Calculate spatial correlation between two locations — calc_spatial

Computes the Pearson spatial–correlation coefficient \(\mathcal{C}_{ij}\) (Keeling & Rohani 2002) for a pair of locations i and j from single infection time-series per location.

Usage

calc_spatial_correlation(I_i, I_j, N_i = 1, N_j = 1)

Arguments

I_i

Numeric vector. Total infections in location i at each reporting time.

I_j

Numeric vector. Total infections in location j at each reporting time. Must be the same length as I_i.

N_i

Numeric scalar or vector. Population size(s) of location i.

If a scalar, the value is recycled across all time points.
If a vector, it must be the same length as the infection series and supplies time-varying population sizes.
Default is 1, implying that infection counts are already expressed as prevalences.

N_j

Numeric scalar or vector. Population size(s) of location j. Recycling and length rules mirror those of N_i. Default 1.

Value

Numeric scalar in the interval [-1, 1] giving the spatial correlation between the two locations, or NA_real_ if the calculation is not possible (e.g. all values NA, zero variance).

Details

The prevalence series are \(y_{it} = I_{it} / N_{i,t}\) and \(y_{jt} = I_{jt} / N_{j,t}\), where the population sizes \(N_{i,t}\) and \(N_{j,t}\) may be either scalars (constant over time) or vectors the same length as the infection series (time-varying).

Rows containing NA in either prevalence series are removed automatically. If fewer than two paired observations remain, the function returns NA_real_. A consistency check stops execution if any computed prevalence exceeds 1.

References

Keeling M.J., Rohani P. (2002) Ecology Letters 5, 20–29.

Examples

set.seed(1)
t  <- 20
I_i <- rpois(t,  8)
I_j <- rpois(t, 12)
N_i <- round(seq(9.8e4, 1.02e5, len = t))   # growing population
N_j <- 8e4                                   # constant population
calc_spatial_correlation(I_i, I_j, N_i, N_j)
#> [1] 0.1570293