Gradients of the seven scenarios of Peres-Neto et al. (2012)

Two gradients on a transect, as in Appendix C of Peres-Neto et al. (2012). Unless stated, x is evenly spaced on [-15, 15] and y is x in random order, so that the two are independent.

Usage

logistic_gradients(scenario, n_sites = 31)

Arguments

scenario

Number of the scenario, from 1 to 7.

n_sites

Number of sites.

Value

Data frame with one row per site: x and y, the gradients that generate the data, and x_test and y_test, the ones to analyse.

Details

1. The two gradients are equally important and independent.

2. They are equally important and correlated: y is x plus a N(0, 1) error.

3. They are independent, and y is less important: data come from y, and y_test is y with unit variance plus a N(0, 1) error. On the scale of y this error would have no effect, and with unit variance the results agree with Table 5.

4. Neither is important: data come from scenario 1, and x_test and y_test are N(0, 1) deviates, to estimate the type I error.

5. y has a broad spatial scale, the first Moran's eigenvector map (MEM), and x is in random order along the transect.

6. y has an intermediate spatial scale, the third MEM, and x is as in scenario 5.

7. x is the first MEM and y the third.

MEMs are rescaled to [-15, 15].

References

Peres-Neto, P. R., Leibold, M. A., & Dray, S. (2012). Assessing the effects of spatial contingency and environmental filtering on metacommunity phylogenetics. Ecology, 93, S14–S30. doi:10.1890/11-0494.1

Examples

set.seed(1)
head(logistic_gradients(6))
#>     x          y x_test     y_test
#> 1 -13  -5.740251    -13  -5.740251
#> 2 -10 -10.606602    -10 -10.606602
#> 3  -6 -13.858193     -6 -13.858193
#> 4  13 -15.000000     13 -15.000000
#> 5  14 -13.858193     14 -13.858193
#> 6  -1 -10.606602     -1 -10.606602