bray_curtis: Bray-Curtis distance
In abdiv: Alpha and Beta Diversity Measures

Description Usage Arguments Details Value Examples

The Bray-Curtis distance is the Manhattan distance divided by the sum of both vectors.

1	bray_curtis(x, y)

x, y

Numeric vectors

For two vectors x and y, the Bray-Curtis distance is defined as

d(x, y) = \frac{∑_i |x_i - y_i|}{∑_i x_i + y_i}.

The Bray-Curtis distance is connected to many other distance measures in this package; we try to list some of the more important connections here. Relation to other definitions:

Equivalent to vegdist() with method = "bray".
Equivalent to the braycurtis() function in scipy.spatial.distance for positive vectors. They take the absolute value of x_i + y_i in the denominator.
Equivalent to the braycurtis and odum calculators in Mothur.
Equivalent to D_14 = 1 - S_17 in Legendre & Legendre.
The Bray-Curtis distance on proportions is equal to half the Manhattan distance.
The Bray-Curtis distance on presence/absence vectors is equal to the Sorenson index of dissimilarity.

The Bray-Curtis distance between x and y. The Bray-Curtis distance is undefined if the sum of all elements in x and y is zero, in which case we return NaN.

x <- c(15, 6, 4, 0, 3, 0)
y <- c(10, 2, 0, 1, 1, 0)
bray_curtis(x, y)

# For proportions, equal to half the Manhattan distance
bray_curtis(x / sum(x), y / sum(y))
manhattan(x / sum(x), y / sum(y)) / 2