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Cranial myologyThe muscular origin and insertion sites interpreted in the cranium and mandible of each species are identified in Fig. 1; the 3D reconstructed cranial adductor muscles are shown in Fig. 2 (Incisivosaurus and Citipati) and Fig. 3 (Khaan and Conchoraptor).Figure 1Locations of reconstructed jaw adductor muscle origin and insertion sites for Incisivosaurus gauthieri (a-c), Citipati osmolskae (d-f), Khaan mckennai (g-i), and Conchoraptor gracilis (j-l). Crania are shown in dorsolateral view (a,d,g,j) with temporal and postorbital bars removed to better show medial regions within supratemporal fenestra. The left sides of the crania are shown in anteroventral view (b,e,h,k) with lower temporal and postorbital bars removed to better show posterior and lateral regions within supratemporal fenestra. Mandibles shown in dorsolateral view (c,f,i,l), lateral muscle insertions sites are shown on the left rami, medial insertion sites on the right rami. Scale bars 50 mm. Muscle abbreviations given in results section.Full size imageFigure 2Reconstructed jaw adductor musculature of Incisivosaurus gauthieri (a-d) and Citipati osmolskae (e–h) shown complete in lateral view (a,e), anterolateral view with mAMES removed (b,f), posterolateral view with mAME complex removed (c,g), and ventral view with only the mPT muscles (mPTv removed on left). Scale bars 50 mm, legend colour coded to identify individual muscles. Muscle abbreviations given in results section.Full size imageFigure 3Reconstructed jaw adductor musculature of Khaan mckennai (a-d) and Conchoraptor gracilis (e–h) shown complete in lateral view (a,e), anterolateral view with mAMES removed (b,f), posterolateral view with mAME complex removed (c,g), and ventral view with only the mPT muscles (mPTv removed on left). Scale bars 50 mm, legend colour coded to identify individual muscles. Muscle abbreviations given in results section.Full size imagem. adductor mandibulae externus medialis (mAMEM)The origin site of the mAMEM is less clear than others of the mAME group31 and we reconstruct it, as others have done, in the posterior portion of the supratemporal fossa12,13,16 where it is constrained anterolaterally and anteromedially by the positions of mAMES and mAMEP (Fig. 1). This region comprises parts of the squamosal and parietal in all four taxa and is generally vertical, concave, and featureless in all apart from Citipati. In this taxon, within the supratemporal fossa, the squamosals and parietals are flattened and orientated to form a deep and concave platform directly perpendicular to the line of action of this muscle (Fig. 1e).
The extent and direction of the mAMEM body are somewhat constrained in all taxa by the anterior, dorsal, and posterior edges of the squamosal, quadrate flange, and epipterygoid respectively.The insertion sites are typically unclear12,31. The surangular dorsomedially forms a shelf that overhangs the adductor fossa in Citipati, Khaan, and Conchoraptor (potentially taphonomically exaggerated in the latter two). Insertion onto the dorsomedial and posterior margin of the coronoid eminence (along with insertion of the mAMEP onto the eminence) has been suggested for the mAMEM12,13,31,38, but the palatal morphology (especially in the oviraptorids) restricts space around the coronoid eminence so that we do not reconstruct both the mAMEM and mAMEP as inserting in this area. Instead, we reconstruct the mAMEM as inserting on the shelf-like upper part of the surangular’s dorsomedial surface, posterior to the more anterior insertion of the mAMEP, allocating roughly half of the available surface to each (Fig. 1c,f,i,l). This insertion surface is unclear and largely reconstructed in Incisivosaurus where there is less well-defined slight convexity on the upper part of the medial surangular surface (Fig. 1c). This area of the retrodeformed mandible model for Conchoraptor uses material from Khaan and the two are thus similar (Fig. 1i,l).It is possible the mAMEM and mAMEP merged along their path or did indeed both insert in relation to the coronoid eminence39 but ultimately this would not change reconstructed bite force results significantly.m. adductor mandibulae externus profundus (mAMEP)The mAMEP generally has a medial and/or anteromedial origin within the supratemporal fenestra. A vertical crest, similar to that interpreted as the anterior border of the origination site in Carcharodontosaurus and Daspletosaurus31, Allosaurus40, Corythosaurus41, and Erlikosaurus12, is also identified in Citipati19 (Fig. 1d). We interpret it as the boundary between the mAMEP and mPSTs origins. A small sharp prominence, perhaps similar, is present on the lateral surface of the braincase in Incisivosaurus (Fig. 1a). The surface is more featureless in Khaan and Conchoraptor (Fig. 1g,j), so the anterior limit of the mAMEP origin is constrained by the origin area of the mPSTs (in turn based on the extent and position of the laterosphenoid).In Citipati, a pneumatic opening in the posterolateral wall of the parietal (visible at the posterior of the mAMEP origin in Fig. 1d), underneath where the squamosal contacts the parietal to form the posteromedial margins of the supratemporal fenestra, seems to limit the mAMEP origin posteriorly, dividing it from the mAMEM. A similar opening is not as large or obvious in the other taxa, but similar limits to the origination sites are constrained by the geometry of the supratemporal fenestra. The dorsal extent of the origin is also clear in Citipati where a sharp lateral edge, running from the frontal-parietal contact posterolaterally to form the posterior boundary of the supratemporal fossa, separates the dorsal surface of the parietals from their lateral surfaces that contribute to the supratemporal fossa (Fig. 1d). This edge may function for muscle attachment similarly as suggested for a parietal ridge in the oviraptorid Osoko2.We reconstruct the mAMEP inserting more anteriorly than mAMEM on the mandible (Fig. 1c,f,i,l), including around the apex of the coronoid elevation itself, along with the mAMES, specifically on the dorsomedial surface of coronoid prominence31,39.m. adductor mandibulae externus superficialis (mAMES)In all taxa, the mAMES can be reliably hypothesised to originate on the supratemporal bar31 (Fig. 1b,e,h,k). In oviraptorosaurs, this is formed by the postorbital and squamosal. The supratemporal bars in all taxa are mediolaterally flattened, with the medial surface directed slightly ventromedially, more so in Citipati than the others (Fig. 1e). The postorbital bars are concave along almost the entire medial surface in Citipati. In the other taxa, only the squamosal contribution is concave, with the postorbital ramus being flat or perhaps weakly convex in Khaan (Fig. 1h). There are no clear osteological signs of the extent of the mAMES origin site so we restrict it to the medial surfaces of the supratemporal bar as the ventral surface is narrow (as the bars are mediolaterally thin) and the medial surface is slightly orientated in the correct muscle direction in all taxa. The mAMES is reconstructed as originating along the full extent of this medial surface with its anterior and posterior limits constrained by the origins of the mPSTs and mAMEM respectively.The main body of the jugal has a trough-like gently concave medial surface in all taxa (especially so in Conchoraptor where the postorbital process of the jugal also has confluent concavity on its posteromedial surface) that appears like its form would neatly wrap over the exterior of the mAMES as it bulged outwards laterally and followed it anteroventrally on its origin-insertion path.The mAMES likely inserts onto the dorsolateral edge and lateral surface of the surangular31,39, on a shelf running from the coronoid process to the articular (Fig. 1c,f,i,l). This shelf is more strongly defined in the later diverging taxa, especially Citipati (Fig. 1f) and Khaan (Fig. 1i). The mandibles of the oviraptorids bear apically triangular coronoid eminences, which are anteriorly displaced compared to those of other herbivorous dinosaurs. This has been hypothesized to increase mechanical advantage and attachment area for the temporal musculature as an adaptation for a stronger crushing bite3,8,38. The anteriorly displaced coronoid eminence in oviraptorids has been hypothesized to indicate a more anteriorly extending mAMES (as suggested for some ornithischians39,42). The mAMES is reconstructed thus here. The insertion site is constrained ventrally by the reconstructed extent of the mPTv insertion site, and dorsomedially by the insertions of the mAMEM and mAMEP, which insert onto the dorsomedial surface of the surangular.m. adductor mandibulae posterior (mAMP)The mAMP is a well-constrained muscle of the adductor chamber, consistently attaching to the lateral surface of the quadrate in an extant phylogenetic bracket31. We reconstruct the origin site as the lateral surface of the pterygoid flange of the quadrate (Fig. 1), covering most of this broad flat wing but not encroaching on the epipterygoid (where the mPSTp is present) and pterygoids (where the mPTd originates). No clear muscle scar is apparent in any of the studied taxa. The mAMP origin may also have extended posterodorsally onto the confluent lateral surface of the squamosal, where a curved ridge may demark an expanded origin site for the mAMP in Conchoraptor (Fig. 1j)5; Khaan has a similar morphology (Fig. 1g). This expansion is not reconstructed in earnest—the organization of the other muscle volumes, particularly the passage of the mAMEM, would only permit a thin sliver of extra volume to be created on the expanded origin site, not significantly increasing overall volume, direction, or morphology of the mAMP.The mAMP inserts in the adductor fossa on the medial mandibular surface (Fig. 1c,f,i,l), occupying most of its main extent and posterior and ventral margins31. The adductor fossa in the oviraptorids is large and anteriorly displaced19,38,39 and much more significant than that of Incisivosaurus (Fig. 1c).m. pseudotemporalis superficialis (mPSTs)In all four taxa, the mPSTs originates on the anterior and/or anteromedial wall of the supratemporal fenestra. In Citipati, the area is formed predominantly by the capitate process of the laterosphenoid and the posterior portions of the frontal (Fig. 1d). This surface is concave and rugose. The lateral surface of the laterosphenoid is also rugose, indicating a muscle attachment19. The site is bounded laterally by the postorbital, and two ridges may constrain the origin site of the mPSTs 19: a sharp ridge runs posteromedially from the capitate process of the laterosphenoid to the epipterygoid contact, forming the ventral boundary, and a vertical ridge on the medial wall of the supratemporal fossa constrains the origin posteromedially, demarking it from the mAMEM. A triangular anterodorsal-posteroventral sloping surface (where a clear frontoparietal fossa has been lost in derived oviraptorids) extends to the dorsotemporal fossa. The anterodorsal extent of the mPSTs origin site on this surface is unclear. The frontoparietal fossa has been argued as a vascular space in dinosaurs rather than a site of muscle attachment43, and we place the mPSTs similarly (43; Fig. 7 therein), extending into this sloping triangular space but not wholly filling it. We do not reconstruct any attachment of the mPSTs extending onto the frontal processes of the postorbitals.In Khaan, the origin site is less well preserved (Fig. 1g). The mPSTs origin is placed in a similar position to Citipati and may extend slightly onto the lateral surface of parietals which contribute to the area. Similarly, in Conchoraptor (Fig. 1j), there is more of a contribution of the parietal to the anterior wall of supratemporal fenestra, but very little or no contribution of the frontal. In Conchoraptor, the whole origin site is more anteromedially positioned, and exhibits a large smooth exposure of the laterosphenoid. There are no obvious scars or ridges in the above-mentioned area of Khaan and Conchoraptor. In Incisivosaurus, the anterior corner of the supratemporal fossa is narrow and the mPSTs is more anteromedially positioned (Fig. 1a). The origin site likely comprises the laterosphenoid and small parts of the frontal and parietal.The insertion of the mPSTs is likely related to the medial aspect of the coronoid elevation and parts of the medial adductor chamber39. As the medial regions of the coronoid elevation are occupied by the mAMEP in our reconstruction we position the mPSTs, as the deepest temporal muscle, inserting into the anterior portion of the medial mandibular fossa31 and its anterodorsal rim (Fig. 1c,f,i,l).m. pseudotemporalis profundus (mPSTp)The mPSTp likely attached to the epipterygoid when present in dinosaurs31. When first described in detail, the epipterygoid of C. osmolskae (Fig. 1d) was noted as the largest of any known theropod, with a unique strongly twisted body and dorsal tip hosting robust muscle scars19. We therefore locate the mPSTp origin site on the epipterygoid of each taxon with confidence and reconstruct its origin along the length of the epipterygoid, which is present in all four taxa (though partially reconstructed in Khaan and Conchoraptor) (Fig. 1g,j).The insertion site is problematic but based on extant taxa the muscle likely inserted along the medial surface of the coronoid process or surangular 31. As the coronoid process is occupied by the insertions of the mAMES and mAMEP, we position the insertion of the mPSTp dorsomedially on the surangular, occupying the dorsal rim of the mandibular adductor fossa, the position being largely constrained dorsally by the insertions of the mAMEM and mAMEP (Fig. 1c,f,i,l).m. pterygoideus dorsalis (mPTd)The origin site of the mPTd is reconstructed as the linear dorsal surface of the pterygoid in all oviraptorids where a longitudinal concavity runs anteriorly along their length anterior of the pterygoid flange (Khaan has a convex dorsal surface but the origin site is modelled similarly (Fig. 1h), and possibly the anteriormost dorsolateral surface of the pterygoid flange. The site is limited anteriorly and anterolaterally by the palatines and ectopterygoids, onto which no attachment was modelled as they are relatively small and delicate. In Incisivosaurus, the anterior extent of the origin site is constrained by the level of the jugal ramus of the ectopterygoid anterolaterally and the main body of the ectopterygoid laterally to around a longitudinal concavity on the dorsal surface of the pterygoid (Fig. 1a)—there seems very little/no origination on the palatine.The mandibular insertion of the mPTd is commonly regarded to be onto the medial surface of the articular and retroarticular process31. We reconstruct the mPTd in this position (Fig. 1c,f,i,l), inserting in the narrow medial surface of the posterior aspect of the mandibular ramus, under the medial facet of the articular glenoid and posteriorly onto the medial surface of the retroarticular process.m. pterygoideus ventralis (mPTv)The mPTv is well constrained through phylogenetic bracketing and we reconstruct it in the oviraptorids as originating along the ventral surface of the pterygoid, probably also extending onto the ventral aspect of the pterygoid flange31 and posteriorly terminating before the contact with the quadrate. The anterior of the origin is reconstructed as the level of the ectopterygoid contact, with the site entering the longitudinal ventral concavity that is anteriorly confluent with the choanae. In Citipati, the pterygoid flange is noted as reduced compared to typically carnivorous theropods, maintaining a roughly consistent width throughout its length (Fig. 1e), as suggested by19 to indicate a relatively small m. pterygoideus. However, the main pterygoid body of oviraptorids is relatively elongate. This may be an adaptation to open space for an expanded mAME group to insert onto the mandible, whilst maintaining volume of the mPT. The pterygoids of Incisivosaurus are also elongate and reduced in width (Fig. 1b), though not as extreme as in the derived oviraptorids 24. The origin of the mPTv on the pterygoid ventral surface is interpreted as running from the posteroventral margin anteriorly into a trough medial to the ectopterygoid, and lateral of a ventral flange termed the accessory ventral flange by Xu et al.22, terminating anteriorly before the palatine contact.In all taxa, the mPTv wraps around the ventral surface of the mandibular rami and inserts on the broad section of the lateral surface of the mandible (Fig. 1c,f,i,l), predominantly comprising the angular.Bite force estimatesMeasurements of the final volumetric muscle reconstructions are given in Table 1 along with the calculated muscle contraction force, resultant force acting on the mandible, and relative contribution of each muscle. The oviraptorid oviraptorosaurians show greater muscle volumes compared to the earlier diverging Incisivosaurus. This is confirmed by greater muscle CSA values relative to cranial surface area in Citipati (1.80 × 10–2), Khaan (1.77 × 10–2), and Conchoraptor (1.37 × 10–2), compared to Incisivosaurus (1.21 × 10–2). Table 2 shows the inlever and outlever measurements used to calculate bite force resulting from each cranial muscle (and their relative contribution) and the total estimated bite force in each species, for three different bite positions. These range from 349–499 N in Citipati down in order of cranial size to 53–83 N in Incisivosaurus. Complete calculations and values for Tables 1 and 2 along with measurements for the cranial models are documented in SI 2.Table 1 Geometric measurements of reconstructed muscles and estimated contraction force (Fmus = (volume / length) × 0.3 N/mm2 × 1.532,34). Insertion angles of muscles measured in the sagittal ((alpha)) and coronal ((beta)) planes used to calculate resultant vertical force acting on mandible ((Fres = Fmus times cosalpha times cosbeta)).Full size tableTable 2 Bite force estimates (newtons) for each species, calculated (Fbite = (Fres × Linlever) ÷ Loutlever) for three points on their primary palate: the anterior tip of the beak/teeth; the middle level of the palate/toothrow; the tooth-like projection in the posterior of the oviraptorid palate/the posteriormost teeth. Percentages in brackets reported next to the bite force estimates for the oviraptorid taxa show how much greater these estimates are compared to values that would be predicted by scaling up the bite force estimates of Incisivosaurus by cranial surface area.Full size tableThe condition of the oviraptorid oviraptorosaurian skull is characterised by an increased volume for adductor musculature and increased mechanical advantage resulting from anteroposterior shortening, compared with the more conventional theropod skull geometry of the earlier diverging Incisivosaurus. Estimated bite forces conserve a greater proportion of the resultant force applied to the mandible (Fbite/Fres) in the oviraptorids compared with Incisivosaurus. This results from greater mechanical advantage in the oviraptorids’ jaw for all bite positions, though the difference relative to Incisivosaurus is greatest anteriorly (see Table 3.) These two factors result in their comparatively stronger estimated bite forces, an increase of 17–84% greater (depending on species and bite position; see Table 2) than would be predicted by scaling by cranial surface area. The increased relative bite force of the oviraptorids is not a result of more beneficial muscle insertion angles; there is no clear difference in the ratio of resultant muscle force acting on the mandible to the actual muscle force produced (Fres/Fmus) between Incisivosaurus (0.894) and the three later diverging taxa (Citipati, 0.856; Khaan, 0.851; Conchoraptor, 0.899).Table 3 Mechanical advantage values for the three different positions of the bite force estimates.Full size tableThe relative contribution of the different cranial muscles to bite force is broadly similar in each species (Fig. 4). The mPTv is typically the largest component, followed closely by the mAMES, then the rest of the mAME complex. Citipati differs from the others with a relatively stronger mAMES and mAMEM, and a relatively low value for the mPTv. The width of the Citipati cranium and mandible make the mPTv less vertically orientated and the reconstruction of the mPTv (in all taxa) is less well constrained by bone and other muscle volumes—its volume could be underestimated in all models. No clear difference emerges between Incisivosaurus and the later diverging oviraptorids in the relative contributions of cranial muscles to bite, apart from a slightly relatively weaker mPSTp and mPSTs—reconstructed muscles are proportionally similar but relatively larger in the oviraptorids. The bite force estimates of the four oviraptorosaurians (including Incisivosaurus) are significantly greater than estimates (from similar digital methods) made for other putatively herbivorous theropods of much larger body mass (Fig. 5) both relatively and absolutely.Figure 4The relative contribution of each cranial muscle to total estimated bite force by species. Note that the condition of Citipati appears the most dissimilar to all others in its comparatively stronger mAMEM, mAMES and weaker mPTv.Full size imageFigure 5Comparison of the estimated bite forces in multiple positions of Incisivosaurus and three oviraptorid oviraptorosaurians with other likely herbivorous theropod taxa that have had estimates made using similar digital volumetric methods12,13 show the oviraptorosaurians (oviraptorids especially) are capable of much stronger bite forces both relative to body mass and absolutely. Body mass values from Zanno and Makovicky11.Full size imageGape analysisThe early diverging oviraptorosaurian Incisivosaurus showed the highest estimates of optimal (25.0°) and maximum gape limit (49.5°) compared with the oviraptorid oviraptorosaurians, though not by much; estimates for gape limit in Khaan were lowest (20.5° and 40.0°), marginally less than Citipati (21.0° and 41.0°). Values for Conchoraptor (23.0° and 46.0°) lie between Incisivosaurus and the others. Figure 6 shows these estimates along with charts of the muscle cylinder strains that they are derived from. The anteriormost cylinder representing the mPTv constrains optimal and maximum gape in all but Citipati, in which it is constrained by the anteriormost regions of the mAMES. In this taxon the postorbital half of the skull is particularly low, sloping posteriorly, and the relatively low upper temporal bar directs the strong mAMES ventromedially to a prominent coronoid process of the surangular of the mandible. This leads to a shorter resting length for this muscle, causing its extension during jaw opening to exceed our tension limits just before the mPTv (which is the next most extended). The mAMEM is also relatively more extended in Citipati. The other three species are more similar in relative muscular strain, reinforcing the finding that relative muscle strength and arrangement in Citipati has more differences compared with other oviraptorids, than between some oviraptorids (Khaan and Conchoraptor) and earlier diverging oviraptorosaurians (Incisivosaurus).Figure 6Estimates of the gape angle limit of optimal tension and the maximum limit of gape for muscle tension in Incisivosaurus gauthieri (a), Citipati osmolskae (b), Khaan mckennai (c), and Conchoraptor gracilis (d) from a muscle resting length at a gape angle of 5°. Bar charts show the strain factors of individual modelled muscle cylinders at optimal and maximum tension limit; anteriormost muscle cylinders suffixed ‘1’, posteriormost suffixed ‘2’. Muscle cylinders (and corresponding bars) are colour coded yellow and red when exceeding 130% and 170% of resting length respectively, otherwise green. Note that the anterior mPTv constrains gape in all species apart from Citipati which is constrained by the anterior mAMES. Scale bars 50 mm. Muscle abbreviations given in results section.Full size imageActing antagonistically to the jaw closing muscles is the m. depressor mandibulae (mDM), primarily responsible for jaw depression (opening). It originates from around the paroccipital processes of the cranium, inserting onto the dorsal aspect of the retroarticular process of the mandible31,39. During the gape analysis, we checked mDM length change (from a shorter state at the maximum and optimal estimated gape angles to an elongated state at the 5° resting jaw angle) was not unrealistic. Strain values of the mDM were all calculated to be below the maximum strain limit (1.7) we modelled for the jaw adductors. From its shortest (maximum gape limit) the mDM in Incisivosaurus was extended by a factor of 1.08 at the estimated optimal gape limit and 1.20 the 5° resting jaw angle, Citipati reached 1.11 and 1.33 respectively, Khaan reached 1.16 and 1.48, and Conchoraptor reached 1.19 and 1.67.The oviraptorosaurians show estimated gape limits much lower than those of carnivorous theropods tested by Lautenschlager12, more like herbivorous theropod Erlikosaurus (optimal tension limit 24.0°; maximum tension limit 49.0°; resting gape of 6°). It is noted that herbivorous species exhibit lower gape angles than carnivorous species23,44, and thus our estimates of gape angle may be further support for a herbivorous diet among oviraptorosaurians (when considered against other theropods). Lautenschlager 12 notes that experimental results document gape angle in modern birds can reach angles up to around 40°. The maximum gape angles estimated for these oviraptorosaurians are similar to experimental results of gape angle in birds among passerines and Galliformes, which can reach around 40°45,46,47,48 (though this can be greater in parrots49)—a functional similarity between the crania of birds and oviraptorids which, beyond superficial beaked appearance, are quite dissimilar. More

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DataSpatial gridWe created a grid whose units measure 250 m by 250 m based on the census tract layer for the city of Rio de Janeiro from the Instituto Brasileiro de Geografia e Estatística [Brazilian Institute of Geography and Statistics] (IBGE) website https://www.ibge.gov.br/geociencias/organizacao-do-territorio/malhas-territoriais. Uninhabited locations were excluded.Dengue cases on the gridDengue is a disease of compulsory notification in Brazil, and cases are notified at the Sistema de Informação de Agravos de Notificação [Information System on Diseases of Compulsory Declaration] (SINAN). Dengue cases notified in Rio de Janeiro between January 2010 and March 2015 were geocoded according to address of residency, and then counted for each grid unit by the Secretariat of Health of the city. We obtained the monthly dengue cases data aggregated at the grid level.Population on the gridThe population data is obtained from the Census 2010 (IBGE) (https://www.ibge.gov.br/estatisticas/downloads-estatisticas.html) and it is available at the census tract level. The census tract areas vary in size and can be bigger than the unit of the grid, primarily in the least densely populated zones of the city. To overcome this issue, we cropped from the census tract layer the areas classified as non-urbanized (such as water bodies, swamps, agricultural areas, green areas, beaches, rocky outcrops) in 2010 by the City Hall of Rio de Janeiro (layer available at http://www.data.rio/datasets/uso-do-solo-2010). The population of each census tract is distributed randomly (uniformly) in the areas obtained after deleting the non-urban areas. The population within the units is computed by adding the grid layer. To create the grid and edit the census tract layer we used QGIS (version 3.6.3)45, and to obtain the population in the grid we used the R software46 with the packages tidyverse47 and sf48. We verify the accuracy of our estimated population by comparison with the WordPop dataset49 (see detailed description and Supplementary Fig. 12 and Supplementary Note 2). We chose the WorldPop dataset because: (i) the estimates are also calculated based on census data and are available for 2010, (ii) the pixel size is 100 m, smaller than the size of our grid unit, and (iii) it is open access.Since the units are in fact small and most of them conserve their area of 250 m by 250 m (Supplementary Fig. 1A), we consider population density as the population of each unit. For consistency, we do not consider units with small effective areas and/or populations sizes less than, or equal to, 10 in our analysis. In total, 8954/20212 units were so excluded. This choice circumvents the problem of high sensitivity to random population distribution, and urban vs. non-urban classification, in very small and/or sparsely populated areas. It also facilitates model simulation and does not affect the peak ratio pattern (Supplementary Fig. 1B).Peak ratio and spatial aggregationSince units are small, we binned them into G groups and aggregated their times series of reported cases. The groups were generated according to two aspects: (1) the geographical location of the units as determined by the administrative divisions of the city (10 areas, 33 regions, and 160 neighborhoods); and (2) the population of the units based on quantiles in order to obtain equal size groups. We considered specifically four different partition levels, resulting in 12, 25, 50, and 100 groups with about 900, 450, 225, and 100 units, respectively (from a total number of 11,247 units for the whole city). Groups of unequal size can introduce different statistical effects (it is not the same, for example, to calculate a mean value using 1000 or 10 elements). To compare quantities across groups it is therefore prudent to define groups with the same number of elements. In particular, this consideration becomes important for a large number of groups. Since the population density distribution (number of individuals per unit) is not uniform, groups defined with “equidistant” boundaries would exhibit very different numbers of elements.Given a unit u, we define its time series ({{{{{{bf{v}}}}}}}_{{{{{{bf{u}}}}}}}={{c}_{u}({t}_{1}),{c}_{u}({t}_{2}),…,{c}_{u}({t}_{f})}), where ({c}_{u}({t}_{i})) is the number of reported cases of dengue at time ({t}_{i}) (i = 1, 2, …f) (and the bold symbol is used to indicate a vector). Thus, the aggregated time series is given by$${{{{{{bf{V}}}}}}}_{{{{{{bf{g}}}}}}}=mathop{sum}limits_{uin g}{{{{{{bf{v}}}}}}}_{{{{{{bf{u}}}}}}}={{C}_{g}({t}_{1})=mathop{sum}limits_{uin g}{c}_{u}({t}_{1}),{C}_{g}({t}_{2})=mathop{sum}limits_{uin g}{c}_{u}({t}_{2}),…,{C}_{g}({t}_{f})=mathop{sum}limits_{uin g}{c}_{u}({t}_{f})},$$with (g=1,2,…,G). Then, for each ({{{{{{bf{V}}}}}}}_{{{{{{bf{g}}}}}}}) we computed the ratio between the sizes of the second and first DENV4 peaks, that is$${{{{{rm{peakrati}}}}}}{{{{{{rm{o}}}}}}}_{{{{{{rm{g}}}}}}}=frac{{ma}{x}_{tin {season}2}{{C}_{g}({t}_{1}),{C}_{g}({t}_{2}),…,{C}_{g}({t}_{f})}}{{ma}{x}_{tin {season}1}{{C}_{g}({t}_{1}),{C}_{g}({t}_{2}),…,{C}_{g}({t}_{f})}}$$
(1)
(Supplementary Fig. 2).The deterministic SIR modelAlthough dengue is a vector-borne disease, for simplicity we omitted the explicit representation of the dynamics of the mosquito population, and treated vector transmission via the seasonality of the transmission rate26. Thus, for each unit u, the deterministic SIR model is based on the following traditional differential equations:$$frac{d{S}_{u}}{{dt}}=mu {N}_{u}-beta {S}_{u}frac{{I}_{u}}{{N}_{u}}-mu {S}_{u}$$$$frac{d{I}_{u}}{{dt}}=beta {S}_{u}frac{{I}_{u}}{{N}_{u}}-gamma {I}_{u}-mu {I}_{u}$$
(2)
$$frac{d{R}_{u}}{{dt}}={gamma I}_{u}-mu {R}_{u},$$where ({S}_{u},{I}_{u},{R}_{u}), are, respectively, the number of susceptible, infected, and recovered individuals, and ({N}_{u}) the number of inhabitants, of the spatial unit u. Parameter (mu) is the mortality rate (equal to the birth rate), and (gamma) is the recovery rate. The seasonal transmission rate is specified as (beta (t)={beta }_{0}(1+delta {{sin }},(omega t+phi ))). The units are considered independent of each other, and the initial conditions establish that the whole population of each unit is susceptible to the virus (({S}_{u}(t=0)={N}_{u}) and ({I}_{u}left(t=0right)={R}_{u}left(t=0right)=0forall u)). Transmission begins with one infected individual at a time ({t}_{0u}ge t=0) where ({t}_{0u}) is obtained from the data.Since the goal of this model is to examine the representative dynamics of different population densities, we binned the units according to their population into 12 groups, and computed the mean value of their number of inhabitants ({N}_{g}=langle {N}_{uin g}rangle) and of their arrival times of the infection ({t}_{0g}sim langle {t}_{0uin g}rangle) (where g = 1, …, 12). We then simulated the system considering the 12 sets ({{N}_{g},{t}_{0g}}) as given.The stochastic modelSince units will suffer local extinction of transmission, a major component of a stochastic implementation is the description of the local reintroduction of the virus, namely the arrival of a ‘spark’ or imported infection, in analogy to fire spread. Because space is described by a highly-resolved lattice, we considered that well-mixed transmission applies within each unit. Moreover, in lieu of  explicit spatial coupling between units, we postulated  the importation of infection through the specification of a spark rate.For this purpose, we constructed a binary representation of the time series of cases per month by defining the spatial units either as positive or negative according to whether they reported cases or not (Supplementary Fig. 3). Then, to derive a spark rate we explored the dynamics of the number of positive units as follows,$${U}^{{{mbox{+}}}}(t+{dt})={U}^{{{mbox{+}}}}(t)+{U}_{{{{{{{mathrm{new}}}}}}}}^{{{mbox{+}}}}(t,t+{dt})-{U}_{{{{{{{mathrm{extinct}}}}}}}}^{{{mbox{+}}}}(t,t+{dt})$$
(3)
The number of positive units at time ({t+dt}) is equal to the number of positive units at time t, plus the number of units that have been infected ({{U}_{{{{{{{mathrm{new}}}}}}}}}^{{{mbox{+}}}}(t,t+{dt})) between t and t + dt, minus the number of units that were infected at t but are no longer infected at t + dt (i.e., the number of ‘extinctions’ between t and t + dt, ({{U}_{{{{{{{mathrm{extinct}}}}}}}}}^{{{mbox{+}}}}(t,t+{dt}))).Since uninfected units (i.e., negative units) require the arrival of a spark to become positive, the following equation specifies the mean of ({{U}_{{{{{{{mathrm{new}}}}}}}}}^{{{mbox{+}}}}(t,t+{dt})) under the assumption that a small unit is unlikely to receive more than a single spark in a period of time dt$${{langle }}{U}_{{{{{{{mathrm{new}}}}}}}}^{{+}}(t,t+{dt}){{rangle }}simeq {N}_{{{{{{{mathrm{sparks}}}}}}}}(t,t+{dt})frac{{U}^{{-}}(t)}{U},$$
(4)
where ({N}_{{{{{{{mathrm{sparks}}}}}}}}(t,t+{dt})) is the number of sparks produced between t and t + dt, ({U}^{{{{-}}}}(t)) is the number of negative units at a time t, and (U) is the total number of units in the city ((U={U}^{{{mbox{+}}}}+{U}^{{{{-}}}})).By introducing Eq. (4) into Eq. (3) we obtain,$${U}^{{{mbox{+}}}}(t+{dt})simeq {U}^{{{mbox{+}}}}(t)+{N}_{{{{{{{mathrm{sparks}}}}}}}}(t,t+{dt})frac{{U}^{{{{-}}}}(t)}{U}-{{U}_{{{{{{{mathrm{extinct}}}}}}}}}^{{{mbox{+}}}}(t,t+{dt})$$
(5)
From Eq. (5) we can now compute the spark rate per unit ({{sigma }_{u}}^{{emp}}(t,t+{dt})) from the high-resolution incidence data as$${{sigma }_{u}}^{{emp}}(t,t+{dt})=frac{{N}_{{{{{{{mathrm{sparks}}}}}}}}(t,t+{dt})}{U}simeq frac{{U}^{{{mbox{+}}}}(t+{dt})-{U}^{{{mbox{+}}}}(t)+{U}_{{{{{{{mathrm{extinct}}}}}}}}(t,t+{dt})}{{U}^{{{{-}}}}(t)}$$
(6)
In order to address the effects of human density on the spark rate, we binned the spatial units according to their population into G groups. To avoid statistical effects due to group size, we considered population quantiles. Then, by applying Eq. (6) to each of these groups, we obtained an empirical spark rate per unit that depends on human density,$${sigma }_{uin g}^{{emp}}(t,t+{dt})={sigma }_{u}^{{emp}}(t,t+{dt}{{{{{rm{;}}}}}}{N}_{g}),$$
(7)
where ({N}_{g}={{langle }}{N}_{uin g}{{rangle }}) with g = 1, 2, …, G.SimulationsThe associated differential equations of the stochastic model are those shown on Eq. (2) but the transmission component has now an additional term ({sigma }_{u}) to describe the importation of infections.$$frac{d{S}_{u}}{{dt}}=mu {N}_{u}-left(beta {S}_{u}frac{{I}_{u}}{{N}_{u}}+{sigma }_{u}right)-mu {S}_{u}$$$$frac{d{I}_{u}}{{dt}}=left(beta {S}_{u}frac{{I}_{u}}{{N}_{u}}+{sigma }_{u}right)-gamma {I}_{u}-mu {I}_{u}$$
(8)
$$frac{d{R}_{u}}{{dt}}={gamma I}_{u}-mu {R}_{u}$$Since the inferred spark rate from the data (Eq. (7)) is obtained from observed infections, we computed the spark rate ({sigma }_{u}) as:$${sigma }_{uin g}={{{{{{mathrm{Poisson}}}}}}}({{sigma }_{uin g}}^{{emp}}/rho )$$
(9)
where (rho) is the reporting rate.The model shown on Eq. (8) was formulated as stochastic by incorporating demographic noise (with the different events represented as Poisson processes). It was implemented in R with the package pomp50. We also considered measurement error by assuming that the observed number of cases ({{C}_{u}}^{{obs}}) during a period of time T is,$${{C}_{u}}^{{obs}}left(Tright)={{{{{{mathrm{binomial}}}}}}}left(rho ,{C}_{u}left(Tright)right),$$
(10)
where ({C}_{u}(T)) is the number of cases computed in the unit u. We simulated the 11,247 units that compose the city of Rio de Janeiro, and aggregated the resulting time series as for the empirical data (see Peak ratio section).The parameters of the model are given in Supplementary Table 1. We relied on parameters estimated for dengue transmission in Rio de Janeiro by ref. 26. Those estimates were obtained for the aggregated city and for the emergence of DENV1. We use these parameters here as a sufficiently realistic set for illustrating and exploring the behavior of the stochastic model with population density. Moreover, with the exception of the spark rate, the model parameters were considered the same for all units. In particular, we applied a uniform reporting rate because access to the nearest public healthcare clinic does not show a dependency on population density (see Supplementary Note 1).Reporting summaryFurther information on research design is available in the Nature Research Reporting Summary linked to this article. More

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Plant materials, growth conditions and salt treatmentsSoil samples were performed as in previous experiments with S. europaea25, seeds were collected at two maternal sites, the first of which represents natural salinity related to inland salt springs at the health resort of Ciechocinek (Cie) (52°53′N, 18°47′E) characterised by a high soil salinity of ca 100 dS m−1 (~ 1000 mM NaCl), and the second of which is associated with soda factory waste that affects the local environment in Inowrocław-Mątwy (Inw) (52°48′N, 18°15′E) and with a lower salinity of ca 55 dS m−1 (~ 550 mM NaCl). The complete soil description is reported in Piernik et al.51 and Szymanska et al.52,53. Populations are isolated by a distance of ca 40 km without any saline environment between them, however, they were somehow connected due to the presence of salt springs in the nineteenth century. The seeds came from one generation and were collected in early November 2018. The seeds were germinated and grown according to the same steps reported in Cárdenas-Pérez et al.25 with a slight modification in the number of salt treatments at 0, 200, 400, 600, 800 and 1000 mM NaCl. In total, 144 plants were cultivated, and, therefore, a complete randomised factorial design 26 was used, which included (12 plants × 6 treatments × 2 populations) with 14 response variables. After 2 months of development, anatomical analysis such as cell area (A), roundness (R) and maximum cell diameter (Cdiam) were estimated in 12 samples, whereas high and low methyl esterified pectins (HM-HGs and LM-HGs), proline (P), hydrogen peroxide (HP), total soluble protein (Prot), catalase activity (CAT), peroxidase activity (POD), chlorophyll a, b and total (Cha, Chb and TC), carotenoid (Carot) contents, as well as SeNHX1 and SeSOS1 gene expression, were all determined per triplicate (plants were randomly selected). The collection of plant material, comply with relevant institutional, national, and international guidelines and legislation, IUCN Policy Statement on Research Involving Species at Risk of Extinction and Convention on the Trade in Endangered Species of Wild Fauna and Flora. The voucher specimen of the plant material has been deposited in a publicly available herbarium of the Nicolaus Copernicus University in Toruń (Index Herbarium code TRN), deposition number not available (dr. hab. Agnieszka Piernik, prof. NCU undertook the formal identification of plant species, and permission to work with the seeds was provided by the Regional Director of Environmental Protection in Bydgoszcz, WOP.6400.12.2020.JC).Anatomical image analysisFrom the middle primary branch (fleshy segment shoot) of S. europaea plant treatments (0, 200, 400, 600, 800 and 1000 mM NaCl), slices of fresh tissue were obtained by cutting them with a sharp bi-shave blade. The thinner slices of approximately 0.5 mm were selected and used in the microstructure analysis. The size and shape of the stem-cortex cells from the fresh water-storing tissue were characterised by a light microscope (Olympus BX51, USA) connected to a digital camera (DP72 digital microscope camera) and digital acquisition software (DP2-BSW). The microscope images were captured at a magnification of 10 ×/0.30 in RGB scale and stored in TIFF format at 1280 × 1024 pixels. A total of 300 ± 50 cells from five individuals per treatment were analysed. Finally, the shape and size of the cells were obtained from the captured images. Cell image analysis (IA) was performed in ImageJ v. 1.47 (National Institutes of Health, Bethesda, MD, USA). The following anatomical parameters were obtained. Firstly, the cell area (A) was estimated as the number of pixels within the boundary. Secondly, the maximum cell’s diameter (Cdiam) was determined by the distance between the two points separated by the largest coordinates in different orientations, and the cell roundness (R) was obtained through the equation R = (4 A)/(π (Cdiam)2)—where a perfectly round cell has R = 1.0, while elongated cells will show an R → 0. Finally, the degree of succulence (S) in stem was calculated according to24 with slight change S = (Fresh Weight-Dry Weight)/stem Area, where the Area of the stem (As) was calculated as: As = π × r2, the diameter of the stems was obtained according to Cárdenas-Pérez et al.25.Immunolocalisation experimentsThe samples dissected from the middle segment of the shoot (3 individuals per treatment) were prepared for embedding in BMM resin (butyl methacrylate, methyl methacrylate, 0.5% benzoyl ethyl ether (Sigma) with 10 mM DDT (Thermo Fisher Scientific) according to Niedojadło et al.54. Next, specimens were cut on a Leica UCT ultramicrotome into serial semi-thin cross sections (1.5 µm) that were collected on Thermo Scientific Polysine adhesion microscope slides. Before immunocytochemical reaction, the resin was removed with two changes of acetone and washed in distilled water and PBS pH 7.2. After incubation with blocking solution containing 2% BSA (bovine serum albumin, Sigma) in PBS pH 7.2 for 30 min at room temperature, the sections were incubated with anti-pectin rat monoclonal primary antibody JIM7 (recognises partially methylesterified epitopes of homogalacturonan [HG] but does not bind to fully de-esterified HGs) or antibody LM19 (recognises partially methylesterified epitopes of HG and binds strongly to de-esterified HGs) (Plant Probes) diluted 1:50 in 0.2% BSA in PBS pH 7.2 overnight at 4 °C. After washing with PBS pH 7.2, the material was incubated with AlexaFluor 488-conjugated goat anti-rat secondary antibody (Thermo Fisher Scientific) diluted 1:1000 in 0.2% BSA in PBS pH 7.2 for 1 h at 37 °C. Finally, the sections were washed in PBS pH 7.2, dried at room temperature and covered with ProLongTMGold antifade reagent (Thermo Fisher Scientific). The control reactions were performed with the omission of incubation with primary antibodies. Semithin sections were analysed with an Olympus BX50 fluorescence microscope, with an UPlanFI 1009 (N.A. 1.3) oil immersion lens and narrow band filters (U-MNU, U-MNG). The results were recorded with an Olympus XC50 digital colour camera and CellB software (Olympus Soft Imaging Solutions GmbH, Germany).Fluorescence quantitative evaluationFor the quantitative measurement, each experiment was performed using consistent temperatures, incubation times and concentrations of antibodies. The aforementioned ImageJ (1.47v) software was used for image processing and analysis. The fluorescence intensity was measured for five semi-thin sections for each experimental population (Inowrocław and Ciechocinek) at the same magnification (100 ×) and the constant exposure time to ensure comparable results. The threshold fluorescence in the sample was established based on the autofluorescence of the control reaction. The level of signal intensity was expressed in arbitrary units (a.u.) as the mean intensity per μm2 according to Niedojadło et al.54.Biochemical analysisProline content (P) was measured according to Ábrahám et al.55. Five hundred milligrams of fresh stem material was minced on ice and homogenised with 3% aqueous sulfosalicylic acid solution (5 μl mg−1 fresh plant material), centrifuged at 18,000×g, 10 min at 4 °C, and the supernatant was collected. The reaction mixture: 100 μl of 3% sulphosalicylic acid, 200 μl of glacial acetic acid, 200 μl of acidic ninhydrin reagent and 100 μl of supernatant. Acidic ninhydrin reagent was prepared according to Bates et al.56. The standard curve for proline in the concentration range of 0 to 40 μg ml−1. The standard curve equation was y = 0.0467x − 0.0734, R2 = 0.963. P was expressed in mg of proline per gram of fresh weight. Hydrogen peroxide (HP) levels were determined according to the methods described by Velikova et al.57, and 500 mg of stem tissues were homogenised with 5 ml trichloroacetic acid 0.1% (w:v) in an ice bath. The homogenate was centrifuged (12,000×g, 4 °C, 15 min) and 0.5 ml of the supernatant was added to potassium phosphate buffer (0.5 ml) (10 mM, pH 7.0) and 2 ml of 1 M KI. The absorbance was read at 390 nm, and the HP content was given on a standard curve from 0 to 40 mM. The standard curve equation was y = 0.0188x + 0.046, R2 = 0.987. HP concentrations were expressed in nM per gram of fresh weight. Chlorophylls (Cha and Chb) and carotenoids were extracted from fresh plant stems (100 mg) using 80% acetone for 6 h in darkness, and then centrifuged at 10,000 rpm, 10 min. Supernatants were quantified spectrophotometrically. Absorbance was determined at 646, 663 and 470 nm and calculations were performed according to Lichtenthaler and Wellburn58, when 80% of acetone is used as dissolvent. Total chlorophyll content was calculated as the sum of chlorophyll a and b contents.Total CAT activity was determined spectrophotometrically by following the decline in A240 as H2O2 (ε = 39.9 M−1 cm−1) was catabolised, according to the method of Beers and Sizer59. Decrease in absorbance of the reaction at 240 nm was recorded after every 20 s. One unit CAT was defined as an absorbance change of 0.01 units min−1. Total POD activity was determined spectrophotometrically by monitoring the formation of tetraguaiacol (ε = 26.6 mM−1 cm−1) from guaiacol at A470 in the presence of H2O2 by the method of Chance and Maehly60. Increase in absorbance of the reaction solution at 470 nm was recorded after every 20 s. One unit of POD activity was defined as an absorbance change of 0.01 units min−1. Total soluble protein (Prot) content was measured according to Bradford61 using bovine serum albumin (BSA) as a protein standard. Fresh leaf samples (1 g) were homogenised with 4 ml Na-phosphate buffer (pH 7.2) and then centrifuged at 4 °C. Supernatant and dye were pipetted in spectrophotometer cuvettes and absorbances were measured using a UV–vis spectrophotometer (PG instruments T80) at 595 nm62. Prot was determined based on the standard curve y = 1.6565x + 0.0837, R2 = 0.982, for total soluble protein in the concentration range of 0 to 1.2 mg ml−1 BSA. Triplicates per treatment were used for each analysis.Total RNA isolationAfter 2 months of salt treatment, shoots of S. europaea plants (3 individuals per treatment) were washed several times with tap water and then three times with miliQ water. After drying, plant material was frozen in liquid nitrogen, and stored at − 80 °C. Total RNA isolation was performed using RNeasy Plant Mini Kit (Qiagen, Hilden, Germany) according to the manufacturer’s protocol. The quality and quantity of RNA was checked on 1.5% agarose gels in TAE (Tris–HCl, acetic acid, EDTA, pH 8.3) buffer stained with ethidium bromide, and by spectrophotometric measurement (NanoDrop Lite, Thermo Fisher Scientific, Waltham, MA, USA).Cloning of SOS1 gene from S. europaea (SeSOS1)One microgram (1 µg) of total RNA isolated from shoots of S. europaea was primed with 0.5 µg of oligo (dT)20 primer for 5 min at 70 °C. Then 4 µl of ImProm-II 5 × reaction buffer, 2 mM MgCl2, 0.5 mM each dNTP, 20 U of recombinant RNasin ribonuclease inhibitor, and 1 µl of ImProm-II reverse transcriptase (Promega, Madison, WI, USA) were added to a final volume of 20 µl. The reaction was performed at 42 °C for 60 min. To design degenerate primers for SOS1, cDNA sequences from Arabidopsis thaliana (NM_126259.4), Lycopersicon esculentum (AJ717346.1), Mesembryanthemum crystallinum (EF207776.1), Oryza sativa (AY785147.1), Triticum aestivum (AY326952.3), Salicornia brachiata (EU879059.1) were obtained from NCBI GeneBank. The sequences were aligned using the Clustal Omega tool (https://www.ebi.ac.uk/Tools/msa/clustalo/) and three pairs of degenerate primes were designed (listed in Table 4). The PCR reaction mixture includes cDNA, 0.2 µM each primer, 0.2 mM each dNTP, 4 µl of 5 × HF buffer, and 0.5 U of Phusion High-Fidelity DNA polymerase (Thermo Fisher Scientific, Waltham, MA, USA) in a total volume of 20 µl. The thermal conditions were as follows: 98 °C for 30 s, 98 °C for 10 s, gradient between 48 °C and 56 °C for 20 s, 72 °C for 60 s, 32 cycle, final extension for 10 min at 72 °C. A pair of primers deg2_F and deg2_R yielded a PCR product with expected size. The PCR product was purified from agarose gel, cloned into pJET1.2 vector (Thermo Fisher Scientific, Waltham, MA, USA) according to manufacturer’s protocol and sequenced (Genomed, Warsaw, Poland). The obtained partial cDNA sequence was named SeSOS1 and deposited in NCBI GeneBank (acc. no. MZ707082).Table 4 Sequences of the primers used for cloning of SeSOS1 and quantitative real-time PCR.Full size tableReverse transcription reaction and quantitative real-time PCR (qPCR) SeNHX1 and SeSOS1 gene expression analysisPrior to reverse transcription reaction, RNA was treated with DNaseI (Thermo Fisher Scientific, Waltham, MA, USA). The cDNA was synthesised from 1.5 µg of total RNA using a mixture of 2.5 µM oligo(dT)20 primer and 0.2 µg of random hexamers with NG dART RT Kit (Eurx, Gdańsk, Poland) according to the manufacturer’s protocol. The reaction was performed at 25 °C for 10 min, followed by 50 min at 50 °C. The cDNA was stored at − 20 °C.The PCR reaction mixture includes 4 µl of 1/20 diluted cDNA, 0.5 µM gene-specific primers (Table 4) and 5 µl of LightCycler 480 SYBR Green I Master (Roche, Penzberg, Germany) in a total volume of 10 µl. Clathrin adaptor complexes (CAC) was used as a reference gene63. The reaction was performed in triplicate (technical replicates) in LightCycler 480 Instrument II (Roche, Penzberg, Germany). The thermal cycling conditions were as follows: 95 °C for 5 min, 95 °C for 10 s, 60 °C for 20 s, 72 °C for 20 s, 40 cycles. The SYBR Green I fluorescence signal was recorded at the end of the extension step in each cycle. The specificity of the assay was confirmed by the melt curve analysis i.e., increasing the temperature from 55 to 95 °C at a ramp rate 0.11 °C/s. The fold-change in gene expression was calculated using LightCycler 480 Software release 1.5.1.62 (Roche, Penzberg, Germany).Statistical and multivariate analysisIn order to determine the projection of the effect of salt treatment in plants we followed Cárdenas-Pérez et al.25 methodology. A principal component analysis (PCA) was developed using XLSTAT software version 2019.4.165. For this analysis, 14 variables were used, (A, Cdiam, R, Prot, CAT, POD, HM-HGs, LM-HGs, P, HP, Cha, Chb, TC, Carot), arranged in a matrix with the average values obtained from replicates of each treatment and population. A two-way ANOVA comparing treatments within populations and populations within treatments was conducted for all the results with the Holm–Sidak method. The data was fit with a modified three parameter exponential decay using SigmaPlot version 11.066. The relationships between variables were performed using a Pearson analysis, while a significance test (Kaisere Meyere Olkin) was performed in order to determine which variables had a significant correlation with each other (α = 0.05). Then, a 3D plot was developed using the three principal component factors according to the Kaiser criterion which stated that the factors below the unit are irrelevant. The three main factorial scores of the PCA from each sample were used to calculate the distance (D) between the two points (populations) under the same treatment P1 = (x1, y1, z1) and P2 = (x2, y2, z2) in 3D space of the PCA (Eq. 1).$$D ( {P_{1} ,, P_{2} } ) = sqrt {( {x_{2} – x_{1} } )^{2} + ( {y_{2} – y_{1} } )^{2} + ( {z_{2} – z_{1} } )^{2} }$$
(1)
where x, y, and z are the three main factorial scores in the PCA corresponding to the evaluated treatment in Inw and in Cie. Distances were used to evaluate and determine in which salt treatment the greatest differences between the populations were recorded. More

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