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Convert similarity metrics to dissimilarity metrics

Source: R/similarity_dissimilarity_conversion.R
similarity_to_dissimilarity.Rd

This function converts a data.frame of similarity metrics between sites into dissimilarity metrics (beta diversity).

Usage

similarity_to_dissimilarity(similarity, include_formula = TRUE)

Arguments

similarity

The output object from similarity() or dissimilarity_to_similarity().

include_formula

A boolean indicating whether metrics based on custom formula(s) should also be converted (see Details). The default is TRUE.

Value

A data.frame with additional class bioregion.pairwise, providing dissimilarity metric(s) between each pair of sites based on a similarity object.

Note

The behavior of this function changes depending on column names. Columns Site1 and Site2 are copied identically. If there are columns called a, b, c, A, B, C they will also be copied identically. If there are columns based on your own formula (argument formula in similarity()) or not in the original list of similarity metrics (argument metrics in similarity()) and if the argument include_formula is set to FALSE, they will also be copied identically. Otherwise there are going to be converted like they other columns (default behavior).

If a column is called Euclidean, its distance will be calculated based on the following formula:

Euclidean distance = (1 - Euclidean similarity) / Euclidean similarity

Otherwise, all other columns will be transformed into dissimilarity with the following formula:

dissimilarity = 1 - similarity

See also

For more details illustrated with a practical example, see the vignette: https://biorgeo.github.io/bioregion/articles/a3_pairwise_metrics.html.

Associated functions: dissimilarity similarity_to_dissimilarity

Author

Maxime Lenormand (maxime.lenormand@inrae.fr)
Boris Leroy (leroy.boris@gmail.com)
Pierre Denelle (pierre.denelle@gmail.com)

Examples

comat <- matrix(sample(0:1000, size = 50, replace = TRUE,
prob = 1 / 1:1001), 5, 10)
rownames(comat) <- paste0("s", 1:5)
colnames(comat) <- paste0("sp", 1:10)

simil <- similarity(comat, metric = "all")
simil
#> Data.frame of similarity between sites
#>  - Total number of sites:  5 
#>  - Total number of species:  10 
#>  - Number of rows:  10 
#>  - Number of similarity metrics:  7 
#> 
#> 
#>    Site1 Site2   Jaccard Jaccardturn  Sorensen   Simpson       Bray   Brayturn
#> 2     s1    s2 0.6666667   1.0000000 0.8000000 1.0000000 0.14954683 0.16445183
#> 3     s1    s3 0.5000000   0.7142857 0.6666667 0.8333333 0.07591241 0.12956811
#> 4     s1    s4 0.6250000   0.7142857 0.7692308 0.8333333 0.23641070 0.24596050
#> 5     s1    s5 0.5555556   0.7142857 0.7142857 0.8333333 0.15248401 0.25747508
#> 8     s2    s3 0.8000000   0.8000000 0.8888889 0.8888889 0.37885057 0.57063712
#> 9     s2    s4 0.6000000   0.7500000 0.7500000 0.8571429 0.15324472 0.17594255
#> 10    s2    s5 0.7000000   0.7777778 0.8235294 0.8750000 0.51927543 0.77423823
#> 14    s3    s4 0.6000000   0.7500000 0.7500000 0.8571429 0.20597015 0.37163375
#> 15    s3    s5 0.7000000   0.7777778 0.8235294 0.8750000 0.31553398 0.31795947
#> 20    s4    s5 0.5000000   0.5555556 0.6666667 0.7142857 0.04426559 0.07899461
#>      Euclidean a b c   A    B    C
#> 2  0.002157589 6 0 3  99  503  623
#> 3  0.001250767 5 1 4  78  524 1375
#> 4  0.002461588 5 1 2 137  465  420
#> 5  0.001090607 5 1 3 155  447 1276
#> 8  0.001473415 8 1 1 412  310 1041
#> 9  0.002130648 6 3 1  98  624  459
#> 10 0.001582132 7 2 1 559  163  872
#> 14 0.001356957 6 3 1 207 1246  350
#> 15 0.001194697 7 2 1 455  998  976
#> 20 0.001084698 5 2 3  44  513 1387

dissimilarity <- similarity_to_dissimilarity(simil)
dissimilarity
#> Data.frame of dissimilarity between sites
#>  - Total number of sites:  5 
#>  - Total number of species:  10 
#>  - Number of rows:  10 
#>  - Number of dissimilarity metrics:  7 
#> 
#> 
#>    Site1 Site2   Jaccard Jaccardturn  Sorensen   Simpson      Bray  Brayturn
#> 2     s1    s2 0.3333333   0.0000000 0.2000000 0.0000000 0.8504532 0.8355482
#> 3     s1    s3 0.5000000   0.2857143 0.3333333 0.1666667 0.9240876 0.8704319
#> 4     s1    s4 0.3750000   0.2857143 0.2307692 0.1666667 0.7635893 0.7540395
#> 5     s1    s5 0.4444444   0.2857143 0.2857143 0.1666667 0.8475160 0.7425249
#> 8     s2    s3 0.2000000   0.2000000 0.1111111 0.1111111 0.6211494 0.4293629
#> 9     s2    s4 0.4000000   0.2500000 0.2500000 0.1428571 0.8467553 0.8240575
#> 10    s2    s5 0.3000000   0.2222222 0.1764706 0.1250000 0.4807246 0.2257618
#> 14    s3    s4 0.4000000   0.2500000 0.2500000 0.1428571 0.7940299 0.6283662
#> 15    s3    s5 0.3000000   0.2222222 0.1764706 0.1250000 0.6844660 0.6820405
#> 20    s4    s5 0.5000000   0.4444444 0.3333333 0.2857143 0.9557344 0.9210054
#>    Euclidean a b c   A    B    C
#> 2   462.4803 6 0 3  99  503  623
#> 3   798.5092 5 1 4  78  524 1375
#> 4   405.2419 5 1 2 137  465  420
#> 5   915.9208 5 1 3 155  447 1276
#> 8   677.6954 8 1 1 412  310 1041
#> 9   468.3407 6 3 1  98  624  459
#> 10  631.0586 7 2 1 559  163  872
#> 14  735.9429 6 3 1 207 1246  350
#> 15  836.0323 7 2 1 455  998  976
#> 20  920.9158 5 2 3  44  513 1387