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Although Malar et al. “do not exclude the possibility that the genes identified by Mateus et al. are involved in mating,” they qualify the homology inference between genes differentially expressed in the co-inoculation treatment and genes involved in mating in other fungal species as “spurious evolutionary relationships” or “not the best ortholog”. Those statements imply that they attach no importance to the demonstrated sequence homology relationships identified in Mateus et al. Orthology does not necessarily imply conservation of gene function and genes with equivalent functions are not necessarily orthologs [3]. Therefore, it is misleading to assume that two genes have the same function when interpreting the role of a “best candidate ortholog” identified in silico. Moreover, relying only on an in silico search for exploring orthologs can lead to serious problems for inferring function as none of the search algorithms are free from bias if subfunctionalization or neofunctionalization events occurred among the homologs.Malar et al. have not considered, or have misunderstood, the experimental evidence on gene expression in interpreting their homology search. It is not surprising that their “best homologs” were not upregulated, because we already saw that those genes were not upregulated in the original dataset. Our approach comprised performing an experiment to identify genes that were specifically upregulated when two isolates coexisted in planta. We then identified their putative function by homology. We did not look at whether the genes were the closest orthologs. However, we discussed the limitations of an homology approach to identify gene function [2]. To our surprise, a consistent set of 20 genes was upregulated in the co-inoculation treatment in different host plants, and 9 of these 20 (upregulated in more than one host plant) shared the common feature of homology to genes involved in different steps of mating in other fungal species (Figs. 3 and 4 of Mateus et al.).Malar et al. claim the identification of hundreds of hits of the 18 genes differentially expressed in Mateus et al. “against the high-quality protein databases from the JGI Mycocosm Rhiir2” (referring to the protein database “Rhiir2” of R. irregularis). In fact, Malar et al. compared the 18 genes against “all protein gene catalogs of fungal species from the JGI fungal genomic resource” comprising 1318 taxa. The interpretation of the number of hits on a such large dataset is misleading because if a gene is highly conserved across the fungal kingdom, we would expect hundreds of hits in this database. In contrast, if an R. irregularis gene is highly specific to the Glomeromycotina taxa, we would expect very few hits (because there are less Glomeromycotina genomes in the database). Consequently, the number of hits in Table 1 from Malar et al. reflect the size of the database used and how conserved a given gene is, rather than whether a gene is from a large gene family. Malar et al. identified the so-called “closest ortholog” in R. irregularis of fungal mating genes from other fungal species by showing the “best hit” using OrthoMCL. However, differentiating paralogs from orthologs is a complicated task, in very distant species, especially if the organisms are highly paralogous. A more cautious analysis for each gene, including a confirmation that they are located in similar genomic locations, would lend more certitude that a given gene could be an ortholog. Consequently, the evaluation of RNA expression of their “best hit” remains incomplete in terms of the effort to find the best orthologs. More

The underpinning method employed to construct a STR may affect the shape, scaling exponent (w), and fit of the STR power function. Here we used three differing approaches to construct STRs; including, what we term in this study, the ‘every possible window’ (EPW) [10], ‘cumulative moving window’ (CMW) [8], and ‘moving window’ (MW) approaches. The differences in each method are extensively detailed in the Material and Methods. The STRs for the bacterial communities within each of the tree-hole islands were plotted, of which all relationships were significant (Fig. 1 and Table S1). Overall, the resulting STR power law exponents (w) were found to range from 0.048 to 0.350 (Fig. 1) and were typically within the exponent ranges observed from meta-analyses of STRs for a wide range of animals, plants, and microbial communities [9,10,11]. However, these values varied by the approach used to construct STRs (Fig. 2A). The EPW based w values ranged from 0.048 to 0.128, with a mean w of 0.088 ± 0.029 (mean ± SD). The CMW w values ranged from 0.073 to 0.150, with a mean w = 0.111 ± 0.029. Whereas, the MW minimum and maximum w values were 0.223 ± 0.350, with a mean of 0.289 ± 0.044 (Fig. 2A). The EPW and CMW w values were significantly lower than the MW w values (Fig. 2A). However, they were not significantly different from each other, despite that EPW values were uniformly lower (Fig. 2A).Fig. 1: Species-time relationships for the tree-hole bacterial communities.A, B, and C represent species–time relationships (STR) constructed using every possible window, cumulative moving window, and moving window approaches, respectively. Given in each instance is the tree-hole number (TH1–TH10) and the STR power law equation. All STRs were significant (P  More

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Study areasNine large forest dynamics plots of areas between 20 and 50 ha were used in the present study (Supplementary Table 1). The forest plots are part of the ForestGEO network4 and are situated in Asia and the Americas at locations ranging in latitude from 9.15° N to 45.55° N. Tree species richness among the plots ranges from 36 to 468. All free-standing individuals with diameter at breast height (dbh) ≥1 cm were mapped, size measured and identified. We focused our analysis here on individuals with dbh ≥ 10 cm (resulting in a sample size of 131,582 individuals) and focal species with more than 50 individuals (resulting in 289 species). The 10 cm size threshold excludes most of the saplings and enables comparisons with previous spatial analyses20,35,47,48. Shrub species were also excluded.Some of our analyses require estimation of the ratio βfi/βff that describes the relative individual-level competitive effect18 of individuals of species i on an individual of the focal species f. We used for this purpose phylogenetic distances49 based on molecular data, given in Myr, that assume that functional traits are phylogenetically conserved19,26,27. In this case, close relatives are predicted to compete more strongly or to share more pests than distant relatives26. To obtain consistent measures among forest plots, phylogenetic similarities were scaled between 0 and 1, with conspecifics set to 1, and a similarity of 0 was assumed for a phylogenetic distance of 1,200 Myr, which was somewhat larger than the maximal observed distance (1,059 Myr). This was necessary to avoid discounting crowding effects from the most distantly related neighbours26.Observed spatial patterns at species-rich forestsFigure 1 and Supplementary Data Table 1 show the intraspecific variation in our three crowding indices nkff, nkfh and nkfβ that can be approximated by gamma distributions. To assess how well the gamma distribution described the observed distribution, we used an error index defined as the sum of the absolute differences of the two cumulative distributions divided by the number of bins (spanning the two distributions). The maximal value of the error index is one, and a smaller value indicates a better fit.Equations (6, 8 and 9) relate the measures of the emerging spatial patterns (that is, kff, kfh and Bf) to macroscale properties and conditions for species coexistence. Even though our multiscale model (equation (7)) is simplified, it allows for a direct comparison with the emerging patterns in our nine fully stem-mapped forest plots. We estimate the key quantities of equations (8) and (9) directly from the forest plot data (Fig. 4), with the exception of the carrying capacities Kf, which were indirectly estimated from the observed species abundances (assuming approximate equilibrium; equation (8) and Supplementary Data Table 1). This allowed us to estimate the feasibility index µf (equation (9)). Because statistical analyses with individual-based neighbourhood models19,26 based on neighbourhood crowding indices have shown that the performance of trees depends on their neighbours for R between 10 and 15 m, we estimate all measures of spatial neighbourhood patterns with a neighbourhood radius of R = 10 m. Analyses with R = 15 or R = 20 gave similar results.The spatial multispecies model and equilibriumWe use a general macroscale model to describe the dynamics of a community of S species:$$frac{{N_fleft( {t + {Delta}t} right) – N_fleft( t right)}}{{{Delta}t}} = N_fleft( t right)left[ {left( {r_f – 1} right) + s_fexp left( { – alpha _{ff}N_fleft( t right) – mathop {sum }limits_{i ne f} alpha _{fi}N_i(t)} right)} right]$$
(11)
where rf is the mean number of recruits per adult of species f within time step Δt, sf is a density-independent background survival rate of species f and the αfi are the population-level interaction coefficients, yielding αff = c γff kff βff and αfi = c γfβ kfh βff Bf (equation (6)). The βfi are the assumed individual-level interaction coefficients between individuals of species i and f; kff = Kff(R) / π R2 and kfh = Kfh(R) / π R2 measure intraspecific clustering and interspecific segregation, respectively, with Kff(R) being the univariate K function for species f and Kfh(R) the bivariate K function describing the pattern of all heterospecifics ‘h’ around individuals of species f. A is the area of the observation window.Following equation (5), Bf can be estimated as$$B_f = frac{{bar n_{fbeta }}}{{bar n_{f{mathrm{h}}}}} = frac{{mathop {sum }nolimits_{i ne f} left[ {ck_{fi}N_ileft( t right)} right]frac{{beta _{fi}}}{{beta _{ff}}}}}{{mathop {sum }nolimits_{i ne f} left[ {ck_{fi}N_ileft( t right)} right]}} = frac{{mathop {sum }nolimits_{i ne f} k_{fi}N_ileft( t right)frac{{beta _{fi}}}{{beta _{ff}}}}}{{k_{f{mathrm{h}}}mathop {sum }nolimits_{i ne f} N_ileft( t right)}},$$
(12)
and is the weighted average of the relative individual-level interaction coefficients βfi/βff between species i and the focal species f, weighted by the mean number of individuals of species i in the neighbourhoods of the individuals of the focal species (that is, c kfi Ni(t)). For competitive interactions, Bf ranges between zero and one; Bf = 1 indicates that heterospecific and conspecific neighbours compete equally, and smaller values of Bf indicate reduced competition with heterospecific neighbours. The denominator can be rewritten in terms of segregation kfh to all heterospecifics and the total number of heterospecifics ∑i≠f Ni(t).The analytical expression of the equilibrium (equation (8)) relies on the assumption that the values of Bf are approximately constant in time. This assumption may not apply in our model during the initial burn-in phase of the simulations if the βfi/βff show large intraspecific variability (Supplementary Text and Figs. 1–5). The underlying mechanism is the central niche effect introduced by Stump45 where a species has reduced average fitness if it has high niche overlap with competitors.Finally, the factors γff = ln(1 + bff βff) (bff βff)−1 and γfβ = ln(1+ bfβ βff) (bfβ βff)−1 describe the influence of the variance-to-mean ratios bff and bfβ of the gamma distribution of the crowding indices nkff and nkfβ, respectively. For high survival rates during one time step (for example, >85%), the values of γff and γfβ are close to one; in this case the exponential function in equation (1a) can be approximated by its linear expansion and γff = γfβ = 1.In equilibrium we have (Nf(t + Δt) ‒ Nf(t))/Δt = 0, which leads, with equation (7), to:$$N_f^{ast} = left( {K_f – frac{{alpha _{f{mathrm{h}}}}}{{alpha _{ff}}}J^{ast} } right) left( {1 – frac{{alpha _{f{mathrm{h}}}}}{{alpha _{ff}}}} right)^{-1}$$
(13)
with (K_f = – {mathrm{ln}}left( {frac{{1 – r_f}}{{s_f}}} right) left( alpha _{ff} right)^{-1}) and the total number of individuals being (J^{ast} = sum _iN_i^{ast}). Rewriting equation (13) yields (frac{K_f}{J^{ast}} = left( frac{N_f^{ast}}{J^{ast}} right) left(1- frac{alpha_{f{mathrm{h}}}}{alpha_{ff}}right) + frac{alpha_{f{mathrm{h}}}}{alpha_{ff}}). For αfh/αff  More