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Fast Moran's I Autocorrelation Index

Source: R/moranfast.R
moranfast.Rd

This function computes Moran's I autocorrelation coefficient for a numeric vector x using a matrix of weights. The method follows Gittleman and Kot (1990). This function is an implementation of ape::Moran.I(), but rewritten in C++ to be substantially faster and more memory-efficient.

Usage

moranfast(
  x,
  weight,
  na_rm = TRUE,
  scaled = FALSE,
  alternative = c("two.sided")
)

Arguments

x

(numeric) A numeric vector (e.g., environmental values extracted from occurrence records).

weight

(matrix) A matrix of spatial weights (e.g., a distance or inverse-distance matrix). The number of rows must be equal to the length of x.

na_rm

(logical) whether to remove missing values from x. Default is TRUE.

scaled

(logical) whether to scale Moran's I so that it ranges between –1 and +1. Default is TRUE.

alternative

(character) The alternative hypothesis tested against the null hypothesis of no autocorrelation. Must be one of "two.sided", "less", or "greater". Default is "two.sided".

Value

A list with the following components:

  • observed – The observed Moran's I.

  • expected – The expected value of Moran's I under the null hypothesis.

  • sd – The standard deviation of Moran's I under the null hypothesis.

  • p.value – The p-value of the test based on the chosen alternative.

References

Gittleman, J. L., & Kot, M. (1990). Adaptation: statistics and a null model for estimating phylogenetic effects. Systematic Zoology, 39(3), 227–241.

Examples

# Load example data
data("occurrences", package = "RuHere")
# Filter occurrences of Araucaria
occ <- occurrences[occurrences$species == "Araucaria angustifolia", ]
# Load example of raster variables
data("worldclim", package = "RuHere")
# Unwrap Packed raster
r <- terra::unwrap(worldclim)
# Extract values for bio_1
bio_1 <- terra::extract(r$bio_1,
                        occ[, c("decimalLongitude", "decimalLatitude")],
                        ID = FALSE, xy = TRUE)
#Remove NAs
bio_1 <- na.omit(bio_1)
# Convert values to numeric
v <- as.numeric(bio_1$bio_1)
# Compute geographic distance matrix
d <- fields::rdist.earth(x1 = as.matrix(bio_1[, c("x", "y")]), miles = FALSE)
# Inverse-distance weights
d <- 1/d
# Fill diagonal with 0
diag(d) <- 0
# Remove finite values
d[is.infinite(d)] <- 0
# Compute Moran's I
m <- moranfast(x = v, weight = d, scale = TRUE)
# Print results
m
#> $observed
#> [1] 0.1940452
#> 
#> $expected
#> [1] -0.00128866
#> 
#> $sd
#> [1] 0.009968915
#> 
#> $p.value
#> [1] 0
#>