Lab 3

Question 1

##question 1 - two other ways to do the above function
#rpoispp(500)|>
  #plot()
randomplot <- rpoispp(500)
plot(randomplot)

Question 2: It adds the contour lines and points overtop of the existing density map

Question 3: It shows how many data points are within a grid cell

Question 4:

# Print results table
print(results)

##   Number.of.Points Grid.Cells   P.value Interpretation
## 1              555        400 0.7947421     Likely CSR
## 2              495        400 0.7180999     Likely CSR
## 3              490        400 0.4633854     Likely CSR

Question 5:

pp <- rpoispp(function(x,y) {200*x + 200*y})
quadrat.test(pp, nx=8, ny=8)

## Warning: Some expected counts are small; chi^2 approximation may be inaccurate

## 
##  Chi-squared test of CSR using quadrat counts
## 
## data:  pp
## X2 = 101.74, df = 63, p-value = 0.002879
## alternative hypothesis: two.sided
## 
## Quadrats: 8 by 8 grid of tiles

#1st operation: p-value = 0.00904 , unlikely
#2nd operation: p-value = 0.02313 , unlikely
#3rd operation: p-value = 0.05535 , likely

Question 6: It does not affect the interpretation of the p-values, only the possibility of CSR being more or less likely

plot(split(lansing))

plot(split(lansing)$hickory)

Question 7: Area = 924×924 = 853,776 square feet

Question 8: There are 2251 trees in the dataset

npoints(lansing)

## [1] 2251

Question 9: Ignoring misc., the most abundant is hickory and the least abundant is black oak

table(marks(lansing))

## 
## blackoak  hickory    maple     misc   redoak whiteoak 
##      135      703      514      105      346      448

Question 10: a) The most abundant, hickory, looks dispersed but with some aggregated areas, and the second most abundant, maple, looks aggregated. b) The least abundant, black oak, looks to be aggregated

plot(split(lansing)$hickory)

plot(density(split(lansing)$hickory))

plot(split(lansing)$maple)

plot(density(split(lansing)$maple))

plot(split(lansing)$blackoak)

plot(density(split(lansing)$blackoak))

Question 11: All three tests produced vlaues below 0.05 and so all three are significant

quadrat.test(Hickory, nx = 8, ny = 8)

## 
##  Chi-squared test of CSR using quadrat counts
## 
## data:  Hickory
## X2 = 318.91, df = 63, p-value < 2.2e-16
## alternative hypothesis: two.sided
## 
## Quadrats: 8 by 8 grid of tiles

quadrat.test(Maple, nx = 8, ny = 8)

## 
##  Chi-squared test of CSR using quadrat counts
## 
## data:  Maple
## X2 = 352.12, df = 63, p-value < 2.2e-16
## alternative hypothesis: two.sided
## 
## Quadrats: 8 by 8 grid of tiles

quadrat.test(Blackoak, nx = 8, ny = 8)

## Warning: Some expected counts are small; chi^2 approximation may be inaccurate

## 
##  Chi-squared test of CSR using quadrat counts
## 
## data:  Blackoak
## X2 = 182.16, df = 63, p-value = 3.27e-13
## alternative hypothesis: two.sided
## 
## Quadrats: 8 by 8 grid of tiles

Question 12: The result from this shows a spatial pattern with the Hickory trees being highly structured and likely aggregated

hickory <- split(lansing)$hickory

quadrat.test(hickory, nx = 3, ny = 3)

## 
##  Chi-squared test of CSR using quadrat counts
## 
## data:  hickory
## X2 = 163.8, df = 8, p-value < 2.2e-16
## alternative hypothesis: two.sided
## 
## Quadrats: 3 by 3 grid of tiles

quadrat.test(hickory, nx = 5, ny = 5)

## 
##  Chi-squared test of CSR using quadrat counts
## 
## data:  hickory
## X2 = 233.45, df = 24, p-value < 2.2e-16
## alternative hypothesis: two.sided
## 
## Quadrats: 5 by 5 grid of tiles

quadrat.test(hickory, nx = 7, ny = 7)

## 
##  Chi-squared test of CSR using quadrat counts
## 
## data:  hickory
## X2 = 319.17, df = 48, p-value < 2.2e-16
## alternative hypothesis: two.sided
## 
## Quadrats: 7 by 7 grid of tiles

Question 13:

# given: plot(apply(nndist(rpoispp(500), k=1:500), 2, FUN = mean))
#other way 1:
apply(nndist(rpoispp(500), k=1:500), 2, FUN = mean)|> plot()

#other way 2:
nn_means <- apply(nndist(rpoispp(500), k = 1:500), 2, mean)
plot(nn_means,
     xlab = "Neighbor Order (k)",
     ylab = "Average Nearest Neighbor Distance",
     main = "Mean NND (Stored in Variable)")

Question 14: This suggests that maple trees are closer together than they would be at random

plot(apply(nndist(rpoispp(500), k=1:100), 2, FUN = mean),
       xlab = "Neighbor Order (k)",
       ylab = "Average Nearest Neighbor Distance",
       main = "ANN Values for Different Neighbor Orders",
       type = "b",                 # Plot points connected by lines
       pch = 19)                   # Solid circles for points
  nn_distances <- nndist(split(lansing)$maple, k = 1:100)
  ann_values <- colMeans(nn_distances)
  points(1:length(ann_values), ann_values,
       pch = 5)                         #Open squares for points

Question 15: the plot suggestese the cells are clustering

pp <- rpoispp(function(x,y) {200*x + 200*y})
plot(Gest(pp))

  G_env <- envelope(rpoispp(500), Gest, nsim = 95, alpha  = 0.05)

## Generating 95 simulations of CSR  ...
## 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
## 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
## 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
## 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
## 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 
## 95.
## 
## Done.

  plot(G_env)

Question 16: The data goes slightly above the confidence band, suggesting some clustering / clumping

G_env_hickory <- envelope(split(lansing)$hickory, Gest, nsim = 99)

## Generating 99 simulations of CSR  ...
## 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
## 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
## 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
## 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
## 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
## 99.
## 
## Done.

plot(G_env_hickory)

Question 17: The data goes above the confidence band for most of the plot, suggesting that the points cluster / clump together

G_env_blackoak <- envelope(split(lansing)$blackoak, Gest, nsim = 99)

## Generating 99 simulations of CSR  ...
## 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
## 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
## 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
## 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
## 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
## 99.
## 
## Done.

plot(G_env_blackoak)

Question 18: The data goes below the confidence band, suggesting some that the data is regular rather than random

G_env_cells <- envelope(cells, Gest, nsim = 99)

## Generating 99 simulations of CSR  ...
## 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
## 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
## 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
## 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
## 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
## 99.
## 
## Done.

plot(G_env_cells)

Question 19: The data goes above the confidence band for most of the plot, suggesting that the points cluster / clump together

data(longleaf)
G_env_longleaf <- envelope(longleaf, Gest, nsim = 99)

## Generating 99 simulations of CSR  ...
## 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
## 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
## 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
## 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
## 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
## 99.
## 
## Done.

plot(G_env_longleaf)

Lab 3

Kinsey Snodgrass

2025-09-11

Question 1

Question 2: It adds the contour lines and points overtop of the existing density map

Question 3: It shows how many data points are within a grid cell

Question 4:

Question 5:

Question 6: It does not affect the interpretation of the p-values, only the possibility of CSR being more or less likely

Question 7: Area = 924×924 = 853,776 square feet

Question 8: There are 2251 trees in the dataset

Question 9: Ignoring misc., the most abundant is hickory and the least abundant is black oak

Question 10: a) The most abundant, hickory, looks dispersed but with some aggregated areas, and the second most abundant, maple, looks aggregated. b) The least abundant, black oak, looks to be aggregated

Question 11: All three tests produced vlaues below 0.05 and so all three are significant

Question 12: The result from this shows a spatial pattern with the Hickory trees being highly structured and likely aggregated

Question 13:

Question 14: This suggests that maple trees are closer together than they would be at random

Question 15: the plot suggestese the cells are clustering

Question 16: The data goes slightly above the confidence band, suggesting some clustering / clumping

Question 17: The data goes above the confidence band for most of the plot, suggesting that the points cluster / clump together

Question 18: The data goes below the confidence band, suggesting some that the data is regular rather than random

Question 19: The data goes above the confidence band for most of the plot, suggesting that the points cluster / clump together