilibrium) for the island closer to the mainland is the S value for the island located farther from the mainland. In addition, she finds that the closer island's extinction rate is the extinction rate on the farther island. higher than; the same as the same as; lower than higher than; lower than lower than; the same as the same as; higher than lower than; higher than

The researcher determines that the S value (number of species at equilibrium) for the island closer to the mainland is higher than the S value for the island located farther from the mainland. In addition, she finds that the closer island's extinction rate is same as the extinction rate on the farther island.

Explanation:

In bio-geographical research of islands, the s-value is the species value of an island ecosystem. This is used to calculate the biodiversity of the island and is dependent on the size of an island and its distance from the mainland.

This is in accordance with the equilibrium theory of island biogeography (ETIB) which states that immigration of species is higher in islands close to mainland and the extinction of species depends on the size of the island; i.e., rate is high in smaller islands and less in larger islands.  

In the given case, the researcher is comparing the species value of two islands and concludes that the island near the mainland has a higher species value than the one that is far which correlates with the ETIB theory.  

The fact that the extinction rates of the species of both the islands were found to be the same is because both the islands are of the same size, which also correlates with the ETIB theory.