tabula

Overview

tabula provides an easy way to examine archaeological count data (artifacts, faunal remains, etc.). This package includes several measures of diversity, e.g. richness, rarefaction, diversity, turnover, similarity, etc. It also provides matrix seriation methods for chronological modeling and dating. The package make it easy to visualize count data and statistical thresholds: rank/abundance plots, Ford and Bertin diagrams, etc.

Installation

Install the released version of tabula from CRAN:

install.packages("tabula")

Or install the development version from GitHub with:

# install.packages("devtools")
devtools::install_github("nfrerebeau/tabula")

Usage

tabula provides a set of S4 classes that extend the matrix data type from R base. These new classes represent different special types of matrix.

• Abundance matrix:
  • CountMatrix represents count data,
  • FrequencyMatrix represents frequency data.
• Logical matrix:
  • IncidenceMatrix represents presence/absence data.
  • OccurrenceMatrix represents a co-occurence matrix.

It assumes that you keep your data tidy: each variable (taxa) must be saved in its own column and each observation (case) must be saved in its own row.

These new classes are of simple use, on the same way as the base matrix:

# Define a count data matrix
quanti <- CountMatrix(data = sample(0:10, 100, TRUE),
                      nrow = 10, ncol = 10)

# Define a logical matrix
# Data will be coerced with as.logical()
quali <- IncidenceMatrix(data = sample(0:1, 100, TRUE),
                         nrow = 10, ncol = 10)

tabula uses coercing mechanisms (with validation methods) for data type conversions:

# Create a count matrix
A1 <- CountMatrix(data = sample(0:10, 100, TRUE),
                  nrow = 10, ncol = 10)

# Coerce counts to frequencies
B <- as(A1, "FrequencyMatrix")

# Row sums are internally stored before coercing to a frequency matrix
# (use totals() to get these values)
# This allows to restore the source data
A2 <- as(B, "CountMatrix")
all(A1 == A2)
#> [1] TRUE

# Coerce to presence/absence
C <- as(A1, "IncidenceMatrix")

# Coerce to a co-occurrence matrix
D <- as(A1, "OccurrenceMatrix")

Analysis

count <- as(compiegne, "CountMatrix")

Sample richness

richness(count, method = c("margalef", "menhinick", "berger"), simplify = TRUE)
#>   margalef  menhinick
#> 5 1.176699 0.07933617
#> 4 1.323459 0.07568907
#> 3 1.412383 0.07905694
#> 2 1.429741 0.08432155
#> 1 1.428106 0.08381675

Heterogeneity and evenness measures

Diversity can be measured according to several indices (sometimes refered to as indices of heterogeneity):

diversity(count, method = c("shannon", "brillouin", "simpson", "mcintosh", "berger"), simplify = TRUE)
#>    shannon brillouin   simpson  mcintosh    berger
#> 5 1.311123  1.309565 0.3648338 0.3983970 0.5117318
#> 4 1.838332  1.836827 0.2246218 0.5287042 0.3447486
#> 3 2.037649  2.036142 0.1718061 0.5883879 0.3049316
#> 2 2.468108  2.466236 0.1038536 0.6812886 0.1927510
#> 1 2.297495  2.295707 0.1267866 0.6472862 0.1893524

Note that berger, mcintosh and simpson methods return a dominance index, not the reciprocal form usually adopted, so that an increase in the value of the index accompanies a decrease in diversity.

Evenness is a measure of how evenly individuals are distributed across the sample:

evenness(count, method = c("shannon", "brillouin", "simpson", "mcintosh"), simplify = TRUE)
#>     shannon brillouin   simpson  mcintosh
#> 5 0.5111691 0.5109738 0.2108442 0.5479357
#> 4 0.6788396 0.6787091 0.2967952 0.7091340
#> 3 0.7349264 0.7348441 0.3637822 0.7806408
#> 2 0.8901817 0.8901334 0.6018087 0.9035975
#> 1 0.8286460 0.8285786 0.4929544 0.8585271

Turnover

The following method can be used to acertain the degree of turnover in taxa composition along a gradient (β-diversity) on qualitative (presence/absence) data.

It assumes that the order of the matrix rows (from 1 to n) follows the progression along the gradient/transect.

turnover(count, method = c("whittaker", "cody", "routledge1",
                           "routledge2", "routledge3", "wilson"),
         simplify = TRUE)
#>  whittaker       cody routledge1 routledge2 routledge3     wilson 
#> 0.05263158 1.50000000 0.00000000 0.04061480 1.04145086 0.09868421

Similarity coefficients

β-diversity can also be measured by addressing similarity between pairs of sites:

similarity(count, method = "morisita")
#>   5         4         3         2         1
#> 5 1 0.9162972 0.7575411 0.6670201 0.6286479
#> 4 1 1.0000000 0.8879556 0.7964064 0.7106784
#> 3 1 1.0000000 1.0000000 0.8251501 0.6637747
#> 2 1 1.0000000 1.0000000 1.0000000 0.9224228
#> 1 1 1.0000000 1.0000000 1.0000000 1.0000000

Seriation

# Build an incidence matrix with random data
incidence <- IncidenceMatrix(data = sample(0:1, 400, TRUE, c(0.6, 0.4)),
                             nrow = 20)

# Get seriation order on rows and columns
# Correspondance analysis-based seriation
(indices <- seriate(incidence, method = "correspondance", margin = c(1, 2)))
#> Permutation order for matrix seriation: 
#>    Row order: 10 12 9 16 17 15 1 18 13 4 7 6 11 20 3 19 14 5 8 2 
#>    Column order: 2 7 13 17 8 5 12 10 16 1 11 14 15 9 6 19 20 18 4 3 
#>    Method: correspondance

# Permute matrix rows and columns
incidence2 <- permute(incidence, indices)

# Plot matrix
library(ggplot2)
plotMatrix(incidence) + 
  labs(title = "Original matrix") +
  scale_fill_manual(values = c("TRUE" = "black", "FALSE" = "white"))
plotMatrix(incidence2) + 
  labs(title = "Rearranged matrix") +
  scale_fill_manual(values = c("TRUE" = "black", "FALSE" = "white"))

Visualization

tabula makes an extensive use of ggplot2 for plotting informations. This makes it easy to customize diagramms (e.g. using themes and scales).

Bertin of Ford (battleship curve) diagramms can be plotted, with statistic threshold (B. Desachy's sériographe [1]). The positive difference from the column mean percentage (in french "écart positif au pourcentage moyen", EPPM) represents a deviation from the situation of statistical independence. EPPM is a usefull graphical tool to explore significance of relationship between rows and columns related to seriation.

plotBar(count, EPPM = TRUE)

Matrix plot is displayed as a heatmap. The PVI matrix (B. Desachy's matrigraphe) allows to explore deviations from independence (an intuitive graphical approach to χ2),

plotMatrix(count, PVI = TRUE) +
  ggplot2::scale_fill_gradient2(midpoint = 1)

Spot matrix (no doubt easier to read than a heatmap [2]) allows direct examination of data (above/below some threshold):

plotSpot(count, threshold = mean)

Ranks vs abundance plot can be used for abundance models (model fitting will be implemented in a futur release):

plotRank(count, log = "xy")

[1] Desachy, B. (2004). Le sériographe EPPM : un outil informatisé de sériation graphique pour tableaux de comptages. Revue archéologique de Picardie, 3(1), 39–56. DOI: 10.3406/pica.2004.2396

[2] Adapted from Dan Gopstein's original spot matrix.