Figure 1.
Simulation procedure for a simplified scenario with one spatial dimension and one environmental variable.
Note that capitalized variables indicate vectors. After defining the strengths of niche breadth (n) and dispersal breadth (d) the regional species pool phylogeny was generated (shown with 8 species for simplicity), species' global relative abundances (F) were randomly assigned from a lognormal abundance distribution, and species' environmental optima (T) along the environmental axis were evolved while tracking species' range centroids (R) along the spatial dimension. Environmental conditions (E) and spatial positions (S) were then defined for twenty local sites. To assemble a community at site k the environmental condition (Ek) and spatial position (Sk) of site k were compared to the environmental optima (Ti) and range centroid (Ri), respectively, for each species i. From these environmental and spatial differences probabilities were found from Gaussian distributions (blue and red curves), the variances of which were n and d, respectively. A probability of incidence for species i at site k () was then found as the product of the global relative abundance (Fi) and probabilities based on environmental (
) and spatial (
) distances for species i. To generate the vector of relative abundances for site k the regional species pool was then sampled 10,000 times with replacement, where
gave the probability of choosing species i.
Figure 2.
Effects of assembly processes on the relationship between environmental optima and range centroids.
The strengths of environmental filtering, dispersal limitation, and environmental spatial structure constrain the evolutionary-time-scale relationship between species' intrinsic environmental optima (functional trait value) and the spatial position where their abundance is maximized (the range centroid). Simulation output when both processes are strong (n = d = 0.0001; panels A,C) or weak (n = d = 10; panels B,D). The environment has either weak (≈0.3; panels A,B) or strong (
≈0.95; panels C,D) spatial structure. All axes are normalized as standard normal deviates, with mean zero and standard deviation of one. Solid red lines represent the one to one line and solid blue lines are linear regressions. (A) When both processes are strong but there is little environmental spatial structure, a moderately tight relationship emerges between species' trait values and the positions of their range centroids. (C) Increasing the degree of environmental spatial structure leads to a much tighter, one to one relationship. (B,D) Irrespective of how spatially structured the environment is, when both processes are weak there is no relationship between species' trait values and the positions of their range centroid.
Table 1.
Major assumptions and tools used in the theoretical framework developed here.
Table 2.
Idealized trait-space covariance () matrix for the evolution of species environmental optima (Trait) and range centroids (Space).
Figure 3.
Patterns of variance partitioning across combinations of assembly processes.
(Left 2 columns) Interpolated variance partitioning across eleven values each of niche breadth (increasing from left to right on each x-axis) and dispersal breadth (increasing from bottom to top on each y-axis) for three β-diversity metrics. The left column is variance partitioned only to the environment, the right column is variance partitioned only to space. Larger niche breadth results in weaker environmental filtering, and a larger dispersal breadth results in weaker dispersal limitation. The intuitive expectation is that variance partitioned to only the environment should decrease moving from the left to the right within each panel in the left column, and variance partitioned only to space should decrease from the bottom to the top within each panel in the right column. Colors in all panels are scaled the same and both axes are log10-scale. (Far right column) Across all replicate simulations, the ratio of dispersal breadth to niche breadth is plotted against the ratio of variance partitioned to space only and variance partitioned to environment only. Both axes are log10-scale. Solid black lines indicate ratios of one. Points are color-coded by the summed variance explained individually by space and environment. Each panel includes data across the 100 replicate simulations for each combination of dispersal and niche breadths. Results using phylogenetic or functional NN were qualitatively similar to those using phylogenetic or functional SOR and are not shown. See Fig. S1 for phylogenetic and functional PW and the space-or-environment ‘shared’ component of partitioned variance.
Figure 4.
Example of using ‘empirical’ (see text) analyses of β-diversity to infer community assembly processes.
For each β-diversity metric, empirical variance partitioning results are first compared to model-based expectations. The regions of process space where model expectations closely match empirical results for variance partitioned to space (grey) or the environment (black) are shown. Regions where model expectations are consistent with both the space and environmental variance partitioning results are highlighted in red. (A) Results for BC; (B) Results for phylogenetic SOR, where yellow delineates regions of overlap in panel A. (C) Results for functional PW, where yellow delineates the intersection of red and yellow regions in panel B. True values of niche (n) and dispersal breadths (d) must reside where yellow and red intersect in panel C. The actual parameter values in this test case were n = d = 0.0001, consistent with the inference provided by combining taxonomic, phylogenetic and functional β-diversity.