I'm stuck on which statistic to use with a spatial data set to resolve population concentrations in a large area, when I have only sampled a small area relative to that large area. Here's an example of my problem: somewhere there exists some hypothetical organism, the volcanobeast, that has a distribution in space, with a true concentration somewhere between 1 and 2 organisms per meter ^2, as follows.
library(tidyverse) library(cowplot) data("volcano") v2 = (volcano - min(volcano))/max(volcano) * 4 v3 <- reshape2::melt(v2) %>% rename(Xpos = Var1, Ypos = Var2) ggplot(v3, aes(x = Xpos, y = Ypos, fill = value)) + geom_raster() + scale_fill_viridis_c()
Here each square is a kilometer plot of land and the value is the number of organisms per meter squared on that plot of land. Observe that the data are autocorrelated in space. Nearby squares have similar values to eachother.
Let's say I sample one meter square within each kilometer of land. I think, that if these organisms are randomly distributed, I will get values per square meter that follow a poisson distribution (please correct me if I am wrong).
v4 <- v3 %>% mutate(meas = map_dbl(value, ~rpois(1, lambda = .))) ggplot(v4, aes(x = Xpos, y = Ypos, fill = meas)) + geom_raster() + scale_fill_viridis_c()
So here, we have the number of volcanobeasts sampled per square meter, on each 1 km plot of land. I am wondering if, using my knowledge that the data are autocorrelated and that I am drawing from a poisson distribution, I can get an estimate and confidence interval of the true concentration of volcanobeasts in each square kilometer.
Any suggestion on what might be the appropriate statistic for this? Thanks!