The ** varPart **function, now included in the modEvA package (Barbosa et al. 2014), performs

**variation partitioning**(Borcard

*et al*. 1992) among

**two factors**(e.g. Ribas

*et al*. 2006) or

**three factors**(e.g. Real

*et al*. 2003) for either multiple

**linear regression**models (LM) or

**generalized linear models**(GLM).

If you have** linear** **models**, **input** data for *varPart* are the coefficients of determination (**R-squared** values) of the linear regressions of the target variable on all the variables in the model, on the variables related to each particular factor, and (when there are 3 factors) on the variables related to each pair of factors. The **outputs **are the **amounts of variance explained exclusively by each factor**, the **amounts explained exclusively by** the **overlapping effects** of each pair of factors, and the amount explained by the overlap of the 3 factors if this is the case (e.g. Real *et al*. 2003). The amount of variation not explained by the complete model is also provided.

If you have **generalized linear models** (GLMs) such as logistic regression or the favourability function, you have no true R-squared values from these models; **inputs** can be **squared coefficients** of (Spearman’s) **correlation between** the model **predictions given by each factor or pair of factors** and the **predictions of the complete model** (e.g. Muñoz & Real 2006), **or** **the R-squared** values of the corresponding **logit ( y) functions** (Real et al. 2013),

**or an adjusted**(De Araújo et al. 2014). Consequently,

**R-squared****output**values are not the total amounts of variance (of the target variable) explained by factors and overlaps, but rather their proportional

**contribution to the total variation explained by the model**. The amount of unexplained variation is not available for GLMs.

varPart <- function(A, B, C = NA, AB, AC = NA, BC = NA, ABC = NA, model.type = NULL, A.name = "Factor A", B.name = "Factor B", C.name = "Factor C", plot = TRUE, plot.digits = 3, cex.names = 1.5, cex.values = 1.2, main = "", cex.main = 2, plot.unexpl = TRUE) { # version 1.7 (17 Mar 2017) if (!is.null(model.type)) message ("NOTE: Argument 'model.type' is no longer used.") partials c(A, B, C, AB, BC, AC, ABC) if (is.finite(partials[c(1:2, 4)]) && is.na(partials[c(3, 5:7)])) twofactors TRUE else if (all(is.finite(partials))) twofactors FALSE else stop ("You must provide numeric values for either A, B and AB (for variation partitioning among two factors) or A, B, C, AB, BC, AC and ABC (for variation partitioning among three factors). See Details.") if (!all(na.omit(partials) >= 0 & na.omit(partials) <= 1)) stop ("Values must be between 0 and 1.") totalexpl ifelse(twofactors, AB, ABC) unexpl 1 - totalexpl if (twofactors) { Apure c(paste("Pure", A.name), paste("Pure", B.name), paste0("Pure ", A.name, "_", B.name, " overlap"), "Unexplained") results data.frame(c(Apure, Bpure, ABoverlap, unexpl), row.names = output.names) } else { # end if 2 factors Apure C BCoverlap c(paste("Pure", A.name), paste("Pure", B.name), paste("Pure", C.name), paste0("Pure ", A.name, "_", B.name, " overlap"), paste0("Pure ", B.name, "_", C.name, " overlap"), paste0("Pure ", A.name,"_", C.name," overlap"), paste0(A.name,"_",B.name,"_",C.name," overlap"), "Unexplained") results data.frame(c(Apure, Bpure, Cpure, ABoverlap, BCoverlap, ACoverlap, ABCoverlap, unexpl), row.names = output.names) } # end else colnames(results) "Proportion" if (plot) { # adapted from Daniel's http://stackoverflow.com/questions/1428946/venn-diagrams-with-r circle function(x, y, r) { ang seq(0, 2*pi, length = 100) xx cos(ang) yy sin(ang) polygon(xx, yy) } # end circle funtion (by Daniel) Apure round(Apure, plot.digits) # shorten values for plotting Bpure round(Bpure, plot.digits) ABoverlap round(ABoverlap, plot.digits) if(!twofactors) { Cpure round(Cpure, plot.digits) BCoverlap round(BCoverlap, plot.digits) ACoverlap round(ACoverlap, plot.digits) ABCoverlap round(ABCoverlap, plot.digits) } if (twofactors) { plot(0, 0, ylim = c(-1, 10), xlim = c(-1, 7), type = "n", axes = FALSE, ylab = "", xlab = "", main = main, cex.main = cex.main) circle(3,3,3) circle(3,6,3) text(x = c(3, 3), y = c(9.5, -0.5), labels = c(A.name, B.name), cex = cex.names) text(x = c(3, 3, 3), y = c(7, 4.75, 2), c(Apure, ABoverlap, Bpure), cex = cex.values) } else { # end if 2 factors plot(0, 0, ylim = c(-1, 10), xlim = c(-1, 10), type = "n", axes = FALSE, ylab = "", xlab = "", main = main, cex.main = cex.main) circle(3, 6, 3) circle(6, 6, 3) circle(4.5, 3, 3) text(x = c(2.5, 6.5, 4.5), y = c(9.5, 9.5, -0.5), labels = c(A.name, B.name, C.name), cex = cex.names, adj = c(0.5, 0.5, 0)) text(x = c(1.8, 7.2, 4.5, 4.5, 2.8, 6.2, 4.5), y = c(6.6, 6.6, 2, 7, 4, 4, 5), labels = c(Apure, Bpure, Cpure, ABoverlap, ACoverlap, BCoverlap, ABCoverlap), cex = cex.values) } # end if 2 factors else if (plot.unexpl) { rect(-1, -1, 10, 10) text(x = -0.9, y = -0.2, label = paste0("Unexplained\n", round(unexpl, plot.digits)), adj = 0, cex = cex.values) } } # end if plot results }

[presented with Pretty R]

You just need to copy the function above, paste it into R and press *enter*. An example of how to use it then is provided below. The results are returned numerically and also plotted in a diagram:

# if you have a linear model (LM), use (non-adjusted) R-squared values # for each factor and for their combinations as inputs: varPart(A = 0.456, B = 0.315, C = 0.281, AB = 0.051, BC = 0.444, AC = 0.569, ABC = 0.624, A.name = "Spatial", B.name = "Human", C.name = "Environmental", main = "Small whale") # if you have a generalized linear model (GLM), # you can use squared correlation coefficients # of the predictions of each factor with those of the complete model: varPart(A = (-0.005)^2, B = 0.698^2, C = 0.922^2, AB = 0.696^2, BC = 0.994^2, AC = 0.953^2, ABC = 1, A.name = "Topographic", B.name = "Climatic", C.name = "Geographic", main = "Big bird",plot.unexpl = FALSE)

You can change the number of digits in the plotted values with the argument *plot.digits*. You can also change the character sizes of the plot’s main title, circle names, and values, using arguments *cex.main*, *cex.names* and *cex.values*. Note that these **results derive from arithmetic operations between your input values**, and they always sum up to 1; **if your input is incorrect, the results will be incorrect** as well.

**References**

Barbosa A.M., Brown J.A., Jiménez-Valverde & Real R. (2014) modEvA – an R package for model evaluation and analysis. R package, version 0.1.

Borcard D, Legendre P, Drapeau P (1992) Partialling out the spatial component of ecological variation. *Ecology* 73: 1045-1055

De Araújo, C.B., Marcondes-Machado, L.O. & Costa, G.C. (2014) The importance of biotic interactions in species distribution models: a test of the Eltonian noise hypothesis using parrots. *Journal of Biogeography* 41: 513-523 (DOI: 10.1111/jbi.12234)

Muñoz, A.-R. & Real, R. (2006) Assessing the potential range expansion of the exotic monk parakeet in Spain. *Diversity and Distributions* 12: 656–665.

Real, R., Barbosa, A.M., Porras, D., Kin, M.S., Márquez, A.L., Guerrero, J.C., Palomo, L.J., Justo, E.R. & Vargas, J.M. (2003) Relative importance of environment, human activity and spatial situation in determining the distribution of terrestrial mammal diversity in Argentina. *Journal of Biogeography* 30: 939-947.

Real R., Romero D., Olivero J., Estrada A. & Márquez A.L. (2013) Estimating how inflated or obscured effects of climate affect forecasted species distribution. *PLoS ONE* 8: e53646. doi:10.1371/journal.pone.0053646

Ribas, A., Barbosa, A.M., Casanova, J.C., Real, R., Feliu, C. & Vargas, J.M. (2006) Geographical patterns of the species richness of helminth parasites of moles (*Talpa* spp.) in Spain: separating the effect of sampling effort from those of other conditioning factors. *Vie et Milieu* 56: 1-8.

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