If I understand you correctly you wish to test the spatial relationship between the presence of disease in two species. The bivariate Cross-K statistic should get at this spatial relationship. You do not need the negative data [0] in each species. Unfortunately, bivariate point pattern statistics are not available in ArcGIS. Your only real option is conducting the analysis in R (http://cran.r-project.org/). I have included code that provides an example of a Cross-K, with a Monte Carlo simulation for significance testing, using the spatstat package. The simulated example will not be significant, so the simulation envelope will always encompass the full distribution. Applying this to real data will provide more sensible results. My example creates the simulated data in a SpatialPointsDataFrame sp object, which is what you get when you read point shapefiles using the readOGR function in rgdal. This should make it easy to apply the code example to your data. Most everything else is plug-and-play. In the code, the column name containing disease presence is called "MARKS", so you will need to change it to match your data. Please note that the way I have the analysis implemented, it returns the Besag-L(d) statistic which is a standardized version of the Ripley's-K(r) where the expected null is centered at 0. Some additional information and references on K(r) and L(d) is provided in this thread (http://forums.arcgis.com/threads/6160-K-Function). # ADD REQUIRED PACKAGES require(rgdal) require(sp) require(spatstat) options(scipen=5) # SIMULATE 1000 RANDOM OBS WITH A BINOMINAL [0,1] MARK COLUMN, THE ASSUMPTION IS THAT A # VALUE OF 1 & 2 REPRESENTS PRESENCE OF DESEASE IN EACH SPP i=1000 spp1 <- SpatialPointsDataFrame(cbind(round(runif(i), 2), round(runif(i), 2)), data.frame(ID=seq(1,i,1), MARKS=rbinom(i,1,0.5))) spp2 <- SpatialPointsDataFrame(cbind(round(runif(i), 2), round(runif(i), 2)), data.frame(ID=seq(1,i,1), MARKS=rbinom(i,1,0.5))) # RECODE spp2 MARKS AS 2 spp2@data$MARKS[spp2@data$MARKS == 1] <- 2 ############################################# ###### START MONTE CARLO CROSS-K ANALYSIS HERE ###### ############################################# # COMBINE INTO A SINGLE sp POINT OBJECT AND COERCE MARKS COL TO FACTOR spp <- rbind( spp1[spp1@data$MARKS > 0 ,], spp2[spp2@data$MARKS > 0 ,]) spp@data$MARKS <- as.factor(spp@data$MARKS) # CREATE CONVEX HULL FOR ANALYSIS WINDOW W=ripras(coordinates(spp)) # COERCE TO spatstat ppp OBJECT AND CREATE MARKS spp.ppp=as.ppp(coordinates(spp), W) spp.ppp=setmarks(spp.ppp, as.factor(spp$MARKS)) # ESTIMATE BANDWIDTH area <- area.owin(W) lambda <- spp.ppp$n/area ripley <- min(diff(W$xrange), diff(W$yrange))/4 rlarge <- sqrt(1000/(pi * lambda)) rmax <- min(rlarge, ripley) bw <- seq(0, rmax, by=rmax/10) # CALCULATE PERMUTED CROSS-K AND PLOT RESULTS Lenv <- envelope(spp.ppp, fun="Kcross", r=bw, i="1", j="2", nsim=99, nrank=5, transform=expression(sqrt(./pi)-bw), global=TRUE) plot(Lenv, main="Cross K", xlab="Distance", ylab="L(r)", legend=F, col=c("white","black","grey","grey"), lty=c(1,2,2,2), lwd=c(2,1,1,1) ) polygon( c(Lenv$r, rev(Lenv$r)), c(Lenv$lo, rev(Lenv$hi)), col="lightgrey", border="grey") lines(supsmu(bw, Lenv$obs), lwd=2) lines(bw, Lenv$theo, lwd=1, lty=2) legend("topleft", c(expression(hat(L)(r)), "Simulation Envelope", "theo"), pch=c(-32,22), col=c("black","grey"), lty=c(1,0,2), lwd=c(2,0,2), pt.bg=c("white","grey"))
