Raup-Crick Dissimilarity with Unequal Sampling Densities of Species

Function finds the Raup-Crick dissimilarity which is a probability of number of co-occurring species with species occurrence probabilities proportional to species frequencies.

raupcrick(comm, null = "r1", nsimul = 999, chase = FALSE, ...)

Arguments

comm	Community data which will be treated as presence/absence data.
null	Null model used as the `method` in `oecosimu`.
nsimul	Number of null communities for assessing the dissimilarity index.
chase	Use the Chase et al. (2011) method of tie handling (not recommended except for comparing the results against the Chase script).
...	Other parameters passed to `oecosimu`.

Details

Raup-Crick index is the probability that compared sampling units have non-identical species composition. This probability can be regarded as a dissimilarity, although it is not metric: identical sampling units can have dissimilarity slightly above \(0\), the dissimilarity can be nearly zero over a range of shared species, and sampling units with no shared species can have dissimilarity slightly below \(1\). Moreover, communities sharing rare species appear as more similar (lower probability of finding rare species together), than communities sharing the same number of common species.

The function will always treat the data as binary (presence/ absence).

The probability is assessed using simulation with oecosimu where the test statistic is the observed number of shared species between sampling units evaluated against a community null model (see Examples). The default null model is "r1" where the probability of selecting species is proportional to the species frequencies.

The vegdist function implements a variant of the Raup-Crick index with equal sampling probabilities for species using exact analytic equations without simulation. This corresponds to null model "r0" which also can be used with the current function. All other null model methods of oecosimu can be used with the current function, but they are new unpublished methods.

Value

The function returns an object inheriting from dist which can be interpreted as a dissimilarity matrix.

References

Chase, J.M., Kraft, N.J.B., Smith, K.G., Vellend, M. and Inouye, B.D. (2011). Using null models to disentangle variation in community dissimilarity from variation in \(\alpha\)-diversity. Ecosphere 2:art24 doi: 10.1890/ES10-00117.1

Note

The test statistic is the number of shared species, and this is typically tied with a large number of simulation results. The tied values are handled differently in the current function and in the function published with Chase et al. (2011). In vegan, the index is the number of simulated values that are smaller or equal than the observed value, but smaller than observed value is used by Chase et al. (2011) with option split = FALSE in their script; this can be achieved with chase = TRUE in vegan. Chase et al. (2011) script with split = TRUE uses half of tied simulation values to calculate a distance measure, and that choice cannot be directly reproduced in vegan (it is the average of vegan raupcrick results with chase = TRUE and chase = FALSE).

Examples

## data set with variable species richness
data(sipoo)
## default raupcrick
dr1 <- raupcrick(sipoo)
## use null model "r0" of oecosimu
dr0 <- raupcrick(sipoo, null = "r0")
## vegdist(..., method = "raup") corresponds to 'null = "r0"'
d <- vegdist(sipoo, "raup")
op <- par(mfrow=c(2,1), mar=c(4,4,1,1)+.1)
plot(dr1 ~ d, xlab = "Raup-Crick with Null R1", ylab="vegdist")
plot(dr0 ~ d, xlab = "Raup-Crick with Null R0", ylab="vegdist")
par(op)

## The calculation is essentially as in the following oecosimu() call,
## except that designdist() is replaced with faster code
if (FALSE)
oecosimu(sipoo, function(x) designdist(x, "J", "binary"), method = "r1")