Access this dataset on Dryad

Authors:

• Jesse John Parsons
• John G. L. Morris

Contact: Jesse J. Parsons, jessejparsons97@gmail.com

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Description of the data and file structure

What this dataset is

This dataset contains the trait data, phylogenetic trees, raw skull measurements, analysis
code and model outputs behind a phylogenetic comparative study of pupil shape in
721 mammal species. The study asks whether two features of a species, how vertically its
eye sockets (orbits) are oriented and how large its body is, predict whether the species
has a vertically elongated pupil, after accounting for activity period (day, night or in
between) and foraging mode (herbivore, active predator or ambush predator).

Terms used throughout, in plain language:

• Pupil shape. The shape of the constricted pupil: circular, vertical slit, vertical
  subcircular (taller than wide but not a slit) or horizontal.
• Orbit verticality. The angle, in degrees, between the plane of the eye-socket rim and
  the palate (Heesy 2005). Higher values mean a more upright eye socket.
• Diel activity. When a species is active: by day (diurnal), by night (nocturnal),
  irregularly through both (cathemeral) or at twilight (crepuscular).
• Phylogenetic analysis. Statistics that treat species as related through an
  evolutionary tree. Each model was fitted on 25 alternative published trees and the
  results were pooled.
• MCMC (Markov chain Monte Carlo). The Bayesian method used to fit the models. Results
  are summarised from long chains of random draws.
• Observed versus imputed. Orbit verticality is measured for 368 of the 721 species.
  "Observed" analyses use only those species; "imputed" analyses fill the gaps with values
  predicted from close relatives on the tree.
• Models 1 to 3. The three statistical models, defined under "Key to models and model
  terms".
• Ray tracing. A small optical simulation of a cat eye comparing how much light enters
  through vertical and round pupils.

File tree

All files are supplied in one archive, Parsons_Morris_2026_pupil_shape_data.zip, which
unzips to the folder shown below: 65 files in 7 top-level items, about 1.1 GB in total. Almost all of the size is the six
.rds files of fitted models (1.13 GB together); everything else is under 10 MB.

README.md                                     this file
Results.output/                               model outputs and tables (30 files)
├── Model1_all_pooled_results.csv
├── Model1_imputed_pooled_results.csv
├── Model1_observed_pooled_results.csv
├── Model2_all_pooled_results.csv
├── Model2_imputed_pooled_results.csv
├── Model2_observed_pooled_results.csv
├── Model3_all_pooled_results.csv
├── Model3_imputed_pooled_results.csv
├── Model3_observed_pooled_results.csv
├── pupil_summary_workbook.xlsx
├── diagnostics/                              MCMC convergence summaries (4 files)
│   ├── model1_imputed_diagnostics_summary.csv
│   ├── model1_observed_diagnostics_summary.csv
│   ├── model2_diagnostics_summary.csv
│   └── model3_diagnostics_summary.csv
├── imputation_justification/                 checks on the imputation (10 files)
│   ├── section1_phylo_signal.csv
│   ├── section2_complete_case_bias.csv
│   ├── section2_missingness.csv
│   ├── section2_missingness_vs_bodysize.csv
│   ├── section2_sample_sizes.csv
│   ├── section3_crossval_summary.csv
│   ├── section4_accuracy_by_order.csv
│   ├── section4_accuracy_by_pupil.csv
│   ├── section5_observed_vs_imputed.csv
│   └── section6_imputed_value_realism.csv
├── model1.imputed/
│   └── model1.imputed_all_results.rds        372 MB
├── model1.observed/
│   └── model1.observed_all_results.rds       110 MB
├── model2.all/
│   ├── model2.imputed_all_results.rds        287 MB
│   └── model2.observed_all_results.rds       110 MB
└── model3.all/
    ├── model3.imputed_all_results.rds        174 MB
    └── model3.observed_all_results.rds        81 MB
Supplementary_Data_Files/                     the four tables cited as electronic supplementary data (4 files)
├── Supplementary_Data_S1_missingness_by_order.csv
├── Supplementary_Data_S2_imputation_accuracy_by_order.csv
├── Supplementary_Data_S3_MCMC_convergence.csv
└── Supplementary_Data_S4_per_tree_estimates.xlsx
data/                                         inputs to all models (2 files)
├── Mammal_PupilTraits.csv                    the species trait table (721 species)
└── Upham2011_sample25_binom.nex              25 phylogenetic trees
orbit.measurements/                           raw skull landmark data (3 files)
├── Landmark_coordinates.csv
├── Landmark_coordinates_README.txt
└── Specimen_sources_and_credits.csv
ray.tracing/                                  optical simulation (10 files)
├── README_ray_tracing.txt
├── code/
│   └── Ray_Tracing_Pipeline.R
├── inputs/
│   ├── Cat_Schematic_Eye.OPT
│   ├── Chief_Rays.RAY
│   ├── Chief_Rays.xlsx
│   ├── Ray_Tracing_Main.RAY
│   ├── Ray_Tracing_Main.xlsx
│   └── Vertical_vs_Round_Pupil_Diameter.xlsx
└── outputs/
    ├── Lens_Metrics_by_Angle.csv
    └── Vertical_vs_Round_Differences.csv
scripts/                                      R code for the comparative analysis (15 files)
├── 0_trees/
│   └── sample_posterior_trees.R
├── 1_models/
│   ├── model.2.observed.and.imputed.r
│   ├── model.3.observed.and.imputed.r
│   ├── model1_imputed.R
│   └── model1_observed.R
├── 2_pooling_summaries/
│   ├── Model.summaries.r
│   └── pool_posteriors_from_combined.R
├── 3_diagnostics/
│   ├── model1_diagnostics.R
│   ├── model2_diagnostics.R
│   └── model3_diagnostics.R
├── 4_imputation_validation/
│   └── imputation_justification.R
├── 5_figures/
│   ├── MCC_Tree_colours.r
│   ├── publication_figures.R
│   └── trait_trees.R
└── 6_other/
    └── pupil_summary_script.R

Conventions used in every file

• Missing values are written NA in all CSV files.
• Species names follow the tip labels of the Upham et al. (2019) mammal phylogeny,
  written Genus_species with an underscore (column Upham_TipLabel). The landmark files
  use Genus species with a space.
• CSV files are comma-separated, UTF-8, with a single header row. Text fields that
  contain commas are enclosed in double quotes.
• File naming. Model1, Model2, Model3 identify the statistical model;
  observed and imputed identify which version of the orbit-verticality data was used;
  all means the observed and imputed results are stacked in one file. section1 to
  section6 in imputation_justification/ refer to the six sections of the script that
  produces them, not to sections of the manuscript.
• Standardised predictors. Continuous predictors were converted to z-scores (mean 0,
  standard deviation 1) within each model's dataset before fitting. Column or term names
  beginning z_ are these standardised variables. Model coefficients for them are per
  standard deviation of the predictor, not per degree or per gram.
• Scale of model coefficients. All models are categorical (logistic) MCMCglmm models
  with the residual variance fixed, so coefficients are on the latent logit (log-odds) scale and are
  large in absolute value. Their sign and whether the 95% credible interval excludes zero
  are the quantities of interest; magnitudes are not directly comparable to ordinary
  logistic-regression coefficients.

Key to models and model terms

All three models are Bayesian phylogenetic mixed models fitted with the R package
MCMCglmm (family categorical), with the phylogeny as a random effect, fitted separately
on each of the 25 trees in data/Upham2011_sample25_binom.nex.

MCMC settings: Model 1 observed, Model 2 and Model 3: 400,000 iterations, burn-in
100,000, thinning 150, giving 2,000 retained posterior draws per tree and 50,000 pooled
draws across 25 trees. Model 1 imputed: 200,000 iterations, burn-in 50,000, thinning
100, giving 1,500 draws per tree and 37,500 pooled.

Term codes that appear in the term, Parameter (raw) and Parameter columns of the
results files:

In Supplementary_Data_S3_MCMC_convergence.csv and Supplementary_Data_S4_per_tree_estimates.xlsx
the same terms are also written out in words, e.g. Vertical: Orbit verticality for
traitPupil3.Vertical:z_orbit, and Diel - Cathemeral/crepuscular for Diel3Intermediate
or Diel_WallsIntermediate.

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data/

data/Mammal_PupilTraits.csv

The species trait table used by every model and figure. One row per species, 721 rows,
20 columns. Species belong to 19 orders and 84 families. All 721 species have a pupil
shape, diel category, foraging category, body mass and diet; 368 have a measured orbit
verticality and 353 have NA.

data/Upham2011_sample25_binom.nex

A Nexus-format text file containing 25 phylogenetic trees, each with the same 5,911
extant mammal species as tips, with branch lengths in millions of years. The trees are a
random sample (R set.seed(1)) from the 10,000-tree Bayesian posterior of Upham et al.
(2019), specifically the "completed" 5,911-species, topology-constrained,
fossil-tip-dated set (their data S7, file
MamPhy_fullPosterior_BDvr_Completed_5911sp_topoCons_FBDasZhouEtAl_all10k_v2_nexus.trees).
Each tree has been pruned to the 5,911 extant species (the Anolis outgroup and fossil
tips removed) and tip labels shortened to Genus_species. The trees appear in the file in
the order in which they were sampled; "Posterior tree ID" 1 to 25 in the results files is
the position of a tree in this file. The models prune each tree to the species present in
the trait table before fitting (712 of the 721 species match a tip; 9 do not and are
dropped from phylogenetic analyses).

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orbit.measurements/

Raw three-dimensional landmark coordinates for the 174 specimens landmarked for this study,
and the provenance of every specimen. Landmarks were
placed on 3D cranial models (computed tomography (CT) scans and surface scans) in the free software 3D Slicer,
following Heesy (2005). The 3D models themselves are not included and remain subject
to their repositories' terms; every row carries enough information to retrieve the
source model.

How orbit verticality is calculated from these landmarks: the palatal plane is fitted
through Prosthion, Left_M1 and Right_M1; the orbital plane of one side is fitted
through that side's orb_superius, orb_inferius and orb_anterius. Orbit verticality is
the angle between the two planes, calculated for each orbit and averaged. Where only one
orbit could be landmarked (20 of 174 specimens, which therefore have 6 rather than 9
landmarks) the single value is used. The angle does not depend on the coordinate frame, so
no alignment or scaling of the scans was needed.

orbit.measurements/Landmark_coordinates.csv

1,505 rows (one per landmark point), 9 columns. 174 specimens of 174 species.

orbit.measurements/Specimen_sources_and_credits.csv

174 rows (one per specimen), 9 columns. Gives the source media, rights holder, re-use
terms and the credit statement requested by the data provider for every specimen in
Landmark_coordinates.csv.

orbit.measurements/Landmark_coordinates_README.txt

Plain-text file. The measurement protocol, landmark definitions and column descriptions
above are reproduced in it, together with repository citations and the permissions
statement for University of Michigan Museum of Zoology (UMMZ) specimens. All of its
content is also in this README.

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Supplementary_Data_Files/

The four tables cited in the manuscript as electronic supplementary data S1 to S4. S1 to S3 are
reformatted copies of tables in Results.output/ with the column names spelled out; the
source of each is noted. S4 is the full workbook of per-tree and pooled model estimates.

Supplementary_Data_S1_missingness_by_order.csv

How many species in each mammalian order have a measured orbit verticality. 19 rows (one
per order), 6 columns. Same content as Results.output/imputation_justification/section2_missingness.csv.

Supplementary_Data_S2_imputation_accuracy_by_order.csv

How accurately the phylogenetic imputation recovers orbit verticality, by order, from a
cross-validation in which 20% of species with measured values were withheld at random,
imputed from the rest, and compared with their true values; repeated once on each of the
25 trees. 15 rows (orders with at least one withheld species), 9 columns. Same content as
Results.output/imputation_justification/section4_accuracy_by_order.csv.

Supplementary_Data_S3_MCMC_convergence.csv

Convergence summary for every fixed-effect term of all six model fits. 62 rows, 7
columns. Same content as the four files in Results.output/diagnostics/, combined.

Supplementary_Data_S4_per_tree_estimates.xlsx

Per-tree and pooled fixed-effect estimates for all six model fits. Written by
scripts/2_pooling_summaries/Model.summaries.r, which names its output
Results.output/Supplementary_Tables.xlsx; the file is supplied here only once, under
this name.

Excel workbook, one sheet named "Supplementary Tables", 1,622 rows. Five tables are
stacked down the sheet, each introduced by a one-row title in column A that states the
model, data version, number of species and MCMC settings, followed by its own header row.
Rows whose 95% credible interval excludes zero are formatted bold blue.

Sections 1 to 4 are per-tree estimates, one row per tree per term:

Columns of sections 1 to 4:

Section 5 (rows 1567 to 1622) is the pooled estimates for all six fits, i.e. the content of
the six observed/imputed *_pooled_results.csv files, with these columns: Model,
Model type, Parameter, Parameter (raw), Pooled posterior mean, Pooled SE,
Pooled lower 95% CI, Pooled upper 95% CI, N posterior trees, % iterations positive,
% iterations negative, % iterations consistent, Direction, CI excludes zero.
These correspond one-to-one to the CSV columns described above.

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Results.output/

The nine Model*_pooled_results.csv files

Pooled fixed-effect estimates: the final results of the three models. "Pooled" means the
retained MCMC draws from all 25 per-tree fits were concatenated into one posterior sample,
so the uncertainty includes both within-tree and between-tree (phylogenetic) uncertainty.

• Model1_observed_pooled_results.csv (10 rows), Model1_imputed_pooled_results.csv (10 rows)
• Model2_observed_pooled_results.csv (7 rows), Model2_imputed_pooled_results.csv (7 rows)
• Model3_observed_pooled_results.csv (14 rows), Model3_imputed_pooled_results.csv (14 rows)
• Model1_all_pooled_results.csv (20 rows), Model2_all_pooled_results.csv (14 rows),
  Model3_all_pooled_results.csv (28 rows): the observed and imputed files for that
  model stacked one above the other, with no new information.

All nine share the same 12 columns:

pupil_summary_workbook.xlsx

Excel workbook of descriptive summaries of the trait table. Five sheets:

Diet.category is the largest of the three diet components (Herbivore,
Vertebrate faunivore or Invertebrate faunivore), or Omnivore when two components tie
for largest. Diel3 on the Summary sheet is the three-level grouping used in Model 1
(Diurnal; Intermediate = cathemeral + crepuscular; Nocturnal = strict + flexible).

diagnostics/

MCMC convergence summaries, one row per model term. These are the source of
Supplementary_Data_S3_MCMC_convergence.csv.

• model1_observed_diagnostics_summary.csv (10 rows) and
  model1_imputed_diagnostics_summary.csv (10 rows): columns term, n_trees,
  min_ESS, median_ESS, pct_stationary.
• model2_diagnostics_summary.csv (14 rows) and model3_diagnostics_summary.csv
  (28 rows): the same columns preceded by model_type (observed or imputed).

imputation_justification/

Ten tables that test whether phylogenetic imputation of orbit verticality is justified.
They are produced in six sections by one script, scripts/4_imputation_validation/imputation_justification.R.
Unless stated, "orbit" means Orbit.verticality in degrees, "all species" means the
Model 1 dataset (721 species, 368 observed) and "non-diurnal non-horizontal" means the
Model 2/3 dataset (441 species, 257 observed; 436 / 254 after matching to the tree).

section1_phylo_signal.csv (8 rows). Is orbit verticality phylogenetically
conserved, so that relatives are informative? Long format: block groups rows,
metric names the statistic, value is its value, p_value its p-value where one
exists, n the number of species used.

section2_sample_sizes.csv (2 rows). Columns dataset, n_total, n_observed,
n_missing, pct_missing: species counts and percentage with missing orbit
verticality for the two datasets.

section2_missingness.csv (19 rows). Missingness by order; identical in content to
Supplementary Data S1. Columns Order, n_total, n_observed, n_missing,
pct_missing, high_missing (TRUE if pct_missing > 60).

section2_missingness_vs_bodysize.csv (3 rows). Is missingness related to body size?

section2_complete_case_bias.csv (3 rows, metric and value). Among non-diurnal
species, the mean orbit verticality using observed species only
(nondiurnal_mean_orbit_observed_only), the mean after adding imputed values
(nondiurnal_mean_orbit_imputation_inclusive), and their difference in degrees
(complete_case_shift_deg).

section3_crossval_summary.csv (2 rows). Overall cross-validation accuracy of the
imputation: 20% of measured species withheld at random, imputed from the rest under
Brownian motion, compared with their true values; repeated once per tree (25 repeats,
different random draw each time).

section4_accuracy_by_order.csv (15 rows). Cross-validation accuracy by order;
identical in content to Supplementary Data S2. Columns order, n_withheld,
n_observed, MAE, RMSE, bias, true_range, scaled_MAE_pct, high_error
(TRUE if scaled_MAE_pct > 30). All error columns in degrees.

section4_accuracy_by_pupil.csv (4 rows). Cross-validation accuracy by pupil shape.
Columns pupil, n_withheld, MAE, R2, CCC, bias, true_range,
scaled_MAE_pct, defined as above.

section5_observed_vs_imputed.csv (7 rows). Do Model 2's conclusions change between
the observed and imputed fits? One row per term.

section6_imputed_value_realism.csv (8 rows). Are the imputed values plausible? Long
format with subset (all_species or nondiurnal) and group.

The six .rds files

model1.observed/model1.observed_all_results.rds, model1.imputed/model1.imputed_all_results.rds,
model2.all/model2.observed_all_results.rds, model2.all/model2.imputed_all_results.rds,
model3.all/model3.observed_all_results.rds, model3.all/model3.imputed_all_results.rds.

Each is an R object file, readable only in R (readRDS(), with the MCMCglmm package
installed). Each holds the 25 fitted MCMCglmm models for one model and data version, one
per tree with all retained posterior draws, plus the per-tree results table and the run
settings. They allow the results to be re-pooled or re-summarised without re-running the
models, which takes several hours each. Everything reported in the paper is also in the
CSV and xlsx files.

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ray.tracing/

A separate optical simulation. Light rays were traced through a schematic (idealised,
rotationally symmetric) model of a domestic cat eye (Vakkur & Bishop 1963) in the free optical design program
Beam4 (Stellar Software), to compare the effective light-collecting aperture of a vertical
and a round pupil of matched area at 17 incident angles (0° to 80° in 5° steps, measured
from the optical axis) and five levels of pupil constriction. The Beam4 files are plain
text and can be read in any text editor; running them requires Beam4.

Coordinate conventions in all Beam4 files and the two .xlsx ray tables: distances in
millimetres; Z is along the optical axis (positive into the eye), X horizontal
(nasal-temporal), Y vertical (superior-inferior). X0, Z0 are a ray's starting point,
U0, V0 its direction cosines in X and Y (the X and Y components of the unit vector
along the ray; the Z component W0 is left to Beam4's default), and X1, Z1, Y1 the
point where Beam4 found the ray to intersect surface 1, the anterior corneal surface.
Column definitions follow the Beam Four user guide (Stellar Software, chapters 9 and 10).

inputs/

Columns of Cat_Schematic_Eye.OPT (Beam4 headers):

code/Ray_Tracing_Pipeline.R

R script. Reads Chief_Rays.xlsx and Ray_Tracing_Main.xlsx, projects each boundary
ray's corneal intersection onto the plane perpendicular to the chief ray at that angle,
and computes for each pupil shape × constriction level × angle the effective aperture
width (span of the nasal and temporal rays), height (sum of the superior and inferior
ray offsets) and elliptical area, then compares vertical with round. Writes the two
files in outputs/.

outputs/

Lens_Metrics_by_Angle.csv (170 rows = 2 shapes × 5 levels × 17 angles, 6 columns)

Vertical_vs_Round_Differences.csv (85 rows = 5 levels × 17 angles, 11 columns)

README_ray_tracing.txt

Plain-text description of the ray-tracing folder and workflow. Its content is included
above.

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scripts/

R scripts for the comparative analysis, numbered in the order they are run. All are plain
text. Each is run from the top-level folder of this dataset, e.g.
Rscript scripts/1_models/model1_observed.R; paths inside the scripts are relative to it.

The three scripts in 5_figures/ draw the figures in the related article (Figures 1 and 2,
and electronic supplementary material figures S2 and S3). The figures themselves are
published with the article and are not included in this dataset. The scripts save them to
Results.output/figures/; create that folder before running them.

---

Sharing/Access information

Links to other publicly accessible locations of the data: this Dryad dataset is the primary
location of these data. The four files in Supplementary_Data_Files/ are also cited as
electronic supplementary material of the related article (see Related publication below).

Data derived from other sources

• Phylogeny. Upham NS, Esselstyn JA, Jetz W. 2019 Inferring the mammal tree:
  species-level sets of phylogenies for questions in ecology, evolution, and conservation.
  PLoS Biology 17, e3000494. Posterior trees from Dryad,
  https://doi.org/10.5061/dryad.tb03d03 (data S7). 25 trees are redistributed here in
  data/Upham2011_sample25_binom.nex.
• Diel activity. Cox DTC, Gardner AS, Gaston KJ. 2021 Diel niche variation in mammals
  associated with expanded trait space. Nature Communications 12, 1753. Two Apodemus
  species from the bioRxiv preprint linked in the Diel.reference column.
  Lasiorhinus latifrons: Finlayson GR, White CR, Dibben R, Shimmin GA, Taggart DA. 2010
  Activity patterns of the southern hairy-nosed wombat (Lasiorhinus latifrons)
  (Marsupialia: Vombatidae) in the South Australian Murraylands. Australian Mammalogy 32,
  39–46, https://doi.org/10.1071/AM09024.
• Diet percentages and body mass. Primarily from PHYLACINE 1.2: Faurby S, Davis M, Pedersen RØ,
  Schowanek SD, Antonelli A, Svenning J-C. 2018 PHYLACINE 1.2: the phylogenetic atlas of
  mammal macroecology. Ecology 99, 2626.
• Foraging mode (predators). Banks MS, Sprague WW, Schmoll J, Parnell JA, Love GD.
  2015 Why do animal eyes have pupils of different shapes? Science Advances 1,
  e1500391, https://doi.org/10.1126/sciadv.1500391. CarniTraits version 1.5.3: Wooster EIF et al.
  2024 Functional traits of the world's late Quaternary terrestrial mammalian predators.
  Global Ecology and Biogeography 33, e13909, https://doi.org/10.1111/geb.13909 (data at
  https://github.com/Eamonn-wooster/CarniTraits).
  Plus the species-specific sources listed in the Foraging type: link to reference and
  Full foraging reference columns.
• Pupil shape. Scored from photographs on iNaturalist (https://www.inaturalist.org)
  and CalPhotos (https://calphotos.berkeley.edu), and from the published sources linked
  in the Pupil shape: link to photograph or reference column.
• Orbit verticality, published values. Heesy CP. 2005 Function of the mammalian
  postorbital bar. Journal of Morphology 264, 363–380, https://doi.org/10.1002/jmor.10334.
  Gaillard C, MacPhee RDE, Forasiepi AM. 2023 Seeing through the eyes of the sabertooth
  Thylacosmilus atrox (Metatheria, Sparassodonta). Communications Biology 6, 257,
  https://doi.org/10.1038/s42003-023-04624-5. Source of the value for Sarcophilus harrisii.
• 3D cranial models used for the landmark data (models not redistributed):
  MorphoSource (Boyer DM, Gunnell GF, Kaufman S, McGeary TM. 2017 MorphoSource: archiving
  and sharing 3-D digital specimen data. Paleontological Society Papers 22, 157–181);
  Phenome10K (Goswami A. 2015 Phenome10K: a free online repository for 3-D scans of
  biological and palaeontological specimens, www.phenome10k.org, CC BY-NC 4.0);
  University of Michigan Deep Blue Data (two UMMZ deposits, cited by DOI in
  Specimen_sources_and_credits.csv); Sketchfab (two models, CC BY 4.0: Mammal Research
  Institute PAS, Poland, 2021, Lynx lynx skull; University of Wyoming Libraries, 2020,
  UWYMV:Mamm:5842 Vulpes velox skull). Per-specimen rights holders, terms and requested
  credit lines are in orbit.measurements/Specimen_sources_and_credits.csv. Fourteen
  specimens are University of Michigan Museum of Zoology (UMMZ) CT scans; the UMMZ Mammal
  Division confirmed that publishing these landmark coordinates is permitted under the
  UMMZ Digital Data Usage terms, and the data were provided courtesy of the UMMZ.
• Cat schematic eye for ray tracing. Vakkur GJ, Bishop PO. 1963 The schematic eye in
  the cat. Vision Research 3, 357–381, https://doi.org/10.1016/0042-6989(63)90009-9.
• Cat pupil dimensions for ray tracing. Hammond P, Mouat GSV. 1985 The relationship
  between feline pupil size and luminance. Experimental Brain Research 59, 485–490,
  https://doi.org/10.1007/BF00261338.

Related publication

Parsons JJ, Morris JGL. Orbit verticality and body size as predictors of vertical
pupils in nocturnal mammals. Submitted to Proceedings of the Royal Society B.

---

Code/Software

Software needed to open each file type

R environment

The analyses were run in R 4.4.2 (2024-10-31) on macOS. Package versions are those
installed when the outputs were produced; all are free and on CRAN.

Model fitting is slow: each model script fits 25 MCMCglmm models with 200,000 to 400,000
iterations and takes several hours on a desktop computer.

Run order to reproduce the outputs

1. (Optional) scripts/0_trees/sample_posterior_trees.R, only if regenerating
   data/Upham2011_sample25_binom.nex; requires downloading the Upham et al. (2019)
   posterior from Dryad (see Sharing/Access information).
2. scripts/1_models/ (four scripts, any order): fit the models, writing the .rds files.
3. scripts/2_pooling_summaries/pool_posteriors_from_combined.R: the pooled CSVs.
4. scripts/2_pooling_summaries/Model.summaries.r: the results workbook (Supplementary Data S4).
5. scripts/3_diagnostics/ and scripts/4_imputation_validation/: diagnostics and
   imputation checks.
6. scripts/5_figures/ and scripts/6_other/: figures (not included) and descriptive summaries.
7. Ray tracing is independent: run the .RAY files in Beam4 with Cat_Schematic_Eye.OPT
   loaded, copy the intersection coordinates into the two .xlsx input tables, then run
   ray.tracing/code/Ray_Tracing_Pipeline.R.