Biodiversity Assessment Using Hill-Number Functional Tools

Tools for biodiversity assessment through Hill-number diversity profiles treated as functions of the order q. The package computes the profiles of Hill (1973) , their analytical first and second derivatives, curvature, radius of curvature, arc length, cumulative integral functions, profile areas, area-based rankings and relative changes over time, together with static and interactive three-dimensional biodiversity surfaces. The functional approach follows Di Battista, Fortuna and Maturo (2017) , Maturo and Di Battista (2018) and Maturo (2018) .

BioFTF

BioFTF provides functional tools for biodiversity assessment based on Hill-number diversity profiles. The profile of each community is treated as a function of the order q and summarised by its derivatives, curvature, radius of curvature, arc length, cumulative integral function and area. When rows are ordered in time, the profiles form a biodiversity surface that can be drawn as a static or rotatable figure and compared with a second surface.

Installation

install.packages("BioFTF")

Example

library(BioFTF)

x <- matrix(c(54, 20, 17,  6,  3,
              25, 25, 25, 25,  0,
              35, 35, 30,  0,  0),
            nrow = 3, byrow = TRUE)
rownames(x) <- c("A", "B", "C")

hill_profile(x, domain = c(0, 1, 2, Inf))
hill_profile_plot(x, from = 0, to = 10, n = 501)
hill_first_derivative(x, domain = c(0, 1, 2))
hill_area(x)
hill_ranking(x)

D(0) is species richness, D(1) the exponential of Shannon entropy and D(2) the inverse Simpson concentration. The default domain is 0 <= q <= 2; from, to, n and domain change it. Negative orders are rejected unless allow_negative = TRUE, because for q < 0 the Hill number exceeds species richness and is driven by the rarest species.

Surfaces

years <- 2018:2023
z <- matrix(c(40, 30, 15, 10,  5,
              35, 30, 18, 12,  5,
              30, 28, 20, 15,  7,
              25, 25, 22, 18, 10,
              20, 24, 24, 20, 12,
              15, 22, 25, 22, 16),
            nrow = length(years), byrow = TRUE)
rownames(z) <- years

hill_total_change(z)
hill_surface_plot(z, from = 0, to = 10, n = 121, plot = "static")
hill_surface_plot(z, from = 0, to = 10, n = 121)   # rotatable, needs plotly

Versions 1.x

Versions 1.x computed the same tools on the Patil-Taillie beta profile over -1 <= beta <= 1, which corresponds to 0 <= q <= 2 through q = beta + 1. The old function names (beta(), area(), arc(), ...) are deprecated and now return the Hill-number tools; see ?"BioFTF-deprecated".

References

Di Battista, T., Fortuna, F. and Maturo, F. (2017). BioFTF: An R package for biodiversity assessment with the functional data analysis approach. Ecological Indicators, 73, 726-732. https://doi.org/10.1016/j.ecolind.2016.10.032

Maturo, F. and Di Battista, T. (2018). A functional approach to Hill's numbers for assessing changes in species variety of ecological communities over time. Ecological Indicators, 84, 70-81. https://doi.org/10.1016/j.ecolind.2017.08.016

Maturo, F. (2018). Unsupervised classification of ecological communities ranked according to their biodiversity patterns via a functional principal component decomposition of Hill's numbers integral functions. Ecological Indicators, 90, 305-315. https://doi.org/10.1016/j.ecolind.2018.03.013