toposimilar: Resemblance between Process Point Patterns
In SyNet: Inference and Analysis of Sympatry Networks

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

Produces a weighted matrix of sympatric association between species from their points of occurrence.

1	toposimilar(dotdata)

dotdata

Object of class 'dotdata'

This function accounts for the strength of sympatric relationships between species. In considering traditional approaches to measure sympatry, distributions are coded into some contour maps and the percentage of overlap between distributions is then calculated. Here, there is independence from explicit species areas, so arbitrary enclosing areas for the raw points of occurrence are avoided. On the contrary, this function focuses on the resemblance between patterns of spatial occupancy followed by the records themselves.

The minimum spanning tree (MST) of species dots are used as the operational tool to capture the skeleton of their spatial pattern. If two sets of points associated to a pair of species are both close and interpenetrated (i.e. exhibit a similar pattern and likely belong to an underlying area of common membership), the MST of the joint set of points is expected to be formed by several arcs connecting interspecific pair of points. For a pair of species, sympatry is considered when their joint set of points gives rises to a MST not longer than the sum of the individual MST lengths associated to each species. If two species have a single record each, they are considered maximally sympatric if they co-occur at the same single point.

Returns a matrix that expresses the spatial similarity between species point sets. Non-negative values suggest sympatry and denote the relative strength of association in the interval [0, 1]. Negative values suggest allopatry and correspond (their absolute image) to the shortest geographical gap between dot sets.

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).

Dos Santos D.A., Deutsch R. 2010. The Positive Matching Index: a New Similarity Measure with Optimal Characteristics. Pattern Recognition Letters 31: 1570-1576.

Objects of class 'dotdata' are created via procdnpoint.

  data(mayflynz)
  aux <- procdnpoint(mayflynz)
  # Infer the weighted sympatry matrix and display 
  # a portion of its entries.
  head(toposimilar(aux))

Loading required package: tkrplot
Loading required package: tcltk
Warning messages:
1: no DISPLAY variable so Tk is not available 
2: loading Rplot failed 
             [,1]         [,2]         [,3]      [,4]         [,5]         [,6]
[1,]    1.0000000    0.3817998    0.6919001 -114.0997    0.5266072    0.6377646
[2,]    0.3817998    1.0000000    0.3623227 -305.5403    0.2920513    0.3203403
[3,]    0.6919001    0.3623227    1.0000000 -139.5928    0.6897253    0.8546891
[4,] -114.0996973 -305.5403223 -139.5927794    1.0000 -139.5927794 -139.5927794
[5,]    0.5266072    0.2920513    0.6897253 -139.5928    1.0000000    0.6571592
[6,]    0.6377646    0.3203403    0.8546891 -139.5928    0.6571592    1.0000000
             [,7]       [,8]         [,9]         [,10]        [,11]
[1,]    0.7811762 -1235.9838    0.5779683 -142.29079000    0.4442608
[2,]    0.3442210 -1580.8902    0.6282465 -480.19788069    0.2248347
[3,]    0.6887792  -975.5609    0.4676007    0.07950638    0.7152973
[4,] -185.8037896 -1887.9946 -139.5927794 -830.95952808 -334.9135621
[5,]    0.4993200  -554.6823    0.4797940    0.34489504    0.6167872
[6,]    0.6475910  -951.9365    0.4225059    0.10771075    0.6730457
             [,12]        [,13]        [,14]        [,15]         [,16]
[1,]  -630.6373195    0.7365251    0.6539110    0.5320382    0.15669031
[2,]  -940.1090972    0.3703104    0.3385958    0.2186969 -136.98078888
[3,]  -327.1334703    0.8517057    0.9156225    0.7380831    0.19132245
[4,] -1228.3739249 -105.9730387 -139.5927794 -139.5927794 -567.44467569
[5,]     0.1410847    0.5908456    0.6795478    0.8164868    0.02559792
[6,]  -314.6070633    0.7768944    0.7720268    0.6638417    0.16468954
            [,17]        [,18]         [,19]         [,20]         [,21]
[1,]    0.4433467 -109.4652010    0.02915172 -147.30145010 -320.71138074
[2,]    0.3016354 -395.7636007 -352.51817171 -499.66567571 -630.58367790
[3,]    0.6696655    0.2390157    0.32927990    0.03301319  -46.04252129
[4,] -305.5403223 -722.7678078 -763.97099251 -874.73874955 -954.53819920
[5,]    0.7115880    0.2896263    0.40188404    0.34253345    0.01040109
[6,]    0.6841568    0.2488488    0.29918952    0.06575656    0.00000000
            [,22]     [,23]         [,24]        [,25]       [,26]        [,27]
[1,] -372.1251830    0.0000    0.19889554    0.5443960   0.4931477 -117.4650127
[2,] -671.4135223    0.0000    0.16437383    0.4121930   0.2545392 -408.2991423
[3,]  -59.4153651    0.0000    0.04218904    0.7061705   0.7227953    0.1298353
[4,] -980.3657876 -305.5403 -431.38502551 -285.9217151 -82.5080836 -770.5575415
[5,]    0.3184629    0.0000    0.10573847    0.6609104   0.7823755    0.4143849
[6,]  -52.8363142    0.0000    0.12833183    0.6611839   0.6670451    0.1500679
            [,28]         [,29]        [,30]      [,31]        [,32]
[1,]    0.5336634 -7.242875e+02    0.4742707  -315.7902    0.4530565
[2,]    0.2437278 -1.046919e+03    0.1763298  -669.0399    0.8546434
[3,]    0.5584680 -4.349826e+02    0.5310601  -167.2829    0.3444471
[4,] -306.0298525 -1.342735e+03 -145.4949201 -1028.3443 -305.5403223
[5,]    0.3317002  4.196488e-02    0.5955185  -112.2095    0.3009606
[6,]    0.4740526 -4.170733e+02    0.5170038  -121.8747    0.3576757
           [,33]        [,34]        [,35]        [,36]        [,37]
[1,]   0.7978846    0.7330532    0.4987937    0.4207156    0.4811253
[2,]   0.3640711    0.3122216    0.2854266    0.2815423    0.2113759
[3,]   0.5964541    0.7621951    0.7610719    0.7155483    0.6756133
[4,] -23.9341140 -139.5927794 -171.4099700 -260.7594649 -215.8493879
[5,]   0.5084760    0.6159593    0.6204678    0.5814828    0.5664688
[6,]   0.5891334    0.6967336    0.7349587    0.6170950    0.6682742
           [,38]        [,39]       [,40]
[1,]   0.6201106    0.5903461   0.5853170
[2,]   0.2856780    0.4635046   0.2977110
[3,]   0.7501427    0.4265058   0.6710372
[4,] -82.5080836 -105.9730387 -99.6300888
[5,]   0.8332826    0.3931751   0.6509665
[6,]   0.7181556    0.4203015   0.7092974