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Appendix A
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Simulation procedures to assess the performance of the beta-diversity and
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phylogenetic community composition approaches
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The first set of simulations was based on a community matrix of 100 sites and 50
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species, whereas the second set of simulations was based on a grassland plant community
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data set (Kembel and Cahill 2011) containing 76 species distributed across 27
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communities in grasslands in Alberta, Canada. The data set also included five
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environmental variables: habitat type (mixedgrass or fescue grassland), slope, aspect,
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slope position, and moisture regime. All variables were continuous, with the exception of
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habitat type which was coded as either 1 (fescue) or 2 (mixedgrass).
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1 – Generate an environmental vector E (100 communities x 1) containing uniformly
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distributed random values between 0 and 100.
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2 – Generate a phylogenetically structured P vector (50 species x 1) using a Brownian
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evolved “trait”. The trait was generated using the function fastBM in the R package
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phytools (Revell 2012). P was then transformed to vary between -1 and 101.
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3 – Generate a vector h (50 species x 1) containing uniformly distributed random values
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between 0 and 30. These values represent the height (expected maximum abundance) of
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any given species at its optimum.
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4 – Generate a vector  (50 species x 1) containing normally distributed random values
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with standard deviation 10 and a mean tolerance µtol. We considered two simulation
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scenarios in which µtol was set either as 5 or 10, the latter providing a greater tolerance
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and hence a weaker expected signal between species distributions, phylogeny and
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environment.
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5 – Generate a unimodal response for the jth species at the ith site as follows:
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é -(Ei - Pj )2 ù
Lij = h j exp ê
ú
2s 2j
êë
úû
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The values in Lij were the transformed into Poisson deviates in order to generate a
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species distribution abundance matrix. Although the values in L represent abundances,
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we have in this paper considered only the case of presence-absence data and therefore
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values were transformed accordingly.
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We have also considered the situation of two gradients. In this case, we generated
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two independent phylogenetically structured traits (P i1 and Pi2) and two independent
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environmentally structured environments (E i1 and Ei2) and L was generated as follows:
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é -(Ei1 - Pj1 )2 ù
é -(Ei2 - Pj2 )2 ù
Lij = h j exp ê
ú exp ê
ú
2s 2j
2s 2j
êë
úû
êë
úû
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Note that the same tolerance was used for each species in both gradients. In order
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to assess the type I error and statistical power of the two frameworks, we considered four
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scenarios: 1 – both phylogeny and environment were unimportant in structuring L 37
Instead of using a phylogenetically structured trait, we used a P simply containing
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normally distributed values without any phylogenetic signal. After L was generated,
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another E vector also containing uniformly distributed random values between 0 and 100
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was used in the gradient analyses instead. 2 – only environment but not phylogeny was
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important - Instead of using a phylogenetically structured trait, we generated L based on
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a P vector containing normally distributed values without any phylogenetic signal and the
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original E used to generate L was used in the gradient analyses. 3 – only phylogeny but
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not environment structured species distributions – L was generated using the original P
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vector but once L was generated, E was replaced by another randomly generated vector
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that was then used in the gradient analysis instead of the original one. 4 – both phylogeny
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and environment structured species distributions – L was generated using the original P
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and E, which in turn were also used in the gradient analyses. For each scenario, we
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generated 1000 sample matrices with 1 or 2 gradients based on two values for µtol (5 or
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10), giving a total of 16 000 simulations involving the three test procedures (row, column
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and row/column). Given that calculation of the phylogenetic beta-diversity matrices (100
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x 100) was computationally intensive, especially given that they need to be recalculated
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at each permutation involving columns randomizations, we limited the number of
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permutations to 99.
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Using the phylogenetic community composition approach (see results for the
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empirical data set), both the row and column-based permutation test showed a significant
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link between the grassland species distributions, phylogeny, and environmental affinities.
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Moreover, because both the row and column based approaches were significant, we knew
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that both the phylogeny and environment were related to the grassland distribution.
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Because the phylogeny was related to species distributions, we needed to condition
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species distributions on phylogenetic information that was capable of mimicking the
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scenarios used in the first set of simulations: 1 – both phylogeny and environment were
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unimportant in structuring L - we created a vector containing normally distributed values
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without any phylogenetic signal and built a “phylogeny” (dendrogram) based on this
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vector that was then applied in both frameworks; a row permuted version of matrix E
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was used instead of the original matrix of environmental variable. 2 – only environment
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but not phylogeny was important – a random phylogeny was created in the same way as
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the first case, but the original matrix E was used in the gradient analysis. 3 – only
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phylogeny but not environment structured species distributions – we created a vector
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containing normally distributed values with a phylogenetic signal and built a “phylogeny”
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(dendrogram) based on this vector that was then used in the gradient analyses; a row
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permuted version of E was used instead of the original one. 4 – both phylogeny and
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environment structured species distributions – we used a “phylogeny” created in the same
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way as in scenario 3 and E was not manipulated. Two types of phylogenetically
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structured vectors were used in this latter scenario. One containing a weak signal based
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on a “trait” evolved under a Brownian motion model, and another containing a strongly
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phylogenetically conserved trait. The conserved trait was generated by manipulating the
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phylogenetic tree according to Pagel’s (1999) delta transformation. By giving delta a
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value of 0.01, branch lengths were much shorter than the original values and using this
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tree allowed us to generate highly phylogenetically conserved traits. We conducted 1000
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simulations for each scenario. Although the PCC approach is computationally much
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faster, we restricted the number of permutations to 99 so that type I error and power
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estimates (the number of rejections over 1000) were comparable across both frameworks.
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