Chapter 6 Essential Biodiversity Variables

6.1 SDM

rspatial

6.2 Diversity

Biological diversity analyses typically use multivariate techniques to assess variation in data sets comprising sampling events and cases. A sampling event can be across time and space. In biodiversity analysis three cases are the most common:

• Taxonomic diversity (species);

• Functional diversity (biological form); and

• Genetic diversity (allellic frequency, phylogeny etc).

Variation in these three dimensions can be directly compared both within and between these different dimensions of biological diversity.

6.2.1 Types of analyses - Patitioning \(\alpha\), \(\beta\), \(\gamma\) etc. diversity

Two forms of diversity analyses are currently widely used; classic diversity measures (eg. species richness, Shannons diversity index etc.) and numbers equivalents representation of the underlying diversity distribution. This second form was first introduced in Hill (1973) and a number of resources are now available for computing both forms. See the forum piece Forum: Partitioning diversity in Ecology (2010) for a fuller discussion on the use of numbers equivalents.

Both types of diversity partitioning are used for all types of analyses and we present resources which are available for both forms: - Resources for classic diversity measures - Resources for numbers equivalents.

6.2.2 Data form

Within the R environment both methods require data to be in the wide format. See [link to page explaining shift from long to wide].

Table 6.1: Table 6.2: Example of wide format

	class_1	class_2	class_3	class_4	class_5	class_6	class_7	class_8	class_9	class_10
Site_1	68	97	89	74	44	2	81	13	73	93
Site_2	39	85	37	42	25	45	100	22	87	34
Site_3	1	21	34	38	70	18	13	93	83	10
Site_4	34	54	89	20	39	22	40	28	90	1
Site_5	87	74	44	28	51	78	89	48	48	43
Site_6	43	7	79	20	42	65	48	33	64	59
Site_7	14	73	33	44	6	70	89	45	94	26
Site_8	82	79	84	87	24	87	23	21	96	15
Site_9	59	85	35	70	32	70	84	31	60	58
Site_10	51	37	70	40	14	75	29	17	51	29

6.2.3 Classic diversity measures

People have used many different indices to measure diversity. These include:

6.2.4 \(\alpha\) diversity

\(\alpha\) diversity refers to the diversity at a single site. There are a number of different indices to caclculate the most common are:

• Species richness;
• Shannon/shannon weaver index;
• Simpson;
• Inverse Simpson; and
• Gini Simpson

The R libraries vegan, adiv, abdiv all provide methods to calculate these measures as well as a wealth of others. Within abdiv the funtion alpha_diversity lists the \(\alpha\) diversity measures available within the package. Whilst not exhaustive it is a large list.

There are also ways of estimating \(\alpha\) diversity through rarefaction as well as modeling and visualising its different aspects in both vegan and adiv.

6.2.5 \(\beta\) diversity and dissimilarities

The \(\beta\) diversity is a measure of the change in composition and/or abundance between sites. There is a long history of methods to measure this particular aspect of diversity. This has resulted in multiple indices and dissimilarities. Commonly used indices include:

• Jaccard;
• Sørrensen;
• Bray-Curtis;
• Hellinger distance,
• Chord distance

An extensive list of \(\beta\) diversities are available through the function betadiver in the vegan package as well as beta_diversity in the abdiv package.

Methods for analysing \(\beta\) diversity are included in the libraries betapart, vegan, adiv and ade4.

6.2.6 Additional related diversities

Measures of dark diversity (those species that are absent from an ecosystem but which belong to its species pool, (Pärtel, Szava-Kovats, and Zobel 2011)) and \(\zeta\) diversity (a measure of species pool overlap, (Hui and McGeoch 2014)) have been developed. These measures are instituted in the libraries:

• DarkDiv dark diversity; and
• zetadiv zeta diversity

6.2.7 Numbers equivalents

Numbers equivalents account for the nested heirarchies in \(\alpha\), \(\beta\) and \(\gamma\) diversity. A number of different libraries have now been developed:

• Hill numbers: Hill (1973)
  • adiv
  • HillR
  • iNext
• Tsallis entropy: Marcon and Hérault (2015)
  • adiv
  • entropart
• Crossing point theory: Patil and Taillie (1982)
  • BioFTF

6.2.8 Example of analysis of diversity

In this example we use the sampling event “Vegetation data from sheep grazing experiment at alpine site in Hol, Norway” available here.

Downloading the Darwin core archive which contains a … TO BE DONE…

6.2.8.1 Event data

6.2.8.2 Occurence data

References

Ellison, Aaron M. 2010. “Partitioning Diversity1.” Ecology 91 (7): 1962–63. https://doi.org/https://doi.org/10.1890/09-1692.1.

Hill, M. O. 1973. “Diversity and Evenness: A Unifying Notation and Its Consequences.” Ecology 54 (2): 427–32. https://doi.org/10.2307/1934352.

Hui, Cang, and Melodie A. McGeoch. 2014. “Zeta Diversity as a Concept and Metric That Unifies Incidence-Based Biodiversity Patterns.” The American Naturalist 184 (5): 684–94. https://doi.org/10.1086/678125.

Marcon, Eric, and Bruno Hérault. 2015. “Decomposing Phylodiversity.” Methods in Ecology and Evolution 6 (3): 333–39. https://doi.org/https://doi.org/10.1111/2041-210X.12323.

Pärtel, Meelis, Robert Szava-Kovats, and Martin Zobel. 2011. “Dark Diversity: Shedding Light on Absent Species.” Trends in Ecology & Evolution 26 (3): 124–28. https://doi.org/10.1016/j.tree.2010.12.004.

Patil, G. P., and C. Taillie. 1982. “Diversity as a Concept and Its Measurement.” Journal of the American Statistical Association 77 (379): 548–61. https://doi.org/10.1080/01621459.1982.10477845.