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Countries have yet to agree to protect at least 30% of land, a crucial target proposed in the global biodiversity deal.Credit: Roberto Schmidt/AFP via Getty

A beleaguered global deal to save the environment got a financial boost last week when Germany announced that it was upping its funding for international biodiversity conservation to €1.5 billion (US$1.49 billion) a year — an increase of €0.87 billion — making it the largest national financial pledge yet to save nature. The announcement came at a 20 September meeting in New York City, where political leaders, businesses and conservation and Indigenous-rights groups came together to rally momentum and support ahead of the United Nations biodiversity summit in Montreal, Canada, in December.Conservationists welcomed the extra funding, but warned that other wealthy countries must also reach deeper into their pockets to ensure that nations agree on a new biodiversity agreement, called the Post-2020 Global Biodiversity Framework. Estimates suggest that an additional US$700 billion annually is needed to protect the environment.Concerns over insufficient financing for global biodiversity conservation have stalled negotiations and threaten to derail attempts to finalize a deal in Montreal. The forthcoming summit will be the 15th meeting of the Conference of the Parties (COP15) to the UN’s Convention on Biological Diversity.Announcing the new funds, German Chancellor Olaf Scholz said: “With this contribution, we want to send a strong signal for an ambitious outcome of the biodiversity COP-15.”Claire Blanchard, head of global advocacy at WWF, a conservation group, told Nature that the extra funding “is highly significant” and sends an important signal that rich countries are prepared to step up.But she adds: “More signals of this kind will be needed to create the environment conducive to constructive dialogue in the negotiation room.”Andrew Deutz, a specialist in biodiversity law and finance at the Nature Conservancy, a conservation group in Arlington, Virginia, says he expects further funding announcements to come in the run up to and at the COP15.Other pledgesSeveral key political leaders, including Justin Trudeau, Canada’s prime minister, echoed calls for rich nations to make urgent progress to secure the biodiversity deal. Trudeau urged countries to agree on two crucial targets proposed in the biodiversity framework, both to be met by 2030: to halt and reverse biodiversity loss, and to protect at least 30% of land and seas.The new funding was bolstered by other pledges and developments, including a promise from a partnership of some of the world’s wealthiest private philanthropic foundations and charities to add to the $5 billion they have already committed to conservation, if other countries promise more funds.The partnership — which includes the Bezos Earth Fund, an environmental fund financed by entrepreneur Jeff Bezos — has already spent around $1 billion of its promised financing over the past two years, says Cristián Samper, head of the Wildlife Conservation Society, a not-for-profit group. Samper was speaking on behalf of the partnership at the meeting in New York City.Frans Timmermans, vice-president of the European Commission, reaffirmed that Europe would double its international biodiversity funding to $1.13 billion annually — a promise originally announced in September last year. Timmermans told the meeting that the European Union would set out more details about the funding soon.Funding shortfallAlso at the meeting, a group of four countries comprising Ecuador, Gabon, the Maldives and the United Kingdom launched a joint 10-point plan to bridge the biodiversity finance gap, which is estimated at $700 billion annually.The plan sets out the financial commitments and policy reforms needed to finance biodiversity on the required scale. For example, it encourages wealthy and lower-income nations to allocate new funds for biodiversity and to quickly deliver on their existing financial pledges. It requires donor countries to ensure that funds for overseas development do no harm to biodiversity. And it asks countries to dedicate a portion of their national funding for climate change to activities that also protect and conserve nature.The plan also commits countries to ensuring that public finance is invested in ways that benefit biodiversity, and to reviewing national subsidies and redirecting those that are harmful to nature. It calls on businesses to assess and disclose commercial risks associated with biodiversity decline, and to set quantitative targets to reduce their impact on the natural world. And it encourages multilateral development banks — such as the World Bank in Washington DC — and international financial institutions to ensure that their investments benefit biodiversity, and asks that they report on their biodiversity funding in time for COP-15.So far, 15 countries, including Canada, Germany and Norway, as well as the EU have endorsed the plan.“The plan provides a clear pathway for bridging the global biodiversity finance gap. Its significance lies in the political signal it sends,” says Blanchard.António Guterres, secretary-general of the UN, urged political leaders to “act now and at scale” to secure biodiversity financing and ensure agreement on the framework. “If negotiations continue at their slow pace, we are headed to failure,” he told the meeting. More

Structural characterization of slag samplesThe FTIR spectra of granulated blast furnace slag (Sample 1), waste slag dumped in landfill (Sample 2) and combination of both 50% granulated blast furnace slag + 50% waste slag dumped in landfill (Sample 3) are presented in Fig. 1.Figure 1FTIR spectra of slag samples.Full size imageBy analysing the spectrum (detailed figure) in the range of 700–1100 cm−1, it can be found that there are obvious absorption peaks in the spectrum of all the slag samples. The granulated blast furnace slag shows the characteristic absorption bands at 3640, 1418, 980, 944, 861, 753 and 710 cm−1. The band at 3640 cm−1 is assigned to the stretching vibration of the hydroxyl group originated from the weakly absorbed water molecules on the slag surface24. The characteristic absorption bands at 1418, 861 and 710 cm−1 are ascribed to the asymmetric stretching mode and bending mode of carbonate group, respectively and the band at 980 cm−1 are attributable to the stretching vibrations of Si–O25. The band at 944 and 752 cm−1 represent the internal vibration of [SiO4]4− and [AlO4]5− tetrahedral and comes from Si (Al)–O-antisymmetric stretching vibration26.The different vibration modes for the sample of waste slag can be observed in the FTIR spectrum. The absorption bands shown are at 1418, 873, 712, 667 and 419 cm−1. The peak at 1418 cm−1 is assigned to the asymmetric stretching mode and bending mode of carbonate group. Calcite phase is confirmed by characteristic peaks at 712 cm−1 (ʋ2 out of plane bending vibration of the CO3−2 ion) and 873 cm−1 peak (ʋ2 split in-plane bending vibrations of the CO3−2 ion27. Calcium aluminate phase is identified by characteristic peak at 419 cm−128. Peak around 667 cm−1 is described as absorption band for different M–O (metal oxide) such as Al–O, Fe–O, Mg–O etc.29.In the case of combination of both 50% granulated blast furnace slag and 50% waste slag dumped in landfill the intensity of absorption peaks is smaller in comparison with Sample 1 and Sample 2 of slag. The characteristic absorption peaks (978 and 753 cm−1) which correspond with characteristic peaks of Sample 1 are shifted compared to the Sample 1, assigned to the stretching vibrations of Si–O and to the Si (Al)–O-antisymmetric stretching vibration, respectively, can provide important evidence of chemical interaction between Sample 1 and Sample 2. The decrease of the intensity of the bands appearing at 875 and 709 cm−1 cans be attributed to overlapping the vibrations of the CO3−2 ion from calcite phase.Figure 2 presents the SEM micrographs of the slag samples (Sample 1–3). One can see the characteristic morphology- the sizes and the forms of the slag samples.Figure 2SEM images of slag samples.Full size imageAt larger magnifications it can be observed that the surface is rough and uneven, and one can notice rounded grain-like rugged formations. The slag samples display aggregated particles with average diameter of a few microns. Also, in these rounded formations it can be seen different morphologies like spheres, rods, boards specific each compound/phase from metallurgical slags.Figure 3 illustrates the EDX elemental analysis of granulated blast furnace slag (Sample 1), waste slag dumped in landfill (Sample 2) and combination of both 50% granulated blast furnace slag + 50% waste slag dumped in landfill (Sample 3).Figure 3EDX elemental map of slag samples.Full size imageOne can observe that the predominant elements in the examined area are constated in carbon, oxygen, calcium, and iron, confirming the FTIR spectra.Figure 4 shows EDX spectra of slag samples recorded on different selected punctual area, to obtain more information about the elemental composition of specific areas. For all the tested slag samples have similar elements content.Figure 4EDX spectra analysis of slag samples.Full size imageThe selected punctual areas are highlighted thus: the spheric structure are with yellow line and the structure like boards are with green line for all the analysed slag samples. In the case of Sample 1 for both structures the values of chemical elements present are similar and the silicon has a higher value at spheric structure which can be correlated with the presence of silica (SiO2). The higher content of calcium reveals that the Sample 1 is blast furnace slag dominated by calcium and silicon compositions. In the case of slag dumped in landfill (Sample 2) the content of carbon increase for both structures and some chemical elements like titanium, barium, manganese doesn`t appear in EDX spectra and the explanation for this phenomenon is that the slag was dumped in landfill for more than 30 years. One can observe for combination of both 50% granulated blast furnace slag + 50% waste slag dumped in landfill (Sample 3) that the values of all the chemical elements for both spheric and board-like structure are between the first two samples, confirming the FTIR spectra regarding chemical interaction between Sample 1.XRD patterns of the slag samples with the phases identified are shown in Fig. 5. Sample 1 show minor peaks of free CaO and MgO, which may be deleterious and cause reduction in strength. The phases and amorphous contents of the Sample 1 granulated blast furnace slag are broadly consistent with literature30. Sample 3 of slag consists of crystalline phase – Ca2Mg2SiO7, Ca2Fe2AlO5, CaCO3 and CaO as observed by the XRD analysis. In terms of the relations of phase thermal equilibrium, the compounds identified form an isomorphic series of melilites that is specific to basic metallurgical slags.Figure 5X-ray diffraction patterns of slag samples.Full size imageIn Table 1 are presented the values expressed as ppm of chemical element detected in slag samples (Sample 1, 2 and 3).Table 1 XRF analysis of the slag samples.Full size tableThe results show a large quantity of calcium in all three samples of slag. Also, the elements detected such as Fe, Al, Mg and Si are in accordance with XRD spectra.Physical–chemical characterization of soil-slag mixturesThe chemical composition of the major elements that compound the soil, soil- slag and slag samples was determined by XRF. The values expressed as ppm of chemical elements are presented in Table 2. In the case of soil sample the content of the main constituents is iron, titanium, manganese, and potentially toxic elements (PTE) such as arsenic, zinc, copper, and cobalt. For soil-slag 1 with weight ratio soil: slag (1:1) it can be observed the disappearance of the potentially toxic elements (PTE) founded in soil sample and the decrease of concentration value of zinc. When the weight ratio of slag increases at 3 (soil-slag 2 sample) the values of main component increased in accordance with values of slag sample, but in the case of soil-slag 3 sample where the weight ratio of soil is bigger (3) it can be observed the cobalt presence. Based on these XRF results we can say that take place an elimination of potentially toxic elements in contaminated soil by applying slag in a bigger proportion.Table 2 XRF analysis of the soil-slag samples.Full size tableWith the aid of a pH meter, CONSORT C 533 the important parameters of soil and slag solutions were measured as: the pH, conductivity, and the salinity, as shown in Table 3. The data presented in Table 3 suggest that the soil sampled has the pH = 5.2 corresponding to a medium acid soil, which does not sustain a high fertility and is not able to offer proper conditions for crops. Also, the pH of soil has important influence on soil fertility, decreases the availability of essential elements and the activity of soil microorganisms which can determine calcium and magnesium deficiency in plants and decreases phosphorous availability. The pH value of slag solution (12.5) corresponds as strongly basic character which is beneficial in amelioration process of acidic soils and the presence of this type of slag sustain the improving of soil characteristics, too. For the soil-slag samples the pH value increase with the increasing of the weight ratio of slag and the mixtures soil-slag obtained can be framed into the category of weakly alkaline soils.Table 3 The physical–chemical characteristics of soil and slag solutions.Full size tableThe data given in Table 4 show that the humidity of soil is bigger and decreases in soil-slag samples with adding of slag content. The values of total soil-slag porosity are between 40 and 50% and depends on the density and apparent density of the soil being influenced by the mineralogical composition, the content of organic matter and the degree of compaction and loosening of the soil, the crystalline structure of soil minerals.Table 4 The physical–chemical characteristics of soil-slag samples.Full size tableConsidering the structural and morphological characterization of the investigated slag samples we propose a recipe of blast furnace slag and of waste slag dumped in landfill in accordance with the waste directive 2008/98/EC regarding the strategic goal of EU to a complete elimination of the disposal of wastes. The slag dump of Steel Plant of Galati has an enormous quantity of unused waste slag which may be mixed with granulated blast furnace slag, to save the natural resources used as raw materials in the metallurgical technological process.The presence of Ca2+ in the composition of the slag can maintain high alkalinity in the soil for a long time in the natural environment. The alkaline pH of the soil may contribute to a decrease the available concentration of heavy metals by reducing metal mobility and bonding metals into more stable fractions. One of the objectives of this research is improving the quality of the environment by using the mixture between two different slags on agricultural lands and reintroducing them in the agricultural centre, especially in acid soils. Acidic soils are characterized by an acidic pH that has spread in recent years due to excessive fertilizers or far too aggressive work31. The production is significantly influenced, and the treatment of acid soils is usually done using a series of natural materials (lime, dolomite), the consumption being approx. 20 t/hectare depending on the acidity of the soil and the nature of the plants grown on the respective surfaces.Our research consists in improving the characteristics and qualities of the acidic soils and helping to reintroduce it into the agricultural circuit by transforming a waste into a new material friendly-environmental, the mixture of blast furnace slag and waste slag dumped in landfill. More

Ethical statementThis research project was ethically reviewed and approved by the Ethics Committee of the Instituto Gulbenkian de Ciência (license reference: A009.2018), and by the Portuguese National Entity that regulates the use of laboratory animals (DGAV – Direção Geral de Alimentação e Veterinária (license reference: 008958). All experiments conducted on animals followed the Portuguese (Decreto-Lei n° 113/2013) and European (Directive 2010/63/EU) legislations, concerning housing, husbandry and animal welfare.Escherichia coli clonesThe ancestral invader E. coli strain expresses a Yellow Fluorescent Protein (YFP), and carries streptomycin and ampicillin resistance markers for easiness of isolation from the mouse feces [galK::amp (pZ12)::PLlacO−1-YFP, strR (rpsl150), ΔlacIZYA::scar]. An E. coli strain used for the in vivo competition experiments is isogenic to the ancestral invader but expresses a Cyan Fluorescent Protein (CFP) and carries streptomycin and chloramphenicol resistance markers [galK::chlor (pZ12)::PLlacO−1-CFP, strR (rpsl150), ΔlacIZYA::scar]. The resident E. coli lineage was isolated from the feces along time using McConkey + 0.4% lactose medium, as previously described9. All the resident clones sampled from each mouse belong to E.coli phylogenetic group B9. The invader E. coli strains (YFP and CFP) derive from the K-12 MG1655 strain (DM08) and exhibit a gat negative phenotype, gatZ::IS112. The resident E. coli clone used for the competition experiments in the mouse gut expresses a mCherry fluorescent protein and a chloramphenicol resistance marker, allowing to distinguish the invader and resident strains in the mice feces.E. coli clones were grown at 37 °C under aeration in liquid media Luria broth (LB) from SIGMA — or McConkey and LB agar plates. Media were supplemented with antibiotics streptomycin (100 µg/mL), ampicillin (100 µg/mL) or chloramphenicol (30 µg/mL) when specified.Serial plating of 1X PBS dilutions of feces in LB agar plates supplemented with the appropriate antibiotics were incubated overnight and YFP, CFP or mCherry-labeled bacterial numbers were assessed by counting the fluorescent colonies using a fluorescent stereoscope (SteREO Lumar, Carl Zeiss). The detection limit for bacterial plating was ~300 CFU/g of feces9.In vivo evolution and competition experimentsAll mice (Mus musculus) used in this study were supplied by the Rodent Facility at Instituto Gulbenkian de Ciência (IGC) and were given ad libitum access to food (Rat and Mouse No.3 Breeding (Special Diets Services) and water. Mice were kept at 20-24 °C and 40-60% humidity with a 12-h light-dark cycle. For the in vivo evolution experiment we used the gut colonization model previously established9. Briefly, mice drank water with streptomycin (5 g/L) only for 24 h before a 4 h starvation period of food and water. The animals were then inoculated by gavage with 100 µL of an E. coli bacterial suspension of ~108 colony-forming units (CFUs). Mice A2, B2, D2, E2, G2, H2 and I2 were successfully colonized with the invader E. coli, while mice C2 and F2 failed to be colonized. Six- to eight-week-old C57BL/6 J non-littermate female mice were kept in individually ventilated cages under specified pathogen-free (SPF) barrier conditions at the IGC animal facility. Fecal pellets were collected during more than one year ( >400 days) and stored in 15% glycerol at −80 °C for later analysis. In the competition experiments between the invader ancestral E. coli and evolved populations, we colonized the mice using a 1:1 ratio of each genotype, with bacterial loads being assessed and frozen on a daily basis after gavage.In vivo competition experiments in which the two modes of selection (directional and diversifying) were acting for a longer time period were performed using evolved invader E. coli populations colonizing mice D2, B2 and A2, H2. Here we used both male (n = 8) and female (n = 8) C57BL/6 J mice aged six- to eight-week-old treated with streptomycin during 3 days before gavage. E. coli populations evolving for short time periods do not allow for strong conclusions on which mode of selection is taking place. Evolved invader populations such as I2 or G2 were therefore not used for in vivo fitness assays. To assess the impact of the mouse resident E. coli in the competitive fitness of dgoR we performed one-to-one competitions between the invader ancestral and dgoR KO clones. We first homogenized the mice microbiotas by co-housing the animals during seven days. The animals (n = 6, female C57BL/6 J mice aged six- to eight-week-old) were then maintained under co-housing and given streptomycin-supplemented (5 g/L) water during seven days to break colonization resistance and eradicate their resident E. coli. At this point, the co-housed mice were removed from the antibiotic-supplemented water for two days. The following day, one group of mice was gavaged with an mCherry-expressing resident E. coli (n = 3 mice) while the other group (n = 3) was not, with all animals being individually caged from this point on and receiving normal water without antibiotic. The day after gavage, all mice were colonized with a mix (1:1) of the invader ancestral and the dgoR KO clones, and the bacterial loads were assessed and frozen on a daily basis.Microbiota analysisFecal DNA was extracted with a QIAamp DNA Stool MiniKit (Qiagen), according to the manufacturer’s instructions and with an additional step of mechanical disruption32. 16 S rRNA gene amplification and sequencing was carried out at the Gene Expression Unit from Instituto Gulbenkian de Ciência, following the service protocol. For each sample, the V4 region of the 16 S rRNA gene was amplified in triplicate, using the primer pair F515/R806, under the following PCR cycling conditions: 94 °C for 3 min, 35 cycles of 94 °C for 60 s, 50 °C for 60 s, and 72 °C for 105 s, with an extension step of 72 °C for 10 min. Samples were then pair-end sequenced on an Illumina MiSeq Benchtop Sequencer, following Illumina recommendations. Sampling for microbiota analysis was performed until the microbiota composition stabilized (~1 year after the antibiotic perturbation).QIIME2 version 2017.1133 was used to analyze the 16 S rRNA sequences by following the authors’ online tutorials (https://docs.qiime2.org/2017.11/tutorials/). Briefly, the demultiplexed sequences were filtered using the “denoise-single” command of DADA2 version 1.1434, and forward and reverse sequences were trimmed in the position in which the 25th percentile’s quality score got below 20. Diversity analysis was performed following the QIIME2 tutorial35. Beta diversity distances were calculated through Unweighted Unifrac36. For taxonomic analysis, OTU were picked by assigning operational taxonomic units at 97% similarity against the Greengenes database version 13 (Greengenes 13_8 99% OTUs (250 bp, V4 region 515 F/806 R))37.Whole-genome sequencing and analysis pipelineDNA was extracted38 from E. coli populations (mixture of  > 1000 clones) or a single clone growing in LB plates supplemented with antibiotic to avoid contamination. DNA concentration and purity were quantified using Qubit and NanoDrop, respectively. The DNA library construction and sequencing were carried out by the IGC genomics facility using the Illumina Miseq platform. Processing of raw reads and variants analysis was based on the previous work39. Briefly, sequencing adapters were removed using fastp version 0.20.040 and raw reads were trimmed bidirectionally by 4 bp window sizes across which an average base quality of 20 was required to be retained. Further retention of reads required a minimum length of 100 bps per read containing at least 50% base pairs with phred scores at or above 20. BBsplit (part of BBMap version 38.9)41 was used to remove likely contaminating reads as explained previously39. Separate reference genomes were used for the alignment of invader (K-12 (substrain MG1655; Accession Number: NC_000913.2)) and resident (Accession Number: SAMN15163749) E. coli genomes. Alignments were performed via three alignment approaches: BWA-sampe version 0.7.1742, MOSAIK version 2.743, and Breseq version 0.35.144,45. Final average alignment depths for invader and resident populations across time points equalled 302 (median = 236) and 253 (median = 235), respectively. While Breseq provides variant analysis in addition to alignment, other variant calling approaches were used to identify putative variation in the sequenced genomes, and to verify data from Breseq. A naïve pipeline39 using the mpileup utility within SAMtools version 1.946 and a custom script written in python was employed. Only reads with a minimum mapping quality of 20 were considered for analysis, and variant calling was limited to bases with call qualities of at least 30. At these positions, a minimum of 5 quality reads had to support a putative variant on both strands (with strand bias, pos. strand / neg. strand, above 0.2 or below 5) for further consideration. Finally, mutations were retained if detected in more than one of the alignment approaches, and if they reached a minimum frequency of 5% at a minimum of one time point sampled. Further simple and complex small variants were considered from freebayes version 0.9.2147 with similar thresholds, while insertion sequence movements and other mobile element activity was inferred via is mapper version 248 and panISa version 0.1.649, as well as Breseq, as previously described39. All putative variants were verified manually in IGV version 2.750,51. Raw sequencing reads were deposited in the sequence read archive under bioproject PRJNA666769. Population dynamics of lineage-specific dynamics and the resulting Muller plots were inferred manually and are meant strictly as a means of presenting the data. In order to generate these plots, mutations were sorted by frequency (descending for each time point at which the population was sampled). The largest frequency mutations were considered major lineages within which minor frequency mutations occurred. Assuming that a mutation, which arises subsequent to a preexisting mutation (an already differentiated lineage) cannot exceed the frequency of that preexisting mutation at any point, and will fluctuate in frequency with the preexisting one, we assigned mutations to the lineages within each population. While this resolved the majority of high frequency and medium frequency mutations, low-frequency mutations within the Muller plots cannot be placed with high confidence, and are only included for completeness.Prophage induction rateTo calculate the maximum prophage induction rate we grew E. coli lysogenic clones, starting with the same initial OD600 values: ~0.1 (Bioscreen C system, Oy Growth Curves Ab Ltd), with agitation at 37 °C in LB medium in the presence or absence of mitomycin C along time (5 µg/mL)9. The OD600 values were normalized by dividing the ones in the presence of mitomycin C by the ones in the absence of mitomycin C (sampling interval: 30 min). The LN of this ratios along time originates a lysis curve, where the maximum slope corresponds to the maximal prophage induction rate for each clone analyzed. We tested evolved clones from mouse A2, H2 and G2 against the ancestral clone which only carries the Nef and the KingRac prophages. We also tested clones of the resident strain that had evolved in the presence of the invader for more than 400 days (these clones were sampled from mouse A2).
E. coli growth rate, growth curves, cell aggregation, biofilm and motility capacityTo calculate the maximum bacterial growth rate, we grew E. coli lysogenic clones, starting with the same initial OD600 values: ~0.1 (Bioscreen C system, Oy Growth Curves Ab Ltd), with agitation at 37 °C in LB medium along time using reading intervals of 30 min. The LN of the OD600 values along time originates a growth curve, where the maximum slope corresponds to the maximum bacterial growth rate for each clone analyzed.To test for metabolic differences of the psuK/fruA mutation, growth curves of evolved lysogenic E. coli clones, bearing the Nef and KingRac prophages, with or without the psuK/fruA mutation were performed with the same initial OD600 value (~0.03) for each clone. The clones were grown in glucose (0.4%) minimal medium (MM9-SIGMA) with or without pseudouridine (80 μM) and absorbance values were obtained using the Bioscreen C apparatus during 12 h.Frozen stocks of E. coli clones were used to seed tubes with 5 mL of liquid LB. These were incubated overnight at 37 °C under static conditions to assess the formation of cell flocks/clumps, observable to the naked eye, in order to evaluate the formation of cell aggregates. Biofilm was tested according a previously published protocol52 and to evaluate the motility capacity we adapted the protocol from Croze and colleagues53. Briefly, overnight E. coli clonal cultures grown with agitation at 37 °C in 5 mL LB medium supplemented with streptomycin (100 ug/mL) were adjusted to the same absorbance and a 3uL volume was dropped on top of soft agar (0.25%). Plates were incubated at 37 °C and photos were taken at day 1, 2 and 5 post-inoculation to assess swarming motility phenotype.Number of E. coli generations during mouse gut colonizationTo estimate the number of generations of E. coli in the mouse gut, we used a previously described protocol to measure the fluorescent intensity of a probe specific to E. coli 23 S rRNA (as a measure of ribosomal content) that correlates with the growth rate of the bacterial cells54. We measured the number of generations of the ancestral E. coli clone while colonizing the gut of 2 mice, treated during 24 h with streptomycin (5 g/L) before gavage, during 25 days.Plasmid DNA extraction and PCR detection of ~69Kb (repA) and ~109Kb (repB) plasmidsPlasmid DNA was extracted from overnight cultures using a Plasmid Mini Kit (Qiagen), according to the manufacturer’s guidelines. Specific primers for the amplification of repA and repB genes, were used to determine the frequency of the 68935 bp (~69 Kb) and 108557 bp (~109 Kb) plasmids, respectively, in the invader E. coli population.The primers used for repA gene were:repA-Forward: 5’-CAGTCCCCTAAAGAATCGCCCC-3’ and repA-Reverse: 5’-TGACCAGGAGCGGCACAATCGC-3’.For repB the primer sequences were:repB-Forward: 5’-GTGGATAAGTCGTCCGGTGAGC-3’ and repB-Reverse: 5’-GTTCAAACAGGCGGGGATCGGC3’.PCR amplification of plasmid-specific genes was performed in 12 isolated random clones from mouse A2 at days 104 and 493. PCR reactions were performed in a total volume of 25 μL, containing 1 μL of plasmid DNA, 1X Taq polymerase buffer, 200 μM dNTPs, 0.2 μM of each primer and 1.25 U Taq polymerase. PCR reaction conditions: 95 °C for 3 min, followed by 35 cycles of 95 °C for 30 s, 65 °C for 30 s and 72 °C for 30 s, finalizing with 5 min at 72 °C. DNA was visualized on a 2% agarose gel stained with GelRed and run at 160 V for 60 min.Construction of the dgoR KO mutantP1 transduction was used to construct a ΔdgoR mutant (dgoR KO). This KO strain was created by replacing the wild-type dgoR in the invader ancestral YFP-expressing genetic background by the respective knock-out from the KEIO collection, strain JW562755, in which the dgoR sequence is replaced by a kanamycin resistance cassette. The presence of the cassette was confirmed by PCR using primers dgoK-F: GCGATGTAGCGAGCTGTC, and yidX-R: GGGAATAAACCGGCAGCC. PCR reactions were performed in a total volume of 25 μL, containing 1 μL of DNA, 1X Taq polymerase buffer, 200 μM dNTPs, 0.2 μM of each primer and 1.25 U Taq polymerase. PCR reaction conditions: 95 °C for 3 min, followed by 35 cycles of 95 °C for 30 s, 65 °C for 30 s and 72 °C for 30 s, finalizing with 5 min at 72 °C. DNA was visualized in a 2% agarose gel stained with GelRed and run at 160 V for 60 min.RNA extraction, DNAse treatment, RT-PCR and qPCRThe Qiagen RNeasy Mini Kit was used for RNA extraction. RNA concentration and quality were evaluated in the Nanodrop 2000 and by gel-electrophoresis. DNase treatment was performed with the RQ1 DNase (Promega) by adding 0.5 μl of DNase to 1 μg of RNA and 1 μl buffer in a final volume of 15 ul, followed by incubation 30 min at 37 °C. Afterwards, 1 ul of stop solution was added and incubation for 15 min at 65 °C was performed to inactivate the DNase. As a control for complete DNA digest a PCR was performed on the reactions including positive controls. Reverse transcription was performed with M-MLV RT[-H] (Promega) by mixing 1 μg of RNA with 0.5 μl random primers (Promega) and nuclease free water to a volume of 15 μl, incubation at 70 °C for 5 min and a quick cool down on ice. Afterwards the reverse transcription was accomplished by adding 5 μl of RT buffer, 0.5 μl RT enzyme and 2 μl dNTP mix, followed by incubation for 10 min at 25 °C, 50 min at 50 °C and 10 min at 70 °C. The resulting cDNA was diluted 100-fold in nuclease free water before changes in gene expression were detected using the The QuantStudio 7Flex (Applied Biosystems) with iTaq Universal SYBR Green Supermix (BioRad) and the following cycling protocol: Hold stage: 2 min at 50 °C, 10 min at 95 °C. PCR stage (40 cycles): 15 s at 95 °C, 30 s at 58 °C, 30 s at 60 °C. Melt curve stage: 15 s at 95 °C, 1 min at 50 °C then increments of 0.05 °C/s until 95 °C. Melt curve analysis was performed to verify product homogeneity. All reactions included six biological and three technical replicates for each sample. A relative quantification method of analysis with normalization against the endogenous control rrsA and employing the primer specific efficiencies was used according to the Pfaffl method (add reference). The primers used were designed with PrimerQuest (idt). The used primer sequences were: psuK – TGCGTTAGCAGCGATTGA, AATTTACGCCTGGTGGAGTAG; arcA – GATTCATGGTACGGGACAGTAG, CCGTGACAACGAAGTCGATAA; yjtD – CGCACATGGATCTGGTGATA, GGCGTGGCGTAGTAATGATA and rrsR – GTCAGCTCGTGTTGTGAAATG, CCCACCTTCCTCCAGTTTATC.Statistics and reproducibilityCorrelation between microbiota diversity measures and E. coli loads (CFU) or persistence (1-presence or 0-absence) was performed in R using the statistical package rmcorr (version 0.5.2)56 and lme4 (version 1.1-10)57, respectively. The rate of accumulation of new ISs in vivo was compared using Wilcoxon paired signed ranked test for expected and observed insertions, while the rate of selective sweeps correlation was performed using the Spearman Correlation test. Selective sweeps were taken to be mutations or HGT events that reached  > 95% frequency in the population and kept high frequency until the end of the colonization. Statistical analysis of prophage induction as well as biofilm levels was performed using the Mann-Whitney test in GraphPad Prism (version 8.4.3). A single sample T-Test was used test if the growth rate of evolved invader clones deviates from the mean of the ancestral. A Wilcoxon rank sum test with continuity correction was used to compare the relative expression levels of the evolved clones with the ancestral. P values of x0 are of order of their inverse selection coefficient (up to logarithmic corrections):$${{{{{rm{G}}}}}}left(xright)approx 1,{{{{{rm{T}}}}}}left(xright)sim frac{1}{s}.$$
(1)

Clonal interference under uniform directional selection. This mode occurs in asexual populations when adaptive mutations become frequent enough to interfere with one another59,60,61. Only a fraction of the established adaptive mutations reaches fixation; sojourn times to intermediate frequencies are set by a global coalescence rate (widetilde{sigma }) that is higher than the typical selection coefficient of individual mutations62:

$${{{{{rm{G}}}}}}left(xright) < 1,{{{{{rm{T}}}}}}left(xright)sim frac{1}{widetilde{sigma}}.$$ (2) Details of these dynamics depend on the spectrum of selection coefficients and on the overall mutation rate, which set the strength of clonal interference. For moderate interference, where a few concurrent beneficial mutations compete for fixation, we expect a roughly exponential drop of the frequency propagator, (Gleft(xright)sim {{exp }}left(-lambda xright)), reflecting the probability that a trajectory reaches frequency x without interference by a stronger competing clade. Moderate interference generates an effective neutrality for weaker beneficial mutations and at higher frequencies63. This regime has been mapped for influenza64. In the asymptotic regime of a travelling fitness wave, where many beneficial mutations are simultaneously present, the fate of a mutation is settled in the range of small frequencies; that is, at the tip of the wave65. In this regime, emergent neutrality affects the vast majority of beneficial mutations and most of the frequency regime66. Hence, the frequency propagator rapidly drops to its asymptotic value (Gleft(x=1right)ll 1.) Adaptation under diversifying selection. More complex selection scenarios involve selection within and between ecotypes, i.e., subpopulations occupying distinct ecological niches67,68. An important factor generating niches and ecotypes is the differential use of food and other environmental resources. In this mode, ecotype-specific, conditionally beneficial mutations reach intermediate frequencies after a time given by their within-ecotype selection coefficients, but fixation can be slowed down or suppressed by diversifying (negative frequency-dependent) cross-ecotype selection18, $${{{{{rm{G}}}}}}left(xright)approx 1,{{{{{rm{T}}}}}}left(xright)sim frac{1}{s},left(xlesssim ,frac{1}{2}right)$$ (3) $${{{{{rm{G}}}}}}left(xright) < 1,{{{{{rm{T}}}}}}left(xright)gg frac{1}{s}left(xto 1right).$$ (4) The details depend on the details of the eco-evolutionary model (synergistic vs. antagonistic interactions, carrying capacities, amount of resource competition vs. explicitly frequency-dependent selection). In a model with directional selection within ecotypes, conditionally beneficial mutations rapidly fix within ecotypes, but lead only to finite shifts of the ecotype frequencies. In the simplest case, the resulting dynamics of ecotype frequencies is diffusive, resulting in an effectively neutral turnover of ecotypes18. Given negative frequency-dependent selection between ecotypes, fixations become even rarer and can be completely suppressed; that is, ecotypes can become stable on the time scales of observation. The separation of time and selection scales between intra- and cross-ecotype frequency changes is expected to be a robust feature of ecotype-dependent selection: sojourn of adaptive alleles to intermediate frequencies is fast, fixation is slower and rarer. In other words, ecotype-dependent selection is characterized by two regimes of coalescence times T(x).Frequency propagators and the coalescence time spectra expected under these evolutionary modes are qualitatively sketched in Supplementary Fig. 11. For periodic sweeps under directional selection (dark green, left column), G(x) depends weakly on x and T(x) is set by rapid sweeps for all x. For clonal interference under directional selection (green, center column), G(x) decreases substantially with increasing x and T(x) becomes uniformly shorter. Under negative frequency-dependent selection (brown, right column), G(x) decreases substantially with increasing x, while T(x) substantially increases for large x and diverges in case of strong frequency-dependent selection generating stable ecotypes (dashed lines). (see Supplementary Fig. 11 for the results of simulations assuming a model of direction selection or assuming a resource competition model where ecotype formation occurs31.The ({{{{{boldsymbol{p}}}}}})-({{{{{boldsymbol{tau }}}}}}) selection testThis test is based on qualitative characteristics of the functions G(x), T(x) and does not depend on details of the evolutionary process. We evaluate G(x) and T(x) for host-specific families of frequency trajectories; sojourn times are counted from an initial frequency x0=0.01. Origination times at this frequency are inferred by backward extrapolation of the first observed trajectory segment; the reported results are robust under variations of the threshold x0 and the extrapolation procedure. We then compute two summary statistics: the probability (p) that a mutation established at an intermediate frequency xm reaches near-fixation at a frequency xf,$$p=frac{{{{{{rm{G}}}}}}({x}_{f})}{{{{{{rm{G}}}}}}({x}_{m})},$$ (5) and the corresponding fraction of sojourn times,$$tau=,frac{{{{{{rm{T}}}}}}({x}_{f})}{{{{{{rm{T}}}}}}({x}_{m})}.$$ (6) Here we use xm=0.3 and xf=0.95 to limit the uncertainties of empirical trajectories at low and high frequency; however, the selection test is robust under variation of these frequencies. We find evidence for different modes of evolution: The long-term frequency trajectories of mice B2, D2 and E2 are consistent with predominantly frequency-dependent selection (Fig. 2, Fig. 4a–c). The propagator G(x) is a strongly decreasing function of x, resulting in fixation probabilities (p) 0.6, as measured by time ratios τ  > 3.

The trajectories of mice A2, G2, and I2 show a signature of recurrent selective sweeps and clonal interference under uniform directional selection (Fig. 4a–c). The propagator G(x) is a decreasing function of x, resulting in fixation probabilities (p=0.2-0.8), depending on the strength of clonal interference. Fixation times are short, giving time ratios (tau lesssim 2).

The shorter trajectory of mouse H2 signals periodic sweeps under uniform directional selection (Fig. 3, Fig. 4a–c). The origination rate of mutations is lower than in the longer trajectories, and G(x) shows a weak decrease with (p=1.) Sojourn times T(x) are short and grow uniformly with x, resulting in a time ratio τ=2.25. This pattern is expected under directional selection in the low mutation regime: (Tleft(xright)={{log }}left[x/(1-x)right]/{s}) for individual mutations with a uniform selection coefficient s, leading to τ=2.0 for xm=0.3 and xf=0.95 (this value is marked as a dashed line in Fig. 4c).

The trajectories of non-mutator lines in the long-term in vitro evolution experiment of Good et al1, evaluated over the first 7500 generations, show an overall signal of clonal interference under uniform directional selection (Fig. 4c, Supplementary Fig. 12). The frequency propagators G(x) are strongly decreasing functions of x and sojourn times T(x) grow uniformly with x. We find (p=0.2-0.8) and (tau lesssim 2), similar to the pattern in mice A2, G2, and I2.

Code for Selection testsThe code for selection tests from the mutation frequency trajectories can be found in the Supplementary Information file.Reporting summaryFurther information on research design is available in the Nature Research Reporting Summary linked to this article. More

Study areasThe study took place in the cities of Basel, Lausanne, Lugano and Zurich, in Switzerland. Basel, Lausanne and Zurich are located north of the Alps, in the geographical region of the Central Plateau (Supplementary Fig. S1). This region stretches from Lake Geneva in the southwest to Lake Constance in the northeast and is the most densely populated region in Switzerland. Zurich is the largest city of Switzerland and encompasses 88 km2 with a total human resident population of 420,21741. Lausanne and Basel are smaller than Zurich, with a surface of 41 and 24 km2 and a total population of 139,408 and 173,232, respectively41. The climate in these three cities is moderately continental, with cold winters often reaching freezing temperatures in January, and warm summers. Lugano is located in Ticino, south of the Alps (Supplementary Fig. S1), where the climate is strongly affected by the Mediterranean Sea, with mild winters and summers warm and humid, sometimes hot. Lugano is the smallest of the four cities with 50,603 residents in 26 km241.Aedes albopictus is well established in Lugano since 2009 and an integrated vector management is constantly implemented to contain the numbers of the mosquito at a manageable level. This consists of an intensive surveillance, with oviposition traps distributed according to a grid system, several control interventions, such as the removal of breeding sites and the systematic application of larvicides in public areas, mainly in catch basins, and extensive public information campaigns24,26. In Basel, two populations of Ae. albopictus are established since 2018: a first population in an area adjacent to the motorway toll on the border with France and a second population in an area near the border with Germany27. The mosquito has also been recorded repeatedly at various locations in the city of Basel and the surveillance indicates that the mosquito is spreading42. Control actions are taken exclusively within the perimeter of repeated detections of the mosquito and include regular treatment of catch basins with larvicides, distribution of flyers and door-to-door information campaigns42. In Zurich, Ae. albopictus was first detected in 2016 in a bus station for international coach services located in the centre of the city, near the main train station. Thanks to immediate surveillance and control actions (i.e., treatment of catch basins in the area with larvicides), to date there is no established population within the perimeter of the bus station despite continuous repeated introductions40. A small population was also detected in 2018 in a suburban neighbourhood in the Wollishofen district of Zurich, approximately 5 km southwest from the international bus station. Also in this case, immediate surveillance and control actions, including larval control and door-to-door information, were taken with success and no adults, eggs or aquatic stages have been found in 2020 and 202140. In Lausanne, no tiger mosquito has been reported to date (Swiss Mosquito Network, http://www.mosquitoes-switzerland.ch (accessed on 17 February 2022)).Microclimate dataBased on a previous investigation we conducted in Ticino, Basel and Zurich20, we focused the microclimate monitoring on ordinary stormwater catch basins positioned on the side of public roads. In each city, we monitored ten catch basins located either in urban context (defined as areas with high-density development, consisting of apartment blocks, commercial or industrial units) or in residential areas consisting mainly of houses with private gardens located in peri-urban area (Supplementary Table S1, Supplementary Fig. S2). The catch basins were usually homogeneous in dimension, in the same city, although we recorded variations in depth. In Basel, we included catch basins located in the urban area near the border with France, in which Ae. albopictus is established. In Zurich, we included catch basins located in the international bus station, where Ae. albopictus was recorded in summer, and in the residential area of Wollishofen, where a small population of Ae. albopictus was detected and then likely eradicated. In Lausanne, some catch basins were selected in potential points of introduction of the mosquito (e.g., near a campsite, the main train station, etc.). In Lugano, Ae. albopictus was established in all the locations selected.A sensor device was installed in each selected catch basin. The sensor devices were built in house. The development of the devices and the Wireless Sensor Network (WSN) has been described in detail by Strigaro et al.29. Briefly, the device consisted of a waterproof plastic box containing a LoPy Micro-Controller Unit (Pycom, Guildford, United Kingdom), a waterproof temperature probe (accuracy of ± 0.5 °C), a light sensor (measuring illuminance arriving at the sensor device, in lux), an SD card, the rechargeable batteries and other parts. The main box, with the light sensor, was hung on the inside wall of the catch basin. The temperature probe was attached to the wall at a depth ranging from 0.3 to 0.5 m, depending on the depth of the catch basin and the level of the water in the catch basin. The probe was placed in direct contact with the inside wall of the catch basin, in order to measure the microclimatic conditions where the mosquito eggs are potentially laid. The data collected was transmitted to a data warehouse based on istSOS, an open-source Python based implementation of the Sensor Observation Service standard (SOS) of the Open Geospatial Consortium (OGC)43. The data was transmitted through the Swisscom Low Power Network (LPN) LoRaWAN (Swisscom Ltd, Ittigen, Switzerland): the data sent by the sensor devices was received by a Swisscom Gateway and then sent to the data warehouse29.In addition to the sensor devices installed in the catch basins, four devices were installed outside four catch basins in each city, except in Lugano, where three devices were installed. These external devices were placed in vegetation representing potential resting habitats for Ae. albopictus adults in the reproductive season, at 1–2 m above the ground and analyzed to confirm the close similarity between measured external temperatures and MeteoSwiss gridded temperature data. However, since the main goal of the data collection was to model the differences between MeteoSwiss gridded temperature data and catch basins’ temperatures, only a small number of external sensors were deployed. Microclimate data were collected from beginning of December 2019 to end of February 2020, a period defined as cold season, with acquisition interval set at one hour. In Lugano, data collection started on the 12th or 13th of December 2019.Local climate dataWe used two types of local climate data. The first type is the momentary hourly free-air temperatures recorded at 2 m above ground level by permanent weather stations. The weather stations belong to SwissMetNet, the automatic monitoring network of MeteoSwiss. For each city, we selected the weather station closest to the study area (Supplementary Table S1, Supplementary Fig. S2) and temperature data were retrieved from https://gate.meteoswiss.ch/idaweb (source: MeteoSwiss, Zurich-Airport, Switzerland; accessed on 12 August 2021).The second type of local climate data is the MeteoSwiss spatial climate daily datasets (source: MeteoSwiss). These temperature datasets are constructed through interpolation of daily minimum, maximum, and mean temperatures from a network of approximately 90 SwissMetNet permanent weather stations to a 1 km resolution grid in the Swiss coordinate system CH190344,45. This results in three temperature datasets describing the km-scale distribution of day-to-day temperature variations in Switzerland. We referred to them as gridded temperature data. Each monitored catch basin and external device was assigned, based on its geographical position, to the corresponding 1 km × 1 km cell of the climate grid. Each cell was identified with its MeteoSwiss (MS) number (Supplementary Table S1).Data analysisThe hourly temperatures were used to compute daily mean, maximum and minimum temperatures and daily temperature ranges, which were calculated as the difference between the maximum and minimum daily temperature. Temperatures of catch basins and external habitats were compared to temperatures of permanent weather stations and to the gridded temperatures both graphically and using the nonparametric Mann–Whitney U-test, for which a P value of  More

Experimental designA 2-year field experiment was conducted at the Modern Agricultural Research and Development Base of Henan Province (113° 35′–114° 15′ E, 34° 53′–35° 11′ N). In order to enhance the diversity of LAI data, a split-plot design with a variety of field management measures and three replications was selected for the experiment (Fig. 1). The size of each experiment plot was 40 m2, the soil texture was predominantly sandy loam and sandy clay loam, as determined by textural analysis of soil samples collected before planting. Maize cultivar Dedan-5 was used in the experiment, which was planted on June 12, 2019, and June 20, 2020, with a row spacing of 42 cm and a planting density of 7 seedlings·m−2. The soil and cultivar in field experiments were representatives of those in the region. The irrigation, pesticide, and herbicide control practices followed local management for maize production.Figure 1The experimental design.Full size imageLAI measurements and UAV-based image acquisitionThe measurements of LAI were conducted at four growth stages including the tasseling stage (TS), flowering stage (FS), grain-filling stage (GS), and milk-ripe stage (MS) of maize in 2019 and 2020, a total of 264 LAI data of maize were collected during the 2-year field trial (Table 1). In order to reduce the impact of plant variability, the random sampling method was used to collect LAI samples. For each plot, three plants were randomly selected to measure the total green leaf area with the non-destructive portable leaf area meter (Laser Area Meter CI-203; CID Inc.). And the average leaf area of selected plants represented the single plant leaf area in each experiment plot. The LAI of each plot wasTable 1 Description of samplings.Full size table$$mathrm{LAI}=mathrm{LA}*mathrm{D}$$
(1)
where (mathrm{LA}) is the leaf area of a single plant in each plot; (mathrm{D}) is the planting density in one square meter.PHANTOM 4 PRO (DJI-Innovations Inc., Shenzhen, China) is a multi-rotor UAV equipped with a 20-megapixel visible-light camera that was employed to capture digital images. Aerial observations were conducted on the same dates as the LAI measurements, which was between 10:30 a.m. and 2:00 p.m. local time when the solar zenith angle was minimal. The UAV was flown automatically based on preset flight parameters and waypoints, with a forward overlap of 80% and a side overlap of 60%. A three-axis gimbal integrated with the inertial navigation system stabilized the camera, the automatic camera mode with fixed ISO (100) and a fixed exposure was used during the flight. Altogether, 4192 images were taken in eight flights from a flight height of 29.36 m above ground, with a spatial resolution of 0.008 m.The measurements of maize LAI were carried out with permission from the Modern Agricultural Research and Development Base of Henan Province. All experiments were carried out in accordance with relevant institutional, national, and international guidelines and legislation.Image pre-processingDJI Terra (version 2.3.3) was used to generate ortho-rectified images based on the structure from motion algorithms and a mosaic blending model. The main procedures are as follows: (1) extract feature points and match features according to the longitude, latitude, elevation, roll angle, pitch angle, and heading angle of each image; (2) build dense 3D point clouds by using dense multi-view stereo matching algorithm; (3) build a 3D polygonal mesh based on the vector relationship between each point in the dense cloud; (4) establish a 3D model with both external image and internal structure by merging the mosaic image into the 3D model; (5) generate digital orthophoto map (DOM).Vegetation indices (VIs) derived from the UAV-based digital imageryDigital imagery records the intensity of visible red (R), green (G), and blue (B) bands in individual pixels24. In order to enhance the vegetation parameters contained in the digital image, fourteen commonly used RGB-based VIs were collected, and their correlation with the LAI of maize at different growth stages was evaluated. Table 2 shows the detailed information of the selected RGB-based VIs.Table 2 RGB-based VIs for LAI estimation.Full size tableCentered on the point where LAI was measured, regions of interests (ROIs) with a size of 100*100 were clipped from the digital image. Python 3.7.3 was used for extracting the R, G, B information of maize and computing the RGB-based VIs from ROIs. In order to reduce the effects of light and shadow, the R, G, B color space of the image was normalized according to the followings:$$mathrm{r}=frac{R}{R+G+B}$$
(2)
$$g=frac{G}{R+G+B}$$
(3)
$$b=frac{B}{R+G+B}$$
(4)
where r, g, and b are the normalized values. R, G, B are the pixel values from the digital images based on each band.Pearson correlation analysisBefore regression analysis, the Pearson correlation analysis was performed to determine the relationship between maize LAI and different RGB-based VIs extracted from the digital image. Pearson correlation coefficient ((mathrm{r})) reflects the degree of linear correlation between two variables, which is between − 1 and 1. The calculation formula of Pearson correlation coefficient was expressed as follows:$$mathrm{r}= frac{sum_{i=1}^{n}left({X}_{i}-overline{X }right)left({Y}_{i}-overline{Y }right)}{sqrt{sum_{i=1}^{n}{left({X}_{i}-overline{X }right)}^{2}}sqrt{sum_{i=1}^{n}{left({Y}_{i}-overline{Y }right)}^{2}}}$$
(5)
where (X), (mathrm{Y}) are variables, (n) is the number of variables.Regression methodsLinear regression (LR)Linear regression is an approach for modelling the relationship between dependent and independent variables. The case of one independent variable is called unary linear regression (ULR), the expressions can be expressed as follows:$$mathrm{y}={beta }_{0}+{beta }_{1}x+varepsilon $$
(6)
where (varepsilon ) is deviation, which satisfies the normal distribution. (x), (mathrm{y}) are variables. ({beta }_{0}), ({beta }_{1}) are the intercept and slope of the regression line, respectively.For more than one independent variable, the regression process is called multiple linear regression (MLR), the expressions can be expressed as:$$mathrm{y}={beta }_{0}+{beta }_{1}{x}_{1}+{beta }_{2}{x}_{2}+dots +{beta }_{n}{x}_{n}$$
(7)
where ({x}_{1}),( {x}_{2}), …, ({x}_{n}), (mathrm{y}) are variables, ({beta }_{0}), ({beta }_{1}), ({beta }_{2}), …, ({beta }_{n}) are coefficients that determined by least square method and gradient descent method38.The RGB-based VIs with the highest Pearson correlation coefficient was used to establish the ULR model, and VIs with a correlation coefficient higher than 0.7 were used to establish the MLR model. In each growth stage, 70% of observation data were randomly selected for establishing models, and the remaining 30% of data were used as the testing dataset to assess the model performance.Back propagation neural networks (BPNN)In this study, a three-layer BPNN model was established for LAI estimation (Fig. 2). RGB-based VIs with a correlation coefficient higher than 0.7 were selected as the input variables. Tan-Sigmoid activation function was used in the hidden layer, and the Levenberg–Marquardt algorithm was selected as the training function. The maximum epoch of BPNN training was set to 1000, the learning rate was set to 0.005, and the MSE was set to 0.001. The observation data set was split into the training set and the testing dataset with a ratio of 7:3. The training dataset was used to fit the weights and bias of the BPNN model, the testing dataset was used to evaluate the model performance. Before training, data normalization was conducted for the input and output variables, and the denormalization was required to convent the output variable back into the original units after training.Figure 2Three-layer BPNN model.Full size imageRandom forest (RF)RF is a non-parametric ensemble ML method that operates by constructing a multitude of decision trees at training time and outputting the average prediction of the individual trees (Fig. 3). The bootstrapping approach was used to collect different sub-training data from the input training dataset to construct individual decision trees.Figure 3Random forest model.Full size imageThe construction process of RF regression model is as follows:

(1)

The value of (mathrm{n}_mathrm{estimators}) was tested from 50 to 1000 in increments of 50, and the value of 500 was finally selected according to higher R2 and lower RMSE.

(2)

At each node per tree, (mathrm{m}_mathrm{try}) RGB-based VIs was randomly selected from all 14 vegetation indices, and the best split was chosen according the lowest Gini Index. (mathrm{m}_mathrm{try}) was tested from 3 to 10, and the final value was 6.

(3)

The other parameters in the RF model were kept as default values according to the (mathrm{RandomForestRegressor}) function in (mathrm{Scikit}-mathrm{learn library}).

(4)

For each tree, the data splitting process in each internal node was repeated from the root node until a pre-defined stop condition was reached.

(5)

Similar with LR and BPNN model, the RGB-based VIs with a correlation coefficient higher than 0.7 were selected as the input variables, and the output variable is LAI.

Data analysis and performance evaluationThe repeated random sampling validation method was used to evaluate the generalization performance of different models. The training and testing dataset were randomly split 500 times. For each split, the LR, BPNN, and RF models were fitted to the training dataset, and the estimation accuracy was evaluated using the testing dataset. The coefficient of determination (R2), root mean square error (RMSE), and Akaike information criterion (AIC) of the training dataset were used for the assessment of models39, and the estimation accuracy was evaluated by R2 and RMSE of the testing dataset. Mathematically, a higher R2 corresponds to a smaller RMSE, and thus represents better model performance. The procedures of LAI inversion using UAV-based digital imagery and ML methods were shown in Fig. 4.Figure 4Flowchart of LAI inversion using UAV-based remote sensing and ML methods.Full size imageThe construction and evaluation of models was performed using Python 3.7.3 in Windows 10 operating system with Intel Core i7-9700 processor, 3.00 GHz CPU, and 32 GB RAM. The processing software is Spyder. The statistical analysis and figure plotting were performed in R × 64 4.0.3. More