# Beta diversity metrics between sites in a moving window along environmental gradients The function computes eight metrics of beta diversity according to an informed environmental gradient. It selects a given number of environmentally-neighborhood sites in a moving window to obtain beta diversity. ```r betaRegDisp(y, x, xy.coords = NULL, ws = 3, method.1 = "jaccard", method.2 = "ruzicka", method.3 = "ruzicka", independent.data = FALSE, illust.plot = FALSE) ``` ## Arguments - `y`: Response matrix, where rows are sites and columns are species. - `x`: Predictor vector. A vector of the environmental gradient under study with the same number of sites as in matrix `y`. Make sure the order of samples in `y` and `x` is the same. - `xy.coords`: Geographical coordinates. A matrix with two columns of XY decimal degree geographical coordinates, which are used to compute euclidean distance among sites. Rows must be sites in the same order as in `y` and `x`. - `ws`: Window size or number of sites to be used in the computation of the distinct beta-diversity metrics or between-site dissimilarities. It must be a positive integer higher than 2. - `method.1`: For beta-diversity metrics 1 to 3 (see details). A dissimilarity index available in the `vegdist`. The options are: "euclidean", "jaccard", "bray", "manhattan", "canberra", "kulczynski", "gower", "morisita", "horn", "mountford", "raup", "binomial", "chao", "altGower", "cao", "mahalanobis". - `method.2`: For beta-diversity metrics 4 and 5 (see details). A dissimilarity index available in the `beta.div`. The options are: "hellinger", "chord", "log.chord", "chisquare", "profiles", "percentdiff", "ruzicka", "divergence", "canberra", "whittaker", "wishart", "kulczynski", "jaccard", "sorensen", "ochiai", "ab.jaccard", "ab.sorensen", "ab.ochiai", "ab.simpson", "euclidean". - `method.3`: For beta-diversity metrics 6, 7, and 8 (see details). A multisample dissimilarity index available in the `beta.multi.abund`. The options are: "ruzicka" and "bray". - `independent.data`: Should windows not superpose each other? If `independent.data=TRUE`, sites do not enter more than once in the dissimilarity calculations, that is, sites are included in a single window. - `illust.plot`: Should a window plot be open and illustrate how the window moves along the gradient? ## Details The function computes eight beta-diversity metrics among sites included in a set (window) of length `ws`. See details in Dala-Corte et al. (2019). Metrics 1-3 uses dissimilarity indices available in `vegdist`: 1. Mean pair-wise dissimilarity between sites in a window; 2. Mean dissimilarity between focal site and the other sites in a window. If an odd number is informed in `ws`, the focal site is the central site in relation to its neighbours in the window. If an even number is informed in `ws`, the focal site is the first site in the window; 3. Mean distance of sites to their group centroid in a Principal Coordinate (PCoA) space computed using `betadisper`; Metrics 4-5 uses dissimilarity indices available in `beta.div`: 4. Total sum of squares (SS) of the window sites (Legendre and De Caceres, 2013); 5. Local contributions to beta diversity (LCBD; Legendre and De Caceres, 2013); Metrics 6-8 uses dissimilarity indices available in `beta.multi.abund`: 6. Total multiple-site dissimilarities for a selected window of sites; 7. Nestedness component of multiple-site dissimilarities for a selected window of sites; 8. Turnover component of multiple-site dissimilarities for a selected window of sites. ## Returns A matrix with 10 columns (or 12 if `xy.coords` is informed). Values in columns are sorted according to the enviromental gradient, from the lowest to the highest value. Columns correspond to: 1. `grad` - The environmental gradient (predictor vector, `x`); 2. `mean.grad` - Mean value of the environmental gradient of sites selected in each window; 3. `mean.diss.pairs` - Mean pair-wise dissimilarity between sites in a selected window (metric 1); 4. `diss.focal` - Mean dissimilarity between focal site and the other sites (metric 2); 5. `mean.dist.cent` - Mean distance of sites to their group centroid in a Principal Coordinate (PCoA) space (metric 3); 6. `SS.group` - Total sum of squares (SS) of the sites in a window (metric 4); 7. `SS.focal` - Local contributions to beta diversity (LCBD), which represents how much a focal site contributed to the total window SS; 8. `beta.TOT` - Total multiple-site dissimilarity; 9. `beta.NES` - Nestedness component of multiple-site dissimilarity; 10. `beta.TUR` - Turnover component of multiple-site dissimilarity; 11. `mean.geodist` - If `xy.coords` is provided, the mean linear euclidean distance between sites in the a window is returned. 12. `focal.geodist` - If `xy.coords` is provided, the mean linear euclidean distance of the focal site in relation to its neighbours in the window is returned. ## References Anderson, M.J., K.E. Ellingsen and B.H. McArdle. 2006. Multivariate dispersion as a measure of beta diversity. Ecology Letters 9: 683-693. Baselga, A. 2010. Partitioning the turnover and nestedness components of beta diversity. Global Ecology and Biogeography 19: 134-143. Baselga, A. 2017. Partitioning abundance-based multiple-site dissimilarity into components: balanced variation in abundance and abundance gradients. Methods in Ecology and Evolution 8: 799-808. Dala-Corte, R.B., L.F. Sgarbi, F.G. Becker and A.S. Melo. 2019. Beta diversity of stream fish communities along anthropogenic environmental gradients at multiple spatial scales. Environmental Monitoring and Assessment 191:288. Legendre, P. and M. De Caceres. 2013. Beta diversity as the variance of community data: dissimilarity coefficients and partitioning. Ecology Letters 16: 951-963. ## Author(s) Luciano F. Sgarbi, Renato B. Dala-Corte and Adriano S. Melo ## See Also `vegdist`, `betadisper`, `beta.div`, `beta.multi` ## Examples ```r ## Example 1. A simmulated community matrix with a known structure of increasing ## beta diversity by turnover # n is the total sample sites # LocS is the number of spp per site # MaxS is the total number of spp in the matrix # All samples will contain LocS species. The first sample will contain presences # for the first LocS species. The subsequent samples will contain LocS presences # spread over a increasing set of species. The assignment of presences for the # second sample to the last sample is done randomly. The last sample will # contain LocS presences assigned randomly to the MaxS species. Thus, for a # window size of 3 (ws=3) and a dataset of 10 samples, beta diversity for the # samples 1-3 will be much lower than for samples 8-10. SimComm <- function(n = 19, MaxS = 24, LocS = 8){ s <- seq (LocS, MaxS, length.out = n) mat <- matrix(0, n, MaxS, dimnames = list(paste("site", 1:n, sep = "_"), paste("sp", 1:MaxS, sep = "_"))) for(i in 1:n){ mat[i, sample(1:s[i], LocS)] <- 1 } mat <- mat[, colSums(mat)!=0] return(mat) } mat <- SimComm(n = 19, MaxS = 24, LocS = 8) #Creating an environmental gradient: grad <- 1:nrow(mat) b.resu <- betaRegDisp(y = mat, x = grad, xy.coord = NULL, ws = 3, method.1 = "jaccard", method.2 = "ruzicka", method.3 = "ruzicka", independent.data = FALSE, illust.plot = FALSE) ##Ploting all the output of the object for the simmulated community op <- par(no.readonly = TRUE) par(mfrow = c(5, 2), oma = c(1, 0, 1, 0.1), mar = c(1.5, 3, .1, .1), cex = 1, las = 0) for(i in 1:ncol(b.resu)){ plot(b.resu[, 1], b.resu[, i], ylab = colnames(b.resu)[i], cex.lab = .9, cex.axis = 0.9, tcl = -0.2, mgp = c(1.5, .2, 0), pch = 15, col = "grey") } mtext("Environmental gradient", cex = 1.3, 1, -0.1, outer = TRUE) par(op) ##Example 2 data(varespec) data(varechem) grad <- varechem[, "Baresoil"] resu <- betaRegDisp(y = varespec, x = grad, ws = 3, method.1 = "jaccard", method.2 = "ruzicka", method.3 = "ruzicka", independent.data = FALSE, illust.plot = FALSE) #Plotting all the outputs of the function: op <- par(no.readonly = TRUE) par(mfrow = c(5, 2), oma = c(1, 0, 1, 0.1), mar = c(1.5, 3, .1, .1), cex = 1, las = 0) for(i in 1:ncol(resu)){ plot(resu[, 1], resu[, i], ylab = colnames(resu)[i], cex.lab = .9, cex.axis = 0.9, tcl = -0.2, mgp = c(1.5, .2, 0), pch = 15, col = "grey") } mtext("Environmental gradient", cex = 1.3, 1, 0, outer = TRUE) par(op) ```

betaRegDisp.rd function