sim.relt: Calculate additive and relative partitioning.

Description

Enables the calculation of three $\beta$-diversity measures closely related to each other: additive partitioning, multiplicative partitioning (Whittaker 1960), reverse multiplicative partitioning (Whittaker 1960, full change notion).

Usage

sim.relt(veg, coord = NULL, dn, method = "additive", test = TRUE, 
permutations = 100, ...)
sim.rel(veg, coord=NULL, dn, method="additive", ...)

Arguments

veg

A species matrix. The function takes only presence/absence into account. However the translation is done automatically by assuming that zero means no occurrence, whereas any value > 0 is transformed to 1

coord

A two column data.frame defining the geographic positions of the sampling units. Should give (in this order) the x- and y-values in UTM or similar coordinates. Defaults to NULL. Triggers also if the similarity measures should only incorporate

A numeric or a two value vector. In the first case it gives the distance until which sampling units should be considered as neighbors. In the second the two values define a ring around each plot. Plots which fall into the ring are considered as neighbors.

method

Which similarity measure should be calculated. Give a partial match to "additive", "relative" or "reverse". See details.

test

Shall significance be tested? Defaults to true. Does only make sense when coord and dn is given. In general sim.relt calls sim.rel to calculate the values. So the latter will rarely used by the user dire

permutations

The number of permutations. Defaults to 100 which allows for a p-level of 0.01

...

Arguments to other functions.

Value

The function returns either a named vector (if coord and dn are set) or a data.frame with the following items. The last three are only added if test = TRUE.
nnbsNumber of neighbours of the respective plot. Results from the neighbour definition dn. If this was not given it reflects the total number of plots in the data-set.
n.specNumber of species on the focal plot. If dn and coord were not given it reflects the total number of species in the data-set
valueThe calulated $\beta$-diversity. The name of the column changes respectively.
sim.testThe p-value of the significance test for the diversity values.
sigThe significance decision tested against alpha = 0.05. "*" means that the respective $\beta$-value is significantly different from random.
sig.prefixMarks against which tail significance of $\beta$-values was tested. If the initial value is lower than the mean of the permuted values the lower tail is tested (sig.prefix = "-") and vice versa (sig.prefix = "+").

encoding

UTF-8

Details

Three different diversity measures related to the concept of $\beta$-diversity can be calculated with this function. Besides the definition of $\beta$-diversity as the turnover in species composition (Whittaker 1960), Whittaker defined the relation between $\gamma$- and $\alpha$-diversity as $\beta$-diversity where $\alpha$ is the mean species richness found on local plots or sampling units and $\gamma$-diversity is the species richness throughout a reference area (e.g. an investigation area). However, $\gamma$ could also be defined for smaller units e.g. for a focal plot and its neighbours, which is done in the function when coord and dn are set. $\beta$-diversity in terms of multiplicative diversity is calculated when method is set to "relative". "reverse" simply means that the relation is calculated vice versa ($\frac{\bar{\alpha}}{\gamma}$) which results in numbers between 0 and 1 whereas the original formula gives results from 1 ($\bar{\alpha}=\gamma$) upwards. An upper end is not defined. However, increasing values indicate increasing heterogeneity in species composition. The idea of "additive partitioning" (Lande 1996, Vellend 2001, Veech 2002) takes Whittakers approach further. Out of the criticism that $\beta$ in Whittakers sense does not exhibit the same units (species numbers) as $\alpha$- and $\gamma$-diversity here $\beta$-diversity results as the subtract of $\gamma$- and $\alpha$-diversity. It expresses the average amount of diversity not found in a single, randomly-chosen sample. It is also rather calculated for a whole data-set. Here we apply it as well to a moving window of a focal plot and its neighbours ifcoord and dn are set. The idea of $\gamma$-diversity might be questioned in general, as its quality is not different from $\alpha$. Only the geographic extent is changed and often definition becomes problematic. Imagine a temporal study where different numbers of species are found throughout the years - Is $\gamma$ then the overall species richness, or the species richness in one year? Furthermore $\beta$-diversity is not clearly defined. There are even more definitions to it then mentioned here (e.g. Qian et al. 2005) so it may be better to use 'differentiation-diversity' instead. Significance is tested with a simple Monte-Carlo procedure. The initial value of the respective index is tested against a number of values which are calculated from a random reshuffling of the original species matrix. So the hypothesis tested is, that the observed pattern (for each focal plot) is different from random. This is meaningless when coord and dn are not set.

References

Jurasinski, G. & Retzer, V. in prep. Measuring multi-plot similarity with presence-absence data. Ecology in prep. Lande, R. (1996) Statistics and partitioning of species diversity and similarity along multiple communities. Oikos 76: 25-39. Qian, H., Ricklefs, R. E. & White, P. S. (2005) Beta diversity of angiosperms in temperate floras of eastern Asia and eastern North America. Ecology Letters 8: 15-22. Veech, J. A., Summerville, K. S., Crist, T. O. & Gering, J. C. (2002) The additive partitioning of species diversity: recent revival of an old idea. Oikos 99: 3-9. Vellend, M. (2001) Do commonly used indices of beta-diversity measure species turnover? Journal of Vegetation Science 12: 545-552. Whittaker, R. H. (1960) Vegetation of the Siskiyou Mountains, Orgeon and California. Ecological Monographs 30: 279-338.