Supplement 1. An R library "mso" for the spatial partitioning of ordination results from PCA, RDA, CA, and CCA, including a diagnostic plot.

<h2>File List</h2><blockquote> <h3><i><b>All files at once</b></i></h3> <blockquote> <p><a href="mso_1.6-1.tar.gz">mso_1.6-1.tar.gz</a></p> </blockquote> <h3><i><b>Source code</b></i></h3> <blockquote> <p><a href="mso.R">mso.R</a></p> <p><a href="plot.mso.R">plot.mso.R</a></p> </blockquote> <h3><i><b>Help files/documentation</b></i></h3> <blockquote> <p><a href="mso.RD">mso.RD</a></p> <p><a href="index.txt">index.txt</a></p> <p><a href="description.txt">description.txt</a></p> </blockquote> </blockquote><h2>Description</h2><p>An archive containing the mso library with functions mso.R and plot.mso.R (source code) as well as a help file mso.Rd, an index and a description file as required for an R package. The mso library requires the R base and the mva and vegan libraries, all of which can be downloaded from <a href="http://cran.r-project.org/">http://cran.r-project.org/</a>.</p> <p>The function mso.R adds an attribute vario, containing variograms of different variance components, to an object of class cca, generated by the functions cca or rda of the vegan library. The function plot.mso.R provides various options for a diagnostic plot and associated significance tests (see paper). For details, see the help file.</p> <p> </p

Supplement 2. R code for analysis of oribatid mite data.

<h2>File List</h2><div> <a href="Rcode_oribatid.r">Rcode_oribatid.r</a> (MD5: cff114d383995cbea34bf4acd232f463)</div><h2>Description</h2><div> Rcode_oribatid.r contains R code for analysis of the oribatid mite data with SCR.</div

Supplement 1. R code for analysis of simulated data.

<h2>File List</h2><div> <p><a href="Rcode_simulations.r">Rcode_simulations.r</a> (MD5: 6b104d150c5a84507fc200044b4e4a61)</p> </div><h2>Description</h2><div> Rcode_simulations.r contains R code for recreating the simulated data set and performing various steps of SCR on the example data.</div

Appendix A. A worked example that demonstrates the calculations.

A worked example that demonstrates the calculations

Appendix A. A worked example of spatial covariance in plant communities.

A worked example of spatial covariance in plant communities

R scripts

R scripts for analyzing both sets of simulations (individual and deme level), and additional spatial coordinate files for Lotterhos & Whitlock (2015) data at http://dx.doi.org/10.5061/dryad.mh67

Model selection with multiple regression on distance matrices leads to incorrect inferences

<div><p>In landscape genetics, model selection procedures based on Information Theoretic and Bayesian principles have been used with multiple regression on distance matrices (MRM) to test the relationship between multiple vectors of pairwise genetic, geographic, and environmental distance. Using Monte Carlo simulations, we examined the ability of model selection criteria based on Akaike’s information criterion (AIC), its small-sample correction (AICc), and the Bayesian information criterion (BIC) to reliably rank candidate models when applied with MRM while varying the sample size. The results showed a serious problem: all three criteria exhibit a systematic bias toward selecting unnecessarily complex models containing spurious random variables and erroneously suggest a high level of support for the incorrectly ranked best model. These problems effectively increased with increasing sample size. The failure of AIC, AICc, and BIC was likely driven by the inflated sample size and different sum-of-squares partitioned by MRM, and the resulting effect on delta values. Based on these findings, we strongly discourage the continued application of AIC, AICc, and BIC for model selection with MRM.</p></div

Results from a single simulation run.

<p>The absolute values (top row), delta values Δ_<i>i</i> (middle row), and model weights <i>w</i>_<i>i</i> (bottom row) for node-based analysis (Node: left column), distance-based analysis with low correlation (Dist (LC): middle column), and distance-based analysis with high correlation (Dist: (HC): right column) as a function of the number of spurious random variables added sequentially to the correct model with a single meaningful predictor <i>x</i>₁ (<i>ρ</i>_<i>xy</i> = 0.6) for node-based, based on <i>n</i> = 100.</p

Proportional selection of the correct model by means of MRM among 1000 simulated data sets for different levels of correlated predictors.

<p>The proportion of 1000 simulated data sets where each of the five candidate models were selected as the best model using AIC (top row), AICc (middle row), and BIC (bottom row) with three different sample sizes <i>n</i> = 30 (left column), <i>n</i> = 100 (middle column), <i>n</i> = 300 (right column) for the node-based analysis with low correlation (Node LC), the distance-based analysis with low correlation (Dist LC), and the distance-based analysis with high correlation (Dist HC). We were primarily interested in determining whether AIC, AICc, and BIC selected the correct model containing three meaningful variables with tapering effects (black) or selected an underfitted (dark grey) or overfitted (light grey) model.</p