Code

plot(rpoispp(500))

Question 1

Question 2

What does add=T do in the above lines of code?.

T means true and in this code means to overlay this new desity map over the “pp”.

code

plot(quadratcount(pp,nx = 10,ny = 10))

Question 3

What do the numbers within the squares mean?

The numbers within each box represet how many of the random 500 points that were generated are in each box.

Question 4

Repeat this operation 3 times and create a table reporting your a) number of points, b) number of grid cells, c) P-values, and d) Interpret your P-values. Items a), b), c), an d) should be columns in your table. There should be three rows. One for each iteration.

Code

quadrat.test(rpoispp(500),nx = 20,ny = 20)
## Warning: Some expected counts are small; chi^2 approximation may be inaccurate
## 
##  Chi-squared test of CSR using quadrat counts
## 
## data:  rpoispp(500)
## X2 = 407.57, df = 399, p-value = 0.7452
## alternative hypothesis: two.sided
## 
## Quadrats: 20 by 20 grid of tiles
quadrat.test(rpoispp(500),nx = 20,ny = 20)
## Warning: Some expected counts are small; chi^2 approximation may be inaccurate
## 
##  Chi-squared test of CSR using quadrat counts
## 
## data:  rpoispp(500)
## X2 = 412.96, df = 399, p-value = 0.6086
## alternative hypothesis: two.sided
## 
## Quadrats: 20 by 20 grid of tiles
quadrat.test(rpoispp(500),nx = 20,ny = 20)
## Warning: Some expected counts are small; chi^2 approximation may be inaccurate
## 
##  Chi-squared test of CSR using quadrat counts
## 
## data:  rpoispp(500)
## X2 = 400.31, df = 399, p-value = 0.9444
## alternative hypothesis: two.sided
## 
## Quadrats: 20 by 20 grid of tiles

Question 5

Repeat this operation 3 times. Report and interpret your P-values.

Code

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 = 99.847, df = 63, p-value = 0.004289
## alternative hypothesis: two.sided
## 
## Quadrats: 8 by 8 grid of tiles
plot(density(pp))
plot(pp, pch = 1, add = TRUE)

pp <- rpoispp(function(x,y){200*x + 200*y})
quadrat.test(pp, nx=3, ny=3)
## 
##  Chi-squared test of CSR using quadrat counts
## 
## data:  pp
## X2 = 43.654, df = 8, p-value = 1.323e-06
## alternative hypothesis: two.sided
## 
## Quadrats: 3 by 3 grid of tiles
plot(density(pp))
plot(pp, pch = 1, add = TRUE)

pp <- rpoispp(function(x,y){200*x + 200*y})
quadrat.test(pp, nx=100, ny=100)
## Warning: Some expected counts are small; chi^2 approximation may be inaccurate
## 
##  Chi-squared test of CSR using quadrat counts
## 
## data:  pp
## X2 = 10177, df = 9999, p-value = 0.2101
## alternative hypothesis: two.sided
## 
## Quadrats: 100 by 100 grid of tiles
plot(density(pp))
plot(pp, pch = 1, add = TRUE)

Question 6

Try different numbers of grid cells in your quadrat test. Does this affect your interpretation of the P-values obtained?

The higher grid amounts make the P value higher slighly but still over a small number. Smaller grid amounts visually are less grouped together possibly and larger amounts are more global trend spread out.

Code

plot(split(lansing))

plot(split(lansing)$hickory)

data(lansing)

trees <- split(lansing)
names(trees)
## [1] "blackoak" "hickory"  "maple"    "misc"     "redoak"   "whiteoak"
hickorytrees <- trees$hickory

plot(hickorytrees)

Question 7

What is the area in sq. ft. of the study region for the lansing data?

window: rectangle = [0, 1] x [0, 1] units (one unit = 924 feet)

Code

lansing$window
## window: rectangle = [0, 1] x [0, 1] units (one unit = 924 feet)

Question 8

What is the total number of trees in the lansing dataset?

there are 2251 points (which are trees)

Code

numberoftrees <- npoints(lansing)
numberoftrees
## [1] 2251

Question 9

What are the most and least abundant trees in the lansing dataset (ignoring “misc”).

Most abundant hickory (703) | Least abundant is Blackoak (135)

Code

table(marks(lansing))
## 
## blackoak  hickory    maple     misc   redoak whiteoak 
##      135      703      514      105      346      448

Quesiton 10

Characterize the pattern for each of the a) two most abundant species, and for b) the least abundant species (ignore “misc”) as either random, aggregated, or dispersed based only on your visual interpretation of the plots you generated using plot, density, contour, quadrat_count, or hist(quadrat_count()).

Most Common Mapel-aggrigated in clumps | Hickory 2nd most common - I think dispersed due to wide gaps. Least Common - Blackoak dispersed and scatterd | redoak - dispersed, there is some aggregation and dispersment

Code

plot(density(trees)$maple)

plot(density(trees)$hickory)

plot(density(trees)$blackoak)

plot(density(trees)$redoak)

Question 11

Perform a quadrat analysis (quadrat test) for a) each of the two most common tree types and b) the least common tree type (ignoring “misc”). Interpret your P-values.

Most common - These are such a small number for the P Value that there NOT RANDOM Mapel - p-value < 2.2e-16 Hickory - p-value < 2.2e-16

Least Common These are such a small number for the P Value that there NOT RANDOM Blackoak - p-value < 2.2e-16 Redoak - p-value = 1.061e-05

Code

quadrat.test(trees$maple)
## 
##  Chi-squared test of CSR using quadrat counts
## 
## data:  trees$maple
## X2 = 216.93, df = 24, p-value < 2.2e-16
## alternative hypothesis: two.sided
## 
## Quadrats: 5 by 5 grid of tiles
quadrat.test(trees$hickory)
## 
##  Chi-squared test of CSR using quadrat counts
## 
## data:  trees$hickory
## X2 = 233.45, df = 24, p-value < 2.2e-16
## alternative hypothesis: two.sided
## 
## Quadrats: 5 by 5 grid of tiles
quadrat.test(trees$blackoak)
## 
##  Chi-squared test of CSR using quadrat counts
## 
## data:  trees$blackoak
## X2 = 145.56, df = 24, p-value < 2.2e-16
## alternative hypothesis: two.sided
## 
## Quadrats: 5 by 5 grid of tiles
quadrat.test(trees$redoak)
## 
##  Chi-squared test of CSR using quadrat counts
## 
## data:  trees$redoak
## X2 = 67.439, df = 24, p-value = 1.061e-05
## alternative hypothesis: two.sided
## 
## Quadrats: 5 by 5 grid of tiles

Question 12

Run several quadrat tests for “hickory” using different quadrat numbers. Is the interpretation of your results robust to variation in quadrat size?

With the results below I would say this is the over all trend of our data set

Code

q1 <- quadrat.test(trees$hickory, nx = 3, ny = 3)
q2 <- quadrat.test(trees$hickory, nx = 5, ny = 5)
q3 <- quadrat.test(trees$hickory, nx = 10, ny = 10)

Question 13

Illustrate two other ways you can do this.

Code

plot(apply(nndist(rpoispp(500), k=1:500), 2, FUN = mean))

NNDC <- plot(apply(nndist(rpoispp(500), k=1:500), 2, FUN = mean))

plot(colMeans(nndist(rpoispp(500), k=1:500), 2))

Quesiton 14

What does the plot suggest about the pattern of maple trees in this landscape?

The plot above suggestes that hte data is clustered because the curve lies below the null curve = trees are closer to their neighbors than expected

Code

hist(apply(nndist(rpoispp(500), k=1:500), 2, FUN = mean))

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

What does the plot suggest about the pattern of cells?

This plot suggests that the distrabution may be regular spacing because its consistatly above the ANN curve.

Code

n_cells <- npoints(cells)

plot(apply(nndist(rpoispp(n_cells), k=1:n_cells), 2, mean),
     type="b", pch=19,
     xlab="Neighbor Order (k)",
     ylab="Average NN Distance",
     main="ANN: Cells vs Random")

nn_cells <- nndist(cells, k=1:n_cells)
ann_cells <- colMeans(nn_cells)
points(1:length(ann_cells), ann_cells, pch=5)

Question 16

##Does the data wander beyond the bounds of the confidence band? If so, above or below? Does this graph suggest randomness, clumping or aversion in the hickory data? This data for Hickory trees does in fact go over outside of the bounds.This is suggesting small amounts of clumping because there are a few more shorter distances than would be expected if it was random.

Code

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)

G_env_hickory <- envelope(split(lansing)$hickory, 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_hickory, main="G-function: Hickory")

Question 17

Does the data wander beyond the bounds of the confidence band? If so, above or below? Does this graph suggest randomness, clumping or aversion in the blackoak data?

This data for Black oak is almost always consistatly above our line meaning the data is clumping

Code

G_env_blackoak <- envelope(split(lansing)$blackoak, 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_blackoak, main="G-function: Blackoak")

Question 18

Does the data wander beyond the bounds of the confidence band? If so, above or below? Does this graph suggest randomness, clumping or aversion in the cells data?

This data for the Cells is constantly below the graph meaning it is experiencing a dispersed or regular patern.

Code

G_env_cells <- envelope(cells, 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_cells, main="G-function: Cells")

Question 19

Does the data wander beyond the bounds of the confidence band? If so, above or below? Does this graph suggest randomness, clumping or aversion in the longleaf data?

This data for Longleafs is consistantly above our graphed line and so the data is clumping.

Code

G_env_longleaf <- envelope(longleaf, 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_longleaf, main="G-function: Longleaf")