lab14_exercises

library(spatstat)

## Warning: package 'spatstat' was built under R version 4.1.2

## Loading required package: spatstat.data

## Warning: package 'spatstat.data' was built under R version 4.1.2

## Loading required package: spatstat.geom

## Warning: package 'spatstat.geom' was built under R version 4.1.2

## spatstat.geom 2.3-0

## Loading required package: spatstat.core

## Warning: package 'spatstat.core' was built under R version 4.1.2

## Loading required package: nlme

## Loading required package: rpart

## spatstat.core 2.3-2

## Loading required package: spatstat.linnet

## Warning: package 'spatstat.linnet' was built under R version 4.1.2

## spatstat.linnet 2.3-0

## 
## spatstat 2.2-0       (nickname: 'That's not important right now') 
## For an introduction to spatstat, type 'beginner'

library(sf)

## Warning: package 'sf' was built under R version 4.1.2

## Linking to GEOS 3.9.1, GDAL 3.2.1, PROJ 7.2.1

# Tree Locations
urkiola.sf <- st_read("C:/Users/taylu/OneDrive/Documents/Geog6000/Datafiles/urkiola/urkiola/urkiola.shp")

## Reading layer `urkiola' from data source 
##   `C:\Users\taylu\OneDrive\Documents\Geog6000\Datafiles\urkiola\urkiola\urkiola.shp' 
##   using driver `ESRI Shapefile'
## Simple feature collection with 1245 features and 5 fields
## Geometry type: POINT
## Dimension:     XY
## Bounding box:  xmin: 2.1 ymin: 0.1 xmax: 219.1 ymax: 149.9
## CRS:           NA

# Park Boundary
urkiola.win <- st_read("C:/Users/taylu/OneDrive/Documents/Geog6000/Datafiles/urkiola/urkiola/urkiolaWindow.shp")

## Reading layer `urkiolaWindow' from data source 
##   `C:\Users\taylu\OneDrive\Documents\Geog6000\Datafiles\urkiola\urkiola\urkiolaWindow.shp' 
##   using driver `ESRI Shapefile'
## Simple feature collection with 1 feature and 3 fields
## Geometry type: POLYGON
## Dimension:     XY
## Bounding box:  xmin: 0.05 ymin: 0.05 xmax: 219.95 ymax: 149.95
## CRS:           NA

urkiola.win <- as.owin(urkiola.win)
# First extract coordinates
urkiola.crds <- st_coordinates(urkiola.sf)
## Convert to ppp
urkiola.ppp <- ppp(x = urkiola.crds[,1], y = urkiola.crds[,2], marks = as.factor(urkiola.sf$tree), window = urkiola.win)
plot(urkiola.ppp)

Give the intensity using the summary function

summary(urkiola.ppp)

## Marked planar point pattern:  1245 points
## Average intensity 0.06564029 points per square unit
## 
## Coordinates are given to 1 decimal place
## i.e. rounded to the nearest multiple of 0.1 units
## 
## Multitype:
##       frequency proportion  intensity
## birch       886  0.7116466 0.04671269
## oak         359  0.2883534 0.01892760
## 
## Window: polygonal boundary
## single connected closed polygon with 44 vertices
## enclosing rectangle: [0.05, 219.95] x [0.05, 149.95] units
##                      (219.9 x 149.9 units)
## Window area = 18967 square units
## Fraction of frame area: 0.575

The average intensity is 0.06564029 poinyd per square unit

Plot the distribution of the two tree species

plot(split(urkiola.ppp), main = "All marks")

oak <- plot(split(urkiola.ppp)$oak, main = "Distribution of Oak Trees")

birch <- plot(split(urkiola.ppp)$birch, main = "Distribution of Birch Trees")

Make the kernal density of each species

plot(density(split(urkiola.ppp)))

After observing the density plots, I noticed that they do not suggest these two species co-occur within the park.

Use Ripley’s K function (Oak Tree)

urkiola.oak <- split(urkiola.ppp)$oak
urkiola.birch <- split(urkiola.ppp)$birch

oak.ktest <- Kest(urkiola.oak)
plot(oak.ktest)

Use the envelope function to test the obtained Ripley’s K against a hypothesis of Complete Spatial Randomness

oakkest.mc = envelope(urkiola.oak, fun='Kest', nsim=99, verbose=FALSE)
plot(oakkest.mc, shade=c("hi", "lo"))

summary(oakkest.mc)

## Pointwise critical envelopes for K(r)
## and observed value for 'urkiola.oak'
## Obtained from 99 simulations of CSR
## Alternative: two.sided
## Upper envelope: pointwise maximum of simulated curves
## Lower envelope: pointwise minimum of simulated curves
## Significance level of Monte Carlo test: 2/100 = 0.02
## Data: urkiola.oak

Using the Monte Carlo test, it is understood that the significance level is 2/100 = 0.02. The observed line shown in the figure above indicates that the oak species is clustered because the observed line is above the theoretical line.

Ripley’s K Function (Birch Tree)

birch.ktest <- Kest(urkiola.birch)
plot(birch.ktest)

Envelope function for Birch

birchkest.mc <- envelope(urkiola.birch, fun = 'Kest', nsim = 99, verbose = FALSE)
plot(birchkest.mc, shade = c("hi", "lo"))

summary(birchkest.mc)

## Pointwise critical envelopes for K(r)
## and observed value for 'urkiola.birch'
## Obtained from 99 simulations of CSR
## Alternative: two.sided
## Upper envelope: pointwise maximum of simulated curves
## Lower envelope: pointwise minimum of simulated curves
## Significance level of Monte Carlo test: 2/100 = 0.02
## Data: urkiola.birch

The birch species also shows the observed line above the theoretical line, meaning this species also has a clustered pattern. Again, after using the Monte Carlo test, we see a significance level of 2/100 = 0.02.

Envelope with KCross function

urkiola.kcross <- envelope(urkiola.ppp,
                           Kcross,
                           i = "oak",
                           j = "birch",
                           nsim = 99,
                           verbose = FALSE)
plot(urkiola.kcross)

summary(urkiola.kcross)

## Pointwise critical envelopes for "K"["oak", "birch"](r)
## and observed value for 'urkiola.ppp'
## Obtained from 99 simulations of CSR
## Alternative: two.sided
## Upper envelope: pointwise maximum of simulated curves
## Lower envelope: pointwise minimum of simulated curves
## Significance level of Monte Carlo test: 2/100 = 0.02
## Data: urkiola.ppp

According to the figure and summary above, the combined distribution of both species are random because the observed curve is following the theoretical line within the envelope.

lab14_exercises

Taylor Lundquist

12/6/2021

Give the intensity using the summary function

The average intensity is 0.06564029 poinyd per square unit

Plot the distribution of the two tree species

Make the kernal density of each species

After observing the density plots, I noticed that they do not suggest these two species co-occur within the park.

Use Ripley’s K function (Oak Tree)

Use the envelope function to test the obtained Ripley’s K against a hypothesis of Complete Spatial Randomness

Using the Monte Carlo test, it is understood that the significance level is 2/100 = 0.02. The observed line shown in the figure above indicates that the oak species is clustered because the observed line is above the theoretical line.

Ripley’s K Function (Birch Tree)

Envelope function for Birch

The birch species also shows the observed line above the theoretical line, meaning this species also has a clustered pattern. Again, after using the Monte Carlo test, we see a significance level of 2/100 = 0.02.

Envelope with KCross function

According to the figure and summary above, the combined distribution of both species are random because the observed curve is following the theoretical line within the envelope.