A novel phylogenetic comparative model reveals strong signals for early high disparity in ichthyosaurs
Abstract
Early high disparity, where clades reach maximum morphological diversity early in their history, is often observed in the fossil record. Since there are currently no suitable methods to model these Early High Disparity (EHD) processes accurately, we introduce a new phylogenetic comparative method (PCM) to address this gap by combining two evolutionary modes--Ornstein-Uhlenbeck (OU) and Early Burst (EB)--leading to an initial surge in disparity until an early maximum, driven by the EB component, after which disparity declines due to OU constraints. We tested the EHD model on ichthyosaur skull length data and found it to be the best fit in nearly all cases compared to other modes. The median time of peak disparity (TEHD) is about 231.1 million years ago, during the Triassic, roughly 12.4% into the ichthyosaur lineage. To explore how environmental and geological factors might influence peak disparity, we performed changepoint analyses on sea level, sea surface temperature, rock area, and sedimentary sequence ages. While changepoints in temperature at 237.2 Ma and sequence boundaries at 238 Ma were closest to TEHD, no significant changepoints appeared to match TEHD.
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Claude Opus 5.5 · xhigh effort · 8 Nov 2026 · from the full text of version 1 (1 Oct 2026) · CC BY 4.0
Combining Early Burst and Ornstein-Uhlenbeck processes, an Early High Disparity model best fits ichthyosaur skull length across 108 phylogenies, placing median peak disparity at 231.1 Ma.
Many fossil clades reach maximal disparity early and then decline, yet existing phylogenetic comparative models assume steadily rising or stable variance, or capture only an early burst rather than the whole rise and fall. The work provides an explicit Early High Disparity model that can be fit by maximum likelihood and tested against Brownian Motion, Ornstein-Uhlenbeck and Early Burst alternatives.
Key results
ShownThe Early High Disparity (EHD) model fit ichthyosaur skull length better than the Brownian Motion (BM), Ornstein-Uhlenbeck (OU) and Early Burst (EB) models on nearly all time-calibrated trees.
Across 108 phylogenies, EHD had the lowest AICc in 92% of cases (ΔAICc = 0) and was retained in 99% under ΔAICc ≤ 2. Mean AICc was 144.14 for EHD vs 152.40 for EB, the next-best model, a gap of 8.26 units. · Results; Early High Disparity Model Fitting
ShownUnder the fitted EHD parameters, disparity peaked early in the clade's history, giving a bottom-heavy profile with maximum disparity in the Carnian stage.
Median TEHD was 231.1 Ma (CI 230.75–232.2 Ma), about 12.4% of the way through a total tree duration of 157.39 Myr. Mean α was 0.35 and mean ρ was 0.92. Ancestral state X0 = 4.34 vs optimum θ = 7.07. The Carnian spans 237–227 Ma. · Results; Discussion; Figure legends
SuggestedNo peak-time estimate lies near the end-Triassic boundary, so that mass extinction probably did not create the preference for EHD. Some estimates instead move toward the origin of ichthyosaurs.
No TEHD estimate across the 108 trees approaches the end-Triassic boundary. Parameter combinations with stronger early expansion or stronger constraint (α, ρ) move the peak toward the Permian–Triassic boundary at 251.9 Ma. · Discussion; Figure legends
ShownSea level and marine rock area changepoints fell well after the estimated disparity peak. Sea surface temperature and sequence-boundary shifts near 237 Ma came before it, the latter by about 6 Myr, so no tested series coincided precisely with the peak.
Single changepoints: sea level 217.5 Ma, sea surface temperature ∼237.2 Ma, rock area 214 Ma, sequence boundaries ∼237 Ma (approximately 6 Myr before TEHD of 231.1 Ma). Three-changepoint models: sea level 247.3, 238.5 and 219 Ma; temperature 247, 239 and 206 Ma. · Results; Changepoint Analyses: Paleoenvironmental and…
ClaimedThe authors propose that Triassic sea-level rise enlarged nearshore ecospace and drove early disparification. They suggest later regression and warming then favoured pelagic, smaller-bodied forms, producing the decline.
The evidence is qualitative alignment only. Sea level rose from 247 Ma to 238.5 Ma, then fell to 217 Ma. The 238.5 Ma changepoint comes before TEHD and lies outside its CI (230.75–232.2 Ma). After 217 Ma sea level rose again, but disparity did not recover. · Discussion
Methods, data and reproducibility
EHD combines the Early Burst rate decay (ρ) with Ornstein-Uhlenbeck attraction (α) toward an optimum θ, which gives analytical moments and a peak time, TEHD. Models were fit by maximum likelihood with the Glinv pruning framework (PCMBase/PCMFit/PCMkappa) and ranked against BM, OU and EB by AICc. TEHD was then compared with Triassic changepoints from segmented regression.
- Time-calibrated ichthyosaur phylogenies (Hedman method) taken from a prior study · ichthyosaurs (extinct marine reptiles) · n = 108 trees, each with 108 taxa
- Ichthyosaur skull length plus total body length, orbit length and sclerotic diameter; missing skull lengths filled by phylogenetic imputation · ichthyosaurs (extinct marine reptiles) · n = over half of species lacking measured skull length · 10.5281/zenodo.22896982 (code and data deposit)
- Triassic sea-level curves, truncated to the Triassic
- Triassic sea surface temperature time series
- Triassic marine rock area estimates downloaded from Macrostrat
- Triassic sedimentary sequence ages, converted to durations by first differences
- Monte Carlo simulations of EB, OU and EHD processes, plus trait simulations from best-fit EHD parameters · n = 1000 time-series of 100 time-steps; 500 EHD trait simulations
- Methods & tools
- PCMBase (R), PCMFit (R), PCMkappa (custom R package with EB and EHD functions), Rphylopars (phylogenetic imputation), segmented (R package, changepoint regression), Macrostrat, Hedman method (tree time-calibration), AICc model selection, Monte Carlo simulation
- Data & accessions
- https://doi.org/10.5281/zenodo.22896982
- Software & environment
- R packages PCMBase, PCMFit, custom PCMkappa, Rphylopars and segmented; no package versions are stated.
- Reproducibility gaps
- No package versions or hardware are reported. The extracted text does not identify the source study for the phylogenies and skull lengths.
Limitations (6)
- Only one continuous trait (skull length) is analysed. Earlier studies used discrete craniodental matrices, and the authors caution that different traits or anatomical regions may carry different temporal disparity signals. · stated by the authors
- The sequence-age changepoint (238 Ma) falls near the disparity peak and the Carnian Pluvial Episode. More condensation and unconformities in earlier Triassic sequences could produce an apparent EHD pattern. · stated by the authors
- The study does not test how diversity dynamics and geological sampling interact with EHD inference. The authors note that changes in species richness and sampling structure could affect model support. · stated by the authors
- The authors raise, but do not test, the possibility that selective extinction of morphologically extreme taxa during the Carnian Pluvial Episode contributed to the EHD signal. · stated by the authors
- Over half of taxa lacked skull length, and these values were filled by Rphylopars imputation. No fit on measured taxa alone is reported, so the imputation's assumptions could shape which evolutionary mode wins. · noted in this summary
- No simulation study of EHD identifiability, parameter recovery or false-positive rate against BM, OU and EB is reported. Changepoint alignment is judged by proximity, not by a formal association test. · noted in this summary
Who should read:Read this if you model trait evolution in fossil clades and want a maximum-likelihood alternative to Early Burst and OU that captures an early disparity peak followed by a decline.
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