The idea that diversity in isolated habitats depends on rates of colonization and extinction is part of the equilibrium theory of biogeography.

The equilibrium theory of biogeography, formulated by Robert MacArthur and Edward O. Wilson, elucidates how species diversity in isolated habitats is influenced by the rates of colonization and extinction. Here's a detailed breakdown of this concept:

1. Colonization: This refers to the process by which new species arrive at an isolated habitat. The rate of colonization is affected by factors such as the distance from the source of species and the biological characteristics of the species themselves. Generally, species are more likely to colonize islands (or isolated habitats) that are closer to their source populations.

2. Extinction: This is the process whereby species disappear from a habitat. The rate of extinction in an isolated environment increases as the number of species increases due to factors such as competition for resources and predation. Moreover, smaller habitats tend to have higher extinction rates due to fewer available resources and less diverse habitats.

3. Equilibrium: The theory posits that there is a balance, or equilibrium, between the rates of colonization and extinction. When these two rates are equal, the diversity of species in the habitat stabilizes. If either rate changes, it can result in shifts in species diversity. For example, if colonization increases (perhaps due to a lower distance to the mainland), species diversity may increase until it reaches a new equilibrium.

4. Implications: The equilibrium theory has significant implications for conservation biology, especially in the context of habitat fragmentation and island biogeography. Understanding these rates can help in the management of protected areas and the preservation of biodiversity.

In summary, the equilibrium theory of biogeography provides a framework for understanding how isolated ecosystems evolve over time through the interplay of colonization and extinction rates, ultimately influencing biodiversity.