Delimiting the modelling background for scattered uneven occurrence data

In species distribution modelling and ecological niche modelling (SDM & ENM), the region from where background or pseudoabsence points are picked is key to how well a model turns out. This region should include sufficient localities for the model to assess the species’ (non-)preferences, but it should also be within the species’ reach AND reasonably evenly surveyed for it. Survey bias within the background or the pseudoabsence region can seriously reduce model quality.

Yet, real-life occurrence data (especially at the wide scale of species distributions) often are strongly biased, and it’s rarely straightforward to define an adequate region around the existing points. Very nice criteria exist that work well in theory, but not under most actual scenarios of biodiversity data bias. Until recently, my preferred approach was a buffer around the known occurrences, whose radius was e.g. the mean pairwise distance between them (as a rough measure of their spatial spread, or the spatial reach of the species), or half the width of the area defined by the occurrences (usually better for elongated distributions or surveys):

# download some example occurrence records:

occs <- geodata::sp_occurrence("Rupicapra", "pyrenaica", args = c("year=2024"))


# map occurrence records:

occs <- terra::vect(occs, geom = c("lon", "lat"), crs = "EPSG:4326")
terra::plot(occs, cex = 0.2, ext = terra::ext(occs) + 4)
cntry <- geodata::world(path = tempdir())
terra::plot(cntry, lwd = 0.2, add = TRUE)
# note you should normally clean these records from errors before moving on!


# compute mean distance and width of occurrence records:

occs_mdist <- mean(terra::distance(occs))
occs_width <- terra::width(terra::aggregate(occs))


# compute buffers around occurrences using both metrics:

occs_buff_d <- terra::aggregate(terra::buffer(occs, width = occs_mdist))
occs_buff_w <- terra::aggregate(terra::buffer(occs, width = occs_width / 2))


# plot both buffers and occurrence records:

par(mfrow = c(1, 2))
terra::plot(occs_buff_d, col = "yellow", border = "orange", lwd = 3, ext = terra::ext(occs) + 4, main = "Mean distance")
terra::plot(cntry, lwd = 0.2, add = TRUE)
terra::plot(occs, cex = 0.2, add = TRUE)
terra::plot(occs_buff_w, col = "yellow", border = "orange", lwd = 3, ext = terra::ext(occs) + 4, main = "Half width")
terra::plot(cntry, lwd = 0.2, add = TRUE)
terra::plot(occs, cex = 0.2, add = TRUE)

This may work well for relatively evenly surveyed species or regions, where we can reasonably assume that most of the buffered area has been (roughly evenly) surveyed, and that most places without presence are likely absences. However, many species have isolated records in remote understudied areas, with survey effort hugely imbalanced across the distribution range. So, a buffer with a uniform radius will not work well:

occs <- geodata::sp_occurrence("Lutra", "lutra", args = c("year=2024"))

# everything else same code as above...

You can use smaller multipliers for distance and width, but these uniform-radius buffers will always include large regions with only scarce and isolated occurrence records, where it cannot be assumed that absence of records mostly reflects absence of the species. Normally I would terra::erase() from the buffer the regions that look insufficiently surveyed, but that implies discarding potentially valuable occurrence data.

So, my latest approach consists of finding clusters of occurrence points that are within a given distance of one another; and then defining a varying buffer radius of, e.g., the width or the mean pairwise distance among the points in each cluster, down-weighted by the distance to other points or clusters (as an indicator of isolated observations in under-surveyed areas). This way, the modelling background will avoid areas that were most likely not surveyed, yet without discarding the occurrence records from those areas. I’ve implemented several variations of this and related approaches in the new getRegion() function of R package fuzzySim (version 4.26):

# try regions with two different methods:

reg1 <- fuzzySim::getRegion(occs, type = "inv_dist")
terra::plot(cntry, lwd = 0.2, add = TRUE)
terra::plot(reg1, lwd = 4, border = "orange", add = TRUE)

reg2 <- fuzzySim::getRegion(occs, type = "clust_width", width_mult = 0.5)
terra::plot(cntry, lwd = 0.2, add = TRUE)
terra::plot(reg2, lwd = 4, border = "orange", add = TRUE)

Read the function help file for all the different options available, and try them out to see what feels best for your study system. Feedback and bug reports welcome!