# Species association between each pair of species

`sp.pair.Rd`

Compute species association between each pair of species.

    sp.pair(matr)

## Arguments

matr | Standard community matrix, with rows representing sites and columns representing species.

## Details

If `a`, `b`, `c`, `d` denote the co-occurrence the two species A and B, where:

`a` = number of plots occupied both by A and B.

`b` = number of plots only have A.

`c` = number of plots only have B.

`d` = number of plots without A or B.

`N` = `a+b+c+d`

Then, it is possible to compute:

Chi square (Yate's correction): `chi^{2}=((((a*d-b*c)-0.5*N)^2)*N)/(a+b)*(a+c)*(b+d)*(c+d)`

V ratio: `V = ((a+d)-(b+c))/(a + b + c + d)`

Jaccard index: `Jaccard =a/(a + b + c)`

Ochiai index: `Ochiai = a/sqrt((a+b)*(a+c))`

Dice index: `Dice = 2*a/(2*a + b + c)`

The Association Coefficient(`AC`):

if `a*d >= b*c`:

`AC = (a*d - b*c)/((a+b)*(b+d))`

if `a*d < b*c and a <= d`:

`AC = (a*d - b*c)/((a+b)*(a+c))`

if `a*d < b*c and a > d`:

`AC = (a*d - b*c)/((b+d)*(c+d))`

Point correlation coefficient

(`PCC`):

`PCC = {a*d-b*c}/{(a+b)*(a+c)*(c+d)*(b+d)}`

## Value

chisq

  Chi Square matrix

V

  `V` positive or negative association

Ochiai

  Ochiai's index

Dice

  Dice's index

Jaccard

  Jaccard's index

Pearson

  Pearson's correlation coefficient

Spearman

  Spearman's rank correlation coefficient

PCC

  Point correlation coefficient

AC

  Association coefficient

## References

HURLBERT, S. H. (1969). A coefficient of interspecific association. Ecology, 50(1), 1-9.

WANG, B. S., & PENG S. L. (1985). Studies on the Measuring Techniques of Interspecific Association of Lower-Subtropical Evergreen-Broadleaved Forests. I. The Exploration and the Revision on the Measuring Formulas of Interspecific Association. Chinese Journal of Plant Ecology, 9(4), 274-285.

JIAN, M. F., LIU, Q. J., ZHU, D., & YOU, H. (2009). Inter-specific correlations among dominant populations of tree layer species in evergreen broad-leaved forest in Jiulianshan Mountain of subtropical China. Chinese Journal of Plant Ecology, 33(4), 672-680.

ZHOU, X. Y., WANG, B. S., LI, M. G., & ZAN, Q. J. (2000). An analysis of interspecific associations in secondary succession forest communities in Heishiding Natural Reserve, Guangdong Province. Chinese Journal of Plant Ecology, 24(3), 332-339

## Author

Jinlong Zhang jinlongzhang01@gmail.com

## See also

See Also as `sp.assoc` for computing association for all the species.

## Examples

    data(testdata)
    spmatrix <- data2mat(testdata)
    result <- sp.pair(spmatrix)