Spatial processes and evolutionary models: a critical review

Evolution is a fundamentally population level process in which variation, drift, and selection produce both temporal and spatial patterns of change. Statistical model fitting is now commonly used to estimate which kind of evolutionary process best explains patterns of change through time, using models like Brownian motion, stabilizing selection (Ornstein-Uhlenbeck), and directional selection on traits measured from stratigraphic sequences or on phylogenetic trees. But these models assume that the traits possessed by a species are homogeneous. Spatial processes such as dispersal, gene flow, and geographic range changes can produce patterns of trait evolution that do not fit the expectations of standard models, even when evolution at the local-population level is governed by drift or a typical OU model of selection. The basic properties of population level processes (variation, drift, selection, and population size) are reviewed and the relationship between their spatial and temporal dyna..., Animation files (.mov) can be opened with QuickTime or other viewers.
Mathematica files (.nb) are best opened in Mathematica from Wolfram, Inc. where they can be executed as well as insepected, but the are stored in ASCII and can be opened as text files in MS Word, Apple TextEdit, LibreOffice, or even a terminal.  PDF copies of the NB files are also provided so that a user without Mathematica can view these files with full formatting.
Comma-delimited files (.csv) can be opened with MS Excel, LibreOffice, or in text editors.  
PDF files can be opened in Adobe Acrobat reader and a small number of other applications., These data were produced by a computational agent-based model set on an island platform that was entirely exposed during lowstands with three peaks 2 m above platform height that remained exposed as isolated islands during highstands. The entire island platform was gridded into 5,000 cells (50 x 100), each of which could potentially be occupied by a local population.
Eustasy  (sea level change) was modelled as a sine wave through 2.5 cycles using the equation -5·Sin(0.005π·x – π) -4, where x is time measured in model steps (Fig. 3B). This equation causes sea-level to start 3 m below platform height (thus exposing the entire platform at the beginning of each model run), cresting at 2 m above platform height at highstands (thus inundating everything except the very peaks of the three islands) and dropping to 8 m below platform height during lowstands.
An evolving species was modelled through space and time using a metapopulation concept. At the beginning of each run, a single founder popu..., # Data from: Spatial processes and evolutionary models: a critical review

## Description of the data and file structure

### S1 Multiple adaptive peak model

Fig. 2C shows random trait evolution in a three-peak OU model. This animation shows how aa similar run unfolds.

**Included files:**

* S1_MultipeakAnimation.mov Animation in QuickTime format.

### S2 Mathematica code for the computational model

The computational model in this paper was run in Mathematica (Wolfram, 2018) with the aid of the Phylogenetics for Mathematica 5.1 package (Polly, 2018) and the Quantitative Paleontology for Mathematica 5.0 package (Polly, 2016). This code creates the island platform and performs a single model run.

**Included files:**

* Polly2018SpatialProcessesCodeForDriftOnAnIsland.nb An executable Wolfram Mathematica notebook.
* Polly2018SpatialProcessesCodeForDriftOnAnIsland.pdf A readable PDF copy of the Wolfram Mathematica notebook.

### S3 Raw output from computational model runs

The fo...