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Collection of the samplesTen (10) wood pellet samples were purchased from a different location in B&H, of known suppliers from the market (supermarkets, garden shops, and gas stations). The samples were accompanied by a declaration describing that nine of them were originated from B&H, and one of them was from Italy. Characteristics of collected wood pellet samples (type of wood, energetic value, declared moisture, declared and determined ash amount) are listed in Table 1. All of the samples were analyzed for moisture and ash content. Additionally, in ash samples of mentioned wood pellets, heavy metal concentration (Cd, Co, Cr, Cu, Fe, Mn, Ni, Pb, and Zn) was determined.Table 1 Characteristic of analyzed samples wood pellets.Full size tableAll pellet samples were originated from B&H, purchased from different cities, often used for house heating, instead of sample S3 which was from Italy.Ash determination of wood biomass samplesThe wood pellet samples were oven-dried at 105 °C for 24 h. The content of ash was determined by gravimetric method according to the procedure published by Pan and Eberhardt18 as follows: pellet samples, 1 g (± 0.1 mg) of each was weighed into a previously annealed ceramic pot (m1) and burned in a muffle furnace (Nabertherm) for one hour at 300 °C, following by increasing the temperature to 400 °C for one hour more and then burning the samples for next six hours at 550 °C. The procedure is repeated until a constant mass (m2) was reached. The ash content is determined by the Eq. (1):$${text{Ash content}}, % = frac{{{text{(m}}_{2} – {text{m}}_{{1}} {)}}}{{{text{m}}_{{{text{sample}}}} }} times {100 }{text{.}}$$
(1)
Preparation of samplesThe chemical determinations of the heavy metals in wood pellet ashes (Table 2) were made by wet digestion by soaking the samples in 25 mL of 65% HNO3 in polytetrafluoroethylene (PTFE) vessels. After evaporation of the nitrogen oxides, the vessels were closed and allowed to react for 14 h at 80 °C, following by cooling to room temperature. Then, the digest was filtered, transferred to a 25 mL volumetric flask, and filled up with redistilled water to the mark. All samples and blank were prepared in three replicates19,20,21.Table 2 Heavy metal concentrations (mg kg−1 d.w.) in the wood pellet ashes.Full size tableHeavy metal analysisMetal analyses in ash samples of mentioned wood pellets were performed using a flame atomic absorption spectrometry (Varian AA240FS) for Mn, Fe, Pb, and Zn and graphite furnace (Varian AA240Z) for Cd, Co, Cr, Cu, and Ni. A blank probe was prepared using the same digestion method to avoid the matrix effect. Standard metal solutions used for the calibration graphs were prepared by diluting 1000 mg L−1 stock single-element atomic absorption standard solutions of Cd, Co, Cr, Cu, Fe, Mn, Ni, Pb, and Zn (Certipur Grade, Merck, Germany). Linear calibration graphs with correlation coefficients  > 0.99 were obtained for all analyzed metals. The accuracy of the method was evaluated using the standard reference materials: Fine Fly Ash (CTA-FFA-1, Institute of Nuclear Chemistry and Technology Poland) and Fly Ash from pulverized coal (BCR-038, Institute of reference materials and measurements-IRMM, Belgium). The obtained results were in the range of the reference materials. The detection limit (LOD) and limit of quantification (LOQ) for the nine analyzed metals were calculated based on Xb + 3 SDb and Xb + 10 SDb, respectively, where Xb is the mean concentration of the blank sample (n = 8) and SDb is the standard deviation of the blank for eight readings22. The values of the LOD were: Cd (0.61 µg L−1), Co (0.49 µg L−1), Cr (0.67 µg L−1), Cu (20.10 µg L−1), Fe (83.85 µg L−1), Mn (6.42 µg L−1), Ni (1.12 µg L−1), Pb (23.77 µg L−1), Zn (58.68 µg L−1), and LOQ values were: Cd (1.25 µg L−1), Co (1.41 µg L−1), Cr (1.42 µg L−1), Cu (47.66 µg L−1), Fe (111.2 µg L−1), Mn (16.14 µg L−1), Ni (2.70 µg L−1), Pb (47.73 µg L−1) and Zn (71.05 µg L−1).Pollution evaluationThe metal pollution index (MPI) as the geometric mean of the concentration of all metals found in ashes of wood samples was calculated by the following Eq. (2)23:$${text{MPI}} = left( {{text{C}}_{1} cdot {text{C}}_{2} cdot cdots {text{C}}_{{text{k}}} } right)^{{1/{text{k}}}} ,$$
(2)
where C1 is the concentration value of the first metal, C2 is the concentration value of the second metal, Ck is the concentration value of the kth metal.Evaluation of the presence and the grade of anthropogenic activity were demonstrated through the calculation of the enrichment factor (EF), widely used in environmental issues24. To understand which elements were relatively enriched in the different wood pellet ash samples, the heavy metal enrichment factor was calculated relative to soil values according to Eq. (3)25.$${text{EF}} = frac{{left( {frac{{{text{C}}_{{text{k}}} }}{{{text{E}}_{{{text{ref}}}} }}} right)_{{{text{ashes}}}} }}{{left( {frac{{{text{C}}_{{text{k}}} }}{{{text{E}}_{{{text{ref}}}} }}} right)_{{{text{soil}}}} }},$$
(3)
where Ck is the concentration of the element in the sample or the soil, Eref the concentration of the reference element used for normalization. A reference element is an element commonly stable in the soil characterized by the absence of vertical mobility and/or degradation phenomena. As in many studies as a reference element were Fe, Al, Mn, Sc, or total organic carbon used26,27. Therefore Fe has been chosen as reference material in this study. Iron is one of the major constituents of soil, as well as the average chemical constituent of the upper continental crust26.Health risk assessmentThe general exposure equations used in this study were adapted according to the US Environmental Protection Agency guidance28,29,30. The daily exposure (D) to heavy metals via wood pellet ash was calculated for the three main routes of exposure: (i) direct ingestion of ash particles (Ding); (ii) inhalation of suspended particles via mouth and nose (Dinh); and (iii) dermal absorption to skin adhered ash particles (Ddermal). Equations (4) to (6) were used to calculate exposure via ingestion, inhalation, and dermal route, respectively22,31.$${text{D}}_{{{text{ing}}}} = {text{ C }} cdot frac{{{text{ IngR }} cdot {text{ EF }} cdot {text{ ED}}}}{{{text{BW }} cdot {text{ AT}}}}{ } cdot {text{CF}}1{, }$$
(4)
$${text{D}}_{{{text{inh}}}} = {text{ C }} cdot frac{{{text{ InhR}} cdot {text{ EF }} cdot {text{ ED}}}}{{{text{PEF }} cdot {text{ BW }} cdot {text{ AT}}}}{, }$$
(5)
$${text{D}}_{{{text{dermal}}}} = {text{ C }} cdot frac{{{text{ SA }} cdot {text{ SL }} cdot {text{ABS }} cdot {text{EF }} cdot {text{ ED}}}}{{{text{BW }} cdot {text{ AT}}}}{ } cdot {text{CF}}1{, }$$
(6)

where c (mg kg−1) is the heavy metals concentrations in ash samples; IngR (mg day−1) is the conservative estimates of dust ingestion rates, 50 for adults, 200 for children30,32; InhR (m3 h−1) is the inhalation rate, 2.15 for adults, 1.68 for children32; EF (h year−1) is the exposure frequency, 1225 for adults and children22; ED (years) is the exposure duration, 70 for adults, 6 for children22; BW (kg) is the body weight, 80 for adults, 18.60 for children32; AT (days) is the averaging time, 25,550 for adults, 2190 for children22; PEF is the particle emission factor (m3 kg−1), 6.80 × 108 for adults and children31; SA (cm3) is the exposed skin area, 6840 for adults, 2550 for children32; SL (mg cm−2) is the skin adherence factor, 0.22 for adults, 0.27 for children32; ABS is the dermal absorption factor, 0.001 for adults and children31; CF1 is the unit conversation factor, 10–6 for adults and children22.The potential non-carcinogenic risk for each metal was estimated using the Hazard coefficient (HQ), as suggested by US EPA33. The HQ under various routes of exposure such as ingestion (HQing), inhalation (HQinh), and dermal (HQdermal) was calculated as a ratio of daily exposure (D) to reference dose of each metal (RfD) according to Eq. (7)32.$${text{HQ}}_{{text{k}}} = frac{{{text{D}}_{{text{k}}} }}{{{text{RfD}}}},$$
(7)

where k is ingestion, inhalation, or dermal route. The total hazard index (HI) of heavy metal for all routes of exposure was calculated as a sum of HQing, HQinh, and HQdermal as given in Eq. (8)34.$${text{HI}} = {text{ HQ}}_{{text{ing }}} + {text{ HQ}}_{{text{inh }}} + {text{ HQ}}_{{text{dermal }}} .$$
(8)
The carcinogenic risk (Risk) for potential carcinogenic metals was calculated by multiplying the doses by the corresponding slope factor (SF), as given in Eq. (9)35. The carcinogenic oral, inhalation, and dermal SF, as well as dermal absorption toxicity values, were provided from the Integrated Risk Information System30. The reference doses for Pb were taken from the Guidelines for Drinking Water Quality published by the World Health Organization36.$${text{Risk}} = { }mathop sum limits_{{{text{k}} = 1}}^{{text{n}}} {text{D}}_{{text{k}}} cdot {text{ SF}}_{{text{k}}} ,$$
(9)
where SF is the cancer slope factor for individually metal and k route of exposure (ingestion, inhalation, or dermal path). The total cancer risk (Risktotal) of potential carcinogens was calculated as the sum of the individual risk values using the following Eq. (10).$${text{Risk}}_{{{text{total}}}} = {text{Risk}}_{{{text{ing}}}} + {text{Risk}}_{{{text{inh}}}} + {text{Risk}}_{{{text{dermal}}}} .$$
(10) More

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Two databases including yield, management, and weather data for maize (n = 17,013) and soybean (n = 24,848) involving US crop performance trials conducted in 28 states between 2016 to 2018 for maize and between 2014 to 2018 for soybean, were developed (Fig. 1). Crop yield and management data were obtained from publicly available variety performance trials which are typically performed yearly in several locations across each state (see methods for more information). Final databases were separated in training (80% of database) and testing (20% of database) datasets using stratified sampling by year, use of irrigation, and soil type. For each crop, an extreme gradient boosting (XGBoost, see methods for more information) algorithm to estimate yield based on soil type and weather conditions (E), seed traits (G) and management practices (M) was developed (see variables listed in Tables S1 and S2 for maize and soybean, respectively, and data science workflow in Fig. S1).Figure 1Locations where maize and soybean trials were performed during the examined period. The map was developed in ArcGIS Pro 2.8.0 (https://www.esri.com).Full size imageThe developed algorithms exhibited a high degree of accuracy when estimating yield in independent datasets (test dataset not used for model calibration) (Fig. 2). For maize, the root mean square error (RMSE) and mean absolute error (MAE) was a respective 4.7 and 3.6% of the dataset average yield (13,340 kg/ha). For soybean, the respective RMSE and MAE was 6.4 and 4.9% of the dataset average yield (4153 kg/ha). As is evident in the graphs (Fig. 2), estimated yields exhibited a high degree of correlation with actual yields for both algorithms in the independent datasets. For maize and soybean, 72.3 and 60% of cases in the test dataset deviated less than 5% from actual yields, respectively. Maximum deviation for maize and soybean reached 43 and 70%, respectively. Data points with deviations greater than 15% from actual yield were 1.5% in maize and 3.6% in soybean databases. These results suggest that the developed algorithms can accurately estimate maize and soybean yields utilizing database-generated information involving reported environmental, seed genetic, and crop management variables.Figure 2Actual versus algorithm-derived maize (left) and soybean (right) yield in test datasets. Black solid line indicates y = x, red short-dashed lines, black dashed lines, and red long-dashed lines indicate ± 5, 10, and 15% deviation from the y = x line. RMSE, root mean square error; MAE, mean absolute error; r2, coefficient of determination; n = number of observations. Each observation corresponds to a yield of an individual cropping system in a specific environment (location-year).Full size imageIn contrast to statistical models, ML algorithms can be complex, and the effect of single independent variables may not obvious. However, accumulated local effects (ALE) plots14 can aid the understanding and visualization of important and possibly correlated features in ML algorithms. For both crops, indicatively important variables included sowing date, seeding rate, nitrogen fertilizer (for maize), row spacing (for soybean) and June to September cumulative precipitation (Fig. 3). Across the entire region and for both crops, the algorithm-derived trends suggest that above average yields occur in late April to early May sowing dates, but sharply decrease thereafter. Similar responses have been observed in many regional studies across the US for both, maize15,16,17,18 and soybean19. Similarly, simulated yield curves due to increasing seeding rate are in close agreement with previous maize20,21 and soybean22 studies. The maize algorithm has captured the increasing yield due to increasing N fertilizer rate. The soybean algorithm suggests that narrower row spacing resulted in above average yield compared to wider spacing. Such response has been observed in many regions across the US23. Season cumulative precipitation between 400 and 700 mm resulted in above average yields for both crops.Figure 3Accumulated local effect plots for maize sowing date (A), seeding rate (B), Nitrogen fertilizer rate (C), and cumulative precipitation between June and September (mm) (D), and soybean sowing date (E), seeding rate (F), row spacing (G), and cumulative precipitation between June and September (mm) (H).Full size imageThe responses in the ALE plots (Fig. 3) suggest that these algorithms have captured the general expected average responses for important single features. Nevertheless, our databases include hundreds of locations with diverse environments across the US and site-specific crop responses which may vary due to components of the G × E × M interaction. We argue that, instead of examining a single or low-order management interactions, site-specific evaluation of complex high order interactions (a.k.a. cropping systems) can reveal yield differences that current research approaches cannot fully explore and quantify. For example, sowing date exerts a well-known impact on maize and soybean yield. For each crop separately, by creating a hypothetical cropping system (a single combination of all management and traits in Tables S1 and S2) in a randomly chosen field in south central Wisconsin (latitude = 43.34, longitude = -89.38), and by applying the developed algorithms, we can generate estimates of maize and soybean yield. For that specific field and cropping system (out of the vast number of management combinations a farmer can choose from), maize yield with May 1st sowing was 711 kg/ha greater (6% increase) than June sowing (Fig. 4A). By creating scenarios with 256 background cropping system choices (Table S3), the resultant algorithm-derived yield estimate difference for the same sowing date contrast (averaged across varying cropping systems) was smaller but still positive (3% increase), although the range of possible yield differences was wider (Fig. 4B). However, when comparing, instead of averaging, the estimated yield potential among the simulated cropping systems, a 2903 kg/ha yield difference (25% difference) was observed (Fig. 4C). Interestingly, when focusing on the early sown fields that were expected to exhibit the greatest yield, the same yield difference was observed (Fig. 4D). This result shows that sub-optimal background management can mitigate the beneficial effect of early sowing (Table S4).Figure 4Maize yield difference (in kg/ha and percentage) due to sowing date (May 1st vs. June 1st) for a single identical background cropping system (A), maize yield difference due to sowing date when averaged across 256 (3 years × 256 cropping systems = 768 year-specific yields) (B), maize yield variability in each of the 256 cropping systems (C), and maize yield variability in each of the 128 cropping systems with early sowing (D). Soybean yield difference due to sowing date (May 1st vs June 1st) for a single identical background cropping system (E), soybean yield difference due to sowing date when averaged across 128 (5 years × 128 cropping systems = 640 year-specific yields) (F), soybean yield in each of the 128 cropping systems (G) and soybean yield variability due in each of the 64 cropping systems with early sowing (H). Within each panel, the horizontal red and grey lines indicate the boxplot with maximum and minimum yield, respectively. In the left four panels, boxes delimit first and third quartiles; solid lines inside boxes indicate median and green triangles indicate means. Upper and lower whiskers extend to maximum and minimum yields. Each maize and soybean cropping system is a respective 8-way and a 7-way interaction of management practices in a randomly chosen field in Wisconsin, USA (Table S3 and S5, respectively).Full size imageIn the case of soybean, a May 1st sowing resulted in greater yield (588 kg/ha; a 14% increase) than a June 1st in the single background cropping system (Fig. 4E). The result was consistent when yield differences due to sowing date were averaged across 128 background cropping system choices (Table S5) (Fig. 4F). Similar to what was observed in maize, among all cropping systems, yield varied by 1704 kg/ha (44% difference) (Fig. 4G). When focusing only on the early sown fields, a 1181 kg/ha yield difference (27% yield increase) was observed (Fig. 4H). In agreement with maize, this result highlights the importance of accounting for sub-optimal background management which can mitigate the beneficial effect of early sowing (Table S6).We note here the ability of farmers to change management practices can be limited due to an equipment constraint (e.g., change planter unit row width) or simply impossible (e.g., change the previous year’s crop). Thus, recommended management practices that were evaluated in studies that used specific background management may not be applicable in some instances. The benefits of the foregoing approach, which involves extensive up-to-date agronomic datasets and high-level computational programing, can have important and immediate implications in future agricultural trials. Our approach allows for more precise examination of complex management interactions in specific environments (soil type and growing season weather) across the US (region covered in Fig. 1). The ability to extract single management practice information (even across cropping systems) is also possible by utilizing ALE plots, or by calculation of the frequency at which a given level/rate of a management practice appeared among the highest yielding cropping systems (Tables S4 and S6).Among all available 30-d weather variables, many were strongly correlated in both crop databases (Figs. S2 and S3 for maize and soybean, respectively). Models using all 30-d interval variables with r  More

Sampling and genotypingWe collected hair and cheek swab samples from 77 men from geographically and linguistically distinct groups of the Caucasus: Kartvelian speakers from Georgia and Turkey, Northeast Caucasian speakers and Turkic speakers from the Russian Federation and Armenian speakers from Georgia’s southern province of Javakheti, descendants of the families displaced from Mush and Erzurum provinces of eastern Turkey in the early nineteenth century (Table 1, Fig. 1). To maximize the representativeness of the genetic signature of each population, the samples were collected from locals with no ancestors from outside of the respective ethnic/geographic population over the last three generations. DNA was extracted from follicles of 10–12 male chest hairs and cheek swab samples. Extraction was performed using Qiagen DNeasy Blood and Tissue kit, following the manufacturer’s recommendations (Qiagen, Valencia, CA, USA). The DNA samples were genotyped for 693,719 autosomal and 17,678 X-chromosomal SNPs by Family Tree DNA (FTDNA—Gene By Gene, Ltd, Houston, TX, www.familytreedna.com).Table 1 Modern study populations of the Caucasus. Latitude and longitude georeference population hubs.Full size tableFigure 1The distribution of the study populations: averaged centroids of ancient populations (uniquely colored points in the main map, see Table 2 for details) and hubs of the modern Caucasian populations (identified in the inset map, see Table 1 for details). Glacial human refugia extracted from Gavashelishvili and Tarkhnishvili5 are shaded in purple. The map is generated using QGIS Desktop 3.10.6-A Coruña (https://qgis.org).Full size imageOur dataset of modern Caucasian genotypes was supplemented with published 10 modern Mbuti (Supplementary Table S1) and 122 Upper Paleolithic-Mesolithic human genotypes, retrieved as a part of 1240 K dataset from David Reich’s Lab website, Harvard University (https://reich.hms.harvard.edu/downloadable-genotypes-present-day-and-ancient-dna-data-compiled-published-papers; see Supplementary Table S2 for details). The ancient genotypes were selected such that they either dated from the LGM or fell within the glacial refugia identified by Gavashelishvili and Tarkhnishvili5. We did so in order to maximize the genetic signature of potential refugial populations in our analysis. We divided the ancient genotypes into 2000-year-long intervals, and then grouped each of these intervals into geographic units (hereafter ancient populations, Table 2, Fig. 1). The modern and ancient genotypes were merged using PLINK 1.9 (PLINK 1.9: www.cog-genomics.org/plink/1.9/27.Table 2 Ancient study populations. The ancient genotypes are divided into 2000-year-long intervals, and then each of these intervals is grouped into geographic units (i.e. ancient populations). Age, latitude and longitude are averaged across each ancient population (see Supplementary Table S2 for details).Full size tableEthics statementThe research team members, through their contacts in the studied communities, inquired whether locals would voluntarily participate in genetic research that would help clarify the genetic makeup of the Caucasus. A verbal agreement was made with volunteer donors of DNA samples, according to which the results would be communicated, electronically or in hard copy, with participants individually. Participants were informed that, upon the completion of the lab work, the research would be published without mentioning the names of sample donors. Those who agreed provided us with the envelopes containing their chest hairs or cheek swab samples, with the birthplace of their ancestors (last three generations) written on the envelope or a piece of paper. In accordance with the preferences of the sample donors, the agreement was verbal and not written. The envelopes and papers are stored as evidence of voluntary provision of the samples and the related information. Analysis of data was done anonymously, using only location and ethnic information; only the first and third authors of the manuscript had access to names associated with the samples. Therefore, this study was based on noninvasive and nonintrusive sampling (volunteers provided hair and swab samples they collected themselves), and the information destined for open publication does not contain any personal information. The study methodology and the procedure of verbal consent was discussed in detail with and approved by the members of the Ilia State University Commission for Ethical Issues before the field survey started, and the commission decided that formal ethical approval was not needed for conducting this study. This is confirmed in a letter from the commission chairman, a copy of which has been provided to the journal editor as part of the submission process.Genetic affinity and geographyFirst, we measured genetic affinity between the modern Caucasian populations, and between the modern populations and the ancient populations of hunter-gatherers, and then tested whether the genetic affinity between these populations was determined by geographic features. Data were mapped using QGIS Desktop 3.10.6-A Coruña, whereas graphs were created using the “ggplot2” package28 in R version 3.5.229.To evaluate genetic affinities and structure of the modern populations, we used Wright’s fixation index (Fst), inbreeding coefficient, admixture analysis and the principal component analysis (PCA). For these procedures we filtered the raw SNP genotypes in PLINK 1.9, first removing all SNPs with the minor allele frequency  0.3, calculated in windows of 50 bp size and 10 bp steps (–maf 0.05 –indep-pairwise 50 10 0.3). Since all individuals in our dataset possess a single copy of the X-chromosome, we did not expect any differential ploidy bias, and SNPs on the X were treated similarly to those on the autosomes. Fst pairwise values were calculated using the smartpca program of EIGENSOFT30 with default parameters, inbreed: YES, and fstonly: YES. The relationship between the modern populations based on Fst values was visualized by constructing a neighbor-joining tree using the “ape” package31 in R version 3.5.2. The average and standard deviation of the inbreeding coefficient for each population was calculated using “fhat2” estimate of PLINK 1.9. The LD pruned genotypes were used in ADMIXTURE 1.3.032, performed in unsupervised mode in order to infer the population structure from the modern individuals. The number of clusters (k) was varied from 2 to 7 and the fivefold cross-validation error was calculated for each k33. We conducted principal components analysis in the smartpca program of EIGENSOFT30, using default parameters and the lsqproject: YES and numoutlieriter: 0 options. Eigenvectors of principal components were inferred with the modern populations from the Caucasus, while the ancient populations were then projected onto the PCA plots. We also assessed the relatedness between sampled individuals using kinship coefficients estimated by KING34.To quantify genetic affinities between the modern and ancient populations, we used the programs qp3Pop and qpDstat in the ADMIXTOOLS suite (https://github.com/DReichLab35 for f3- and f4-statistics, respectively. f3-statistics of the form f3(X,Y,Outgroup) measure the amount of shared genetic drift of populations X and Y after their divergence from an outgroup. We used an ancient population and a modern Caucasian population for X, Y and Mbuti as an outgroup. f4-statistics of the form f4(Outgroup,Test;X,Y) show if population Test is equally related to X and Y or shares an excess of alleles with either of the two. In the f4-statistic calculation we used Mbuti for Outgroup, a modern population of the Caucasus for Test, and X and Y for contemporaneous ancient populations. This meant that f4  0 indicated higher genetic affinity between the test population and Y.To quantify geographic features, we derived least-cost paths and measured least-cost distances (LCD) between the modern and ancient populations using the Least Cost Path Plugin for QGIS. The computation of LCD considers a friction grid that is a raster map where each cell indicates the relative difficulty (or cost) of moving through that cell. A least-cost path minimizes the sum of frictions of all cells along the path, and this sum is the least-cost distance (LCD). For impedance to human movement and expansion, we used 15 geographic features (Table 3). All gridded geographic features (i.e. raster layers) were resampled to a resolution of 1 km using the nearest-neighbor assignment technique. All possible subsets of the 15 geographic features, that did not cancel out each other, were used to calculate different variables of LCD. We assumed that most human movements occurred during climate warming events when the earth’s surface was not dramatically different from that of today, and hence used the current data of the geographic features.Table 3 Geographic features used in combinations to calculate least-cost distances (LCD) between ancient populations and modern Caucasians.Full size tableLinking genetic affinity and geographyGeneralized additive models (GAMs) were used to fit the outgroup f3-statistic to time and variously calculated LCD between the modern and ancient populations using the “mgcv” package36 in R version 3.5.2. Time between the modern and ancient populations was measured in BP (years before present, defined by convention as years before 1950 CE). We used GAMs because without any assumptions they are able to find nonlinear and non-monotonic relationships. GAMs were fitted using a Gamma family with a log link function. Penalized thin plate regression splines were used to represent all the smooth terms. The restricted maximum likelihood (REML) estimation method was implemented to estimate the smoothing parameter because it is the most robust of the available GAM methods36.Model and variable selection were performed by exploring LCD, time BP and the interaction term. The predictive power of the models was evaluated through a tenfold cross-validation. The cross-validation of many models was handled through R’s parallelization capabilities37,38. The best model was selected by the mean squared error of the cross-validation. Akaike’s Information Criterion (AIC) is generally used as a means for model selection. However, we preferred cross-validation for model selection because AIC a priori assumes that simpler models with the high goodness of fit are more likely to have the higher predictive power, while cross-validation without any a priori assumptions measures the predictive performance of a model by efficiently running model training and testing on the available data.We additionally validated the effect of different subsets of geographic features by assessing the relationship between statistically significant values of f4-statistic (i.e. |Z| > 3) and each subset. The relationship between f4-statistic of the form of f4(Outgroup,Test;X,Y) and geographic features was determined by measuring the agreement between the negative/positive signs of f4-statistic and the difference in LCD (LCD.D) for each pair of contemporaneous ancient populations X and Y. LCD.D was calculated as (LCD1–LCD2), where LCD1 was least-cost distance between the test population and X, and LCD2 was least-cost distance between the test population and Y. LCD.D  0 indicated less least-cost distance between Test and Y. So, the same sign of f4 and LCD.D values indicated agreement between geographic proximity and genetic affinity. We used Cohen’s kappa39 to measure the agreement.In order to test if geographic features (Table 3) accounted for present-day genetic differentiation in the Caucasus, we measured the relationship between Fst and LCD across the modern populations using the Mantel test in the “vegan” package40 in R version 3.5.2. In addition, we checked whether contribution from ancient samples was related to today’s genetic differentiation. To do so, we calculated median of f3-statistic of ancient populations of each geographic grouping (e.g. the following 6 populations made up one group: Balkans 39,950–41,950 BP, Balkans 37,950–39,950 BP, Balkans 31,950–33,950 BP, Balkans 9950–11,950 BP, Balkans 7950–9950 BP, Balkans 5950–7950 BP). Then we measured the manhattan distance of f3 median values of all combinations of the geographic groupings between the modern populations and compared the results to Fst and LCD using the Mantel test. More

Regular structures and isothermal theoremFor networks where each node represents a single individual, the isothermal theorem of evolutionary graph theory shows that the fixation probability is the same as the fixation probability of a well-mixed population if the temperature distribution is homogeneous across the whole population1. The temperature of a node defined as the sum over all the weights leads to that node. This theorem extends to structured meta-populations for any migration probability (lambda ): If the underlying structure of the meta-population that connects the patches is a regular network and the local population size is identical in each patch, the temperature of all individuals is identical, regardless of the value of the migration probability. Therefore, the fixation probability in a population with such a structure is the same as the fixation probability in a well-mixed population of the same total population size (N=sum _{j=1}^M N_j), given by ( phi _{mathrm{wm}}^N(r)).Small migration regimeIf the migration probability is small enough such that the time between two subsequent migration events (( sim frac{1}{lambda } )) is much longer than the absorption time within any patch, then at the time of each migration event we may suppose that the meta-population is in a homogeneous configuration22,28. In other words, the low migration regime is an approximation in which we neglect the probability that the meta-population is not in a homogeneous configuration at the time of migration events. We define a homogeneous configuration of the meta-population as a configuration in which in all patches either all individuals are mutants, or all are wild-types.Therefore, instead of having (2^N) states, where N is the population size, the system has only (2^M) states, where M is the number of patches. Thus, we can calculate the fixation probability exactly as in the case of a standard evolutionary graph model where each node represents a single individual but with a modified transition probabilities.In a network with homogeneous patches, in order to increase the number of homogeneous mutant-patches one individual mutant needs to migrate to one of its neighbouring homogeneous wild-type-patches and reaches fixation there. For example if node j is occupied by mutants and one of its neighbouring patches, node k, is occupied by wild-types, the probability that one mutant individual from patch j migrates to patch k and reaches fixation there is (frac{lambda }{mathrm{deg} (j)}phi _{mathrm{wm}}^{N_{k}}(r) ), where (mathrm{deg} (j) ) is the degree of node j to take into account that the mutant can move to different patches. This is analogous to the probability that one mutant in node j replaces one wild-type in node k ,(T^{jrightarrow k}), in the network of individuals.Similarly, if node j is occupied by wild-types and one of its neighbouring patches, node j, is occupied by mutants the probability that one wild-type individual from patch j migrates to patch k and reaches fixation there equals to (frac{lambda }{mathrm{deg} (j)}phi _{mathrm{wm}}^{N_{k}}(1/r) ) where (mathrm{deg} (j) ). Overall, we can move from network of individuals to the network of homogeneous patches by replacing the transition probabilities with the product of migration and fixation probabilities.Two-patch meta-populationThe simplest non-trivial case is the fixation probability in a two-patch meta-population with different local size for small migration probability (lambda ). If the migration probability (lambda ) is very small, a new mutant first needs to take over its own patch and only then the first migrant arrives in the second patch. To be more precise, the time between two migration events has to be much higher than the typical time that it takes for the migrant to take over the patch or go extinct again38. In this case, we can divide the dynamics into two phases: A first phase in which a mutant invades one patch and a second phase in which a homogeneous patch of mutants invades the whole meta-population. Assume a new mutation arises in patch 1. Only if this mutant reaches fixation in patch 1, it also has a chance to reach fixation in patch 2. When patch 1 consists of only mutants and patch 2 consists of only wild-types, there are two possibilities for the ultimate fate of the mutant:

(i)

Eventually, the offspring of one mutant selected from patch 1 for reproduction will migrate to patch 2 and reach fixation there. The wild-type goes extinct. This happens with probability ( frac{N_1 r}{N_1 r+N_2} phi _{mathrm{wm}}^{N_2}(r)).

(ii)

Eventually, the offspring of one wild-type selected from patch 2 for reproduction will migrate to patch 1 and the mutant goes extinct. This occurs with probability ( frac{N_2}{N_1r+N_2} phi _{mathrm{wm}}^{N_1}(tfrac{1}{r})).

Therefore, the probability that a single mutant arising in patch 1 reaches fixation in the entire population is $$begin{aligned} phi _{mathrm{wm}}^{N_1}(r) frac{frac{N_1 r}{N_1 r+N_2} phi _{mathrm{wm}}^{N_2}(r)}{frac{N_1 r}{N_1 r+N_2} phi _{mathrm{wm}}^{N_2}(r)+frac{N_2}{N_1r+N_2} phi _{mathrm{wm}}^{N_1}left( tfrac{1}{r}right) }=phi _{mathrm{wm}}^{N_1}(r) phi _{mathrm{wm}}^{N_2}(r) frac{1 }{ phi _{mathrm{wm}}^{N_2}(r) +frac{N_2}{N_1} frac{1}{r}phi _{mathrm{wm}}^{N_1} left( tfrac{1}{r}right) }. end{aligned}$$
(3a)
Similarly the probability that a mutant arising in patch 2 takes over the whole population equals$$begin{aligned} phi _{mathrm{wm}}^{N_2}(r) phi _{mathrm{wm}}^{N_1}(r) frac{1 }{phi _{mathrm{wm}}^{N_1}(r)+frac{N_1}{N_2} frac{1}{r} phi _{mathrm{wm}}^{N_2}left( tfrac{1}{r}right) }. end{aligned}$$
(3b)
If we assume that the mutant arises in a patch with a probability proportional to the patch size, the average fixation probability (phi _{bullet !!-!!bullet }) in a two patch population for small migration probability is the weighted sum of Eqs. (3a) and (3b),$$begin{aligned} phi _{bullet !!-!!bullet }&= phi _{mathrm{wm}}^{N_1}(r) phi _{mathrm{wm}}^{N_2}(r) nonumber \&quad times left( frac{frac{N_1}{N_1+N_2} }{ phi _{mathrm{wm}}^{N_2}(r) +frac{N_2}{N_1} frac{1}{r}phi _{mathrm{wm}}^{N_1}left( tfrac{1}{r}right) } +frac{frac{N_2}{N_1+N_2} }{ phi _{mathrm{wm}}^{N_1}(r) +frac{N_1}{N_2} frac{1}{r} phi _{mathrm{wm}}^{N_2}left( tfrac{1}{r}right) }right) . end{aligned}$$
(4)
In the case of neutrality, (r=1), we recover (phi _{bullet !!-!!bullet } = frac{1}{N_1+N_2})—the fixation probability in a population of the total size of the two patches. For identical patch sizes, ( N_1=N_2 ), Eq. (4) simplifies to$$begin{aligned} phi _{bullet !!-!!bullet } = left( phi _{mathrm{wm}}^{N_1}(r)right) ^2 frac{1}{phi _{mathrm{wm}}^{N_1}(r)+frac{1}{r} phi _{mathrm{wm}}^{N_1}left( tfrac{1}{r}right) } = phi _{mathrm{wm}}^{2 N_1}(r), end{aligned}$$
(5)
where the simplification to the fixation probability within a single population of size (2N_1) reflects the validity of the isothermal theorem.For (N_1 ne N_2), we approximate Eq. (4) for weak and strong selection. Let us first consider highly advantageous mutants, (r gg 1). In this case, we have (phi _{mathrm{wm}}^{N_1}(r) gg phi _{mathrm{wm}}^{N_1}(tfrac{1}{r})) and thus we can neglect the possibility that a wild-type takes over a mutant patch if patch sizes are sufficiently large. The probability (phi _{bullet !!-!!bullet } ) then becomes a weighted average reflecting patch sizes. For identical patch size (N_1=N_2 = N/2), it reduces to (phi _{bullet !!-!!bullet } approx phi _{mathrm{wm}}^{N_1}(r)=phi _{mathrm{wm}}^{N/2}(r)). In other words, taking over the first patch is sufficient to make fixation in the entire population certain. For patches of very different size, (N_1 gg N_2), we have (N approx N_1) and find (phi _{bullet !!-!! bullet } approx phi _{mathrm{wm}}^{N}(r), ) which implies that fixation is driven by the fixation process in the larger patch, regardless of where the mutant arises. Note that there is a difference between the case of identical patch size and very different patch size . The case of highly disadvantageous mutants, (r ll 1), can be handled in a very similar way.Next, we consider weak selection, (r approx 1). We can approximate the fixation probability as (phi _{mathrm{wm}}^{N}(r^{pm 1}) approx frac{1}{N} pm frac{N-1}{2N} (r-1)). With this, we find$$begin{aligned} phi _{bullet !!-!!bullet } approx frac{1}{N_1+N_2} +frac{1}{2} left( 1 – frac{1}{N_1+N_2} -frac{(N_1-N_2)^2}{(N_1^2+N_2^2)^2} N_1 N_2right) (r-1). end{aligned}$$
(6)
For identical patch size (N_1=N_2 = N/2), this reduces to$$begin{aligned} phi _{bullet !!-!!bullet } approx tfrac{1}{N} +tfrac{N-1}{2N} (r-1), end{aligned}$$
(7)
which is the known result for a single population of size (N=N_1+N_2). When patches have very different size, (N_1 gg N_2) such that (N approx N_1), we recover the same result. Thus, the difference between the fixation probability of a two-patch meta-population with identical patch size and the fixation probability of a two-patch meta-population with very different patch size that we found for highly advantageous mutants is no longer observed for weak selection.When migration probabilities become larger, our approximation is no longer valid and we need to rely on numerical approaches. Figure 2 illustrates the difference between the fixation probability of a two-patch structure meta-population and the equivalent well-mixed population of size (N_1+N_2 ) when migration is low using Eq. (4) and comparing with the numerical approach in Ref.39.While the fixation probability of the two-patch meta-population is very close to the fixation probability of the well-mixed population40, a close inspection reveals an interesting property: For low migration probabilities and (N_1 ne N_2), the two patch structure is a suppressor of selection in the original sense of Lieberman et al.1: For advantageous mutations, (r >1), it decreases the fixation probability, whereas for disadvantageous mutations, (r1) and negative for (r1 ) the minimum fixation probability occurs when the two patch sizes are identical, ( N_1=N_2=N/2 ). Similarly, for fitness values ( r More

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Technological advancements improve our ability to manage natural resources. This is particularly relevant for small scale fisheries, where there is a need for low-cost data sources to improve our understanding of fishing effort, catch, and the associated sustainability of fish resources required for global food security. GPS trackers have now been widely used to study the behaviour of small-scale fisheries25,40. We found focusing on patterns of vessel movement to be a low-cost, reliable approach to identify fishing grounds, as well as to understand both the spatial and temporal usage of AFADs, and ultimately predicting the resulting catch.We acknowledge that the number of actual AFADs used by our tracked vessels is likely much higher than the number estimated in this study. This is in part due to our requirement for a potential AFAD to have been visited at least two times before we considered it a confirmed AFAD. These criteria significantly reduced the number of AFADs reported (from 139 to 72 AFADs). However, we erred on the cautious side as we were unable to distinguish between AFAD fishing and other non-AFAD fishing behaviours, such as bait fishing, that might involve vessels being stationary. Furthermore, given that the length of trip for a vessel is 5 to 20 days, the one-month period over which a SPOT Trace tracker is deployed means there is a maximum of two fishing trips possible during our observation period. This leads to the potential that even the tracked vessels may have additional AFADs they use outside of the fishing trips observed in this study period.Another source of underestimation in AFAD numbers may come from the distance parameter we employed in our analysis. During the ground-truthing, only two out of three visited AFADs were detected by DBSCAN. This is because the radius of movement between two of the FADs (Fig. 2) was overlapping. This is possible, as currents and winds displace AFADs synchronously, and thus tangling is reduced, allowing AFADs to be deployed closer together than the sum of their surface radii. Therefore, the distance among vessel positions clustered two AFADs, identifying them as a single AFAD, given the criteria we applied. The implication of this potential for multiple AFADs within a DBSCAN cluster is that the locations we detected could actually represent a much larger number of AFADs that are deployed close together. Future extensions of this work could include estimating the number of AFADs within clusters using the geometric pattern of the boundary of the cluster. For instance, a figure-eight shaped boundary would indicate there are two FADs in a cluster rather than one. However, SPOT Trace deployments would need to be longer to provide adequate data to distinguish this subtlety.Since our study did not include records from the first time each of the AFADs were deployed, we were unable to determine the absolute lifetime of AFADs in the region. However, based on the vessel tracking data, only a few AFADs were visited for nearly one year implying that AFADs might be failing in less than one year. Because the record of AFAD usage is from the vessel perspective, when the tracker on a vessel is removed at the end of its month long deployment, the record stops while the AFADs may still exist and remain in use. If other vessels in the study use the same AFAD, the record for that AFAD will continue, but if not, it ends with the removal of the tracker from the vessel using it. Hence, the lifespan of AFADs we report is an estimate that should be treated as a minimum lifespan. Moreover, since fishers tend to deploy AFADs in a particular fishing location, it is also possible that the fisher has deployed a new AFAD in the same location. However, given the deployment precision required this may not be as big of a source of error as underestimation.Conversely, from long periods of inactivity at individual AFADs (as shown in Fig. 4), we suspect that some AFADs may have been lost and replaced over the course of the longer use patterns we observed. These inactivity periods take place during the wet season, which typically has rougher weather and poorer fishing conditions, particularly for small vessels. Hence, we might anticipate fewer vessel days at sea or the loss of AFADs due to failure of their moorings during periods of high swell. The asynchrony in the time at which inactivity patterns begin and end, however, suggests that a lack of fishing activity is unlikely to be the sole source of the observed inactivity periods and that there is likely a contribution from AFAD loss and replacement. With additional tracking data on individual vessels, it might be possible to disentangle these differences by looking for subtle shifts in the centres of the spatial clusters, indicating a new deployment. However, the current observations are inadequate to provide this level of resolution.The AFAD sharing practices identified in our study reveal a management opportunity to reduce the number of AFADs deployed. The use of AFADs can be maximized by extending the users beyond the owners of an individual AFAD, or by considering AFADs a community resource. While perhaps not suitable in all areas, given that sharing AFAD is relatively widespread, this presents a viable option. Developing a management system that allows limits on the total number of AFADs but provides for a system of rotating access may allow for the establishment of a biologically sustainable system of AFADs whilst minimizing social and economic disruption to the fishers. Moreover, it may also reduce the incentives for fishers to keep AFAD locations private.The catch data obtained from the port sampling allowed us to identify the factors that influence the total catch. The number of AFADs visited is the main factor that significantly affects the weight of catch by a vessel on a fishing trip, given the average catch of a vessel. Trip success increased as more AFADs were visited, but then declined sharply beyond 3 AFADs. Similarly, for a given vessel, as trip lengths increased, catches were lower.This pattern might be expected if fishers are considered as central place foragers in the context of the optimal foraging theory41. Vessels typically leave and return to the same port. Presumably while at sea, they attempt to either maximize their catch or at least satisfy a minimum required catch to meet their fixed costs. In either event, one would expect fishers to extend their trip length if catch rates are low to try to meet their objective, subject to other constraints such as fuel supply or adverse weather. In this context, if they visit an AFAD and have a low catch rate, one would expect fishers to move to another AFAD. Thus together, the number of AFADs visited and the length of the trip provide a reliable predictor of the quality of a fishing trip, in terms of variation around the average for a given vessel. This information is very useful, as it suggests that the SPOT Tracking data, or other vessel tracking information, can be used as a proxy for port sampling. Thus, remote monitoring of the vessels can be used to get some measure of stock status, via catch rates, or as a check against port sampling or logbooks to check their veracity. Given the rapidly falling cost of technologies, such as the SPOT trackers used in this study, proxies for catch rates such as the one we developed here could facilitate fleet-wide monitoring. In Indonesia, with a quarter-million small scale vessels spread across thousands of islands this scalability is critical, and given Indonesia has the third highest marine catch in the world42, the resulting management improvements have global ramifications.The case of Indonesian FAD management challenges reflects current global FAD management challenges, especially in artisanal coastal fisheries in Pacific island countries where AFADs are commonly used43. We found that AFAD deployments in Indonesia are very dense, and frequently well inside the minimum ten nautical miles spacing required by law. Based on our study, it is also clear that vessels are using more than the three AFADs limit allowed in current regulations. These high densities and usage rates could be reducing the effectiveness of AFADs to aggregate the fish by dividing the fish concentration among close AFADs and thus decreasing catch rates. Moreover, the current concentrated use of AFADs could also be leading to large numbers of lost and abandoned AFAD structures, with significant impacts on the ecosystem and local habitats44,45. Fishers could deploy fewer AFADs, thus decreasing their potential impacts. The regulation of AFADs in Indonesia, which has been in place since 2014, is still not effectively enforced due to technical issues. Moreover, the users of this type of FAD are dominated by small-scale fishers whose livelihoods and food supplies likely depend on the additional efficiency, making management more problematic.Expansion of the current study from a monthly sampling approach to continuous monitoring of vessels would greatly improve our ability to discern AFAD use patterns, infer catch dynamics, and ultimately investigate the potential for management strategies that could balance maximizing the benefits from AFAD deployments and controlling their environmental and social impacts. Ultimately minor technological improvements which extend tracking device lifetimes, along with links to other electronic monitoring approaches such as low-cost onboard cameras or electronic logbooks and landing records could allow cost effective monitoring of the vast small scale fleet in Indonesia, leading to better fishery outcomes at a significantly reduced cost. Expanding these approaches, particularly in the case of rapidly falling technology costs, has significant promise for improving management across the many fisheries and sectors in Indonesia, and elsewhere.Most of the global FADs are managed by the regional fisheries management organizations (RFMOs), and not all member countries have implemented regulations regarding FAD use46,47 (IOTC, 2018). Given the large proportion of world tuna production which is dominated by floating object fishing, compared to fishing on free schooling tuna48, more investment in FAD management will likely yield an overall improvement in fisheries management and catch sustainability. Paired with addressing management of Indonesia’s very large small scale tuna sector, which lands half the national catch, these regulations could significantly improve sustainability in the Indo-Pacific region. More