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AMALIA algorithm for matching of sample and reference lead isotope data

Source: R/Amalia_algorithm.R
amalia.Rd

Implements the AMALIA (A Matching Algorithm for Lead Isotope Analyses) algorithm as described in Rodríguez et al. (2023). For each sample, the algorithm identifies analytically identical reference data by comparing lead isotope ratios within their combined analytical uncertainties across three independent isotope ratio dimensions.

Usage

amalia(
  df,
  ref,
  ratios_204 = c("206Pb/204Pb", "207Pb/204Pb", "208Pb/204Pb"),
  ratios_206 = c("204Pb/206Pb", "207Pb/206Pb", "208Pb/206Pb"),
  error_204 = c("206Pb/204Pb_err2SD", "207Pb/204Pb_err2SD", "208Pb/204Pb_err2SD"),
  error_206 = c("204Pb/206Pb_err2SD", "207Pb/206Pb_err2SD", "208Pb/206Pb_err2SD"),
  id_sample = "ID",
  id_ref = "ID",
  triplet = c("204Pb", "206Pb", "both")
)

Arguments

df

Data frame with sample data including isotope ratios, their analytical errors and an ID column.

ref

Data frame with reference data including isotope ratios, their analytical errors and an ID column. Must have the same column names as df.

ratios_204

Character vector of length 3 with column names of the 204Pb-normalised isotope ratios. Must be identical in df and ref. Default to c("206Pb/204Pb", "207Pb/204Pb", "208Pb/204Pb").

ratios_206

Character vector of length 3 with column names of the 206Pb-normalised isotope ratios. Must be identical in df and ref. Only used when triplet = "206" or triplet = "both". Default to c("206Pb/204Pb", "207Pb/206Pb", "208Pb/206Pb").

error_204

Character vector of length 3 with column names of the analytical uncertainty in 2SD for the 204Pb-normalised ratios. Must be identical in both df and ref. Default to c("206Pb/204Pb_err2SD", "207Pb/204Pb_err2SD", "208Pb/204Pb_err2SD").

error_206

Character vector of length 3 with column names of the analytical uncertainty (2SD) for the 206Pb-normalised ratios. Must be identical in both df and ref. Only used when triplet = "206" or triplet = "both". Default to c("206Pb/204Pb_err2SD", "207Pb/206Pb_err2SD", "208Pb/206Pb_err2SD").

id_sample

String with the column name of the sample IDs in df. Default is "ID".

id_ref

String with the column name of the reference groups in ref. Default is "ID".

triplet

Character string specifying which isotope ratio triplet to use for matching. One of "204" (206/204, 207/204, 208/204), "206" (206/204, 207/206, 208/206), or "both" (a match must pass both triplets simultaneously, following Rodríguez et al. 2023). Default is "204".

Value

A list of three elements:

  • summary_matches: Data frame with with the number of reference data matches per sample.

  • matches: Data frame with every sample-reference pair that passed the AMALIA matching criteria.

  • unmatched: Character vector with the IDs of samples with no matches in the reference data.

Details

For each sample-reference pair, the function checks whether the absolute difference between their isotope ratios is smaller than or equal to the combined analytical uncertainty (sum of both 2SD errors) for all three ratios in the selected triplet simultaneously.

When triplet = "both", only pairs that pass in both the 204Pb and 206Pb triplet spaces are returned, following the strict application recommended by Rodríguez et al. (2023).

References

Rodríguez, J., Sinner, A.G., Martínez-Chico, D. and Santos Zalduegui, J.F. (2023). AMALIA, A Matching Algorithm for Lead Isotope Analyses: Formulation and proof of concept at the Roman foundry of Fuente Spitz (Jaén, Spain). Journal of Archaeological Science: Reports 51, 104192. https://doi.org/10.1016/j.jasrep.2023.104192

Examples

df <- data.frame(
  ID = c("Art1", "Art2", "Art3"),
  `206Pb/204Pb` = c(18.244, 18.419, 18.050),
  `207Pb/204Pb` = c(15.634, 15.658, 15.620),
  `208Pb/204Pb` = c(38.407, 38.638, 38.157),
  `206Pb/204Pb_err2SD` = c(0.001, 0.001, 0.001),
  `207Pb/204Pb_err2SD` = c(0.001, 0.001, 0.001),
  `208Pb/204Pb_err2SD` = c(0.002, 0.002, 0.002),
  `204Pb/206Pb` = c(0.0537, 0.0539, 0.0554),
  `207Pb/206Pb` = c(0.857, 0.850, 0.865),
  `208Pb/206Pb` = c(2.105, 2.098, 2.114),
  `204Pb/206Pb_err2SD` = c(0.00001, 0.00001, 0.00001),
  `207Pb/206Pb_err2SD` = c(0.00001, 0.00001, 0.00001),
  `208Pb/206Pb_err2SD` = c(0.00004, 0.00004, 0.00004),
  check.names = FALSE
)

ref <- data.frame(
  ID = c("Ore_A", "Ore_B", "Ore_C"),
  `206Pb/204Pb` = c(18.242, 18.500, 18.048),
  `207Pb/204Pb` = c(15.633, 15.700, 15.619),
  `208Pb/204Pb` = c(38.405, 38.800, 38.155),
  `206Pb/204Pb_err2SD` = c(0.001, 0.001, 0.001),
  `207Pb/204Pb_err2SD` = c(0.001, 0.001, 0.001),
  `208Pb/204Pb_err2SD` = c(0.002, 0.002, 0.002),
  `204Pb/206Pb` = c(0.0543, 0.0543, 0.0543),
  `207Pb/206Pb` = c(0.857, 0.850, 0.865),
  `208Pb/206Pb` = c(2.105, 2.098, 2.114),
  `204Pb/206Pb_err2SD` = c(0.00001, 0.00001, 0.00001),
  `207Pb/206Pb_err2SD` = c(0.00001, 0.00001, 0.00001),
  `208Pb/206Pb_err2SD` = c(0.00004, 0.00004, 0.00004),
  check.names = FALSE
)

amalia(df, ref)
#> 2 sample(s) without matches: Art2, Art3
#> $summary_matches
#>   sample_id n_matches
#> 1      Art1         1
#> 2      Art2         0
#> 3      Art3         0
#> 
#> $matches
#>   sample_id ref_id
#> 1      Art1  Ore_A
#> 
#> $unmatched
#> [1] "Art2" "Art3"
#>