DOI: 10.5061/dryad.99pj691
title: Data from: Spatial processes and evolutionary models: a critical review

description: 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 dynamics is
 discussed. Typical evolutionary models used in palaeontology incorporate
 the temporal component of these dynamics, but not the spatial. Range
 expansions and contractions introduce rate variability into drift
 processes, range expansion under a drift model can drive directional
 change in trait evolution, and spatial selection gradients can create
 spatial variation in traits that can produce long-term directional trends
 and punctuation events depending on the balance between selection
 strength, gene flow, extirpation probability, and model of speciation.
 Using computational modelling that spatial processes can create
 evolutionary outcomes that depart from basic population-level notions from
 these standard macroevolutionary models.
description: Animation files (.mov) can be opened with QuickTime or other
 viewers. Mathematica files (.nb) are best opened
 in <em>Mathematica </em>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.
description: 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 population was
 randomly placed on the platform with a local population size (N) of 10, a
 trait value of 0, a phenotypic variance (P) of 0.002, and a heritability
 (h2) of 0.5. Recalling that the rate of genetic drift is h2·P/N, drift in
 local populations (demes) was modelled as a random change drawn from a
 normal distribution with a mean of zero and a variance of 0.001. The
 heritability value was chosen realistic for morphological traits, but the
 other two values were arbitrarily chosen (see discussion below about
 consequences of higher or lower rates of drift). At each model step each
 local population: (1) reproduced a new generation in its own cell,
 undergoing a drift event at the same time; (2) had a chance of expanding
 its range by giving rise to a new local population in any or all of the
 adjacent cells (P = 0.8 for each cell); and becoming locally extinct (P =
 0.2). Each new population, like its parent, had N=10, P=0.2, h2=0.5, and a
 trait mean equal to the parent’s after a new drift event. If a population
 expanded into an already occupied cell, the two populations are merged
 through reproduction by averaging their phenotypes and resetting N=10. The
 averaging of traits in cohabiting populations creates gene flow since a
 phenotype in one area can spread via dispersal and reproduction to
 another. If the cell was covered by water the probability of extirpation
 rose to 1.0.  The geographic range of the species
 expands when populations move into empty cells and contracts when
 populations are extirpated. Sea-level thus changes the geographic range
 and the number of extant local populations. At lowstands the species tends
 to grow to approximately 5,000 local populations that cover the entire
 platform, and at highstands it contracts to as few as 12 populations
 subdivided between the three isolated islands.  The
 computational model was run in Mathematica (Wolfram Research, 2018) with
 the aid of the Phylogenetics for Mathematica 5.1 package (Polly, 2018a)
 and the Quantitative Paleontology for Mathematica 5.0 package (Polly,
 2016). Code for the model and full outputs of all nine model runs can be
 found in associated data S2 of Polly (2019).  The raw output is available
 in this archive. Models were run on Indiana University’s Karst
 high-throughput computer cluster.  A full description
 of this data set can be found in Polly (2019). Polly,
 P.D. 2016. Quantitative Paleontology for Mathematica. Version 5.0.
 Department of Earth and Atmospheric Sciences, Indiana University:
 Bloomington, Indiana. https://github.com/pdpolly/Quantitative-Paleontology-for-Mathematica  Polly, P.D. 2018a. Phylogenetics for Mathematica. Version 5.0. Department of Earth and Atmospheric Sciences, Indiana University: Bloomington, Indiana. https://github.com/pdpolly/Phylogenetics-for-Mathematica  Polly, P. D. 2019. Spatial processes and evolutionary models: a critical review. Palaeontology, 62: 175-195. (10.1111/pala.12410) 
description: # 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 folders in this section contain the raw output from nine
 computational model runs. **Included files for each run:** * metadata.csv
 Title, date, and starting parameters for the run. * summary.csv
 Comma-delimited file with the species-level mean and variance for each of
 the 1,000 steps of the model run. * timeNN.csv (x1000) Comma-delimited
 files, one for each step in the computational model, containing a 50 x 100
 table of the trait value for the local population inhabiting each grid
 cell of the island platform. Unoccupied cells are empty. NN in the file
 name is the model step (1-1000). ### S4 Results from model runs The
 folders in this section contain the analytical results from the nine
 computational model runs. **Included files:** * RunNTitle.mov (x9)
 Animations in QuickTime .mov format showing the spatial distribution of
 traits during each model run. N in the nine file names is the number of
 the run and Title in the file name is the formal title of that run based
 on the date it started. * EvolutionaryModelFittingResults.pdf A PDF file
 showing the evolutionary model fitting results for all nine computational
 model runs. ### S5 Example data This CSV file contains the molar tooth
 data used for model fitting in Fig. 5. See See Polly (1997) for a full
 description of the taxa, the measurements, and their stratigraphic
 placement. ### Included files: * S5_Polly2018ExampleData.csv Data in
 comma-delimited (CSV) format. ## Code/Software The code used to generate
 the data in this package is included in this repository. It was written
 for *Mathematica*, which is normally run through a "notebook"
 (nb) interface that doubles as execution control and an archival document
 similar to a word processor file. The .nb file can be opened in a text
 editor and parsed, but the text is filled with *Mathematica* formatting
 tags like "Cell" and "RowBox" as well as image data
 that is in machine-readable format that are unrelated to the computational
 code itself. Users who do not have access to *Mathematica* can refer to
 the PDF copy of the notebook to see the code in a more readable format, as
 well as the graphics and comment lines that explain its implementation.