Determinants of Soil Field‐Saturated Hydraulic Conductivity Across Sub‐Saharan Africa: Texture and Beyond

Soil infiltration is critical for water security and related ecosystem services. This infiltration, the ability of soils to absorb water at their surface, is controlled by the soil hydraulic conductivity. Despite recent efforts in assembling measurements of soil hydraulic conductivity, global databases and derived pedotransfer functions lack coverage in the tropics. Here, we present soil infiltration measurements and other indicators of soil and land health collected systematically in 3,573 plots from 83 100 km2 sites across 19 countries in sub‐Saharan Africa. We use these data to (a) determine field‐saturated hydraulic conductivity (Kfs) and (b) explore which variables best predict variation in Kfs. Our results show that sand content, soil organic carbon (SOC), and woody cover had a positive relationship with Kfs, whereas grazing intensity and soil pH had a negative relationship. Our findings highlight that, despite soil texture being important, structure also plays a critical role. These results indicate considerable potential to improve soil hydrological functioning through management and restoration practices that target soil structure. Enhancing SOC content, limiting animal stocking, promoting trees, shrubs, and other vegetation cover, and preventing soil erosion can increase Kfs and improve water security. This data set can contribute to improving Earth system and land surface models for applications in Africa.

, in particular the mitigation of floods and droughts, water purification and regulation, and erosion control.When soil infiltration capacity is high, more water can enter the soil surface and become available both for soil-and groundwater recharge.Enhanced infiltration capacity can eventually lead to an increase in groundwater recharge and dry season flow (Ilstedt et al., 2016;Krishnaswamy et al., 2013), which in turn can improve water security.In contrast, low infiltration capacity results in more surface runoff, thereby increasing the risk of flooding, soil erosion, and siltation of water bodies.Hence, understanding soil infiltration capacity is critical for soil and water management.Such understanding is particularly urgent under climate change, as it will likely increase the frequency and intensity of heavy precipitation and droughts (Loukas et al., 2008;Seneviratne et al., 2021).
Soil infiltrability into an initially unsaturated soil is typically high during the early stages of the infiltration process and tends to decrease asymptotically over time as infiltration proceeds (Hillel, 1998).As the soil saturates, soil infiltrability approaches a steady, gravity-driven rate known as the soil steady-state infiltrability or final infiltration capacity.Steady-state infiltrability is thus independent of initial soil water content and approximates saturated hydraulic conductivity (Hillel, 1998).Saturated hydraulic conductivity depends on soil texture and structure and is higher in soils with large conducting pores.Soil pores can be textural pores (i.e., the pores between the primary mineral particles) or structural pores such as interaggregate cracks, decayed root channels, or wormholes (Dexter, 2004).Coarse-textured soils with relatively large pores typically have a higher saturated hydraulic conductivity than clay soils with smaller pores (Ferré & Warrik, 2004;Saxton et al., 1986).Pedotransfer functions developed to predict soil hydraulic conductivity from soil properties are primarily based on texture or other easy-to-measure attributes such as bulk density or organic carbon content-for example, Rosetta (Schaap et al., 2001;Zhang & Schaap, 2017) or hydraulic properties of European soils (Wösten et al., 1999).These pedotransfer functions may be insufficient to adequately assess field-saturated hydraulic conductivity due to the importance of structural porosity, especially under real-world conditions in the field (Bonetti et al., 2021;Fatichi et al., 2020;Gupta, Lehmann, et al., 2021;Jarvis et al., 2013;Pachepsky & Rawls, 2004;Rahmati et al., 2018;Vereecken et al., 2010;Wösten et al., 2001;Zhang et al., 2020).
Several processes and practices can influence soil structural porosity and, thereby, soil hydrological functioning.Changes in land cover and land use can alter the infiltration capacity of soils through concurrent changes in the quality and quantity of soil organic matter inputs, the structure and abundance of soil biota communities, the characteristics of root systems, and the overall structure of soils.Soil organic matter promotes biological activity and aggregation in soils, which can improve infiltration capacity (Franzluebbers, 2002;Lado, Paz, & Ben-Hur, 2004), although in some cases increases in organic matter content can have the opposite effect (Araya & Ghezzehei, 2019;Jarvis et al., 2013;Larsbo et al., 2016;Nemes et al., 2005;Wang et al., 2009).Roots and soil biota, in particular macroinvertebrates, can further enhance infiltration through the creation of macropores and persistent soil aggregates (Beven & Germann, 2013;Lavelle et al., 2006;Weiler & Naef, 2003).Conversion of forests, woodlands, and natural grasslands to agriculture typically results in reduced infiltration capacity (Bormann et al., 2005;Lal, 1996;Lulandala et al., 2022;Nyberg et al., 2012;Zimmermann & Elsenbeer, 2008).This, in turn, can adversely affect various aspects of hydrological functioning, including reduced dry-season flows, increased surface runoff, and enhanced soil erosion (Bruijnzeel, 2004).Land management can potentially reverse such degradation and contribute to maintaining or improving hydrological functioning and derived ecosystem services.Adopting practices such as agroforestry, controlled grazing, and conservation tillage can improve soil infiltration capacity (Abdelkadir & Yimer, 2011;Bargués Tobella et al., 2014;Benegas et al., 2014;Ilstedt et al., 2007;Lulandala et al., 2022;Moreno et al., 1997;Mwendera & Saleem, 1997;Zhang et al., 2007).Similarly, tree planting or natural regeneration following the abandonment of croplands, pastures, or degraded grasslands can progressively restore soil infiltration capacity (Bonell et al., 2010;Colloff et al., 2010;Ilstedt et al., 2007;Lal, 1996;Zhao et al., 2013;Zimmermann et al., 2010).However, evidence is often restricted to observations and experiments conducted at the local level.
Understanding soil infiltration and surface water redistribution processes at scales relevant for management requires an assessment of saturated hydraulic conductivity over broad areas.However, soil saturated hydraulic conductivity is extremely variable in space, and individual measurements represent only a limited area (Nielsen et al., 1973;Usowicz & Lipiec, 2021;Warrick, 1998).Obtaining sufficient field observations to characterize saturated hydraulic conductivity at the landscape or regional level is difficult due to the cost, time, and effort associated with traditional field techniques.Using less complex methods such as single-ring infiltrometers (Bouwer, 1986;Reynolds & Elrick, 1990) allows for higher sampling intensity, which is usually preferred Project Administration: Aida Bargués-Tobella, Leigh Ann Winowiecki, Tor-Gunnar Vågen Supervision: Leigh Ann Winowiecki, Tor-Gunnar Vågen Visualization: Aida Bargués-Tobella Writing -original draft: Aida Bargués-Tobella Writing -review & editing: Leigh Ann Winowiecki, Douglas Sheil, Tor-Gunnar Vågen even if at the expense of relatively higher uncertainty in the individual measurements (Bagarello et al., 2004;Nimmo et al., 2009).Pedotransfer functions for estimating soil hydraulic properties have also been developed to reduce the need for costly field measurements (Schaap et al., 2001;Wösten et al., 1999).However, these functions are often developed for specific regions, especially North America and Europe, which limits their broader geographical applicability, particularly in the tropics (Botula et al., 2012;Gupta, Hengl, et al., 2021;Hodnett & Tomasella, 2002;Tomasella et al., 2000;Young et al., 1999).Similarly, the soil data and resulting methods tend to neglect natural areas and focus on agricultural land.In an effort to address these geographical and landuse limitations, Rahmati et al. (2018) gathered published infiltration data to create the Soil Water Infiltration Global database (SWIG), which contains single infiltration curves and accompanying data, including data on soil properties and land management, from 215 sites across 53 countries.Efforts to compile data on soil hydraulic properties for specific regions in the tropics include the Hydrophysical Database for Brazilian Soils (HYBRAS) (Ottoni et al., 2018) and the soil infiltration and saturated hydraulic conductivity database of the soils of Rio de Janeiro (Martins et al., 2022).Africa lacks such databases, and the region remains sparsely represented in SWIG and other global databases.
Here, we present soil infiltration measurements and other soil and land health indicators collected systematically across sub-Saharan Africa.These detail 3,573 plots from 83 100 km 2 sites across 19 countries.We use these data to (a) determine field-saturated hydraulic conductivity (K fs ), and (b) explore which variables best explain the variation in K fs .Variables include soil texture, pH, soil organic carbon (SOC), visible signs of erosion, vegetation structure, herbaceous cover, woody cover, and impact of grazing.

Study Sites and Field Sampling Design
The data presented and used in this study were collected following the Land Degradation Surveillance Framework (LDSF), an established sampling approach for landscape-level assessment of soil and land health (Vågen & Winowiecki, 2020).The data derive from 3,573 plots from 83 sites distributed across 19 countries in sub-Saharan Africa and covering diverse climates and contexts (Figure 1a; detailed site-specific information can be found in Table S1 in Supporting Information S1).These LDSF sites were selected at random across a region of interest or placed in a specific location representing an area of particular interest or planned activities (interventions).
The LDSF employs a spatially stratified hierarchical (nested) sampling scheme with four levels corresponding to different spatial scales (Figure 1): sites (100 km 2 ), clusters (1 km 2 ) nested within sites, plots (1,000 m 2 ) nested within clusters, and sub-plots (100 m 2 ) nested within plots.Each site is divided into 16 tiles, and cluster centroid locations are randomized within each tile.Within each cluster, 10 sampling plots are placed at random.Each plot contains four subplots.We only used data from the plots where soil infiltration was measured, which was typically in three plots per cluster (i.e., 48 plots per site.Figure 1b), although the number of plots with complete infiltration and soil data varied slightly among sites (Table S1 in Supporting Information S1).

Field Data Collection
Field data were collected both at the plot and sub-plot levels following the LDSF protocol (Vågen & Winowiecki, 2020).Plot coordinates were recorded at the center of subplot one with an accuracy better than 5 m.Soil infiltration measurements were conducted at the center of each plot using a single-ring infiltrometer (Bouwer, 1986) consisting of a metal cylinder with an inner radius of 78 mm and a height of 20-30 cm.The infiltrometer was inserted at least 20 mm into the soil, taking care to minimize soil surface disturbance.Before starting the infiltration measurements, the soil within the infiltration ring was pre-wetted to increase the chances of reaching steady-state conditions.Water was gently poured to fill the infiltration ring to the top, covering the soil surface to minimize surface disturbance, and ponding was maintained for 15 min.After pre-wetting, the infiltration measurements started and were carried out for 2.5 hr.A ruler was fixed on the inner side of the infiltration ring to measure the water level.The ring was then refilled, and the initial ponding depth was recorded.After 5 min, the final ponding depth was recorded, and the ring was immediately refilled to the start level.This procedure was repeated at 5-min intervals during the first 30 min of the experiment, 10-min intervals during the following 60 min, and 20-min intervals during the remaining 60 min.Intervals were adjusted as necessary when infiltration was too fast or too slow to obtain accurate readings.
In each plot, the dominant vegetation structure was classified into forest, woodland, bushland, shrubland, wooded grassland, grassland, or annual cropland following FAO's Land Cover Classification System (Di Gregorio & Jansen, 1998).Woody and herbaceous vegetation cover were visually assessed within each sub-plot and scored following a modified Braun-Blanquet cover-abundance rating scale (Braun-Blanquet, 1932) into either 0 (absent), 1 (<4%), 2 (4%-15%), 3 (15%-40%), 4 (40%-65%) and 5 (>65% vegetation cover).The four sub-plot ratings were averaged to obtain plot-level estimates of woody and herbaceous vegetation cover.Visible signs of soil erosion (rill, gully, or sheet) were recorded within sub-plot 1, which is where infiltration measurements were carried out.In addition, the impact of grazing was assessed at the plot level using a scale from 0 (no impact) to 3 (severe impact) based on visible signs of grazing and browsing.
Topsoil samples (0-20 cm) were collected from the center of each sub-plot using a soil auger and combined into a composite plot-level sample.These samples were air-dried before shipping them to the soil laboratory for analysis.

Determination of Topsoil Field-Saturated Hydraulic Conductivity (K fs )
We applied Nimmo et al. (2009)'s method to analyze ponded infiltration from within a single-ring infiltrometer under falling-head conditions and determine the field-saturated hydraulic conductivity (K fs ).The formula for K fs (Equation 1) compensates for non-constant falling head and subsurface radial spreading typical of small-diameter infiltration rings like the ones used in this study: where t 0 and t are the initial and final time, λ is the soil macroscopic capillary length, D and D 0 are the initial and final ponding depths within the infiltration ring, and L G is the ring-installation scaling length (Equation 2): where b is the inner radius of the infiltration ring (78 mm), d is the ring insertion depth (20-40 mm), and C 1 and C 2 are empirically determined constants with recommended values of 0.316 π and 0.184 π, respectively (Reynolds et al., 2002).
The soil macroscopic capillary length parameter (λ), which here is the reciprocal of the soil macroscopic capillary length as defined by Reynolds and Elrick (1990) and Reynolds et al. (2002) (α*), represents the relative importance of gravity and capillary forces during ponded infiltration (Reynolds et al., 2002).We used a value of α* of 0.012 mm −1 (i.e., λ = 83.33 mm), as this value has previously been shown to be adequate for most soils with structural development (see Elrick et al. (1989) and Reynolds et al. (2002)).
We applied Equation 1 to all infiltration measurements, regardless of whether they were at (quasi-)steady state or not.We then fitted an asymptotic function to each individual curve of corrected ponded infiltration rates over time and extracted the asymptote value, which represents K fs for that specific plot.Asymptote curves were fitted using the R package nls.multstart, which uses non-linear least square regression with the Levenberg-Marquardt algorithm (Padfield & Matheson, 2020).

Soil Laboratory Analyses
Soil samples were analyzed using mid-infrared (MIR) spectroscopy at the ICRAF Soil-Plant Spectral Diagnostics Laboratory in Nairobi, Kenya.Soil MIR spectroscopy is a well-established, non-destructive, rapid, and cost-effective method for predicting key soil properties such as SOC, pH and texture, enabling landscape-level assessments of soil health (Terhoeven-Urselmans et al., 2010;Vågen et al., 2016;Winowiecki et al., 2016).Prior to analysis, air-dried soil samples were ground and sieved through a 2 mm mesh.A subsample was further ground to attain a particle size between 20 and 53 μm.These subsamples were then scanned and analyzed in triplicate for MIR absorbance using a Tensor 27 HTS-XT MIR spectrometer (Bruker Optics, Karlsruhe, Germany), and the spectra were subsequently processed following Terhoeven-Urselmans et al. ( 2010).
Soil texture, pH, and SOC were simultaneously predicted from MIR spectra using Random Forest regression models (Breiman, 2001) built with data from ICRAF's global soil MIR spectral library following the methods developed by Vågen et al. (2016).Today, the library consists of spectra from about 162,000 samples and data on soil properties obtained using traditional analytical methods for 10% of these samples (including those used in this study).For this reference set of soil samples, soil pH was measured using an Eutech Cyberscan 1,100 pH meter on a 1:2 soil/water solution prepared by shaking 20 g of soil with 40 ml of deionized water for 30 min.SOC content was analyzed by dry combustion using an Elemental Analyzer Isotope Ratio Mass Spectrometer from Europa Scientific after removing inorganic C with 0.1 N HCl, at the IsoAnalytical Laboratory (United Kingdom).Finally, soil textural analyses were conducted using a LA-950 Laser Diffraction Particle Size Distribution Analyzer (HORIBA Scientific) after shaking each soil sample for 4 min in a dispersing solution of 1% sodium hexametaphosphate (calgon).The U.S. Department of Agriculture (USDA) soil particle-size classification system was used, which defines the size limit between sand and silt at 50 μm (USDA, 2017).No adjustment was applied to the soil particle-size distribution data obtained with the laser diffractometer to bring the values closer to those measured by classical sieve-sedimentation methods.Random Forest regression models were trained on the reference set of soil samples with both MIR spectra and associated data obtained using traditional analytical methods as outlined in Vågen et al. (2016).These models achieve a good prediction accuracy (R 2 > 0.95) for the soil properties that concern our investigation (Table 1).

Mixed-Effects Models
Given the nested structure of the LDSF data (Site:Cluster:Plot), we used hierarchical models (Zuur et al., 2013) with Site and Cluster as nested random effects.In other words, we applied a 2-way nested random structure with sites, and clusters within sites.Furthermore, since K fs is positive, continuous, and skewed, and to take care of variance heterogeneity, we used a gamma generalized linear mixed-effects model (Zuur et al., 2013) with a log-link function and random intercept: Soil organic carbon (SOC; g kg where: i is the Site.i = 1, …, 83 j is the jth cluster within site i. j = 1, …, 16 k is the kth observation (plot) within cluster j. k = 1, 2, 3 r is a shape parameter (gamma distribution) site i is the site-level random intercept cluster i,j is the cluster-level random intercept Mixed-effects models have become an increasingly popular tool for analyzing complex ecological data (Harrison et al., 2018;Zuur et al., 2009).Linear mixed-effects models and generalized linear mixed-effects models (GLMMs) are particularly suited to the analysis of highly structured data sets like ours containing discrete groupings of non-independent observational units that are hierarchical in nature.Mixed-effects models have advantages over regular linear models as they can account for non-independence and heterogeneity.Nevertheless, underlying assumptions and model selection and interpretation require care (Harrison et al., 2018).
Here, we follow the best practices and guidelines for such analyses provided by Zuur et al. (2013Zuur et al. ( , 2009) ) and Harrison et al. (2018).
Gamma GLMMs were fitted using the function glmmTMB within the glmmTMB package in R (Brooks et al., 2017).We fit four initial candidate models (Table 2).All four models included interactions between soil texture (either expressed as sand content or texture class) and the remaining covariates, as we expected it to influence the effect of the other covariates.We defined three soil texture classes, sandy (>50% sand content), clay (>50% clay content), and clay loam (<50% sand content and <50% clay content).Ordinal categorical variables (i.e., woody and herbaceous vegetation cover ratings and grazing impact rating) were treated as continuous covariates to simplify model structure and preserve ordering.Continuous covariates were standardized (x − mean(x)/sd(x)) to fit the models in order to improve model performance and interpretability (Schielzeth, 2010).
Model selection involved two steps.First, we applied model selection on the covariates, dropping non-significant interaction terms from the four initial candidate models using likelihood-ratio tests via the drop1 function in the stats package in R (Chambers & Hastie, 1992).Second, the best model was selected from the four final candidate models (Table 2).The model with the lowest Akaike's Information Criterion (AIC) is considered to be the best in that it optimizes the trade-off between fit and complexity (Burnham & Anderson, 2004).
In the model validation, we followed Zuur et al. (2013) to check that model assumptions were not violated.Plots of Pearson residuals (residuals vs. fitted values, residuals vs. model covariates, and residuals vs. spatial coordinates) were used to visually assess the lack of heteroscedasticity, non-linear patterns, and spatial correlation.To aid with non-linear pattern detection, we fitted a smoother to the residuals versus model covariates plots via the geom_smooth function in the ggplot2 package in R. We also used variograms of the residuals to confirm the lack of spatial correlation.Histograms of the random intercepts were used to check that the assumption of normality of random effects was fulfilled.Plots of random effects versus residuals and variograms of the random effects were also used to check the lack of spatial correlation.Models were checked for multicollinearity using the function check_collinearity in the performance package in R (Lüdecke et al., 2021), which uses the variance inflation factor.Model assumptions were not violated.
Model performance indices, including marginal and conditional R 2 (Nakagawa et al., 2017), Interclass Correlation Coefficient (ICC, Hox et al. (2017)) and AIC, were computed using the function model_performance within the performance package in R (Lüdecke et al., 2021).Marginal R 2 comprises variance explained by only the fixed effects, while conditional R 2 comprises the variance explained by both the fixed and random effects (Nakagawa et al., 2017).

Random Forest Regression Models
We used Random Forest regression models (Breiman, 2001)    widely used across a broad range of disciplines, including ecology and soil science (Biau & Scornet, 2016).The popularity of Random Forest models is mainly due to their predictive performance and versatility, with few restrictions on the nature of the data.Their main drawback is that they can be complex to interpret.In addition to being a powerful prediction tool, a key application is the quantification of the relative importance of the candidate explanatory variables (Grömping, 2015;Molnar, 2022).
Model covariates included sand and clay content, SOC content, soil pH, erosion presence, vegetation structure class, grazing impact rating, and herbaceous and woody cover rating.Random Forest regression models were fitted using the tidymodels framework in R (Kuhn & Wickham, 2020), with the ranger package (Wright & Ziegler, 2017) as the underlying engine.First, the data set was split into training (80%) and test (20%) sets using simple random sampling.The training set was then used to fit the model and tune its parameters.We performed parameter tuning for mtry, that is, the number of variables randomly selected at each node, and trees, that is, the number of trees in the forest/ensemble.First, we conducted a grid search in which different combinations of the two parameters were explored (mtry = 1-10 and trees = 100, 250, and 500).Multiple models were trained on resampled data sets (k-fold cross-validation, k = 10) using the different combinations of mtry and trees.We then evaluated how well these models performed based on the cross-validated estimates of two standard performance metrics, Root Mean Squared Error (RMSE) and Mean Absolute Error.Based on this, we selected the best combination of mtry and trees (mtry = 2, trees = 500).The final model was then built with the selected values of the parameters.Overall model performance was evaluated on the test set using R 2 and RMSE as the performance metrics.
The importance of each explanatory variable was assessed using the Mean Decrease in Accuracy (MDA) or Permutation Importance measure (Breiman, 2001).The MDA is a measure of variable importance, and it is constructed from the Random Forest model prediction accuracy (the Mean Squared Error, MSE, in the case of regression models), which is assessed using the out-of-bag (OOB) observations.The MDA for a particular variable represents the normalized average (among trees in a forest) increase in the MSE made by a tree when randomly permuting the observations for that variable in the OOB samples.The more important a variable is as a predictor, the higher this increase will be.
To clarify how predicted K fs varied across the observed ranges of the model covariates, we constructed partial dependence plots (Friedman, 2001) using the pdp package in R (Greenwell, 2017).Partial dependence plots illustrate the marginal effect a specific feature of interest has on the predicted outcome of a machine learning model (Friedman, 2001;Molnar, 2022).These plots visualize the direction, strength, and form of relationships, although they might not capture the full complexity of the model (Molnar, 2022).
All data analyses were conducted using R version 4.0.0 (R Core Team, 2015).

Overview
The sample set consists of data from 3,573 plots across 83 sites.Of these plots, 45% were under cropland, whereas the vegetation structure in the remaining plots was classified as either shrubland (17%), grassland (10%), bushland (9%), wooded grassland (7%), woodland (7%), or forest (5%) (Table S2 in Supporting Information S1).The distribution of vegetation structure classes varied among sites, but cropland was the predominant class (≥50% of the plots) in 36 out of 83 sites (Figure S1 in Supporting Information S1).Plot-average woody and herbaceous vegetation cover ratings (0-5) varied within and among sites, with an overall mean value of 1.7 and 2.8, respectively (Figure S2 in Supporting Information S1).On average, half of the plots per site had visible signs of erosion, but erosion prevalence varied significantly among sites (Figure S3 in Supporting Information S1).The overall mean impact of grazing rating (0-3) was 1.1, but it varied within and among sites (Figure S4 in Supporting Information S1).Overall, 57% of the plots presented visible signs of grazing and browsing (impact of grazing rating ≥1).This proportion was highest for plots classified as bushland (84%), followed by wooded grassland (75%), grassland (75%), shrubland (69%), cropland (46%), and forest (26%) (Figure S5 in Supporting Information S1).
Topsoil field-saturated hydraulic conductivity (K fs ) for the 3,573 measures followed a right-skewed distribution with a median value of 41.2 mm hr −1 and an interquartile range of 57.7 mm hr −1 (Figure 2, Table S3 in Supporting Information S1).K fs varied within and among sites; Median K fs for the 83 sites ranged from 6.8 (at Temki, Chad) to 160.9 mm hr −1 (Mbinga, Tanzania), and, in general, sites with higher median K fs also exhibited higher variability (Figure 2).Soil sand content, SOC content, and pH also varied within and among sites (Figure 3).In general, SOC content increased, and soil pH decreased with humidity.Sites with lower median SOC also had lower variability in SOC.The sampled soils had relatively low silt content (below 50%); 53% of them had more than 50% clay content, while only 19% had more than 50% sand content (Table S4 in Supporting Information S1 and Figure 4b).
Overall, there was a moderate and positive correlation of K fs with SOC content (r = 0.18), woody cover rating (r = 0.13), soil sand content (r = 0.1), and herbaceous cover rating (r = 0.08), and a negative correlation of K fs with soil pH (r = −0.22), the impact of grazing rating (r = −0.15),and soil clay content (r = −0.09)(Figure S6 in Supporting Information S1).Sites with a more humid climate tended to have higher K fs than drier sites (Figure 2), as indicated by the positive correlation between site mean aridity index (AI = mean annual precipitation/mean annual potential evapotranspiration) and median K fs (r = 0.3).Median K fs per aridity class across all plots also decreased with increasing aridity (Figure 4a).Overall, coarser soils had higher K fs than more fine-textured ones (Figure 4).However, as humidity increased, the effect of soil texture on K fs was less pronounced (Figure 4a).Interestingly, more extreme K fs values (above the overall 95th percentile) occurred not only in sandy soils but also in soils with more than 50% clay content (Figure 4b).

General Linear Mixed-Effects Model
The best model explaining K fs (see Table 2 for the final model formulation) had a marginal and conditional R 2 of 0.15 and 0.33, respectively (Table 3).Sand and SOC content had a significant positive effect on K fs (Figures 5  and 6).In contrast, the impact of grazing and soil pH had a significant negative effect.The effect of vegetation structure was also significant, with shrublands, wooded grasslands, croplands, woodlands, bushlands, and forests having an increasingly positive effect on K fs compared to grasslands.On the other hand, herbaceous cover and the presence of erosion had a positive and negative effect, respectively, on K fs , although not statistically significant.
The relationship between field-saturated hydraulic conductivity and SOC content, erosion, vegetation structure, and grazing impact varied with soil texture.The positive effect of SOC on K fs (Figure 6b) was stronger in fine-textured soils as opposed to soils with higher sand content (Figure 6c).According to the 95% confidence intervals from the selected gamma GLMM model, there were no significant differences in K fs between plots with or without visible signs of erosion for the average sand content; nonetheless, the presence of erosion in coarser soils had a negative relationship with K fs (Figure 6d).The relationship with vegetation structure also varied depending on soil texture.Overall, K fs increased with increasing tree cover, from grasslands to forests (Figure 6f).Higher sand content was associated with higher K fs across all vegetation structure classes, particularly in the case of woodlands, bushlands, and forests (Figure 6g).Finally, grazing was associated with lower values of K fs (Figure 6h).This negative pattern was more pronounced for finer soils with little sand than for soils with higher sand content, although sand content increased overall K fs .

Random Forest Regression Model
Sand and clay content were the most important covariates for predicting K fs , followed by SOC content, whereas the presence of erosion was the least important (Figure 7).
Partial dependence plots showed a positive relationship between K fs and sand content, SOC, herbaceous and woody cover ratings, and a negative relationship with clay content, pH and grazing (Figure 8).The relationship between sand content and predicted K fs was most pronounced between sand content values of 50% and 75% (Figure 8a).On the other hand, the relationship with clay content was strongest for values below 25%, while increases in clay content above this threshold did not have a substantial effect on predicted K fs (Figure 8b).There was a positive relationship between SOC and predicted K fs up to around 60 g kg −1 , and thereafter predicted K fs leveled off and appeared to be unaffected by SOC (Figure 8c).However, SOC content above 60 g kg −1 was rare (only 1.5%

Table 3 Summary of the Optimal Gamma Generalized Linear Mixed-Effects Model Explaining Variation in Field-Saturated Hydraulic Conductivity (K fs )
of samples were above this threshold); hence, this relationship should be interpreted cautiously.Predicted K fs declined with increasing soil pH up to values around 7, while it remained low and relatively unchanged in the case of alkaline soils (Figure 8d).In the case of herbaceous cover, predicted K fs varied little over the ratings 0-4, but increased between 4 and 5 (i.e., between 40%-65% and >65% herbaceous cover) (Figure 8i).The effect of grazing on predicted K fs was strongest between ratings of 0 and 2 (Figure 8e).Predicted K fs varied with vegetation structure class, and it was higher in classes with more trees (such as forest or bushland) compared to grasslands, shrublands or croplands (Figure 8g).Similarly, woody cover had a positive relationship with predicted K fs (Figure 8h).Finally, predicted K fs was slightly lower (57 vs. 59 mm hr −1 ) in plots with erosion than in plots without erosion (Figure 8f).

Discussion
Previously, representative observations of soil hydraulic properties in Africa were few and of mixed form and quality (Gupta, Hengl, et al., 2021;Rahmati et al., 2018;Schaap et al., 2001;Wösten et al., 1999;Zhang & Schaap, 2017).Our data set expands existing regional and global databases of soil hydraulic properties, improving coverage for Africa and providing field data for underrepresented land uses and soils.As such, we envision that our data set can contribute to improved understanding and prediction of soil hydraulic properties and to improved Earth system and land surface models.In particular, we see great potential to validate and improve the performance of regional and global predictions of K s .In our analyses of these unique data, we used established methods (Nimmo et al., 2009) to estimate topsoil K fs from field measurements of soil infiltration in 3,573 plots across 83 sites in sub-Saharan Africa.Median K fs across these sites spanned a similar range to median K fs values for different soil texture classes from the SWIG database (6.8-160.9 vs. 2.8-150 mm hr −1 ) (Rahmati et al., 2018).
The positive correlation between within-site variability in K fs and median K fs is also consistent with previous findings (Nyberg et al., 2012;Takoutsing et al., 2022).In general, K fs tended to be higher in more humid versus drier sites.This likely results from differences in inherent soil properties on the one hand and differences in net primary production and, subsequently, in SOC and soil structure on the other; these factors are discussed in detail below.
Results from the GLMM and Random Forest models show that soil sand content, SOC content, and woody cover had a positive relationship with K fs , whereas grazing impact and soil pH had a negative relationship.Our findings also indicate that soil texture (sand and clay content) and SOC were the most important covariates for predicting K fs .As expected, K fs increased with sand content, with some variation depending on climate.The positive effect of the coarse-textured fractions on K fs agrees with previous findings (Lehmann et al., 2021;Saxton et al., 1986;Tomasella et al., 2003).This relationship was less marked in more humid sites, likely due to potential differences in clay type and mineralogy between drier and more humid sites.While low-activity (non-swelling) clay   minerals predominate in the humid tropics, more active (swelling) clay minerals are more common in drylands (Lehmann et al., 2021).Soils dominated by swelling clay minerals (e.g., smectite) are dispersive and, when saturated, have very low hydraulic conductivity.In contrast, weathered kaolinite-dominated soils such as Ferralsols (Oxisols) are highly permeable due to their stable micro-aggregated structure and low dispersibility (Hodnett & Tomasella, 2002;Lado & Ben-Hur, 2004;Lehmann et al., 2021;van den Berg et al., 1997).Our observations of extreme (>95th percentile) K fs values occurring in soils with more than 50% clay content were surprising but may reflect such micro-aggregated structure or the presence of macropores such as those created by roots and soil fauna and cracks in some vertic soils.Our results also show a negative relationship between soil pH and K fs, with a substantial drop at around 7. Soil pH can indicate the degree of weathering and can thus also be related to clay mineralogy and exchangeable base cation concentration (Hodnett & Tomasella, 2002).Soils from drier sites tended to have higher pH values, which may reflect the dominance of more active and dispersive clays as well as a higher concentration of monovalent base cations that contribute to the dispersion of clay aggregates and soil structure degradation (Rengasamy et al., 2016) and, therefore, lower K fs .Mills et al. (2006) also found a similar negative trend between pH and infiltrability for soils in Namibia and South Africa, which they ascribed to an increase in clay dispersibility with increasing pH.Future work needs to investigate further the effect of clay mineralogy in K fs .Current soil databases used to train pedotransfer functions of soil hydraulic properties are strongly biased toward temperate regions with higher silt content and different clay minerals than tropical soils, which highlights the importance of increasing the amount of data from tropical soils in these databases when used for global predictions (Botula et al., 2012;Gupta, Hengl, et al., 2021;Tomasella et al., 2000).Our data set helps fill this gap.Our results also support the importance of considering dominant clay mineral types, not just clay fraction, when estimating soil hydraulic properties in the tropics (Lehmann et al., 2021).
Topsoil organic carbon content had a positive relationship with K fs .SOC is crucial in supporting soil's physical quality (Dexter, 2004;Rawls et al., 2004) and is a major indicator of overall soil health (Bagnall et al., 2023;Cardoso et al., 2013;Lal, 2016).In general, SOC is considered to improve soil aggregation (Beare et al., 1994;Castro Filho et al., 2002) and porosity (Adams, 1973) and, as a result, saturated hydraulic conductivity (Lado, Paz, & Ben-Hur, 2004;Mbagwu & Auerswald, 1999).Our findings support this understanding and provide a broader evidence base.We also found that the implied effect of SOC on K fs was texture-dependent, with a more substantial positive relationship for fine-textured soils than for coarser ones.This is consistent with the results of Araya and Ghezzehei (2019) for U.S. soils in the USKSAT database (Pachepsky & Park, 2015), who found that K s increased with SOC across all textural classes except for sand and loamy sand.These results might be explained by the formation of organic matter and clay complexes that enhance soil porosity and reduce clay dispersibility in water (Dexter et al., 2008).Our results also indicate that, while at low to moderate SOC contents coarser soils exhibit higher K fs than more fine-textured soils, this trend is reversed for high SOC contents.Our finding that K fs is positively associated with SOC contrasts with other studies that found a negative relationship (Jarvis et al., 2013;Larsbo et al., 2016;Nemes et al., 2005;Wang et al., 2009).This negative relationship has been linked to greater soil water repellency and soil tortuosity as soil organic matter content increases.While our results indicate that the positive relationship between K fs and SOC is less strong for coarser compared to more fine-textured soils, they do not support any negative K s -SOC relationship.This suggests that, overall, in our data set, the positive effect of SOC on soil aggregation outweighs any negative effects of SOC on K fs .Nevertheless, given that other studies found evidence of a negative K s-SOC relationship, we recognize that this may still occur under specific conditions.Future studies should further explore these relationships and identify the conditions under which the relationship might be negative.Taken together, our results and interpretations suggest considerable potential to enhance soil hydrological functioning through the adoption of land use and management practices that increase SOC, particularly in the case of fine-textured soils.Such practices include agroforestry, cover crops, crop residue retention, reduced tillage, and optimal livestock stocking rates (Minasny et al., 2017;Paustian et al., 2016;Vågen et al., 2005).Increasing SOC can improve soil hydrological functioning while yielding many other benefits, from increased food and nutrition security to climate change mitigation (Johnston et al., 2009;Lal, 2006Lal, , 2010;;Vågen & Winowiecki, 2013;Vågen et al., 2005), and should hence be key in land restoration efforts.
Vegetation structure was strongly associated with K fs , with grasslands and forests exhibiting the lowest and highest K fs values, respectively.These results and those from the Random Forest model suggest that woody cover, especially tree cover, has a positive impact on K fs .These findings are consistent with a meta-analysis conducted by Ilstedt et al. (2007) showing that tree planting in the tropics, both in afforestation and agroforestry, improves soil infiltration capacity across a wide range of conditions and humidity levels.More recent studies in the tropics further support these findings (Abaker et al., 2018;Benegas et al., 2014;Bonnesoeur et al., 2019;Filoso et al., 2017;Leite et al., 2018;Lozano-Baez et al., 2019, 2021;Mens et al., 2023;Niemeyer et al., 2014;Nyamadzawo et al., 2007;Zwartendijk et al., 2017).The positive impacts appear due to increased litter inputs, improved soil biological activity, and enhanced aggregation and macropore formation (e.g., root and faunal channels) (Bargués Tobella et al., 2014;Belsky et al., 1989Belsky et al., , 1993;;Niemeyer et al., 2014;Zwartendijk et al., 2017).
Our results suggest that the effect of vegetation structure on K fs is texture-dependent, with a stronger effect of tree cover on K fs for more coarse-textured soils.This finding somehow disagrees with previous observations showing that the recovery of infiltration capacity following tree planting in the tropics is slower in the case of sandy soils (Lozano-Baez et al., 2019), although our data set does not allow testing this.Along the same lines, Niemeyer et al. (2014) found that the relationship between woody cover and K fs along a vegetation gradient in dry tropical Nicaragua was greater for fine-textured soils than for coarser soils, which they ascribed to the impact of root-macropore formation on K fs in fine-textured soils.Our results, which differ from these observations, may partly be explained by the so-called "inverse texture effect" observed in dryland ecosystems and by which coarser soils appear to support taller and denser perennial vegetation than finer soils (Gupta et al., 2022;Noy-Meir, 1973).Such apparently contradictory observations indicate that the combined relationship of woody vegetation and soil texture on K fs is complex and requires further investigation.Overall, our findings support the importance of incorporating some measure of woody vegetation cover into models to predict K fs (Bonetti et al., 2021;Niemeyer et al., 2014).Our results also show a smaller, but still positive, effect of herbaceous cover on K fs .Results from the Random Forest model suggest that increases in herbaceous cover between 0% and 40% (ratings 0-4) have little relationship with K fs , whereas increases above 40% have a larger positive effect, underscoring the value of maintaining a high herbaceous cover.Grasslands exhibited the lowest K fs values of all vegetation structure classes, even compared to croplands.These results contrast with findings from a global meta-analysis on the impact of land use on soil hydraulic properties showing that grasslands had higher K values than comparable soil under cultivation (Robinson et al., 2022).Our vegetation structure classes do not fully reflect the land use intensity nor the land use history; many plots classified as grasslands were degraded, and some corresponded to abandoned croplands or land under fallow, which may help explain our results.Future studies using this data set might benefit from a more detailed analysis of the impacts of land use and land use change on K fs .Different plant species will likely have different influences on infiltration via litter quality and quantity, root traits, microclimate, and associated soil fauna (Mens et al., 2023).This also raises important research questions for future studies.
Increasing grazing impact had a negative effect on K fs , especially in fine-textured soils.This is in line with previous local studies showing that soil infiltration capacity decreases with grazing intensity across different land cover classes (Lulandala et al., 2022;Mwendera & Saleem, 1997;Savadogo et al., 2007;Talore et al., 2016;Vandandorj et al., 2017).The negative impact of grazing has been attributed primarily to soil compaction through animal trampling and reduced structural pore space, as indicated by higher soil bulk density values in more heavily grazed areas (Dudley et al., 2002;Lai & Kumar, 2020;Lulandala et al., 2022).In addition, heavy grazing can lead to reductions in plant cover and biomass, and SOC (Dlamini et al., 2016;Eldridge et al., 2016;Kikoti et al., 2015;Lai & Kumar, 2020;Lulandala et al., 2022;Savadogo et al., 2007), which can also contribute to decreasing infiltration capacity.Heavy livestock grazing and other anthropogenic activities can dilute or override the positive impacts of woody vegetation on K fs (Ghimire et al., 2013(Ghimire et al., , 2014;;Lulandala et al., 2022).In this first study of this data set, we did not consider the interaction between grazing intensity and vegetation structure class due to the limited number of observations, which did not allow us to fit more complex models.This and other potentially relevant interactions should be investigated in future studies.Livestock grazing is a widespread land use in Sub-Saharan Africa, where millions rely on livestock for their livelihood (Robinson et al., 2011;Thornton, 2002).Our results highlight the importance of actively managing livestock stocking rates to prevent and reverse the degradation of soil hydrological functioning.
The presence of visible signs of erosion had a weak to no relationship with K fs, though for coarse-textured soils, K fs tended to be lower in such plots.Erosion can lead to the formation of seals at the soil surface that reduce infiltration capacity, thus increasing overland flow and soil erosion (Singer & Le Bissonnais, 1998;Singer & Shainberg, 2004).Previous studies show that soils with intermediate clay content (ca.10%-40%) have less stable aggregates and are more susceptible to seal formation and pore-clogging compared to soils with higher clay content (>40%), which may contribute to our results (Ben-Hur et al., 1985;Lado, Ben-Hur, & Shainberg, 2004).Similarly, Yair (1992) found that surface sealing in fine-textured soils was low due to the high stability and strong flocculation of clay-rich aggregates.Removal of SOC and reduced vegetation cover following erosion (Lal, 2005) can also reduce infiltration capacity.In turn, decreased infiltration capacity can increase infiltration-excess overland flow, and, as a result, increase erosion further, especially under high rainfall intensities.This positive (self-reinforcing) feedback loop amplifies land degradation and can lead to a degraded state that is hard to reverse (D'Odorico et al., 2013;Scheffer & Carpenter, 2003).Erosion is one of the most critical and widespread land degradation processes in Sub-Saharan Africa and elsewhere (Montanarella et al., 2016;Vågen & Winowiecki, 2019).Improving soil infiltration capacity can help prevent and curb such processes.
Our findings support the view that soil texture is a major determinant of K fs , while also underlining the additional role of soil structure and soil structure-altering processes.These additional factors are indicated by the positive relationships between K fs and SOC and vegetation cover (in particular woody vegetation) and the negative relationship between K fs and grazing and erosion.These relationships suggest significant opportunities to improve soil hydrological functioning by adopting land management practices that protect and enhance soil structure.Practices that reduce compaction and erosion, and/or enhance soil organic matter, vegetation cover, and soil microbial and faunal activity are likely to prove beneficial (Bronick & Lal, 2005;Meurer et al., 2020;Pagliai et al., 2004).The application of compost and manure, as well as mulching, alternative tillage systems, crop rotation, and improved grazing management, may all contribute (Bronick & Lal, 2005;Conant et al., 2017;Minasny et al., 2017;Pagliai et al., 2004).Protecting and promoting tree cover inside and outside forests, for instance, through agroforestry and maintaining trees on field boundaries, steeper slopes, and around drainage features, will likely be beneficial as well (Bargués Tobella et al., 2014;Ilstedt et al., 2016).Subsequent improvements in soil hydrological functioning can bolster the delivery of related ecosystem services -including water provisioning and purification, the regulation of hydrological flows, erosion control, biomass production, and biodiversity conservation (Bünemann et al., 2018;Keesstra et al., 2016).We thus recommend that land management practices that enhance soil structure and hydrological functioning be widely promoted across the region.
Our data and analyses represent a major improvement on previous studies but can be further improved.
Our data set encompasses various climates and settings, although it may not fully represent sub-Saharan Africa.Notably, data remains limited in Southern and Central Africa, including the Congo Basin, and approximately 95% of our sites are not in arid climates.In terms of land use and cover, forests and woodlands remain underrepresented.In terms of measurements, we were constrained by the soil and land health indicators measured as part of the LDSF, which were selected in part for their cost-effectiveness, while other aspects that we have not considered could influence soil structure and K fs .Variables that identify and capture variation in clay mineralogy, the soil biota, vegetation, and herbivory all warrant further attention.
We also see a need to explore the role and form of SOC and its relationship to other soil and site properties in greater detail.In addition to increasing the data set and coverage, alternative statistical approaches, like Bayesian hierarchical modeling, may offer insights in future analyses.Our field surveys followed a systematic approach to minimize measurement errors and ensure consistency among the data collection teams.
Remaining uncertainties relate to field measurements, particularly soil infiltration (Nimmo et al., 2009;Reynolds, 2008), and the estimation of K fs (Bagarello et al., 2014;Nimmo et al., 2009;Reynolds, 2008).In our data set, we provide both the measured and estimated K fs values.This permits others to use and assess different estimation methods beyond the scope of this study.

Conclusions
Taken together, results from this study indicate that, across the 83 study sites in sub-Saharan Africa, K fs is linked with soil texture and soil structure, which highlights the importance of considering both when estimating K fs , as suggested by others (e.g., Fatichi et al., 2020or Bonetti et al., 2021).Incorporating attributes that influence soil structure when estimating K fs is especially urgent for applications in the tropics, where the impacts of soil structure on hydrologic response are more prominent due to the prevalence of high-intensity rainfall events and soils with high contents of clay (Bonell, 1993;Bonetti et al., 2021;Tomasella et al., 2000;Wohl et al., 2012).We provide evidence for the importance of structure-altering processes, including compaction, aggregation, and burrowing by roots and soil fauna, in determining K fs , as indicated by the relationships between K fs and SOC, grazing impact, vegetation cover, pH, and erosion.Our findings also suggest that soil texture regulates many of these relationships.Hence, while inherent soil properties influence K fs , dynamic properties affected by land use and management are also crucial.This underscores the potential of management and restoration practices to maintain and promote soil hydrological functioning.Effort must be placed on promoting practices that improve soil structure and avoiding those that worsen it.Enhancing SOC content, limiting livestock stocking rates, promoting vegetation cover, particularly woody vegetation, and preventing and halting soil erosion, can thus maintain and enhance K fs .This evidence can guide sustainable land management practices and restoration interventions for improved soil health and water security.

Figure 1 .
Figure 1.(a) Location of the 83 Land Degradation Surveillance Framework (LDSF) sites.The grid layer represents the annual average aridity index (AI = mean annual precipitation/mean annual potential evapotranspiration) over the period 1970-2000 (Trabucco & Zomer, 2019).(b) Example of an LDSF site (10 × 10 km) in Hoima, Uganda, showing the location of the sampling plots.(c) Plot outline, showing the four sub-plots.

)
, Sand: Sand content (%), SOC: Soil organic carbon content (g C kg −1 ), pH: Soil pH, Erosion: Presence of erosion within subplot 1 (binary), VegStructure: Vegetation structure class, ImpactGrazing: Grazing impact rating, HerbCoverRate: Herbaceous cover rating, WdCoverRate: Woody cover rating, Texture: Soil texture class.The fixed component includes main effects of covariates and the interaction between sand content or texture class and the other covariates.

Figure 2 .
Figure 2. Boxplots (Q1, median, Q3) of topsoil field-saturated hydraulic conductivity (K fs ) for the 83 sites included in the study.The color indicates the average site aridity class (UNEP, 1992) for the period 1970-2000, based onTrabucco and Zomer (2019).The overall distribution of K fs is also shown with a marginal density plot.The x-axis is limited to 400 mm hr −1 to improve data visualization (only seven observations were above this threshold).

Figure 3 .
Figure 3. Boxplots (Q1, median, Q3) and marginal density plots of sand content (a), soil organic carbon (b), and pH (c) for the 83 study sites included in the study.The color indicates the average site aridity class (UNEP, 1992) for the period 1970-2000, based on Trabucco and Zomer (2019).The sites are ordered by their aridity index, from more arid to more humid sites.

Figure 4 .
Figure 4. (a) Density plots showing the distribution of field-saturated hydraulic conductivity (K fs ) values per aridity class (UNEP, 1992) and soil texture class (sandy: sand content >50%; clay: clay content >50%; clay loam: sand content <50% and clay content <50%).The dotted lines show the overall distribution of K fs per aridity class, and the dotted vertical lines correspond to median values.The triangles along the x axes indicate median values per textural class (b) Soil texture ternary diagram of the samples.The color scale is related to the magnitude of K fs .Extreme K fs values are highlighted in white (i.e., greater than the 95% percentile of 165 mm hr −1 ).
(beta coefficients), their associated 95% confidence intervals (CI) and corresponding p-values are shown (both based on Wald Z statistics).The random effects, number of observations, sites and clusters within sites, the marginal and conditional R 2 , and the Interclass Correlation Coefficient (ICC) are included.The estimates of the fixed effects are based on the standardized values of continuous covariates.Sand: Sand content (%), SOC: Soil organic carbon content (g C kg −1 ), Erosion: Presence of erosion (binary), VegStructure: Vegetation structure class, ImpactGrazing: Grazing impact rating, pH: Soil pH, HerbCoverRate: Herbaceous cover rating.The effects and corresponding p-values for the factor variables Erosion and VegStructure are in relation to their baseline levels (absence of erosion and grassland, respectively).

Figure 5 .
Figure 5.Fixed effects standardized estimates of the optimal gamma generalized linear mixed-effects model explaining field-saturated hydraulic conductivity (K fs ) and associated 95% confidence intervals.Asterisks indicate the significance level of the corresponding p-values (***p < 0.001, **p < 0.01, *p < 0.05).Sand: Sand content (%), SOC: Soil organic carbon content (g C kg −1 ), Erosion: Presence of erosion (binary), VegStructure: Vegetation structure class, ImpactGrazing: Grazing impact rating, HerbCoverRate: Herbaceous cover rating.The effects for Erosion and VegStructure are in relation to their baseline levels (absence of erosion and grassland, respectively).

Figure 6 .
Figure 6.Marginal effects of the optimal gamma generalized linear mixed-effects model model explaining field-saturated hydraulic conductivity (K fs ) and associated 95% confidence intervals.Predicted values of K fs are shown as a function of the main terms (left column) and the interaction terms (right column).Observe that the y-axes have different scales.The plots show the predicted K fs as a function of the predictor variable(s) on the x-axis while considering mean values of all other continuous predictor variables and baseline levels of factor variables Erosion and Vegetation structure (absence of erosion and grassland, respectively).Interactions between sand content and soil organic carbon (c), erosion (e), vegetation structure class (g), and Impact Grazing (i) are illustrated based on sand content first (Q1), second (Q2) and third quartile (Q3) values, which are shown as vertical lines in (a).

Figure 8 .
Figure 8. Partial dependence plots showing the marginal effect of the model covariates (A-J) on the predicted field-saturated hydraulic conductivity (K fs ) using a Random Forest regression model.Marks on the x-axis indicate the data distribution (deciles, minimum and maximum values).

Table 2
Candidate Fitted Gamma Generalized Linear Mixed-Effects Models