library(spatstat)
library(raster)
library(sp)

plot(bei$x, bei$y, pch = 19, cex = 0.5, main = "Spatial distribution of individuals in the 50-ha Barro Colorado plot", 
    xlab = "x coordinate [m]", ylab = "y coordinate [m]", frame = FALSE)
abline(h = 0, col = "grey")
abline(h = 500, col = "grey")
abline(v = 0, col = "grey")
abline(v = 1000, col = "grey")


# coarsening the predictor data into the 50 x 50 m grid by taking the mean
# of the 5 x 5 m grid cells:
elev <- raster(bei.extra[[1]])
# cropping the data so that they have exactly 500 x 1000 cells
ext <- extent(2.5, 1002.5, 2.5, 1002.5)
elev <- crop(elev, ext)
# aggregating the elevation data
elev50 <- aggregate(elev, fact = 10, fun = mean)

# fitting the point data into the 50 x 50 m grid
xy <- data.frame(x = bei$x, y = bei$y)
n50 <- rasterize(xy, elev50, fun = "count")
# replacing the NA values by 0
n50[is.na(n50)] <- 0

plot(stack(elev50, n50), main = c("Predictor: Mean Elevation in 50x50 m cells", 
    "Response: # of Individuals in 50x50 m cells"), axes = FALSE)