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The sharedFav function below implements the graphical analyses of Acevedo et al. (2010, 2012) on biogeographical interactions. It takes two vectors of favourability values at different localities for, respectively, a stronger and a weaker competing species (or two equally strong competitors), and plots their favourableness or shared favourability to assess potential competitive interactions.

 sharedFav <- function(strong_F, weak_F, conf = 0.95, main = "Shared favourability") { stopifnot(length(strong_F) == length(weak_F)) opar <- par(no.readonly = T) par(mar = c(4, 4, 2, 4.5)) F_intersection <- fuzzyOverlay(cbind(strong_F, weak_F), op = "intersection") F_union <- fuzzyOverlay(cbind(strong_F, weak_F), op = "union") Fovl <- sum(F_intersection, na.rm = TRUE) / sum(F_union, na.rm = TRUE) brks <- seq(0, 1, by = 0.1) bins <- 1:10 bin <- cut(F_intersection, breaks = brks, labels = bins) strong_mean <- tapply(strong_F, INDEX = bin, FUN = mean) weak_mean <- tapply(weak_F, INDEX = bin, FUN = mean) strong_ci <- tapply(strong_F, INDEX = bin, FUN = function(x) t.test(x, conf.level = conf, na.action = na.pass)$conf.int) weak_ci <- tapply(weak_F, INDEX = bin, FUN = function(x) t.test(x, conf.level = conf)$conf.int) strong_ci[names(Filter(is.null, strong_ci))] <- NA weak_ci[names(Filter(is.null, weak_ci))] <- NA strong_ci_up <- unlist(lapply(strong_ci, [, 2)) strong_ci_dn <- unlist(lapply(strong_ci, [, 1)) weak_ci_up <- unlist(lapply(weak_ci, [, 2)) weak_ci_dn <- unlist(lapply(weak_ci, [, 1)) bin_size <- table(bin) names(bin_size) <- names(bins) props <- bin_size / length(bin) bin <- as.integer(bin) bar_plot <- barplot(rep(NA, length(bins)), ylim = c(0, 1), xlab = "Favourability intersection", ylab = "Mean favourability", names.arg = brks[-1], main = main) col_bar <- "grey50" col_ci <- "grey" poly_left <- mean(bar_plot[2:3]) poly_right <- mean(bar_plot[8:9]) polygon(x = c(poly_left, poly_left, poly_right, poly_right), y = c(0, 1, 1, 0), col = "lightgrey", border = NA, density = 25, angle = -45) par(new = TRUE) barplot(props, col = col_bar, border = FALSE, xaxt = "n", yaxt = "n", add = TRUE) axis(side = 4, col = col_bar, col.axis = col_bar, col.ticks = col_bar, col.lab = col_bar) mtext(side = 4, line = 3, "Proportion of localities", col = col_bar) abline(h = 0.8, col = "grey", lty = 3) strong_x <- bar_plot - 0.1 weak_x <- bar_plot + 0.1 arrows(strong_x, strong_ci_dn, strong_x, strong_ci_up, code = 3, length = 0.03, angle = 90, col = col_ci) arrows(weak_x, weak_ci_dn, weak_x, weak_ci_up, code = 3, length = 0.03, angle = 90, col = col_ci) lines(x = strong_x, y = strong_mean, lwd = 2, lty = 1) lines(x = weak_x, y = weak_mean, lwd = 2, lty = 2) points(x = strong_x, y = strong_mean, pch = 20) points(x = weak_x, y = weak_mean, pch = 15, cex = 0.8) par(opar) return(Fovl) } 

The function returns the fuzzy overlap index and a shared favourability plot similar to those of Acevedo et al. (2010, 2012). For more details, examples of use and additional references, see the help files of these functions in package fuzzySim >= 2.2, currently available on R-Forge. Special thanks to Pelayo Acevedo and Darío Chamorro for clarifications on how to build the plot!

References

Acevedo P., Ward A.I., Real R. & Smith G.C. (2010) Assessing biogeographical relationships of ecologically related species using favourability functions: a case study on British deer. Diversity and Distributions, 16: 515-528

Acevedo P., Jiménez-Valverde A., Melo-Ferreira J., Real R. & Alves, P.C. (2012) Parapatric species and the implications for climate change studies: a case study on hares in Europe. Global Change Biology, 18: 1509-1519

Richerson P.J. & Lum K. (1980) Patterns of plant species and diversity in California: relation to weather and topography. American Naturalist 116: 504-536