Generates relative abundance of species for niche-based models (D.A. Murray).

### Options

`PRINT` = string token |
Controls printed output (`model` , `expected` , `replications` ); default `mode` , `expe` |
---|---|

`MODELTYPE` = string token |
The niche model (`powerfraction` , `fixedratio` , `preemption` , `randomfraction` , `macarthurfraction` ); default `powe` |

`METHOD` = string token |
Whether to use the Fortran DLL to calculate the relative abundance (`dll` , `commands` ); default `*` uses the DLL in Windows implementations, and commands for other platforms |

`POWER` = scalar |
Power for the Power fraction model, must be in the range 0 to 1 |

`URATIO` = scalar |
Ratio for the fixed ratio model |

`SEED` = scalar |
Seed for random number generator for the random division of the niche space; default 0 |

`PLOT` = string token |
Plots the average relative abundance (`relativeabundance` ); default rela |

### Parameters

`NREPLICATES` = scalars |
Number of replications |
---|---|

`NSPECIES` = scalars |
Number of species |

`EXPECTED` = variates |
Saves the expected average relative abundance |

`SDEXPECTED` = variates |
Saves the standard deviation for the expected mean relative abundance |

### Description

The relative abundance of species can be modelled using deterministic models, such as the log series, or by stochastic models based on assumed patterns of resource use, such as niche-based models. `ECNICHE`

can be used to simulate relative abundances (proportional abundance of species) for niche-apportionment, where species are considered to be associated with different processes of niche division, and sequential breakage models. Niche apportionment and sequential breakage models generate relative abundances using a two step process. In the first step the target niche (the total niche space in the very first step) is divided using a given probability distribution, for example, a random selection using the uniform distribution. In the second step a new target niche space is selected using a probabilistic weighting. The process is then repeated by dividing a selected target niche and selecting a new niche for division. `ECNICHE`

includes Tokeshi’s (1993, 1996) niche apportionment models for the dominance preemption, random fraction, power fraction and MacArthur fraction. The dominance preemption model assumes that each species in turn preempts over half the remaining niche space and is dominant over all remaining species combined. The random faction model represents the situation where new species compete for the niche space of existing species, and takes a random proportion of the previously existing niche. Therefore, species with different niche sizes or abundances have the same chance of being selected for a subsequent niche division. In the power fraction model, the probability of selection is proportional to niche size (or abundance) raised to a power exponent k (0 ≤ k ≤ 1). In the MacArthur fraction model (broken-stick model) the probability of a niche being selected for division is related to its size. So, larger niches are more likely to be invaded by species. `ECNICHE`

also provides the sequential breakage model where the target niche is selected at random and then divided to produce two segments relative to a ratio such as 0.75:0.25.

The number of replications for the model are specified using the `NREPLICATES`

parameter. The `NSPECIES`

parameter specifies the number of species within the assemblage. The mean relative abundance of species and associated standard deviations can be saved using the `EXPECTED`

and `SDEXPECTED`

parameters respectively.

The model to use to generate the relative abundances for the species is specified by the `MODELTYPE`

option. The power for the Power fraction model is specified using the `POWER`

option, and must range between 0 and 1. For the sequential breakage model, the largest value of the ratio of division is specified using the `URATIO`

option, and must range between 0.5 and 1. The `SEED`

option specifies the seed to use in the random division of the niche space. The default value of zero continues an existing sequence of random numbers or, if the generator has not yet been used in this run of Genstat, initializes the generator automatically.

For a large number of replications the calculation of the relative abundance of species can be slow. For the PC Windows implementation, a Fortran DLL is available that uses the `OWN`

calculate function. By default the procedures uses the DLL, however, you can choose to use the Genstat commands by setting option `METHOD=commands`

.

The `PRINT`

option controls printed output, with settings:

`model` |
the niche model, |
---|---|

`expected` |
the expected mean relative abundance, |

`replications` |
the relative abundances for each replication; this can produce a lot of output, so it is recommended that this be used only for monitoring. |

By default `PRINT=model,expected`

.

The `PLOT`

option controls whether `ECNICHE`

produces a plot of the average relative abundance on the log scale; the default `PLOT=relativeabundance`

gives the plot.

Options: `PRINT`

, `MODELTYPE`

, `METHOD`

, `POWER`

, `URATIO`

, `SEED`

, `PLOT`

.

Parameters: `NREPLICATES`

, `NSPECIES`

, `EXPECTED`

, `SDEXPECTED`

.

### Method

For the dominance preemption model the niche space is divided by a random (uniform) split between 0.5 and 1.0. This model is similar to the geometric series, and over many replications will produce a similar distribution of species abundance when *k* = 0.75 (see `ECFIT`

for details of geometric series). For the power fraction the probability of a niche being selected for division is *p _{i}* =

*a*

*x*, where

_{i}^{k}*a*is constant common to all the species in an assemblage and ∑

_{i}{

*a*

*x*} = 1, and

_{i}^{k}*x*denotes the niche size of species

_{i}*i*. The random fraction is formed using the power fraction model with

*k*= 0, i.e. a size-independent selection probability. Similarly, the MacArthur fraction is calculated using the power fraction with

*k*= 1, i.e. probability of selection is a linear function of the segment length. The sequential breakage or fixed ratio model uses a deterministic division where the segments are divided to produce lengths relative to a ratio, such as 0.75:0.25.

### References

Magurran, A.E. (2003). *Measuring Biological Diversity*. Blackwell, Oxford.

Tokeshi, M. (1993). Species Abundance Patterns and Community Structure. *Advances in Ecological Research*, 24, 111-186.

Tokeshi, M. (1996). Power fraction: a new explanation of relative abundance patterns in species-rich assemblages. *Oikos*, 75, 543-550.

### See also

Commands for: Ecological data.

### Example

CAPTION 'ECNICHE examples'; STYLE=meta ECNICHE [MODELTYPE=randomfraction; SEED=179398] 250;25 ECNICHE [MODELTYPE=power; POWER=0.2] 250;25