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Overview of U.S. domestic migration flowsThe most recent ACS county-to-county flow dataset26 reports that about 45.6 million people migrated to the U.S. per year during the period 2015–2019, which corresponds to 14.2% of the U.S. population27. Approximately 43.5 million annual moves corresponded to domestic migration (moves within the U.S.28), while 2.1 million accounted for inflows of individuals from other countries (viz. international immigration).With respect to domestic migration, 25.7 million people per year migrated within the same county, thus showing that the highest share of domestic flows (59%) is intra-county. Annually, about 10.4 people moved between different counties within the same state, thus intra-state flows account for 24% of the domestic migration (Supplementary Fig. 1), mainly driven by the search for more affordable housing, better jobs, and for family reasons such as change in marital status29. Long distance moves, captured by inter-state flows, represent the remaining 17% of domestic flows, which comprises about 7.5 million moves per year. Here, we will refer to these domestic migration flows as inflows or outflows, and netflows (inflows-outflows).The United States Office of Management and Budget (OMB) classifies counties as metropolitan, micropolitan, or neither30. A metropolitan statistical area contains a core urban area of at least 50,000 population. A metro area represents a functional delineation of an urban area with a network of strong socioeconomic ties, and provision of infrastructure services31,32,33. A micropolitan statistical area contains an urban core of at lest 10,000 but less than 50,000 inhabitants. There are over 380 metropolitan statistical areas in the U.S., each composed of one or more counties, accounting for about 86% of the total U.S. population and comprising approximately 28% of the land area of the country. For this reason, our analysis focuses on the growth dynamics of MSA counties. Supplementary Fig. 2 shows the 3141 counties (administrative subdivisions of the states) in the U.S., comprising about 321 million inhabitants in the starting year of the ACS 5-Year survey period (2015–2019) of our analysis26.Population growth has two components, namely natural growth and migration. Natural growth accounts for births minus deaths, and migration comprises domestic and international migration. With recent trends showing that births and natural increase have declined in the U.S. and in recent years contribute less to overall city population growth34,35, migration patterns become more relevant to the study of city population growth. Because the ACS flow files contain international inflows only, the relative importance of migrations on population growth is here addressed by x = ∣Inflows−Outflows∣/∣Births−Deaths∣ (Supplementary Figs. 3, 4), which is the ratio between domestic netflows and natural growth. The statistical distribution of this quantity computed for all U.S. counties is well fitted by a lognormal distribution, and shows that x≥1 for 76.5% of counties. For most counties, domestic migration dominates population growth, and understanding the spatial structure of domestic netflows (and their distribution within a city) is crucial to the comprehension of the mechanisms behind the heterogeneity of city population growth.At this spatial granularity, we observe a strong heterogeneity among the U.S. counties (Supplementary Fig. 2) for the period 2015 − 2019, along with examples of specific MSAs. In particular, the relative dispersion of counties relative growth due to netflows is higher than one for about 85% of the metro areas, indicating a large heterogeneity within the same city and pointing towards the spatial structure of domestic migration. The observed difference in the netflows stresses the relevance of our approach: counties belonging to the same city may have specific growth rates due to population flow patterns, thus indicating preferential flow destinations and pinpointing the direction in which the city has expanded.Heterogeneity of inter- and intra-city flowsInter-city flows represent the major component of the total flows (~55%), while intra-city flows represent ~25%. Flows between metro and micro areas, and between metro and non-statistical areas are the smallest components, with ~13% and ~7%, respectively. Given that about 80% of the domestic migration are composed of intra- and inter-city flows, we will focus our attention on describing the structure of intra- and inter-city flows, but in the Supplementary Information we offer a brief analysis of flows between metro and micro areas, and between metro and non-statistical areas.Inter-city flows are not uniform across the U.S. cities. The most intense annual netflows ( >2000 people per year), accounting for approximately 17% of the entire inter-city U.S. netflows, are mainly from New York and Chicago to California and Florida (Fig. 2), and from Los Angeles to neighboring cities. Notably, netflows among the Midwestern cities are mostly negative and below the threshold we set. These flows are mainly responsible for increasing or decreasing the population of a given city. Intra-city flow patterns, illustrated with the 7 most populous U.S. cities with more than 5 counties, are also non-uniform.Fig. 2: Heterogeneity of inter- and intra-city netflows.The map (A) suggests that the domestic redistribution of people between different U.S. metro areas are non-uniform: the black arrows, indicating the direction of the most intense inter-city netflows (higher than 2000 people per year), reveal migration trends from northern and eastern cities to western and southern regions. Cities (composed of one or more counties) are colored according to the relative growth (viz. population growth adjusted by population) of the whole MSA during the 2015–2019 period, and the black intensity and the thickness of the arrows are proportional to the netflows. Alaska and Hawaii are not shown. Panels (B–H), which are close-up of New York (B), Chicago (C), Dallas (D), Houston (E), Washington D.C. (F), Philadelphia (G), Atlanta (H), suggest that the most intense intra-city netflows are oriented radially outwards: people are moving from core to external counties. Here, counties are colored according to their relative growth in the 2015–2019 period and the width of the arrows is proportional to the netflows between origin and destination counties.Full size imageOur analysis reveals that city centers (defined as the core county with the highest population density) are more likely to have negative netflows, indicating that people are leaving the central regions of cities. The arrows in Fig. 2 indicate the direction of the most intense netflows, supporting this finding and highlighting that there is a trend of people moving from internal to external regions, contributing to population growth and spatial expansion of U.S. cities. In fact, we found no correlation between relative population growth (viz. population growth by county size) and distance from the core county (Supplementary Fig. 5A) for the 46 cities with more than 5 counties, with relative growth about 0.03 ± 0.05. On the other hand, we found that relative natural growth (Supplementary Fig. 5B) is negatively correlated with the distance to core county, thus natural growth is less relevant as a component of growth in the outer regions of cities. Consequently, our results show that not only the contribution of each component of growth changes with distance to core county, but also that the internal redistribution of people is an important mechanism of growth, mainly in the external counties.We also examined variability in inter- and intra-city flows within the 50 states (Supplementary Fig. 6). Total flows within a state increase, as expected, with the state population. Two special cases are, however, of interest: (1) two states (Vermont and Rhode Island) with small populations have only one MSA, in which case within-state inter-city flows are zero; and (2) nearly 40%, or 149, of MSAs have only one county, in which case intra-city flows could not be estimated. For all other cases, we observe on average an equal split between inter- and intra-city flows, but with considerable variability among the states, with a mean about 0.5 and standard deviation about 0.2. A generalization of the intra- and inter-city migratory patterns for all 46 cities with more than 5 counties shows that the percentage of migrants from intra- and inter-city flows are of the same order of magnitude (Fig. 3).Fig. 3: Roles of intra- and inter-city flows in driving the heterogeneous population growth of cities.We define the core county as the one with the highest population density, and we plot the percentage of inflows due to intra- (A) and inter-city flows (B) of each county within a city as a function of its distance to the core county. The percentage of outflows due to intra- and inter-city flows are shown in (C) and (D), respectively. The positive correlation of the relative growth with distance due to intra-city flows in (E), along with the lack of correlation due to inter-city flows in (F), indicates that intra-city flows are mainly responsible for increasing the population in the external regions of cities. The sizes of red circles and blue squares are proportional to the city population. The range of distances is split into equally spaced bins. The number of counties n within each bin, from left to right, is 46, 1, 4, 7, 7, 17, 21, 31, 36, 38, 34, 31, 31, 30, 20, 20, 21, 14, 17, 9, 9, 6, 4, 2, 5, 5, 2, 1. The black dots and the error bars indicate the mean and the 90% interval, respectively, of the counties within the corresponding bin. We also show the Pearson correlation coefficient R and the p-value associated with the two-sided test of the null hypothesis of non-correlation.Full size imageApart from the core county, flows from the same city correspond to about 50% of the inflow of people in the counties, presenting a slightly positive correlation with their distance from the city center (Fig. 3A). The low percentage for the core county indicates that it is not the major destination of flows from the same city. The percentage of inflows from other cities is higher in the core county and decays as we move towards the suburbs (Fig. 3B). The moderate negative correlation of this percentage with the distance reveals that inflows from other cities are more likely to concentrate in the core regions of a city.The percentage of outflows directed from the core county to other counties within the same city has a slightly negative correlation with the distance of the origin county to the city center, so it is more likely to find intra-city flows with outflows from internal regions (Fig. 3C). The core county is an exception again, suggesting that it is less likely that someone leaving the core county will move to another county within the same city. The slightly negative correlation of the percentage of outflows directed to other cities suggests that there is a trend of people leaving the core county and the central regions to move to other cities (Fig. 3D). The high percentage of inflows (Fig. 3B) and outflows (Fig. 3D) in the central region due to inter-city flows implies that the central regions of cities are more dynamic and diverse and that people tend to move to counties with similar levels of urbanization. The same pattern is observed for flows between metro and micro areas, and for metro and non-statistical areas, allowing us to conclude that people moving from rural areas are more likely to move to the external regions of a city (Supplementary Fig. 7).The positive correlation of the relative growth with the distance due to intra-city flows (Fig. 3E) shows that the resulting intra-city redistribution of people, given by the difference between inflows and outflows, is such that there is a trend from core county to the external counties (viz. suburbs). When compared to the relative growth due to inter-city flows (Fig. 3F), which do not show any trend and that have negative values for the most distant counties, it becomes clear that intra-city flows play a major role in the population increase observed in outer regions of cities. Interestingly, large circle and square dots in Fig. 3E and F suggest that the loss of people due to inter-city netflows is more intense than the gain of people due to intra-city netflows in some external counties of the largest metro areas, thus explaining the population decline in some outer regions of New York and Chicago (as shown in Fig. 2B and C).The population growth due to intra-city flows is also depicted in Fig. 4. The concentration of flows below the diagonal captures the heterogeneity and the preferential destination of intra-city netflows. We observe that people are more likely to move to lower population density counties when moving from one place to another within the same city, as exemplified by 7 cities in panel A. Panel B summarizes this analysis for the 46 cities with more than 5 counties by showing the fraction ({{{{{{{mathcal{F}}}}}}}}) of intra-city netflows to lower density counties. We note that more than 93% of the cities have ({{{{{{{mathcal{F}}}}}}}} > 0.5) and that there is a positive correlation of ({{{{{{{mathcal{F}}}}}}}}) with the city population, and C shows the rank of cities according to the fraction of intra-city netflows to lower density counties.Fig. 4: People are moving to counties with lower population density.A The population density of the origin (ρo) and destination (ρd) counties of intra-city netflows for New York, Chicago, Dallas, Houston, Washington D.C., Philadelphia, Atlanta, reveal that the majority of the flows occur from high to low-density counties. The size of the symbols are proportional to the intensity of the netflow, and the black line corresponds to y = x. B The fraction of netflows to lower density counties ({{{{{{{mathcal{F}}}}}}}}) has a positive correlation with city population when we consider the 46 MSAs with more than 5 counties, suggesting that intra-city netflows to lower density counties are more frequent as the city size increases. We also show the Pearson correlation coefficient R and the p-value associated with the two-sided test of the null hypothesis of non-correlation. C The ranking of the cities according to ({{{{{{{mathcal{F}}}}}}}}).Full size imagePopulation density does not seem to play a major role in driving flows between counties of different cities. The fraction of inter-city netflows to lower density counties is about 57% when we consider all the 384 MSAs. The heterogeneity in the inter-city netflow pattern can be assessed by analyzing ({{{{{{{mathcal{F}}}}}}}}) versus the population of the destination city (Fig. 5A, B) and ({{{{{{{mathcal{F}}}}}}}}) versus the population of the origin city (Fig. 5C, D). The negative correlation of ({{{{{{{mathcal{F}}}}}}}}) with the population of the destination city in panel A indicates that inflows are more likely to come from lower density counties as the destination city size increases. The positive correlation of ({{{{{{{mathcal{F}}}}}}}}) with the population of the origin city in panel C reveals that outflows tend to be directed to lower density counties as the origin city size increases. The trends observed in panels A and C reveal that inter-city flows are more likely between counties with different population densities rather than between counties with similar population densities. Panels B and D show the rank order of cities according to a function of the destination city size and the origin city size, respectively.Fig. 5: Inter-city flow patterns depend on the population size of the origin and destination cities.Each point corresponds to a particular city. A Fraction ({{{{{{{mathcal{F}}}}}}}}) of netflows going to lower density counties versus the population of the destination city. Inflows to counties of large cities (with population greater than 106, dashed line) usually comes from counties with lower population densities. B Rank of cities according to the share of inflows from lower density counties. C Fraction ({{{{{{{mathcal{F}}}}}}}}) versus the population of the origin city. Outflows from counties of large cities usually go to cities with lower density counties. D The rank of cities according to the share of inter-city netflows to lower density counties is presented. The dots are colored according to the city population density (darker red means higher density). We also show the Pearson correlation coefficient R and the p-value associated with the two-sided test of the null hypothesis of non-correlation.Full size imageWe would expect that there might be preferential locations within a given city to which people move due to various factors such as lower costs of housing and employment opportunities. However, it seems that house prices have little to no effect on intra-city netflows (Supplementary Fig. 8). While the fraction of intra-city netflows to counties with less expensive houses is about 0.8 for cities like New York, Chicago and Washington, this fraction is about 0.2 for cities like Dallas, Houston and Philadelphia. The lack of a clear national pattern highlights the specificity of each city and the heterogeneity of the regional housing market in the U.S.36,37. On the other hand, the fraction of intra-city netflows to counties with lower unemployment rates is higher than 0.5 for about 2/3 of the cities (Supplementary Fig. 9), thus showing that people are more likely to move to counties with lower unemployment rates.Statistical structure of inter-city flowsIntra-city flows capture the internal redistribution of population, without altering the total city population. In this context, we focus on inter-city flows to investigate whether or not extreme flows play an important role in shaping the growth of counties as observed at the city level5. For cities, Verbavatz and Barthelemy5 introduce a stochastic equation to describe population growth, composed of two terms. The first term accounts for out-of-system growth, which includes natural growth and international migration, and the second term accounts for the growth due to domestic netflows. They find that total netflows adjusted by population size can be well approximated by a Lévy distribution, and this heavy-tailed distribution indicates that rare and extreme inter-city flows (viz. migratory shocks) dominate city population growth.Here, we find that, for counties, the distribution of total netflows adjusted by population size, which is represented by ζi and captures the intensity of inter-city migratory flows (see the section “Methods” for details), can be approximated by a Gaussian distribution (Fig. 6). The lack of a heavy tail in the empirical distribution of ζi suggests the absence of extreme flows at the county level, thus indicating that the growth of counties can be described by smoother migratory process than cities. Given that cities do experience migratory shocks5, our findings indicate that cities redistribute inflows among its different counties, leading to a spill-over effect that dampens flow shocks at the county level.Fig. 6: Extreme shocks are dissipated at the county level.The distribution of ζi, which is the sum of the netflows of a county i adjusted by its population, suggests that migratory events are exponentially bounded at the county level since ζi is well described by a Gaussian distribution. The distribution of ζi is computed here for all the counties with at least 50.000 inhabitants. We also show the result of the two-sided KS test under the null hypothesis that ζi follows a Gaussian distribution.Full size imageHeterogeneity of international inflowsThe highest share of international inflows is concentrated in large cities. About 40% of the international inflows are destined to the top 10 (~2.6%) largest metro areas of the U.S. New York is the first with 8.5% of international inflows, followed by Los Angeles and Miami with 5.4% and 5.0%, respectively. Indeed, international inflows Yk scale superlinearly with the population Sk of the metro area k (Fig. 7A), thus larger cities have more immigrants per capita than smaller cities.Fig. 7: International inflow scales superlinearly with city size.Panel (A) shows the number of international immigrants as a function of the city size S for the 384 U.S. metro areas. The performance of the model Y = Y0Sθ, in which θ = 1.19 (95% CI [1.13, 1.24]) and Y0 = 4.10−4 is a normalization constant, is assessed by the coefficient of determination R2. Note that the spread of empirical data around the model narrows as the size of the city increases. Panel (B) shows the rank of the metro areas and the residues, which captures the deviation from the null model thus highligthing cities receiving more/less than expected international inflows. Names of the cities are followed by two-letter state abbreviations.Full size imageInterestingly, this gain with scale is also observed in socioeconomic city metrics as crime, GDP, innovation and wealth creation due to the manifestation of nonlinear agglomeration phenomena38,39,40. Using Y = Y0Sθ as a null model, we can compute deviations from the average behavior by means of residuals given by (log ({Y}_{k}/{Y}_{0}{S}_{k}^{theta }))38. The rank of the residues (Fig. 7B) shows that college towns are among the top metro areas receiving more international inflows than expected, while large cities as Los Angeles, New York, Atlanta, and Chicago are among the metro areas receiving less international inflows than expected.The spatial distribution of international inflows within cities is shown in Supplementary Fig. 10. The highest share of inflows is concentrated at core counties, and the percentage of inflows decreases dramatically with the distance from the core county. This result suggests that inflow of international migrants is an important component of population growth, particularly at the core regions of large cities.Robustness of our findingsPatterns of population redistribution change from time to time in the U.S., and are affected by several factors. For instance, in the 1960s non-metropolitan counties lost about 3 million people due to outflows to metropolitan counties, while the reverse trend was observed in the 1970s when non-metropolitan counties experienced net inflows of about 2.6 million people41. Wardwell and Brown in41 indicate that three factors might be among the main reasons of such change, namely economic decentralization, preference for rural living, and modernization of rural life. The temporal influence of factors as socioeconomic conditions, transportation infrastructure, natural amenities, and land use and development on population growth in rural and suburban areas is explored in42. Changes in rural migration patterns are also studied in43, where age-specific rural migration patterns from 1950 to 1995 are analyzed. In44, the authors explore redistribution trends across U.S. counties from 1980 to 1995 split into three five year periods (1980–1985, 1985–1990, 1990–1995), and45 analyzes changes in age-specific nationwide migration patterns from 1950 to 2010.The spatial structure of migration patterns may indeed change from time to time; our results correspond to the current intra- and inter-city redistribution trends, based on the most recent ACS migration flow files. We present a thorough empirical and statistical analysis of domestic migration flows among U.S. cities ans counties. Our study also introduces a framework that can be used for analyzing and comparing internal redistribution of people across different time periods. Indeed, we extended our analysis for two other time periods, 2005–2009 and 2010–2014. With respect to the spatial distribution of intra- and inter-city flows, similar trends are observed in both periods (Supplementary Figs. 12, 13), namely inter-city flows are responsible for the highest share of inflows to core counties, and intra-city flows are responsible for the highest share of inflows to external counties. We also explored the role of population density in driving netflows between counties within the same metro area in 2005–2009 and 2010–2014. The results (Supplementary Figs. 14 and 15) indicate that 95.7% of cities were dominated by intra-city moves to lower density counties in 2005–2009, and this percentage dropped to 76.1% in 2010–2014. Our findings indicate that the trends we report here are taking place since 2005 but with different intensities.The robustness of our findings is checked with additional migration data from the Internal Revenue Service (IRS), which reports the year-to-year address changes on individual tax returns filled with the IRS46. The results obtained with the analysis of IRS datasets from periods 2015–2016, 2016–2017, 2017–2018, 2018–2019 (Supplementary Figs. 16, 17, 18, 19), reveal similar trends to those we found using ACS data. Particularly, we observe that, for all periods considered, the correlation between intra-city netflow/S and distance to core county is stronger than we found with ACS data, thus highlighting the role of intra-city flows in driving population to external regions of cities. The main difference between both datasets is in the percentage of intra- and inter-city inflows and outflows: while ACS data indicates that both flows have approximately the same contribution to the total flows, the IRS data indicates that, besides the core county, intra-city flows are responsible for about 80% of inflows and outflows of metro areas. More

Attention combination mechanismDue to the difficulty in extracting features from target areas in images, the high computational effort of the model and the low accuracy of detection are addressed. As shown in Fig. 3, we introduce a lightweight feedforward convolutional attention module CBAM after the backbone network Focus module of the YOLOv5s network model. The SE-Net (Squeeze and Excitation Networks) channel attention module is posted at the end of the backbone network. We propose an attention combination mechanism based on the YOLOv5s network model and name the improved network model YOLOv5s-CS. Where the CBAM module has a channel number of 128, a convolutional kernel size of 3 and a step size of 2, the SELayer has a channel number of 1024 and a step size of 4.Figure 3YOLOv5 backbone network structure before and after improvement.Full size imageConvolutional block attention module networkIn 2018, Woo et al.25 proposed the lightweight feedforward convolutional attention module CBAM. The CBAM module focuses on feature information from both channels and space dimensions and combines feature information to some extent to obtain more comprehensive reliable attentional information26. CBAM consists of two submodules, the channel attention module (CAM) and spatial attention module (SAM), and its overall module structure is shown in Fig. 4a.Figure 4Principle of CBAM.Full size imageThe working principle of the CAM is shown in Fig. 4b. First, the feature map F is input at the input entrance. Second, the global maximum pooling operation and the global average pooling operation are applied to the width and height of the feature map respectively to obtain two feature maps of the same size. Third, two feature maps of the same size are input to the shared parameter network MLP at the same time. Finally, the new feature map output from the shared parameter network is subjected to a summation operation and a sigmoid activation function to obtain the channel attention features ({M}_{c}).The channel attention module CAM is calculated as shown in Formula (1):$${text{M}}_{rm{c}}({text{F}}){=sigma}({text{MLP (AvgPool (F))}}+ {text MLP (MaxPool (F)))}{=sigma}({rm{W}}_{1}({text{W}}_{0}({text{F}}_{{{rm{avg}}}^{rm{c}}}))+{rm{W}}_{0}({rm{W}}_{1}({rm{F}}_{{{rm{max}}}^{rm{c}}})))$$
(1)
where σ represents the sigmoid function, MLP represents the shared parameter network, ({text{W}}_{0}) and ({text{W}}_{1}) represent the shared weights, ({text{F}}_{text{avg}}^{text{c}}) is the result of feature map F after global average pooling, and ({text{F}}_{text{max}}^{text{c}}) is the result of feature map F after global maximum pooling.The working principle of SAM is shown in Fig. 4c. The feature map F’ is regarded as the input of the SAM. F’ is obtained by multiplying the input of SAM with the output of CAM. First, the global maximum pooling operation and the global average pooling operation are applied to the channels of the feature map to obtain two feature maps of the same size. Second, two feature maps that have completed the pooling operation are stitched at the channels and the feature channels are dimensioned down using the convolution operation to obtain a new feature map. Finally, spatial attention features ({text{M}}_{text{s}}) are generated using the sigmoid activation function.The spatial attention module (SAM) is calculated, as shown in Formula (2):$${text{M}}_{text{s}}left({text{F}}right) {=sigma}left({text{f}}^{7 times 7}left(left[{text{AvgPool}}left({text{F}}right)text{;MaxPool}left({text{F}}right)right]right)right) {=sigma}left({text{f}}^{7 times 7}left(left[{text{F}}_{text{avg}}^{text{s}} ; {text{F}}_{text{max}}^{text{s}}right]right)right)$$
(2)
where σ is the sigmoid function, ({text{f}}^{7 times 7}) denotes the convolution operation with a filter size of 7 × 7, ({text{F}}_{text{avg}}^{text{s}}) is the result of the feature map after global average pooling, and ({text{F}}_{text{max}}^{text{s}}) is the result of the feature map after global maximum pooling.Squeeze and excitation networkIn 2018, Hu et al.27 proposed a single-path attention network structure SE-Net. SE-Net uses the idea of an attention mechanism to analyze the relationship feature maps by modeling and adaptively learning to obtain the importance of each feature map28 and then assigns different weights to the original feature map for updating according to the importance. In this way, SE-Net pays more attention to the features that are useful for the target task while suppressing useless feature information and allocates computational resources rationally to different channels to train the model to achieve better results.The SE-Net attention module is mainly composed of two parts: the squeeze operation and excitation operation. The structure of the SE-Net module is shown in Fig. 5.Figure 5The SE-Net module structure.Full size imageThe squeeze operation uses global average pooling to encode all spatial features on the channel as local features. Second, each feature map is compressed into a real number that has global information on the feature maps. Finally, the squeeze results of each feature map are combined into a vector as the weights of each group of feature maps. It is calculated as shown in Eq. (3):$${text{Z}}_{text{c}}={text{F}}_{text{sq}}left({text{u}}_{text{c}}right)=frac{1}{text{H} times {text{W}}}sum_{text{i=1}}^{text{H}}sum_{text{j=1}}^{text{W}}{{text{u}}}_{text{c}}left(text{i,j}right) , , , $$
(3)
where H is the height of the feature map, W is the feature map width, u is the result after convolution, z is the global attention information of the corresponding feature map, and the subscript c indicates the number of channels.After completing the squeeze operation to obtain the channel information, the feature vector is subjected to the excitation operation. First, it passes through two fully connected layers. Second, it uses the sigmoid function. Finally, the output weights are assigned to the original features. It is calculated as follows:$$text{s} = {text{F}}_{text{ex}}left(text{z,W}right){=sigma}left({text{g}}left(text{z,W}right)right){=sigma}left({text{W}}_{2}{delta}left({text{W}}_{1}{text{z}}right)right)$$
(4)
$$widetilde{{text{x}}_{rm{c}}}={text{F}}_{rm{scale}}left({text{u}}_{rm{c}}, {text{s}}_{rm{c}}right)={text{s}}_{rm{c}}{{text{u}}}_{rm{c}}$$
(5)
where σ is the ReLU activation function, δ represents the sigmoid activation function, and ({text{W}}_{1}) and ({text{W}}_{2}) represent two different fully connected layers. The vector s represents the set of feature mapping weights obtained through the fully connected layer and the activation function. (widetilde{{x}_{c}}) is the feature mapping of the x feature channel, ({text{s}}_{text{c}}) is a weight, and ({text{u}}_{text{c}}) is a two-dimensional matrix.Target detection layerThe garbage in rural areas is a smaller target and has fewer pixel characteristics, such as capsule, button butteries. Therefore, we insert a small target detection layer to improve the head network structure based on the original YOLOv5s network model for detecting objects with small targets to optimize the problem of missed detection in the original network model. The YOLOv5s network structure with the addition of the small target detection layer is shown in Fig. 6 and named YOLOv5s-STD.Figure 6The YOLOv5s-STD network structure.Full size imageIn the seventeenth layer of the neck network, operations such as upsampling are performed on the feature maps so that the feature maps continue to expand. Meanwhile, in the twentieth layer, the feature maps obtained from the neck network are fused with the feature maps extracted from the backbone network. We insert a detection layer capable of predicting small targets in the thirty-first layer. To improve the detection accuracy, we use a total of four detection layers for the output feature maps, which are capable of detecting smaller target objects. In addition to the three initial anchor values based on the original model, an additional set of anchor values is added as a way to detect smaller targets. The anchor values of the improved YOLOv5s network model are set to [5, 6, 8, 14, 15, 11], [10, 13, 16, 30, 33, 23], [30, 61, 62, 45, 59, 119] and [116, 90, 156, 198, 373, 326].Bounding box regression loss functionThe loss function is an important indicator of the generalization ability of a model. In 2016, Yu et al.29 proposed a new joint intersection loss function IoU for bounding box prediction. IoU stands for intersection over union, which is a frequently used metric in target detection. It is used not only to determine the positive and negative samples, but also to determine the similarity between the predicted bounding box and the ground truth bounding box. It can be described as shown in the Eq. (6):$$text{IoU} = frac{left|text{A} capleft.{text{B}}right|right.}{left|{text{A}} cupleft.{text{B}}right|right.}$$
(6)
where the value domain of IoU ranges from [0,1]. A and B are the areas of arbitrary regions. Additionally, when IoU is used as a loss function, it has to scale invariance, as shown in Eq. (7):$$text{IoU_Loss} = 1-frac{left|text{A} cap left.{text{B}}right|right.}{left|{text{A}} cup left.{text{B}}right|right.}$$
(7)
However, when the prediction bounding box and the ground truth bounding box do not intersect, namely IoU = 0, the distance between the arbitrary region area of A and B cannot be calculated. The loss function at this point is not derivable and cannot be used to optimize the two disjoint bounding boxes. Alternatively, when there are different intersection positions, where the overlapping parts are the same but in different overlapping directions, the IoU loss function cannot be predicted.To address these issues, the idea of GIoU (Generalized Intersection over Union)30, in which a minimum rectangular Box C of A and B is added, was proposed in 2019 by Rezatofighi et al. Suppose the prediction bounding box is B, the ground truth bounding box is A, the area where A and B intersect is D, and the area containing two bounding boxes is C, as shown in Fig. 7.Figure 7GIoU evaluation chart.Full size imageThen, the GIoU calculation, as shown in Formula (8), is:$$text{GIoU}= text{IoU}-frac{text{|C}-left({text{A}} cup {text{B}}right)text{|}}{text{|C|}}$$
(8)
The GIoU_Loss is calculated as (9):$$text{GIoU_Loss=1}-{text{IoU}}-frac{text{|C}-left({text{A}} cup {text{B}}right)text{|}}{text{|C|}}$$
(9)
The original YOLOv5 algorithm uses GIoU_Loss as the loss function. Comparing Eqs. (6) and (8), it can be seen that GIoU is a new penalty term (frac{text{|C}-left({text{A}} cup {text{B}}right)text{|}}{text{|C|}}) that is added to IoU and is clearly represented by Fig. 7.Although the GIoU loss function solves the problem that the gradient of the IoU loss function cannot be updated in time and the prediction bounding box, the direction of the ground truth bounding box is not consistent when predicting, but there are still disadvantages, as shown in Fig. 8.Figure 8Comparsion of loss values.Full size imageFigure 8 shows three different position relationships formed when the predicted bounding box and the ground truth bounding box overlap exactly. Among them, the ratio of the length to width of the green grounding truth bounding box is 1:2, and the red predicted bounding box has the same aspect ratio as the ground truth bounding box, but the size is only one-half of the green ground truth bounding box. When the prediction bounding box and the ground truth bounding box completely overlap, the GIoU degenerates to the IoU, and the GIoU value and IoU value for the three different position cases are 0.45 at this time. The GIoU loss function does not directly reflect the distance between the prediction bounding box and the ground truth bounding box. Therefore, we introduce the CIoU (Complete Intersection over Union)31 loss function to replace the original GIoU loss function in the YOLOv5 algorithm and continue to optimize the prediction bounding box.Therefore, the CIoU is calculated as (10):$$text{GIoU_Loss}=1-text{IoU}-frac{text{|C}-left({text{A}} cup {text{B}}right)text{|}}{text{|C|}}$$
(10)
where b and ({text{b}}^{text{gt}}) denote the centroids of the prediction bounding box and the ground truth bounding box, respectively, ({rho}) is the Euclidean distance between the two centroids, and c is the diagonal length of the minimum closed area formed by the prediction bounding box and the ground truth bounding box.(alpha) is the parameter used to balance the scale, and v is the scale consistency used to measure the aspect ratio between the prediction bounding box and the ground truth bounding box, as shown in Eqs. (11) and (12).$$alpha =frac{text{v}}{left(1-text{IoU}right)+{text{v}}^{{prime}}}$$
(11)
$$text{v} = frac{4}{{pi}^{2}}{left({text{arctan}}frac{{omega}^{text{gt}}}{{text{h}}^{text{gt}}}- text{arctan}frac{{omega}^{text{p}}}{{text{h}}^{text{p}}}right)}^{2}$$
(12)
Therefore, the expression of CIoU_Loss can be obtained according to Eqs. (10), (11) and (12).$$text{CIoU_Loss} =1-text{CIoU}=1-text{IoU}+frac{{rho}^{2}left(text{b,}{text{b}}^{text{gt}}right)}{{text{c}}^{2}}{+ alpha v }$$
(13)
Optimization algorithmAfter optimizing the loss function of the network model, the next step is to optimize the hyperparameters of the network model. The function of the optimizer is to adjust the hyperparameters to the most appropriate values while making the loss function converge as much as possible32. In the target detection algorithm, the optimizer is mainly used to calculate the gradient of the loss function and to iteratively update the parameters.The optimizer used in YOLOv5 is stochastic gradient descent (SGD). Since a large number of problems in deep learning satisfy the strict saddle function, all the local optimal solutions obtained are almost as ideal. Therefore, SGD algorithm is not trapped in the saddle point and has strong generality. However, the slow convergence speed and the number of iterations of SGD algorithm are still problems that need to be improved. Adam algorithm has both the first-order momentum in the SGD algorithm and combines the second-order momentum in AdaGrad algorithm and AdaDelta algorithm, Adaptive&Momentum. Adam formula can be described as follows:$${m}_{t}={beta }_{1}{m}_{t-1}+left(1-{beta }_{1}right){g}_{t}$$
(14)
$${v}_{t}={beta }_{2}{v}_{t-1}+left(1-{beta }_{2}right){g}_{t}^{2}$$
(15)
$${widehat{m}}_{t}=frac{{m}_{t}}{1-{beta }_{1}^{t}}$$
(16)
$${widehat{v}}_{t}=frac{{v}_{t}}{1-{beta }_{2}^{t}}$$
(17)
where ({beta }_{1}) and ({beta }_{2}) parameters are hyperparameters and g is the current gradient value of the error function, ({m}_{t}) is the gradient of the first-order momentum and ({v}_{t}) is the gradient of the second-order momentum.Adam is an adaptive one-step random objective function optimization algorithm based on a low-order moment. It can replace the traditional first-order optimization algorithm for the stochastic gradient descent process. It is able to update the weights of the neural network adaptively based on the data trained during the iterative process. The Adam optimizer occupies fewer memory resources during the training process and is suitable for solving the problems of sparse gradients and large fluctuations in loss values33. Therefore, we use the Adam optimization algorithm instead of the SGD optimization algorithm to train the network model based on the YOLOv5s network model. The calculation is shown in Table 3.Table 3 Computing method of the Adam optimizer.Full size tablewhere ({alpha}) is a factor controlling the learning rate of the network, ({beta}^{{prime}}) is the exponential decay rate of the first-order moment estimate, ({beta}^{{primeprime}}) is the exponential decay rate of the second-order moment estimate, and ({varepsilon}) is a constant that tends to zero infinitely as the denominator. More

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Serpentinite-hosted systems are rare and extreme habitats in which a hydrothermal process, serpentinization, alters ultramafic mantle rocks and yields hyperalkaline fluid rich in molecular hydrogen (H2) and reduced one-carbon compounds [1,2,3,4,5,6,7,8]. These fluids are often electron acceptor depleted—oxygen, nitrate, sulfate, etc. are absent (i.e., anoxic) and even the least favorable exogenous acceptor, carbon dioxide (CO2), is limiting due to the high alkalinity. Though previous studies explore the diversity of organisms in serpentinite-hosted systems, we have little insight into how indigenous H2-utilizing microorganisms combat the unique metabolic challenges in situ. One recent study shows strategies that methane-generating archaea employ to oxidize H2 in situ [9], but how other microorganisms (i.e., H2-utilizing anaerobic bacteria) overcome the electron acceptor limitation is poorly understood. Further, given that life is theorized to have emerged as H2-utilizing lithotrophs in early Earth serpentinite-hosted systems [10,11,12,13,14,15,16,17,18,19,20,21,22,23,24], modern lithotrophs inhabiting such ecosystems may represent valuable extant windows into the metabolism of primordial organisms. In this study, we pair metagenomics and thermodynamics to characterize uncultured putative anaerobic H2 utilizers inhabiting alkaline H2-rich serpentinite-hosted systems (Hakuba Happo hot springs in Hakuba, Japan, and The Cedars springs in California, USA; pH ~10.9 and ~11.9, respectively [25,26,27]) and elucidate novel, potentially ancient, lithotrophic strategies.Thermodynamics and geochemistryThe two primary strategies for utilizing H2 under anoxic conditions without favorable exogenous electron acceptors are methanogenesis and homoacetogenesis. As bacteria were detected in both Hakuba and The Cedars, yet archaea were absent in Hakuba, we focused our analyzes on metabolic strategies supporting bacterial H2 utilization (i.e., homoacetogenesis). To evaluate whether homoacetogenesis is viable in situ, we examined the in situ geochemical environment and the thermodynamics of H2/formate utilization and homoacetogenesis. The spring waters of both Hakuba and The Cedars contained H2 (e.g., 201–664 μM in Hakuba [27]). Formate, another compound thought to be abiotically generated through serpentinization, was also detected in Hakuba (8 μM in drilling well #3 [28]) and The Cedars (6.9 µM in GPS1). Acetate has also been detected in situ (4 μM in Hakuba [28] and 69.3 µM in The Cedars GPS1), suggesting these ecosystems may host novel H2- and/or formate-utilizing homoacetogens. Thermodynamic calculations using newly measured and published geochemical data (Tables S1 and S2) confirmed that H2 and formate are reductants in situ (i.e., H2 = 2H+ + 2e−/Formate− = H+ + CO2 + 2e−): the Gibbs free energy yields (∆G) for oxidation (coupled with physiological electron carriers NADP+, NAD+, and ferredoxin) are less than −4.78 kJ per mol H2 and −24.92 kJ per mol formate in Hakuba, and −10.73 and −22.03 in The Cedars respectively (H2 concentration was not available for The Cedars so the highest concentration observed in Hakuba [664 µM] was used; see Supplementary Results). However, serpentinite-hosted systems impose a unique challenge to homoacetogenesis—a key substrate, CO2, is at extremely low concentrations due to the high alkalinity. We estimate that the aqueous CO2 concentration is below 0.0006 nM in Hakuba (pH 10.7 and  +24.92 or +22.02 kJ per mol formate). Thus, catabolic reduction of CO2 to acetate is thermodynamically challenging in situ and may only run if investing ATP (e.g., Calvin–Benson–Bassham cycle [−6 ATP; ∆G of −361.68 kJ per mol acetate in Hakuba] or reductive tricarboxylic acid [−1 ATP; −61.68 kJ per mol]). Under CO2 limitation, autotrophs are known to accelerate CO2 uptake through HCO3− dehydration to CO2 (carbonic anhydrase) or carbonate mineral dissolution, but both only modify kinetics and are not effective in changing the maximum CO2 concentration (determined by equilibrium with carbonate species). In addition, in Hakuba, the CO32− concentration is too low (84.7 nM CO32−) to cause carbonate mineral precipitation (e.g., [CO32−] must exceed 38.5 µM given Ks of 5 ×  10−9 for CaCO3 and [Ca2+] of 0.13 mM).Based on thermodynamic calculations, the energy obtainable from H2/CO2-driven homoacetogenesis is too small to support life in many serpentinite-hosted systems, yet acetate is detected in some of these ecosystems (Fig. S2 and Table S2; note that we cannot exclude the possibility that acetate may be produced abiotically by water–rock reactions [30]). Thus, CO2-independent electron-disposing metabolism may have been necessary for extremophilic organisms to gain energy from H2 in the hyperalkaline fluids of hydrothermal systems. Here, we explore the metabolic capacities of organisms living in serpentinite-hosted systems to gain insight into potential metabolic strategies for utilizing H2 under the extreme conditions in situ.Diverse putative H2- and formate-utilizing organismsThrough metagenomic exploration of the two serpentinite-hosted systems (Table S3), we discover a plethora of phylogenetically novel organisms encoding genes for H2 and formate metabolism (19 bins with 73.2–94.8% completeness and 0.0–8.1% contamination [86.1% and 3.8% on average respectively]; available under NCBI BioProject PRJNA453100) despite challenges in acquisition of genomic DNA (15.7 and 18.9 ng of DNA from 233 and 720 L of filtered Hakuba Happo spring water, respectively; RNA was below the detection limit). We find metagenome-assembled genomes (MAGs) affiliated with lineages of Firmicutes (e.g., Syntrophomonadaceae and uncultured family SRB2), Actinobacteria, and candidate division NPL-UPA2 [31] (Fig. S3). We also recovered MAGs for a novel lineage, herein referred to as “Ca. Lithacetigenota”, that inhabits both Hakuba and The Cedars and, to our knowledge, no other ecosystems (Figs. 1, 2a, S3, and S4). The average amino acid identity (AAI) between Ca. Lithacetigenota and neighboring phyla (Coprothermobacterota, Dictyoglomi, Thermodesulfobiota [GTDB-defined phylum], Thermotogae, and Caldiserica) was comparable to the average interphylum AAI among the neighboring phyla (45.33 ± 0.86% vs 45.17 ± 0.99%), suggesting that Ca. Lithacetigenota represents a novel phylum-level lineage (Fig. 2a, b). These genomes encode enzymes for oxidizing H2 and formate (i.e., hydrogenases and formate dehydrogenases [32,33,34,35,36,37,38,39]; see Supplementary Results), suggesting that organisms in situ can employ H2 and formate as electron donors.Fig. 1: Ribosomal protein tree including high-quality MAGs from 74 GTDB-defined phylum-level lineages.Representative genomes (highest quality based on a score defined as completeness – 5*contamination, both estimated by CheckM) were chosen for bacterial classes that contain at least one genome the meet the following criteria: (i) cultured organisms with ≥90% completeness, ≤5% contamination (as estimated by CheckM), and ≤ 20 contigs; (ii) uncultured organisms with ≥85% completeness, ≤3% contamination, and ≤20 contigs; and (iii) Ca. Patescibacteria with ≥60% completeness and ≤1 contig. Universally conserved ribosomal proteins were collected from each genome, aligned with MAFFT v7.394, trimmed with BMGE v1.12 (-m BLOSUM30 -g 0.67 -b 3), and concatenated. A maximum likelihood tree was calculated using IQ-TREE v2.1.3 with the UDM0064LCLR model (-m Poisson+UDM0064LCLR), ultrafast bootstrap approximation, and SH-like approximate likelihood ratio test (-B 1000 -alrt 1000; bootstrap values are recalculated with BOOSTER using the -tbe option). Branches with ≥90% ultrafast bootstrap support and ≥80% SH-alrt support are indicated with black circles. Archaeal and eukaryotic genomes were used as an outgroup. The inter-domain branch was shortened with a break to 1/10 of the calculated length for illustrative purposes. Phylogenetic groups corresponding to “Gracilicutes” and “Terrabacteria” are indicated yellow and blue respectively. Ca. Lithacetigenota are highlighted (magenta). See Supplementary Fig. S4 for full tree.Full size imageFig. 2: “Ca. Lithacetigenota” phylogeny, lithotrophic acetate generation pathways, and comparative genomics with neighboring phyla.a A maximum likelihood tree was calculated for a concatenated alignment of universally conserved ribosomal protein sequences from representative genomes of individual phyla (aligned with MAFFT v7.394 [default parameters] and trimmed with BMGE v1.12 (−m BLOSUM30 −g 0.67 −b 3) using IQ-TREE v2.1.3 with the UDM0064LCLR model (-m Poisson+UDM0064LCLR), ultrafast bootstrap approximation, and SH-like approximate likelihood ratio test (-B 1000 -alrt 1000; bootstrap values are recalculated with BOOSTER using the -tbe option). Branches with ≥90% ultrafast bootstrap support and ≥80% SH-alrt support are indicated with black circles. Phylum names are shown for NCBI taxonomy (italicized) or GTDB classification (*). b The average inter-phylum AAI (as calculated by CompareM) was calculated using GTDB species representatives. c Putative metabolic pathways potentially adapted to the CO2-limited hyperalkaline conditions encoded by “Ca. Lithacetigenota” members and others: formate- and glycine-reducing acetate generation. Arrow colors indicate oxidative (pink), reductive (blue), ATP-yielding (orange), and ATP-consuming (green) steps. d Venn diagram of COGs/NOGs (as predicted by eggnog-mapper) fully conserved across all members of each phylum (genomes included in GTDB release 95 with completeness ≥85% and contamination ≤5%). COGs/NOGs related to lithotrophy and alkaliphily are highlighted. * “COG” abbreviated.Full size image“Ca. Lithacetigenota” has unique site-adapted metabolismInspection of the serpentinite-hosted environment-exclusive phylum “Ca. Lithacetigenota” reveals specialization to H2-driven lithotrophy potentially suitable for the low-CO2 in situ conditions (Fig. 2c). We discover that The Cedars-inhabiting population (e.g., MAG BS5B28, 94.8% completeness and 2.9% contamination) harbors genes for H2 oxidation ([NiFe] hydrogenase Hox), a nearly complete Wood-Ljungdahl pathway, and an oxidoreductase often associated with acetogenesis—NADH:ferredoxin oxidoreductase Rnf [40, 41] (Tables S4 and S5). One critical enzyme, the formate dehydrogenase, is missing from all three “Ca. Lithacetigenota” MAGs from The Cedars (and unbinned contigs), indicating that these bacteria can neither perform H2/CO2-driven nor formate-oxidizing acetogenesis (Fig. 2c). However, even without the formate dehydrogenase, the genes present can form a coherent pathway that uses formate rather than CO2 as a starting point for the “methyl branch” of the Wood–Ljungdahl pathway (i.e., formate serves as an electron acceptor; Fig. 2c). This is a simple yet potentially effective strategy for performing homoacetogenesis while circumventing the unfavorable reduction of CO2 to formate. Coupling H2 oxidation with this formate-reducing pathway is thermodynamically viable as it halves the usage of CO2 (3H2 + Formate− + CO2 = Acetate− + 2H2O; ∆G of −29.62 kJ per mol acetate) and, as a pathway, is simply an intersection between the conventional H2/CO2-driven and formate-disproportionating acetogenesis (Fig. 2c and S5). Although use of formate as an electron acceptor for formate-oxidizing acetogenesis is quite common, no previous homoacetogens have been observed to couple H2 oxidation with acetogenesis from formate, likely because CO2 has a much higher availability than formate in most ecosystems.The Hakuba-inhabiting “Ca. Lithacetigenota” (HKB210 and HKB111) also encodes Hox for H2 oxidation but lacks genes for homoacetogenesis (no homologs closely related to The Cedars population genes were detected even in unbinned metagenomic contigs). We suspect that this population forgoes the above H2/formate-driven homoacetogenesis because the estimated energy yield of the net reaction in situ (∆G of −19.94 kJ per mol acetate) is extremely close to the thermodynamic threshold of microbial catabolism (slightly above −20 kJ per mol) and, depending on the actual threshold for “Ca. Lithacetigenota” and/or even slight changes in the surrounding conditions (e.g., ∆G increases by 1 kJ per mol if H2 decreases by 20 µM decreases in Hakuba), the metabolism may be unable to recover energy. Through searching the physicochemical environment for alternative exogenous electron acceptors and MAGs for electron-disposing pathways, we detected a low concentration of glycine in situ (5.4 ± 1.6 nM; Table S6) and found genes specific to catabolic glycine reduction (see next paragraph). We suspect that some portion of this glycine is likely geochemically generated in situ, given that (a) glycine is often detected as the most abundant amino acid produced by both natural and laboratory-based serpentinization (e.g., H2 + Formate = Formaldehyde ⇒ Formaldehyde + NH3 = Glycine) [10, 16, 42,43,44,45,46,47] and (b) no other amino acid was consistently detectable (if glycine was cell-derived, other amino acids ought to also be consistently detected).For utilization of the putatively abiotic glycine, the Hakuba “Ca. Lithacetigenota” encodes glycine reductases (Grd; Fig. 3 and S6; Tables S4 and S5)—a unidirectional selenoprotein for catabolic glycine reduction [48, 49]. Based on the genes available, this population likely specializes in coupling H2 oxidation and glycine reduction (H2 + Glycine− → Acetate− + NH3; Fig. 2c). Firstly, the genomes encode NADP-linked thioredoxin reductases (NADPH + Thioredoxinox → NADP+ + Thioredoxinred) that can bridge electron transfer from H2 oxidation (H2 + NADP → NADPH + H+) to glycine reduction (Glycine− + Thioredoxinred → Acetyl-Pi + NH3 + Thioredoxinox). Secondly, though glycine reduction is typically coupled with amino acid oxidation (i.e., Stickland reaction in Firmicutes and Synergistetes [48, 50]), similar metabolic couplings have been reported for some organisms (i.e., formate-oxidizing glycine reduction [via Grd] [51] and H2-oxidizing trimethylglycine reduction [via Grd-related betaine reductase] [52]). Thirdly, Grd is a rare catabolic enzyme, so far found in organisms that specialize in amino acid (or peptide) catabolism, many of which are reported to use glycine for the Stickland reaction (e.g., Peptoclostridium of Firmicutes and Aminobacterium of Synergistetes [53]). Lastly, the population lacks any discernable fermentative (propionate [methylmalonyl-CoA pathway], butyrate [reverse beta oxidation], lactate [lactate dehydrogenase], and alanine [alanine dehydrogenase]) and respiratory (aerobic [terminal oxidases], nitrate [nitrate reductase, nitrite reductase, nitric oxide reductase, nitrous oxide reductase], sulfate [dissimilatory sulfate reductase and sulfite reductase], other sulfurous compounds [molybdopterin-binding protein family sulfurous compound reductases], and metals [outer membrane cytochrome OmcB]) electron disposal pathways and oxidative organotrophy (Tables S4 and S5). Although the BS5B28 genome encodes a bifunctional alcohol/aldehyde dehydrogenase and aldehyde:ferredoxin oxidoreductase, no complete sugar or amino acid degradation pathways could be identified, suggesting that these genes have a physiological role unrelated to ethanol fermentation. Further, though formate and glycine transporters were absent in the genomes, a survey of transporters (annotated in UniProtKB 2021_03 [54]) revealed that no alkaliphiles (organisms with optimum pH ≥ 9.5 in the DSMZ BacDive database [55]) encoded known formate transporters (focA; TIGR04060) or amino acid permeases (PF00324) (ABC transporters were not considered as substrate specificity for these complexes cannot be annotated reliably), indicating that alkaliphiles likely employ unknown transport proteins. Reflecting the lack of other catabolic pathways, the Hakuba “Ca. Lithacetigenota” MAGs display extensive genome streamlining, comparable to that of Aurantimicrobium [56, 57], “Ca. Pelagibacter” [58], and Rhodoluna [59] in aquatic systems, as also reported for other organisms inhabiting serpentinite-hosted systems [60, 61] (Fig. S7). Thermodynamic calculations show that H2-oxidizing glycine reduction is favorable in situ (∆G°’ of −70.37 kJ per mol glycine [∆G of −85.84 in Hakuba]; Fig. S1). Further, based on the pathway identified, this putative metabolism is >10 times more efficient in recovering energy from H2 (1 mol ATP per mol H2) than acetogenesis utilizing H2/CO2 (0.075 mol ATP per mol H2 based on the pathway Acetobacterium woodii utilizes) or H2/formate (0.075 mol ATP per mol H2, assuming no energy recovery associated with the formate dehydrogenase). We also detect glycine reductases in The Cedars “Ca. Lithacetigenota”, indicating that it may also perform this metabolism (∆G of −76.87 in The Cedars, assuming 201 µM H2).Fig. 3: Evolution and distribution of glycine reductases.a Phylogeny of serpentinite-hosted microbiome glycine reductase subunit GrdBE homologs (Hakuba Happo hot spring*, The Cedars springs†, and other serpentinite-hosted system metagenomes#) and a brief scheme for evolutionary history of Grd. Grd-related COG1978 homologs were collected from the representative species genomes in GTDB, filtered using a GrdB motif conserved across members of phyla known to perform glycine-reducing Stickland reaction (see Methods and Supplementary Fig. S6) and clustered with 75% amino acid sequence similarity using CD-HIT (-c 0.75). GrdB-related sarcosine reductase subunits were excluded by identification of a GrdF motif conserved across sequences that form a distinct cluster around the biochemically characterized Peptoclostridium acidaminophilum GrdF. GrdE neighboring GrdB were collected. D-proline reductase subunits PrdBA (homologous to GrdB and GrdE respectively) was used as an outgroup. GrdB+PrdB and GrdE+PrdA were aligned (MAFFT v7.394) and trimmed (BMGE v1.12 -m BLOSUM30 -g 0.05) separately, then concatenated. A maximum likelihood tree was calculated using IQ-TREE v2.1.3 (-m LG+C20+G+F) and 1000 ultrafast bootstrap replicates (bootstrap values are recalculated with BOOSTER). Branches with ≥95% ultrafast bootstrap support are indicated with pink circles. Serpentinite-hosted system-derived sequences are shown in blue and taxa that may have gained GrdB through horizontal transfer are shown in green. Though the GrdB motif did not match, the closest (and only) detectable archaeal homolog (COG1978) identified in Ca. Bathyarchaeota is included. An axis break is used for the branch connecting GrdBE (and the Ca. Bathyarchaeota homolog) and outlier PrdBA for readability (10% of actual length). See Supplementary Fig. S6 for complete tree and full branch length between GrdBE and PrdBA. In the brief scheme of Grd evolution (top left), the cladogram topology is based on Fig. S4. Vertical transfer (red lines in cladogram) and horizontal transfer (black arrows) inferred from tree structures are shown. Phyla that may have acquired Grd vertically (red) and horizontally (gray) are indicated. GTDB phyla belonging to Firmicutes were grouped together. * GTDB-defined phylum-level lineage nomenclature. b Number of glycine reductase-encoding GTDB-defined species representatives (GTDB r95) associated with different environments. Only genomes with both GrdB and GrdE were included.Full size imageGiven the phylogenetic and metabolic uniqueness of these populations, we report provisional taxonomic assignment to “Ca. Lithacetigenota” phyl. nov., “Ca. Lithacetigena glycinireducens” gen. nov., sp. nov. (HKB111 and HKB210), and “Ca. Psychracetigena formicireducens” gen. nov., sp. nov. (BS525, BS5B28, and GPS1B18) (see Supplementary Results). Based on a concatenated ribosomal protein tree, this serpentinite-hosted ecosystem-associated candidate phylum is closely related to the deepest-branching group of bacterial phyla in “Terrabacteria”, one of the two major of lineages Bacteria (Fig. 1). Comparative genomics shows that “Ca. Lithacetigenota” shares 623 core functions (based on Bacteria-level COGs/NOGs predicted by eggnog-mapper shared by the two highest quality Hakuba and The Cedars MAGs HKB210 and BS5B28; Fig. 2d). When compared with the core functions of two closest related phyla (Caldiserica and Coprothermobacterota), 176 functions were unique to “Ca. Lithacetigenota”, including those for NiFe hydrogenases (and their maturation proteins), selenocysteine utilization (essential for Grd), and sodium:proton antiporter for alkaliphily. With Coprothermobacterota, 232 functions were shared, including Grd, thioredoxin oxidoreductase (essential for electron transfer to Grd), and additional proteins for NiFe hydrogenases and selenocysteine utilization, pointing toward importance of H2 metabolism and glycine reduction for these closely related phyla. More importantly, among bacterial phyla in the deep-branching group, “Ca. Lithacetigenota” represents the first lineage inhabiting hyperalkaliphilic serpentinite-hosted ecosystems, suggesting that these organisms may be valuable extant windows into potential physiologies of primordial organisms who are thought to have lived under hyperalkaline conditions (albeit with 4 billion years of evolution in between; see discussion regarding Grd below).Widespread glycine reduction in serpentinite-hosted systemsUncultured members of Chloroflexi (Chloroflexota) class Dehalococcoidia inhabiting The Cedars and Firmicutes (Firmicutes_D) class SRB2 in Hakuba and The Cedars also possess glycine reductases (Table S5). In addition, these populations encode hydrogenases and formate dehydrogenases, suggesting that they may also link H2 and formate metabolism to glycine reduction. Closely related glycine reductases were also detected in other studied serpentinite-hosted systems (47–94% amino acid similarity in Tablelands, Voltri Massif, and Coast Range Ophiolite) [1, 2, 7]. Phylogenetic analysis of the glycine-binding “protein B” subunits GrdB and GrdE reveals close evolutionary relationships between glycine reductases from distant/remote sites (Fig. 3a and S6). Note that Tablelands spring glycine reductase sequences were not included in the analysis as they were only detected in the unassembled metagenomic reads (4460690.3; 69.7–82.2% similarity to Hakuba SRB2). Overall, “Ca. Lithacetigenota”, Dehalococcoidia, and SRB2 glycine reductases are all detected in at least two out of the seven metagenomically investigated systems despite the diverse environmental conditions (e.g., temperature). Thus, we propose glycine as an overlooked thermodynamically and energetically favorable electron acceptor for H2 oxidation in serpentinite-hosted systems. We suspect that glycine reduction may be a valuable catabolic strategy as the pathway requires few genes/proteins (a hydrogenase, Grd, acetate kinase, and thioredoxin oxidoreductase) and conveniently provides acetate, ammonia, and ATP as basic forms of carbon, nitrogen, and energy.Phylogenetic analysis of glycine reductases (Fig. 3a and S6) shows that the novel homologs recovered from serpentinite-hosted systems represent deep-branching lineages distantly related from those detectable in published genomes (GTDB r95 species representatives). Further comparison of the topology with a ribosomal protein-based genome tree (Fig. 2a) indicates that the two deep-branching serpentinite-hosted system-affiliated lineages (Ca. Lithacetigenota and novel Chloroflexi family) and Firmicutes vertically inherited glycine reductases. Thus, catabolic glycine reduction can be traced back to the concestor of these three lineages, suggesting the metabolism at least dates back to the ancestor of “Terrabacteria”. We further identified an archaeal GRD homolog (in Miscellaneous Crenarchaeota Group [MCG] or Ca. Bathyarchaeota member BA-1; Fig. 3a and S6), but whether this gene functions as a glycine reductase (GrdB motif not fully conserved) and, further, truly belong to this clade (source is metagenome-assembled genome) remains to be verified. Reconstruction of the ancestral Grd sequence and estimation of its pH preference (via AcalPred) showed that the ancestral enzyme likely had good efficiency under alkaline conditions (pH  > 9; probability of 0.9973 and 0.9858 for GrdB and GrdE, respectively). Thus, the currently available data suggest that Grd (and catabolic glycine reduction) is an ancient bacterial catabolic innovation in an alkaline habitat, dating back to one of the deepest nodes in the bacterial tree.While we detect glycine reductases in many serpentinite-hosted systems, examination of genomes derived from other natural ecosystems shows that only 107 species (species representatives in GTDB r95; 0.35% of all GTDB species) inhabiting such habitats encode GrdBE (Fig. 3b and S6). This is a level comparable to rare artificial contaminant-degrading enzymes (e.g., tetrachloroethane dehalogenase pceA—65 species [encoding KEGG KO K21647 based on AnnoTree with GTDB r95 and default settings [62]]; dibenzofuran dioxygenase—258 species [K14599 and K14600]). Most glycine reductase homologs are found in species affiliated with host-associated (mostly human body and rumen) or artificial habitats (360 species), the majority of which belong to the phylum Firmicutes. We suspect that glycine reduction has low utility in most natural ecosystems (e.g., no excess glycine via abiotic generation and no severe nutrient/electron acceptor limitation) and has been repurposed by some anaerobes for the fermentative Stickland reaction in organic-rich ecosystems (e.g., host-associated ecosystems) where excess amino acids are available but access to favorable electron acceptors is limited (Fig. 3b) (notably, glycine is the dominant amino acid in collagen [ >30%], the most abundant protein in vertebrate bodies).Other characteristics of putative indigenous homoacetogensIn contrast with members of “Ca. Lithacetigenota”, several other putative homoacetogenic populations encode the complete Wood–Ljundgahl pathway (Tables S4 and S5), indicating that other forms of acetogenesis may also be viable in situ. One putative homoacetogen in The Cedars, NPL-UPA2, lacks hydrogenases but encodes formate dehydrogenases. Although the NPL-UPA2 population cannot perform H2/formate-driven acetogenesis, it may couple formate oxidation with formate-reducing acetogenesis—another thermodynamically viable metabolism (∆G of –50.90 kJ per mol acetate in The Cedars; Fig. S5). The pathway uses CO2 as a substrate but has lower CO2 consumption compared to H2/CO2 homoacetogenesis and can produce intracellular CO2 from formate. A recent study also points out that methanogens inhabiting serpentinite-hosted environments oxidize formate presumably to generate intracellular CO2 [9]. In Hakuba, an Actinobacteria population affiliated with the uncultured class UBA1414 (MAG HKB206) encodes hydrogenases and a complete Wood–Ljungdahl pathway (Table S5) and, thus, may be capable of H2/formate or the above formate-disproportionating acetogenesis (Fig. 2c and S5). Indeed, the UBA1414 population was enriched in Hakuba-derived cultures aiming to enrich acetogens using the H2 generated by the metallic iron–water reaction [63] (Fig. S8). Many populations encoding a complete Wood–Ljungdahl pathway possess monomeric CO dehydrogenases (CooS unassociated with CODH/ACS subunits; NPL-UPA2, Actinobacteria, Syntrophomonadaceae [Hakuba and The Cedars], and Dehalococcoidia [The Cedars]; Table S4). Although CO is below the detection limit in Hakuba (personal communication with permission from Dr. Konomi Suda), another study shows that CO metabolism takes place in an actively serpentinizing system with no detectable CO [64]. Given that CO is a known product of serpentinization [7, 64], it may be an important substrate for thermodynamically favorable acetogenesis in situ. However, further investigation is necessary to verify this (e.g., need to measure CO at multiple time points).Another interesting adaptation observed for all putative homoacetogens detected in Hakuba and The Cedars was possession of an unusual CODH/ACS complex. Although Bacteria and Archaea are known to encode structurally distinct forms of CODH/ACS (designated as Acs and Cdh respectively for this study), all studied Hakuba/The Cedars putative homoacetogens encode genes for a hybrid CODH/ACS that integrate archaeal subunits for the CO dehydrogenase (AcsA replaced with CdhAB) and acetyl-CoA synthase (AcsB replaced with CdhC) and bacterial subunits for the corrinoid protein and methyltransferase components (AcsCDE) (Table S4). The Firmicutes lineages also additionally encode the conventional bacterial AcsABCDE. Given that all of the identified putative homoacetogens encode this peculiar hybrid complex, we suspect that such CODH/ACS’s may have features adapted to the high-pH low-CO2 conditions (e.g., high affinity for CO2 and/or CO). In agreement, a similar hybrid CODH/ACS has also been found in the recently isolated “Ca. Desulforudis audaxviator” inhabiting an alkaline (pH 9.3) deep subsurface environment with a low CO2 concentration (below detection limit [65, 66]) [67].Implications for primordial biologyThe last universal common ancestor (LUCA) is hypothesized to have evolved within alkaline hydrothermal mineral deposits at the interface of serpentinization-derived fluid and ambient water (e.g., Hadean weakly acidic seawater) [22,23,24]. Although such interfaces no longer exist (i.e., ancient Earth lacked O2 but most water bodies contain O2 on modern Earth), modern anoxic terrestrial and oceanic ecosystems harboring active serpentinization [1,2,3,4,5,6,7,8] may hold hints for how primordial organisms utilized H2 under hyperalkaline CO2-depleted conditions (e.g., post-LUCA H2-utilizing organisms that ventured away from the interface towards the alkaline fluids). Our findings suggest that unconventional modes of lithotrophy that take advantage of geogenic reduced carbon compounds (e.g., formate and glycine) as exogenous electron acceptors may have been viable approaches to circumventing thermodynamic issues and obtaining energy from H2 oxidation in situ. The strategies we discover are largely exclusive to the bacterial domain (archaeal CO2 reduction does not involve formate as an intermediate and, to our knowledge, glycine reduction is limited to Bacteria) and originated deep in the bacterial tree, suggesting they may have been relevant in the divergence towards the bacterial and archaeal domains. Notably, the estimated alkaliphily of the ancestral Grd also points towards the relevance of this metabolism in ancient alkaline habitats. More

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