Iteratively, optimally split a connectivity matrix
Description
Algorithm for iteratively determining subpopulations of highlyconnected sites. Uses an iterative method described in Jacobi et al. (2012)
Usage
1 2 3 4 
Arguments
conn.mat 
A square connectivity matrix. 
normalize.cols 
A boolean indicating if columns of conn.mat should be normalized by the sum of all elements in the column. Defaults to TRUE. 
make.symmetric 
A string indicating how to force conn.mat to be symmetric. "mean" (the default) will replace C_ij by (C_ij + C_ji)/2. "max" will replace C_ij by the maximum of C_ij and C_ji. 
remove.diagonal 
A boolean indicating if the diagonal elements of conn.mat should be removed before determining the subpopulations. Defaults to FALSE. 
cycles 
Number of times to pass over values in betas. 
betas 
Vector of beta values to try. If not given, will
default to 
steps 
Number of beta values to produce using betasVectorDefault. Ignored if betas argument is explicitly given. 
... 
further arguments to be passed to 
Value
A list with the following elements:
betas 
Vector of all beta values tested 
num.subpops 
Vector of number of subpopulations found for each value of beta 
qualities 
Vector of the quality statistic for each subpopulation division 
subpops 
A matrix with dimensions dim(conn.mat)[2] X length(betas) indicating which subpopulation each site belongs to 
best.splits 
A list indicating for each number of
subpopulations, which column of subpops contains the division with
the lowest quality statistic. E.g.,

Note
In Jacobi et al. (2012) paper, the connectivity matrix is
oriented so that C_ij is dispersal from i to j, whereas in this R
package, the connectivity matrix is oriented so that C_ij is
dispersal from j to i. This choice of orientation is arbitrary,
but one must always be consistent. From j to i is more common in
population dynamics because it works well with matrix
multiplication (e.g., settlers = conn.mat %*% eggs
).
Author(s)
David M. Kaplan dmkaplan2000@gmail.com
References
Jacobi, M. N., Andre, C., Doos, K., and Jonsson, P. R. 2012. Identification of subpopulations from connectivity matrices. Ecography, 35: 10041016.
See Also
See also splitConnMat
,
recSplitConnMat
, mergeSubpops
,
qualitySubpops
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18  library(ConnMatTools)
data(chile.loco)
num < prod(dim(chile.loco)) / sum(chile.loco)
betas < betasVectorDefault(n=num,steps=4)
chile.loco.split < optimalSplitConnMat(chile.loco,normalize.cols=FALSE,
betas=betas)
# Extra 3rd division
print(paste("Examining split with",names(chile.loco.split$best.splits)[1],
"subpopulations."))
pops < subpopsVectorToList(chile.loco.split$subpops[,chile.loco.split$best.splits[[1]]$index])
reduce.loco < reducedConnMat(pops,chile.loco)
sr < selfRecruitment(reduce.loco)
lr < localRetention(reduce.loco)
rlr < relativeLocalRetention(reduce.loco)
