Additivity of allopolyploid climatic niches
The null hypothesis of allopolyploid niche additivity (i.e. the combination of diploid progenitors’ niches, thereafter the expected allopolyploid niche) was tested by comparing the observed allopolyploid niche to the expected niche modeled from combined occurrences of both its progenitors. The two metrics D and S of niche overlaps between the observed and expected niches of the allopolyploid species were estimated as before, with niche similarity test for D. Similarly, observed and expected niche centroids and breadths were compared using ANOVA and Tukey tests.
For each allopolyploid species, differences between the observed and the expected climatic niches were decomposed following the USE framework, and niche stability S thus corresponds to the fraction of the observed allopolyploid niche overlapping with the combination of both progenitors’ niches. The fraction of the observed allopolyploid niche deviating from the additivity of progenitors (i.e. niche shift) was decomposed into niche contraction U (i.e. proportion of unoccupied space as compared to expectations) and niche expansion E (i.e. proportion of newly occupied space).
Isolation-by-distance and isolation-by-environment in diploid and allopolyploid species
To what extent demographic vs ecological processes shaped genetic variation was addressed by signals of genetic isolation-by-distancevs isolation-by-environment within each species (Wang et al. 2013). Patterns of isolation-by-distance expected under restricted dispersal of neutral genes were tested by comparing Euclidian geographic and genetic pairwise distances through Mantel tests with 20,000 permutations in vegan . Genetic distances among individuals were estimated using Rousset’s a statistics (analogous to FST/(1-FST)) in SPAGeDi (Hardy & Vekemans 2002).
Patterns of isolation-by-environment expected when selection favors gene exchanges among individuals from similar climatic conditions (Wanget al. 2013; Wang & Bradburd 2014) were tested through partial Mantel tests associating genetic, geographic and climatic distances invegan . Following Legendre & Fortin (2010), correlations of genetic distances with Euclidian distances from PCs of the common climatic space while accounting for joint spatial structure were interpreted as isolation-by-environment. Provided the questioned performance of such tests (e.g. Legendre et al . 2015), corresponding patterns were confirmed through multivariate Redundancy Analysis (RDA) associating individual allelic frequencies to the geographical coordinates and/or coordinates along PCs of the climatic space with 20,000 permutations in the R-package adespatial (Drayet al. 2019).

Results

Species phylogeny and genetic additivity of diploids in allopolyploids
Amplicon sequencing of 402 accessions from the eight diploid-allopolyploid Aegilops species yielded robust allelic variation at plastid loci (Fig. S2) and at 30 low-copy nuclear genes (Text S1, Fig. S3). Phylogenies of plastid and nuclear loci among representative samples resolved species in monophyletic clades and unambiguously related the different allopolyploids to their respective maternal x paternal diploid progenitors (Fig. 2A). Consistent with taxonomy, multi-labeled nuclear species trees accounting for reticulation related Ae. crassa (DDMM) to ancestors of Ae. comosa (MM) and other diploids that have hybridized with Ae. tauschii (DD). Divergent nuclear haplotypes within Ae. crassa(Cr_k2) were related to distinct diploid lineages and included hexaploids (DDDDMM) of more recent origin (Fig. S3 and S4). Phylogenies further supported independent origins of multiple lineages within all allopolyploid species. Nuclear loci indicated an origin of Ae. geniculata (UUMM) combining ancestors of Ae. umbellulata (UU; identified as the maternal progenitor by plastid loci) and of Ae. comosa (MM), with specific samples presenting divergent sequences from distinct diploid lineages and supporting multiple origins of this allopolyploid. Multiple origins of Ae. triuncialis (UUCC) were patent from plastid haplotypes shared with both diploids Ae. caudata (CC) and Ae. umbellulata (UU) and nuclear loci congruently supporting such bidirectional hybridization at the origin of this allopolyploid (Fig. S5). Independent maternal lineages of Ae. cylindrica (DDCC) were supported by distinct plastid haplotypes ofAe. tauschii (DD) and nuclear loci that identified Ae. caudata (CC) as the paternal progenitor. Allopolyploids originated at different times, as indicated by the divergence of their alleles from corresponding diploids (Fig. S3). Cautious interpretations of molecular dating show that allopolyploids Ae. crassa andAe. geniculata originated more than 1 Mya, whereas youngerAe. cylindrica and Ae. triuncialis appeared later (>0.2 Mya) and also went through repeated range contraction-expansion during the late Pleistocene.
Based on this phylogenetic framework, allopolyploid species (exceptAe. crassa whose ancestral maternal progenitor is elusive) were consistent with the expected genetic additivity of their diploid progenitors and presented similar proportions of segregating haplotypes from each subgenome (Table S2). Patterns of genetic additivity were further consistent with the relative age of allopolyploid species, with oldest species such as Ae. geniculata showing 41.9% of haplotypes from both subgenomes having diverged from diploids, whereas youngest species such as Ae. cylindrica presented only 3.6% of derived and mostly (94.3%) conserved haplotypes (Fig. 2B).
Genetic structure within diploid and allopolyploid species
Variation segregating at nuclear loci within species was congruent with the hypothesis of genetic additivity. Proxies of genetic diversity were consistently higher in allopolyploids (AR = 2.3–5.9, h = 0.50-0.63 andv = 0.13-0.017) than in their respective progenitor diploids (AR = 2.78-4.77, h = 0.33-0.50 and v = 0.002-0.007; Table 1). Allopolyploid species showed not only higher phylogenetic diversity (v ) than diploids but also the pattern of fixed heterozygosity (Ho = 0.56-0.66) expected by the strict combination of divergent diploid loci.
To address phylogeographic processes having shaped genetic variation in diploids and allopolyploids, the genetic structure across the distribution range of each species was inferred using STRUCTURE (Fig. 3). Most species presented an optimal number of two or three genetic clusters and high genetic diversity across Anatolia (Fig. S4). Multiple spatially-coherent genetic clusters were co-existing within all species across that region, whereas genetically admixed individuals indicative of secondary contact between intraspecific lineages were mostly reported in the Thyracian plain (between the Balkans and Western Anatolia), the Taurus chain (between Western and Eastern Anatolia) and the Anatolian Diagonal (separating Eastern Anatolia from the Irano-Turanian region). In contrast to expectation based on their relative age, all diploid species presented locally differentiated genetic clusters across their restricted range, whereas polyploid species showed large areas outside Anatolia dominated by specific genetic clusters. Such phylogeographic patterns are consistent with cycles of range contraction-expansion having shaped coherent hotspots and melting spots of genetic diversity among wild wheats.
Climatic niches of diploids and allopolyploids
The climatic niche of each Aegilops species was modeled in a common background based on 20 bioclimatic factors and that summarized 70.69% of the variation along its first two principal components representative of the Mediterranean-temperate vs.Atlantic-continental climatic gradients (Fig. 4).
Comparative niche modeling addressed the hypothesis that allopolyploids are the ecological additivity of diploid species. Climatic niches modeled among the eight species showed specific but consistent D overlap (Fig. S6 and Table S3) and niche stability S values ranging from 0.39 to 0.93 (Fig. 4). Diploid species presented divergent climatic niche centroids, with Ae. tauschii and Ae. umbellulata being more continental than Ae. caudata and Ae. comosa , and relatively low niche breadths (Table S4). In contrast, all allopolyploid species, except Ae. crassa , presented relatively broad climatic niches that were largely coherent with niche additivity of their progenitors (Fig. 4). The observed niche of allopolyploids presented higher similarity to the one predicted based on diploids than expected by chance (Table S3). Alternative insights from bootstraping of observed niche centroids confirmed this pattern with significant but generally low differences to the expected niche centroids based on progenitors (Table S4; Fig. S7). Similarly, independent bioclimatic factors rarely supported different preferences in allopolyploids as compared to diploids (Table S4). Alternative approaches were thus largely congruent and indicate that allopolyploids occupy a combination of climatic ranges from their diploid progenitors.
Decomposition of the climatic niche of allopolyploids as compared to the combination of diploid ones confirmed niche conservatism in allopolyploid wild wheats (Fig. 4). They indeed presented substantial niche stability (S = 0.72-0.93) and limited evidence of niche contraction (U = 0.01-0.18). Evidence of niche expansion (E = 0.06-0.19) indicated that some allopolyploids occupied conditions beyond the combined range of diploid progenitors toward novel temperate or continental climates. Corresponding areas were however mostly located near range margins and were rarely occupied over significant geographic space (Fig. S8), contrasting with predictions that allopolyploids fill a new ecological niche. Only Ae. geniculata showed noticeable niche expansion across aridity gradients of Palestine, suggesting colonization of novel environments.
The geographical projection of modeled niches was coherent with the distribution ranges of each species and, as expected under non-equilibrium, suitable sites were not all occupied (Fig. S9). Large areas with suitable conditions were available for all species in the Iberian Peninsula or North Africa, although only allopolyploids densely occupy such regions. Range filling further assessed how the different species were distributed across space with tolerable conditions and showed that diploids effectively occupied only a low fraction of their suitable areas (0.05 to 0.25) as compared to allopolyploids (0.40 and 0.51; Table 1). Being robust to variable sampling effort (Fig. S10), such estimates indicate a greater filling of suitable space by allopolyploids than diploids.