# Species Distributions.

### Description

A Species Distribution is a (preferably named) vector containing species abundances or probabilities.

### Usage

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 | ```
as.SpeciesDistribution(x)
## S3 method for class 'data.frame'
as.SpeciesDistribution(x)
## S3 method for class 'integer'
as.SpeciesDistribution(x)
## S3 method for class 'numeric'
as.SpeciesDistribution(x)
## S3 method for class 'SpeciesDistribution'
plot(x, ..., Distribution = NULL,
type = "b", log = "y", main = NULL, xlab = "Rank", ylab = NULL)
is.SpeciesDistribution(x)
as.ProbaVector(x, Correction = "None", Unveiling = "None",
RCorrection = "Chao1", JackOver = FALSE, CEstimator = "ZhangHuang",
CheckArguments = TRUE)
## S3 method for class 'data.frame'
as.ProbaVector(x, Correction = "None", Unveiling = "None",
RCorrection = "Chao1", JackOver = FALSE, CEstimator = "ZhangHuang",
CheckArguments = TRUE)
## S3 method for class 'integer'
as.ProbaVector(x, Correction = "None", Unveiling = "None",
RCorrection = "Chao1", JackOver = FALSE, CEstimator = "ZhangHuang",
CheckArguments = TRUE)
## S3 method for class 'numeric'
as.ProbaVector(x, Correction = "None", Unveiling = "None",
RCorrection = "Chao1", JackOver = FALSE, CEstimator = "ZhangHuang",
CheckArguments = TRUE)
is.ProbaVector(x)
as.AbdVector(x, Round = TRUE)
## S3 method for class 'data.frame'
as.AbdVector(x, Round = TRUE)
## S3 method for class 'integer'
as.AbdVector(x, Round = TRUE)
## S3 method for class 'numeric'
as.AbdVector(x, Round = TRUE)
is.AbdVector(x)
``` |

### Arguments

`x` |
An object. |

`Distribution` |
The distribution to fit on the plot. May be |

`Round` |
If |

`Correction` |
A string containing one of the possible corrections to estimate a probability distribution: |

`Unveiling` |
A string containing one of the possible unveiling methods to estimate the probabilities of the unobserved species: |

`RCorrection` |
A string containing a correction recognized by |

`JackOver` |
If |

`CEstimator` |
A string containing an estimator recognized by |

`type` |
The plot type, see |

`log` |
The axis to plot in log scale, |

`main` |
The main title of the plot. if |

`xlab` |
The X axis label, "Rank" by default. |

`ylab` |
The Y axis label. if |

`...` |
Additional arguments to be passed to |

`CheckArguments` |
Logical; if |

### Details

`SpeciesDistribution`

objects include `AbdVector`

and `ProbaVector`

objects.

`as.AbdVector`

just sets the class of the numeric or integer `x`

so that appropriate versions of community functions (generic methods such as `Diversity`

) are applied. Abundance values are rounded (by default) to the nearest integer.

`as.ProbaVector`

normalizes the vector so that it sums to 1. If `Correction`

is not `"None"`

, the observed abundance distribution is used to estimate the actual species distribution. The list of species will be changed: zero-aundance species will be cleared, and some unobserved species will be added. First, observed species probabilities are estimated folllowing Chao and Shen (2003), *i.e.* input probabilities are multiplied by the sample coverage, or according to more sophisticated models: Chao *et al.* (2013, single-parameter model), or Chao *et al.* (2015, two-parameter model). The total probability of observed species equals the sample coverage. Then, the distribution of unobserved species can be unveiled: their number is estimated according to `RCorrection`

(if the Jackknife estimator is chosen, the `JackOver`

argument allows using the order immediately over the optimal one). The coverage deficit (1 minus the sample coverage) is shared by the unobserved species equally (`Unveiling = "unif"`

, Chao *et al.*, 2013) or according to a geometric distribution (`Unveiling = "geom"`

, Chao *et al.*, 2015).

These functions can be applied to data frames to calculate the joint diversity (Gregorius, 2010).

`SpeciesDistribution`

objects can be plotted. The `plot`

method returns the estimated parameters of the fitted distribution. The broken stick has no parameter, so the maximum abundance is returned.

### Note

Fisher's alpha (Fisher *et al.*, 1943) is estimated to fit the log-series distribution. The estimation is done by the `fisher.alpha`

function of package `vegan`

. It may differ substantially from the estimation returned by `optimal.theta`

from package `untb`

.

### Author(s)

Eric Marcon <Eric.Marcon@ecofog.gf>, Bruno Herault <Bruno.Herault@ecofog.gf>

### References

Chao, A. and Shen, T. J. (2003). Nonparametric estimation of Shannon's index of diversity when there are unseen species in sample. *Environmental and Ecological Statistics* 10(4): 429-443.

Chao, A., Wang, Y. T. and Jost, L. (2013). Entropy and the species accumulation curve: a novel entropy estimator via discovery rates of new species. *Methods in Ecology and Evolution* 4(11):1091-1100.

Chao, A., Hsieh, T. C., Chazdon, R. L., Colwell, R. K., Gotelli, N. J. (2015) Unveiling the Species-Rank Abundance Distribution by Generalizing Good-Turing Sample Coverage Theory. *Ecology* 96(5): 1189-1201.

Fisher R.A., Corbet A.S., Williams C.B. (1943) The Relation Between the Number of Species and the Number of Individuals in a Random Sample of an Animal Population. *Journal of Animal Ecology* 12: 42-58.

Gregorius H.-R. (2010) Linking Diversity and Differentiation. *Diversity* 2(3): 370-394.

### See Also

`rgeom`

, `rlnorm`

, `rCommunity`

### Examples

1 2 3 4 5 6 | ```
# Load Paracou data (number of trees per species in two 1-ha plot of a tropical forest)
data(Paracou618)
# Ns is the total number of trees per species
Ns <- as.AbdVector(Paracou618.MC$Ns)
# Whittaker plot, poorly fitted by a log-normal distribution
plot(Ns, Distribution = "lnorm")
``` |

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