Alpha diversity index
mm_alpha_diversity.RdCalculate index diversity within a particular area or ecosystem; usually expressed by the number of species (i.e., species richness) in that ecosystem.
Usage
mm_alpha_diversity(
data,
to_community = TRUE,
index = "shannon",
site_column,
species_column,
size_column = NULL,
margin = 1
)Arguments
- data
A data frame containing species observation data.
- to_community
Logical; if
TRUE, the function first transformsdatainto a community matrix format where sites are rows and species are columns before computing indices. Default isTRUE.- index
A character vector specifying the diversity index to calculate. Accepted values are
"shannon","simpson","invsimpson","evenness", and"pielou". Multiple indices can be computed simultaneously by providing a vector.- site_column
The column name in
datathat represents the site or location where species were recorded.- species_column
The column(s) in
datarepresenting species or taxa. This can be a single column name, a range of column indices (e.g.,2:5), or a selection helper (e.g.,dplyr::starts_with("sp_")).- size_column
(Optional) The column in
datacontaining the count or abundance of individuals per species. IfNULL, the function assumes each row represents one individual.- margin
An integer specifying whether diversity calculations should be performed by row (
margin = 1) or by column (margin = 2). Default is1(row-wise).
Value
A tibble with diversity index values for each site.
The first column corresponds to site_column, followed by one or more columns containing
the computed diversity indices, depending on the values specified in the index argument.
Details
Simpson diversity index
Simpson (1949) introduced a diversity index that quantifies the likelihood of two randomly chosen individuals belonging to the same species. This probability increases as diversity decreases; in a scenario with no diversity (only one species), the probability reaches 1. Simpson's Index is computed using the following formula:
$$D = \sum_{i=1}^{S} \left( \frac{n_{i}}{N} \right)^2$$
where \(n_{i}\) is the number of individuals in species i, N = total number of individuals of all species, and \(\frac{n_{i}}{N} = pi\) (proportion of individuals of species i), and S = species richness. The value of Simpson’s D ranges from 0 to 1, with 0 representing infinite diversity and 1 representing no diversity, so the larger the value of D, the lower the diversity. For this reason, Simpson’s index is often as its complement (1-D). Simpson's Dominance Index is the inverse of the Simpson's Index (\(1/D\)).
Shannon-Weiner Diversity Index
Shannon-Weiner Diversity Index is a measure of diversity that takes into account both species richness and evenness, introduced by Claude Shannon in 1948. Commonly referred to as Shannon's Diversity Index, it is based on the concept of uncertainty. For instance, in a community with very low diversity, there is a high level of certainty (or low uncertainty) about the identity of a randomly selected organism. Conversely, in a highly diverse community, the uncertainty increases, making it harder to predict which species a randomly chosen organism will belong to (low certainty or high uncertainty).
$$H = -\sum_{i=1}^{S} p_{i} * \ln p_{i}$$
where \(p_{i}\) = proportion of individuals of species i, and ln is the natural logarithm, and S = species richness. The value of H ranges from 0 to Hmax. Hmax is different for each community and depends on species richness. (Note: Shannon-Weiner is often denoted H' ).
Pielou or Evenness diversity index
Species evenness refers to the relative abundance of each species within an environment. For example, if there are 40 foxes and 1000 dogs, the community is uneven because one species dominates. However, if there are 40 foxes and 42 dogs, the community is much more even, as the species are more balanced in number. The degree of evenness in a community can be quantified using Pielou's evenness index (Pielou, 1966):
$$J=\frac{H}{H_{\max }}$$
The value of J ranges from 0 to 1. Higher values indicate higher levels of evenness. At maximum evenness, J = 1. J and D can be used as measures of species dominance (the opposite of diversity) in a community. Low J indicates that 1 or few species dominate the community.
References
Pielou, E.C. (1966). The measurement of diversity in different types of biological collections. Journal of Theoretical Biology, 13, pp. 131–144. doi:10.1016/0022-5193(66)90013-0.
Simpson, E.H. (1949). Measurement of diversity. Nature, 163, pp. 688. doi:10.1038/163688a0
Shannon, C.E. (1948). A mathematical theory of communication. The Bell System Technical Journal, 27, pp. 379-423.https://doi.org/10.1002/j.1538-7305.1948.tb01338.x
Examples
cam_data <- read.csv(system.file('penessoulou_season1.csv', package = 'maimer'))
# Transform data to community format and compute diversity indices
alpha1 <- cam_data %>%
mm_alpha_diversity(
to_community = TRUE,
size_column = number,
site_column = camera,
species_column = species,
index = c("shannon", "evenness", "invsimpson")
)
# Alternative method using a manually transformed community matrix
alpha2 <- cam_data %>%
mm_to_community(site_column = camera, species_column = species,
size_column = number, values_fill = 0) %>%
mm_alpha_diversity(
to_community = FALSE,
site_column = camera,
species_column = 2:11,
index = c("shannon", "evenness", "invsimpson")
)
alpha2
#> # A tibble: 13 × 4
#> camera shannon evenness invsimpson
#> <chr> <dbl> <dbl> <dbl>
#> 1 CAMERA 10 0.103 0.045 1.04
#> 2 CAMERA 3 0.974 0.423 2.46
#> 3 CAMERA 5 0.893 0.388 2.18
#> 4 CAMERA 8 0.224 0.097 1.12
#> 5 CAMERA 2 0.509 0.221 1.34
#> 6 CAMERA 1 1.14 0.497 2.73
#> 7 CAMERA 12 0 0 1
#> 8 CAMERA 4 1.31 0.57 3.55
#> 9 CAMERA 11 0 0 1
#> 10 CAMERA 3 - Bait 0.562 0.244 1.6
#> 11 CAMERA 1 - Bait 0 0 1
#> 12 CAMERA 19 0.637 0.276 1.80
#> 13 FCPEN 0.131 0.057 1.06
# Compare results
all(alpha1 == alpha2) # TRUE
#> [1] TRUE