Silver sagebrush (A. cana) response to prescribed fire

Background

This project occurred during the summer of 2023 at the USDA Agricultural Research Services Fort Keogh Livestock and Range Research Laboratory, located in Miles City, MT. The purpose of this study is to determine the effects of prescribed fire on silver sagebrush (Artemisia cana) in the US Great Northern Plains. The heights, major diameters, and minor diameters of 101 A. cana plants were recorded. The plant was then cut down, dried at 60°C for 4 days, and weighted. A linear model for mass, height, major diameter, minor diameter was then created using the R statistical environment.

Regression

Statistics

Linear Model

BagMass <- 
  read_excel("NoahSilverSagebrushData.xlsx",
             sheet = 'BagTares') %>%
  group_by(BagSize) %>%
  summarize(
    bagmass = mean(Mass))

SagebrushData <-
  read_xlsx("NoahSilverSagebrushData.xlsx", sheet = "LinearRegressData") %>%
  mutate(Mass = case_when(
     BagSize ==
      "g" ~ MassGrams - filter(BagMass, BagSize == "g") $bagmass
  )) %>%
  select( - MassGrams, - BagSize) %>%
  mutate(Area = (pi*(Diameter)/2*(Diameter2)/2))

Sagelm <-
  lm(Mass ~ Diameter + Diameter2 + Height, data = SagebrushData)

summary(Sagelm)

## 
## Call:
## lm(formula = Mass ~ Diameter + Diameter2 + Height, data = SagebrushData)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -291.07  -42.31  -20.17   10.52  455.75 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)  
## (Intercept) -51.7295    29.3588  -1.762   0.0812 .
## Diameter      0.1877     0.7120   0.264   0.7926  
## Diameter2     1.4047     0.7892   1.780   0.0782 .
## Height        1.7847     0.7844   2.275   0.0251 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 97.44 on 97 degrees of freedom
## Multiple R-squared:  0.3382, Adjusted R-squared:  0.3177 
## F-statistic: 16.52 on 3 and 97 DF,  p-value: 9.495e-09

Graphs

3D Scatterplot of Sagebrush Height vs. Mass vs. Area*

*For the purpose of 3-dimensional visualization, area is expressed as Elliptical Area = (pi)(Diameter/2)(Diameter2/2)

# 3D-Plot

open3d()

plot3d( 
  x = SagebrushData$Area, y = SagebrushData$Mass, z = SagebrushData$Height,
  xlab="Elliptical Area", ylab="Mass", zlab="Height",
  col = "red", type = "s", size = 1)

Histograms

# 3D-Plot

SagebrushData %>%
  ggplot(aes(x = Mass)) + theme_bw(16) + 
  geom_histogram(aes(y = after_stat(.data[["density"]])),      
                 binwidth = 37,
                 colour = "black",
                 fill = "lightyellow")+
  geom_density(alpha = .5, fill = "lightblue") +
  labs(y = "Density", 
       x = "Mass (g)")

SagebrushData %>%
  ggplot(aes(x = Height)) + theme_bw(16) + 
  geom_histogram(aes(y = after_stat(.data[["density"]])),      
                 binwidth = 4,
                 colour = "black",
                 fill = "lightyellow")+
  geom_density(alpha = .5, fill = "lightblue") +
  labs(y = "Density", 
       x = "Height (cm)")

SagebrushData %>%
ggplot(aes(Height, Mass)) +           
  geom_point(
    shape = 21,
    fill = "RED",
    stroke = .5,)+
  stat_smooth(method = "lm")+
  theme_bw(14)

## `geom_smooth()` using formula = 'y ~ x'