Biodiversity on island chains: Neutral model simulations

A neutral ecology model is simulated on an island chain, in which neighboring islands can exchange individuals but only the first island is able to receive immigrants from a metacommunity. It is found by several measures that $\alpha$-diversity decreases along the chain. Subtle changes in taxon abundance distributions can be detected when islands in the chain are compared to diversity-matched single islands. The island chain is found to have unexpectedly rich dynamics. Significant $\beta$-diversity correlations are found between islands in the chain, which are absent between diversity-matched single islands. The results potentially apply to human microbial biodiversity and biogeography and suggest that measurements of interindividual and intraindividual $\beta$-diversity may give insights into microbial community assembly mechanisms.

Figure 1

Candidate explanations for a variation in human microbial diversity based on stochastic community assembly and the theory of island biogeography: (a) variable immigration rate model and (b) island chain model.

Figure 2

(Color online) Aspects of diversity on island chains of length $n$: (a) diversity index $⟨D⟩$, (b) number of taxa $⟨K⟩$, (c) monodominance probability $⟨{\varphi }_J⟩$, and (d) ${\mu }_{\text{eff}}$ for equivalent single islands calculated from Eq. (14). The dashed lines in (b) and (c) are the $⟨D⟩$-matched single island results for $n=9$.

Figure 3

(Color online) Abundance distributions for the odd-numbered islands in an island chain of length $n=9$: (a) the probability $⟨p\left(\omega \right)⟩$ that a randomly selected individual belongs to a taxon of relative abundance $\omega$ and (b) the cumulative distribution function of the same. The results (solid lines) are compared to the theoretical expectations for $⟨D⟩$-matched single islands calculated from Eq. (9) (dashed lines).

Figure 4

(Color online) Preston plots of $⟨{\varphi }_k⟩$, binned by octave, for odd-numbered islands in an island chain of length $n=9$. The results (solid lines) are compared to the theoretical expectations for $⟨D⟩$-matched single islands calculated from Eq. (8) (dashed lines).

Figure 5

(Color online) Diversity variation along a chain of $n=9$ islands as measured by ${\mu }_{\text{eff}}$ normalized by $J{m}_2$: (a) varying $m_2$ only at fixed $J$ (the inset shows the same data without the normalization), (b) varying $m_1=m_2$ at fixed $J$, and (c) varying $m_1=m_2=1/J$. The dashed line in (c) is ${\mu }_{\text{eff}}=e^{-0.3n}$.

Figure 6

(Color online) Heat maps of two measures of diversity correlations between pairs of islands in a chain of length $n=9$: (a) the normalized codominance index $⟨D^{\left(rs\right)}⟩/{⟨D⟩}_M$ and (b) the comonodominance correlation function defined in Eq. (16) (note the logarithmic color scale). Other parameters are as for Fig. 3. In (b) a cell is colored white if there are 10 or fewer instances that are comonodominated out of ${10}^5$ samples.

Figure 7

(Color online) Autocorrelation functions on island chains: (a) for the odd-numbered islands in a chain of length $n=9$ and (b) for the last island in chains of varying length $n$. A factor $1/n$ is included in the time scale for convenience. The dotted line in (b) is Eq. (13) for a single island. The inset in (b) shows $m_{\text{eff}}^{-1/2}$ as a function of $n$, where $m_{\text{eff}}$ is determined by fitting the data in the main plot to an exponential decay; see also Table . Other parameters are as for Fig. 3.

Figure 8

(Color online) Autocorrelation functions for the first island in island chains of varying length $n$. The dotted line is Eq. (13) for a single island. Other parameters are as for Fig. 3.

Figure 9

(Color online) Approach to steady state for the central island of a chain of length $n$ islands starting from either a completely monodominated state (lower curves) or a flat abundance distribution (upper curves; flat means the $N_i$ are equalized subject to ${\sum }_{i=1}^K{N}_i=J$). The $n=1$ case is for a single island. Time is scaled by the terminal relaxation time $1/m_{\text{eff}}$ (see Table ). Other parameters are as for Fig. 3.