bray_curtis {abdiv} | R Documentation |

## Bray-Curtis distance

### Description

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

### Usage

```
bray_curtis(x, y)
```

### Arguments

### Details

For two vectors `x`

and `y`

, the Bray-Curtis distance is defined
as

`d(x, y) = \frac{\sum_i |x_i - y_i|}{\sum_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

```
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
```

[Package

*abdiv* version 0.2.0

Index]