# Variation partitioning for zeta diversity Variation partitioning of zeta diversity for a specific order (number of assemblages or sites) over distance and environmental variables. ```r Zeta.varpart( msgdm.mod, num.part = 2, reg.type = "glm", family = stats::gaussian(), method.glm = "glm.fit.cons", cons = -1, cons.inter = 1, kn = -1, bs = "mpd" ) ``` ## Arguments - `msgdm.mod`: An object return by function `Zeta.msgdm`. - `num.part`: Number of partitions of zeta diversity. Can be 2 or 3. - `reg.type`: Type of regression for the multi-site generalised dissimilarity modelling. Options are "glm" for generalised linear models, "ngls" for negative linear models, "gam" for generalised additive models, "scam" for shape constrained additive models, and "ispline" for I-spline models, as recommended in generalised dissimilarity modelling by Ferrier **et al**. (2007). - `family`: A description of the error distribution and link function to be used in the `glm`, `gam` and `scam` models (see `family` in package `stats` for details of family functions). - `method.glm`: Method used in fitting the generalised linear model. The default method "glm.fit.cons" is an adaptation of method `glm.fit2` from package `glm2` using a negative least squares regression in the reweighted least squares. Another option is "glm.fit2", which corresponds to method `glm.fit2`; see help documentation for `glm.fit2` in package `glm`. - `cons`: type of constraint in the glm if `method.glm = "glm.fit.cons"`. Default is -1 for negative coefficients on the predictors. The other option is 1 for positive coefficients on the predictors. - `cons.inter`: type of constraint for the intercept. Default is 1 for positive intercept, suitable for Gaussian family. The other option is -1 for negative intercept, suitable for binomial family. - `kn`: Number of knots in the GAM and SCAM. Default is -1 for determining kn automatically using Generalized Cross-validation. - `bs`: A two-letter character string indicating the (penalized) smoothing basis to use in the scam model. Default is "`mpd`" for monotonic decreasing splines. see `smooth.terms` in package `mgcv` for an overview of what is available. ## Returns `Zeta.varpart` returns a data frame with one column containing the variation explained by each component `a` (the variation explained by distance alone), `b` (the variation explained by either distance or the environment), `c` (the variation explained by the environment alone) and `d` (the unexplained variation). ## Details Note that, for a given regression, the variation explained is computed as 1-(RSS/TSS)*(v-1)/(v-p-1), where RSS is the residual sum of squares and TSS is the total sum of squares, v is the number of variables used in the regression (which is greater than the original number of variables for I-splines) and p is the number of samples. 1-(RSS/TSS) corresponds to the classical R-squared for linear regression only, and results for non-linear regressions should be interpreted with caution. The environmental variables can be numeric or factorial, and `order` must be greater than 1. For numeric variables, the pairwise difference between sites is computed and combined according to `method`. For factorial variables, the distance corresponds to the number of unique values over the number of assemblages of sites specified by `order`. Zeta is regressed against the differences of values of the environmental variables divided by the maximum difference for each variable, to be rescaled between 0 and 1. If `!is.null(xy)`, distances between sites are also divided by the maximum distance. ## Examples ```r utils::data(bird.spec.coarse) xy.bird <- bird.spec.coarse[,1:2] data.spec.bird <- bird.spec.coarse[,3:193] utils::data(bird.env.coarse) data.env.bird <- bird.env.coarse[,3:9] zeta.bird <- Zeta.msgdm(data.spec.bird, data.env.bird, xy.bird, sam = 100, order = 3) zeta.varpart.bird <- Zeta.varpart(zeta.bird, method.glm = "glm.fit2") zeta.varpart.bird dev.new() pie.neg(zeta.varpart.bird[4:7,1], density = c(4, 0, 8, -1), angle = c(90, 0, 0, 0), labels = c("distance", "undistinguishable", "environment", "unexplained"), radius = 0.9) ########## utils::data(Marion.species) xy.marion <- Marion.species[,1:2] data.spec.marion <- Marion.species[,3:33] utils::data(Marion.env) data.env.marion <- Marion.env[3:4] zeta.marion <- Zeta.msgdm(data.spec.marion, data.env.marion, xy.marion, sam = 100, order = 3, normalize = "Jaccard") zeta.varpart.marion <- Zeta.varpart(zeta.marion, method.glm = "glm.fit2") zeta.varpart.marion dev.new() pie.neg(zeta.varpart.marion[4:7,1], density = c(4, 0, 8, -1), angle = c(90, 0, 0, 0), labels = c("distance", "undistinguishable", "environment", "unexplained"), radius = 0.9) ``` ## References Hui C. & McGeoch M.A. (2014). Zeta diversity as a concept and metric that unifies incidence-based biodiversity patterns. **The American Naturalist**, 184, 684-694. Borcard, D., Legendre, P. & Drapeau, P. (1992). Partialling out the spatial component of ecological variation. **Ecology** 73, 1045-1055. Legendre, P. & Legendre, L.F. (2012). **Numerical ecology**, 3rd English edition. Elsevier Science BV, Amsterdam. ## See Also `Zeta.decline.mc`, `Zeta.order.mc`, `Zeta.decline.ex`, `Zeta.order.ex`, `Zeta.msgdm`, `pie.neg`

Zeta.varpart function