Identification of the mode of evolution in incomplete carbonate successions

Abstract

Background: The fossil record provides the unique opportunity to observe evolution over millions of years, but is known to be incomplete. While incompleteness varies spatially and is hard to estimate for empirical sections, computer simulations of geological processes can be used to examine the effects of the incompleteness in silico. We combine simulations of different modes of evolution (stasis, (un)biased random walks) with deposition of carbonate platforms strata to examine how well the mode of evolution can be recovered from fossil time series, and how test results vary between different positions in the carbonate platform and multiple stratigraphic architectures generated by different sea level curves.

Results: Stratigraphic architecture and position along an onshore-offshore gradient has only a small influence on the mode of evolution recovered by statistical tests. For simulations of random walks, support for the correct mode decreases with time series length. Visual examination of trait evolution in lineages shows that rather than stratigraphic incompleteness, maximum hiatus duration determines how much fossil time series differ from the original evolutionary process. Gradual directional evolution is more susceptible to stratigraphic effects, turning it into punctuated evolution. In contrast, stasis remains unaffected.

Conclusions: • Fossil time series favor the recognition of both stasis and complex, punctuated modes of evolution. • Not stratigraphic incompleteness, but the presence of rare, prolonged gaps has the largest effect on trait evolution. This suggests that incomplete sections with regular hiatus frequency and durations can potentially preserve evolutionary history without major biases. Understanding external controls on stratigraphic architectures such as sea level fluctuations is crucial for distinguishing between stratigraphic effects and genuine evolutionary process.

Keywords: Carbonate platform; Fossil record; Mode of evolution; Paleobiology; Paleontology; Stratigraphy; Time series; Trait evolution.

Fig. 1

Study design for testing the mode of evolution in the stratigraphic domain. Computationally, first sampling positions are determined, then the age-depth model is used to determine the times that correspond to these positions. Last, the trait evolution at said times are simulated. The simulated mean trait values are the values observable at the sampled stratigraphic positions

Fig. 2

The outcome of simulating carbonate platforms in the stratigraphic domain. A Scenario A: deposition based on a fictional sea-level curve. B Scenario B: deposition based on the sea-level curve from Miller et al. [69] for the last 2.58 Myr. Graphs represent the position in the middle of the simulated grid along the strike

Fig. 3

Simulated carbonate platforms in the time domain. A-C Scenario A. D-F Scenario B. (A, C Computers & Geosciences, Modeling for Environmental Change) Chronostratigraphic (Wheeler) diagrams. B, E Sea level curves used as input for the simulation. C, F Facies volumes. Graphs represent the position in the middle of the simulated grid along the strike

Fig. 4

Stratigraphic completeness and distribution of hiatus durations along the onshore-offshore gradient in scenario A (left) and B (right). Maximum hiatus duration in scenario B is four times lower than in scenario A, while completeness is comparable

Fig. 5

Spatial variability of the preservation of evolution in scenario A. A Age-depth models at varying distances from shore (B) three simulations of Brownian drift in the time domain (C), (D), (E), (F), (G) preservation of the lineages from (B) in the stratigraphic domain at 2 km, 6 km, 8 km, 10 km, and 12 km from shore in platform A. The same evolutionary history (B) is preserved differently dependent on where it is observed (C to G)

Fig. 6

Differential preservation of different modes of evolution at the same location. First row: preservation of three lineages evolving according to the stasis (A), Brownian motion (B), and Brownian drift (C) model 6 km offshore in scenario A. Second row: The corresponding true evolutionary history in the time domain. The change in traits observable in stratophenetic series over a gap depends on the directionality of evolution and gap duration – Stasis is unaffected by the gaps, while the directional Brownian drift displays jumps in phenotype over long gaps in the stratigraphic record

Fig. 7

Effects of completeness vs. hiatus duration. Brownian drift in the time domain (A), 2 km offshore in scenario A (B), and 6 km offshore in scenario B (C). In these sections, stratigraphic completeness differs by only 2%, but preservation of the lineages differs drastically due to the presence of few, but long hiatuses in scenario A generated by prolonged intervals of low sea level

Fig. 8

AICc weights of modes of evolution in the time domain under simulations of (A) stasis; (B) Brownian motion; (C) Brownian drift as a function of time series length. The sampled time interval is 2 Ma long (corresponding to the duration of scenario A), and is sampled with increasing frequency to reflect increasing sampling efforts. Abbreviations for the tested modes are: GRW - general random walk, Stasis – stasis, URW – undirected random walk. Boxplot shows median and interquartile range (IQR) as hinges. Upper/lower whiskers are at most 1.5 IQR from the hinge, outliers are not shown

Fig. 9

AICc weights of different modes of evolution in the stratigraphic domain in scenario A (first row, A-C) and for time series of equal length, but without stratigraphic biases (second row, D-F) under simulated stasis (first column), Brownian motion (second column), and Brownian drift (third column). The highlighted boxes are the correct test result for the simulated mode of evolution. Abbreviations for the tested modes are: GRW - general random walk, Stasis – stasis, URW – undirected random walk. Boxplot shows median and interquartile range (IQR) as hinges. Upper/lower whiskers are at most 1.5 IQR from the hinge, outliers are not shown

Fig. 10

AICc weights of different modes of evolution in the stratigraphic domain in scenario B (first row, A-C) and for time series of equal length, but without stratigraphic biases (second row, D-F) under simulated stasis (first column), Brownian motion (second column), and Brownian drift (third column) at different positions in the platform. The highlighted boxes are the correct test result for the simulated mode of evolution. Abbreviations for the tested modes are: GRW - general random walk, Stasis – stasis, URW – undirected random walk. Boxplot shows median and interquartile range (IQR) as hinges. Upper/lower whiskers are at most 1.5 IQR from the hinge, outliers are not shown