Background

We mapped the spatial locations of all trees >2 cm dbh in two sites: the Beineke Stand ("Old Growth", ca. 1700's) and the Pasture Lot (mid-successional, abandoned ca. 1930). The Pasture Lot site was 40 x 30 m and the Beineke Stand site was 60 x 30 m. In addition, we have available to us data collected from a mature forest in the Hopper (probably used as a woodlot in the 1800's) from last year's class. We will use these data to analyze spatial patterns as a function of species, tree age, and stand age. These hypothesis are fleshed out in a paper by Condit et al. (2000) which you will need to read as background and to answer the questions in this worksheet:

Condit, R., et al. 2000. Spatial Patterns in the Distribution of Tropical Tree Species. Science 288:1414-1418.

Methods

Historically, we have used the Poisson and Nearest Neighbor methods to analyze spatial patterns for data collected in this lab. Unfortunately, these methods are not very sensitive, and although previous courses have highlighted suggestive patterns, results have always been equivocal. This year, we will use R to perform a more sophisticated analysis of spatial structure based on Ripley's K Statistic. Ripley's K Statistic is very similar to the approach used by Condit et al. (2000). Ripley's K Statistic is a measure of the number of neighbors as a function of distance. Under a Poisson process (i.e., random spatial distribution), the expected number of neighbors increases linearly with area. Thus, values of Ripley's K Statistic greater than expected indicate clumping at that spatial scale and values below expected indicate evenness at that spatial scale. Note that one of the values of Ripley's K Statistic is that it retain information on the scale-dependence of spatial patterns!

Analysis

First will need to download the data files:

• SpatialPasture.csv
• SpatialBeineke.csv
• SpatialHopper.csv

Next, you will want to import the data. Be sure to use the summary() function to visualize the data. Especially important will be to see the information for "Species" to evaluate which species for each data set have enough individuals to analyze!

pasture <- read.csv("SpatialPasture.csv")
beineke <- read.csv("SpatialBeineke.csv")
hopper  <- read.csv("SpatialHopper.csv")

Next you will want to load two libraries and function that I wrote to facilitate the graphical analysis of these data.

library(lattice)
library(spatial)

K.plot <- function(data, subset=NULL, ...) {
  ## Input = data frame with X and Y variables reflecting spatial coords.
  subset <- eval(substitute(subset), envir = data)
  if (!is.null(subset)) data <- subset(data, subset)
  N <- dim(data)[1] # Total sample size
  ## Below we calculate the region assuming a sampling quadrat of 5m^2
  ppregion(0,5*ceiling(max(data$X)/5),0,5*ceiling(max(data$Y)/5))
  ## Below we calculate Ripley's K statisic and simulate CI's
  K.stat <- Kfn(list(x=data$X,y=data$Y),15, 150)
  K.CI <- eval(substitute(Kenvl(15, 150, Psim(N))))
  ## Below we plot the result
  plot(K.stat$x,K.stat$y, type="l", xlab="Distance (m)", ylab="L(t)",
       cex.lab=1.5, col="blue", sub=paste("Sample Size = ", N), ... )
  lines(K.CI$x,K.CI$u,lty=2, col="red") # Lower CI
  lines(K.CI$x,K.CI$l,lty=2, col="red") # Upper CI
}

Finally, you can analyze the data, first by creating a map for each site and then by creating the plots of Ripley's K statistic (examples below). For the plots of Ripley's K statistic, if the blue line goes above the red CI that indicates aggregation - below evenness - at that spatial scale:

xyplot(Y~X, group=Species, data=pasture, auto.key=TRUE)
## Note: older versions of R and xyplot() generate a grey background.
## If so, you can change this by appending the option
## par.settings=list(background="white") to your xyplot() command.

K.plot(pasture)                          # All Pasture data
K.plot(pasture, subset=DBH<20)           # Pasture data, trees <20cm DBH only
K.plot(beineke, subset=Species=="Beech") # Beineke data, Beech trees only
K.plot(hopper, subset=Size=="S")         # Hopper data, small trees only

Finally, note that for the Pasture and Beineke data sets, the DBH of trees are available while for the Hopper data set, trees are classified as large or small (DBH is not available).

These analyses can be repeated for any set of data and subset statements that you choose.

Questions

In this worksheet, you will analyze the data for the Beineke, Pasture, and Hopper sites to evaluate the general hypotheses listed below.

• Trees become more evenly spaced with increasing stand age
• Older trees are more evenly spaced than younger trees
• Different species show different spacing patterns, e.g., due to species-specific differences in reproduction/seed dispersal, etc.

Turn in the plots that accompany the above analyses along with a brief synopsis that addresses the original hypotheses and that compares your results to those presented by Condit et al. (2000).