Alpha diversity

Species richness
Shannon diversity index
Simpson diversity index
Pielou evenness index
Margalef richness index
Menhinick diversity index
Brillouin diversity index
Hill numbers
Whittaker’s alpha diversity
Renyi diversity
Chao1 diversity
ACE diversity
Chao2 diversity
Jackknife diversity
EstimateS diversity
EstimateS rarefaction curves
EstimateS extrapolation curves
EstimateS diversity partitioning
EstimateS beta diversity
EstimateS gamma diversity
Species richness is a measure of the number of different species in an area. It is a simple and intuitive measure of diversity, but it does not take into account the relative abundance of different species.

Shannon diversity index is a measure of diversity that takes into account both the number of species and their relative abundance. It is calculated as follows:

$$H’ = -\sum_{i=1}^S p_i \log p_i$$

where $S$ is the number of species, $p_i$ is the proportion of individuals in the community that belong to species $i$, and the sum is over all species.

The Shannon diversity index is always greater than or equal to the species richness, and it is equal to the species richness when all species are equally abundant.

Simpson diversity index is another measure of diversity that takes into account both the number of species and their relative abundance. It is calculated as follows:

$$D = 1 – \sum_{i=1}^S p_i^2$$

The Simpson diversity index is always less than or equal to the Shannon diversity index, and it is equal to the Shannon diversity index when all species are equally abundant.

Pielou evenness index is a measure of how evenly the individuals in a community are distributed among the different species. It is calculated as follows:

$$J’ = \frac{H’}{S}$$

The Pielou evenness index is always greater than or equal to 0, and it is equal to 1 when all species are equally abundant.

Margalef richness index is a measure of diversity that is based on the number of species and the number of individuals in each species. It is calculated as follows:

$$R = \frac{S}{\sum_{i=1}^S \sqrt{N_i}}$$

where $S$ is the number of species, $N_i$ is the number of individuals in species $i$, and the sum is over all species.

The Margalef richness index is always greater than or equal to the species richness, and it is equal to the species richness when all species have the same number of individuals.

Menhinick diversity index is a measure of diversity that is based on the number of species and the total number of individuals in the community. It is calculated as follows:

$$D = \frac{S}{\sqrt{N}}$$

where $S$ is the number of species and $N$ is the total number of individuals.

The Menhinick diversity index is always greater than or equal to the species richness, and it is equal to the species richness when all species have the same number of individuals.

Brillouin diversity index is a measure of diversity that is based on the number of species and the number of possible interactions between species. It is calculated as follows:

$$D = \frac{S}{\sum_{i=1}^S \sum_{j=1}^S \pi_{ij}}$$

where $S$ is the number of species, $\pi_{ij}$ is the probability that two individuals from species $i$ and $j$ will interact, and the sum is over all pairs of species.

The Brillouin diversity index is always greater than or equal to the species richness, and it is equal to the species richness when all species are equally abundant and all pairs of species have the same probability of interacting.

Hill numbers are a family of diversity indices that are based on the number of species and the number of possible ways to partition the community into species groups. The most common Hill number is the first Hill number, which is calculated as follows:

$$H_1 = -\sum_{i=1}^S p_i \log p_i$$

where $S$ is the number of species, $p_i$ is the proportion of individuals in the community that belong to species $i$, and the sum is over all species.

The other Hill numbers are calculated in a similar way, but they use different weights for the different species groups.

Whittaker’s alpha diversity is a measure of diversity within a single community. It is calculated as follows:

$$\alpha = \sum_{i=1}^S H_i$$

where $S$ is the number of species and $H_i$ is the $i$th Hill number.

Renyi diversity is a measure of diversity that is based on the Shannon diversity index. It is calculated as follows:

$$D_\alpha = \frac{1}{\alpha – 1} \log \sum_{i=1}^S p_i^\alpha$$

where $
Species richness is a measure of the number of different species in a community. It is often used as a simple index of biodiversity.

Shannon diversity index is a measure of the diversity of a community based on the relative abundance of each species. It is calculated as follows:

$$H’ = -\sum_{i=1}^S p_i \log_2 p_i$$

where $p_i$ is the proportion of individuals in the community that belong to species $i$.

Simpson diversity index is a measure of the diversity of a community based on the probability that two randomly chosen individuals from the community will belong to different species. It is calculated as follows:

$$D = 1 – \sum_{i=1}^S p_i^2$$

where $p_i$ is the proportion of individuals in the community that belong to species $i$.

Pielou evenness index is a measure of the evenness of the distribution of species abundances in a community. It is calculated as follows:

$$J’ = \frac{H’}{\log_2 S}$$

where $H’$ is the Shannon diversity index and $S$ is the number of species in the community.

Margalef richness index is a measure of the diversity of a community based on the number of species and the total number of individuals in the community. It is calculated as follows:

$$R = \frac{S}{\sqrt{N}}$$

where $S$ is the number of species in the community and $N$ is the total number of individuals in the community.

Menhinick diversity index is a measure of the diversity of a community based on the number of species and the number of individuals in each species. It is calculated as follows:

$$D = \frac{S}{\sum_{i=1}^S \sqrt{n_i}}$$

where $S$ is the number of species in the community, $n_i$ is the number of individuals in species $i$, and the sum is over all species in the community.

Brillouin diversity index is a measure of the diversity of a community based on the number of species, the total number of individuals in the community, and the number of links between individuals. It is calculated as follows:

$$D = \frac{S}{\sqrt{N + \sum_{i=1}^S \sum_{j=1}^S a_{ij}}}$$

where $S$ is the number of species in the community, $N$ is the total number of individuals in the community, $a_{ij}$ is the number of links between individuals of species $i$ and $j$, and the sum is over all pairs of species in the community.

Hill numbers are a family of diversity indices that are based on the number of species and the number of links between individuals. They are calculated as follows:

$$H_\alpha = -\sum_{i=1}^S p_i^\alpha$$

where $p_i$ is the proportion of individuals in the community that belong to species $i$ and $\alpha$ is a positive real number.

Whittaker’s alpha diversity is a measure of the diversity of a community within a given habitat. It is calculated as follows:

$$\alpha = \sum_{i=1}^S p_i H_\alpha$$

where $p_i$ is the proportion of individuals in the community that belong to species $i$, $H_\alpha$ is the Hill number of species $i$, and the sum is over all species in the community.

Renyi diversity is a measure of the diversity of a community based on the number of species and the number of links between individuals. It is calculated as follows:

$$D_\alpha = \frac{1}{\alpha-1} \log \sum_{i=1}^S p_i^\alpha$$

where $p_i$ is the proportion of individuals in the community that belong to species $i$ and $\alpha$ is a positive real number.

Chao1 diversity is a measure of the diversity of a community based on the number of individuals in the community and the number of unique species that have been observed. It is calculated as follows:

$$C_1 = \frac{S_1}{\sqrt{N}}$$

where $S_1$ is the number of unique species that have been observed and $N$ is the total number of individuals in the community.

ACE diversity is a measure of the diversity of a community based on the number of individuals
1. Which of the following is a measure of the number of different species in a community?
(a) Species richness
(b) Shannon diversity index
(c) Simpson diversity index
(d) Pielou evenness index

Which of the following is a measure of the probability that two randomly chosen individuals from a community will belong to different species?
(a) Species richness
(b) Shannon diversity index
(c) Simpson diversity index
(d) Pielou evenness index
Which of the following is a measure of the average number of species that would be found in a sample of a given size from a community?
(a) Species richness
(b) Shannon diversity index
(c) Simpson diversity index
(d) Pielou evenness index
Which of the following is a measure of the probability that two randomly chosen individuals from a community will belong to the same species?
(a) Species richness
(b) Shannon diversity index
(c) Simpson diversity index
(d) Pielou evenness index
Which of the following is a measure of the diversity of a community based on the number of species and the relative abundance of each species?
(a) Species richness
(b) Shannon diversity index
(c) Simpson diversity index
(d) Pielou evenness index
Which of the following is a measure of the diversity of a community based on the number of species and the probability that two randomly chosen individuals from the community will belong to different species?
(a) Species richness
(b) Shannon diversity index
(c) Simpson diversity index
(d) Pielou evenness index
Which of the following is a measure of the diversity of a community based on the number of species and the average number of species that would be found in a sample of a given size from the community?
(a) Species richness
(b) Shannon diversity index
(c) Simpson diversity index
(d) Pielou evenness index
Which of the following is a measure of the diversity of a community based on the number of species and the probability that two randomly chosen individuals from the community will belong to the same species?
(a) Species richness
(b) Shannon diversity index
(c) Simpson diversity index
(d) Pielou evenness index
Which of the following is a measure of the diversity of a community at a single point in time?
(a) Alpha diversity
(b) Beta diversity
(c) Gamma diversity
Which of the following is a measure of the diversity of a community between two or more habitats?
(a) Alpha diversity
(b) Beta diversity
(c) Gamma diversity
Which of the following is a measure of the diversity of a community across an entire landscape?
(a) Alpha diversity
(b) Beta diversity
(c) Gamma diversity
Which of the following is a method for estimating species richness?
(a) EstimateS
(b) Rarefaction curves
(c) Extrapolation curves
(d) Diversity partitioning
Which of the following is a method for estimating the diversity of a community based on the number of species found in a sample of a given size?
(a) EstimateS
(b) Rarefaction curves
(c) Extrapolation curves
(d) Diversity partitioning
Which of the following is a method for estimating the diversity of a community based on the number of species found in a sample of a given size and the number of species that would be expected to be found in a sample of that size if the community were at equilibrium?
(a) EstimateS
(b) Rarefaction curves
(c) Extrapolation curves
(d) Diversity partitioning
Which of the following is a method for estimating the diversity of a community based on the number of species found in a sample of a given size and the number of species that would be expected to be found in a sample of that size if the community were at equilibrium, and the relative abundance of each species?
(a) EstimateS
(b) Rarefaction curves
(c) Extrapolation curves
(d) Diversity partitioning