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The data were recorded under the DarwinCore standard55,56 in a matrix named “Benthic biota of CIMAR-Fiordos and Southern Ice Field Cruises”58. The occurrence dataset contains direct basic information (description, scope [temporal, geographic and taxonomic], methodology, bibliography, contacts, data description, GBIF registration and citation), project details, metrics (taxonomy and occurrences classification), activity (citations and download events) and download options. The following data fields were occupied:Column 1: “occurrenceID” (single indicator of the biological record indicating the cruise and correlative record).Column 2: “basisOfRecord” (“PreservedSpecimen” for occurrence records with catalogue number of scientific collection, “MaterialCitation” for any literature record).Column 3: “institutionCode” (The acronym in use by the institution having custody of the sample or information referred to in the record).Column 4: “collectionCode” (The name of the cruise).Column 5: “catalogNumber” (The repository number in museums or correlative number).Column 6: “type” (All records entered as “text”).Column 7: “language” (Spanish, English or both).Column 8: “institutionID” (The identifier for the institution having custody of the sample or information referred to in the record).Column 9: “collectionID” (The identifier for the collection or dataset from which the record was derived).Column 10: “datasetID” (The code “CONA-benthic-biota-database” for entire database).Column 11: “recordedBy” (Author/s who recorded the original occurrence [publication source]).Column 12: “individualCount” (Number of individuals recorded).Column 13: “associatedReferences” (Publication source [report and/or paper/s] for each record).Column 14: “samplingProtocol” (The sampling gear for each record).Column 15: “eventDate” (The date-time or interval during which the record occurred).Column 16: “eventRemarks” (Comments or notes about the event).Column 17: “continent” (Location).Column 18: “country” (Location).Column 19: “countryCode” (The standard code for the country in which the location occurs).Column 20: “stateProvince” (Location, refers to the Administrative Region of Chile).Column 21: “county” (Location, refers to the Administrative Province of Chile).Column 22: “municipality” (Location, refers to the Administrative Commune of Chile).Column 23: “locality” (The specific name of the place).Column 24: “verbatimLocality” (The original textual description of the place).Column 25: “verbatimDepth” (The original description of the depth).Column 26: “minimumDepthInMeters” (The shallowest depth of a range of depths).Column 27: “maximumDepthInMeters” (The deepest depth of a range of depths).Column 28: “locationRemarks” (The name of the sample station of the cruise).Column 29: “verbatimLatitude” (The verbatim original latitude of the location).Column 30: “verbatimLongitude” (The verbatim original longitude of the location).Column 31: “verbatimCoordinateSystem” (The coordinate format for the “verbatimLatitude” and “verbatimLongitude” or the “verbatimCoordinates” of the location).Column 32: “verbatimSRS” (The spatial reference system [SRS] upon which coordinates given in “verbatimLatitude” and “verbatimLongitude” are based)Column 33: “decimalLatitude” (The geographic latitude in decimal degrees).Column 34: “decimalLongitude” (The geographic longitude in decimal degrees).Column 35: “geodeticDatum” (The spatial reference system [SRS] upon which the geographic coordinates given in “decimalLatitude” and “decimalLongitude” was based).Column 36: “coordinateUncertaintyInMeters” (The horizontal distance from the given “decimalLatitude” and “decimalLongitude” describing the smallest circle containing the whole of the location).Column 37: “georeferenceRemarks” (Notes about the spatial description determination).Column 38: “identifiedBy” (Responsible for recording the original occurrence [publication source]).Column 39: “dateIdentified” (The date-time or interval during which the identification occurred.)Column 40: “identificationQualifier” (A taxonomic determination [e.g., “sp.”, “cf.”]).Column 41: “scientificNameID” (An identifier for the nomenclatural details of a scientific name).Column 42: “scientificName” (The name of species or taxon of the occurrence record).Column 43: “kingdom” (The scientific name of the kingdom in which the taxon is classified).Column 44: “phylum” (The scientific name of the phylum or division in which the taxon is classified).Column 45: “class” (The scientific name of the class in which the taxon is classified).Column 46: “order” (The scientific name of the order in which the taxon is classified).Column 47: “family” (The scientific name of the family in which the taxon is classified).Column 48: “genus” (The scientific name of the genus in which the taxon is classified).Column 49: “subgenus” (The scientific name of the subgenus in which the taxon is classified).Column 50: “specificEpithet” (The name of the first or species epithet of the “scientificName”).Column 51: “infraspecificEpithet” (The name of the lowest or terminal infraspecific epithet of the “scientificName”).Column 52: “taxonRank” (The taxonomic rank of the most specific name in the “scientificName”).Column 53: “scientificNameAuthorship” (The authorship information for the “scientificName” formatted according to the conventions of the applicable nomenclatural Code).Column 54: “verbatimIdentification” (A string representing the taxonomic identification as it appeared in the original record).The information sources (see Fig. 2b) provided a total of 107 publications (22 cruise reports and 85 scientific papers; see Fig. 2c). Nineteen of the 22 cruise reports reviewed provided species occurrence records8,28,29,30,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46, one provided qualitative or descriptive data, with no recorded occurrences31, and two did not provide information on benthic biota (CIMAR-9 and −23 cruises). Of all the scientific papers reviewed, 74 provided records of species occurrences (Table 2), while 11 did not provide any record, as they were data without occurrences of geographically referenced species or with descriptive or qualitative information: Foraminifera59,60,61,62, Annelida63,64,65,66, Fishes67, Mollusca68 and Echinodermata69. The phyla with the highest number of publications were the following: Annelida (present in 18 reports and 21 papers), Mollusca (in 14 and 20), Arthropoda (in 10 and 18), Echinodermata (in 10 and 9), Chordata (in 10 and 9) and Foraminifera (in 4 and 10).Table 2 Publications with >100 occurrences, indicating the main recorded taxa.Full size tableThe information registry includes data on occurrences and number of individuals for 8,854 records (files in the database), representing 1,225 species (Fig. 3). The main taxa in terms of occurrence and number of species were Annelida (mainly Polychaeta), Foraminifera, Mollusca and Arthopoda (mainly Crustacea), together accumulating ~70% of total occurrences and ~73% of the total species (Fig. 3). The large number of recorded occurrences of Myzozoa (10%) should be highlighted, which, however, only represent about 32 species. Echinodermata represented ~8% of occurrences and 7% of species.Fig. 3Occurrences and total species by taxon, considering large taxonomic groups of the benthic biota recorded in the CIMAR 1 to 25 and CDHS-1995 cruises. The absolute values of occurrences and species are represented in parentheses.Full size imageThe cruises with the highest number of occurrences were CIMAR-2 (with 1,424), followed by CIMAR-8 (1,040) and CIMAR-16 (813) (Fig. 4). Three dominant taxonomic groups were recorded in most cruises, except for cruises CIMAR-1, CIMAR-4, CIMAR-17, CIMAR-18 and CIMAR-24 (Fig. 4). The cruises with the highest number of species recorded were CIMAR-2 (with 335), CIMAR-3 (328) and CIMAR-8 (323) (Fig. 5). Three or fewer dominant taxonomic groups were recorded only in the CIMAR-1, CIMAR-4, CIMAR-17, CIMAR-18 and CIMAR-24 cruises (Fig. 5).Fig. 4Total occurrences and percentages per dominant taxon recorded in each of the CIMAR 1 to 25 and CDHS-1995 cruises. The absolute values of occurrences per dominant taxon are represented in parentheses.Full size imageFig. 5Total species and percentages per dominant taxon recorded in each of the CIMAR 1 to 25 and CDHS-1995 cruises. The absolute values of species per dominant taxon are represented in parentheses.Full size imageThe latitudinal bands 42°S and 45°S are those with the highest number of occurrences (Fig. 6), while the 56°S and 46°S bands had the fewest. The highest number of species was recorded in the 52°S and 50°S latitudinal bands, while, as with the occurrences, the lowest values corresponded to the 56°S and 46°S latitudinal bands (Fig. 6).Fig. 6Occurrences and number of species recorded by latitudinal band from the CIMAR 1 to 25 and CDHS-1995 cruises. SEP: South-eastern Pacific.Full size image More

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Our approach uses hypothetical 30 cm fixed depth samples taken at three successive time points (t0, t1, and t2) with prescribed changes in SOC (1.4% to 1.6%) and BD (1.5–1.1 g cm−3) over these time points (Table 1). The 30 cm soil depth is the common international standard for sampling and analysis required for SOC stock assessment and adhered to by carbon accounting and market organizations6,18. The changes we adopted (a 27% decrease in BD and a 14% increase in SOC) while relatively large, are consistent with those reported in the literature. For example, Reganold and Palmer reported a 25% decrease in BD (1.2–0.9 g cm−3) in neighboring farms with differing management practices23, and Syswerda et al. observed a 17% increase in SOC concentration (10.4–12.2 g C kg soil−1) when converting from a conventionally to organically managed row crop rotation21.Table 1 Hypothetical changes in bulk density (BD) and soil organic carbon (SOC) concentration in 30 cm fixed depth samples at time points t0, t1 and t2 along with calculated values of SOC stock and total soil mass and mineral soil mass.Full size tableIn Table 1, the total soil mass, mineral soil mass, and the SOC stock of the fixed depth samples were calculated by equations as described in the introduction from our prescribed changes in BD and SOC values.ScenariosWe compared hypothetical ESM correction scenarios with our 30 cm fixed depth sample at each time point (Table 2, Figs. 2, 3).Table 2 Hypothetical ESM scenarios showing variation with depth for bulk density (BD) and soil organic carbon (SOC) at each sampling time point, along with the sample depth intervals investigated.Full size tableFigure 2Flow chart of the definition, sampling, and SOC stock correction for a theoretical data set at time points t0, t1, and t2 for scenarios s1 with linear distributions of BD and SOC and s2 with a linear increase in BD and exponential decrease in SOC with depth. Scenario s2 is sampled at (a) 10 cm, (b) 15 cm, and (c) 30 cm intervals.Full size imageFigure 3Scenarios (S1 and S2), showing (a) bulk density variation (BD, g cm−3), and (b) soil organic carbon (SOC, %) variation by depth (0–30 cm) at each time point (t0, t1, and t2). For scenario 2, the single 30 cm depth interval was used (2c). See Table 1 and 2 for details.Full size imageScenario 1We carried out the ESM correction on a 30 cm sample and assumed that the sample was homogenous throughout the profile, with constant SOC and BD values at each time point.To correct for the error in SOC stock estimation when using fixed depth soil sampling, we used  Eqs.2a, 2b and 2c that consider changes in BD28,35. The adjusted soil depth resulting from the change in BD is calculated as:$${mathrm{M}}_{mathrm{n}}= {mathrm{M}}_{mathrm{i}}$$
(2a)
$${mathrm{D}}_{mathrm{a}}*{mathrm{BD}}_{mathrm{n}}*left(1-mathrm{k}*{mathrm{SOC}}_{mathrm{n}}right)={mathrm{D}}_{mathrm{i}}*{mathrm{BD}}_{mathrm{i}}*left(1-mathrm{k}*{mathrm{SOC}}_{mathrm{i}}right)$$
(2b)
$${mathrm{D}}_{mathrm{a}}={mathrm{D}}_{mathrm{i}}*frac{{mathrm{BD}}_{mathrm{i}}}{{mathrm{BD}}_{mathrm{n}}}*frac{1-mathrm{k}*{mathrm{SOC}}_{mathrm{i}}}{1-mathrm{k}*{mathrm{SOC}}_{mathrm{n}}}$$
(2c)
where Mi = Initial mineral soil mass per area (left[frac{M}{{L}^{2}}right]) , Mn = New mineral soil mass per area (left[frac{M}{{L}^{2}}right]) , Da = Adjusted soil surface depth (left[Lright]) , BDi = Initial bulk density (left[frac{M}{{L}^{3}}right]) , BDn = New bulk density (left[frac{M}{{L}^{3}}right]) , SOCi = Initial SOC as a decimal percent (left[frac{M}{M}right]) , SOCn = New SOC as a decimal percent (left[frac{M}{M}right]) , Di = Initial depth (left[Lright]).To conform with Eq. (2a), an increase in SOC over time results in a displacement of some soil mineral mass from the sample, whereas a decrease in SOC over time requires some soil mineral mass to be replaced34. Multiplying the BD by the mineral fraction of the soil (left(1-mathrm{k}*{mathrm{SOC}}right)) for each time point allowed us to compare equivalent mineral mass28. The effect of a change in SOC on mineral mass is small, with a 1% change in SOC equating to approximately a 2% change in apparent depth. This adjustment relates SOC per unit of mineral mass of the fine fraction ( 2 mm)20. The corrected apparent depth can then be used to calculate the corrected SOC stock of a single layer, fixed depth sample (Eq. 3).$$SO{C}_{stock}={D}_{a}*BD*SOC$$
(3)
Scenario 2In ESM correction scenarios 2a, 2b, and 2c, we imposed variable, dynamic BD and SOC values with depth over time (Table 2, Figs. 2, 3). To investigate these profiles, we determined the SOC and BD values throughout the soil depth by separating the soil into one (1) cm depth increments (i.e., 0–1 cm, 1–2 cm, etc.). We refer to this calculated incremental profile as the scenario 2 baseline. We assumed that our prescribed SOC concentration varied with depth following an exponential decay. To represent this decay, we simulated the global average distribution of SOC concentration with depth on crop land36, following the distribution from Hobley and Wilson37 (Eq. 4),$$SOCleft(dright)=SO{C}_{infty }+left(SO{C}_{o}-SO{C}_{infty }right)times {e}^{-dk}$$
(4)
where SOC (d) is the SOC concentration at depth (d), ({SOC}_{infty }) is the infinity SOC concentration, SOC0 is the SOC concentration at the soil surface, and k is the decay rate. We solved for the decay rate, initial SOC0, and infinity ({SOC}_{infty }) to fit the global average distribution for the 30 cm profile36 and then scaled the SOC concentration to our 30 cm fixed depth sample’s average SOC (1.4%) at t0 (Fig. 3).In scenarios 2a, 2b, and 2c, the BD increased linearly with depth38,39. At the initial time point (t0), we varied the BD values by ± 10% of the BD average over the 30 cm depth, such that for example, BD at t0 (profile average of 1.5 g cm−3) was 1.35 g cm−3 and 1.65 g cm−3 for the upper (0–1 cm) and lower (29–30 cm) depth increment, respectively. For each sequential time point, as the average BD decreased, the soil expanded. To determine the expansion, the depth of the initial sample (e.g., at t0) that filled the 30 cm depth in the subsequent sample (e.g., at t1) was calculated as the initial depth multiplied by the ratio of the average initial BD over the average new BD (e.g., 1.5/1.3 = 1.15 for t0/t1).The linear increase in BD with depth of each following time point maintained the average BD of scenario 1. We then varied the new BD by ± the percent change in the average BD between the time periods (see annotated scripts “main.R” and “functions.R” in Supplementary Material 1 for the development of the theoretical dataset). We then divided each initial BD increment (using soil mass for every 1 cm depth increment) by the new BD in the expanded increment (using soil mass for every  > 1 cm depth increment) to determine the expanded depth of each increment. The SOC value at the initial time represented the same, now expanded, ( > 1 cm) increments, as SOC is a ratio of mass. We used a linear decay rate that was twice that of the percent change in BD between time points to maintain an average BD that was consistent with scenario 1. To model the subsequent fixed depth sample, the BD and SOC concentration values of this expanded soil profile were then interpolated back to the 30 × 1 cm increments of the scenario 2 baseline depth. This calculation preserved the prescribed average BD of the new time point by only expanding the initial SOC concentration.We adjusted the SOC concentration of the next time point to maintain the average SOC concentrations of the 30 cm fixed depth sample, (see annotated scripts “main.R” and “functions.R” in Supplementary Material 1). Because the BD changed between time points and because the SOC stock in the 30 cm fixed depth sample was known, we determined the change in SOC stock between time points by subtracting the average SOC stock in the prior sample from the new sample. We then weighted this change across the 30 cm profile using the distribution of the global soil SOC in the top 30 cm to simulate SOC stratification with reduced tillage or agricultural intensification40. We then multiplied this change by the BD to convert back to SOC concentration and added the delta ((Delta )) SOC value to the prior sample. A worked example is shown in Supplementary Material 2 “Correction Example”.At each time point we split the soil profile at 10 cm and 15 cm depth intervals to create samples for scenarios 2a (3 soil intervals) and 2b (2 soil intervals), respectively. Note that scenario 2c is mathematically equivalent to scenario 1—with only one sample depth interval (30 cm) the sample contains no data on varying SOC or BD. The samples for 2a and 2b were generated by summing the total mass per area and SOC stock values from the scenario 2 baseline to produce single sample values of total soil mass per area and SOC concentration values per depth interval (as would be determined in a laboratory) and calculating BD and mineral mass.In scenario 2, any required additional mineral mass and the associated SOC values were ‘placed’ at the base of the sample to represent a soil profile that had expanded below the fixed 30 cm depth. To account for this, we calculated the increase in adjusted sample depth and accumulated additional soil mineral mass with the lowest sample depth interval of each split sample (Eqs. 5 and 6).$$mathrm{Delta D}={D}_{a}-{D}_{i}$$
(5)
$$SO{C}_{stock}={(D}_{1}*B{D}_{1}*SO{C}_{1}+dots + {(D}_{j}+Delta D)*B{D}_{j}*SO{C}_{j}))*10^2 (mathrm{g}/mathrm{cm}^{2})/(mathrm{Mg}/mathrm{ha})$$
(6)
where (mathrm{ Delta D}) is the apparent change in depth needed to generate the same mineral mass of the initial sample and the subscript j is the number of sample depth intervals from 1 to j.Varying BD linearly with depth introduces additional complexity in the calculation of the apparent depth. Each sample depth interval may expand (or contract in cases not explored here) at differing rates. Here, the over or under sampling of soil mineral mass is no longer constant with depth and the correction for apparent depth (Da) is estimated with linear interpolation using the BD of each sampling depth interval (i.e., 10 cm, 15 cm, or 30 cm). To do so, we calculated the mineral mass in each depth interval, determined their difference between the initial sample time point and new sample time point, and converted the change in mineral mass to a depth, where:$${mathrm{D}}_{mathrm{a}}={mathrm{D}}_{mathrm{i}}+frac{left(mathrm{sum}left({mathrm{D}}_{mathrm{ij}}*{mathrm{BD}}_{mathrm{ij}}*(1-mathrm{k}*{mathrm{soc}}_{mathrm{ij}}right))- mathrm{sum}left({mathrm{D}}_{mathrm{nj}}*{mathrm{BD}}_{mathrm{nj}}*(1-mathrm{k}*{mathrm{soc}}_{nmathrm{j}})right)right)}{{mathrm{BD}}_{{mathrm{nj}}_{mathrm{bottom}}}*1-mathrm{k}*{mathrm{soc}}_{n{mathrm{j}}_{mathrm{bottom}}}}$$
(7)
where jbottom is the lowest sample depth interval, and other terms are as previous. Using Eqs. (5), (6), and (7), with variable BD and SOC values, SOC stock can be corrected using samples split into the 10 cm and 15 cm sampling depth intervals. More

The ecological baseline in TirezThe geology and the climate of the Tirez region favored the generation and maintenance of a type of hypersaline habitat characterized by extreme seasonality: the sulfate-chlorine waters, with sodium and magnesium cations, showed significant seasonal variations15. The alkaline pH, the low oxidant value for the redox potential of the water column and the highly reduced sediments imposed extreme conditions (see Table 1 and Supplementary Information for details). This extreme seasonality requires to define a valid representative ecological baseline to compare the ecology of the lagoon between 2002 and 2021 and, in this way, set the basis to proposing our model of ecological succession with increasing dryness as a “time-analog” for early Mars. Taxonomic data from 2002 is a snapshot of the community during one season, so we include in our discussion the results presented by Montoya et al. (2013) from a sample campaign carried out in 2005, because they16 analyzed both water and sediment and during both the wet and dry seasons.We consider here only the results obtained by Montoya et al.16 by gene cloning, since those obtained by isolation and sequencing are not comparable. At the level of large groups, no major seasonal differences were observed: Pseudomonadota, followed by Bacteroidetes, were the dominant phyla, in both water and sediments, and both in the dry and the rainy seasons; although Alphaproteobacteria was the dominant class in water, while Gammaproteobacteria was dominant in sediments (in both dry and rainy seasons). With respect to the archaeal domain, all the identified sequences were affiliated to Halobacteriales order, mainly Halorubrum (water) and Halobacterium (sediment), both within Halobacteriaceae family. We can consider these results presented in Montoya et al.16 as the “ecological baseline” for Tirez, however taken with a grain of salt, because only 43 bacterial and 35 archaeal sequences, including rainy and dry seasons and water and sediments, were considered for analysis.Prokaryotic diversity in 2002As can be expected for an extreme environment, the bacterial diversity detected in 2002 was low, although we cannot exclude the possibility that this may reflect the limitation of DNA sequencing techniques at the time. 59% of the obtained clones in the then-wet sediments corresponded to the Malaciobacter genus. Malaciobacter (previously named17 Arcobacter) is an aerotolerant Epsilonproteobacteria. Species within this genus are moderately halophilic, e.g., M. halophilus, capable to grow in up to 4% NaCl. Even though the role that Malaciobacter can play in the environment is not known, it seems to thrive in aquatic systems, like sewage, with a high organic matter content17: e.g., M. canalis, M. cloacae, or M. defluvii.After Malaciobacter-like clones, the next most numerous group belongs to the phylum Bacillota (27% of the sequenced clones; Table 2). Under stressful environmental conditions, members of the genus Virgibacillus produce endospores, a very useful property in an extreme and variable environment (ionic strength, temperature, light intensity), easy to compare with early Mars. Endospores facilitate species survival, allowing them to overcome drastic negative changes, like dry periods, and to germinate when the conditions are favorable again. The closest identified species was the halotolerant V. halodenitrificans, but with low homology, not far from other halotolerant (e.g., V. dokdonensis) or halophilic (e.g., V. marismortui) species within the same genus. The other Gram-positive clones belong to the order Clostridiales. These clones cluster in two taxonomic units related with the strictly anaerobic genus Tissierella.Despite the abundance of Pseudomonadota, their biodiversity was very low, reduced to only two genera within the Epsilon- and Delta-proteobacteria. Six sequences affiliated to Deltaproteobacteria, and clustered in one OTU (salB38, similarity 96.6% with Desulfotignum), were retrieved. Its presence in anaerobic media rich in sulfates (Table 1) seems reasonable. In fact, sulfate-reducing activity was detected using a specific enrichment assay.Finally, one taxon belonging to the phylum Spirochaetota (previously named Spirochaetes) was identified. The presence of Spirochaetota in this system is not strange because members of the genus Spirochaeta are very often found in mud and anaerobic marine environments rich in sulfates18. Moreover, the closest species to SalB63, although with a low similarity of 87%, was Spirochaeta bajacaliforniensis, a spirochete isolated19 from a microbial mat in Laguna Figueroa (Baja California), an extensive hypersaline lagoon with high gypsum content, very similar, although much bigger, than Tirez lagoon.The diversity within the domain Archaea was very low in 2002. The phylogenetic analysis of 96 clones indicate that they correspond to one specie belonging to the obligate halophile genus Methanohalophilus. Their high similarity (99.3%) with several species of Methanohalophilus, such as M. portucalensis (isolated from sediments of a solar saltern in Portugal), M. mahii (isolated from sediments of the Great Salt Lake), or M. halophilus (isolated20 from a cyanobacterial mat at Hamelin Pool, Australia), makes impossible its adscription to any particular species level. Methanohalophilus is strictly methylotrophic, which is consistent with this environment, given that the methylotrophic methanogenesis pathway, non-competitive at low-salt conditions, is predominant at high saline concentrations21. We further confirmed methanogenic activity in Tirez by the measurement of methane by gas chromatography in enrichment cultures.Prokaryotic diversity in context of other studies between 2002 and 2021It was challenging to establish a timeline for the succession of the populations involved, because the scarcity of data harvested and published so far from Tirez. However, combining our results with the few data available in Montoya et al.16 and Preston et al.22 on samplings carried out on 2005 and 2017, respectively, we can see a clear predominance of the phylum Pseudomonadota: Epsilonproteobacteria, i.e. Arcobacter-like, and Deltaproteobacteria, mainly sulfate-reducing bacteria (this work, sampling 2002), and Gammaproteobacteria16 when Tirez maintained a water film, to eventually a final predominance of Gammaproteobacteria, e.g. Chromatiales and Pseudomonadales, in the dry Tirez (this work, 2020 sampling). The Bacillales order has remained widely represented both in the wet and dry Tirez.Regarding the archaeal domain, the few references available (Refs.16,22; this work) confirm that the members of the Halobacteriaceae family are well adapted to both the humid and dry ecosystems of Tirez, being predominant in both conditions. Preston et al.22 found that the second most abundant group of archaea in the dry sediments of Tirez was the Methermicoccaceae family, within the Methanosarcinales order, Methanomicrobia class. Taking into account the results obtained in the dry Tirez (Preston et al.22; and this work, sample 2020), the methanogenic archaea have decreased drastically through time, probably due to salt stress and the competition with sulfate-reducing bacteria.Prokaryotic diversity in 2021From a metabolic point of view, most of the bacteria present today in the sediment are chemoorganotrophs, anaerobes, and halophilic or halotolerant. Scarce information is available about the predominant OTU, Candidate Division OP1. The OP1 division was one of the main bacterial phyla in a sulfur-rich sample in the deepest analyzed samples from the Red Sea sediments under brine pools23. In addition, the phylogenetically related Candidate division KB1 has been observed in deep-sea hypersaline anoxic basins at Orca Basin (Gulf of Mexico), and other hypersaline environments24. Eight of the nine genera identified show coverage greater than 1% of the sequences: i.e., Rubinisphaera, Halothiobacillus, Thiohalophilus, Anaerobacillus/Halolactibacillus, Halomonas, Halothermothrix, and Aliifodinibius are halophilic or halotolerant genera13,25.Regarding archaea, our analyses reveal archaeal groups that seem to thrive in sediments from extreme environments, e.g., marine brine pools/deep water anoxic basins or hypersaline lakes. The most abundant OTU, Thermoplasmata KTK4A, was found prominent and active in the sediment of Lake Strawbridge, a hypersaline lake in Western Australia26, and in soda-saline lakes in China27. The creation of a Candidatus Haloplasmatales, a novel order to include KTK4A-related Thermoplasmata, has been proposed27. On the other hand, both in the aforementioned soda-saline lakes in China27 and in a sulfur-rich section of the sediments from below the Red Sea brine pools23, retrieved sequences were assigned to Marine Benthic Groups B, D, and E. Finally, in the section of nitrogen-rich sediments from the aforementioned Red Sea brine pools, the unclassified lineage ST-12K10A represented the most abundant archaeal group. In the Tirez Lagoon sediment after desiccation, all Methanomicrobia readings belonged to this group.The significance and implications of an ecosystem characterized in 2021 by high diversity, high inequality, and lack of isolated representatives, resides in that Tirez is today an ecosystem in which many (most) of the species/OTUs present are dormant, and they do not play any metabolic role. Hence the high percentage of raretons, greater than 80% for both bacteria and archaea, which are actually present in the lagoon but with only one or two copies each. Only those species adapted to the conditions imposed by the extreme environment are able to actually thrive, and consequently only a few species carry out all the metabolic activity. We conclude that the microbiota in Tirez today represents an ecosystem with a high resilience capacity in the face of environmental changes that may occur.We want to clearly highlight that the technique available in 2002 to study the microbiota of the Tirez lagoon only allowed to obtain a low-resolution image, but that was the state-of-the-art procedure at the time, and the Tirez lagoon cannot be sampled again with the conditions back in 2002, which no longer exist and are not expected to return. Although we have kept in storage several samples of water and sediment from the 2002 Tirez lagoon, it is reasonable to assume that those laboratory microcosms would have chemically and microbiologically changed during the last 20 years, and as such no longer represent reliable replicas of the original lagoon, so we cannot use them for the purposes of this work. Therefore, we are aware that any comparisons of the 2002 laboratory results with the much more robust results obtained by Illumina in 2021 need to be taken with a grain of salt. With all the precautions required, in a high-level, first-order comparison, the most noticeable difference between 2002 and 2021 is a drastic change in the microbial Tirez population. Only some OTUs within Bacillales (Virgibacillus/Anaerobacillus), sulfate-reducing Deltaproteobacteria (Desulfotignum/Desulfobacteraceae-Desulfovibrio), and Spirochaetes are shared among the 2002 and 2021 samples. This comparison is enough for the purposes of this work, as we are interested in the evolution of the lagoon system as a whole to establish a “time-analog” with the wet-to-dry transition on early Mars, and not in the particular outcome of each and every OTU in Tirez. With the results at hand, we conclude that, since 2002, the lacustrine microbiota has shifted to one more adapted to the extreme conditions in the dry sediments, derived from the gradual and persistent desiccation concluding ca. 7 years ago (i.e., completely desiccated in 2015), such as lack of light, absence of oxygen, and lack of water availability. This shift has likely been triggered because organisms that were originally in the lagoon but at low abundance in 2002 became dominant as they were better adapted to desiccation, and because the incoming of new microorganisms transported by birds or wind28.Lipid biomarkers analysis of the desiccated lake sedimentsThe analysis of cell membrane-derived lipid compounds on the dry lake sediments at present allow to provide another perspective of the microbial communities inhabiting the Tirez lagoon, by contributing additional information about the ecosystem and depositional environment. It is important to note that, analyzing only the 2021 lake sediments, we cannot differentiate between lipidic biomarkers of the microorganisms inhabiting Tirez in 2002 and before from those left behind by the microorganisms living in the dried sediments today. Instead, the analyses of lipid biomarkers provide clues about the different microorganisms that have populated Tirez through time, including both older communities inhabiting the former aqueous system and also younger communities better adapted to the present dry conditions. Thus, the lipid biomarkers analysis can be considered as a time-integrative record of the microbial community inhabiting Tirez during the last decades.Based on the molecular distribution of lipid biomarkers, the presence of gram-positive bacteria was inferred from the relative abundance of the monounsaturated alkanoic acid C18:1[ω9], or iso/anteiso pairs of alkanoic acids from 12 to 17 carbons29 with dominance of i/a-C15:0 and i/a-C17:0 (Fig. 3B). In contrast, generally ubiquitous alkanoic acids such as C16:1[ω7], C18:1[ω7], or C18:2[ω6] suggested a provenance rather related to gram-negative bacteria30. The combined detection of the i/a-C15:0 and i/a-C17:0 acids, with dominance of the iso over the anteiso congeners, together with other biomarkers such as the mid-chain branched 10Me16:0, the monounsaturated C17:1, or the cyclopropyl Cy17:0 and Cy19:0 acids, may be associated with a community of SRB31 in today´s dry sediments of Tirez. Specifically, most of those alkanoic acids have been found in a variety of Deltaproteobacteria and/or Bacteroidota (previously named Bacteroidetes). The presence of archaea was deduced from the detection of prominent peaks of archaeol in the polar fraction32 (Fig. 3C), as well as squalene and relatives (dihydrosqualene and tetrahydrosqualene) in the apolar fraction33 (Fig. 3A). Squalene and a variety of unsaturated derivatives are present in the neutral lipid fractions of many archaea with high abundances in saline lakes34. The relative abundance of autotrophs over heterotrophs35 can be estimated by the ratio of the autotrophically-related pristane and phytane over the both autotrophically- and heterotrophically-produced n-C17 and n-C18 alkanes ([Pr + Ph]/[n-C17 + n-C18]). A ratio of 0.56 in the Tirez sediments suggest the presence of a relevant proportion of heterotrophs in the ancient lacustrine system.Furthermore, the lipid biomarkers analysis was able to detect compounds specific of additional microbial sources, such as cyanobacteria36 (n-C17, C17:1, or 7Me-C15 and 7Me-C17), microalgae and/or diatoms (phytosterols37; or C20:5, and C22:6 alkanoic acids30), and other photoautotrophs (phytol and potentially degradative compounds such as pristane and phytane31). A relatively higher preservation of the cell-membrane remnants (i.e., lipids) compared to the DNA-composing nucleic acids may contribute to explain the lack of detection of cyanobacteria, diatoms and microalgae, and other phototrophs by DNA analysis (a deficit in our results shared with Montoya et al.16, and Preston et al.22). Although abundant in higher plants38, sterols such as those detected here (i.e., the sterols campesterol, stigmasterol, and β-sitosterol, as well as ergosterol) are also major sterols in some microalgal classes37 (such as Bacillariophyceae, Chrysophyceae, Euglenophyceae, Eustigmatophyceae, Raphidophyceae, Xanthophyceae, and Chlorophyceae), cyanobacteria (β-sitosterol), and fungi (ergosterol39).The carbon isotopic composition of lipid biomarkers provides a rapid screening of the carbon metabolism in a system, by recognizing the principal carbon fixation pathways used by autotrophs. The range of δ13C values measured in the Tirez sediments (from − 33.9 to − 16.1‰) denotes a mixed use of different carbon assimilation pathways, involving mostly the reductive pentose phosphate (a.k.a. Calvin–Benson–Bassham or just Calvin) cycle (from − 19 to − 30‰), and in lesser extent the reductive acetyl-CoA (a.k.a. Wood–Ljungdahl) pathway (from − 28 to − 44‰), and/or the reverse tricarboxylic acid (rTCA) cycle (from − 12 to − 21‰).The lipids synthesized by microorganisms using the Calvin or reductive acetyl-CoA pathway are typically depleted relative to the bulk biomass, particularly those produced via de latter pathway. In the dry Tirez sediments, the majority of the lipid compounds are more depleted in 13C than the bulk biomass (Fig. 4). In particular, the branched alkane DiMeC18 (Fig. 4A) and the SRB-indicative 10Me16:0 acid (Fig. 4B) showed the most depleted δ13C values and suggested the use of the reductive acetyl-CoA pathway. The rest of lipid compounds showed isotopic signatures (from − 16.1 to − 31.4‰) compatible with the prevalence of the Calvin pathway. These values may directly reflect the autotrophic activity of microorganisms fixing carbon via the Calvin cycle or heterotrophic activity of microorganisms growing on their remnants. Thus, the saturated and linear alkyl chains of lipids (i.e., n-alkanes, n-alkanoic acids, and n-alkanols) showing the most negative δ13C values (e.g., alkanes n-C17 and C17:1; or acid C18:1[ω7]) reflect prokaryotic sources of Calvin-users autotrophs (e.g., cyanobacteria or purple sulfur bacteria), while the rest of compounds with slightly less negative δ13C values instead stem from the autotrophic activity of eukaryotes also users of the Calvin cycle (unsaturated fatty acids and sterols) or from the metabolism of heterotrophs such as SRB (iso/anteiso-, other branched, and cyclopropyl fatty acids) and haloarchaea (isoprenoids, phytanol, and archaeol). All in all, the compound-specific isotope composition of the dry sediments in the today´s Tirez lagoon may indirectly reflect the prevailing autotrophic mechanisms in the present lacustrine system of Tirez, by showing isotopic signatures of secondary lipids similar to their carbon source40.In addition, the use of a number of lipid molecular ratios or proxies allow further characterization of the lacustrine ecosystem and depositional environment. For example, the average chain length of the n-alkanes (24.1) suggests a relevant presence of eukaryotic biomass in the lacustrine sediments, since long-chained alkanes ( > C20) are known to originate from epicuticular leaf waxes in higher plants41. Highlighting the relevance of eukaryotes and their ecological roles is one of the major contributions of this work, because previous studies on the microbial ecology of hypersaline environments have been focused primarily on prokaryotes42.The proportion of odd n-alkanes of high molecular chain (i.e., n-C27, n-C29, and n-C31) over even n-alkanes of low molecular chain (i.e., n-C15, n-C17, and n-C19) provides an estimate of the relative abundance of terrigenous over aqueous biomass43, which in Tirez is TAR = 1.8. The Paq index may also be used to differentiate the proportion of terrigenous versus aquatic (emergent and submerged) plant biomass44. A Paq of 0.3 in the Tirez sediments from 2021 supported the relative abundance of land plants. Finally, the depositional environment in the lacustrine system of Tirez may be also characterized analyzing the ratio of pristane over phytane (Pr/Ph), which is higher than 1 when phytol degrades to pristane under oxic conditions45. Assuming that both isoprenoids in the Tirez sediments derived from phytol31, according to their similarly depleted δ13C (Fig. 4A), we can conclude that the sediments in the Tirez lagoon were deposited under predominantly oxic conditions (i.e., Pr/Ph ratio of 1.1).In summary, the lipid biomarkers study revealed useful information about the depositional environment and lacustrine ecosystem, including the presence of active or past autotrophic metabolisms involving prokaryotes (e.g., cyanobacteria and purple sulfur bacteria) and eukaryotes (plants, diatoms and other microalgae), as well as heterotrophic metabolisms of likely SRB and haloarchaea growing on Calvin-users exudates. These results are quite in agreement with the microbial community previously reported16 in sediments from the wet and dry seasons: abundant Gammaproteobacteria and Alphaproteobacteria, together with Algae and Cyanobacteria, dinoflagellates and filamentous fungi, Bacillota, Actinomycetota (previously named Actinomycetes), and a halophilic sulfate-reducing Deltaproteobacteria.Tirez as the first astrobiological “time-analog” for early MarsEarly Mars most likely had a diversity of environments in terms of pH, redox conditions, geochemistry, temperature, and so on. Field research in terrestrial analog environments contribute to understand the habitability of this diversity of environments on Mars in the past, because terrestrial analogues are places on Earth characterized by environmental, mineralogical, geomorphological, or geochemical conditions similar to those observed on present or past Mars9. Therefore, so far analogs have been referred to terrestrial locations closely similar to any of the geochemical environments that have been inferred on Mars, i.e., they are “site-analogs” that represent snapshots in time: one specific environmental condition at a very specific place and a very specific time. Because of this, each individual field analog site cannot be considered an adequate representation of the changing martian environmental conditions through time. Here we introduce the concept of astrobiological “time-analog”, referred to terrestrial analogs that may help understand environmental transitions and the related possible ecological successions on early Mars. In this sense, they should be “time-resolved analogs”: dynamic analog environments where we can analyze changes over time. To the best of our knowledge, this is the first study that looks at the environmental microbiology of a Mars astrobiological analog site over a significant and long period of change, and try to understand the ecological successions to put them in the context of martian environmental evolution.As Mars lost most of its surface water at the end of the Hesperian5,9,12, this wet-to-dry global transition can be considered the major environmental perturbation in the geological history of Mars, and therefore merits to be the first one to be assigned a “time-analog” for its better understanding and characterization. The drying of Mars was probably a stepwise process, characterized by multiple transitions between drier and wetter environments12,47, and therefore the seasonal fluctuations and eventual full desiccation of Tirez represent a suitable analog to better understand possible ecological transitions during the global desiccation of most of the Mars’s surface before the Amazonian (beginning 3.2 Ga).To introduce Tirez as the first Mars astrobiological “time-analog” of the wet-to-dry transition on early Mars, the objective of this study was threefold: first, we wanted to identify the dominant prokaryotic microorganisms in the active Tirez lagoon 20 years ago, a unique hypersaline ecosystem with an ionic composition different from that of marine environments, and therefore potentially analogous to ancient saline lacustrine environments on Mars during the Noachian and into the Hesperian46,47. Our results provide a preliminary basis to hypothesize how the microbial communities on the Noachian Mars could have developed in salty environments with dramatically fluctuating water availability. The requirement to deal with important variations in ionic strength and water availability, involving at times the complete evaporation of the water, could have represented additional constraints48 for microorganisms on early Mars.The second objective of this investigation was the identification of the microbial community inhabiting the desiccated Tirez sediments today, after all the water was lost, as a potential analog to desiccated basins on Mars at the end of the Hesperian1,3,4,47. Our results suggest that hypothetical early microbial communities on early Mars, living with relative abundance of liquid water during the Noachian, would have been forced to adapt to increasingly desiccating surface environments, characterized by extreme conditions derived from the persistent dryness and lack of water availability. Our investigation in Tirez suggest that hypothetical microorganisms at the end of the Hesperian would have needed to evolve strategies similar to those of microorganisms on Earth adapted to living at very low water activity49, to thrive in the progressively desiccating sediments.And the third objective of this investigation was the identification of the lipidic biomarkers left behind by the microbial communities in Tirez, as a guide to searching and identifying the potential leftovers of a hypothetical ancient biosphere on Mars. Lipids (i.e., fatty acids and other biosynthesized hydrocarbons) are structural components of cell membranes bearing recognized higher resistance to degradation relative to other biomolecules, thus with potential to reconstruct paleobiology in a broader temporal scale than more labile molecules50. Our results reinforce the notion that lipidic biomarkers should be preferred targets in the search for extinct and/or extant life on Mars precisely because they are so recalcitrant. More

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Sampling sites and sample preparationCulms of three- to four-year-old of Bambusa vulgaris Schrad. ex J.C., B. maculata Widjaja, and Gigantochloa atter (Hassk) Kurz ex Munro were collected from naturally bamboo forests at four sites in Lombok Island, Indonesia23. The culm age was estimated based on some morphological features (the presence of culm sheath, color, and sound created by tapping with fingers) checked by an experienced bamboo farmer. Figure 1 shows the map of sampling sites and climatic conditions of the sites. Ten individual culms in each species at each site were collected from different clumps and cut 20 cm above the ground (Fig. 2). A total of 120 culms (three species × four sites × 10 individual culms from 10 individual clumps) were collected in the present study (Fig. 2). To determine the longitudinal variations of the anatomical characteristics and mechanical properties, the internode section was collected at 2-m intervals from 2 to 8 m above the ground; a total of 480 internode sections. (120 culms × four heights) were obtained from three species (Fig. 2). The collection of bamboo culms was permitted by Indonesian Institute of Science (Reference no. B-206/SKIKH/KS.02.04/X/2020) and complied with relevant guidelines and regulations of Indonesian CITES Management Authority, Ministry of Environment and Forestry, Indonesia. In addition, the voucher specimen was deposited at the Herbarium Lesser Sunda, University of Mataram, Indonesia under the voucher number of DSR01, 02, and 03 (specimens were identified by Mr. Niechi Valentino). Table 1 shows the culm diameter at 1.3 m above the ground, total culm height, and mean value of culm thickness at four positions23.Figure 1Locations and climate conditions of sampling sites in the present study23. Note: Site I, Tempos (8°41′59″ S, 116°8′40″ E); Site II, Kabul (8°47′21″ S, 116°10′21″ E); Site III, Keruak (8°45′45″ S, 116°28′54″ E); Site IV, Genggelang (8°23′16″ S, 116°15′35″ E). *, mean annual precipitation. The value in the bracket is the mean annual temperature. Climate data were provided from Nusa Tenggara River Basin Management I, Indonesia. Mean monthly temperature and precipitation were calculated by averaging monthly values from 2016 to 2018. Bars indicate the mean values of precipitation. Circles indicate the mean values of temperature. The graph was originally created by R27 (version 4.0.3, https://www.R-project.org/).Full size imageFigure 2Photographs of the clumps in three bamboo species (a–c) and schematic diagrams of experimental procedures (d). Note: a, B. vulgaris; b, B. maculata; c, G. atter. The specimens of fiber area measurement and mechanical properties have the whole culm thickness (including the cortex and inner part of the culm) in the radial direction.Full size imageTable 1 Mean values and standard deviations of growth characteristics in three bamboo species at each site23.Full size tableAnatomical characteristicsThe internode sections were split into two parts: the strips (10 mm in the longitudinal direction) and the small blocks (10 [T] mm by 10 [L] mm by culm thickness in the radial direction) (Fig. 2). The strips and small blocks were the samples for measuring fiber length and fiber area, respectively. In the present study, the fiber area was defined as the sheaths area around the vascular bundles24.To determine the fiber length, small sticks (not including the cortex and the most inner part of the culm) were obtained from the strips with a razor blade (Fig. 2). Randomly selected sticks from each height position (without separation of collected positions of the samples within the radial direction of the culm in a height) were macerated with Schultze’s solution (100 mL of 35% nitric acid containing 6 g potassium chloride) at 70 °C for two hours. The length of 50 fibers was measured in each sample with a digital caliper (CD-15CX, Mitutoyo, Kawasaki, Japan) on a microprojector (V-12B, Nikon, Tokyo, Japan).To measure the fiber area, one block was taken at each height position on each individual culm (Fig. 2). The transverse sections of the blocks were polished with sandpaper sheet (#180, 3 M Japan, Tokyo, Japan), and then their images were captured using a microscope digital camera (DS-2210, Sato Shouji Inc., Kawasaki, Japan) attached to a stereo microscope (SZX12, Olympus, Tokyo, Japan). The fiber area was determined by ImageJ25 (version 1.53e). Binarized images were prepared by ImageJ to distinguish as clearly as possible between the vascular bundle and the background (Fig. 3). The darker area of binarized images in Fig. 3 was identified as fiber sheaths. The fiber area was calculated as follows:$$FAleft( % right) , = A_{fs} /A_{c} times {1}00$$
(1)
where FA = fiber area (%), Afs = the transverse-sectional area of fiber sheath in bamboo culm (mm2), and Ac = the transverse-sectional area of bamboo culm (mm2).Figure 3The photomicrographs of transverse section in B. vulgaris (a and d), B. maculata (b and e), and G. atter (c and f). Note: a, b and c, original image; d, e and f, binarized image processed by ImageJ25 (version 1.53e, https://imagej.nih.gov/ij/). The darker area in photomicrographs (d, e and f) is fiber sheath area.Full size imageMechanical propertiesThe following mechanical properties of culm were measured: bending properties (MOE and MOR), CS, and tensile properties (TM and TS). A total of 480 specimens (one specimen × four heights in an individual × ten individuals × three species × four sites) without node were obtained in each property (Fig. 2).The strips (10 [T] mm × 200 [L] mm × varied culm thickness in the radial direction) were prepared as the specimens for the static bending test (Fig. 2). The static bending test was conducted using a universal testing machine (MSC 5/500–2, Tokyo Testing Machine, Tokyo, Japan). A load was applied to the center of the specimen on the outer cortex surface with 180 mm span and 3 mm min−1 load speed. Due to larger thickness (exceeded 12.9 mm = 180 mm of span / 14) in the radial direction, the span / depth ratio in some specimens was less than 14, indicating that MOR in some specimens might be underestimated due to the occurrence of the shearing strength26. Of 480 specimens, the large culm thickness exceeded 12.9 mm was total 19 specimens from B. vulgaris species collected at 2 m height position from different sites (Site I = four specimens, Site II = six specimens, Site III = four specimens, and Site IV = five specimens). However, all these 19 specimens were broken at the tension side of the specimens during static bending test, which was the normal breaking forms of bending specimens with span / depth ratio less than 14.The load and deflection were recorded with a personal computer, and then MOE and MOR were calculated by the following formulae:$$MOE , left( {GPa} right) , = Delta Pl^{3} / , 4Delta Ybh^{3} , times 10^{ – 3}$$
(2)
$$MOR , left( {MPa} right) , = , 3Pl/ , 2bh^{2}$$
(3)
where ΔP = difference between upper and lower proportional limit within the range of elasticity (N), l = length of the span (mm), ∆Y = deflection due to ∆P (mm), b = width of the specimen (mm), h = height of the specimen (mm), and P = maximum load (N).The compressive test specimen (10 [T] mm × 20 [L] mm × culm thickness in the radial direction) was also prepared (Fig. 2). The test was conducted using a universal testing machine (RTF-2350, A&D, Tokyo, Japan) with a load speed of 0.3 mm min−1. The compressive strength parallel to grain (CS) was calculated by the following formula:$${text{CS }}left( {{text{MPa}}} right) , = P/A_{0}$$
(4)
where P = maximum load (N), and A0 = the cross-sectional area of the specimen (mm2).The tensile tests were conducted using bone-shaped specimens (Fig. 2). The specimen length was 230 (L) mm with a 20 (T) mm width of the specimen grip. The cross-sectional area of the specimen was 2 mm in the tangential direction by culm thickness in the radial direction. A strain gage type extensometer (SG25-10A, A&D, Tokyo, Japan) was used to detect the elongation in the test specimen. The specimen grip sections were attached to small boards (75 mm in length × 40 mm in width × 5 mm in thickness) and then were clamped between the metal grip of a universal testing machine (RTC-2410, A&D, Tokyo, Japan). The tensile load was applied at 1 mm min−1. The tensile strength (TS) and Young’s modulus (TM) were calculated by the following formulae:$${text{TS }}left( {{text{MPa}}} right) , = P/A_{0}$$
(5)
$${text{TM }}left( {{text{GPa}}} right) , = Delta Pl/A_{0} Delta l times {1}0^{{ – 3}}$$
(6)
where P = maximum load (N), A0 = the cross-sectional area of the specimen (mm2), ∆P = difference between upper and lower proportional limit within the range of elasticity (N), l = gauge length (mm), and ∆l = elongation of the original gauge length (mm).The moisture content and air-dry density of each specimen were measured after each mechanical testing by the oven-dry method. The moisture content and air-dry density of the specimen at testing were listed in Table S1.Statistical analysisThe statistical analyses were conducted using R software (version 4.0.3)27. To evaluate the longitudinal variations of the measured properties in each species, the y-intercept, linear, and nonlinear mixed-effects models with each measured property value as a responsible variable, the height position as a fixed effect, and site and individual culm as random effects were developed by the “lmer” function in “lme4” packages28 and the “nlme” function in the “nlme” package29. The following four full models were developed and compared:Model I (y-intercept model):$$Y_{ijk} = alpha_{{1}} + Site_{{{1}k}} + Culm_{{{1}jk}} + e_{ijk}$$
(7)
Model II (linear model):$$Y_{ijk} = , (beta_{0} + Site_{0k} + Culm_{0jk} )X_{ijk} + beta_{{1}} + Site_{{{1}k}} + Culm_{{{1}jk}} + e_{ijk}$$
(8)
Model III (logarithmic model):$$Y_{ijk} = , (gamma_{0} + Site_{0k} + Culm_{0jk} ){text{ ln }}left( {X_{ijk} } right) + gamma_{{1}} + Site_{{{1}k}} + Culm_{{{1}jk}} + e_{ijk}$$
(9)
Model IV (quadratic model):$$begin{gathered} Y_{ijk} = , (zeta_{0} + Site_{0k} + Culm_{0jk} )X_{ijk}^{{2}} + , (zeta_{{1}} + Site_{{{1}k}} + Culm_{{{1}jk}} )X_{ijk} hfill \ + zeta_{{2}} + Site_{{{2}k}} + Culm_{{{2}jk}} + e_{ijk} hfill \ end{gathered}$$
(10)

where Yijk is measured property at the ith height position from the jth individual culm within the kth site, Xijk is the ith height position from the jth individual culm within the kth site, α1, β0, β1, γ0, γ1, ζ0, ζ1, and ζ2 are the fixed effects, Site0k, Site1k, and Site2k are the random effect at the site level, Culm0jk, Culm1jk, and Culm2jk are the random effects at the individual culm level, and eijk is residual. Total 36 derived models (three y-intercept models, 15 linear models, nine logarithmic models, and nine quadratic models) were developed. The model selection was conducted using the Akaike information criterion30. The model with the minimum AIC value was regarded as the most parsimonious model among developed models. In addition, the differences in AIC (ΔAIC) ≤ 2 indicate no significant differences between models, and a simpler model with fewer parameters is preferred31. To evaluate the longitudinal variation, estimated values of each property was calculated at 0.1 m interval from 2.0 to 8.0 m above the ground using fixed-effect parameters of the selected models. Mean value and standard deviation were obtained from the estimated values from 2.0 to 8.0 m in each property. In addition, the coefficient of variation was also calculated from the mean value and standard deviation. The longitudinal variation patterns were classified into four types (Types A to D) based on the model selection (Fig. 4). Although model II to IV was selected, longitudinal variation with the coefficient of variation less than 3.0% was regarded as stable (Type A in Fig. 4).Figure 4Classification of longitudinal variation of bamboo culm property. Note: Lines or curves indicate formulae with fixed-effect parameters in the selected mixed-effect model for explaining longitudinal variation (Tables 3, 4, 5). Coefficient of variation calculated from mean values and standard deviation from 2 to 8 m above the ground estimated by fixed-effect parameters values less than 3.0% is regard as stable variation (Type A), even in selected model is Model II to IV.Full size imageGeographic variations in each bamboo property were estimated by evaluating the variance component of sites and culms as random effects by using the intercept-only linear mixed-effects model. The full model is described as follows:$$Y_{ijk} = mu + Site_{k} + Culm_{jk} + e_{ijk}$$
(11)
where Yijk is the bamboo property at the ith height position of the jth individual culm within kth site, μ is the model intercept or grand mean, Sitek is the random effect of the kth site, Culmjk is random effect of jth individual culm within kth site, and eijk is the residual. The contribution of each level of variation was calculated as a percentage of the total random variation in the best model32,33. More