Description Usage Arguments Details Value Author(s) References See Also Examples

Returns the ACSH score for some set of species of any cardinality.

1 | ```
acshgral(dotdata, species)
``` |

`dotdata` |
Object of class 'dotdata' |

`species` |
Vector of indices specifying the target group of species |

This function generalizes the notion of the ACSH score for pairs of species. It may consider simultaneously many elements from a pool of species. For a given universe of records, the overall ACSH averages the longest interspecific gap measured at each point. The interspecific gap corresponds to the shortest distance between a single point and a given set of species points.

I have implemented a procedure of agglomerative hierarchical clustering based on this measure. I think that results are very promising in the context of marked spatial point processes. This procedure advances on the classification problem stated by Mane et al. (2006). Basically, the idea consists of iteratively merging two items into a larger inclusive cluster so that the generalized acsh score is minimal across the totality of feasible merging scenarios.

A single non-negative real number that denotes the cost (in terms of imaginary spatial displacement) to achieve complete overlap between distributions.

Daniel A. Dos Santos <dadossantos@csnat.unt.edu.ar>

Dos Santos D.A., Cuezzo M.G., Reynaga M.C., Dominguez E. 2011. *Towards a Dynamic
Analysis of Weighted Networks in Biogeography.* Systematic Biology (in press).

Mane S., Kang J., Shekhar S., Srivastava J., Murray C., Pusey A. 2006. *Identifying
Clusters in Marked Spatial Point Processes: A Summary of Results.* Technical Report
06-006. Department of Computer Science and Engineering, University of Minnesota.

The function `acsh`

addresses pairwise comparisons between species
point sets.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 | ```
data(mayflynz)
procnz <- procdnpoint(mayflynz)
nsp <- length(procnz$Label)
testmt <- acsh(procnz)
# Following, we will produce a matrix of ACSH scores for pairs of species,
# but now with the generalized form.
calcmt <- matrix(0, nrow = nsp, ncol = nsp)
for(i in 1:(nsp-1))
for(j in (i+1):nsp)
calcmt[i,j] <- acshgral(procnz, c(i, j))
all(calcmt + t(calcmt) == testmt)
#The previous statement should be TRUE because the generalized ACSH
#corresponds to the standard pairwise ACSH when
#two species are submitted to the function "acshgral".
################
################
# This code makes explicit the above idea of hierarchical clustering based on the minimization
# of the ACSH profile throughout the nested structure of groups formed during the merging process
diag(testmt) <- Inf
newdist <- matrix(-1, nsp, nsp)
notation <- as.character(1:nsp)
classes <- 1:nsp
analyze <- array(TRUE, nsp)
while(max(classes)!= 1) {
aux <- which.min(testmt)
items <- sort(c(row(testmt)[aux], col(testmt)[aux]))
#Update cluster structure and ACSH scores
ngr <- which(classes %in% items)
classes[ngr] <- items[1]
notation[items[1]] <- paste("(", notation[items[1]], " ", notation[items[2]], ")", sep = "")
newdist[items[1], items[2]] <- newdist[items[2], items[1]] <- testmt[aux]
analyze[items[2]] <- FALSE
testmt[items, ] <- testmt[, items] <- Inf
for(i in which(analyze)) {
ogr <- which(classes == classes[i])
if(i == items[1]) next
testmt[items[1], i] <- testmt[i, items[1]] <- acshgral(procnz, c(ngr, ogr))
}
}
#Plot the respective dendrogram
tt <- max(newdist) + 1
newdist <- ifelse(newdist == -1, tt, newdist)
plot(hclust(as.dist(newdist), method = "single"), label = procnz$Label,
cex = 0.7, xlab = "", ylab = "Generalized ACSH")
#Display relationships into a parenthetical notation. You can track the indices of the species in the
#leaves of the following dendrogram
plot(hclust(as.dist(newdist), method = "single"))
cat(notation[1])
``` |

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