1. Introduction

2. Materials and Methods

2.1. Study Area

We selected the eastern United States as our study area, which predominantly covers oak forests [45]. It is comprised of ten states that cover a land area of 1,273,420,251.33 hectares (Figure 1). Our study area was further divided into southern region (low latitude: 30-to-36-degree N latitude), central region (medium latitude: 36-to-37.5-degree N latitude), and northern region (high latitude: 37.5-to-42.5-degree N latitude) WOM rate that contains 678, 747, and 797 plots, respectively. We did a subdivision to our study area due to regional variation as southern region differs from northern region and central region in terms of precipitation patterns and temperature. This divide enables us to capture variations in environmental factors that may affect tree mortality rates. Moreover, dividing the research area into southern, central, and northern regions allows us to investigate how ecological gradients affect WOM rates. For instance, latitudinal variations in soil types, topography, and disturbance regimes can have an impact on WOM mortality and forest health.

Our study area consists of varied tree species, and a wide range of climate, soil, and terrains [46,47,48]. The land structure in the eastern part of the study area is significantly Appalachian plateaus with low mountains, narrow valleys, and sharp edges. On the western portion, the area varies from highly flat central till plains to interior low plateau along with Ozark highlands. The area consists of a variety of ecological regions such as the Ouachita Mountains of Arkansas to the Northern Cumberland Mountains in West Virginia. In the south, central till plains Oak-Hickory of Illinois to Interior Low Plateau Highland Riff of Alabama.

The overall climate in these regions is long, hot summers and cool winters. The mean annual temperature ranges from 4 degrees to 18 degrees Celsius in the east-west gradient with warmer temperatures in the south. The precipitation ranges from 500 mm in the north-west to 1,650 mm in the southeast. Some Appalachian Mountains precipitation goes up to 2,000 mm during spring and fall. The soil types are mostly mollisols, inceptisols, alfisol, and ultisols. These areas consist of a xeric gradient characterized by thin, rocky soils, exposed south, southwest, and wet slopes [48]. Our study area was historically dominated by oaks, hickories, and pines. Today, most of the forest areas have been replaced by agriculture and rapid urbanization [47,49]. In our study area, there are deciduous types of forests such as oaks (Quercus spp.), hickory (Carya spp.), american beech (Fagus grandifolia), ash (Fraxinus spp.), and maple (Acer spp.).

Figure 1. Study area showing forest covers across the eastern US.

Figure 1. Study area showing forest covers across the eastern US.

2.3. Data Processing and Analysis

2.3.1. Selection of Live and Declining White Oak Plots

Annualized data from 1998 to 2019 were processed to locate white oak plots (Table 1). After data processing and refinement of our variables i.e., plot, forest condition, and tree, we selected a plot to narrow our criteria i.e., locating white oaks' plots across accessible forest land. For instance, Missouri contained plot information as a unique plot number related to each county and cycle, and locations (latitudes and longitudes) with surveyed years. We utilized sampled plots that contained at least one accessible forest land condition on the plot. Most importantly, the condition table consisted of similar attributes except for locations that were useful to associated with plots. During this process, we narrowed our condition and tree data with similar criteria i.e., selecting accessible forest land only. We used other important attributes from tree data such as unique plot number, county code, tree species code, diameter, trees per acre, and cycle to identify all white oak trees.

We selected white oak trees identified with species code (e.g., 802) from the tree data. From the same tree data containing white oaks only, we determined the basal area i.e., Basal area of white oak = 0.005454 *(Current Diameter)2 * trees per acre unadjusted. Then, we obtained our information combining forest condition and tree level data based on unique plot numbers. Then, we extracted white oak basal area information from the same set of combined tree and forested condition data. Since we worked only with an annual inventory that clearly limited our timeframe for data processing to each state. For instance, we analyzed our Missouri white oak data in which cycle 5 consisted of survey years grouped from 1999 to 2003 (usually year-wise data). Similarly, other cycles had a set of survey years that went until 2019 which were grouped as cycle 6 (2004 to 2008), cycle 7 (2009 to 2013), and cycle 8 (2014 to 2019). We then grouped other states data with the same process and extracted white oaks from each cycle. To get white oaks plot within a given timeframe, we created an appropriate formula using county and plot number i.e., county code + (plot)/100,000 to connect one cycle to another. With all these processes, we identified all the declining plots of white oaks based on basal area change. We repeated the similar process while working with rest of the states from our study area connecting different cycles to get declining plots for white oaks. During this process, we only utilized the basal area from a single plot so that we could avoid plot repetition. Based on basal areas, we extracted 2,220 declining white oak plots from 7,405 live white oak plots across ten states. For all these data processing steps, we used ArcMap version 10.8.1.

After we finalized our WOM rate data, we further divided our study area into southern, central, and northern region WOM rates. By dividing the study area, we can unravel the complex interplay of ecological, climatic, and geographical factors influencing WOM, laying the groundwork for understanding and regulating spatial patterns at different scales and regions. Moreover, a regional division enables direct comparisons of our areas that identifies similarities and differences in WOM patterns, revealing whether certain spatial trends are consistent across regions or region-specific.

Table 2. Ten states with inventory years, cycles, number of live white oak (WO) plots, and declining WO plots.

Table 2. Ten states with inventory years, cycles, number of live white oak (WO) plots, and declining WO plots.

State	Inventory Years	Cycles	Live WO plots	Declining WO plots
Alabama	2001-2019	8,9, &10	716	166
Arkansas	2000-2019	8,9,10, &11	1,158	400
Illinois	2001-2019	5,6,7, & 8	244	63
Indiana	1999-2019	5,6,7, & 8	206	43
Kentucky	2000-2017	5,6,7, & 8	775	207
Missouri	1999-2019	5,6,7, & 8	1,544	527
Ohio	2001-2019	5,6,7, & 8	337	67
Tennessee	2000-2017	7,8,9, &10	909	305
Virginia	1998-2019	7,8,9,10, &11	855	314
West Virginia	2004-2019	6,7, & 8	661	128
Total			7,405	2,220

2.3.2. White Oak Mortality Rate Analysis

The mortality rate was calculated by using basal areas of surveyed cycles, which were grouped into five years. Some of the white oak plots were remeasured in the period from 1998 to 2019. Hence, we omitted those repeated plots to have accurate results. However, we summed up all those remeasured plots' basal areas to obtain the true basal area. We selected all the basal areas from declining plots of white oaks concerning surveyed years. The declining plots were chosen based on basal area change. Basal area change refers to the decrease in basal area from two consecutive cycles. For instance, we calculated basal area change using cycles as:

$$Reducedbasalarea\left(m^2{ha}^{-1}\right)=Basalareaofcycle6-Basalareaofcycle5$$

(1)

We did the same with all remaining cycles and chose decreased basal areas that directly referred to the declining white oak plots. We calculated the mortality rate in terms of the reduced basal area of white oaks divided by the differences in the surveyed year between two extreme cycles. All those declining plots representing mortality rates were extracted and compiled the results. We calculated the mortality rate as:

$$Mortalityrate\left(m^2{ha}^{-1}{y}^{-1}\right)={\displaystyle \frac{Reducedbasalarea}{(Recentcyclesurveyyear-Oldcyclesurveyyear)}}$$

(2)

We assumed oak forests in this region have mostly gone through the self-thinning stage [57,58,59], and thus reduction of the white oak basal area can be attributed to WOM.

2.3.3. Spatial Distribution Analysis of WOM by Univariate Ripley’s K Function

Our data for white oak mortality was based on specific point events. Ripley’s K function was used for a comparison of observed spatial patterns against those expected under complete spatial randomness (CSR) that provides information for clustering, random, and uniform [60]. Other patterns do not justify the specific patterns such as CSR. Another reason is that edge effects are ignored and significantly impact other patterns that bring biased results [61,62]. However, the K function incorporates edge effects and produces valid results mitigating these issues. The use of Ripley’s K function highlights the visualization of spatial patterns at various scales i.e., small scales, larger scales, and their statistical significance whereas other patterns only highlight higher or lower concentrations without indicating particular patterns and statistical significance at varying scales.

We used Multi-Distance Spatial Cluster Analysis-Ripley’s K function tool [63], which uses nearest neighbor distance to process spatial distribution patterns. ArcMap version 10.8.1 was used for Ripley's K function which defines whether our spatial pattern is cluster, random, or uniform on each analysis scale [64,65]. All 2,220 WOM points from 1998 to 2019 were compiled that contained point locations i.e., longitudes and latitudes. In Ripley's K function tool, the initial distance was 50 km, and the increment distance was 10 km. Edge correction was done by using Ripley's edge correction formula [63], which automatically counts and measures points inside the study area. To test our null hypothesis of CSR, we formed upper and lower confidence envelopes of 99.9% generated from randomizations of 999 plot points using the default random generator in ArcGIS. We examined whether our theoretical curve (K_theo) deviates from CSR or not. If the observed curve (K_obs) is above the theoretical curve and upper envelope, then there is spatial clustering. If it is below the theoretical curve and lower envelope, then WOM points follow spatial dispersion (uniform). There is also a greater chance that both observed and theoretical curves could line up denoting complete spatial randomness or random pattern. We used the transformed K function (L(d)) to represent the graphical interpretation of Ripley's K function.

3. Results

3.1. White Oak Mortality Spatial Distribution Patterns

The white oak mortality (WOM) rate is spread throughout the eastern United States. However, there are differences in the magnitude of mortality rate and density distribution across different locations i.e., the southern, central, and northern regions of WOM rate. The southern region consists mostly of very low followed by low and medium WOM rates across different latitudes and longitudes (Figure 2A). However, there are also a few plots of high as well as very high mortality rates across this region. Despite the larger area of a low and very low density of WOM rate, some locations across the southern region depicted a high-density distribution of WOM rate (e.g., parts of Arkansas and Tennessee; Figure 2B).

Numerous plots of WOM rate were gathered that has been spread across most of the central region of the eastern US. Much of the central region showed very low and low WOM rates, however, there are also numerous plots related to medium, high, and very high WOM rates across this region (Figure 2A). This region has the most diversified forest landscape that consists of very high-density (e.g., parts of Missouri, Arkansas, Virginia etc.) and high-density distribution (e.g., parts of Missouri, Arkansas, Tennessee, Kentucky, and Virginia) of WOM rate as compared to southern and northern regions. Most of this region has been depicted with very low density as well as low and medium density distribution of WOM rate, which is greater than very high and high-density distribution (Figure 2B).

The majority of the northern region contains very few plots of WOM rate distributed across our study area (e.g., Illinois, Indiana, and Ohio). Though this region has very few plots of high to very high WOM rate (e.g., Missouri, west Virginia, and Virginia), the overall plot distribution to WOM rate is higher as compared to other regions (Figure 2A). The density distribution of WOM rate is mostly depicted very low and consists of a few areas of medium, high, and very high-density distribution to certain latitudes and longitudes. Despite the larger area of land mass, this region represented a very low plot distribution of WOM rate (Figure 2B).

The spatial distribution pattern of the WOM rate showed random patterns up to 3000 m, as the observed K value was inside the confidence envelopes, and we accept the null hypothesis (Figure 2). Beyond this point, we reject our null hypothesis, the spatial distribution of WOM rate showed clustered until 20,000 m is statistically significant. It is due to the spatial clustering of WOM rates, as indicated by the observed K value being significantly larger than the expected K function and falling outside the confidence envelopes. This clustering pattern of the WOM rate increases as the distance increases. Most of our pattern analysis for the WOM rate depicted clustered (non-random) patterns at a larger distance across the eastern US. Thus, our spatial distribution pattern analysis of WOM showed more clustering patterns than the random pattern as distance increases.

The kernel density maps for white oaks showed the cluster spatial distribution across the declining plots of white oaks (Figure 2). This density distribution indicated areas for higher or lower concentrations across the eastern US.

Figure 2. Plots (A) and density distribution (B) showing WOM rate across different latitudes and longitudes.

Figure 2. Plots (A) and density distribution (B) showing WOM rate across different latitudes and longitudes.

3.2. Spatial Distribution Patterns at Southern, Central, and Northern Regions WOM Rate

The spatial pattern of the WOM rate across the southern region depicted a clustering pattern until about 360 km, and we reject our null hypothesis. This is because the observed K function is above the expected K function. Also, the observed K function, statistically significant, is completely outside the envelope. This means points of WOM rate in the dataset are more closely spaced than would be expected under spatial randomness. However, the intensity of the clustering pattern, not constant, keeps increasing as the distance increases. Most of the southern region depicted aggregation to WOM rate across the local scale. We found the pattern is random at 360 km to 395 km as the K function, statistically not significant, is completely inside the envelopes. The random pattern of the WOM rate is across a broad scale but covers a low range of distance. This random pattern shows that the point of WOM rate has an equal chance of occurring anywhere in the southern region of our study area. The pattern is mostly uniform as the distance increases from 400km to 550km, and we reject our null hypothesis. It is because the observed K function across a broad scale is consistently below the envelope and is statistically significant as well. It shows that the points of the WOM rate are more regularly spaced than would be expected under spatial randomness. Also, there is a mostly uniform pattern across the larger scale which is more or less similar to the central and northern region WOM rate.

The central region of the WOM rate depicted a slightly lower intensity of observed K function at the local scale in comparison with patterns of southern and central region WOM rates. We found the clustering pattern until 200km across the central region where the intensity of clustering is much smaller, and we reject our null hypothesis. This clustering is because the observed K function, statistically significant, is outside the envelope. This indicates that there is a tendency for WOM rate points to be aggregated together in this region. Unlike other regions, the observed K function is much near to the random line at the local scale. Similarly, there is also a random pattern from 230km to 430 km as observed K function, statistically significant, is completely inside the envelope. It suggests that there is an equal chance of occurring points of WOM mostly at the medium scale than the local scale. However, broad scale is mostly facilitated with a uniform pattern starting from 430 km and beyond, and we reject our null hypothesis. And this uniform pattern is much away from the random line and contains a slightly lower intensity of observed K function in comparison to patterns of southern and northern region WOM rate. Overall, the pattern of WOM rate seems to be more random at the local scale, but at broad scale, it is less uniform, which is similar to southern region of the WOM rate as well.

The WOM rate across the higher latitude or northern region presented more clustering patterns (until 480km) than a random and uniform pattern. We found a complete clustering pattern across local, medium, and parts of broad scales in which the observed K function, statistically significant, is outside the envelope. The clustering pattern at the local scale starts with low intensity which is also much near the random line and slightly at the peak when it reaches around 20 km. This indicates that there is a tendency for WOM rate points to be aggregated or clustered together in this region. However, clustering slightly decreases as it reaches to medium scale and stops at 470km, which is at a broad scale. Unlike the southern and central WOM rates, patterns presented by the observed K function are varied across each scale. It is because random and uniform patterns are presented only across broad scales and across a few ranges of distance. Results show that the observed K function is below the expected K function at 480km to 520km, completely inside the envelope, denoting a random pattern at a broad scale. This tells us that the points are distributed in a manner consistent with complete spatial randomness (CSR). Beyond 520km, there is a uniform pattern at a broad scale but covers few distances in this region. The uniform pattern is since the observed K function is completely outside the envelope and is statistically significant as well, and we reject null hypothesis. This tells us that points are more evenly distributed across this region, and there is a tendency for points to avoid each other.

Figure 3. Ripley’s K function showing various spatial patterns across (A) southern, (B) central, and (C) northern region WOM rates.

Figure 3. Ripley’s K function showing various spatial patterns across (A) southern, (B) central, and (C) northern region WOM rates.

4. Discussion

5. Conclusions

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