fuzzySim (version 4.33)

fuzzyOverlay: Overlay operations based on fuzzy logic

Description

Logical and set operations are useful for comparative distribution modelling, to assess consensus or mismatches between the predictions of different models, and to quantify differences between models obtained for different time periods. Fuzzy set theory (Zadeh 1965, Barbosa & Real 2012) allows performing such operations without converting model predictions from continuous to binary, thus avoiding the application of arbitrary thresholds and the distortion or over-simplification of those predictions. The result is a continuous numerical value quantifying the intersection, union, sum, or other operation among model predictions, whether binary or continuous.

Usage

fuzzyOverlay(data, overlay.cols = NULL, op = "intersection",
na.rm = FALSE, round.digits = 2)

Value

This function returns a vector with length equal to the number of rows in 'data', or (if the input is a SpatRaster) a SpatRaster layer of the same dimensions as the input's first layer, containing the row-wise or pixel-wise result of the operation performed.

Arguments

data

matrix, data frame, or multilayer SpatRaster containing the model predictions to compare.

overlay.cols

vector of the names or index numbers of the columns or layers to compare. The default is all columns or layers in data.

op

character value indicating the operation to perform between the (specified) prediction columns or layers in 'data'. Options are:

• "consensus" for the arithmetic mean of predictions (or the fuzzy equivalent of the proportion of models that agree that the species can potentially occur at each site);

• "fuzzy_and" or "intersection" for fuzzy intersection (minimum value; Zadeh, 1965);

• "fuzzy_or" or "union" for fuzzy union (maximum value; Zadeh, 1965);

• "prob_and" or "prob_or" for probabilistic and/or, respectively (see Details);

• "maintenance" for the values where all predictions for the same row/pixel (rounded to the number of digits specified in 'round.digits') are the same.

If 'data' has only two columns/layers to compare, further options are:

• "xor" for exclusive 'or'

• "AnotB" for the the occurrence of the species in column/layer 1 in detriment of that in column/layer 2;

• "expansion" for the prediction increase in rows/pixels where column/layer 2 has higher values than column/layer 1;

• "contraction" for the prediction decrease in rows/pixels where column/layer 2 has lower values than column/layer 1;

• "change" for a mix of the latter two, with positive values where there is an increase and negative values where there is a decrease in favourability from columns/layers 1 to 2. For expansion, contraction and maintenance, rows/pixels where the values do not satisfy the condition (i.e. second column/layer larger, smaller, or roughly equal to the first) get a value of zero.

na.rm

logical value indicating if NA values should be ignored. The default is FALSE, so rows/pixels with NA in any of the prediction columns/layers get NA as a result.

round.digits

integer value indicating the number of decimal places to be used if op = "maintenance". The default is 2.

Author

A. Marcia Barbosa

Details

If your predictions are probabilities, "prob_and" (probabilistic 'and') gives the probability of all species in 'data' occurring simultaneously by multiplying all probabilities; and "prob_or" (probabilistic 'or') gives the probability of any of them occurring at each site. These can be quite restrictive, though; probabilistic "and" can give particularly irrealistically small values.

If you have (or convert your probabilities to) favourability predictions, which can be used directly with fuzzy logic (Real et al. 2006; see Fav function), you can use "fuzzy_and" or "intersection" to get the favourability for all species to co-occur at each site, and "fuzzy_or" or "union" to get favourability for any of them to occur at each site (Barbosa & Real 2012).

References

Barbosa A.M. & Real R. (2012) Applying fuzzy logic to comparative distribution modelling: a case study with two sympatric amphibians. The Scientific World Journal, 2012, Article ID 428206

Real R., Barbosa A.M. & Vargas J.M. (2006) Obtaining environmental favourability functions from logistic regression. Environmental and Ecological Statistics 13: 237-245.

Zadeh, L.A. (1965) Fuzzy sets. Information and Control, 8: 338-353

See Also

fuzSim, modOverlap and fuzzyRangeChange for overall (not row-wise or pixel-wise) comparisons among model predictions.

Examples

data(rotif.env)

names(rotif.env)


# get model predictions for 3 of the species in rotif.env:

mods <- multGLM(rotif.env, sp.cols = 18:20, var.cols = 5:17, id.col = 1,
step = TRUE, FDR = TRUE, trim = TRUE)

preds <- mods$predictions[ , c("Abrigh_F", "Afissa_F", "Apriod_F")]


# calculate intersection and union among those predictions:

preds$intersect <- fuzzyOverlay(preds, op = "intersection")

preds$union <- fuzzyOverlay(preds, op = "union")

head(preds)


# imagine you have a model prediction for species 'Abrigh' in a future time
# (here we will create one by randomly jittering the current predictions)

preds$Abrigh_imag <- jitter(preds[ , "Abrigh_F"], amount = 0.2)
preds$Abrigh_imag[preds$Abrigh_imag < 0] <- 0
preds$Abrigh_imag[preds$Abrigh_imag > 1] <- 1


# you can calculate row-wise prediction changes from Abrigh to Abrigh_imag:

preds$Abrigh_exp <- fuzzyOverlay(preds, overlay.cols = c("Abrigh_F",
"Abrigh_imag"), op = "expansion")

preds$Abrigh_contr <- fuzzyOverlay(preds, overlay.cols = c("Abrigh_F",
"Abrigh_imag"), op = "contraction")

preds$Abrigh_chg <- fuzzyOverlay(preds, overlay.cols = c("Abrigh_F",
"Abrigh_imag"), op = "change")

preds$Abrigh_maint <- fuzzyOverlay(preds, overlay.cols = c("Abrigh_F",
"Abrigh_imag"), op = "maintenance")

head(preds)