Slope {EcotoneFinder}

Method to calculate the derivative of irregular functions:

Description

Method to calculate the derivative of irregular functions:

Usage

Slope(ecotonefinder, method = c("dca", "fanny", "vegclust", "cmeans",
  "diversity", "all"), window = 3, axis.number = 1,
  groups = ecotonefinder$groups, diversity = c("shannon", "richness",
  "expShannon", "pielou", "all"))

Arguments

ecotonefinder

A list containing elements named in the same way than EcotoneFinder function outcomes

method

The name of the method for which the slopes should be calculated. Correspond to the names of the list.

window

Must be an odd number. The interval to be used for slope calculation. The bigger the window, the more averaged the slope will be.

axis.number

If "dca" is chosen, indicate the number of axis over which to calculate the slope (first axis, first and second axis,...)

groups

If any clustering method is chosen, corresponds to the index of the cluster for which the slope shold be calculated. If "all", the slope will be calculated for all the clusters.

diversity

If "diversity" is chosen in the method argument, define the diversity index for which to calculate the slope. "all" can be chosen.

Details

Slope calculations are done by moving window analysis. The width of the windows is defined by the window argument. For each window, the result of slope coefficient of a linear model (lm function of the stat package) is stored and used to draw the general slope along the gradient. The bigger the window, the more points will be used to compute the linear models, meaning the obtained slopes will be smoother. This also results in the addition of NAs at the ends of the gradient.

The first axis of DCA has been used as a beta-diversity index, and its derivative as a method to locate ecotones (see Brownstein et al., 2013). The Slope function provide the possibility of computing the slope of the other axis, to avoid the loss of information induced by the reduction of the dimentionality of the original data. Similarly, the slopes of the fuzzy clusters can be used to pinpoint the transitions between them. The value of the slopes can be an indicator of the relative sharpness of the transion area. Particularly, as the memberships of the fuzzy clusters range betwwen 0 and 1, these values can readilly be compared between studies and datasets. These values vary depending on the window width and can be very sensible to noise in the original data. A reliable method to mathematically identify breaks is still needed and careful interpretation by the user is still required.

Value

A list of dataframes containing the slope values for the specified methods and the original data.

Examples

 #### Artificial dataset:
 SyntheticTrial <- SyntheticData(SpeciesNum = 21, CommunityNum = 3,
                                 SpCo = NULL ,Length = 500,
                                 Parameters = list(a=rep(60, 3),
                                                   b=c(0,250,500),
                                                   c=rep(0.015,3)),
                                 pal = c("#008585", "#FBF2C4", "#C7522B"))

 ## Analyses:
 SyntheticEcoFinder <- EcotoneFinder(data = SyntheticTrial[,-1],
                                     dist = SyntheticTrial$Distance,
                                     method = "all", groups = 3,
                                     standardize = "hellinger", diversity = "all")

 ## Slope calculation:
 SyntheticSlope <- Slope(SyntheticEcoFinder, method = "all", axis.number = 2,
                         diversity = "all")