The systematic bioturbation of single particles (such as foraminifera)
within deep-sea sediment archives leads to the apparent smoothing of any
temporal signal as recorded by the downcore, discrete-depth mean signal. This
smoothing is the result of the systematic mixing of particles from a wide
range of depositional ages into the same discrete-depth interval. Previous
sediment models that simulate bioturbation have specifically produced an
output in the form of a downcore, discrete-depth mean signal. However,
palaeoceanographers analysing the distribution of single foraminifera
specimens from sediment core intervals would be assisted by a model that
specifically evaluates the effect of bioturbation upon single specimens.
Taking advantage of advances in computer memory, the single-specimen
SEdiment AccuMUlation Simulator (SEAMUS) was created for MATLAB and Octave,
allowing for the simulation of large arrays of single specimens. This model
allows researchers to analyse the post-bioturbation age heterogeneity of
single specimens contained within discrete-depth sediment core intervals
and how this heterogeneity is influenced by changes in sediment accumulation
rate (SAR), bioturbation depth (BD) and species abundance. The simulation
also assigns a realistic
Deep-sea sediment archives provide valuable insight into past changes in
ocean circulation and global climate. The most often studied carrier vessels
of the climate signal are the calcite tests of foraminifera. The tests of
these organisms incorporate isotopes and trace elements of the ambient water
at the time of calcification before sinking to the seafloor sediment
archive after death. Each discrete-depth interval of a sediment core
(typically 1 cm core slices) retrieved from the sea floor can contain many
thousands of specimens. Owing to technical constraints, researchers have
typically had to combine many tens or hundreds of single tests into a single
sample for successful analysis using mass spectrometry. Furthermore,
post-depositional sediment mixing (e.g. bioturbation; Berger and Heath,
1968) of deep-sea sediment means that foraminifera specimens of vastly
differing ages can be mixed into the same discrete-depth interval. The main
consequence of this mixing is that a downcore, discrete-depth multi-specimen
reconstruction of a specific climate proxy will appear to be strongly
smoothed out (on the order of multiple centuries or millennia) when compared
to the original temporal signal (Pisias, 1983; Schiffelbein, 1984; Bard et
al., 1987). Moreover, machine analysis of multi-specimen samples will only
report the mean value and machine error, thus hiding the true distribution
of values within the sample. Advances in mass spectrometry eventually
allowed the analysis of single specimens (Killingley et al., 1981) and,
since single specimens capture a single year or season of the climate signal,
researchers can in principle study the full distribution of isotope or trace
element values obtained within various discrete depths of sediment cores,
thereby making inferences regarding variability in climate, habitat or
specimen morphology for various specific time periods during the Earth's
history (Spero and Williams, 1990; Tang and Stott, 1993; Billups and Spero,
1996; Ganssen et al., 2011; Wit et al., 2013; Ford et al., 2015; Metcalfe et
al., 2015; Ford and Ravelo, 2019; Metcalfe et al., 2019b). However, the
accuracy with which the aforementioned studies can quantify time-specific
variation for a particular climate period, habitat or morphological variable
is strongly dependent upon the constraint of the age range of the specimens
contained within a given discrete-depth interval. The aforementioned studies
still rely upon the age–depth method to assign an age range to all specimens
contained within a discrete-depth interval, and previous models of single-specimen analysis in sediment cores do not include bioturbation (Thirumalai
et al., 2013; Fraass and Lowery, 2017). Such an approach can be problematic
if, to give but one example, an assumed Holocene-age 1 cm slice of sediment
core were to also contain a significant number of Late Glacial specimens,
which could lead to a spurious interpretation of Holocene climate
variability. Ultimately, this problem can be circumvented through the
application of paired analysis of both radiocarbon (
Quantifying the distribution of specimen ages within discrete-depth sediment
intervals is also important for
Here, we present the
The most commonly used mathematical model of bioturbation in deep-sea sediments is the so-called Berger–Heath bioturbation model, which assumes a uniform, instantaneous (on geological timescales) mixing of the bioturbation depth (BD), the uppermost portion of a sediment archive where oxygen availability allows for the active bioturbation of sediments (Berger and Heath, 1968; Berger and Johnson, 1978; Berger and Killingley, 1982). Observations of uniform mean age in the uppermost intervals of sediment archives do indeed support this mixing model (Peng et al., 1979; Boudreau, 1998), and the BD itself has been shown to be related to the organic carbon flux at the seafloor (Trauth et al., 1997). Researchers wishing to carry out transient bioturbation simulations with dynamic input parameters have incorporated the Berger–Heath mathematical model into their computer models, most notably the FORTRAN77 model TURBO (Trauth, 1998), its updated MATLAB version TURBO2 (Trauth, 2013) and the more recent R model Sedproxy (Dolman and Laepple, 2018). In the case of TURBO2, the user inputs a number of idealised, non-bioturbated stratigraphical levels with assigned age, depth, carrier signal and abundance. Subsequently, TURBO2 outputs the bioturbated carrier signal and abundance values corresponding to the inputted stratigraphic levels. Consequently, TURBO2 is of most interest for researchers who would like to understand the perturbation of the mean downcore signal. Sedproxy allows the user to input a climate data in the time domain, along with sediment core variables (such as SAR and BD), after which mathematical computations are used to produce the equivalent bioturbated climate data also in the time domain, whereby single-specimen distributions can also be quasi-inferred.
SEAMUS can be described as a stochastic model, in contrast to the
probabilistic models TURBO2 and Sedproxy. The stochastic approach offers a
number of advantages for the single-foraminifera applications for which
SEAMUS has been developed. Firstly, the stochastic approach allows for a
relatively straightforward execution of transient runs with temporally
dynamic time series inputs for SAR, species
abundance, BD,
The SEAMUS simulation uses an iterative approach that actively simulates the
sedimentation process of single specimens on a per time step basis, whereby
input data in the time domain are converted into the core depth domain. For
each time step, a number of new specimens are added to the top of the
simulated core, with bioturbation subsequently being carried out. SEAMUS
uses the sedimentation and species abundance variables inputted into the time
domain (SAR in the form of an age–depth model, BD vs. time, species abundance
vs. time) to simulate a number of new single specimens per time step. Each of
these specimens are assigned an age,
The SEAMUS simulation is broken down into two main functions that the user
can call. The first function
The
After the creation of all new single specimens within the synthetic core, a
per time step bioturbation simulation of the depth array is carried out.
Specifically, for each time step the depth values corresponding to all
simulated specimens within the time-step-specific active BD are each assigned
a new depth value by way of uniform random sampling of the BD interval. In this
way, uniform mixing of specimens within the BD is simulated following
the established understanding of bioturbation. The per time step bioturbation
simulation is carried out in
Subsequently, all specimen depth values corresponding to the active BD are
assigned new depth values by uniform random sampling of the active BD
itself.
It is recommended that users initiate the
The
Within
The
Users are free to use any input data they please, so long as it abides by the specified requirements as listed in the function documentation. This freedom can allow users to carry out abstract modelling experiments to increase our understanding of the relationship between input parameters, the resulting downcore single-specimen vales and trends in downcore discrete-depth means. Alternatively, users can try to forward-model an actual sediment core record in order to investigate for the possible presence of bioturbation or abundance artefacts within their sediment core record. An existing age–depth model of a sediment core could be used as the dynamic age–depth input for the SEAMUS simulation, although users must be aware that age–depth models may themselves contain artefacts caused by the interaction between bioturbation and abundance. Data regarding downcore abundance estimates could be used as abundance estimates, but similarly, users should be aware that observed downcore abundance in the core depth domain is not the same as original abundance in the time domain. Users could, therefore, experiment in using multiple temporal abundance and bioturbation depth combinations as simulation input and rerunning the simulation with different temporal abundance and bioturbation depth combinations until such time that generated abundance data in depth are similar to the observed abundance in depth. Input climate data for simulations could be based on experimental (fictional) scenarios, geological records or generated from isotope-enabled climate models (Roche, 2013) coupled to, for example, a foraminifera ecology model such as FORAMCLIM (Lombard et al., 2011) or FAME (Roche et al., 2018; Metcalfe et al., 2019a) to produce a fully parameterised “climate-to-sediment-core” model workflow.
In order to evaluate the performance of the SEAMUS model, it is compared
here to the output of the established TURBO2 bioturbation model (Trauth,
2013), which was also authored in the MATLAB environment. The most notable
difference between SEAMUS and TURBO2 is that the latter outputs data in the
form of the perturbation of the mean downcore signal, whereas SEAMUS takes
advantage of recent increases in available computer memory to store and
output a very large array of single elements (foraminifera specimens). The
two models can be compared, therefore, by comparing the mean downcore output
from TURBO2 with the SEAMUS downcore mean value derived from discrete-depth
single-specimen populations. To achieve this comparison, the NGRIP
Approximate run times and memory use in MATLAB and Octave in the
case of a 70 kyr simulation run with 10-year iterations and sediment archive
capacity of 10
Where possible, the processing of arrays for simulation time steps has been
vectorised (i.e. not processed within an iterative loop), in order to
maximise processing speed. For example, the per time step assignment of
single-specimen arrays corresponding to ages and carrier signals all occurs
within fully vectorised code. However, the bioturbation simulation (i.e. the
bioturbation of the assigned depth values) is not vectorised and is carried
out within a single-thread iterative loop, due to each iteration of the
bioturbation simulation being dependent upon the results of the previous
iteration. In order to optimise the processing time on 64-bit computers, all
arrays are stored as 64-bit. Should the user wish to save memory, it is
possible to select the
The SEAMUS model was developed in MATLAB 2017b and has been tested as
compatible with Octave 5.1.0. The
As outlined in the introduction, advances in stable isotope mass
spectrometry have allowed for routine single-specimen analysis, which has
led to increased interest in using geochemical analysis of single-specimen populations
from discrete depths as a potentially powerful tool with which to
reconstruct past changes in climate variability. Such an application
tool, however, still relies upon median downcore age by assigning an age
estimate to all single specimens from a single depth. Climate
variability or seasonality interpretations are clouded, therefore, when single
specimens from a wide range of ages are mixed into the same depth,
especially if the interpretation relies upon detecting extreme climate
events in the form of single-specimen outliers. Using the previously
described (Sect. 3.1; Fig. 1b) SEAMUS simulation, it is possible to
construct a probability heatmap and 95.45 % intervals for the simulated single-specimen
As outlined earlier, it is possible to assign
Example of using output from a SEAMUS simulation to estimate
When picking discrete-depth samples from discrete-depth specimen
populations, palaeoceanographers randomly pick whole specimens to produce a
downcore mean signal. The
Estimating noise induced by subsample size during the picking
process. Based on the SEAMUS simulation in Fig. 1b, six sample size
scenarios are considered:
Estimating downcore age–depth noise induced by absolute species
abundance in three scenarios all involving a constant SAR of 10 cm kyr
Investigating the effect of temporal changes in a species'
abundance upon its discrete-depth age–depth signal in the case of a
simulated sediment core with a constant SAR of 10 cm kyr
The interaction between total specimen abundance and bioturbation creates
downcore noise in the sedimentary record. In Fig. 5, the downcore,
discrete-depth median age increase per centimetre for three SEAMUS
simulations, all with an idealised constant SAR of 10 cm kyr
In the previous sections, scenarios involving constant specimen abundance
were explored. SEAMUS is specifically designed with the ability to process
multiple temporally dynamic inputs. In Fig. 6, the effect of temporally
dynamic species abundance for a theorised Species A is studied, once
again using a scenario with a constant SAR of 10 cm kyr
Similarly, the 95.45 % discrete-depth age range for Species A is much more
constrained in the case of depth intervals located close to the abundance
peaks (Fig. 6d) but less representative of the median age for the total
sediment (all specimens), with Species A being biased towards ages that are too young (Fig. 6e). This bias is an interesting finding, seeing as it has long been
assumed that pooled specimen samples used for dating (e.g.
Deep-sea sediment archives are subject to systematic bioturbation, which can
complicate palaeoclimate reconstructions sourced from sediment cores.
Complications can include artefacts and/or spurious offsets in
The latest release version of the SEAMUS model and accompanying interactive
tutorial (for both MATLAB and Octave) can be downloaded from the Zenodo
public repository (
The author declares that there is no conflict of interest.
Thanks to Laboratoire d'Océanologie et de
Géosciences for kindly hosting me as a guest researcher at
Université du Littoral Côte d'Opal. Brett Metcalfe is thanked for
various discussions about the state-of-the-art of single-specimen
foraminifera analysis (see also the resources at
This research has been supported by the Swedish Research Council (Vetenskapsrådet; grant no. 2018-04992).
This paper was edited by Paul Halloran and reviewed by two anonymous referees.