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Self-organized pattern formation increases functional diversity
TL;DR: A food chain model in which autotroph diversity is described by a continuous distribution of a trait that affects both growth rate and defense against a heterotroph is used, thereby maintaining the adaptive potential of communities in an environment threatened by fragmentation and global change.
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Abstract: Self-organized formation of spatial patterns is known from a variety of different ecosystems, yet little is known how these patterns affect functional diversity of local and regional communities. Here we use a food chain model in which autotroph diversity is described by a continuous distribution of a trait that affects both growth rate and defense against a heterotroph. On a single patch, stabilizing selection always promotes the dominance of a single autotroph species. Two alternative community states, with either defended or undefended species, are possible. In a metacommunity context, dispersal can destabilize these states, and complex spatio-temporal patterns emerge. This creates varying selection pressures on the local autotroph communities, which feed back on the trait dynamics. Local functional diversity increases ten-fold compared to a situation without self-organized pattern formation, thereby maintaining the adaptive potential of communities in an environment threatened by fragmentation and global change.
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Figures
Table 1: Description and values of the model parameters. 
Figure 3: The degree of trait diversity maintenance depends on the mobility of the autotrophs. In panel a) the mean trait variance ν across 6 patches is shown as a measure of local diversity, in b) the variance of mean trait values φ̄ signifies regional diversity. Results were obtained as arithmetic means over 100 simulation runs with randomized initial conditions, error bars denote standard errors. In panels c) and d), the fraction of simulation runs in which local (c, mean(ν) > 10−5) or regional (d, var(φ̄) > 10−2) diversity were maintained, are shown. 
Figure 2: Exemplary time series of autotroph biomass densities (top row), mean traits φ̄ (middle row) and trait variances ν (bottom row, y-axes are scaled with the number at the top left corner of the panels) for spatial systems in cases 1 to 4 with 6 patches. In cases 1 and 2, dN = 10−2, in cases 3 and 4, dN = 1. In all four cases, dA = 10−5 and dH = 10−3. ![Figure 1: a) Example of a static Turing pattern. Here, vegetation (green) and bare soil (yellow) form a labyrinth-like pattern (created with the arid ecosystem model in [Rietkerk et al., 2002]). b) Conceptual representation of the local food chain model. The autotroph community exhibits a continuous (logit-normal) distribution of the trait φ, characterized by the mean φ̄ and the variance ν. A low trait value signifies a low attack rate of the heterotrophs (due to high investment into defense by the autotrophs), at the cost of a low maximal growth rate (visualised by thin arrows), whereas a high trait value leads to a high attack rate but also a high maximal growth rate (thick arrows). c) Shape of the trade-off between maximal growth rate r(φ) vs. attack rate a(φ), mediated by the trait φ.](/figures/figure-1-a-example-of-a-static-turing-pattern-here-31rwe87o.png)
Figure 1: a) Example of a static Turing pattern. Here, vegetation (green) and bare soil (yellow) form a labyrinth-like pattern (created with the arid ecosystem model in [Rietkerk et al., 2002]). b) Conceptual representation of the local food chain model. The autotroph community exhibits a continuous (logit-normal) distribution of the trait φ, characterized by the mean φ̄ and the variance ν. A low trait value signifies a low attack rate of the heterotrophs (due to high investment into defense by the autotrophs), at the cost of a low maximal growth rate (visualised by thin arrows), whereas a high trait value leads to a high attack rate but also a high maximal growth rate (thick arrows). c) Shape of the trade-off between maximal growth rate r(φ) vs. attack rate a(φ), mediated by the trait φ. 
Figure 4: Correspondence between Turing instability and local diversity. Panels a) and c) show the maximum eigenvalue and Floquet multiplier, respectively, of the matrices Tk (Eq. (12)), panels b) and d) show on a logarithmic scale the mean trait variance (averaged over patches and simulation runs), .i.e., the local diversity. For a) and b), the undefended attractor is a fixed point (amax = 1.3), for c) and d) it is a limit cycle (amax = 2.0). In both cases, dA = 10−5.
![Figure 1: a) Example of a static Turing pattern. Here, vegetation (green) and bare soil (yellow) form a labyrinth-like pattern (created with the arid ecosystem model in [Rietkerk et al., 2002]). b) Conceptual representation of the local food chain model. The autotroph community exhibits a continuous (logit-normal) distribution of the trait φ, characterized by the mean φ̄ and the variance ν. A low trait value signifies a low attack rate of the heterotrophs (due to high investment into defense by the autotrophs), at the cost of a low maximal growth rate (visualised by thin arrows), whereas a high trait value leads to a high attack rate but also a high maximal growth rate (thick arrows). c) Shape of the trade-off between maximal growth rate r(φ) vs. attack rate a(φ), mediated by the trait φ.](/figures/figure-1-a-example-of-a-static-turing-pattern-here-31rwe87o.webp)
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