hill {benthos} R Documentation

## Hill's Diversity Numbers

### Description

According to Hill (1973): "a diversity number is figuratively a measure of how many species are present if we examine the sample down to a certain depth among its rarities. If we examine superficially (e.g., by using N[2]) we shall see only the more abundant species. If we look deeply (e.g., by using N[0]) we shall see all the species present."

Hill's diversity numbers are given by:

N_a=∑{i=1}^S (p_i^a)^{1/(1-a)}

Special cases are:

N_-Inf

reciprocal of the proportional abundance of the rarest species;

N[0]

total number of species present;

N[1]

exp(H), where H: Shannon's index (see also `shannon`);

N[2]

reciprocal of Simpson's index (see also `simpson`);

N_Inf

reciprocal of the proportional abundance of the commonest species.

### Usage

```hill(.data = NULL, taxon, count, a = 0)

hill_(.data = NULL, taxon, count, a = 0)

hill0(.data = NULL, taxon, count)

hill0_(.data = NULL, taxon, count)

hill1(.data = NULL, taxon, count)

hill1_(.data = NULL, taxon, count)

hill2(.data = NULL, taxon, count)

hill2_(.data = NULL, taxon, count)
```

### Arguments

 `.data` data in a `data.frame`, `data_frame`, `data.table`, database etc. `taxon` name of column in `.data` containing taxa `count` name of column in `.data` containing counts `a` exponent in Hill's diversity number (R, with special cases for `a ` in 0, 1, 2 (see details))

### Value

numeric vector of Hill's numbers

### Functions

• `hill_`: version suitable for calling from a function (see package lazyeval).

• `hill0`: N[0]

• `hill0_`: N[0], version suitable for calling from a function (see package lazyeval).

• `hill1`: N[1]

• `hill1_`: N[1], version suitable for calling from a function (see package lazyeval).

• `hill2`: N[2]

• `hill2_`: N[2], version suitable for calling from a function (see package lazyeval).

### References

Hill, M.O., 1973. Diversity and Evenness: A Unifying Notation and Its Consequences. Ecology 54:427-432

`species_richness`, `shannon`, `simpson`

### Examples

```     hill(
taxon = c("Euspira pulchella", "Nephtys cirrosa"),
count = c(6, 12),
a = 0
)
hill0(
taxon = c("Euspira pulchella", "Nephtys cirrosa"),
count = c(6, 12)
)

```

[Package benthos version 1.3-6 Index]