Inferential Approach for Evaluating the Association Between Land Cover and Soil Carbon in Northern Ontario

Abstract

Resolving the status of soil carbon with land cover is critical for addressing the impacts of climate change arising from land cover conversion in boreal regions. However, many conventional inferential approaches inadequately gauge statistical significance for this issue, due to limited sample sizes or skewness of soil properties. This study aimed to address this drawback by adopting inferential approaches suitable for smaller samples sizes, where normal distributions of soil properties were not assumed. A two-step inference process was proposed. The Kruskal–Wallis (KW) test was first employed to evaluate disparities amongst soil properties. Generalized estimating equations (GEEs) were then wielded for a more thorough analysis. The proposed method was applied to soil samples (n = 431) extracted within the southern transition zone of the boreal forest (49°–50° N, 80°40′–84° W) in northern Ontario, Canada. Sites representative of eight land cover types and seven dominant tree species were sampled, investigating the total carbon (C), carbon-to-nitrogen ratio (C:N), clay percentage, and bulk density (BD). The KW test analysis corroborated significance (p-values < 0.05) for median differences between soil properties across the cover types. GEEs supported refined robust statistical evidence of mean differences in soil C between specific tree species groupings and land covers, particularly for black spruce (Picea mariana) and wetlands. In addition to the proposed method, the results of this study provided application for the selection of appropriate predictors for C with digital soil mapping.

1. Introduction

Recently, there has been a surge of interest in quantifying the magnitude of carbon stocks in boreal regions. This heightened attention can be attributed, at least in part, to the implications of climate change [1,2], which can induce land cover conversion and land use changes within vast areas of the boreal biome [3]. In conjunction with climate change, economical activities relating to agriculture and forestry can cause shifts in land cover. Consequently, there is a need to address the total carbon (C) content in land management practices and thereby track soil C and associated soil properties. The biggest challenge in accurately assessing C content pertains to estimating the reserves in soil [1]. Specifically, the Earth’s surface harbors significantly larger amounts of C within soil than in comparison to vegetation, with peatlands particularly noteworthy in this regard [1]. Associations typically exist amongst various soil properties in tandem with soil C [4,5], but these associations may not be well resolved. Hence, in investigating soil C, it is instrumental to consider other soil attributes. The enhanced ascertaining of soil C concentrations with respect to land cover in boreal regions can greatly assist policymakers in identifying areas pertaining to tradeoffs for environmental protection. These decisions can mitigate further C release but also facilitate conductive economic growth as relating to agricultural prospects for other localities.

As an application of soil sampling data, digital soil mapping has been gaining predominance, especially with respect to predicting soil C. For boreal regions, this can pertain to organic C concentrations [6] or for the C concentration of mineral soil [2]. Prediction maps of soil properties are common products of digital soil mapping, so as to support stakeholders with decision analyses. Digital soil mapping conjectures that soil is transformed by formation factors, which can correspond to vegetation, climate, topography, time, parent material, or other soil properties. These factors can be paraphrased succinctly by the acronyms scorpan [1,4] or clorpt [5,7]. Environmental covariates, commonly retrieved from remote sensing technologies, are employed as predictors relating to soil formation factors. However, remote sensing technologies do not explicitly conform to nor detect the various soil formation factors, as typically soil is not directly observed; rather, remote sensing technologies are better suited for differentiating between cover types [5], whether pertaining to land management use or vegetation cover. Oftentimes, researchers will initially apply dozens of assorted environmental covariates to predict a targeted soil property, when only a few of these covariates explicate the majority of the predictive power. As a result, research studies are needed to identify key environmental covariates in digital soil mapping. By better discerning the dissimilarities in a soil property with respect to distinct cover types, one can adopt more appropriate environmental covariates that render these variations. In this study, we aim to conduct inferential analysis that is more pertinent, to address this shortcoming between predictors and cover type with digital soil mapping. There is also the issue of confirming whether a sizeable count of samples have been collected, which would establish enough heterogeneity of a targeted soil property amongst different land cover types, so as to warrant digital soil mapping. This consideration is essentially neglected when reviewing sampling design within digital soil mapping research.

Inferential analysis through hypothesis testing can corroborate statistical evidence supporting the variations in soil properties amongst different land cover types. This can be extended to intrinsic associations observed in vegetation cover, including relationships between soil C and the types of tree species present [8,9]. Analysis of variance (ANOVA) is a common method for assessing statistical differences between means in two or more populations [10,11,12]. Significances between soil C content and land use categories [13,14,15] have been established by ANOVA in many studies. Ultimately, this analysis provides support with deducing what physical factors or forcing impact the soil properties. This also pertains to the characteristics of soil properties for particular tree species types or specific land cover usage as for agriculture. As these associations depend on the context of the study area, these are still uncertain for regions of the Canadian boreal forest, and worth investigating. However, the adoption of ANOVA is limited, as normality of targeted properties with respect to populations is presumed [16,17]. For soil samples retrieved from field campaigns, this assumption may be invalid or challenging to validate at a population level. An appropriate test is needed to analyze clustered data, specifically subplots, where the assumption of normality for the underlying distributions of soil properties cannot be inferred.

The Kruskal–Wallis (KW) test is a nonparametric test that is comparable with one-way ANOVA [18]. It assesses the significance of differences with the median, without requiring the assumption of normality for the underlying distributions of the data [19]. Consequently, the KW test, which assesses the median rather than the mean, is less affected by outliers [20] and less likely to inflate significances as it is conservative in rejecting the null hypothesis [18]. Overall, the KW test is a suitable method for determining differences in median values amongst different cover types [21]. This is especially relevant when the underlying distributions of soil properties are unknown and potentially influenced by outliers. However, another important aspect to consider, which is often ignored, is the spatial scale, particularly when examining subplots. It is worth investigating whether there are statistically significant variations in soil properties within these subplots. Nested hypothesis testing can be implemented with the KW test, to substantiate whether soil properties are similar for subplots at a site. This is pertinent with regard to digital soil mapping, as this coincides with the spatial scale of the environmental covariate data wielded. Specifically, this can indicate whether sufficient heterogeneity exists within the samples across cover types to warrant application with digital soil mapping. All in all, the KW test can be adopted as a first step of statistical inference, for assessing disparities amongst each investigated soil property.

As a second step, a more thorough inferential analysis can also be conducted, to obtain differences in estimates with a targeted soil property between specific groupings. Generalized estimating equations (GEEs) have been employed in the medical and social science domains [22,23,24] for obtaining estimates of a targeted property, along with associated confidence intervals. GEEs offer the advantage of not requiring the correct specification of the functional distribution for the response variable [22,23] and can resolve estimates for smaller sample sizes [23]. Additionally, GEEs can be applied to nested data [25], which are encountered when working with samples collected from subplots within the same site. GEEs demonstrate adaptability, permitting application to datasets that may not adhere to conformity constraints imposed by other tests or techniques. By obtaining estimates of mean differences in a targeted property between cover types, GEEs can corroborate which land cover or tree species has a greater effect. Subsequently, this knowledge is adaptable to digital soil mapping, by facilitating the selection of environmental covariates that better encapsulate dissimilarities between cover types. Delving deeper into the topic, it is of interest to investigate which tree species are associated with higher soil C contents. Within the boreal biome, it is well known that wetlands are generally composed of higher C contents than other land cover types [26]. However, differences in soil C content amongst other land cover types are not well understood, and warrant further investigation, including for application with C sequestration [27]. In addition, GEEs can be formulated to estimate soil properties, such as C content, based on soil attributes and information regarding land cover and tree species. Leveraging the abundance of sites with such legacy data can enable an enhanced assessment of C stocks for boreal regions.

The purpose of this study was to investigate the association between soil properties and land cover in the boreal forest of northern Ontario. Of importance was to resolve whether agricultural land cover types, including pastures, contained lower soil C contents than forested sites. Additionally, of interest was to substantiate if sites comprised of particular dominant tree species consisted of more soil C. To resolve this, a two-step inferential analysis was implemented. Firstly, the KW test was adopted to determine whether there were significant median differences in soil properties across the land covers and dominant tree species observed at the sites. Afterwards, GEEs were employed to obtain refined estimates of the mean differences in soil C content between distinct land cover types and tree species groupings. Statistical significances were noted for this inferential analysis. As a final step, to demonstrate versatility, GEEs were exploited to obtain estimates and associated confidence intervals of soil C content, based on soil texture, land cover, and vegetation information. The methodology, results, and discussion are discoursed in the following sections.

2. Materials and Methods

2.1. Study Region

The study areas for the collection of these soil samples align with the southern boreal transition zone within the District of Cochrane in northern Ontario, Canada (80°40′ W to 84° W, 49° N to 50° N). These areas of interest are located within the vicinities of settlements along the Ontario highway 11 corridor. This region is bounded to the northwest by the Ryland community, just west of the town of Hearst, and to the southeast of the town of Cochrane. Explicitly, these study areas encompass Hearst, the Gordon Cosens Forest (GCF), Kapuskasing (within the GCF), and Cochrane. The delineation of the study areas, as well as the locations of the sampling sites (discussed later), are depicted in Figure 1. Within this figure, a canopy height model (CHM) of 10 m spatial resolution is displayed for the backgrounds corresponding to the study areas. This CHM [28] was generated from LiDAR (light detection and ranging) data collected during 2016 and 2017 for the Ontario Ministry of Natural Resources (MNR). The confines of the study areas were delimited in part from the coverage of the LiDAR data; gaps within study areas are due to no LiDAR data retrieved over portions of larger water bodies.

This region was selected for research purposes partly because it is at risk of future land cover conversion as this corridor extends across the southern boreal transition zone. As well, this region was chosen due to current economic prospects, specifically with respect to agricultural activities. In regard to homogeneity, there are minimal variations in climate and topography across this area. Temperature and precipitation averages are relatively consistent throughout the region. For instance, Mattice, located 30 km east of the community of Hearst, has an average annual temperature that is less than 1 °C colder than Cochrane. Additionally, Cochrane receives 5 cm more annual precipitation compared with Mattice [29,30]. The terrain for this region is mostly flat on the landscape scale, with elevations ranging from a minimum of approximately 120 m in northeast localities to a maximum of nearly 350 m northwest of Cochrane. Average elevations are generally higher by about 50 to 100 m across the western study area, in reference to the eastern portions. This district is characterized by the Canadian Shield, with numerous lakes and wetlands, along with a few rivers that traverse the area, primarily following northeast trajectories towards James Bay in the Arctic Ocean. Grayish luvisols dominate the deeper soil horizon layers throughout this region [26]. Accordingly, this district is regarded as boreal clay plains, or colloquially as the Great Clay Belt of northern Ontario. Also present are gleysols and mesisols within the wetland environments [26].

A diverse range of land cover types are prevalent in this area, varying from wetlands and primeval forest to secondary forest, abandoned pastures, hay fields, and cropland. Additionally, there exists recently cleared land, specifically corresponding to deforestation for cropland agriculture purposes. Compacted clearings are also present, which conform to old yard sites. The common endemic tree species for this region comprise black spruce (Picea mariana), balsam fir (Abies balsamea), and trembling aspen (Populus tremuloides). Less prevalent tree species include white spruce (Picea glauca), balsam poplar (Populus balsamifera), and tamarack (Larix laricina). Eastern white cedar (Thuja occidentalis) is quite rare within these study areas, as this region coincides with its northern peripherality; jack pine (Pinus banksiana) does not subsist with appreciable numbers within the defined study areas. The aforementioned tree species and land cover types are present at localities dispersed throughout the domain. However, the bulk of agricultural activity prevails in the Cochrane area, and to a lesser extent to the south and west of the town of Kapuskasing. With the local agriculture, most of the hay fields are swathed and baled, and consist of a perennial cover of brome grass (Bromus) mixed with red clover (Trifolium pratense) or vetch (Vicia sativa). The croplands are seeded annually during the springtime in May, and harvested during the autumn, with oats (Avena sativa) and barley (Hordeum vulgare) being the traditionally sown crops. Recently, varieties of canola (Brassica rapa, B. napus and B. juncea) have increasingly been grown, due to generally greater economic potential.

2.2. Collection and Processing of Soil Samples

Soil samples were extracted following a methodology [31] reviewed in collaboration with forestry scientists and specialists of the Great Lakes Forestry Centre (GLFC), Natural Resources Canada (NRCan), in Sault Ste. Marie, ON, Canada. The methodology was designed to better assess the variability in soil properties within a site. To achieve this, subplots were strategically placed at varying distances from the site center. For each site, soil samples were collected from 3 subplots, located within 2 m radii at 4.5 m, 7.5 m, and 9.5 m of the 0°, 120°, and 240° directional bearings, respectively. Samples were obtained from sites conforming to the various land cover types existing locally within the region, where each site was selected so as to consist of one land cover type. When possible, samples were retrieved from a few sites in close proximity to one another, with each site corresponding to a different cover type. This was implemented to determine whether there were statistically significant differences in soil properties amongst sites with different land covers located near each other.

Samples (n = 421) were collected via three separate field campaigns in September 2018 (12 sites), August 2019 (28 sites), and August–September 2021 (104 sites). The samples were extracted from 5 depth intervals in 2018 and 2019: 0–5 cm, 5–15 cm, 15–30 cm, 30–45 cm, and 90–105 cm. In the 2021 field campaign, samples were only obtained at 0–5 cm and 5–15 cm. A summary of the analyzed soil properties, with respect to these depth layers, is presented in Appendix A in

Table A1. Summary of soil properties at the various depths where samples were extracted and processed. Bulk density (BD) was only assessed on samples from the 0–5 cm and 5–15 cm depth layers. Lower reported sample counts for clay were due to insufficient quantities of material being extracted for some samples. Only samples obtained during the 2018 field campaign for the 90–105 cm depth layer were processed and analyzed.

Soil Property		Summary	Depth Layer
			0–5 cm	5–15 cm	15–30 cm	30–45 cm	90–105 cm
C	(%)	Number of Samples (n)	263	431	106	115	29
		Mean	10.3	9.9	6.5	4.7	4.2
		Standard Deviation	9.9	12.9	11.0	9.0	0.8
		Maximum	47.5	91.7	47.8	48.6	5.6
		Minimum	1.6	0.6	0.6	0.4	1.9
C:N		Number of Samples (n)	263	431	106	112	29
		Mean	15.7	16.2	13.1	25.1	170.2
		Standard Deviation	7.1	6.4	18.2	18.2	91.6
		Maximum	75.3	43.6	170.5	121.3	430.7
		Minimum	3.4	2.1	1.9	6.1	32.6
Clay	(%)	Number of Samples (n)	229	424	99	106	23
		Mean	30.3	25.9	44.9	41.3	46.1
		Standard Deviation	11.7	12.9	15.8	13.6	17.8
		Maximum	54.6	68.6	78.6	68.1	70.2
		Minimum	6.6	1.0	11.4	2.0	7.6
BD	(g/cm3)	Number of Samples (n)	431	431
		Mean	1.03	1.21
		Standard Deviation	0.55	0.56
		Maximum	2.44	2.55
		Minimum	0.10	0.13

. For the deeper depth horizons, it was assessed that soil properties for this region were relatively homogenous, of grayish luvisols, essentially of minimal C and total nitrogen (N) with high C:N (as noted for the 90–105 cm depth layer in Table A1 in Appendix A). Conversely, C was generally maximal in the 0–5 cm and 5–15 cm depth layers. Due in part to the prevalence of tree roots, the 5–15 cm depth layer was resolved as the most biologically relevant for this region, which subsequently was the focus for this research. Overall, the samples were extracted within three main areas within the study region. This consisted of 32 sites near Ryland, 42 sites near Kapuskasing with 3 sites near Fauquier-Strickland within the GCF area in the center of the study region, and 67 sites near Cochrane, for a total of 144 sites. The locations of the sampling sites are indicated in Figure 1. In total, samples were collected for 431 subplots, with 3 subplots per site; it was not feasible to extract samples from a subplot with one site during the September 2018 field campaign. Due to the presence of compacted soil composed of higher clay content below the surface layer, a conventional soil sampler tool was impractical for extracting soil samples, as it was too difficult to retrieve the sampler tool from the ground. Accordingly, the samples were collected by means of soil pits, which were dug down to 30 cm, with the soil samples extracted by bulk density (BD) rings along the exposed edges at the specified depths. For the BD samples, the BD ring was carefully hit with a mallet until the BD ring was fully inserted in the soil layer, so as to obtain samples that completely filled the BD ring. A soil auger was used to obtain soil samples at the 30–45 cm and 90–105 cm depth layers.

The collected soil samples were processed for both chemistry and BD analysis. Before being processed, the samples were first sufficiently air-dried for several months. With regard to processing, separate tests were undertaken to ascertain various soil attributes. The samples for chemistry analysis were assessed to gauge textural components with respect to clay, silt, and sand, as well as concentrations of nutrients such as C and nitrogen (N). This assessment was conducted by A&L Canada Laboratories Inc. (London, ON, Canada) and the GLFC (Sault Ste. Marie, ON, Canada). The BD samples were evaluated at the GLFC. When processing the BD samples, after initial drying, these were further dried in an oven at 110 °C for at least 48 h to remove remaining moisture. Following that, these samples were then pulverized and weighed, minus coarse fragments of rock and root material, to calculate the mass of soil material per fixed volume. For research purposes, the focus of analysis was for the properties of C (here regarded as soil C), clay percentage, BD, and a carbon-to-nitrogen ratio (C:N), which was defined as C divided by N.

The measurements for C and clay were reported in percentage points (%), BD was noted in grams per cubic centimeter (g/cm³), and C:N was unitless. BD by definition pertains to a mass per volume, and was stated in g/cm³, as noted in other studies for the boreal biome in Canada [2]. Units for C, N, and clay component were kept in percentage points (%), as measured and recorded from the lab analysis. A separate study for the boreal biome in Ontario and Quebec [8] reported soil C in percentage points as well. Clay component has been noted in percentage points [32], in conjunction with the textural components of sand or silt [2,33]. Thus, it was decided to report C and clay component in the original measure of percentage points as resolved from the lab, to correspond to concentrations.

2.3. Statistical Analysis

Of importance was to resolve whether statistical differences manifested for each soil property with respect to the various land cover types or dominant tree species present. To address this matter, statistical inference was conducted. As all soil samples were collected within three years of one another, and particular land cover types were only sampled in specific years, statistical inference for year over year effects was not considered. The main soil property investigated was C, which for this study area would typically require a longer time factor [1,4] to yield resolvable changes. The land cover groupings accounted for categories with sites that lately underwent conversion, such as for recently cleared land or abandoned fields. Hence, sites that experienced drastic land cover change were separated into according land cover groupings.

Before conducting inferential analysis, bar plots [21,34] conveying the mean for each dominant tree species, with further specification by cover type, were plotted to visualize trends for the respective soil properties amongst these groupings. Respective standard deviations for each grouping were also plotted as standard errors, centered around the mean values at the top of the bars. The ggplot2 package version 3.5.1 [35] was applied to create the bar and standard error plots. Afterwards, a two-step inferential analysis was carried out. The Kruskal–Wallis test was applied to reveal median differences for each soil property amongst the cover types, which was followed in further detail by the implementation of GEEs for mean differences between specific cover types. GEEs were also later employed to obtain estimates of parameters for soil C, based upon clay percentage and cover type data. The methodologies for the Kruskal–Wallis test and GEEs are explained in the subsequent subsections.

2.3.1. Kruskal–Wallis Test

The Kruskal–Wallis (KW) test was utilized to evaluate the significance of differences between median values in soil properties amongst cover type groupings. This was performed for both dominant tree species and land cover type. The formula for the KW test statistic [36,37] adopted was

$$K={\displaystyle \frac{12}{n\left(n+1\right)}}\left[{\displaystyle \sum }_{i=1}^g{n}_i{\left({\overline{R}}_i-{\displaystyle \frac{n+1}{2}}\right)}^2\right]$$

(1)

Here, $n$ denotes the total number of observations, $g$ is the number of groupings, where there are $n_i$ observations for grouping $i$, and ${\overline{R}}_i$ is the average rank of observations corresponding to grouping $i$. This average rank per grouping is calculated as the arithmetic mean of the index ranking for all observations within that grouping, where the index ranking for each observation is considered in reference to the observations with all groupings. Note that the index ranking is computed when all the observations are ordered in value from smallest to largest, with the observation corresponding to the smallest value being assigned an index ranking of 1, and averages of respective rankings regarded for two or more observations of the same value. The term $\left(n+1\right)/2$ can be purported as an overall average of the assigned ranks [37]; thus, the KW test statistic is maximal when the average rank of observations per grouping deviates from the overall average rank. When the null hypothesis is true, this KW test statistic approximates a ${\chi }_{g-1}^2$ (chi-squared) distribution with corresponding $g-1$ degrees of freedom [37]. With regard to establishing statistical significance, a threshold of 0.05 for the p-values was accepted.

As implemented for this research, the null hypothesis conformed to the case where the medians of the measured soil property were equal across the various cover types. Correspondingly, the alternative hypothesis pertained to a median measured soil property for at least one cover type being different from the medians for the other cover types. Due to relaxed conditions required for application, the KW test was the principal metric employed for statistical inference to ascertain differences in selected soil properties across the various land cover types and dominant tree species groupings. To determine if there existed differences in median values for the sites for the cover types on account of the subplots, a hierarchical KW test was implemented. This nested KW test obtained a nested p-value to report any significance for differences amongst the sites, when calculating medians of measured soil properties based upon the subplots for the sites. For the nested tests, this secondary null hypothesis was that the sites for each cover type had the same median measured soil property; the secondary alternative hypothesis was that the median measured soil property was different for at least one site.

The stats package version 4.4.0 in R [38] was wielded for the statistical inference with the KW test. To facilitate the hierarchical KW testing, with respect to unnested and nested inferences, the reportRmd package version 0.1.0 [39] was employed. Covariate summaries with significance of inferences evaluated were calculated separately for both land cover type and dominant tree species grouping to resolve unnested p-values. In addition, statistical inferences for nested covariate summaries on account of the subplots, denoted as nested p-values, were also computed. Summary tables were generated for each land cover type and tree species grouping to report median values of each grouping for the various soil properties, as well as the respective unnested and nested p-values to infer significance. Note that thresholds for the level of significance for reporting p-values have been denoted with asterisks, with 0.05 significance indicated with one asterisk, 0.01 significance with double asterisks, and 0.001 significance with triple asterisks, respectively.

Effect size has also been calculated to indicate the strength of relationship between the differences in the groups in the KW test. While p-values denote statistical significance, effect size is a metric that corresponds to practical significance [40], as the derivation of effect size is independent of sample size [41]. It has commonly been reported for inferential statistical analysis in health sciences [41,42] and social science research [40,43]. However, this metric is subjective to the context, lacks physical units, is biased for small sample sizes [44], and due to its limited usage, it may not attest as relevant in comparison with other studies related to soil research. Nonetheless, the eta-squared effect size, which is applicable to continuous quantities, has been assessed. It can be computed by dividing the sum of squares of the independent variable by the total sum of squares in the model [45,46]. Hence, the eta-squared effect size is a measure bounded between 0 and 1. A larger effect size indicates greater practical significance, while a smaller effect size signifies that the given variable quantifies less variance. Interpreting eta-squared values based on guidelines [46,47], eta-squared effect size thresholds of 0.01 correspond to a small effect, approximately 0.06 indicate a medium effect, and 0.14 or greater denote a large effect.

2.3.2. Generalized Estimating Equations

A generalized estimating equation (GEE) can be applied to obtain consistent and unbiased estimates of parameters for a generalized linear model [23,48]. In effect, a generalized linear model is a more adaptable form of a regression model. It can facilitate response variables with underlying distributions that need not be normal, related by means of a link function to a linear model [49] so that regression can be feasible for an extended variety of applications. For this research, these parameters for a GEE can correspond to other soil properties and cover type information, which can be utilized as predictors with respect to estimating soil C concentrations. GEEs can be employed for hypothesis testing [23], as these can be applied to clustered data where the assumption of independence between observations is not necessary [23]. Specifically, GEEs can test for differences amongst groupings for properties, when controlling for other covariates.

A brief background with GEEs, following the derivation [22], has been conveyed. For each subject of $i=1,\dots ,M$, the response observations are ${\mathit{y}}_i={\left(y_{i1},\dots ,y_{i{n}_i}\right)}^T$, with $n_i$ number of measurements per subject. The covariate matrix is of form ${\mathit{X}}_i={\left({\mathit{X}}_{i1},\dots ,{\mathit{X}}_{i{n}_i}\right)}^T$ with dimension $n_i\times p$ for $p$ number of covariate variables. Regarding application for the analysis of soil samples, the number of sites correspond to the number of subjects, with the number of measurements amounting to the number of subplots. The respective means and variances, also known as the first two moments of the marginal distribution of $y_{ij}$ [22], are of form $\mathrm{E}\left(y_{ij}\right)={\mu }_{ij}$ and $\mathrm{var}\left(y_{ij}\right)=\varphi v\left({\mu }_{ij}\right)$, where $\varphi$ is a scale parameter and $v$ a variance function. In this context, the objective is to calculate the $p\times 1$ vector $\mathit{\beta }={\left({\beta }_1,\dots ,{\beta }_p\right)}^T$ of unknown parameters, corresponding to the regression parameters of the covariate variables for the generalized linear model. The estimating equation, also known as a quasi-score function [50], can be expressed for the number of $M$ subjects [22] as

$${\displaystyle \sum }_{i=1}^M{\left({\displaystyle \frac{\partial {\mathit{\mu }}_i}{\partial \mathit{\beta }}}\right)}^T{\left[{\mathit{V}}_i\left(\mathit{\alpha }\right)\right]}^{-1}\left({\mathit{y}}_i-{\mathit{\mu }}_i\right)=0_p$$

(2)

In this equation, the variance matrix is of form ${\mathit{V}}_i=\varphi {\mathit{A}}_i^{1/2}{\mathit{R}}_i\left(\mathit{\alpha }\right){\mathit{A}}_i^{1/2}$, where ${\mathit{A}}_i$ is a diagonal matrix of dimension $n_i\times n_i$ with $v\left({\mu }_{ij}\right)$ for each j-th diagonal element. Here, ${\mathit{R}}_i\left(\mathit{\alpha }\right)$ denotes the working correlation matrix [48] for the i-th subject, which consists of hypothesized correlations between the response variables that are dependent upon an association parameter vector $\mathit{\alpha }$ [50]. The working correlation matrix relates to the correlations amongst observations for the same subject [22] and does not need to be correctly assumed [50] as GEEs can be robust to incorrect choices of an initial correlation matrix [24]. The estimating equation can be solved iteratively via weighted least-squares methods, alternating between estimates of $\varphi$, $\mathit{\alpha }$, and $\mathit{\beta }$ by implementing moment estimators of $\varphi$ and $\mathit{\alpha }$ [22]. To approximate a likelihood function, which does not need to be known [22], distributions for univariable or multivariable formulations can be specified with either correlated or uncorrelated error structures [51]. With respect to statistical inference for the fit of a GEE model, the Wald test is utilized; this test statistic approximates an F-distribution for the null hypothesis [52].

As implemented in this study, GEEs were formulated to gauge the mean difference in the targeted soil property between two separate groupings, as set up for the parameters estimated for a generalized linear model. Tukey’s honest significance test was utilized to evaluate for the mean difference between cover types, with this test statistic approximating a studentized range distribution for the null hypothesis [53]. In each comparison, the null hypothesis was that the corresponding $\beta$ parameter relating to the difference in the means was zero, whereas the alternative hypothesis amounted to this difference was not equal to zero. This evaluation via GEEs was employed when assessing for less obvious effects or associations, which may have been more difficult to ascertain with other statistical evaluations. The respective confidence interval (CI) at the 95% confidence level for the bounds of the true population value of the mean difference was also reported for each pairwise difference. This can be interpreted as that approximately 95% of these intervals would contain the true mean difference value for the overall population [54]. As with the KW test for the p-values, a level of 0.05 was considered for inferring statistical significance.

The geepack package version 1.3.11.1 [51,55] within R [38] supported the foundation of the modelling utilized for the GEE analysis. The reportRmd package [39] was applied in formulating the GEE models. Gaussian distributions with uncorrelated error structure were assigned for the GEEs. Both univariable GEEs as well as multivariable GEEs were modelled. Univariable GEEs, based upon the targeted soil property of C, were employed for the statistical inference for mean differences in soil C concentration between the various specific cover types. A multivariable GEE structure was used to estimate soil C, modelled on land cover type, dominant tree species grouping, and clay percentage. Summary tables of these comparisons and results, with estimates of the mean differences as well as corresponding CIs and p-values of significance, have been resolved. To assess the fitting of the multivariable GEE, the coefficient of determination (R²) was reported. The R² conformed to the proportion of variation quantified by the fitted model [56], with a larger R² indicating a better model fit.

3. Results

3.1. Bar Plots

Before detailing statistical inference results, as preliminary analysis, the tabulation depictions of measured properties for the soil samples have been presented by bar plots with standard errors indicated. The soil properties have been summarized by tree species, without reference to land cover type, in Figure 2, for each of C, C:N, clay percentage, and BD. These same properties are also summarized by tree species, but with regard to land cover type, in Figure 3. For each bar plot, mean values are visualized by vertical bars, with the standard errors centered around the mean values as denoted by the tops of the bars.

Upon inspecting the bar plots with standard errors in Figure 2, appreciable relationships between dominant tree species become evident regarding some of these soil properties. Specifically, there are considerable differences between the C concentration in the soil amongst particular tree species, such as between black spruce and white spruce. As expected, the sites with no tree species present have amongst the lowest C. The C:N is fairly consistent over the tree species, ranging from around 13 to about 20, which is expected for surface mineral soil at forested sites [57]. However, there are distinctions between tree species for clay component and BD, with similar characteristics between clay component and BD; that is, BD generally increases as clay component increases. The sites with either no tree species, or those that were predominantly larch or white spruce, had the highest BD. On the contrary, sites conforming to black spruce had the lowest BD.

When regarding the bar plots for dominant tree species with respect to land cover type, as presented in Figure 3, there are noticeable differences amongst land cover types. Note for some land cover types that no tree species are present, hence the allotment to the category conforming to none with respect to dominant tree species; particularly, this is the case with agricultural sites, for crop fields and hay fields or pastures. With respect to land cover type, the heterogeneity between the different cover types is most perceptible when considering C. Wetlands display the highest C values, followed by forested sites. In contrast, crop fields, hay fields, and old yard sites comprise the least amounts of C. BDs are generally highest for old yard sites, crop fields, and hay fields; that is, for land covers that have been compacted as a consequence of agricultural activities. As anticipated, BDs are the lowest for wetlands, which are primarily composed of peat that ordinarily has a lighter mass per volume than that for other soil types. The C:N is more consistent across the land cover types, but is highest for the wetlands and lowest for land cover types with no subsisting tree species. However, even within land cover types, dissimilarities in soil properties amongst the tree species groupings are also evident in Figure 3. In particular, sites populated with black spruce tend to have higher C than those for most other tree species. These associations with C are the subject for statistical inference with the GEEs presented later, concerning mean differences between tree species pairings.

3.2. Kruskal–Wallis Testing

As a first step of inferential analysis, the KW test has been wielded to ascertain statistical significance across cover types. Tabulation tables reporting the median values for the soil properties are presented in

Table 1. Soil property summaries of median values by dominant tree species present at site. Statistical inference of median differences across cover type via the Kruskal–Wallis (KW) test is indicated by unnested p-values and effect size, and by nested p-values for testing of median differences within sites relative to the subplots. For the p-values, the significance level of 0.05 is indicated with one asterisk (*), 0.01 with two asterisks (**), and 0.001 with three asterisks (***), respectively.

Soil Property		Full Sample	Balsam Fir	Balsam Poplar	Black Spruce	Larch	None	Trembling Aspen	White Spruce	Unnested		Nested
		(n = 431)	(n = 39)	(n = 54)	(n = 36)	(n = 36)	(n = 180)	(n = 63)	(n = 23)	Effect Size	p-Value	p-Value
C	(%)	4.3	5.8	7.9	23.4	3.2	3.0	7.1	4.2	0.15	<0.001 ***	0.88
C:N		16.0	17.7	17.8	20.5	13.3	15.1	17.7	13.1	0.07	<0.001 ***	0.88
Clay	(%)	27.0	25.1	20.0	14.0	29.0	29.0	21.0	32.6	0.11	<0.001 ***	0.90
BD	(g/cm3)	1.31	1.01	1.15	0.33	1.37	1.50	1.06	1.22	0.18	<0.001 ***	0.74

as summarized by tree species, and by

Table 2. Soil property summaries of median values by land cover type. Statistical inference of median differences across cover type via the Kruskal–Wallis (KW) test is indicated by unnested p-values and effect size, and by nested p-values for testing of median differences within sites relative to the subplots. For the p-values, the significance level of 0.05 is indicated with one asterisk (*), 0.01 with two asterisks (**), and 0.001 with three asterisks (***), respectively.

Soil Property		Full Sample	Abandoned Field	Crop Field	Hay Field/ Pasture	Old Growth Forest	Old Yard Site/ Clearing	Recently Cleared Land	Secondary Forest/ Woodlot	Wetland	Unnested		Nested
		(n = 431)	(n = 74)	(n = 42)	(n = 75)	(n = 48)	(n = 9)	(n = 24)	(n = 138)	(n = 21)	Effect Size	p-Value	p-Value
C	(%)	4.3	4.6	2.6	2.8	5.2	2.4	3.9	6.2	40.6	0.28	<0.001 ***	0.93
C:N		16.0	15.3	15.7	13.8	17.5	11.4	16.1	16.6	23.6	0.11	<0.001 ***	0.80
Clay	(%)	27.0	28.0	32.0	29.0	22.5	24.0	28.0	25.0	4.0	0.18	<0.001 ***	0.75
BD	(g/cm3)	1.31	1.32	1.71	1.59	1.08	1.91	1.34	1.11	0.22	0.33	<0.001 ***	0.92

as aggregated by cover type. These p-values have been determined by the KW test [36]. Note that the unnested p-values correspond to the testing upon median differences between either tree species (Table 1) or land cover type (Table 2) categories. The nested p-values assess for median differences in the respective soil properties amongst the sites as based upon the subplots.

Inspecting Table 1, the median measured soil properties are evidently different with regard to dominant tree species present at sites, for each of C, C:N, clay percentage, and BD. High significances are also revealed for median differences amongst the land cover types for the same soil properties, as noted in Table 2. For all the soil properties, the reported unnested p-values are less than 0.001, indicating strong evidence of median differences in these respective soil properties between the land cover and vegetation types. For both tables, none of the nested p-values are significant, meaning there are no discerned median differences in the soil properties amongst the sites when considered upon the subplots. This null result justifies modelling at a site level with regard to digital soil mapping. The utilization of environment covariates from remotely sensed technologies of typical spatial resolutions (approximately 30 m) should be valid for digital soil mapping, so that one pixel of rasterized covariate imagery can conform to a site. This, in conjunction with resolved statistical significances across the cover types, infers that sufficient heterogeneity with the samples has been collected so as to merit usage of these samples for digital soil mapping.

With regard to the effect size, median effects (between 0.07 and 0.13) were established for the C:N and clay percentage when testing amongst dominant tree species in Table 1, and for C:N amongst land cover type in Table 2. Otherwise, all other eta-squared effect sizes were 0.14 or greater, indicating a large effect. These results are comparable to what was resolved from the p-values, signifying statistical significance for the median differences in the soil properties across the land covers and tree species groupings.

3.3. Generalized Estimating Equations

As a secondary step, GEEs were employed to obtain refined inferential analysis between specific groupings within cover types. GEEs yielded estimates for mean differences in the soil C concentration between tree species groupings, attained from univariable models. These results are reported in

Table 3. Estimates of mean differences in total carbon (C) between groupings of observed dominant tree species, as established from generalized estimating equations (GEEs). The corresponding estimates for the mean differences, associated lower and upper bounds for 95% confidence intervals (CIs), standard errors, and p-values for significance were determined. For the p-values, the significance level of 0.05 is indicated with one asterisk (*), 0.01 with two asterisks (**), and 0.001 with three asterisks (***), respectively.

Comparison	Estimate	Confidence Bound Lower 95%	Confidence Bound Upper 95%	Standard Error	p-Value
	(%)	(%)	(%)
Balsam Fir—None	8.70	−3.81	21.20	4.34	0.370
Balsam Poplar—None	8.42	−0.66	17.50	3.15	0.088
Black Spruce—None	15.63	2.00	29.26	4.73	0.014 *
Larch—None	0.95	−9.03	10.93	3.46	1.000
Trembling Aspen—None	3.06	−1.79	7.91	1.68	0.492
White Spruce—None	−1.07	−5.70	3.56	1.61	0.993
Balsam Poplar—Balsam Fir	−0.27	−15.15	14.61	5.17	1.000
Black Spruce—Balsam Fir	6.93	−11.09	24.95	6.25	0.912
Larch—Balsam Fir	−7.75	−23.19	7.70	5.36	0.744
Trembling Aspen—Balsam Fir	−5.64	−18.38	7.11	4.42	0.841
White Spruce—Balsam Fir	−9.77	−22.43	2.90	4.40	0.248
Black Spruce—Balsam Poplar	7.20	−8.63	23.04	5.50	0.822
Larch—Balsam Poplar	−7.48	−20.31	5.35	4.45	0.589
Trembling Aspen—Balsam Poplar	−5.36	−14.77	4.04	3.27	0.614
White Spruce—Balsam Poplar	−9.49	−18.79	−0.20	3.23	0.042 *
Larch—Black Spruce	−14.68	−31.05	1.69	5.68	0.111
Trembling Aspen—Black Spruce	−12.57	−26.42	1.29	4.81	0.102
White Spruce—Black Spruce	−16.70	−30.47	−2.92	4.78	0.007 **
Trembling Aspen—Larch	2.11	−8.17	12.39	3.57	0.996
White Spruce—Larch	−2.02	−12.20	8.16	3.53	0.997
White Spruce—Trembling Aspen	−4.13	−9.37	1.11	1.82	0.225

. The corresponding 95% CIs for these estimates were also determined, along with associated standard errors and p-values. Similarly, mean differences between the distinct land cover types with regard to C concentrations within the soil were also estimated. These results are featured in

Table 4. Estimates of mean differences in total carbon (C) between groupings of land cover type, as established by generalized estimating equations (GEEs). The corresponding estimates for the mean differences, associated lower and upper bounds for 95% confidence intervals (CIs), standard errors, and p-values for significance were determined. For the p-values, the significance level of 0.05 is indicated with one asterisk (*), 0.01 with two asterisks (**), and 0.001 with three asterisks (***), respectively.

Comparison	Estimate	Confidence Bound Lower 95%	Confidence Bound Upper 95%	Standard Error	p-Value
	(%)	(%)	(%)
Abandoned Field—Old Growth Forest	−4.54	−16.64	7.57	4.17	0.940
Crop Field—Old Growth Forest	−10.33	−20.53	−0.12	3.51	0.045 *
Hay Field/Pasture—Old Growth Forest	−9.21	−19.53	1.12	3.55	0.116
Old Yard Site/Clearing—Old Growth Forest	−11.40	−21.57	−1.24	3.50	0.017 *
Recently Cleared Land—Old Growth Forest	−3.19	−19.64	13.26	5.66	0.999
Secondary Forest/Woodlot—Old Growth Forest	−3.15	−14.02	7.72	3.74	0.985
Wetland—Old Growth Forest	22.94	10.49	35.39	4.28	<0.001 ***
Crop Field—Abandoned Field	−5.79	−12.46	0.88	2.29	0.138
Hay Field/Pasture—Abandoned Field	−4.67	−11.52	2.18	2.36	0.412
Old Yard Site/Clearing—Abandoned Field	−6.87	−13.48	−0.26	2.28	0.036 *
Recently Cleared Land—Abandoned Field	1.35	−13.18	15.87	5.00	1.000
Secondary Forest/Woodlot—Abandoned Field	1.38	−6.27	9.03	2.63	0.999
Wetland—Abandoned Field	27.48	17.72	37.23	3.36	<0.001 ***
Hay Field/Pasture—Crop Field	1.12	−0.99	3.23	0.73	0.719
Old Yard Site/Clearing—Crop Field	−1.08	−2.19	0.04	0.38	0.065
Recently Cleared Land—Crop Field	7.14	−5.84	20.12	4.47	0.682
Secondary Forest/Woodlot—Crop Field	7.17	3.17	11.18	1.38	<0.001 ***
Wetland—Crop Field	33.27	26.00	40.53	2.50	<0.001 ***
Old Yard Site/Clearing—Hay Field/Pasture	−2.20	−4.12	−0.28	0.66	0.014 *
Recently Cleared Land—Hay Field/Pasture	6.02	−7.05	19.09	4.50	0.841
Secondary Forest/Woodlot—Hay Field/Pasture	6.05	1.75	10.36	1.48	0.001 **
Wetland—Hay Field/Pasture	32.15	24.72	39.58	2.56	<0.001 ***
Recently Cleared Land—Old Yard Site/Clearing	8.22	−4.73	21.17	4.46	0.507
Secondary Forest/Woodlot—Old Yard Site/Clearing	8.25	4.34	12.16	1.35	<0.001 ***
Wetland—Old Yard Site/Clearing	34.34	27.13	41.55	2.48	<0.001 ***
Secondary Forest/Woodlot—Recently Cleared Land	0.04	−13.47	13.55	4.65	1.000
Wetland—Recently Cleared Land	26.13	11.32	40.93	5.09	<0.001 ***
Wetland—Secondary Forest/Woodlot	26.09	17.92	34.27	2.81	<0.001 ***

.

There is evidence to suggest that black spruce sequesters larger amounts of soil C when reviewing Table 3 and comparing the mean difference in soil C between tree species groupings, particularly when no tree species are present (i.e., none). This corroborates that an indicator relating to the presence of black spruce could be an important predictor with respect to the digital soil mapping of soil C in this study area. Likewise, a similar assertion, though of less significance, can be stated with regard to soil C increasing due to the presence of balsam poplar. When considering the mean differences between groupings of land cover type, as noted in Table 4, dissimilarities in soil C concentrations are apparent. As anticipated, the most significant mean differences in soil C are amongst vastly incongruous land cover types. Notably, there prevail considerable significant mean differences in the concentrations of soil C between wetlands and any other land cover type (p-values < 0.001). As well, secondary forest and old growth forest each have significant mean differences in soil C concentration with respect to either crop fields or old yard sites (p-values < 0.05).

GEEs were also exploited to obtain estimates of soil C concentration from the predictors of clay percentage, land cover type, and dominant tree species present, without examining mean differences between groupings of land cover type or dominant tree species. Both univariable and multivariable GEE models were fitted, and these results are shown in

Table 5. Estimates for total carbon (C) with corresponding 95% confidence intervals (CIs) and p-values, for generalized estimating equations (GEEs) formulated with clay component, land cover type, and dominant tree species present at site. This is reported for both univariable and multivariable models. For the p-values, the significance level of 0.05 is indicated with one asterisk (*), 0.01 with two asterisks (**), and 0.001 with three asterisks (***), respectively.

		Univariable		Multivariable
Predictor	Number of Samples	Estimate and 95% CI	p-Value	Estimate and 95% CI	p-Value
	(n)	(%)		(%)
Clay	424	−0.67 (−0.74, −0.60)	<0.001 ***	−0.48 (−0.59, −0.37)	<0.001 ***
Land Cover Type	431		<0.001 ***		<0.001 ***
- Crop Field	42	Reference		Reference
- Abandoned Field	74	5.46 (1.28, 9.64)	0.01 *	2.35 (−1.02, 5.72)	0.17
- Hay Field/Pasture	75	0.88 (−3.28, 5.05)	0.68	−0.59 (−2.71, 1.53)	0.58
- Old Growth Forest	48	9.57 (5.00, 14.14)	<0.001 ***	1.85 (−4.11, 7.81)	0.54
- Old Yard Site/Clearing	9	−0.94 (−8.88, 7.01)	0.82	−5.79 (−8.74, −2.85)	<0.001 ***
- Recently Cleared Land	24	6.39 (0.85, 11.92)	0.02 *	4.74 (−2.77, 12.25)	0.22
- Secondary Forest/Woodlot	138	7.70 (3.88, 11.51)	<0.001 ***	2.68 (−1.40, 6.76)	0.2
- Wetland	21	32.98 (27.20, 38.76)	<0.001 ***	18.00 (11.43, 24.56)	<0.001 ***
Dominant Tree Species	431		<0.001 ***		0.16
- None	180	Reference		Reference
- Balsam Fir	39	6.91 (2.76, 11.06)	0.001 **	1.17 (−5.08, 7.43)	0.71
- Balsam Poplar	54	9.49 (5.84, 13.14)	<0.001 ***	2.96 (−3.11, 9.04)	0.34
- Black Spruce	36	15.45 (11.15, 19.74)	<0.001 ***	7.42 (0.86, 13.99)	0.03 *
- Larch	36	0.44 (−3.85, 4.73)	0.84	0.71 (−3.12, 4.55)	0.71
- Trembling Aspen	63	3.55 (0.11, 7.00)	0.04 *	−1.31 (−5.56, 2.95)	0.55
- White Spruce	23	−1.63 (−6.84, 3.57)	0.54	−0.76 (−4.85, 3.33)	0.72

. The respective 95% CIs are reported for predictor estimates, in comparison to reference categories. These GEEs would be analogous to the context of predicting soil C from physical soil properties and attributes, as for the case of legacy soil data where chemistry analysis results are unavailable.

For the analysis presented in Table 5, crop field was set as the reference land cover type, with none fixed as the reference tree species grouping; this would only configure the bases for the parameter estimates. Note that crop field sites, apart from old yard sites or hay fields, tend to contain the least soil C contents. Therefore, the parameter estimates corresponding to other land cover types were positive with respect to crop fields, with the unit in percentage points. In a similar fashion, with the reference dominant tree species grouping set as none, most tree species groupings contributed to an increase in the C concentration in the soil. The exception here with tree species was for white spruce and also trembling aspen for the multivariable model. Moreover, the negative parameter estimates for the clay percentage related to the C concentration in the soil decreased as the clay percentage increased. When compared to the univariable results, the multivariable model estimated lower parameter values for soil C concentrations, as well as lesser levels of significance. However, an R² of 0.59 was attained for modelling accuracy with the multivariable model. This indicates that a sufficient model to estimate soil C concentration, based on just the clay component percentage, noted land cover type and dominant tree species at the site was feasible for this study area.

4. Discussion

The contrasts between the concentrations of soil C for forested versus the agricultural land cover types, as revealed in Table 4, are evident. These results yield support for the implementation of environmental covariates as derived from remote sensing technologies as predictors with digital soil mapping applications. A canopy height model (CHM) would likely be a prominent environmental covariate to apply as a predictor, as it would account for the differences in height between the agricultural lands with very low CHM for grass and field crops, versus higher CHM for forested localities. In addition, the normalized difference vegetation index (NDVI) could also be of higher importance as its magnitude can distinguish between various vegetation types. From Table 4, it is apparent that wetlands encompass the greatest soil C contents; thus, topographic covariates relating to hydrological considerations could be significant. The inferential statistical analysis here provides corroboration pertaining to physical drivers for soil property disparities. This knowledge can be harnessed to rationalize the selection of more relevant environmental covariates as predictors for modelling with digital soil mapping. Thus, it is beneficial to conduct statistical inferential analysis between soil properties and cover type, particularly for recently processed soil sample data in advance of digital soil mapping applications.

Although both the KW test and GEEs were used to evaluate the significance of differences in the soil properties between cover types, these approached the assessment in distinct ways [19]. The KW test focused on determining the median differences, whereas GEEs were wielded to analyze the mean differences. When considering differences in soil properties across cover types, using the median as a metric is more appropriate than the mean. This is because significant variations or outliers in soil properties may be present. From the bar plots in Figure 3 for soil C, it is evident that there are larger relative variations for abandoned fields and secondary forests. Thus, testing with respect to the median across cover types was more pertinent; outliers can skew incongruous cover types to have similar means. However, for more refined analysis between pairings, the mean would be less affected by outliers for specific cover types. Using the mean differences, GEEs were able to establish the significance of soil C levels between different land cover types, as shown in Table 4. It was found that wetlands exhibited the highest C concentrations, while secondary and old growth forests were determined to have higher soil C contents when compared with crop fields or old yard sites. Consequently, in terms of assessing median or mean differences, employing both of these metrics was complementary as used in the two-step inferential analysis.

The application of GEEs can be extended to legacy soil sample data for inferring estimates of C. In the District of Cochrane, the Ontario Forest Resources Inventory (FRI) has assessed the soil texture family at tree species plots for more than one thousand sites within this vicinity [58]. Based on the soil samples collected in this study, the percentages of clay, silt, and sand have been resolved. These components can be used to assign the soil texture family by means of a texture ternary diagram [32] or an analogous protocol. This research showcases the efficacy of GEEs in estimating C concentrations in soil by considering factors such as the clay component percentage, dominant tree species, and land cover type. By using these models, it is possible to extrapolate predictions of C concentrations, including confidence intervals, by incorporating legacy soil sample data. The FRI data include information on tree species and vegetation, so therefore it can facilitate the categorization of dominant tree species and land cover, and thereby be of use for GEEs to yield predictions. Although these C values would be estimates, this approach is expected to be more accurate than what could be obtained through regression using other methods. This is supported by an acceptable R² obtained for the multivariable GEE model, from the results reported in Table 5.

Discrepancies in parameter estimates, as well as the corresponding significance of inferential results, can arise from whether a univariable or multivariable approach was undertaken for the GEEs. Both approaches were investigated and implemented for this study, with univariable analysis reported for Table 3 and Table 4, and both univariable and multivariable results for Table 5. In general, p-values for mean differences in the soil properties amongst the various groupings were less significant with the multivariable model. As an example, a multivariable formulation with soil C modelled on land cover type, dominant tree species grouping, and clay percentage was also implemented for the statistical inferences of mean differences with soil C amongst tree species groupings. However, when multivariable analysis was carried out, significant p-values of less than 0.05 were not obtained for any pairwise difference between tree species. The occurrence of Type I errors for false positives can be an issue with GEEs [59], which can possibly be minimized by employing multivariable analysis. However, comprehending the results of a multivariable approach might not be as straightforward, as a combination of variables would be responsible for the differences. Statistical significance assessed by a multivariable model can be argued to be stronger than that from a respective univariable model, as by formulation, a multivariable model controls for the effects of more than one predictor. Ultimately, a univariate approach was employed for the inferential statistical analysis, but a multivariate approach could be deemed more appropriate for a study depending upon the context.

With respect to limitations, this study corresponds to the environment of northern Ontario for an area of the boreal forest that receives more precipitation than synonymous regions in western Canada. Expanses of wetlands exist within the boreal biome throughout Canada [26], but it is uncertain how measurements of the concentrations for soil C and associated properties would compare for analogous land cover types. Moreover, these study areas comprised luvisols for the deeper soil horizons, so nonetheless, it is unknown how the C concentrations would compare for the surface layers of soil from neighboring regions of boreal forest. For future studies, recommendations include the extraction of soil samples from an adequate threshold of sites conforming to recently cleared land. This would be intended to ascertain differences between mulching versus burning for deforestation, so as to determine if mulched land retained more soil C. As well, in general, there appeared to be a gain in soil C for what was agricultural land that later became abandoned. Of interest would be the collection of more samples from abandoned fields, to conduct further statistical inference so as to gauge the sequestration of soil C for sites returned to forest cover.

5. Conclusions

Statistical inference approaches applicable for non-normal and smaller samples were wielded to analyze the differences in soil properties amongst various cover types, for a study region located within the southern boreal transition zone in northern Ontario, Canada. This was accomplished by a two-step process involving the KW test and then GEEs. The KW test provided supporting evidence (p-values < 0.05) of median differences in C across the land cover types and dominant tree species. Furthermore, the KW test demonstrated the significance (p-values < 0.05) of median differences in the C:N, clay percentage, and BD across the different cover types. GEEs were wielded to infer additional results regarding soil C contents between specific land cover types and tree species groupings. Wetlands (p-values < 0.001) and forested areas exhibited the highest levels of soil C, whereas agricultural sites contained the lowest concentrations. GEEs were also used to derive estimates for the soil concentration along with corresponding CIs, which depending on context can be applied to legacy soil data. The knowledge gained by resolving the status of soil C between specific land covers can suggest suitable environmental covariates for soil modelling. In particular, the results supported that a tree species indicator for black spruce could act as an important predictor for soil C modelling with digital soil mapping.