Appendix C. Perturbation analysis of the necessary and sufficient conditions for cycles.

Perturbation analysis of the necessary and sufficient conditions for cycles

Appendix A. Local stability analysis of the general model equation (Eq. 11).

Local stability analysis of the general model equation (Eq. 11)

Appendix B. Application of stability conditions in Eq. 14 to specific examples.

Application of stability conditions in Eq. 14 to specific examples

Supplement 1. R code used for simulation.

<h2>File List</h2><blockquote> <p><a href="Simulation code.r">Simulation code.r</a> – Source code to run simulation analysis</p> </blockquote><h2>Description</h2><blockquote> <p>This is the complete code for simulating usage under different environmental scenarios of food/cover availability and fitting GFR models to the synthetic data. The end of the listing contains the following three functions:</p> <p>environ(d,x): Creates a square dxd arena containing a total of x units of resource. The function introduces spatial autocorrelation via kernel smoothing of the resource units. Kernel smoothed map is re-normalized to ensure that x is conserved.</p> <p>movement(d, env1, env2) : This function contains the movement simulation. The parameters pertaining to animal behavior are locally defined, so the function operates as a wrapper. Its input is the dimensionality d of the square arena and the two environmental layers (env1 and env2). Its output is a map of usage.</p> <p>predict.lmer(mod, newdat) : Generates predictions from the fixed effects of mixed model.</p> <p>The main body of the code has the following parts:</p> <p>1. Initialization</p> <p> Parameters regulating the arena size, number of environmental scenarios and overall availabilities of each resource in the arena for each scenario.</p> <p>2. Simulation</p> <p>The functions environ() and movement() are used to generate resource distributions and resulting usage for each environmental scenario.</p> <p>3. Model fitting</p> <p>Here, the data frame is extended with columns for expectations of the two resources in each scenario and four GFR models are fit to the augmented data frame.</p> <p>4. Model validation</p> <p> This part first inspects the goodness-of-fit of the models. It then generates data for a new environmental scenario with unobserved availabilities. The model fitted in part 3 is then used to make predictions about the new scenario. Then follow several different outputs that aim to visualize and quantify the quality of the resulting predictions.</p> </blockquote

Appendix C. Model comparisons for individual wolves.

Model comparisons for individual wolves

Supplementary Information from Inference of the drivers of collective movement in two cell types: <i>Dictyostelium</i> and melanoma

Supplements, supplementary figures and supplementary table

Appendix A. Prior specifications, prior sensitivity, and goodness of fit for the harbor seal example.

Prior specifications, prior sensitivity, and goodness of fit for the harbor seal example

Appendix B. Markov chain Monte Carlo algorithm.

Markov chain Monte Carlo algorithm

Capture histories for lions Panthera leo

Gender, DOB, Pride membership and location by conservancy of lions within community conservancies north of the Masai Mara, Kenya. Presence/absence (1/0) and age category also given for 6 month periods to generate capture history (column AB) for mark-recapture analysis with MARK

Supplement 1. Source code and example data for implementing the Markov chain Monte Carlo algorithm.

<h2>File List</h2><div> <p><a href="MCMCalgorithm.r">MCMCalgorithm.r</a> -- (md5: 66b96318b9d549b5abd7a98178ccc6c8)</p> <p><a href="MCMCalgorithm.c">MCMCalgorithm.c</a> -- (md5: c637bb779c8f04eaf247974a6409ef1b)</p> <p><a href="MCMCalgorithm.dll">MCMCalgorithm.dll</a> -- (md5: 479e438af5b72bb05d8a413b487f8d2e)</p> <p><a href="data.RData">data.RData</a> -- (md5: 25eccac47d5082a651ec6d1040daf939)</p> <p><a href="Initial_values.RData">Initial_values.RData</a> -- (md5: 8da04b2b834f00fe2f7d8669d34e7550)</p> </div><h2>Description</h2><div> <p>MCMCalgorithm.r contains R code for loading the data (data.RData and Initial_values.RData), data pre- and post-processing, loading the dynamic link library file (MCMCalgorithm.dll), and calling the .C function for interfacing the compiled C code (MCMCalgorithm.c) with R (on a machine running Windows). </p> <p>MCMCalgorithm.c contains C code for implementing the MCMC algorithm.</p> <p>MCMCalgorithm.dll is a dynamic link library file containing the compiled C code.</p> <p>data.RData contains the data for 17 harbor seals.</p> <p>Initial_values.RData contains starting values for initialization of the MCMC chain.</p> </div