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Multivariate Geostatistical Modeling of Phytophthora rubi and Pratylenchus penetrans in Red Raspberry Fields

J. B. Contina

J. B. Contina

Driscoll’s Inc.Red Bluff,
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Contina, J. B.
, 
D. R. Kroese

D. R. Kroese

USDA Forest Service, Pacific Northwest Research StationCorvallis,
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Kroese, D. R.
, 
T. W. Walters

T. W. Walters

Walters Ag ResearchAnacortes,
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Walters, T. W.
, 
J. E. Weiland

J. E. Weiland

USDA Agricultural Research Service, Horticultural Crops Research UnitCorvallis,
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Weiland, J. E.
 and 
I. A. Zasada

I. A. Zasada

USDA Agricultural Research Service, Horticultural Crops Research UnitCorvallis,
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Zasada, I. A.
  
Sep 24, 2025
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Article Category: Research Paper
Published Online: Sep 24, 2025
Received: Jan 02, 2025
DOI: https://doi.org/10.2478/jofnem-2025-0038
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© 2025 J. B. Contina et al., published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.

Figure 1:

Layout schematic of a 6 × 10 grid sampling of contiguous quadrats (20 m × 45 m) in the commercial red raspberry production field WA-2 located in Lynden, WA. From the center of each quadrat (red dot), above-ground disease severity was visually assessed and rated; soil and root samples were collected to quantify Phytophthora rubi, Pratylenchus penetrans, and soil texture (sand, silt, clay); and surface field elevations were also recorded at each sampling point.
Layout schematic of a 6 × 10 grid sampling of contiguous quadrats (20 m × 45 m) in the commercial red raspberry production field WA-2 located in Lynden, WA. From the center of each quadrat (red dot), above-ground disease severity was visually assessed and rated; soil and root samples were collected to quantify Phytophthora rubi, Pratylenchus penetrans, and soil texture (sand, silt, clay); and surface field elevations were also recorded at each sampling point.

Figure 2:

LISA for disease rating, Phytophthora rubi DNA concentrations in roots, and Pratylenchus penetrans densities in roots and soil in four commercial red raspberry production fields in Oregon (OR-1 and OR-2) and Washington (WA-1 and WA-2). A positive value for the local Moran’s I indicates that a sampling point has a similar attribute value to the neighboring points (clusters), and a negative value indicates dissimilar attribute values in the local neighborhood (outliers). Solid-filled black shapes indicate the significance of the local Moran’s I coefficient at P < 0.05. LISA, local indicators of spatial association.
LISA for disease rating, Phytophthora rubi DNA concentrations in roots, and Pratylenchus penetrans densities in roots and soil in four commercial red raspberry production fields in Oregon (OR-1 and OR-2) and Washington (WA-1 and WA-2). A positive value for the local Moran’s I indicates that a sampling point has a similar attribute value to the neighboring points (clusters), and a negative value indicates dissimilar attribute values in the local neighborhood (outliers). Solid-filled black shapes indicate the significance of the local Moran’s I coefficient at P < 0.05. LISA, local indicators of spatial association.

Figure 3:

Moran scatterplot for disease rating, Phytophthora rubi DNA concentrations in roots, and Pratylenchus penetrans densities in roots and soil in four commercial red raspberry production fields in Oregon (OR-1 and OR-2) and Washington (WA-1 and WA-2). The scatterplot is characterized by four quadrants corresponding to the four types of spatial association and illustrates relationships between an individual sampling value (standardized observation) and the average values at neighboring sampling points (standardized spatial lags). The lower left and upper right quadrants indicate spatial clustering or PSA. The lower left quadrant is characterized by low values for both the spatial lags and the observations (Low–Low), and in the upper right quadrant, there are high values for both the spatial lags and the observations (High–High). The upper left (Low–High) and lower right (High–Low) quadrants indicate spatial outliers or NSA. The slope of each regression line corresponds to the Moran’s I coefficients listed in Table 2. NSA, negative spatial association; PSA, positive spatial association.
Moran scatterplot for disease rating, Phytophthora rubi DNA concentrations in roots, and Pratylenchus penetrans densities in roots and soil in four commercial red raspberry production fields in Oregon (OR-1 and OR-2) and Washington (WA-1 and WA-2). The scatterplot is characterized by four quadrants corresponding to the four types of spatial association and illustrates relationships between an individual sampling value (standardized observation) and the average values at neighboring sampling points (standardized spatial lags). The lower left and upper right quadrants indicate spatial clustering or PSA. The lower left quadrant is characterized by low values for both the spatial lags and the observations (Low–Low), and in the upper right quadrant, there are high values for both the spatial lags and the observations (High–High). The upper left (Low–High) and lower right (High–Low) quadrants indicate spatial outliers or NSA. The slope of each regression line corresponds to the Moran’s I coefficients listed in Table 2. NSA, negative spatial association; PSA, positive spatial association.

Figure 4:

LISA for soil texture (sand, silt, and clay) and field elevation in four commercial red raspberry production fields in Oregon (OR-1 and OR-2) and Washington (WA-1 and WA-2). A positive value for the local Moran’s I indicates that a sampling point has a similar attribute value to the neighboring points (clusters), and a negative value indicates dissimilar attribute values in the local neighborhood (outliers). Solid-filled black shapes indicate the significance of the local Moran’s I coefficient at P < 0.05. LISA, local indicators of spatial association.
LISA for soil texture (sand, silt, and clay) and field elevation in four commercial red raspberry production fields in Oregon (OR-1 and OR-2) and Washington (WA-1 and WA-2). A positive value for the local Moran’s I indicates that a sampling point has a similar attribute value to the neighboring points (clusters), and a negative value indicates dissimilar attribute values in the local neighborhood (outliers). Solid-filled black shapes indicate the significance of the local Moran’s I coefficient at P < 0.05. LISA, local indicators of spatial association.

Figure 5:

Moran scatterplot for soil texture (sand, silt, and clay) and field elevation in four commercial red raspberry production fields in Oregon (OR-1 and OR-2) and Washington (WA-1 and WA-2). The scatterplot is characterized by four quadrants corresponding to the four types of spatial association and illustrates relationships between an individual sampling value (standardized observation) and the average values at neighboring sampling points (standardized spatial lags). The lower left and upper right quadrants indicate spatial clustering or PSA. The lower left quadrant is characterized by low values for both the spatial lags and the observations (Low–Low), and in the upper right quadrant, there are high values for both the spatial lags and the observations (High–High). The upper left (Low–High) and lower right (High–Low) quadrants indicate spatial outliers or NSA. The slope of each regression line corresponds to the Moran’s I coefficients listed in Table 2. NSA, negative spatial association; PSA, positive spatial association.
Moran scatterplot for soil texture (sand, silt, and clay) and field elevation in four commercial red raspberry production fields in Oregon (OR-1 and OR-2) and Washington (WA-1 and WA-2). The scatterplot is characterized by four quadrants corresponding to the four types of spatial association and illustrates relationships between an individual sampling value (standardized observation) and the average values at neighboring sampling points (standardized spatial lags). The lower left and upper right quadrants indicate spatial clustering or PSA. The lower left quadrant is characterized by low values for both the spatial lags and the observations (Low–Low), and in the upper right quadrant, there are high values for both the spatial lags and the observations (High–High). The upper left (Low–High) and lower right (High–Low) quadrants indicate spatial outliers or NSA. The slope of each regression line corresponds to the Moran’s I coefficients listed in Table 2. NSA, negative spatial association; PSA, positive spatial association.

Figure 6:

Experimental variogram graph for assessing the spatial structure of disease rating, Phytophthora rubi DNA concentrations in roots, and Pratylenchus penetrans densities in roots and soil in four commercial red raspberry production fields in Oregon (OR-1 and OR-2) and Washington (WA-1 and WA-2). The x-axis shows the distance lag, which is created by plotting the average variability between pairs of sampling points, and the y-axis shows the calculated value of the semivariance, where a greater value indicates less spatial correlation between pairs of points. The variogram model type and fitting parameters for each commercial field are listed in Table 3.
Experimental variogram graph for assessing the spatial structure of disease rating, Phytophthora rubi DNA concentrations in roots, and Pratylenchus penetrans densities in roots and soil in four commercial red raspberry production fields in Oregon (OR-1 and OR-2) and Washington (WA-1 and WA-2). The x-axis shows the distance lag, which is created by plotting the average variability between pairs of sampling points, and the y-axis shows the calculated value of the semivariance, where a greater value indicates less spatial correlation between pairs of points. The variogram model type and fitting parameters for each commercial field are listed in Table 3.

Figure 7:

Experimental variogram graph for assessing the spatial structure of soil texture (sand, silt, and clay) and field elevation in four commercial red raspberry production fields in Oregon (OR-1 and OR-2) and Washington (WA-1 and WA-2). The x-axis shows the distance lag, which is created by plotting the average variability between pairs of sampling points, and the y-axis shows the calculated value of the semivariance, where a greater value indicates less spatial correlation between pairs of points. The variogram model type and fitting parameters for each commercial field are listed in Table 3.
Experimental variogram graph for assessing the spatial structure of soil texture (sand, silt, and clay) and field elevation in four commercial red raspberry production fields in Oregon (OR-1 and OR-2) and Washington (WA-1 and WA-2). The x-axis shows the distance lag, which is created by plotting the average variability between pairs of sampling points, and the y-axis shows the calculated value of the semivariance, where a greater value indicates less spatial correlation between pairs of points. The variogram model type and fitting parameters for each commercial field are listed in Table 3.

Figure 8:

Directional experimental variogram graph for assessing potential directional variations in the spatial structure of disease rating, Phytophthora rubi DNA concentrations in roots, and Pratylenchus penetrans densities in roots and soil in four commercial red raspberry production fields in Oregon (OR-1 and OR-2) and Washington (WA-1 and WA-2). Directional angles used for the graph include 0° (North–South), 45° (Northeast–Southwest), 90° (East–West), and 135° (Southeast–Northwest). The overlapping of all the angle point lines indicates no directional variations in the spatial structure of the attribute values (isotropy), while major gaps between the angle point lines indicate the presence of directional trends (anisotropy).
Directional experimental variogram graph for assessing potential directional variations in the spatial structure of disease rating, Phytophthora rubi DNA concentrations in roots, and Pratylenchus penetrans densities in roots and soil in four commercial red raspberry production fields in Oregon (OR-1 and OR-2) and Washington (WA-1 and WA-2). Directional angles used for the graph include 0° (North–South), 45° (Northeast–Southwest), 90° (East–West), and 135° (Southeast–Northwest). The overlapping of all the angle point lines indicates no directional variations in the spatial structure of the attribute values (isotropy), while major gaps between the angle point lines indicate the presence of directional trends (anisotropy).

Figure 9:

Directional experimental variogram graph for assessing potential directional variations in the spatial structure of soil texture (sand, silt, and clay) and field elevation in four commercial red raspberry production fields in Oregon (OR-1 and OR-2) and Washington (WA-1 and WA-2). Directional angles used for the graph include 0° (North–South), 45° (Northeast–Southwest), 90° (East–West), and 135° (Southeast–Northwest). The overlapping of all the angle point lines indicates no directional variations in the spatial structure of the attribute values (isotropy), while major gaps between the angle point lines indicate the presence of directional trends (anisotropy).
Directional experimental variogram graph for assessing potential directional variations in the spatial structure of soil texture (sand, silt, and clay) and field elevation in four commercial red raspberry production fields in Oregon (OR-1 and OR-2) and Washington (WA-1 and WA-2). Directional angles used for the graph include 0° (North–South), 45° (Northeast–Southwest), 90° (East–West), and 135° (Southeast–Northwest). The overlapping of all the angle point lines indicates no directional variations in the spatial structure of the attribute values (isotropy), while major gaps between the angle point lines indicate the presence of directional trends (anisotropy).

Figure 10:

Kriging density graph for comparing the distribution of interpolated values of disease rating, Phytophthora rubi DNA concentrations in roots, and Pratylenchus penetrans densities in roots and soil across four commercial red raspberry production fields in Oregon (OR-1 and OR-2) and Washington (WA-1 and WA-2). The x-axis shows the attribute values of the variable, and the y-axis shows the proportion value assigned to each range of the attribute values.
Kriging density graph for comparing the distribution of interpolated values of disease rating, Phytophthora rubi DNA concentrations in roots, and Pratylenchus penetrans densities in roots and soil across four commercial red raspberry production fields in Oregon (OR-1 and OR-2) and Washington (WA-1 and WA-2). The x-axis shows the attribute values of the variable, and the y-axis shows the proportion value assigned to each range of the attribute values.

Figure 11:

Kriging density graph for comparing the distribution of interpolated values of soil texture (sand, silt, and clay) and field elevation across four commercial red raspberry production fields in Oregon (OR-1 and OR-2) and Washington (WA-1 and WA-2). The x-axis shows the attribute values of the variable, and the y-axis shows the proportion value assigned to each range of the attribute values.
Kriging density graph for comparing the distribution of interpolated values of soil texture (sand, silt, and clay) and field elevation across four commercial red raspberry production fields in Oregon (OR-1 and OR-2) and Washington (WA-1 and WA-2). The x-axis shows the attribute values of the variable, and the y-axis shows the proportion value assigned to each range of the attribute values.

Figure 12:

Spatial distribution of disease rating across four commercial red raspberry production fields in Oregon (OR-1 and OR-2) and Washington (WA-1 and WA-2). The ordinary kriging was used as a probabilistic interpolator to predict disease ratings at one or more unsampled points. Northing divides the map from north to south and Easting from west to east. Northing and Easting are grid references and are expressed in meters.
Spatial distribution of disease rating across four commercial red raspberry production fields in Oregon (OR-1 and OR-2) and Washington (WA-1 and WA-2). The ordinary kriging was used as a probabilistic interpolator to predict disease ratings at one or more unsampled points. Northing divides the map from north to south and Easting from west to east. Northing and Easting are grid references and are expressed in meters.

Figure 13:

Spatial distribution of Phytophthora rubi DNA concentrations in roots across four commercial red raspberry production fields in Oregon (OR-1 and OR-2) and Washington (WA-1 and WA-2). The ordinary kriging was used as a probabilistic interpolator to predict P. rubi DNA in roots at one or more unsampled points. Northing divides the map from north to south and Easting from west to east. Northing and Easting are grid references and are expressed in meters.
Spatial distribution of Phytophthora rubi DNA concentrations in roots across four commercial red raspberry production fields in Oregon (OR-1 and OR-2) and Washington (WA-1 and WA-2). The ordinary kriging was used as a probabilistic interpolator to predict P. rubi DNA in roots at one or more unsampled points. Northing divides the map from north to south and Easting from west to east. Northing and Easting are grid references and are expressed in meters.

Figure 14:

Spatial distribution of Pratylenchus penetrans densities in roots across four commercial red raspberry production fields in Oregon (OR-1 and OR-2) and Washington (WA-1 and WA-2). The ordinary kriging was used as a probabilistic interpolator to predict P. penetrans densities in roots at one or more unsampled points. Northing divides the map from north to south and Easting from west to east. Northing and Easting are grid references and are expressed in meters.
Spatial distribution of Pratylenchus penetrans densities in roots across four commercial red raspberry production fields in Oregon (OR-1 and OR-2) and Washington (WA-1 and WA-2). The ordinary kriging was used as a probabilistic interpolator to predict P. penetrans densities in roots at one or more unsampled points. Northing divides the map from north to south and Easting from west to east. Northing and Easting are grid references and are expressed in meters.

Figure 15:

Spatial distribution of Pratylenchus penetrans densities in soil across four commercial red raspberry production fields in Oregon (OR-1 and OR-2) and Washington (WA-1 and WA-2). The ordinary kriging was used as a probabilistic interpolator to predict P. penetrans in the soil at one or more unsampled points. Northing divides the map from north to south and Easting from west to east. Northing and Easting are grid references and are expressed in meters.
Spatial distribution of Pratylenchus penetrans densities in soil across four commercial red raspberry production fields in Oregon (OR-1 and OR-2) and Washington (WA-1 and WA-2). The ordinary kriging was used as a probabilistic interpolator to predict P. penetrans in the soil at one or more unsampled points. Northing divides the map from north to south and Easting from west to east. Northing and Easting are grid references and are expressed in meters.

Figure 16:

Spatial distribution of the percentage of sand across four commercial red raspberry production fields in Oregon (OR-1 and OR-2) and Washington (WA-1 and WA-2). The ordinary kriging was used as a probabilistic interpolator to predict the percentage of sand at one or more unsampled points. Northing divides the map from north to south and Easting from west to east. Northing and Easting are grid references and are expressed in meters.
Spatial distribution of the percentage of sand across four commercial red raspberry production fields in Oregon (OR-1 and OR-2) and Washington (WA-1 and WA-2). The ordinary kriging was used as a probabilistic interpolator to predict the percentage of sand at one or more unsampled points. Northing divides the map from north to south and Easting from west to east. Northing and Easting are grid references and are expressed in meters.

Figure 17:

Spatial distribution of the percentage of silt across four commercial red raspberry production fields in Oregon (OR-1 and OR-2) and Washington (WA-1 and WA-2). The ordinary kriging was used as a probabilistic interpolator to predict the percentage of silt at one or more unsampled points. Northing divides the map from north to south and Easting from west to east. Northing and Easting are grid references and are expressed in meters.
Spatial distribution of the percentage of silt across four commercial red raspberry production fields in Oregon (OR-1 and OR-2) and Washington (WA-1 and WA-2). The ordinary kriging was used as a probabilistic interpolator to predict the percentage of silt at one or more unsampled points. Northing divides the map from north to south and Easting from west to east. Northing and Easting are grid references and are expressed in meters.

Figure 18:

Spatial distribution of the percentage of clay across four commercial red raspberry production fields in Oregon (OR-1 and OR-2) and Washington (WA-1 and WA-2). The ordinary kriging was used as a probabilistic interpolator to predict the percentage of clay at one or more unsampled points. Northing divides the map from north to south and Easting from west to east. Northing and Easting are grid references and are expressed in meters.
Spatial distribution of the percentage of clay across four commercial red raspberry production fields in Oregon (OR-1 and OR-2) and Washington (WA-1 and WA-2). The ordinary kriging was used as a probabilistic interpolator to predict the percentage of clay at one or more unsampled points. Northing divides the map from north to south and Easting from west to east. Northing and Easting are grid references and are expressed in meters.

Figure 19:

Spatial distribution of field elevation across four commercial red raspberry production fields in Oregon (OR-1 and OR-2) and Washington (WA-1 and WA-2). The ordinary kriging was used as a probabilistic interpolator to predict field elevation at one or more unsampled points. Northing divides the map from north to south and Easting from west to east. Northing and Easting are grid references and are expressed in meters.
Spatial distribution of field elevation across four commercial red raspberry production fields in Oregon (OR-1 and OR-2) and Washington (WA-1 and WA-2). The ordinary kriging was used as a probabilistic interpolator to predict field elevation at one or more unsampled points. Northing divides the map from north to south and Easting from west to east. Northing and Easting are grid references and are expressed in meters.

Coefficient estimates and SE for the OLS, SLM, SDM, SEM, CAR, and SARMA multiple regression models and associated VIF and P values for Phytophthora rubi DNA concentrations in roots regressed against soil texture (sand, silt, and clay) and elevation in four commercial red raspberry production fields in Oregon (OR-1 and OR-2) and Washington (WA-1 and WA-2)_

Field Variablesa OLS SLM SDM SEM CAR SARMA
Estimate SE P VIF Model Estimate SE P Model Estimate SE P Model Estimate SE P Model Estimate SE P Model Estimate SE P Model
OR-1 Intercept 170.82 176.79 0.34 … … 162.61 168.89 0.34 … 630.02 1,137.13 0.58 … 206.50 171.30 0.23 … 165.21 169.63 0.33 … 352.59 174.37 0.04 …
Sand −90.38 93.71 0.34 834 … −86.08 89.52 0.34 … −58.62 85.97 0.50 … −109.83 90.71 0.23 … −87.16 89.91 0.33 … −190.22 91.85 0.04 …
Silt −106.57 106.04 0.32 672 … −101.50 101.30 0.32 …. −69.18 97.38 0.48 …. −129.10 102.67 0.21 …. −103.13 101.73 0.31 …. −219.04 104.35 0.04 ….
Clay −71.96 84.94 0.40 371 …. −68.82 81.13 0.40 …. −43.99 78.40 0.57 …. −86.67 82.50 0.29 …. −69.55 81.53 0.39 …. −150.11 84.75 0.08 ….
Elevation 0.14 0.21 0.52 1 …. 0.14 0.21 0.51 …. −0.27 0.56 0.63 …. 0.18 0.16 0.26 …. 0.12 0.20 0.55 …. 0.34 0.07 <0.001 ….
P …. …. …. …. 0.12 …. …. …. 0.61 …. …. …. 0.002 …. …. …. 0.52 …. …. …. 0.81 …. …. …. <0.001
R2 …. …. …. …. 0.12 …. …. …. 0.13 …. …. …. 0.31 …. …. …. 0.13 …. …. …. 0.12 …. …. …. 0.27
ρ …. …. …. …. …. …. …. …. 0.16 …. …. …. −1.61 …. …. …. …. …. …. …. …. …. …. …. ….
λ …. …. …. …. …. …. …. …. …. …. …. …. …. …. …. …. −0.45 …. …. …. −0.11 …. …. …. −1.00
AIC …. …. …. …. 188.75 …. …. …. 190.52 …. …. …. 184.66 …. …. …. 190.33 …. …. …. 190.69 …. …. …. 179.81
OR-2 Intercept 3.57 5.96 0.55 …. …. 3.77 5.69 0.51 …. 64.68 34.00 0.06 …. 3.71 5.71 0.52 …. 3.81 5.71 0.50 …. 3.75 5.71 0.51 ….
Sand −3.33 3.36 0.33 7 …. −3.35 3.21 0.30 …. −4.27 2.96 0.15 …. −3.29 3.21 0.30 …. −3.31 3.21 0.30 …. −3.25 3.20 0.31 ….
Silt −1.35 2.73 0.62 4 …. −1.39 2.61 0.59 …. −0.90 2.37 0.71 …. −1.35 2.62 0.61 …. −1.33 2.62 0.61 …. −1.33 2.62 0.61 ….
Clay −1.74 4.84 0.72 4 …. −1.95 4.63 0.67 …. −4.48 4.31 0.30 …. −2.11 4.64 0.65 …. −2.24 4.64 0.63 …. −2.28 4.65 0.62 ….
Elevation 0.70 0.43 0.11 1 …. 0.72 0.41 0.08 …. 0.99 0.43 0.02 …. 0.74 0.41 0.07 …. 0.71 0.41 0.08 …. 0.77 0.41 0.06 ….
P …. …. …. …. 0.20 …. …. …. 0.66 …. …. …. 0.08 …. …. …. 0.75 …. …. …. 0.80 …. …. …. 0.70
R2 …. …. …. …. 0.10 …. …. …. 0.10 …. …. …. 0.26 …. …. …. 0.10 …. …. …. 0.10 …. …. …. 0.10
ρ …. …. …. …. …. …. …. …. −0.19 …. …. …. −0.95 …. …. …. …. …. …. …. …. …. …. …. ….
λ …. …. …. …. …. …. …. …. …. …. …. …. …. …. …. …. −0.16 …. …. …. −0.21 …. …. …. −0.22
AIC …. …. …. …. 140.22 …. …. …. 142.03 …. …. …. 138.41 …. …. …. 142.12 …. …. …. 142.16 …. …. …. 142.07
WA-1 Intercept 377.42 178.96 0.04 …. …. 366.48 171.24 0.03 …. 2,253.52 928.36 0.02 …. 433.58 172.67 0.01 …. 394.63 172.45 0.02 …. 623.12 168.46 <0.001 ….
Sand −234.25 110.15 0.04 2,273 …. −227.56 105.39 0.03 …. −307.03 109.63 0.01 …. −269.09 106.27 0.01 …. −245.12 106.14 0.02 …. −385.75 103.65 <0.001 ….
Silt −216.77 102.23 0.04 1,513 …. −210.62 97.81 0.03 …. −283.21 101.50 0.01 …. −249.03 98.70 0.01 …. −226.96 98.56 0.02 …. −359.67 96.37 <0.001 ….
Clay −136.93 69.69 0.05 234 …. −132.92 66.68 0.05 …. −182.98 69.40 0.01 …. −157.58 67.22 0.02 …. −142.08 67.14 0.03 …. −226.26 65.59 <0.001 ….
Elevation 0.16 0.59 0.79 2 …. 0.23 0.59 0.70 …. 0.61 0.96 0.53 …. 0.16 0.53 0.76 …. 0.14 0.54 0.80 …. 0.03 0.47 0.95 ….
P …. …. …. …. 0.06 …. …. …. 0.79 …. …. …. 0.32 …. …. …. 0.56 …. …. …. 0.64 …. …. …. <0.001
R2 …. …. …. …. 0.15 …. …. …. 0.15 …. …. …. 0.26 …. …. …. 0.16 …. …. …. 0.16 …. …. …. 0.33
ρ …. …. …. …. …. …. …. …. 0.10 …. …. …. −0.56 …. …. …. …. …. …. …. …. …. …. …. ….
λ …. …. …. …. …. …. …. …. …. …. …. …. …. …. …. …. −0.35 …. …. …. −0.47 …. …. …. −1.00
AIC …. …. …. …. 205.23 …. …. …. 207.16 …. …. …. 207.30 …. …. …. 206.89 …. …. …. 207.01 …. …. …. 192.91
WA-2 Intercept 31.13 81.32 0.70 …. …. 55.75 74.27 0.45 …. −1,283.90 435.02 0.003 …. 81.42 72.40 0.26 …. 73.91 75.04 0.32 …. 81.12 68.18 0.23 ….
Sand −13.68 46.87 0.77 918 …. −29.74 42.81 0.49 …. 1.43 45.08 0.97 …. −44.84 41.77 0.28 …. −39.77 43.26 0.36 …. −45.34 39.32 0.25 ….
Silt −20.09 48.30 0.68 740 …. −35.34 44.11 0.42 …. −3.13 46.18 0.95 …. −50.61 43.02 0.24 …. −46.71 44.59 0.29 …. −50.56 40.54 0.21 ….
Clay −14.28 35.07 0.69 150 …. −22.02 32.03 0.49 …. 7.21 33.75 0.83 …. −31.23 31.03 0.31 …. −29.04 32.27 0.37 …. −29.98 29.13 0.30 ….
Elevation 0.22 0.41 0.60 1 …. 0.07 0.38 0.86 …. 0.36 0.66 0.58 …. 0.21 0.55 0.71 …. 0.47 0.49 0.34 …. 0.30 0.59 0.61 ….
P …. …. …. …. 0.01 …. …. …. 0.04 …. …. …. 0.72 …. …. …. 0.05 …. …. …. 0.16 …. …. …. 0.01
R2 …. …. …. …. 0.21 …. …. …. 0.26 …. …. …. 0.39 …. …. …. 0.26 …. …. …. 0.24 …. …. …. 0.29
ρ …. …. …. …. …. …. …. …. 0.56 …. …. …. −0.17 …. …. …. …. …. …. …. …. …. …. …. ….
λ …. …. …. …. …. …. …. …. …. …. …. …. …. …. …. …. 0.70 …. …. …. 0.76 …. …. …. 1.82
AIC …. …. …. …. 174.41 …. …. …. 172.22 …. …. …. 168.70 …. …. …. 172.43 …. …. …. 174.42 …. …. …. 170.42

Global Moran’s I test for spatial autocorrelation in the residuals for Phytophthora rubi DNA concentrations in roots, Pratylenchus penetrans densites in root and soil regressed against soil texture (sand, silt, and clay), and field elevation in four commercial red raspberry production fields in Oregon (OR-1 and OR-2) and Washington (WA-1 and WA-2)_

Field Predicted Moran’s I coefficienta P-valueb
OR-1 P. rubi DNA in root −0.018 0.29
P. penetrans in root −0.026 0.39
P. penetrans in soil −0.030 0.45
OR-2 P. rubi DNA in root −0.011 0.39
P. penetrans in root −0.016 0.44
P. penetrans in soil 0.046 0.03
WA-1 P. rubi DNA in root −0.017 0.36
P. penetrans in root −0.001 0.19
P. penetrans in soil 0.100 <0.001
WA-2 P. rubi DNA in root 0.064 <0.001
P. penetrans in root −0.060 0.78
P. penetrans in soil 0.030 0.01

Coefficient estimates and SE for the OLS, SLM, SDM, SEM, CAR, and SARMA multiple regression models and associated VIF and P values for Pratylenchus penetrans densites in roots regressed against soil texture (sand, silt, and clay) and elevation in four commercial red raspberry production fields in Oregon (OR-1 and OR-2) and Washington (WA-1 and WA-2)_

Field Variablesa OLS SLM SDM SEM CAR SARMA
Estimate SE P VIF Model Estimate SE P Model Estimate SE P Model Estimate SE P Model Estimate SE P Model Estimate SE P Model
OR-1 Intercept 22.66 119.13 0.85 …. …. 22.73 114.06 0.84 …. 973.21 805.65 0.23 …. 29.70 115.29 0.80 …. 28.07 114.95 0.80 …. −0.03 111.84 0.99 ….
Sand −12.03 63.15 0.85 834 …. −12.05 60.46 0.84 …. −57.46 62.92 0.36 …. −15.45 61.03 0.80 …. −14.49 60.60 0.81 …. 1.24 58.91 0.98 ….
Silt −10.88 71.46 0.88 672 …. −10.86 68.42 0.87 …. −62.92 71.27 0.38 …. −14.67 69.08 0.83 …. −13.61 68.92 0.84 …. 3.39 66.93 0.96 ….
Clay −14.89 57.24 0.80 371 …. −15.03 54.80 0.78 …. −55.89 57.40 0.33 …. −19.50 55.57 0.73 …. −18.83 55.31 0.73 …. −6.89 54.35 0.90 ….
Elevation 0.10 0.14 0.50 1 …. 0.11 0.14 0.44 …. −0.34 0.41 0.42 …. 0.12 0.10 0.22 …. 0.09 0.12 0.46 …. 0.15 0.05 0.002 ….
P …. …. …. …. 0.37 …. …. …. 0.87 …. …. …. 0.14 …. …. …. 0.35 …. …. …. 0.52 …. …. …. <0.001
R2 …. …. …. …. 0.07 …. …. …. 0.07 …. …. …. 0.18 …. …. …. 0.09 …. …. …. 0.08 …. …. …. 0.31
ρ …. …. …. …. …. …. …. …. −0.07 …. …. …. −0.88 …. …. …. …. …. …. …. …. …. …. …. ….
λ …. …. …. …. …. …. …. …. …. …. …. …. …. …. …. …. −0.60 …. …. …. −0.58 …. …. …. −0.99
AIC …. …. …. …. 141.38 …. …. …. 143.35 …. …. …. 143.80 …. …. …. 142.50 …. …. …. 142.96 …. …. …. 125.53
OR-2 Intercept 3.49 10.82 0.75 …. …. 3.60 10.36 0.73 …. 25.86 63.55 0.68 …. 3.27 10.36 0.75 …. 3.77 10.36 0.72 …. 3.34 10.35 0.75 ….
Sand 0.35 6.10 0.95 7 …. 0.44 5.84 0.94 …. −1.02 5.62 0.86 …. 0.83 5.81 0.89 …. 0.60 5.83 0.92 …. 1.23 5.76 0.83 ….
Silt −3.42 4.96 0.49 4 …. −3.41 4.74 0.47 …. −3.60 4.49 0.42 …. −3.35 4.76 0.48 …. −3.38 4.75 0.48 …. −3.45 4.77 0.47 ….
Clay 1.80 8.80 0.84 4 …. 1.71 8.42 0.84 …. −0.04 8.11 0.99 …. 1.55 8.43 0.85 …. 0.99 8.43 0.91 …. 1.10 8.46 0.90 ….
Elevation −0.92 0.79 0.25 1 …. −0.90 0.75 0.23 …. −1.18 0.80 0.14 …. −0.88 0.74 0.24 …. −0.94 0.75 0.21 …. −0.88 0.72 0.22 ….
P …. …. …. …. 0.49 …. …. …. 0.80 …. …. …. 0.19 …. …. …. 0.66 …. …. …. 0.77 …. …. …. 0.51
R2 …. …. …. …. 0.06 …. …. …. 0.06 …. …. …. 0.17 …. …. …. 0.06 …. …. …. 0.06 …. …. …. 0.07
ρ …. …. …. …. …. …. …. …. −0.10 …. …. …. −0.64 …. …. …. …. …. …. …. …. …. …. …. ….
λ …. …. …. …. …. …. …. …. …. …. …. …. …. …. …. …. −0.22 …. …. …. −0.18 …. …. …. −0.43
AIC …. …. …. …. 211.88 …. …. …. 213.82 …. …. …. 214.17 …. …. …. 213.68 …. …. …. 213.80 …. …. …. 213.44
WA-1 Intercept −76.26 100.24 0.45 …. …. −77.12 95.99 0.42 …. 179.96 501.46 0.72 …. −76.26 96.02 0.43 …. −76.81 96.01 0.42 …. −76.27 96.05 0.43 ….
Sand 46.61 61.70 0.45 2,272 …. 47.17 59.08 0.42 …. 36.20 62.66 0.56 …. 46.62 59.10 0.43 …. 46.94 59.09 0.43 …. 46.62 59.12 0.43 ….
Silt 44.13 57.26 0.44 1,513 …. 44.59 54.83 0.42 …. 33.18 58.03 0.57 …. 44.12 54.85 0.42 …. 44.43 54.84 0.42 …. 44.11 54.87 0.42 ….
Clay 29.62 39.04 0.45 234 …. 30.00 37.38 0.42 …. 22.51 39.73 0.57 …. 29.63 37.39 0.43 …. 29.86 37.39 0.42 …. 29.64 37.41 0.43 ….
Elevation 0.39 0.33 0.24 2 …. 0.40 0.32 0.22 …. 0.23 0.56 0.68 …. 0.39 0.32 0.21 …. 0.39 0.32 0.21 …. 0.39 0.32 0.21 ….
P …. …. …. …. 0.58 …. …. …. 0.88 …. …. …. 0.57 …. …. …. 0.98 …. …. …. 0.99 …. …. …. 0.97
R2 …. …. …. …. 0.05 …. …. …. 0.05 …. …. …. 0.12 …. …. …. 0.05 …. …. …. 0.05 …. …. …. 0.05
ρ …. …. …. …. …. …. …. …. −0.07 …. …. …. −0.25 …. …. …. …. …. …. …. …. …. …. …. ….
λ …. …. …. …. …. …. …. …. …. …. …. …. …. …. …. …. −0.01 …. …. …. −0.02 …. …. …. −0.02
AIC …. …. …. …. 135.68 …. …. …. 137.66 …. …. …. 141.14 …. …. …. 137.68 …. …. …. 137.68 …. …. …. 137.68
WA-2 Intercept −69.62 92.71 0.46 …. …. −80.33 88.63 0.36 …. −555.77 494.67 0.26 …. −85.09 83.81 0.31 …. −105.32 88.00 0.23 …. −102.97 81.30 0.20 ….
Sand 42.80 53.43 0.43 918 …. 49.75 51.18 0.33 …. 49.42 51.62 0.34 …. 52.09 48.36 0.28 …. 63.01 50.72 0.21 …. 62.42 46.93 0.18 ….
Silt 43.95 55.07 0.43 740 …. 50.55 52.68 0.34 …. 52.80 52.88 0.32 …. 52.72 49.63 0.29 …. 65.84 52.22 0.21 …. 63.45 48.10 0.19 ….
Clay 23.00 39.98 0.57 150 …. 26.83 38.16 0.48 …. 31.98 38.73 0.41 …. 29.20 36.41 0.42 …. 37.54 38.05 0.32 …. 36.09 35.40 0.31 ….
Elevation 0.81 0.47 0.09 1 …. 1 0.47 0.03 …. 0.24 0.77 0.75 …. 1.04 0.26 <0.001 …. 0.81 0.37 0.03 …. 1.19 0.17 <0.001 ….
P …. …. …. …. 0.03 …. …. …. 0.45 …. …. …. 0.02 …. …. …. 0.04 …. …. …. 0.23 …. …. …. <0.001
R2 …. …. …. …. 0.18 …. …. …. 0.19 …. …. …. 0.29 …. …. …. 0.24 …. …. …. 0.20 …. …. …. 0.42
ρ …. …. …. …. …. …. …. …. −0.29 …. …. …. −1.29 …. …. …. …. …. …. …. …. …. …. …. ….
λ …. …. …. …. …. …. …. …. …. …. …. …. …. …. …. …. −1.25 …. …. …. −0.87 …. …. …. −0.99
AIC …. …. …. …. 190.14 …. …. …. 191.57 …. …. …. 191.06 …. …. …. 187.75 …. …. …. 190.73 …. …. …. 170.95

Coefficient estimates and SE for the OLS, SLM, SDM, SEM, CAR, and SARMA multiple regression models and associated VIF and P values for Pratylenchus penetrans in soil regressed against soil texture (sand, silt, and clay) and elevation in four commercial red raspberry production fields in Oregon (OR-1 and OR-2) and Washington (WA-1 and WA-2)_

Field Variablesa OLS SLM SDM SEM CAR SARMA
Estimate SE P VIF Model Estimate SE P Model Estimate SE P Model Estimate SE P Model Estimate SE P Model Estimate SE P Model
OR-1 Intercept −36.41 148.53 0.80 …. …. −37.35 142.21 0.79 …. 1,044.05 848.43 0.22 …. −68.40 143.65 0.63 …. −52.73 143.26 0.71 …. −71.80 144.06 0.62 ….
Sand 19.96 78.73 0.80 834 …. 20.50 75.38 0.78 …. −70.87 63.18 0.26 …. 38.28 76.03 0.61 …. 29.76 75.90 0.69 …. 39.88 76.26 0.60 ….
Silt 25.04 89.09 0.78 672 …. 25.66 85.30 0.76 …. −78.09 71.53 0.27 …. 45.24 86.07 0.60 …. 35.89 85.89 0.68 …. 47.07 86.33 0.59 ….
Clay 12.55 71.36 0.86 371 …. 12.91 68.32 0.85 …. −70.68 57.59 0.22 …. 24.91 69.27 0.72 …. 17.65 68.94 0.80 …. 27.04 69.43 0.70 ….
Elevation 0.13 0.18 0.48 1 …. 0.13 0.18 0.46 …. 0.82 0.42 0.05 …. 0.06 0.12 0.61 …. 0.04 0.15 0.77 …. 0.08 0.12 0.53 ….
P …. …. …. …. 0.36 …. …. …. 0.92 …. …. …. <0.001 …. …. …. 0.31 …. …. …. 0.48 …. …. …. 0.37
R2 …. …. …. …. 0.07 …. …. …. 0.07 …. …. …. 0.42 …. …. …. 0.09 …. …. …. 0.08 …. …. …. 0.09
ρ …. …. …. …. …. …. …. …. −0.03 …. …. …. −1.95 …. …. …. …. …. …. …. …. …. …. …. ….
λ …. …. …. …. …. …. …. …. …. …. …. …. …. …. …. …. −0.67 …. …. …. −0.60 …. …. …. −0.43
AIC …. …. …. …. 167.85 …. …. …. 169.84 …. …. …. 149.76 …. …. …. 168.8 …. …. …. 169.35 …. …. …. 169.04
OR-2 Intercept 0.34 5.17 0.95 …. …. −0.45 4.92 0.93 …. 15.33 31.00 0.62 …. −0.02 4.87 0.99 …. 0.03 4.94 0.99 …. −0.01 4.88 0.99 ….
Sand 0.76 2.92 0.80 7 …. 0.87 2.76 0.75 …. −0.32 2.74 0.91 …. 0.82 2.77 0.77 …. 0.69 2.79 0.80 …. 0.79 2.77 0.78 ….
Silt −0.36 2.37 0.88 4 …. −0.15 2.24 0.94 …. −1.28 2.21 0.56 …. −0.02 2.22 0.99 …. −0.34 2.26 0.88 …. −0.01 2.23 0.99 ….
Clay 3.04 4.20 0.47 4 …. 3.13 3.98 0.43 …. 1.99 3.95 0.61 …. 3.10 3.96 0.43 …. 3.60 4.01 0.37 …. 3.13 3.97 0.43 ….
Elevation −0.53 0.38 0.16 1 …. −0.49 0.36 0.16 …. −0.84 0.40 0.03 …. −0.49 0.36 0.18 …. −0.49 0.36 0.18 …. −0.50 0.36 0.17 ….
P …. …. …. …. 0.64 …. …. …. 0.32 …. …. …. 0.95 …. …. …. 0.35 …. …. …. 0.69 …. …. …. 0.37
R2 …. …. …. …. 0.04 …. …. …. 0.06 …. …. …. 0.14 …. …. …. 0.06 …. …. …. 0.05 …. …. …. 0.06
ρ …. …. …. …. …. …. …. …. 0.29 …. …. …. −0.03 …. …. …. …. …. …. …. …. …. …. …. ….
λ …. …. …. …. …. …. …. …. …. …. …. …. …. …. …. …. 0.30 …. …. …. 0.11 …. …. …. 0.34
AIC …. …. …. …. 123.25 …. …. …. 124.26 …. …. …. 126.93 …. …. …. 124.40 …. …. …. 125.09 …. …. …. 124.45
WA-1 Intercept 30.66 99.00 0.76 …. …. 13.45 86.71 0.88 …. 2,135.04 424.48 <0.001 …. −33.96 86.30 0.69 …. −4.70 90.26 0.96 …. −58.12 84.84 0.49 ….
Sand −17.59 60.93 0.77 2,273 …. −7.27 53.37 0.89 …. −140.67 52.15 0.007 …. 21.97 53.10 0.68 …. 4.29 55.54 0.93 …. 37.00 52.21 0.48 ….
Silt −17.61 56.55 0.76 1,513 …. −7.56 49.53 0.88 …. −132.37 48.37 0.006 …. 19.72 49.16 0.69 …. 2.66 51.48 0.96 …. 33.30 48.34 0.49 ….
Clay −15.32 38.55 0.69 234 …. −8.53 33.77 0.80 …. −93.85 33.09 0.004 …. 10.04 33.65 0.77 …. −2.33 35.17 0.95 …. 19.54 33.11 0.55 ….
Elevation 0.68 0.33 0.04 2 …. 0.22 0.30 0.47 …. −0.63 0.44 0.15 …. 0.38 0.39 0.33 …. 0.49 0.35 0.16 …. 0.45 0.37 0.22 ….
P …. …. …. …. <0.001 …. …. …. 0.004 …. …. …. 0.96 …. …. …. 0.02 …. …. …. 0.07 …. …. …. 0.02
R2 …. …. …. …. 0.29 …. …. …. 0.38 …. …. …. 0.59 …. …. …. 0.35 …. …. …. 0.32 …. …. …. 0.35
ρ …. …. …. …. …. …. …. …. 0.70 …. …. …. −0.02 …. …. …. …. …. …. …. …. …. …. …. ….
λ …. …. …. …. …. …. …. …. …. …. …. …. …. …. …. …. 0.72 …. …. …. 0.77 …. …. …. 1.01
AIC …. …. …. …. 134.18 …. …. …. 127.78 …. …. …. 111.71 …. …. …. 130.76 …. …. …. 133.03 …. …. …. 130.58
WA-2 Intercept −60.06 53.39 0.26 …. …. −51.53 49.99 0.30 …. 157.38 292.91 0.59 …. −52.72 49.96 0.29 …. −55.47 50.96 0.28 …. −40.27 49.21 0.41 ….
Sand 36.21 30.77 0.24 918 …. 30.52 28.82 0.29 …. 5.95 30.84 0.85 …. 31.58 28.80 0.27 …. 33.65 29.37 0.25 …. 24.24 28.37 0.39 ….
Silt 38.69 31.71 0.23 740 …. 32.91 29.70 0.27 …. 9.24 31.60 0.77 …. 34.22 29.69 0.25 …. 35.80 30.27 0.24 …. 26.65 29.25 0.36 ….
Clay 22.07 23.02 0.34 150 …. 18.93 21.55 0.38 …. 3.47 23.16 0.88 …. 20.09 21.48 0.35 …. 20.22 21.96 0.36 …. 15.37 21.12 0.47 ….
Elevation −0.03 0.27 0.92 1 …. −0.04 0.25 0.87 …. −0.39 0.46 0.39 …. −0.11 0.32 0.73 …. 0.003 0.27 0.99 …. −0.12 0.34 0.73 ….
P …. …. …. …. 0.08 …. …. …. 0.17 …. …. …. 0.74 …. …. …. 0.38 …. …. …. 0.71 …. …. …. 0.24
R2 …. …. …. …. 0.15 …. …. …. 0.17 …. …. …. 0.25 …. …. …. 0.16 …. …. …. 0.15 …. …. …. 0.16
ρ …. …. …. …. …. …. …. …. 0.45 …. …. …. 0.14 …. …. …. …. …. …. …. …. …. …. …. ….
λ …. …. …. …. …. …. …. …. …. …. …. …. …. …. …. …. 0.42 …. …. …. 0.15 …. …. …. 0.83
AIC …. …. …. …. 123.91 …. …. …. 124.05 …. …. …. 126.10 …. …. …. 125.13 …. …. …. 125.77 …. …. …. 124.55

Coefficient estimates and SE for the OLS, SLM, SDM, SEM, CAR, and SARMA multiple regression models and associated VIF and P values for Pratylenchus penetrans densities in roots regressed against P_ penetrans densities in soil and Phytophthora rubi DNA concentrations in roots in four commercial red raspberry production fields in Oregon (OR-1 and OR-2) and Washington (WA-1 and WA-2)_

Field Variablesa OLS SLM SDM SEM CAR SARMA
Estimate SE P VIF Model Estimate SE P Model Estimate SE P Model Estimate SE P Model Estimate SE P Model Estimate SE P Model
OR-1 Intercept 0.11 0.19 0.59 …. …. 0.05 0.26 0.84 …. −1.19 1.28 0.35 …. 0.10 0.19 0.60 …. 0.11 0.19 0.57 …. 0.09 0.19 0.62 ….
P. penetrans (soil) 0.39 0.09 <0.001 1.02 …. 0.38 0.09 <0.001 …. 0.42 0.10 <0.001 …. 0.39 0.09 <0.001 …. 0.39 0.09 <0.001 …. 0.40 0.09 <0.001 ….
P. rubi DNA 0.02 0.08 0.82 1.02 …. 0.02 0.07 0.79 …. 0.06 0.08 0.46 …. 0.02 0.07 0.83 …. 0.01 0.07 0.87 …. 0.02 0.07 0.83 ….
P …. …. …. …. <0.001 …. …. …. 0.75 …. …. …. 0.56 …. …. …. 0.83 …. …. …. 0.85 …. …. …. 0.75
R2 …. …. …. …. 0.23 …. …. …. 0.23 …. …. …. 0.25 …. …. …. 0.23 …. …. …. 0.23 …. …. …. 0.23
ρ …. …. …. …. …. …. …. …. 0.11 …. …. …. −0.27 …. …. …. …. …. …. …. …. …. …. …. ….
λ …. …. …. …. …. …. …. …. …. …. …. …. …. …. …. …. −0.10 …. …. …. −0.14 …. …. …. −0.18
AIC …. …. …. …. 126.36 …. …. …. 128.26 …. …. …. 130.39 …. …. …. 128.32 …. …. …. 128.33 …. …. …. 128.26
OR-2 Intercept 0.32 0.48 0.52 …. …. 0.55 0.70 0.43 …. −3.38 1.69 0.04 …. 0.19 0.44 0.66 …. 0.07 0.44 0.86 …. −0.09 0.25 0.72 ….
P. penetrans (soil) 0.59 0.7 0.03 1.0 …. 0.60 0.26 0.02 …. 0.64 0.25 0.01 …. 0.64 0.25 0.01 …. 0.69 0.25 0.005 …. 0.71 0.11 <0.001 ….
P. rubi DNA 0.10 0.22 0.67 1.0 …. 0.10 0.22 0.63 …. 0.26 0.21 0.22 …. 0.14 0.22 0.49 …. 0.15 0.22 0.49 …. 0.39 0.21 0.06 ….
P …. …. …. …. 0.08 …. …. …. 0.61 …. …. …. 0.09 …. …. …. 0.36 …. …. …. 0.35 …. …. …. <0.001
R2 …. …. …. …. 0.08 …. …. …. 0.09 …. …. …. 0.17 …. …. …. 0.09 …. …. …. 0.09 …. …. …. 0.33
ρ …. …. …. …. …. …. …. …. −0.21 …. …. …. −0.85 …. …. …. …. …. …. …. …. …. …. …. ….
λ …. …. …. …. …. …. …. …. …. …. …. …. …. …. …. …. −0.44 …. …. …. −1.02 …. …. …. −0.99
AIC …. …. …. …. 206.40 …. …. …. 208.14 …. …. …. 206.19 …. …. …. 207.56 …. …. …. 207.53 …. …. …. 189.57
WA-1 Intercept 0.48 0.14 0.001 …. …. 0.51 0.25 0.04 …. −0.03 0.43 0.94 …. 0.46 0.13 <0.001 …. 0.48 0.13 <0.001 …. 0.45 0.12 <0.001 ….
P. penetrans (soil) 0.09 0.12 0.42 1.0 …. 0.10 0.11 0.38 …. −0.04 0.15 0.81 …. 0.11 0.11 0.30 …. 0.09 0.11 0.42 …. 0.12 0.10 0.22 ….
P. rubi DNA −0.01 0.07 0.85 1.0 …. −0.01 0.07 0.85 …. −0.006 0.07 0.93 …. −0.01 0.07 0.87 …. −0.01 0.07 0.88 …. −0.01 0.06 0.87 ….
P …. …. …. …. 0.71 …. …. …. 0.88 …. …. …. 0.69 …. …. …. 0.72 …. …. …. 0.78 …. …. …. 0.65
R2 …. …. …. …. 0.01 …. …. …. 0.01 …. …. …. 0.06 …. …. …. 0.01 …. …. …. 0.01 …. …. …. 0.01
ρ …. …. …. …. …. …. …. …. −0.06 …. …. …. −0.17 …. …. …. …. …. …. …. …. …. …. …. ….
λ …. …. …. …. …. …. …. …. …. …. …. …. …. …. …. …. −0.17 …. …. …. −0.21 …. …. …. −0.27
AIC …. …. …. …. 134.05 …. …. …. 136.03 …. …. …. 137.17 …. …. …. 135.92 …. …. …. 135.97 …. …. …. 135.84
WA-2 Intercept 0.80 0.49 0.11 …. …. 0.61 0.73 0.40 …. 1.06 1.35 0.43 …. 0.59 0.43 0.18 …. 0.69 0.47 0.14 …. 0.70 0.46 0.13 ….
P. penetrans (soil) 0.47 0.22 0.04 1.0 …. 0.45 0.22 0.04 …. 0.34 0.21 0.10 …. 0.52 0.20 0.01 …. 0.53 0.21 0.01 …. 0.50 0.21 0.02 ….
P. rubi DNA 0.26 0.14 0.06 1.0 …. 0.24 0.14 0.08 …. 0.08 0.14 0.58 …. 0.36 0.12 0.003 …. 0.26 0.13 0.05 …. 0.31 0.13 0.02 ….
P …. …. …. …. 0.03 …. …. …. 0.66 …. …. …. 0.06 …. …. …. 0.51 …. …. …. 0.71 …. …. …. 0.66
R2 …. …. …. …. 0.12 …. …. …. 0.12 …. …. …. 0.29 …. …. …. 0.13 …. …. …. 0.12 …. …. …. 0.12
ρ …. …. …. …. …. …. …. …. 0.13 …. …. …. −0.82 …. …. …. …. …. …. …. …. …. …. …. ….
λ …. …. …. …. …. …. …. …. …. …. …. …. …. …. …. …. −0.40 …. …. …. −0.24 …. …. …. −0.16
AIC …. …. …. …. 190.27 …. …. …. 192.08 …. …. …. 183.53 …. …. …. 191.85 …. …. …. 192.14 …. …. …. 192.08

Global Moran’s I for assessing spatial autocorrelation in disease rating, Phytophthora rubi DNA concentrations in roots, Pratylenchus penetrans densities in roots and soil, soil texture, and elevation in four commercial red raspberry production fields in Oregon (OR-1 and OR-2) and Washington (WA-1 and WA-2)_

Field Variables Moran’s I coefficienta P-valueb
OR-1 Disease rating 0.28 <0.001
P. rubi DNA in root 0.07 0.001
P. penetrans in root 0.04 0.08
P. penetrans in soil 0.04 0.07
Sand 0.11 <0.001
Silt 0.10 0.002
Clay 0.18 <0.001
Elevation 0.75 <0.001
OR-2 Disease rating 0.01 0.22
P. rubi DNA in root −0.02 0.53
P. penetrans in root −0.01 0.40
P. penetrans in soil 0.06 0.01
Sand 0.07 0.009
Silt 0.06 0.01
Clay 0.02 0.20
Elevation 0.10 0.002
WA-1 Disease rating 0.21 <0.001
P. rubi DNA in root 0.08 0.003
P. penetrans in root 0.004 0.29
P. penetrans in soil 0.31 <0.001
Sand 0.28 <0.001
Silt 0.19 <0.001
Clay 0.31 <0.001
Elevation 0.59 <0.001
WA-2 Disease rating 0.51 <0.001
P. rubi DNA in root 0.22 <0.001
P. penetrans in root 0.09 0.003
P. penetrans in soil 0.11 <0.001
Sand 0.42 <0.001
Silt 0.22 <0.001
Clay 0.43 <0.001
Elevation 0.53 <0.001

Global Moran’s I test for spatial autocorrelation in the residuals for visual disease rating regressed against Phytophthora rubi DNA concentrations in roots and Pratylenchus penetrans densities in roots and soil in four commercial red raspberry production fields in Oregon (OR-1 and OR-2) and Washington (WA-1 and WA-2)_

Field Moran’s I coefficienta P-valueb
OR-1 0.13 <0.001
OR-2 −0.01 0.41
WA-1 0.03 0.05
WA-2 0.19 <0.001

Global Moran’s I test for spatial autocorrelation in the residuals for Pratylenchus penetrans densities in root regressed against P_ penetrans densities in soil and Phytophthora rubi DNA concentrations in roots in four commercial red raspberry production fields in Oregon (OR-1 and OR-2) and Washington (WA-1 and WA-2)_

Field Moran’s I coefficienta P-valueb
OR-1 −0.01 0.39
OR-2 −0.03 0.66
WA-1 −0.01 0.36
WA-2 −0.02 0.45

Coefficient estimates and SE for the OLS, SLM, SDM, SEM, CAR, and SARMA multiple regression models and associated VIF and P values for disease rating regressed against Phytophthora rubi DNA in roots, Pratylenchus penetrans in roots and soil in four commercial red raspberry production fields in Oregon (OR-1 and OR-2) and Washington (WA-1 and WA-2)_

Field Variablesa OLS SLM SDM SEM CAR SARMA
Estimate SE P VIF Model Estimate SE P Model Estimate SE P Model Estimate SE P Model Estimate SE P Model Estimate SE P Model
OR-1 Intercept 0.83 0.03 <0.001 …. …. 0.20 0.14 0.15 …. 0.78 0.34 0.02 …. 0.83 0.05 <0.001 …. 0.82 0.03 <0.001 …. 0.83 0.05 <0.001 ….
P. rubi DNA 0.08 0.01 <0.001 1.02 …. 0.07 0.01 <0.001 …. 0.07 0.01 <0.001 …. 0.07 0.01 <0.001 …. 0.09 0.01 <0.001 …. 0.07 0.01 <0.001 ….
P. penetrans (root) 0.01 0.02 0.57 1.30 …. 0.01 0.02 0.52 …. 0.02 0.02 0.20 …. 0.01 0.02 0.62 …. 0.01 0.02 0.71 …. 0.01 0.02 0.66 ….
P. penetrans (soil) −0.04 0.02 0.04 1.32 …. −0.02 0.02 0.15 …. −0.03 0.02 0.10 …. −0.02 0.02 0.19 …. −0.03 0.02 0.04 …. −0.01 0.01 0.42 ….
P …. …. …. …. <0.001 …. …. …. <0.001 …. …. …. 0.79 …. …. …. <0.001 …. …. …. 0.56 …. …. …. <0.001
R2 …. …. …. …. 0.46 …. …. …. 0.57 …. …. …. 0.61 …. …. …. 0.53 …. …. …. 0.46 …. …. …. 0.56
ρ …. …. …. …. …. …. …. …. 0.67 …. …. …. −0.12 …. …. …. …. …. …. …. …. …. …. …. ….
λ …. …. …. …. …. …. …. …. …. …. …. …. …. …. …. …. 0.73 …. …. …. 0.09 …. …. …. 2.06
AIC …. …. …. …. −84.58 …. …. …. −95.82 …. …. …. −96.37 …. …. …. −90.26 …. …. …. −82.92 …. …. …. −95.25
OR-2 Intercept 0.61 0.02 <0.001 …. …. 0.58 0.23 0.01 …. 0.74 0.25 0.003 …. 0.61 0.02 <0.001 …. 0.61 0.02 <0.001 …. 0.61 0.02 <0.001 ….
P. rubi DNA 0.01 0.01 0.27 1.01 …. 0.01 0.01 0.25 …. 0.006 0.01 0.56 …. 0.01 0.01 0.25 …. 0.01 0.01 0.26 …. 0.01 0.01 0.25 ….
P. penetrans (root) 0.008 0.006 0.22 1.09 …. 0.008 0.006 0.21 …. 0.01 0.006 0.08 …. 0.008 0.006 0.18 …. 0.008 0.006 0.19 …. 0.008 0.006 0.18 ….
P. penetrans (soil) 0.01 0.01 0.38 1.09 …. 0.01 0.01 0.36 …. 0.004 0.01 0.74 …. 0.01 0.01 0.35 …. 0.01 0.01 0.35 …. 0.01 0.01 0.34 ….
P …. …. …. …. 0.21 …. …. …. 0.88 …. …. …. 0.58 …. …. …. 0.81 …. …. …. 0.95 …. …. …. 0.77
R2 …. …. …. …. 0.08 …. …. …. 0.08 …. …. …. 0.17 …. …. …. 0.08 …. …. …. 0.08 …. …. …. 0.08
ρ …. …. …. …. …. …. …. …. 0.05 …. …. …. −0.24 …. …. …. …. …. …. …. …. …. …. …. ….
λ …. …. …. …. …. …. …. …. …. …. …. …. …. …. …. …. −0.10 …. …. …. −0.01 …. …. …. −0.13
AIC …. …. …. …. −153.46 …. …. …. −151.48 …. …. …. −152.09 …. …. …. −151.52 …. …. …. −151.47 …. …. …. −151.54
WA-1 Intercept 0.59 0.03 <0.001 …. …. 0.31 0.13 0.01 …. 0.82 0.27 0.003 …. 0.58 0.04 <0.001 …. 0.59 0.03 <0.001 …. 0.58 0.04 <0.001 ….
P. rubi DNA 0.09 0.01 <0.001 1.00 …. 0.08 0.01 <0.001 …. 0.08 0.01 <0.001 …. 0.08 0.01 <0.001 …. 0.09 0.01 <0.001 …. 0.08 0.01 <0.001 ….
P. penetrans (root) −0.01 0.03 0.63 1.01 …. −0.008 0.02 0.74 …. −0.02 0.02 0.48 …. −0.009 0.02 0.74 …. −0.01 0.03 0.59 …. −0.008 0.02 0.73 ….
P. penetrans (soil) −0.05 0.02 0.03 1.01 …. −0.03 0.02 0.18 …. −0.02 0.03 0.51 …. −0.04 0.02 0.11 …. −0.05 0.02 0.04 …. −0.038 0.03 0.14 ….
P …. …. …. …. <0.001 …. …. …. 0.04 …. …. …. 0.36 …. …. …. 0.35 …. …. …. 0.83 …. …. …. 0.28
R2 …. …. …. …. 0.43 …. …. …. 0.46 …. …. …. 0.51 …. …. …. 0.43 …. …. …. 0.43 …. …. …. 0.44
ρ …. …. …. …. …. …. …. …. 0.44 …. …. …. −0.48 …. …. …. …. …. …. …. …. …. …. …. ….
λ …. …. …. …. …. …. …. …. …. …. …. …. …. …. …. …. 0.38 …. …. …. 0.04 …. …. …. 0.63
AIC …. …. …. …. −54.35 …. …. …. −56.27 …. …. …. −55.19 …. …. …. −53.22 …. …. …. −52.40 …. …. …. −53.52
WA-2 Intercept 0.53 0.05 <0.001 …. …. 0.09 0.09 0.27 …. 0.47 0.18 0.009 …. 0.59 0.09 <0.001 …. 0.57 0.05 <0.001 …. 0.62 0.06 <0.001 ….
P. rubi DNA 0.12 0.01 <0.001 1.07 …. 0.08 0.01 <0.001 …. 0.08 0.01 <0.001 …. 0.08 0.01 <0.001 …. 0.12 0.01 <0.001 …. 0.08 0.01 <0.001 ….
P. penetrans (root) 0.01 0.01 0.44 1.14 …. −0.009 0.01 0.39 …. −0.01 0.01 0.22 …. −0.009 0.01 0.40 …. 0.01 0.01 0.44 …. −0.01 0.01 0.20 ….
P. penetrans (soil) 0.07 0.02 0.006 1.08 …. 0.04 0.02 0.02 …. 0.05 0.02 0.009 …. 0.05 0.02 0.01 …. 0.04 0.02 0.08 …. 0.07 0.02 <0.001 ….
P …. …. …. …. <0.001 …. …. …. <0.001 …. …. …. 0.60 …. …. …. <0.001 …. …. …. 0.18 …. …. …. <0.001
R2 …. …. …. …. 0.57 …. …. …. 0.70 …. …. …. 0.73 …. …. …. 0.68 …. …. …. 0.58 …. …. …. 0.68
ρ …. …. …. …. …. …. …. …. 0.67 …. …. …. 0.20 …. …. …. …. …. …. …. …. …. …. …. ….
λ …. …. …. …. …. …. …. …. …. …. …. …. …. …. …. …. 0.84 …. …. …. 0.31 …. …. …. 2.06
AIC …. …. …. …. −76.74 …. …. …. −97.91 …. …. …. −98.44 …. …. …. −92.92 …. …. …. −76.50 …. …. …. −93.94

Fitted models for the experimental variogram analysis for quantifying the extent of spatial autocorrelation in disease rating, Phytophthora rubi DNA concentrations in roots, Pratylenchus penetrans densities in roots and soil, soil texture, and elevation in four commercial red raspberry production fields in Oregon (OR-1 and OR-2) and Washington (WA-1 and WA-2)_

Field Variables Modela Nuggetb Sillc Ranged
OR-1 Disease rating Gaussian 0.01 0.02 102.27
P. rubi DNA in root Gaussian 1.05 0.44 100.72
P. penetrans in root Gaussian 0.50 0.03 29.52
P. penetrans in soil Gaussian 0.76 0.11 50.01
Sand Exponential 0.002 0.003 625.91
Silt Exponential 0.001 0.003 983.76
Clay Gaussian 0.001 0.0005 73.70
Elevation Gaussian 0.002 0.41 107.19
OR-2 Disease rating Exponential 0.004 0.004 644.08
P. rubi DNA in root Gaussian 0.54 0.03 36.47
P. penetrans in root Exponential 1.62 1.17 674.35
P. penetrans in soil Exponential 0 0.39 10.03
Sand Gaussian 0.004 0.002 72.89
Silt Exponential 0.003 0.004 105.97
Clay Gaussian 0.001 0.0007 56.90
Elevation Exponential 0.044 0.15 861.29
WA-1 Disease rating Gaussian 0.03 0.32 439.20
P. rubi DNA in root Exponential 0.37 1.98 37.66
P. penetrans in root Spherical 0.31 0.14 48.26
P. penetrans in soil Spherical 0.08 0.56 94.31
Sand Spherical 0.003 0.004 505.74
Silt Gaussian 0.003 0.002 75.60
Clay Exponential 0.001 0.0004 145.25
Elevation Gaussian 0.024 104.36 2,855.12
WA-2 Disease rating Exponential 0.0005 0.09 265.02
P. rubi DNA in root Exponential 0.89 0.89 362.76
P. penetrans in root Exponential 0.62 0.74 23.00
P. penetrans in soil Exponential 0.13 0.42 49.90
Sand Gaussian 0.002 0.004 59.61
Silt Exponential 0.002 0.006 82.70
Clay Exponential 0 0.002 79.82
Elevation Gaussian 0.01 0.10 96.70

Exploratory data analysis of disease rating, Phytophthora rubi DNA concentrations in roots, Pratylenchus penetrans densities in roots and soil, soil texture, and elevation in four commercial red raspberry production fields in Oregon (OR-1 and OR-2) and Washington (WA-1 and WA-2)_

Field Variables Mean SE Standard deviation VIRa
OR-1 Disease rating 6.53 0.18 1.37 0.29
P. rubi DNA (ng/g root) 681.87 192.78 1,493.29 3,270.30
P. penetrans/g root 16.78 4.80 37.16 82.29
P. penetrans/g soil 50.38 10.62 82.25 134.27
% sand 27.93 0.50 3.90 0.54
% silt 51.45 0.45 3.50 0.24
% clay 20.61 0.34 2.61 0.33
Elevation (m) 6.43 0.38 2.92 1.33
OR-2 Disease rating 3.65 0.08 0.62 0.10
P. rubi DNA (ng/g root) 91.75 64.48 499.49 2,719.20
P. penetrans/g root 337.32 79.88 618.74 1,134.95
P. penetrans/g soil 86.05 9.06 70.17 57.22
% sand 27.93 0.89 6.87 1.69
% silt 45.97 0.88 6.88 1.03
% clay 26.53 0.44 3.44 0.45
Elevation (m) 0.66 0.05 0.39 0.23
WA-1 Disease rating 3.26 0.23 1.79 0.98
P. rubi DNA (ng/g root) 1,106.31 514.86 3,988.13 14,376.77
P. penetrans/g root 16.16 5.96 46.19 132.06
P. penetrans/g soil 26.77 4.89 37.91 53.67
% sand 62.60 0.89 6.87 0.75
% silt 27.27 0.72 5.57 1.14
% clay 10.13 0.29 2.26 0.50
Elevation (m) 1.74 0.13 1.00 0.58
WA-2 Disease rating 5.47 0.22 1.73 0.54
P. rubi DNA (ng/g root) 817.32 440.91 3,415.25 14,270.84
P. penetrans/g root 598.35 97.64 756.33 956.02
P. penetrans/g soil 178.42 26.01 201.51 227.58
% sand 34.01 1.01 7.85 1.81
% silt 51.75 0.92 7.11 0.98
% clay 14.25 0.41 3.18 0.71
Elevation (m) 1.43 0.09 0.73 0.37
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