Philippa Kaur

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Study populations and sequencing strategyDNA libraries were prepared for 1261 D. sylvestris individuals from 115 populations (5–20 individuals per population) under a modified protocol49 of the Illumina Nextera DNA library preparation kit (Supplementary Methods S1.1, Supplementary Data 1). Individuals were indexed with unique dual-indexes (IDT Illumina Nextera 10nt UDI – 384 set) from Integrated DNA Technologies Co, to avoid index-hopping50. Libraries were sequenced (150 bp paired-end sequencing) in four lanes of an Illumina NovaSeq 6000 machine at Novogene Co. This resulted in an average coverage of ca. 2x per individual. Sequenced individuals were trimmed for adapter sequences (Trimmomatic version 0.3551), mapped (BWA-MEM version 0.7.1752,53) against a reference assembly54 (ca. 440 Mb), had duplicates marked and removed (Picard Toolkit version 2.0.1; http://broadinstitute.github.io/picard), locally realigned around indels (GATK version 3.555), recalibrated for base quality scores (ATLAS version 0.956) and had overlapping read pairs clipped (bamUtil version 1.0.1457) (Supplementary Methods S1.1). Population genetic analyses were performed on the resultant BAM files via genotype likelihoods (ANGSD version 0.93358 and ATLAS versions 0.9–1.056), to accommodate the propagation of uncertainty from the raw sequence data to population genetic inference.Population genetic structure and biogeographic barriersTo investigate the genetic structure of our samples (Fig. 2A, Supplementary Fig. S2), we performed principal component analyses (PCA) on all 1261 samples (“full” dataset) via PCAngsd version 0.9859, following conversion of the mapped sequence data to ANGSD genotype likelihoods in Beagle format (Supplementary Methods S1.2). To visualise PCA results in space (Supplementary Fig. S4), individuals’ principal components were projected on a map, spatially interpolated (linear interpolation, akima R package version 0.6.260) and had the first two principal components represented as green and blue colour channels. Given that uneven sampling can bias the inference of structure in PCA, PCA was also performed on a balanced dataset comprising a common, down-sampled size of 125 individuals per geographic region (“balanced” dataset; Fig. 2B, Supplementary Fig. S3; Supplementary Methods S1.2; Supplementary Data 1). Individual admixture proportions and ancestral allele frequencies were estimated using PCAngsd (-admix model) for K = 2–6, using the balanced dataset to avoid potential biases related to imbalanced sampling22,23 and an automatic search for the optimal sparseness regularisation parameter (alpha) soft-capped to 10,000 (Supplementary Methods S1.2). To visualise ancestry proportions in space, population ancestry proportions were spatially interpolated (kriging) via code modified from Ref. 61 (Supplementary Fig. S5).To test if between-lineage admixture underlies admixture patterns inferred by PCAngsd or if the data is better explained by alternative scenarios such as recent bottlenecks, we used chromosome painting and patterns of allele sharing to construct painting palettes via the programmes MixPainter and badMIXTURE (unlinked model)28 and compared this to the PCAngsd-inferred palettes (Fig. 2B, C; Supplementary Methods S1.2). We referred to patterns of residuals between these palettes to inform of the most likely underlying demographic scenario. For assessing Alpine–Balkan palette residuals (and hence admixture), 65 individuals each from the French Alps (inferred as pure Alpine ancestry in PCAngsd), Monte Baldo (inferred with both Alpine and Balkan ancestries in PCAngsd) and Julian Alps (inferred as pure Balkan ancestry in PCAngsd) were analysed under K = 2 in PCAngsd and badMIXTURE (Fig. 2C). For assessing Apennine–Balkan admixture, 22 individuals each from the French pre-Alps (inferred as pure Apennine ancestry in PCAngsd), Tuscany (inferred with both Apennine and Balkan ancestries in PCAngsd) and Julian Alps (inferred as pure Balkan ancestry in PCAngsd) were analysed under K = 2 in PCAngsd and badMIXTURE.To construct a genetic distance tree (Supplementary Fig. S1), we first calculated pairwise genetic distances between 549 individuals (5 individuals per population for all populations) using ATLAS, employing a distance measure (weight) reflective of the number of alleles differing between the genotypes (Supplementary Methods S1.2; Supplementary Data 1). A tree was constructed from the resultant distance matrix via an initial topology defined by the BioNJ algorithm with subsequent topological moves performed via Subtree Pruning and Regrafting (SPR) in FastME version 2.1.6.162. This matrix of pairwise genetic distances was also used as input for analyses of effective migration and effective diversity surfaces in EEMS25. EEMS was run setting the number of modelled demes to 1000 (Fig. 2A, Supplementary Fig. S8). For each case, ten independent Markov chain Monte Carlo (MCMC) chains comprising 5 million iterations each were run, with a 1 million iteration burn-in, retaining every 10,000th iteration. Biogeographic barriers (Fig. 2A, Supplementary Fig. S7) were further identified via applying Monmonier’s algorithm24 on a valuated graph constructed via Delauney triangulation of population geographic coordinates, with edge values reflecting population pairwise FST; via the adegenet R package version 2.1.163. FST between all population pairs were calculated via ANGSD, employing a common sample size of 5 individuals per population (Supplementary Fig. S6; Supplementary Methods S1.2; Supplementary Data 1). 100 bootstrap runs were performed to generate a heatmap of genetic boundaries in space, from which a weighted mean line was drawn (Supplementary Fig. S7). All analyses in ANGSD were performed with the GATK (-GL 2) model, as we noticed irregularities in the site frequency spectra (SFS) with the SAMtools (-GL 1) model similar to that reported in Ref. 58 with particular BAM files. All analyses described above were performed on the full genome.Ancestral sequence reconstructionTo acquire ancestral states and polarise site-frequency spectra for use in the directionality index ψ and demographic inference, we reconstructed ancestral genome sequences at each node of the phylogenetic tree of 9 Dianthus species: D. carthusianorum, D. deltoides, D. glacialis, D. sylvestris (Apennine lineage), D. lusitanus, D. pungens, D. superbus alpestris, D. superbus superbus, and D. sylvestris (Alpine lineage). This tree topology was extracted from a detailed reconstruction of Dianthus phylogeny based on 30 taxa by Fior et al. (Fior, Luqman, Scharmann, Zemp, Zoller, Pålsson, Gargano, Wegmann & Widmer; paper in preparation) (Supplementary Methods S1.3). For ancestral sequence reconstruction, one individual per species was sequenced at medium coverage (ca. 10x), trimmed (Trimmomatic), mapped against the D. sylvestris reference assembly (BWA-MEM) and had overlapping read pairs clipped (bamUtil) (Supplementary Methods S1.3). For each species, we then generated a species-specific FASTA using GATK FastaAlternateReferenceMaker. This was achieved by replacing the reference bases at polymorphic sites with species-specific variants as identified by freebayes64 (version 1.3.1; default parameters), while masking (i.e., setting as “N”) sites (i) with zero depth and (ii) that didn’t pass the applied variant filtering criteria (i.e., that are not confidently called as polymorphic; Supplementary Methods S1.3). Species FASTA files were then combined into a multi-sample FASTA. Using this, we probabilistically reconstructed ancestral sequences at each node of the tree via PHAST (version 1.4) prequel65, using a tree model produced by PHAST phylofit under a REV substitution model and the specified tree topology (Supplementary Methods S1.3). Ancestral sequence FASTA files were then generated from the prequel results using a custom script.Expansion signalTo calculate the population pairwise directionality index ψ for the Alpine lineage, we utilised equation 1b from Peter and Slatkin (2013)31, which defines ψ in terms of the two-population site frequency spectrum (2D-SFS) (Supplementary Methods S1.4). 2D-SFS between all population pairs (10 individuals per population; Supplementary Data 1) were estimated via ANGSD and realSFS66 (Supplementary Methods S1.4), for unfolded spectra. Unfolding of spectra was achieved via polarisation with respect to the ancestral state of sites defined at the D. sylvestris (Apennine lineage) – D. sylvestris (Alpine lineage) ancestral node. Correlation of pairwise ψ and (great-circle) distance matrices was tested via a Mantel test (10,000 permutations). To infer the geographic origin of the expansion (Fig. 3), we employed a time difference of arrival (TDOA) algorithm following Peter and Slatkin (2013);31 performed via the rangeExpansion R package version 0.0.0.900031,67. We further estimated the strength of the founder of this expansion using the same package.Demographic inferenceTo evaluate the demographic history of D. sylvestris, a set of candidate demographic models was formulated. To constrain the topology of tested models, we first inferred the phylogenetic tree of the three identified evolutionary lineages of D. sylvestris (Alpine, Apennine and Balkan) as embedded within the larger phylogeny of the Eurasian Dianthus clade (note that the phylogeny from Fior et al. (Fior, Luqman, Scharmann, Zemp, Zoller, Pålsson, Gargano, Wegmann & Widmer; paper in preparation) excludes Balkan representatives of D. sylvestris). Trees were inferred based on low-coverage whole-genome sequence data of 1–2 representatives from each D. sylvestris lineage, together with whole-genome sequence data of 7 other Dianthus species, namely D. carthusianorum, D. deltoides, D. glacialis, D. lusitanus, D. pungens, D. superbus alpestris and D. superbus superbus, that were used to root the D. sylvestris clade (Supplementary Methods S1.5). We estimated distance-based phylogenies using ngsDist68 that accommodates genotype likelihoods in the estimation of genetic distances (Supplementary Methods S1.5). Genetic distances were calculated via two approaches: (i) genome-wide and (ii) along 10 kb windows. For the former, 110 bootstrap replicates were calculated by re-sampling over similar-sized genomic blocks. For the alternative strategy based on 10 kb windows, window trees were combined using ASTRAL-III version 5.6.369 to generate a genome-wide consensus tree accounting for potential gene tree discordance (Supplementary Methods S1.5). Trees were constructed from matrices of genetic distances from initial topologies defined by the BioNJ algorithm with subsequent topological moves performed via Subtree Pruning and Regrafting (SPR) in FastME version 2.1.6.162. We rooted all resultant phylogenetic trees with D. deltoides as the outgroup70. Both approaches recovered a topology with the Balkan lineage diverging prior to the Apennine and Alpine lineages (Supplementary Fig. S9). This taxon topology for D. sylvestris was supported by high ASTRAL-III posterior probabilities ( >99%), ASTRAL-III quartet scores ( >0.5) and bootstrap values ( >99%). Topologies deeper in the tree were less well-resolved (with quartet scores More

Modular components of the DFTe energy functionalThe central ingredient of DFTe is an energy functional E, assembled according to Eq. (1). The methodology of DFTe can be understood by inspecting the dispersal and environmental energies in Eqs. (2) and (3) without interactions. In our first case study, illustrated in Fig. 2 and Supplementary Fig. 2, we demonstrate that equation (3), in conjunction with Eq. (2), can realistically describe the influence of the environment on species’ distributions. Mechanisms that alter the trade-off between dispersal and environment can be introduced as part of Eint. For instance, back reactions on the environment could be modelled with a bifunctional Ebr[Venv, n] that yields the equilibrated modified environment ({V}_{s}^{{{{{{{{rm{env}}}}}}}}}+delta {E}_{{{{{{{{rm{br}}}}}}}}}[{{{{{{{{bf{V}}}}}}}}}^{{{{{{{{rm{env}}}}}}}}},{{{{{{{bf{n}}}}}}}}]/delta {n}_{s}({{{{{{{bf{r}}}}}}}})), cf. Eq. (5).In the following we make explicit the interaction and resource energies that enter Eq. (1) and are used in our case studies of Figs. 2–7. We let Eint[n] include all possible bipartite interactions$${E}_{gamma }[{{{{{{{bf{n}}}}}}}}]=mathop{sum }limits_{{s,{s}^{{prime} }!=!1}atop {{s}^{{prime} }ne s}}^{S}{int}_{A}({{{{{{{rm{d}}}}}}}}{{{{{{{bf{r}}}}}}}})({{{{{{{rm{d}}}}}}}}{{{{{{{{bf{r}}}}}}}}}^{{prime} }){n}_{s}{({{{{{{{bf{r}}}}}}}})}^{{alpha }_{s}},{gamma }_{s{s}^{{prime} }}({{{{{{{bf{r}}}}}}}},, {{{{{{{{bf{r}}}}}}}}}^{{prime} }){n}_{{s}^{{prime} }}{({{{{{{{{bf{r}}}}}}}}}^{{prime} })}^{{beta }_{{s}^{{prime} }}},$$
(6)
which include amensalism, commensalism, mutualism, and so forth. Here, ({alpha }_{s},, {beta }_{{s}^{{prime} }}ge 0), and the interaction kernels ({gamma }_{s{s}^{{prime} }}) are assembled from fitness proxies of species s and ({s}^{{prime} }) (Supplementary Table 1). Higher-order interactions can be introduced, for example, through (i) terms like ({n}_{s},{gamma }_{s{s}^{{prime} }},{n}_{{s}^{{prime} }},{gamma }_{{s}^{{prime} }{s}^{{primeprime} }}^{{prime} },{n}_{{s}^{{primeprime} }}) that build on pairwise interactions or (ii) genuinely multipartite expressions like ({gamma }_{s{s}^{{prime} }{s}^{{primeprime} }}{n}_{s},,{n}_{{s}^{{prime} }},{n}_{{s}^{{primeprime} }}). Multi-partite interactions based on bipartite interactions do not seem to be an uncommon scenario48. However, there may be systems where nonzero coefficients ({gamma }_{s{s}^{{prime} }{s}^{{primeprime} }}) couple all species. This poses a challenge for mechanistic theories in general. Then, ‘simpler subsystems’ that have to be included in the DFTe workflow of Fig. 1a can only refer to situations where other energy components are absent, such as resource terms or complex environments. For example, the coefficients ({gamma }_{s{s}^{{prime} }{s}^{{primeprime} }}) could be extracted in an experiment with a controlled simple environment and then used to model the interacting species in a real-world setting. For (({alpha }_{s},, {beta }_{{s}^{{prime} }})=(1,1)) we identify the contact interaction in physics as ({gamma }_{s{s}^{{prime} }}propto delta ({{{{{{{bf{r}}}}}}}}-{{{{{{{{bf{r}}}}}}}}}^{{prime} })) with the two-dimensional delta function δ( ), while the Coulomb interaction amounts to setting ({gamma }_{s{s}^{{prime} }}propto 1/|{{{{{{{bf{r}}}}}}}}-{{{{{{{{bf{r}}}}}}}}}^{{prime} }|). The mechanistic effect of these interaction kernels on the density distributions is the same in ecology as it is in physics—a mathematical insight that inspired us to build ecological analogues to the phenomenology of quantum gases, which feature functionals of the kind in Eq. (6). Note that we do not introduce any quantum effects into ecology despite the fact that the mathematical structure of DFTe is borrowed in part from quantum physics. While the contact interaction is a suitable candidate for plants and especially microbes52, we expect long-range interactions (for example, repulsion of Coulomb type) to be more appropriate for species with long-range sensors, such as eyes. Both types of interactions feature in describing the ecosystems addressed in this work.In a natural setting the equilibrium abundances are ultimately constrained by the accessible resources. It is within these limits of resource availability that environment as well as intra- and inter-specific interactions can shape the density distributions. An energy term for penalising over- and underconsumption of resources is thus of central importance. Each species consumes resources from some of the K provided resources, indexed by k. A subset of species consumes the locally available resource density ρk(r) according to the resource requirements νks, which represent the absolute amount of resource k consumed by one individual (or aggregated constituent) of species s. The simple quadratic functional$${E}_{{{{{{{{rm{Res}}}}}}}}}[{{{{{{{bf{n}}}}}}}}]={int}_{A}({{{{{{{rm{d}}}}}}}}{{{{{{{bf{r}}}}}}}})mathop{sum }limits_{k=1}^{K}{{{{{{{{mathcal{L}}}}}}}}}_{k}left({{{{{{{bf{n}}}}}}}},, {rho }_{k}right)equiv zeta {int}_{A}({{{{{{{rm{d}}}}}}}}{{{{{{{bf{r}}}}}}}})mathop{sum }limits_{k=1}^{K}{w}_{k}({{{{{{{bf{r}}}}}}}}){left[mathop{sum }limits_{s=1}^{S}{nu }_{ks}{n}_{s}({{{{{{{bf{r}}}}}}}})-{rho }_{k}({{{{{{{bf{r}}}}}}}})right]}^{2}$$
(7)
proves appropriate. Here, νksns is the portion of resource density ρk that is consumed by species s. That is, νks  > 0 indicates that s requires resource k. If Eq. (7) is the total energy functional, then a single-species system with a single resource equilibrates with density n1(r) = ρ1(r)/ν11 at every position r, and additional DFTe energy components would modify this equilibrium. Predator–prey relationships are introduced by making species k a resource ({rho }_{k}=left]{n}_{k}right[), where (left]nright[) declares n a constant w.r.t. the functional differentiation of E, that is, the predator tends to align with the prey, not the prey with the predator. In view of the energy minimisation, the quadratic term in Eq. (7) entails that regions of low resource density ρk are less important than regions of high ρk. The different resources k have the same ability to limit the abundances, such that the limiting resource k = l at r has to come with the largest of weights wl(r), irrespective of the absolute amounts of resources at r. For example, the weights wk have to ensure that an essential but scarce mineral has (a priori) the same ability to limit the abundances as a resource like water, which might be abundant in absolute terms. To that end, we specify the weights$${w}_{k}({{{{{{{bf{r}}}}}}}})=frac{1}{{bar{rho }}_{k}^{2}}mathop{sum}limits_{s}eta ({nu }_{ks})exp left[sigma left(frac{{lambda }_{ks}}{{lambda }_{ls}}-1right)right],$$
(8)
which are inspired by the smooth minimum function, where σ  λls irrelevant at r. Using ({E}_{{{{{{{{rm{Res}}}}}}}}}), we show that an analytically solvable minimal example of two amensalistically interacting species already exhibits a plethora of resource-dependent equilibrium states (see Supplementary Notes and Supplementary Fig. 1).We specify the DFTe energy functional in Eq. (1) by summing Eqs. (2), (3), (6), and (7) and by (optionally) constraining the abundances to N via Lagrange multipliers μ:$$E[{{{{{{{bf{n}}}}}}}},, {{{{{{{boldsymbol{mu }}}}}}}}]({{{{{{{bf{N}}}}}}}}) equiv E[{{{{{{{bf{n}}}}}}}}]+{E}_{{{{{{{{boldsymbol{mu }}}}}}}}}[{{{{{{{bf{n}}}}}}}}]({{{{{{{bf{N}}}}}}}})\ equiv {E}_{{{{{{{{rm{dis}}}}}}}}}[{{{{{{{bf{n}}}}}}}}]+{E}_{{{{{{{{rm{env}}}}}}}}}[{{{{{{{bf{n}}}}}}}}]+{E}_{gamma }[{{{{{{{bf{n}}}}}}}}]+{E}_{{{{{{{{rm{Res}}}}}}}}}[{{{{{{{bf{n}}}}}}}}]+mathop{sum }limits_{s=1}^{S}{mu }_{s}left({N}_{s}-{int}_{A}({{{{{{{rm{d}}}}}}}}{{{{{{{bf{r}}}}}}}}),{n}_{s}right).$$
(9)
Uniform situations are characterised by spatially constant ingredients ns = Ns/A, ρk = Rk/A, coefficients τs, etc. for the DFTe energy, such that Eq. (9) reduces to a function E(N) with building blocks$${E}_{{{{{{{{rm{dis}}}}}}}}}longrightarrow frac{1}{2,A}mathop{sum }limits_{s=1}^{S}{tau }_{s},{N}_{s}^{2},$$
(10)
$${E}_{{{{{{{{rm{env}}}}}}}}}longrightarrow mathop{sum }limits_{s=1}^{S}{V}_{s}^{{{{{{{{rm{env}}}}}}}}},{N}_{s},$$
(11)
$${E}_{gamma }longrightarrow mathop{sum }limits_{{s,{s}^{{prime} }!=!1}atop {{s}^{{prime} }ne s}}^{S}frac{{N}_{s}^{{alpha }_{s}},{gamma }_{s{s}^{{prime} }},{N}_{{s}^{{prime} }}^{{beta }_{{s}^{{prime} }}}}{{A}^{{alpha }_{s}+{beta }_{{s}^{{prime} }}-1}},$$
(12)
$${E}_{{{{{{{{rm{Res}}}}}}}}}longrightarrow Amathop{sum }limits_{k=1}^{K}{{{{{{{{mathcal{L}}}}}}}}}_{k}left({{{{{{{bf{N}}}}}}}}/A,, {R}_{k}/Aright).$$
(13)
Ecosystem equilibria from the DFTe energy functionalThe general form of Eq. (9) gives rise to two types of minimisers (viz., equilibria): First, we term$${{{{{{{mathcal{H}}}}}}}}({{{{{{{bf{N}}}}}}}})equiv E[tilde{{{{{{{{bf{n}}}}}}}}}]equiv mathop{min }limits_{{{{{{{{bf{n}}}}}}}}}left{E[{{{{{{{bf{n}}}}}}}}],left|,{int}_{A}({{{{{{{rm{d}}}}}}}}{{{{{{{bf{r}}}}}}}}),{{{{{{{bf{n}}}}}}}}({{{{{{{bf{r}}}}}}}})={{{{{{{bf{N}}}}}}}},{{{{{{{rm{(fixed)}}}}}}}}right.right}$$
(14)
the ‘DFTe hypersurface’, with (tilde{{{{{{{{bf{n}}}}}}}}}) the energy-minimising spatial density profiles for given (fixed) N. Second, the ecosystem equilibrium is attained at the equilibrium abundances (hat{{{{{{{{bf{N}}}}}}}}}={int}_{A}({{{{{{{rm{d}}}}}}}}{{{{{{{bf{r}}}}}}}}),hat{{{{{{{{bf{n}}}}}}}}}({{{{{{{bf{r}}}}}}}})), which yield the global energy minimum$${{{{{{{mathcal{H}}}}}}}}(hat{{{{{{{{bf{N}}}}}}}}})=mathop{min }limits_{{{{{{{{bf{N}}}}}}}}},{{{{{{{mathcal{H}}}}}}}}({{{{{{{bf{N}}}}}}}}),$$
(15)
where the minimisation samples all admissible abundances, that is, ({{{{{{{bf{N}}}}}}}}in {left({{mathbb{R}}}_{0}^{+}right)}^{times S}) if no further constraints are imposed.The direct minimisation of E[n] is most practical for uniform systems, which only require us to minimise E(N) over an S-dimensional space of abundances. For the general nonuniform case, we adopt a two-step strategy that reflects Eqs. (14) and (15). First, we obtain the equilibrated density distributions on ({{{{{{{mathcal{H}}}}}}}}) for fixed N from the computational DPFT framework26,27,28,29,30,31. Second, a conjugate gradient descent searches ({{{{{{{mathcal{H}}}}}}}}({{{{{{{bf{N}}}}}}}})) for the global minimiser (hat{{{{{{{{bf{N}}}}}}}}}). Technically, we perform the computationally more efficient descent in μ-space. Local minima are frequently encountered, and we identify the best candidate for the global minimum from many individual runs that are initialised with random μ. Note that system realisations with energies close to the global minimum, especially local minima, are likely observable in reality, assuming that the system can equilibrate at all. There is always an equilibrium if the energy functional is bounded from below, together with the fact that the support (abundances/densities) of the energy functional is finite in any practical application. If some DFTe energy components are chosen (too) negative, the system can be unstable, in which case the energy functional has no minimum and is inappropriate for modelling the equilibrium in question. This means that another energy functional has to be considered, or, in the worst case, that DFTe is incapable of simulating this system. We also caution that no numerical optimisation algorithms for non-convex black-box functions can guarantee to find the global minimum, not even approximately. Without analytically available characteristics of the global minimum, all one may hope for are candidates of the minimiser, and those may not even be local minima—there is no way to be certain that an optimum proposed by a numerical optimisation algorithm is stable.Density-potential functional theory (DPFT) in Thomas–Fermi (TF) approximationDefining$${V}_{s}({{{{{{{bf{r}}}}}}}})={mu }_{s}-frac{delta {E}_{{{{{{{{rm{dis}}}}}}}}}[{{{{{{{bf{n}}}}}}}}]}{delta {n}_{s}({{{{{{{bf{r}}}}}}}})}$$
(16)
for all s, we obtain the reversible Legendre transform$${E}_{{{{{{{{rm{dis}}}}}}}}}^{{{{{{{{rm{L}}}}}}}}}[{{{{{{{bf{V}}}}}}}}-{{{{{{{boldsymbol{mu }}}}}}}}]={E}_{{{{{{{{rm{dis}}}}}}}}}[{{{{{{{bf{n}}}}}}}}]+mathop{sum }limits_{s=1}^{S}{int}_{A}({{{{{{{rm{d}}}}}}}}{{{{{{{bf{r}}}}}}}}),({V}_{s}-{mu }_{s}),{n}_{s}$$
(17)
of the dispersal energy and thereby supplement the total energy with the additional variables V:$$E[{{{{{{{bf{V}}}}}}}},, {{{{{{{bf{n}}}}}}}},, {{{{{{{boldsymbol{mu }}}}}}}}]({{{{{{{bf{N}}}}}}}})={E}_{{{{{{{{rm{dis}}}}}}}}}^{{{{{{{{rm{L}}}}}}}}}[{{{{{{{bf{V}}}}}}}}-{{{{{{{boldsymbol{mu }}}}}}}}]-{int}_{A}({{{{{{{rm{d}}}}}}}}{{{{{{{bf{r}}}}}}}}),{{{{{{{bf{n}}}}}}}}cdot ({{{{{{{bf{V}}}}}}}}-{{{{{{{{bf{V}}}}}}}}}^{{{{{{{{rm{env}}}}}}}}})+{E}_{{{{{{{{rm{int}}}}}}}}}[{{{{{{{bf{n}}}}}}}}]+{{{{{{{boldsymbol{mu }}}}}}}}cdot {{{{{{{bf{N}}}}}}}}.$$
(18)
This density-potential functional is equivalent to (but more flexible than) the density-only functional E[n,  μ](N). The minimisers of E[n] are thus among the stationary points of Eq. (18) and are obtained by solving$${n}_{s}[{V}_{s}-{mu }_{s}]({{{{{{{bf{r}}}}}}}})=frac{delta {E}_{{{{{{{{rm{dis}}}}}}}}}^{{{{{{{{rm{L}}}}}}}}}[{V}_{s}-{mu }_{s}]}{delta {V}_{s}({{{{{{{bf{r}}}}}}}})}$$
(19)
and$${V}_{s}[{{{{{{{bf{n}}}}}}}}]({{{{{{{bf{r}}}}}}}})={V}_{s}^{{{{{{{{rm{env}}}}}}}}}({{{{{{{bf{r}}}}}}}})+frac{delta {E}_{{{{{{{{rm{int}}}}}}}}}[{{{{{{{bf{n}}}}}}}}]}{delta {n}_{s}({{{{{{{bf{r}}}}}}}})}$$
(20)
self-consistently for all ns while enforcing ∫A(dr) ns(r) = Ns. Specifically, starting from V(0) = Venv, such that ({n}_{s}^{(0)}={n}_{s}[{V}_{s}^{(0)}-{mu }_{s}^{(0)}]), we iterate$${n}_{s}^{(i)}mathop{longrightarrow }limits^{{{{{{{{rm{equation}}}}}}}},(20)}{V}_{s}^{(i+1)}={V}_{s}[{{{{{{{{bf{n}}}}}}}}}^{(i)}]mathop{longrightarrow }limits^{{{{{{{{rm{equation}}}}}}}},(19)}{n}_{s}^{(i+1)}=(1-{theta }_{s}),{n}_{s}^{(i)}+{theta }_{s},{n}_{s}left[{V}_{s}^{(i+1)}-{mu }_{s}^{(i+1)}right]$$
(21)
until all ns are converged sufficiently. This self-consistent loop establishes a trade-off between dispersal energy and effective environment V by forcing an initial out-of-equilibrium density distribution to equilibrate at fixed N. We adjust ({mu }_{s}^{(i)}) in each iteration i such that ({n}_{s}^{(i)}) integrates to Ns. Small enough density admixtures, with 0  More

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Extraction of total active proteomes from sediment samplesWe sampled 14 sediments along the coastlines of the Irish Sea, the Mediterranean Sea, and the Red Sea (from 16°N to 53°N), applying uniform sampling and storage procedures. Location details and sediment temperature fluctuations are summarized in Supplementary Table S1. We collected sediments (5 Kg) in triplicate and extracted the total proteins using a well-established microbial detachment procedure67, with some modifications. We mixed 100 g of sediment with 300 ml of sterilized saline solution (5 mM sodium pyrophosphate and 35 g L−1 of NaCl) containing 150 mg L−1 of Tween 80 (from Merck Life Science S.L.U., Madrid, Spain) in an ice water bath. After re-suspension, samples were kept in a water bath ultra-sonicator (Bandelin SONOREX, Berlin, Germany) on ice and sonicated (60 W output) for 120 min. We repeated this procedure twice, with an ice water bath incubation of 60 min between each cycle. We then centrifuged the samples at 500 g for 15 min at 4 °C to remove the sediments in a centrifuge 5810 R (Eppendorf AG, Hamburg, Germany). Supernatants were carefully transferred to a new tube, minimizing disruption of the sediments, and the resulting supernatants were centrifuged at 13,000 g for 15 min at 4 °C to produce microbial cell pellets. We used the resulting cell mix to extract the total protein by mixing the cells with 1.2 ml BugBuster® Protein Extraction Reagent (Novagen, Darmstadt, Germany) for 30 min with shaking (250 rpm). Subsequently, samples were disrupted by sonication using a pin Sonicator® 3000 (Misonix, New Highway Farmingdale, NY, USA) for a total time of 2 min (10 watts) on ice (4 cycles × 0.5 min with 1 min ice-cooling between each cycle). Extracts were centrifuged for 10 min at 12,000 g at 4 °C to separate cellular debris and intact cells. Supernatants were carefully aspirated (to avoid disturbing the pellet), transferred to new tubes, and stored at –80 °C until use. The protein solution was filtered at 15 °C for 7 h using Vivaspin filters (Sartorius, Goettingen, Germany) with a molecular weight (MW) cut-off of 3,000 Da to concentrate the proteins up to a final concentration of 10 mg ml−1, according to the Bradford Protein Assay (Bio-Rad Laboratories, S.A., Madrid, Spain)68. The average total amount of proteins extracted per each 100 g of sediment was 612 µg (interquartile range, 31 µg, see details in Supplementary Fig. S2). In all cases, extensive dialysis of protein solutions against 40 mM 4-(2-hydroxyethyl)-1-piperazineethanesulfonic acid (HEPES) buffer was performed using a Pur-A-LyzerTM Maxi 1200 dialysis kit (Merck Life Science S.L.U., Madrid, Spain)69, and active proteins stored at a concentration of 10 mg ml−1at –86 °C until use. As reported previously70, 2DE was performed using GE Healthcare reagents and equipment, 11 cm IPG strips in the pH range of 3–10 and molecular weight ranging from 10 to 250 kDa (Precision Plus Protein Dual Color Standards #1610374, Bio-Rad Laboratories, S.A., Madrid, Spain). The 2-DE was performed using a validated pooling strategy71, in which proteins extracted from three independent biological replicates (i.e., sediments) were mixed in equal amounts and a total of 150 µg of protein were further loaded per gel. Staining was performed with SYPRO Ruby Protein Gel Stain (Invitrogen, Waltham, MA, USA). The two-dimensional SDS-PAGE (12% acrylamide) gels of extracted proteins are reported in Supplementary Fig. S2 (original gels in Source Data). The same protocol was applied to extract and analyse by SDS-PAGE the total active proteins extracted from sediment samples with different temperature variability levels (HTV, ITV, and LTV) collected in the Red Sea (Supplementary Table S4). The total amount of protein extracted per each 100 g of sediment is given in Supplementary Table S8. Coomassie-stained one-dimension SDS-PAGE (1-DE) gels of extracted proteins are shown in Supplementary Fig. S9 (original gel in Source Data).Source, expression and purification of esterases and EXDOs from a wide geographical rangeWe recovered 83 enzymes (78 esterases and 5 EXDO) from microbial communities inhabiting marine sediments across ten distinct locations from the latitudinal transect described above: Ancona harbour (Anc), Priolo Gargallo (Pri), Gulf of Genoa, Messina harbour (Mes), Milazo harbour (Mil), Mar Chica lagoon (MCh), Bizerte lagoon (Biz), El-Max site (ElMax), Gulf of Aqaba (Aq), and Menai Strait (MS); further details are provided in Supplementary Data S3. Sources of the enzymes were the corresponding shotgun metagenomes (see Supplementary Table S3) and the metagenome clone libraries generated from the extracted DNA71. The sediment sample from the Gulf of Genoa was not used for activity tests and metaproteome analysis because no raw sample material was available; however, because of the possibility to access its shotgun metagenome (see Supplementary Table S3) and a metagenome clone library72, we used the sample for screening esterases to incorporate an additional latitude in our transect. In the case of Menai Strait (Irish Sea), five additional esterases were retrieved from a metagenome obtained from enriched cultures prepared with samples collected on 22nd June 2019 from Menai Strait (School of Ocean Sciences, Bangor University, St. George’s Pier, Menai Bridge, N53°13′31.3″; W4°09′33.3”). The water temperature was 14 °C and the salinity was 32 p.s.u. Two enrichment cultures were set up at 20 °C: (i) SW: seawater enrichment with 0.1% lignin; the enrichment was set up using 50 ml of the sample as inoculum with the addition of 0.1% lignin (Sigma-Aldrich, Gillingham, United Kingdom) (w/v); (ii) AW: algal surface wash-off in seawater, enriched with 0.1% lignin; the enrichment was set up using 50 ml of surface wash-off after mixing of ca. 10 g of Fucus (brown algae) in the seawater and removal of plant tissue, 0.1% lignin (w/v) was added. After 92 days of incubation, 5 ml of each enrichment cultures were transferred into the new flask containing 45 ml autoclaved and filtered seawater with 0.1% lignin. This procedure was repeated on days 185 and 260, and the incubation was stopped on day 365. The DNA was extracted using 12 months using MetaGnome extraction kit (EpiCentre, Biotechnologies, Madison, WI, USA), sequenced on Illumina MiSeq™ platform (Illumina Inc., San Diego, CA, USA) using paired-end 250 bp reads at the Centre for Environmental Biotechnology (Bangor, UK), and sequencing reads were processed and analysed as described previously73.The screening, cloning and activity of a subset of 35 identified esterases have been reported previously72. The remaining 48 enzymes are reported for the first time in this study and were identified using naive and in silico metagenomic approaches, as detailed below. The environmental site from which each enzyme originated and the method employed for its identification are detailed in Supplementary Data S3. For naive screens addressing the recovery of new sequences encoding esterases and EXDO, the large-insert pCCFOS1 fosmid libraries made using the corresponding DNA samples, the CopyControl Fosmid Library Kit (Epicentre Biotechnologies, Madison, WI, USA) and the Escherichia coli EPI300-T1R strain were used. The nucleic acid extraction, construction and the functional screens of such libraries have been previously described72. In brief, fosmid clones were plated onto large (22.5 × 22.5 cm) Petri plates with Luria Bertani (LB) agar containing chloramphenicol (12.5 µg ml−1) and induction solution (Epicentre Biotechnologies; WI, USA), at a quantity recommended by the supplier to induce a high fosmid copy number. Clones were scored by the ability to hydrolyze α-naphthyl acetate and tributyrin (for esterase activity), and catechol (for EXDO activity)72,74. Positive clones presumed to contain esterases and EXDOs were selected, and their DNA inserts were sequenced using a MiSeq Sequencing System (Illumina, San Diego, USA) with a 2 × 150-bp sequencing v2 kit at Lifesequencing S.L. (Valencia, Spain). After sequencing, the reads were quality-filtered and assembled to generate nonredundant meta-sequences, and genes were predicted and annotated via BLASTP and the PSI-BLAST tool72. For in silico screens, addressing the recovery of new sequences encoding esterases, the predicted protein-coding genes, obtained after the sequencing of DNA material from resident microbial communities in each of the samples, were used. The meta-sequences are available from the National Center for Biotechnology Information (NCBI) nonredundant public database (accession numbers reported in Supplementary Data S3). Protein-coding genes identified from the DNA inserts of positive clones (naive screen) or from the meta-sequences were screened for enzymes of interest using the Blastp algorithm via the DIAMOND v2.0.9 program with default parameters (percentage of identity ≥60%; alignment length ≥70; e-value ≤1e−5)29, against the Lipase Engineering sequence databases (to screen for esterases) and AromaDeg database (for EXDO)74. Since the collection of sediments across locations experiencing different MATs was limited by our sampling capacity, to expand our range of exploration at a global scale and to validate our dataset, we added our single enzyme analysis to the seawater metagenomes retrieved from the Tara Ocean Expedition database (accession number in Supplementary Data S4). Due to the volume of sequences generated, this database provides access to a large number of enzymes, including those studied here through homology search. Esterases were selected as target sequences, and the following pipeline was used. First, we selected a sequence encoding an esterase reported as one of the most substrate-ambiguous esterases out of 145 tested (EH1, Protein Data Bank acc. nr. 5JD4) and well-distributed in the marine environment72. Second, we performed a homology search of this sequence against the Tara Ocean metagenome21 to retrieve similar sequences, using the Blastp algorithm via the DIAMOND v2.0.9 program30 (e-value 98% using SDS-PAGE analysis in a Mini PROTEAN electrophoresis system (Bio-Rad Laboratories, S.A., Madrid, Spain). Purified protein was stored at –86 °C until use at a concentration of 10 mg ml−1 in 40 mM HEPES buffer (pH 7.0). A total of approximately 5–40 mg of total purified recombinant protein was obtained from 1 L of culture. Supplementary Fig. S1 illustrates a schematic representation of the pipeline implemented in this work to investigate enzyme activities in a large set of marine samples, starting from samples collected (sediments) and available metagenomes.Enzyme activity assessmentsAll substrates used for activity tests were of the highest purity and, if not indicated otherwise, were obtained from Merck Life Science S.L.U. (Madrid, Spain): 4-nitrophenyl-propionate (ref. MFCD00024664), 4-nitrophenyl phosphate (ref. 487663), 4-nitrophenyl β-D-galactose (ref. N1252), bis(p-nitrophenyl) phosphate (ref. 123943), benzaldehyde (ref. B1334), 2-(4-nitrophenyl)ethan-1-amine (ref. 184802-5G), pyridoxal phosphate (ref. P9255), acetophenone (ref. A10701), NADPH (ref. N5130) and catechol (ref. PHL82372). We directly tested total protein extracts for esterase, phosphatase, beta-galactosidase, and nuclease activity using 4-nitrophenyl-propionate, 4-nitrophenyl phosphate, 4-nitrophenyl β-D-galactose, and bis(p-nitrophenyl) phosphate, respectively, by following the production of 4-nitrophenol at 348 nm (extinction coefficient [ε], 4147 M−1 cm−1), as previously described69. For determination: [total protein]: 5 μg ml−1; [substrate]: 0.8 mM; reaction volume: 200 μl; T: 4–85 °C; and pH: 8.0 (50 mM Tris-HCl buffer). The hydrolysis of 4-nitrophenyl-propionate was used to determine, under these standard conditions, the effects of temperature on the purified esterase. Transaminase activity was determined using benzaldehyde as amine acceptor, 2-(4-nitrophenyl)ethan-1-amine as amine donor, and pyridoxal phosphate as a cofactor, by following the production of a colour amine at 600 nm (extinction coefficient, 537 M−1 cm−1), as previously described75. For determination, [total protein]: 5 μg ml−1; [substrates]: 25 mM; [pyridoxal phosphate]: 1 mM; reaction volume: 200 μL; T: 4-85 °C; and pH: 8.0 (50 mM Tris-HCl buffer). Aldo-keto reductase activity was determined using acetophenone as a substrate and NADPH as a cofactor, by following the consumption of NADPH at 340 nm (extinction coefficient, 6220 M−1 cm−1), as described76. For determination, [total protein]: 5 μg ml−1; [substrate]: 1 mM; [cofactor]: 1 mM; reaction volume: 200 μL; T: 4–85 °C; and pH: 8.0 (50 mM Tris-HCl buffer). We determined EXDO activity using catechol as substrate, by following the increase of absorbance at 375 nm of the ring fission products (extinction coefficient, 36000 M−1 cm−1), as previously described74. For determination, [protein]: 5 μg ml−1; [catechol]: 0.5 mM; reaction volume: 200 μL; T: 4–85 °C; and pH: 8.0 (50 mM Tris-HCl buffer). The hydrolysis of catechol was used to determine, under these standard conditions, the effects of temperature on the purified EXDOs. All measurements were performed in 96-well plates (ref. 655801, Greiner Bio-One GmbH, Kremsmünster, Austria), in biological triplicates over 180 min in a Synergy HT Multi-Mode Microplate Reader (Biotek Instruments, Winooski, VT, USA) in continuous mode (measurements every 30 s) and determining the absorbance per minute from the slopes generated and applying the formula (1). All values were corrected for nonenzymatic transformation.$${Rate}left(frac{mu {mol}}{{{min }}{mg},{protein}}right)= frac{frac{triangle {{{{{rm{Abs}}}}}}}{{{min }}}}{{{{{{rm{varepsilon }}}}}},{{{{{rm{M}}}}}}-1{{{{{rm{cm}}}}}}-1}*frac{1}{0.4,{cm}}*frac{{10}^{6},mu M}{1{{{{{rm{M}}}}}}}\ *0.0002,L*frac{1}{{mg},{protein}}$$
(1)
Shotgun proteomicsProteomics was performed by using total active proteins (extracted as above), which were then subjected to protein precipitation, protein digestion and Liquid Chromatography-Electrospray Ionization Tandem Mass Spectrometric (LC-ESI-MS/MS) analysis, as previously described77. High-quality reference metagenomes corresponding to each sample (BioProject number in Supplementary Table S3) were used for protein calling, with a threshold of only one identified peptide per protein identification because False Discovery Rates (FDR) controlled experiments counter-intuitively suffer from the two-peptide rule. The confidence interval for protein identification was set to ≥95% (p  50 °C for which the second phase transition was chosen to focus on the decomposition of the core. It is important to note that applying CNA to MD simulations at room temperature may lead to an evening out of Tp values for esterases that transition around this temperature, i.e., systems with a Tp at or below room temperature might all be influenced similarly by loosening their bonding network. By contrast, systems with a transition temperature at or above room temperature would still be discriminated against. The data generated in this study for analyzing Tp values have been deposited at researchdata.hhu.de under accession code DOI: 10.25838/d5p-42101 [https://doi.org/10.25838/d5p-42].Relationship of temperature-induced changes in enzymeRelationship between MAT and enzyme response to temperature (i.e., Topt, Td and Tp) were evaluated by performing linear regression in R. In the case of enzymes retrieved from the Tara ocean dataset we calculated first the break point (flexus) using the package segmented in R102 and then we computed separately the linear model describing the two linear regressions before and after the breakpoint. To evaluate the possible relation between enzyme thermal response and other environmental parameters, salinity and pH data were retrieved from Bio-ORACLE52 using GPS coordinates of each location.Environmental characterization and sediment collection from different temperature variability levels in the Red SeaWe recorded the temperatures of surface sediments from March 2015 to September 2016 along the coast of the Red Sea using HOBO data loggers (Onset, USA) in nine stations located at 3, 25, and 50 m depth. Details on the location, depth and temperature fluctuations of the studied sediments are reported in Supplementary Table S4 and Source Data. We first assess the differences in the homogeneity of the temperature variance in the three types of sediments to evaluate the magnitude of thermal variation and then we test the difference among their MATs using a non-parametric ANOVA (Dunnett’s multiple comparisons tests). We identified three different levels of temperature variability (Fig. 3a–c; Supplementary Table S5): high, intermediate, and low thermal variability (HTV, ITV, and LTV, respectively), where sediments experienced temperature variations of 12.8 °C, 8.8 °C, and 6.7 °C, respectively. From each station, we sampled 200 g of surface sediment (0–5 cm depth) in triplicate in August and December 2015 with a Van der Venn grab (1 dm3) equipped with a MicroCat 250 Seabird CTD (Conductivity, Temperature, Depth), which was assembled on board the research vessel R/V Explorer (KAUST). During sampling, we measured the temperature of the sediments and the water layer covering the sediments using a digital thermometer and the CTD, respectively. We conducted all sampling in compliance with the guidelines specified by KAUST and Saudi Arabian authorities.Sediment processing for analysis of bacterial communitiesFrom each sample (in triplicate), we immediately removed subsamples of sediment (n = 54, ~10 g) and stored them at –20 °C for molecular analysis. Separately, sediment 25 ± 1 g was transferred to 50 ml tubes and added 30 ml of filtered (0.2 µm) water from the Red Sea. The tubes were shaken at 500 rpm for one hour and then centrifuged them at 300 g for 15 min to detach the microbial cells in the sediments without affecting their vitality103,104. The supernatant containing the extracted cells was collected in sterile tubes and was immediately used to measure microbial growth rates.Evaluation of bacterial growth in sediments at different temperaturesWe evaluated the microbial growth rate of the heterotrophic community extracted from the sediments under HTV, ITV, and LTV at 10 °C, 20 °C, 30 °C, 40 °C and 50 °C, using Marine Broth as the cultivation medium (Zobell Marine Broth 2216) supplemented with 0.1 g/L cycloheximide; a rich-medium was selected to avoid the nutrient limitation effect that can affect bacterial physiology63,105. We inoculated 96-well plates with 200 µl of cultivation medium and 25 µl of the cell suspension extracted from the sediments. We inoculated the three biological replicates from each station and each level of temperature variability in eight wells, giving a total of 72 wells for each plate, with 24 wells used as a negative control inoculated with water. We assembled a total of three plates for each incubation temperature from August and December. Plates were spectrophotometrically measured at 3 h intervals using an optical density of 600 nm (Spectramax® M5) for 72 h. Wells with optical density 90%) for further analysis (Supplementary Tables S9 and S10). We calculated the compositional similarity matrix (Bray-Curtis of the log-transformed OTU table) with Primer 6109. Using the same software, canonical analysis of principal coordinates (CAP)110 was used to compare the temperature variability samples (temperature variability levels: HTV, ITV, and LTV; season levels: August and December) based on the compositional similarity matrix. We applied permutational multivariate analyses of variance to the matrix (PERMANOVA; main and multiple comparison tests). We tested the occurrence of thermal-decay patterns in sediments with different temperature variability levels using linear regression (Prism 9.2 software, La Jolla California USA, www.graphpad.com) between the bacterial community similarities (Bray-Curtis) and the temperature differences among sediments (∆T°C) at the time of sampling. We calculated alphadiversity indices (richness and evenness) using the paleontological statistics (PAST) software, and their correlation with temperature was modelled using linear regression in Prism 9.2. Spearman correlation among temperature and relative abundance of OTUs within each sediment sample was evaluated; OTUs were classified based on their positive (enriched) and negative (depleted) correlation with sediment temperature.Reporting summaryFurther information on research design is available in the Nature Portfolio Reporting Summary linked to this article. More

Global genetic structure of the pathogen tracks the historical spread of wheatWe assessed the evolutionary trajectory of the pathogen in conjunction with the history of global wheat cultivation (Fig. 1a). For this, we assembled a worldwide collection of Z. tritici isolates from naturally infected fields (Fig. 1b). We selected isolates covering most wheat production areas, both in the center of origin of the crop (i.e., the Fertile Crescent in the Middle East), and in areas where wheat was introduced during the last millennia (i.e., Europe and North Africa), or last centuries (i.e., the Americas and Oceania; Fig. 1c). We called variants in a set of 1109 high-quality short-read resequencing datasets (Supplementary Data 1, 2) covering 42 countries and a broad range of climates. Using a joint genotyping approach, we produced raw variant calls mapped to the telomere-to-telomere assembled reference genome IPO323. To assess genotyping accuracy, we used eight isolates with replicate sequencing data to analyze discrepancies. We adjusted quality thresholds targeting specifically the type of genotyping errors observed in our data set (Fig. S1). The improved filtering yielded 8,406,818 high-confidence short variants (short indels and SNPs). The final variant set included 5,578,488 biallelic SNPs corresponding to 14.1% of the genome.Fig. 1: Global sampling of the wheat pathogen Zymoseptoria tritici retracing the historical spread of its host.a Schematic representation of the introduction of wheat across continents. b Septoria tritici blotch symptoms caused by Z. tritici on wheat leaves. Pictures taken by B. A. McDonald, ETH Zurich. c Map of the sampling scheme for the global collection of 1109 isolates for whole-genome sequencing.Full size imageWe tested whether global diversity patterns of pathogen populations are likely a consequence of the history of wheat cultivation. We first performed unsupervised clustering of genotypes and identified eleven well-supported clusters (Fig. 2a, Figs. S2,3). Over 90% of the genotypes were clearly assigned to a single cluster (Fig. 2a, Supplementary Data 3). Two clusters were identified among genotypes originating from the pathogen center of origin, distinguishing collections from Iran and Middle Eastern regions. Genotypes from Africa and Europe split into two distinct genetic clusters without any apparent secondary structure within clusters. This lack of any fine-scale structure is remarkable given the extensive geographic sampling of European genotypes and suggests extensive gene flow within the continent. Genotypes from Oceania grouped into three distinct clusters marked by collections from Tasmania, the Australian mainland, and New Zealand. Genotypes from North America formed two clusters along a North-South separation. Finally, South American genotypes formed two clusters split along the Andes (Chile versus Argentina and Uruguay). Some uncertainty exists in the assessment of regional population structure by low coverage of major wheat-producing countries such as Russia and Ukraine. Septoria tritici blotch is only sporadically reported in China. In complementary analyses, we found that a phylogenetic network accounting for the high frequency of recombination consistently reflected the global population structure (Fig. S4). A principal component analysis of all genotypes confirmed the nested genetic structure with differentiation at the continent level, subdivisions within some continents and the existence of admixed genotypes (Fig. 2b, Fig. S5).Fig. 2: Global genetic structure based on 1109 genomes.a Map of the genetic clustering based on a thinned genome-wide SNP dataset using sNMF. Each color represents a different genetic cluster, and the sizes of the slices represent the average attribution to the cluster across the isolates from each location. Fractions representing less than 10% of all genotypes of a location were colored in grey to improve clarity. The large pie chart outside of the map represents the proportion of isolates assigned clearly (≥75%) to a single genetic cluster (pure; in teal) and isolates identified as hybrids (admixed) between clusters (in yellow). Names of the clusters include an abbreviation of continents and a more precise geographical location (MEA: Middle East and Africa; NA: North America; SA: South America; OC: Oceania). b Principal component analysis, showing the first and second component (PCs) based on a subset of variants. Colors and shapes indicate the genomic clusters identified with the sNMF method (with hybrids in grey). The marginal distributions represent the distribution for each PC. PCs 1 to 8 are shown in Fig S4. c Population tree based on Treemix, rooted using two genomes from the sister species Z. passerinii and Z. ardabiliae. The colors are the same as in the previous panels and only samples which were fully assigned to a cluster were used. d Diversity estimated with using pi per genetic cluster. The boxplots are ordered according to the tree of panel. c. The lower and upper hinges correspond to the first and third quartiles, the whiskers to the largest value are within 1.5 times the inter-quartile range, and the central horizontal line defines the median. e Linkage disequilibrium (r2) between variants per genetic cluster. Colors are identical among panels.Full size imageWe analyzed the history of population splits and admixture using allele frequency information (Fig. 2c). The analyses largely supported a genetic structure shaped by the introduction of wheat across continents. The historical relationships between clusters show an early divergence of the Middle Eastern and North African clusters matching the early introduction of agriculture in these regions. Populations in Europe and the Americas share a similar time point of divergence consistent with extensive contributions of European genotypes to the Western hemisphere. Oceanian groups have diverged as a single branch from genotypes most closely related to extant European populations. Matching the introduction of wheat to Oceania from the European continent, the Australian and New Zealand pathogen populations share a common origin rooted in European genetic diversity. Populations from Australia show also a striking loss of diversity and higher linkage disequilibrium compared to European diversity consistent with a significant founder effect (Fig. 2d, e). Similarly, populations in South and North America have reduced genetic diversity compared to extant European populations as suggested previously based on Sanger sequencing16. The highest diversity was found in populations from Africa and the Middle East closest to the center of origin. Overall, the global genetic structure of the pathogen reveals multiple founder events associated with the introduction of wheat to new continents.Ongoing gene flow among regions should lead to admixed genotypes. We found that nearly 10% of all analyzed genotypes showed contributions from at least two clusters. The most significant recent gene flow was detected between Middle Eastern/North African clusters and European clusters in North Africa (i.e., Algeria and Tunisia) as well as Southern and Eastern Europe (i.e., France, Italy, Hungary, Ukraine, Portugal, and Spain; Supplementary Data 3). We found a particularly high incidence of recent immigration in a durum wheat population in the south of France. The population consisted only of hybrids or atypical genotypes suggesting either recent migration from North Africa or host specialization on durum wheat varieties. Additionally, we found hybrid genotypes with European ancestry in both North America and in Oceania. The relatively balanced ancestry proportions in these hybrids suggest very recent gene flow dating back to only a few generations. We further investigated past gene flow between clusters by allowing Treemix to infer migration events, thus creating a population network (Fig. S6a–d). Three distinct recent migration events were best explaining the data with specific migration routes from the Middle East/African clusters to North America, from an Australian cluster to South America and between two Oceanian clusters (Fig. S6d). However, the migration events did not affect the overall shape of the inferred population tree (Fig. 2c, Fig. S6b–d). To better understand effects of long-distance gene flow, we investigated the relationship between relatedness among genotypes (i.e., identity-by-state) and geographic distance. At the continent level, we observed a negative relationship between identity-by-state and geographic distance (Fig. S7). The wide distribution of identity-by-state values shows that although closely related isolates tend to be found at closer geographic distance, distantly related isolates can be found at both far and close geographic distances. Long-distance migration events are most likely caused by international trade similar as for other crop pathogens17,18,19. In combination, our findings show an important role of long-distance dispersal impacting the genetic make-up of populations from individual fields to continental scale genetic diversity.Relaxation of genomic defenses against transposable elements concurrent with global spreadTransposable elements (TEs) are drivers of genome evolution. In Z. tritici, TE activity created beneficial mutations for fungicide resistance and virulence on the wheat host20,21. Rapid recent adaptation of the pathogen has benefitted from the activity of TEs with consequences for genome size22. Unchecked transposition of TEs can be deleterious and an array of defenses mechanisms has evolved to counteract their activity both at the genomic and epigenetic level including targeted mutations and silencing23. To analyze the effectiveness of genomic defenses against active TEs, we screened all genomes for evidence of TE insertions. We mapped short-read sequencing data on the reference genome and a species-specific TE sequence library. We classified evidence for TEs in each of the analyzed isolates as reference TEs (i.e. also present in the reference genome) and non-reference TE (i.e. absent). Detected TEs among isolates were binned into loci (width 100 bp) to account for uncertainties about the precise mapping of the insertion point. We found that the frequency spectrum of TE insertions is heavily skewed towards low frequencies with 77% of TE insertions being found in single isolates (~0.1% frequency) and 96% of insertions were found in ten or fewer isolates ( More

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