Proportion of variance in the fossil data explained by an environmental reconstruction

Calculate the proportion of variance in the fossil data explained by an environmental reconstruction with a constrained ordination. This value is compared with a null distribution calculated as the proportion of variance in the fossil data explained by reconstructions from transfer functions trained on random data.

Usage

randomTF(
  spp,
  env,
  fos,
  n = 99,
  fun,
  col,
  condition = NULL,
  autosim,
  ord = rda,
  permute = FALSE,
  models,
  make_models = FALSE,
  ...
)

# S3 method for class 'palaeoSig'
plot(x, variable_names, top = 0.7, adj = c(0, 0.5), p_val = 0.05, ...)

# S3 method for class 'palaeoSig'
autoplot(object, variable_names, nbins = 20, top = 0.7, p_val = 0.05, ...)

Arguments

spp: Data frame of modern training set species data, transformed as required for example with sqrt
env: Data frame of training set environmental variables or vector with single environmental variable
fos: Data frame of fossil species data, with same species codes and transformations as spp
n: number of random training sets. More is better.
fun: Transfer function method. Additional arguments to fun can be passed with ...
col: Some transfer functions return more than one column of results, for example with different WAPLS components. col selects which column of the reconstructions to use. See the relevant transfer function method help file.
condition: Optional data frame of reconstructions to partial out when testing if multiple independent reconstructions are possible.
autosim: Optional data frame of random values. This is useful if the training set is spatially autocorrelated and the supplied data frame contains autocorrelated random variables. If autosim is missing, and permute is FALSE, the transfer functions are trained on random variables drawn from a uniform distribution.
ord: Constrained ordination method to use. rda is the default, cca should also work. capscale won't work without modifications to the code (or a wrapper).
permute: logical value. Generate random environmental variables by permuting existing variable. Only possible if there is only one environmental variable and autosim is missing.
models: list of models made by randomTF with argument make_models = TRUE
make_models: logical, should a list of transfer functions trained on random data be returned
...: Other arguments to the transfer function. For example to change the distance metric in MAT. Also extra arguments to plot.
x: Output from randomTF
variable_names: Names of environmental variables. If missing, taken from env data.frame.
top: Proportion of the figure below the environmental name labels.
adj: Adjust the position that the environmental names are plotted at.
p_val: P value to draw a line vertical line at (with which=2)
object: Output from randomTF
nbins: integer giving number of bins for the histogram

Value

A list with components

PCA: The unconstrained ordination of the fossil data.
preds: A list of the containing the reconstructions for each environmental variable.
MAX: Proportion of the variance explained by the first axis of the unconstrained ordination. This is the maximum amount that a reconstruction of a single variable can explain.
EX: The proportion of the variance in the fossil data explained by each reconstruction.
sim.ex: The proportion of variance explained by each of the random environmental variables.
sig: The p-value of each reconstruction.

If make_models = TRUE, a list of transfer function models is returned.

autoplot.palaeoSig returns a ggplot2 object

Details

The function calculates the proportion of variance in the fossil data explained by the transfer function reconstruction. This is compared with a null distribution of the proportion of variance explained by reconstructions based on random environmental variables. Reconstructions can be partialled out to test if multiple reconstructions are statistically significant. If the environment is spatially autocorrelated, a red-noise null should be used instead of the default white noise null. Red noise environmental variables can be generated with the gstat package.

Any transfer function in the rioja package can be used. Other methods (e.g. random forests) can be used by making a wrapper function.

If reconstructions from several sites are to be tested using the same training set it can be much faster to train the models on random environmental data once and then use them repeatedly. This can be done with make_models = TRUE and then running randomTF again giving the resultant models to the models argument. make_models does not work with MAT.

For some transfer function methods, including WA, the code can be made somewhat faster by coercing the modern and fossil species data to matrices (spp <- as.matrix(spp)), otherwise WA has to do this repeatedly. With MAT, this should not be done as it might cause an error.

Functions

plot(palaeoSig): Plot palaeoSig object
autoplot(palaeoSig): autoplot function for palaeoSig object

Note

If there are only a few fossil levels, obs.cor might have more power. If there are few taxa, tests on MAT reconstructions have more statistical power than those based on WA.

References

Telford, R. J. and Birks, H. J. B. (2011) A novel method for assessing the statistical significance of quantitative reconstructions inferred from biotic assemblages. Quaternary Science Reviews 30: 1272–1278. doi:10.1016/j.quascirev.2011.03.002

Author

Richard Telford richard.telford@uib.no

Examples

require(rioja)
data(SWAP)
data(RLGH)
rlghr <- randomTF(
  spp = sqrt(SWAP$spec), env = data.frame(pH = SWAP$pH),
  fos = sqrt(RLGH$spec), n = 49, fun = WA, col = "WA.inv"
)
rlghr$sig
#>   pH 
#> 0.04 
plot(rlghr, "pH")


require("ggplot2")
autoplot(rlghr, "pH")