designdist {vegan} | R Documentation |

You can define your own dissimilarities using terms for shared and total quantities, number of rows and number of columns. The shared and total quantities can be binary, quadratic or minimum terms. In binary terms, the shared component is number of shared species, and totals are numbers of species on sites. The quadratic terms are cross-products and sums of squares, and minimum terms are sums of parallel minima and row totals.

designdist(x, method = "(A+B-2*J)/(A+B)", terms = c("binary", "quadratic", "minimum"), abcd = FALSE, name)

`x` |
Input data. |

`method` |
Equation for your dissimilarities. This can use terms
`J` for shared quantity, `A` and `B` for totals,
`N` for the number of rows (sites) and `P` for the number of
columns (species). The equation can also contain any R functions
that accepts vector arguments and returns vectors of the same
length. |

`terms` |
How shared and total components are found. For vectors
`x` and `y` the `"quadratic"` terms are `J = sum(x*y)` ,
`A = sum(x^2)` , `B = sum(y^2)` , and `"minimum"` terms
are `J = sum(pmin(x,y))` , `A = sum(x)` and ```
B =
sum(y)
``` , and `"binary"` terms are either of these after transforming
data into binary form (shared number of species, and number of
species for each row). |

`abcd` |
Use 2x2 contingency table notation for binary data:
a is the number of shared species, b and c are the
numbers of species occurring only one of the sites but not in both,
and d is the number of species that occur on neither of the sites. |

`name` |
The name you want to use for your index. The default is to
combine the `method` equation and `terms` argument. |

Most popular dissimilarity measures in ecology can be expressed with
the help of terms `J`

, `A`

and `B`

, and some also involve
matrix dimensions `N`

and `P`

. Some examples you can define in
`designdist`

are:

`A+B-2*J` | `"quadratic"` | squared Euclidean |

`A+B-2*J` | `"minimum"` | Manhattan |

`(A+B-2*J)/(A+B)` | `"minimum"` | Bray-Curtis |

`(A+B-2*J)/(A+B)` | `"binary"` | Sørensen |

`(A+B-2*J)/(A+B-J)` | `"binary"` | Jaccard |

`(A+B-2*J)/(A+B-J)` | `"minimum"` | Ružička |

`(A+B-2*J)/(A+B-J)` | `"quadratic"` | (dis)similarity ratio |

`1-J/sqrt(A*B)` | `"binary"` | Ochiai |

`1-J/sqrt(A*B)` | `"quadratic"` | cosine complement |

`1-phyper(J-1, A, P-A, B)` | `"binary"` | Raup-Crick |

The function `designdist`

can implement most dissimilarity
indices in `vegdist`

or elsewhere, and it can also be
used to implement many other indices, amongst them, most of those
described in Legendre & Legendre (1998). It can also be used to
implement all indices of beta diversity described in Koleff et
al. (2003), but there also is a specific function
`betadiver`

for the purpose.

If you want to implement binary dissimilarities based on the 2x2
contingency table notation, you can set `abcd = TRUE`

. In this
notation `a = J`

, `b = A-J`

, `c = B-J`

, ```
d =
P-A-B+J
```

. This notation is often used instead of the more more
tangible default notation for reasons that are opaque to me.

`designdist`

returns an object of class `dist`

.

`designdist`

does not use compiled code, and may be slow or use
plenty of memory in large data sets. It is very easy to make errors
when defining a function by hand. If an index is available in a
function using compiled code, it is better to use the canned
alternative.

Jari Oksanen

Koleff, P., Gaston, K.J. and Lennon, J.J. (2003) Measuring beta
diversity for presence–absence data. *J. Animal Ecol.*
**72**, 367–382.

Legendre, P. and Legendre, L. (1998) *Numerical Ecology*. 2nd
English ed. Elsevier

## Arrhenius dissimilarity: the value of z in the species-area model ## S = c*A^z when combining two sites of equal areas, where S is the ## number of species, A is the area, and c and z are model parameters. ## The A below is not the area (which cancels out), but number of ## species in one of the sites, as defined in designdist(). data(BCI) dis <- designdist(BCI, "(log(A+B-J)-log(A+B)+log(2))/log(2)") ## This can be used in clustering or ordination... ordiplot(cmdscale(dis)) ## ... or in analysing beta diversity (without gradients) summary(dis)

[Package *vegan* version 1.16-32 Index]