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

## Description

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

## Usage

 1 bray_curtis(x, y) 

## Arguments

 x, y Numeric vectors

## Details

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.

## Value

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.

## Examples

 1 2 3 4 5 6 7 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 

kylebittinger/abdiv documentation built on Jan. 19, 2020, 3:48 a.m.