Spatial weights for individuals (nodes) with coordinates XY
eco.weight(XY, method = c("circle", "knearest", "inverse", "circle.inverse", "exponential", "circle.exponential"), W = NULL, d1 = 0, d2 = NULL, k = NULL, p = 1, alpha = 1, dist.method = "euclidean", row.sd = FALSE, max.sd = FALSE, self = FALSE, latlon = FALSE, ties = c("unique", "min", "random", "ring", "first"))
| XY | Matrix/data frame with projected coordinates. |
|---|---|
| method | Method of spatial weight matrix: "circle", "knearest", "inverse", "circle.inverse", "exponential", "circle.exponential". |
| W | Custom weight matrix, with rownames and colnames identical to the XY data frame with coordinates |
| d1 | Minimum distance for circle matrices. |
| d2 | Maximum distance for circle matrices. |
| k | Number of neighbors for nearest neighbor distance. When equidistant neighbors are present, the program select them randomly. |
| p | Power for inverse distance. Default = 1. |
| alpha | Alpha value for exponential distance. Default = 1. |
| dist.method | Method used for computing distances passed to |
| row.sd | Logical. Should be row standardized the matrix? Default FALSE (binary weights). |
| max.sd | Logical. Should be divided each weight by the maximum of the matrix? Default FALSE (binary weights). |
| self | Should be the individuals self-included in circle or knearest weights? Defalut FALSE. |
| latlon | Are the coordinates in decimal degrees format? Defalut FALSE. If TRUE,
the coordinates must be in a matrix/data frame with the longitude in the first
column and latitude in the second. The position is projected onto a plane in
meters with the function |
| ties | ties handling method for "knearest" method: "unique" (default) for counting the ties as an unique neighbor (i.e), "min" for counting all the ties in a given category but each is counted as a neighbor, "random" for choosing at random a neighbor, "ring" for ring of neighbors, "first" for sequential k values for each neighbor. |
An object of class eco.weight with the following slots:
> W weights matrix
> XY input coordinates
> METHOD weights construction method
> PAR parameters used for the construction of weights
> PAR.VAL values of the parameters used for the construction of weights
> ROW.SD row standardization (logical)
> SELF data self-included (logical)
> NONZERO percentage of non-zero connections
> NONZEROIND percentage of individuals with non-zero connections
> AVERAGE average number of connection per individual
ACCESS TO THE SLOTS The content of the slots can be accessed with the corresponding accessors, using the generic notation of EcoGenetics (<ecoslot.> + <name of the slot> + <name of the object>). See help("EcoGenetics accessors") and the Examples section below
This program computes a weights matrix (square matrix with individuals in rows and columns, and weights wij in cells (i and j, individuals)) under the following available methodologies:
- circle: all the connection between individuals i and j, included in a distance radius, higher than d1 and lower than d2, with center in the individual i, have a value of 1 for binary weights. This distance requires the parameters d1 and d2 (default d1 = 0).
- knearest: the connections between an individual and its nearest neighbors of each individual i have a value of 1 for binary weights. This distance requires the parameter k.
- inverse: inverse distance with exponent p (distance = 1/dij^p, with dij the distance between individuals i and j). This distance requires the parameter p (default p = 1).
- circle inverse: combination of "circle" and "inverse". It is the matrix obtained by multiplying each element in a "circle" binary matrix, and an "inverse" matrix. This distance requires the parameters p, d1 and d2 (default p = 1, d1 = 0).
- exponential: inverse exponential distance with parameter alpha (distance = 1/e^(alpha *dij), with dij the distance between individuals i and j). This distance requires the parameter alpha (default alpha = 1).
- circle exponential: combination of "circle" and "exponential". It is the matrix obtained by multiplying each element in a "circle" binary matrix, and an "exponential" matrix. This distance requires the parameters alpha, d1 and d2 (default alpha = 1, d1 = 0).
In addition to these methods, a spatial weight object can be created assigning a custom W matrix ("W" argument). In this case, the "method" is argument automatically set by the program to "custom" (see te example).
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In row standardization, each weight wij for the individual i, is divided by the sum of the row weights (i.e., wij / sum(wij), where sum(wij) is computed over an individual i and all individuals j).
When self is TRUE, the connection j = i is also included.
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PLOTS FOR ECO.WEIGHT OBJECTS:
A plot method is availble (function "eco.plotWeight") showing static or interactive plots, In the case of using the function eco.plotWeight for the argument type="simple", the connections are shown in two plots: an X-Y graph, with the individuals as points, representing the original coordinates, and in a plot with coordinates transformed as ranks (i.e., each coordinate takes an ordered value from 1 to the number of individuals). The other static method (type="igraph") uses the igraph package to generate a visual attractive graph (force network). Two interactive methods are available: type = "network", to plot an interactive force network, and type = "edgebundle" to plot a circular network. For the cases type = "inverse" or type = "exponential", the program generates a plot of weights values vs distance See the examples below.
# NOT RUN { data(eco3) # 1) "circle" method con <- eco.weight(eco3[["XY"]], method = "circle", d1 = 0, d2 = 500) #---- Different plot styles for the graph ----# # simple eco.plotWeight(con, type = "simple") # igraph eco.plotWeight(con, type = "igraph", group = eco3[["S"]]$structure) # network (interactive) ## click in a node to see the label eco.plotWeight(con, type = "network", bounded = TRUE, group = eco3[["S"]]$structure) # edgebundle (interactive) ## in the following plot, the assignment a group factor, ## generates clustered nodes. ## hover over the nodes to see the individual connections eco.plotWeight(con, type = "edgebundle", fontSize=8, group = eco3[["S"]]$structure) # 2) "knearest" method con <- eco.weight(eco3[["XY"]], method = "knearest", k = 10) eco.plotWeight(con) eco.plotWeight(con, type = "network", bounded = TRUE, group = eco3[["S"]]$structure) # 3) "inverse" method ## scale dependent. In the example, the original coordinates (in km) are converted into m con <- eco.weight(eco3[["XY"]]/1000, method = "inverse", max.sd = TRUE, p = 0.1) con eco.plotWeight(con) # 4) "circle.inverse" method con <- eco.weight(eco3[["XY"]], method = "circle.inverse", d2 = 1000) con eco.plotWeight(con) # 5) "exponential" method ## scale dependent. In the example, the original coordinates (in km) are converted into m con <- eco.weight(eco3[["XY"]]/1000, method = "exponential", max.sd = TRUE, alpha = 0.1) eco.plotWeight(con) # 6) "circle.exponential" method con <- eco.weight(eco3[["XY"]], method = "circle.exponential", d2 = 2000) con eco.plotWeight(con) # 7) CUSTOM WEIGHT MATRIX ## An eco.weight object can be created with a custom W matrix. In this case, ## the rows and the columns of W (weight matrix) must have names, ## that must coincide (also in order) with the name of the XY (position) matrix. require(igraph) ## this example generates a network with the package igraph tr <- make_tree(40, children = 3, mode = "undirected") plot(tr, vertex.size = 10, vertex.label = NA) ## conversion from igraph to weight matrix weights <- as.matrix(as_adj(tr)) ## weight matrix requires named rows and columns myNames <- 1:nrow(weights) rownames(weights) <- colnames(weights) <- myNames ## extract coordinates from the igraph object coord <- layout.auto(tr) rownames(coord) <- myNames plot(layout.auto(tr)) ## custom weight object customw <- eco.weight(XY = coord, W = weights) ## simple plot of the object eco.plotWeight(customw, type = "simple") ## create a vector with groups to have coloured plots myColors <- c(rep(1,13), rep(2, 9), rep(3, 9), rep(4, 9)) eco.plotWeight(customw, type = "igraph",group = myColors) ## in the following plot, the argument bounded is set to FALSE, ## but if you have many groups, it probably should be set to TRUE. # click in a node to see the label eco.plotWeight(customw,type = "network", bounded = FALSE, group = myColors) ## in the following plot, the assignment a group factor, # generates clustered nodes. # hover over the name of the nodes to see the individual connections eco.plotWeight(customw, type = "edgebundle", group = myColors) #### CONVERSION FROM LISTW OBJECTS ##### require(adegenet) # Delaunay triangulation temp <-chooseCN(eco3[["XY"]], type = 1, result.type = "listw", plot.nb = FALSE) con <- eco.listw2ew(temp) eco.plotWeight(con, "network", bounded = TRUE, group = eco3[["S"]]$structure) #----------------------- # ACCESSORS USE EXAMPLE #----------------------- # the slots are accessed with the generic format # (ecoslot. + name of the slot + name of the object). # See help("EcoGenetics accessors") ecoslot.METHOD(con) # slot METHOD ecoslot.PAR(con) # slot PAR ecoslot.PAR.VAL(con) # slot PAR.VAL # }