### Introduction

### Theory, R functions & Examples

en:alpha_beta_diversity

**This is an old revision of the document!**

Plan: Divide the chapter into alpha+gamma diversity section and beta diversity section. One option - use Jurasinsky et al 2009 schema and talk about inventory, differentiation and proportional diversity (inventory = alpha and gamma, differentiation = based on dissimilarity measures, incl. variation within compositional matrix and length of DCA axis; proportional - gamma vs alpha, additive vs multiplicative, using Hill's numbers for it etc.) Other option is to divide the whole topic into several chapters:

- alpha diversity (inventory diversity)
- includes species richness, Shannon entropy, Simpson concentration index, Hill's numbers, effective number of species

- rarefaction and accumulation curves, estimates of unseen species - beta diversity

- differentiation diversity - Legendre's approach, incl. LCBD, mean of pairwise dissimilarity indices, multisite dissimilarity indices
- proportional diversity - Whittaker's beta, beta based on Hill's numbers, Chao's beta diversity (beta differentiation)

**Rarefaction curves**answers the question “what would be the number of species in community if we sampled less individuals/samples”, while accumulation curves shows whether we sampled enough (the curve flattens to asymptote) or we haven't (curve still steeply climbing up).**Accumulation curve**can be extrapolated to get hypothetical richness of larger sample or species pool, while rarefaction curve is basically an interpolation.**Individual-**vs**sample- (incidence)**based data: while individual-based data represent vector with number of individuals recorded for each species in single representative sample of the community, sample-based data consist of a set of sampling units (plots, traps, quadrats, transects), where incidence (presence) of species is recorded for each sampling unit.

packages dealing with rarefaction/accumulation curves: vegan, rich, iNEXT,

(library`specaccum`

`vegan`

) - calculates accumulation curve on the community data matrix (one curve per matrix);`plot`

draws the result (optionally with confidence interval).(library`rarecurve`

`vegan`

) - draws rarefaction curves (each row of the matrix is one curve), without confidence intervals.(library`rarefy`

`vegan`

)(library`rarc`

`rich`

)(library`iNEXT`

`iNEXT`

)

beetles <- read.delim ('http://www.davidzeleny.net/anadat-r/data-download/carabid-beetles-boreal-forest.txt', row.names = 1) rarecurve (t(beetles)) # draw rarefaction curve with confidence intervals rarecurve.ci <- function (x, step.ci = 1) { rar.temp <- apply (com, 1, FUN = function (x) rarefy (x, se = T, sample = 1:sum (x))) plot.new () plot.window (xlim = c(1, max (rowSums (com))), ylim = c(1, max (rowSums (com > 0)) )) box () axis (1) axis (2) for (i in seq (1, length (rar.temp))) { y <- rar.temp[[i]] points (y[1,], type = 'l', col = i) col.ci <- rgb(red = col2rgb (i)[1,], green = col2rgb (i)[2,], blue = col2rgb (i)[3,], alpha = 100, max = 255) for (x.coord in seq (1, length (y[2,]), by = step.ci)) lines (x = c(x.coord, x.coord), y = c(y[1, x.coord] + 1.95*y[2, x.coord], y[1, x.coord] - 1.95*y[2, x.coord]), col = col.ci) } } rarecurve.ci (t(beetles))

iNext package of Chao et al. 2014, maintained by Hsieh T.C. (謝宗震), offers drawing of rarefaction curves with intra- and extrapolation options and confidence intervals. Additionally to rarefied species richness (of Hill numbers 1, 2 and 3) it also calculates sample completeness (coverage) and allows to standardise samples by completenes. More details in this blog post.

- Chao A., Gotelli N.J., Hsieh T.C., Sander E.L., Ma K.H., Colwell R.K. & Ellison A.M. (2014): Rarefaction and extrapolation with Hill numbers: a framework for sampling and estimation in species diversity studies.
*Ecological Monographs*, 84: 45-67.

en/alpha_beta_diversity.1466875169.txt.gz · Last modified: 2017/10/11 20:36 (external edit)