EE 12- Introduction to Island Biogeography

The Species-Area Relationship (SAR)

• The fundamental relationship in macroecology relates the number of species ($S$) to the area ($A$) they occupy.

• Power Law Equation: Generally expressed as $S = cA^z$ or in log-transformed linear form as $(S)=k+z.{log}(A)$ , where $k={log}(c)$ .

• Historical Context:     * Watson (1859): Produced the first species-area curve.     * Arrhenius (1921): Formalized the relationship using data from weeds on Stockholm islands.

• Empirical Evidence: This pattern is consistent across diverse taxa and geographies, including birds on continents (Chile, California, South Africa) and Antillean vertebrates.

Island Biogeography Theory (IBT)

• Developed by Robert MacArthur and E.O. Wilson (1967) to explain why larger or less isolated areas support more species.

• Equilibrium Model: Species richness ($ext{S}$) is determined by the balance between two dynamic rates:     

• * Immigration Rate: Decreases as the number of species on the island increases because fewer newcomers represent new species.    

•  * Extinction Rate: Increases as species richness increases due to competition and smaller population sizes.

• Equilibrium ($\hat{S}$): The point where the immigration rate equals the extinction rate.

• Predictors of Richness:   

•   * Area Effect: Larger islands have lower extinction rates, resulting in a higher equilibrium species richness ($\hat{S}$) compared to small islands.   

•   * Isolation Effect: Islands near a mainland source have higher immigration rates, resulting in a higher $\hat{S}$ than far, isolated islands.

Predicting Extinction and Biodiversity Change

• SAR is used to predict the biological impact of habitat loss or land extension (e.g., Egmont National Park, New Zealand).

• Estimation Formula: Proposed by Pimm and Askins (1995):     $\frac{S_{new}}{S_{orig}} = (\frac{A_{new}}{A_{orig}})^z$

• Calculations with $z \approx 0.25$:     * Habitat Loss: If the area is reduced by half ($0.5$), the proportion of species remaining is approximately $(0.5)^{0.25} = 0.84$.     * Area Extension: If the area is doubled ($2$), the proportional species richness increases to approximately $(2)^{0.25} = 1.19$.

detailed

The Species-Area Relationship (SAR)

• The species-area relationship is a vital principle in macroecology that establishes how the number of species ($S$) is related to the area ($A$) they inhabit. It highlights the intrinsic connection between biodiversity and land area, providing insights into ecological patterns and conservation.

• Power Law Equation: The relationship is commonly represented by the power law equation $S = cA^z$, where $c$ is a constant representing the number of species in a unit area, and $z$ is the scaling exponent that indicates how species richness changes with area. The log-transformed linear form of this equation is expressed as $(S)=k+z.{ m log}(A)$, where $k={ m log}(c)$. This transformation facilitates the analysis of the data, making it easier to observe trends and relationships.

• Historical Context:
    - Watson (1859): The concept of the species-area relationship was first introduced by Watson, who produced the initial species-area curve, which illustrated this relationship.In this early work, he recognized that larger areas tend to support more species.   - Arrhenius (1921): Furthering this idea, Arrhenius formalized the relationship through extensive data collection, particularly focusing on flora on the islands of Stockholm. His work laid the foundation for future ecological studies and reinforced the significance of land area in biodiversity.

• Empirical Evidence: The SAR has been found to be consistent across various taxa and geographical locations. Studies illustrate that birds on continents in places like Chile, California, and South Africa, as well as Antillean vertebrates, follow this predictable pattern. This universality underscores the importance of considering area when assessing biodiversity and ecological health.

Island Biogeography Theory (IBT)

• Developed in 1967 by Robert MacArthur and E.O. Wilson, IBT elucidates why larger or less isolated areas tend to support more species. It combines concepts of ecology, evolution, and geography, providing a theoretical framework for understanding species distribution.

• Equilibrium Model: The species richness ($S$) on islands is determined by the dynamic interplay between two rates:
    - Immigration Rate: This rate declines as the number of species on the island increases because the likelihood of new species arriving diminishes; established species occupy available niches.   - Extinction Rate: Conversely, the extinction rate rises with species richness due to increased competition for resources and the challenges posed by smaller population sizes.

• Equilibrium ($ext{S}$): The equilibrium point is reached when the immigration rate equals the extinction rate, resulting in a stable number of species on the island. This dynamic equilibrium reflects the balance between incoming and outgoing species.

• Predictors of Richness:
    - Area Effect: Larger islands tend to have lower extinction rates, which in turn leads to a higher equilibrium species richness ($ext{S}$) in comparison to smaller islands. This is because the larger area can support greater population sizes, reducing the likelihood of extinction.
    - Isolation Effect: Islands that are closer to mainland sources experience higher immigration rates, which allows these islands to attain a higher $S$ than those located farther away. The distance from source populations significantly influences species turnover and richness.

Predicting Extinction and Biodiversity Change

• The species-area relationship serves as a crucial tool for predicting the biological consequences of habitat loss or land extension, illustrated through the context of Egmont National Park in New Zealand, which showcases the critical role of habitat preservation in maintaining biodiversity.

• Estimation Formula: Proposed by Pimm and Askins (1995), the formula for estimating species changes in response to area modifications is given by $\frac{S_{new}}{S_{orig}} = \left(\frac{A_{new}}{A_{orig}}\right)^z$. This formula enables ecologists to predict how changes in area can directly affect species numbers.

• Calculations with $z \approx 0.25$:
    - Habitat Loss: For instance, if an area is halved ($0.5$), the remaining proportion of species is approximately $(0.5)^{0.25} \approx 0.84$, indicating a substantial loss in biodiversity.   - Area Extension: Conversely, if the area is doubled ($2$), the species richness is predicted to increase to approximately $(2)^{0.25} \approx 1.19$, showcasing that increasing habitat area can enhance biodiversity significantly.