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Comparing Isotope Samples to Reference Data in 3D Space

pointcloud_distribution.Rd

This package compares isotope samples to reference data in 3D space to identify isotopic consistency and the possibility of mixing between sources.

Usage

pointcloud_distribution(
  df,
  ref,
  isotope_sample = c("206Pb/204Pb", "207Pb/204Pb", "208Pb/204Pb"),
  isotope_ref = isotope_sample,
  id_sample = "ID",
  id_ref = id_sample
)

Arguments

df

Data frame with sample data, including isotope ratios and ID columns.

ref

Data frame with reference data, including isotope ratios and group column.

isotope_sample, isotope_ref

Character vectors with column names of isotope ratios. Default to c("206Pb/204Pb", "207Pb/204Pb", "208Pb/204Pb").

id_sample, id_ref

String with the column name of the sample IDs and identifier for the reference groups. Default ID.

Value

A list of three elements:

  • in_hull: logical. Boolean value indicating the inclusion of sample data within the convex hull of the reference data.

  • centroids: data.frame. The coordinates of the centroids (mean values) for each defined reference group.

  • distances: matrix. A distance matrix where rows represent the samples and columns represent the reference centroids, containing the distance of each sample from each centroid.

Details

Calculates the convex hull for the complete set of reference points and all specified subgroups. It determines the inclusion or exclusion of sample isotope values within these hulls.

The function also calculates:

  • The centroid of each reference subgroup as mean value of points within each vertex group.

  • The distance from each sample point to every subgroup's centroid.

Interpretation: Inclusion within a hull suggests the sample is part of the mixing group (main hull) or is highly likely to be the specific end member (subgroup hull). The distance calculation provides a measure of proximity to these end member centers.

Examples

# Create synthetic data
set.seed(24021999)
iso <- c("206Pb/204Pb","207Pb/204Pb","208Pb/204Pb")

# Create synthetic reference data
groups <- LETTERS[1:4]
rand_iso <- function(){c(runif(1, 18.3, 19), runif(1, 15.5, 15.9), runif(1, 37.5, 39))}
list_df <- lapply(groups, function(x){
  ls <- sapply(rand_iso(),  function(g){stats::rnorm(20, g, stats::runif(1, 0.05, 0.1))})
  colnames(ls) <- iso
  ls <- as.data.frame(ls)
  ls$ID <- x
  ls
})
ref <- as.data.frame(do.call(rbind, list_df))

## Create sample data
df <- as.data.frame(sapply(rand_iso(),  function(g){rnorm(20, g, 0.1)}))
colnames(df) <- iso
df$ID <- letters[1:20]
rm(list_df, iso, groups, rand_iso)

# Run pointcloud_distribution
pointcloud_distribution(df, ref, isotope_sample = c("206Pb/204Pb",
"207Pb/204Pb", "208Pb/204Pb"), id_sample = "ID")
#> $in_hull
#>   hull_inout     A     B     C     D
#> a      FALSE FALSE FALSE FALSE FALSE
#> b       TRUE FALSE FALSE FALSE FALSE
#> c       TRUE FALSE FALSE FALSE  TRUE
#> d       TRUE FALSE FALSE FALSE FALSE
#> e      FALSE FALSE FALSE FALSE FALSE
#> f      FALSE FALSE FALSE FALSE FALSE
#> g       TRUE FALSE FALSE FALSE FALSE
#> h       TRUE FALSE FALSE FALSE FALSE
#> i       TRUE FALSE FALSE FALSE  TRUE
#> j      FALSE FALSE FALSE FALSE FALSE
#> k       TRUE FALSE FALSE FALSE FALSE
#> l       TRUE FALSE FALSE FALSE FALSE
#> m       TRUE FALSE FALSE FALSE FALSE
#> n       TRUE FALSE FALSE FALSE FALSE
#> o       TRUE FALSE FALSE FALSE FALSE
#> p       TRUE FALSE FALSE FALSE FALSE
#> q      FALSE FALSE FALSE FALSE FALSE
#> r      FALSE FALSE FALSE FALSE FALSE
#> s       TRUE FALSE FALSE FALSE FALSE
#> t       TRUE FALSE FALSE FALSE FALSE
#> 
#> $centroids
#>   ID 206Pb/204Pb 207Pb/204Pb 208Pb/204Pb
#> 1  A    18.90676    15.63670    38.68651
#> 2  B    18.49755    15.55502    37.49381
#> 3  C    18.73894    15.57353    38.62651
#> 4  D    18.47097    15.58188    38.38394
#> 
#> $distances
#>           A         B         C          D
#> a 0.3467945 1.0100437 0.2557936 0.27944308
#> b 0.5774481 0.7495366 0.4305455 0.19930889
#> c 0.5071899 0.9692208 0.3286081 0.07940771
#> d 0.3930040 1.0215753 0.2334398 0.17040417
#> e 0.3636865 1.0374460 0.2687828 0.28295426
#> f 0.5710444 1.0714041 0.3831217 0.24319115
#> g 0.3687799 1.0232475 0.1855639 0.18551396
#> h 0.5122015 0.8214975 0.3820567 0.16727042
#> i 0.5707212 0.8898764 0.3921051 0.05925920
#> j 0.5694056 0.9690502 0.4517148 0.27574097
#> k 0.4107953 0.8812797 0.2777982 0.19693902
#> l 0.4329620 0.9085274 0.3205349 0.21528808
#> m 0.3588225 0.9118006 0.2644440 0.27353803
#> n 0.3146948 1.0046191 0.2395313 0.30350096
#> o 0.5463120 0.7681217 0.4067310 0.16267856
#> p 0.3810937 1.0223545 0.2278692 0.18371364
#> q 0.4472888 1.0967249 0.3143663 0.26011339
#> r 0.8274133 0.6461316 0.6971180 0.38489301
#> s 0.3634613 1.0412516 0.1787841 0.21774540
#> t 0.1178420 1.1647764 0.1506870 0.43952183
#> 

# cleanup
rm(df, ref)