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Volume 138 Supplement 1

Special Issue: Cephalopods through time

Refining the interpretation of oxygen isotope variability in free-swimming organisms


Serially sampled oxygen isotope ratios (δ18O) from fossil and modern cephalopods may provide new insight into the behavior and longevity of individuals. Interpretation of these data is generally more difficult than similar data from bivalves or brachiopods because the measured δ18O from shell combines both seasonal change and depth change over the life of an individual. In this paper, a simple null model is presented combining the three fundamental controls on a measured δ18O profile in a free-swimming organism: swimming behavior, seasonal water column change, and time averaging in sampling. Model results indicate that seasonal variability in δ18O in a free-swimming organism can be interpreted in locations with strong seasonality through most of the swimming range but is complicated by swimming velocity and is sometimes best expressed by changes in δ18O variance rather than simple sinusoidal patterns. In other locations with a stable thermocline or seasonal ranges in only a small portion of the water column, no variability caused by seasonality would be expected. Furthermore, large ranges of δ18O (~ 4‰) are possible within and between individuals in settings with persistent thermoclines like the tropics, depending on the swimming depth limits and behavior of individuals. These results suggest that future interpretation of serially sampled δ18O should consider seasonal water column variation from either modern or modeling sources in addition to comparison to co-occurring benthic and planktonic organisms. Additionally, this modeling casts doubt on the promise of isotope sclerochronology alone as a growth chronometer in ammonites and other free-swimming fossil organisms and highlights the need for other methods of quantitatively determining age.


The field of sclerochronology has provided important insight into paleoclimate (Jones 1983; Schöne et al. 2011) and evolution (Ivany et al. 2000; Moss et al. 2017). Sclerochronological study involves serially sampling isotope or trace element ratios from accretionary grown skeletal parts in the context of growth banding. Commonly, the δ18O signal in bivalve mollusks is used in interpretation of seasonality caused by changing temperature and can therefore be a growth chronometer because one complete sinusoid can be equated to 1 year of growth [e.g. Moss et al. 2017; Judd et al. 2018]. This interpretation is possible in bivalves because they are effectively sessile in a small area of seafloor and are therefore can function as fixed recorders of environmental conditions. In any long-lived (1 year or more) free swimming organism, environmental conditions recorded in the geochemistry of the shell encompass variation due to movement through an environment as well as seasonal variation in those conditions. Analyses of δ18O in marine fish otoliths, for instance, are commonly interpreted as only reflecting ontogenetic habitat change across a thermal gradient and do not record seasonality (Gerringer et al. 2018; Helser et al. 2018). Lacustrine otolith δ18O, however, is sometimes interpreted to indicate seasonal temperature changes due to strong seasonal variation in lake temperature (Weidel et al. 2007).

Workers doing sclerochronology of cephalopods by interpreting δ18O variability in particular have generally either favored the influence of movement through environments (Landman et al. 1983, 1994; Rexfort and Mutterlose 2006; Lukeneder et al. 2008, 2010; Lukeneder 2015; Linzmeier et al. 2016, 2018) or seasonality (Fatherree et al. 1998; Zakharov et al. 2005, 2011; Lécuyer and Bucher 2006; Dutton et al. 2007; Ellis and Tobin 2019). Because an independent chronometer in the shell has not been identified to determine annual growth rate due to the ambiguity of surficial growth banding (Doguzhaeva 1982; Landman 1983; Bucher et al. 1996), it has been impossible to conclusively test between the two interpretations in deep time. Additionally, heretofore, no model exists to incorporate the influence of both location and seasonality on potentially recorded patterns of δ18O variability in the shells of free swimming cephalopods or free-swimming organisms more generally, and because of this, comparisons with sea surface temperature variability have commonly been done in fossils (Lécuyer and Bucher 2006; Dutton et al. 2007) and occasionally in modern material (Liu et al. 2011).

Modern oceanographic research has provided abundant data on the thermal profiles in the modern ocean [Fig. 1, Locarnini et al. 2013]. These capture temperature change with depth as well as seasonal temperature changes at each depth (Figs. 1, 2). Because cephalopod shell appears to precipitate in oxygen isotope equilibrium with seawater (Tourtelot and Rye 1969; Landman et al. 1994), the temperature data from the World Ocean Atlas can be used to predict what δ18O shell would be precipitated as an individual was passing through a depth. To predict δ18O of aragonite (δ18Oaragonite) in this paper, the temperature equation for inorganic aragonite precipitation calibrated by Kim et al. (2007) is used because it has been calibrated across a wide range of temperatures (0–40 °C). This calibration is within statistical error of the commonly used formula based on biogenic aragonite (Grossman and Ku 1986). The equation is as follows:

$$1000\ln \alpha_{{{\text{aragonite}} - {\text{water}}}} = 17.88 \pm 0.13\left( {\frac{{10^{3} }}{T}} \right) - 31.14 \pm 0.46,$$

where temperature (T) is in K. The 1000lnαaragonitewater notation is nearly equivalent to δ18Oaragonite–δ18Owater across the range of calculations done in this paper. The δ18O of ocean water changes with evaporation and precipitation at the surface as well as thermohaline circulation patterns (LeGrande and Schmidt 2006). Because this change (+ 1‰ vertical change across the top 250 m in the Tropical Atlantic) is small relative to the influence expected for temperature (4–6‰) in the depth ranges modeled here, it is currently not implemented (Fig. 1).

Fig. 1
figure 1

Data from (Locarnini et al. 2013)

Maps showing expected δ18Oaragonite range caused only by temperature between the surface and 400 m depth in the global ocean. Locations for thermocline data used in simulation are indicated by different shapes. White areas near continents are shelves where the seafloor is shallower than 400 m. a Water column structure for August, displaying near-peak northern hemisphere summer temperatures. b Water column structure for February, displaying near-minimum northern hemisphere winter temperatures. The spatially extensive influence of seasonality in the mid-Latitudes is most apparent in the North Atlantic.

Precise swimming behavior and speed of extinct cephalopods is an outstanding area of inquiry and has implications for energetics cephalopod-rich ecosystems (Naglik et al. 2015). Debate has continued around the swimming potential of ammonites in particular because soft tissue preservation is likely not favored (Clements et al. 2017). Extensive work has been done to quantify maximal swimming velocities based on shell morphologies (e.g. Chamberlain and Westermann 1976; Jacobs 1992; Chamberlain 1993; Jacobs and Chamberlain 1996; Lemanis et al. 2015), but telemetry studies of Sepia (Aitken 2001), Loligo (O’Dor et al. 2002), Illex (Nakamura 1993), and Nautilus (O’Dor et al. 1993) suggest sustained swimming velocities are far below maximal velocities and also below predicted optimal swimming velocities (O’Dor 2002). Maximum swimming velocities in many planispiral ammonites were likely to be < 10 cm/s (Jacobs 1992). Slower sustained swimming velocities are therefore more reasonable to model; however, a suite of values can be used. Furthermore, the vertical swimming velocity component is most important to consider in this model because the δ18Oaragonite is controlled by temperature that covaries with depth and is likely smaller than any other velocity in ammonites (Westermann 1996).

This paper provides a null hypothesis for oxygen isotope variability within the shells of free-swimming organisms based on swimming speed, time averaging, and thermal stratification from a variety of locations. The model presented is general and can be applied in both modern and ancient settings when coupled to global or regional climate model results. These simulations suggest that with better constraints on growth rate and potential swimming velocities, water column structure could be determined from serially sampled data of free swimming organisms.


A simple model (SeasMigratR) was constructed in three parts to simulate both the natural variability in the δ18Oaragonite of free-swimming, continuously accreting organism and the effects of time averaging due to inherent limits of necessary sample volumes. The model has been written in the R programming language (R Core Team 2014) and divided into three complimentary functions that are included as supplemental information with this publication. Simplified natural, environmentally induced δ18O variability is achieved through linear interpolation of temperatures at each meter of water depth each day across an entire year (Fig. 2) using data from the World Ocean Atlas (Locarnini et al. 2013). Calculation of δ18O at each depth is done with Eq. 1 (Kim et al. 2007) assuming δ18Owater is uniform and 0‰ (VSMOW, Vienna Standard Mean Ocean Water). Locations used for model results presented in this paper are shown in Fig. 1.

Fig. 2
figure 2

Temperature with depth at the four modeled locations from Fig. 1. Each individual gray point is a monthly average temperature at that depth in that location from (Locarnini et al. 2013). Black lines summarize average annual thermocline shape at each location. Note that the locations EastNA, WestMed, and Upwelling have large annual temperature variability in the upper 100 m of the water column. Additionally, the EastNA water column has a mid-depth temperature high during some portions of the year (left-most points in the figure)

The behavioral component is achieved through a depth-change per hour function. Although other behaviors are potentially modeled, in this paper behavior is implemented as a bound random walk where the hour-to-hour variation is approximated as a normal distribution of vertical velocities with the first standard deviation of velocity set by the velocity inputs listed in the figures. The bounds of the walk are set independently and in the cases modeled below are the surface (0 m) and 400 m water depth. The initial depth is drawn randomly from a uniform distribution between the bounds. If a walk reaches a bound, it must stay between bounds but can continue next to the bound for multiple time-steps. The maximum velocities (1 SD) approximate modern tracking of Nautilus in the wild 0.027 m/s (Carlson et al. 1984; Ward et al. 1984; O’Dor et al. 1993; Dunstan et al. 2011). Minimum velocities are below that of 0.0013 m/s, a slow jetting velocity calculated for hatchling ammonites (Lemanis et al. 2015). Velocity inputs in the model runs shown here are in meters per hour and range from 5 to 100 m/h.

The time averaging of the model has two components, one is the distance or time averaged by a single analysis, and the other is a random ‘rejection’ column created from a uniform distribution with a defined probability of rejection. This rejection flag can be thought of as randomly distributed cracks of alteration or a rejected analysis due to quality control during assessment of mass spectrometry results. This component is not used for the comparison of expected patterns in bulk isotope analyses (Figs. 3, 4, 5, 6, 7). A fixed growth rate of 35 µm/day with a time averaging of 250 µm of growth is used (Fig. 3) and approximates both the rate of growth of modern Nautilus and time averaging of bulk samples (Auclair et al. 2004; Linzmeier et al. 2016). Ammonite age at maturity is thought to range from 1 to 7 years, and growth rate likely varies through time (Bucher et al. 1996), so these fixed rates of growth based on Nautilus are only for consistency. Two more fixed time averaging of 70 µm and 800 µm of growth is used (Fig. 4) to test the sensitivity of the model to growth rate. Serially sampled bulk individuals from the published literature are compared to the 35 µm/day and the averaging of 250 µm growth (equivalent to bulk sampling) from modern locations of similar latitude (Fig. 6).

Fig. 3
figure 3

Model δ18Oaragonite results for 500 simulations of swimming at four distinct locations with three different swimming velocities with a uniform time averaging and growth rate. Solid black lines show the average trajectory for model results. Most lines are nearly horizontal. Dashed bounding lines are the surface (0 m) and deep-water (400 m) temperatures from the World Ocean Atlas (Locarnini et al. 2013) converted to δ18Oaragonite using Eq. 1. The apparent mismatch in the early part of the year from EastNA is due to the maximum temperature being near 100 m depth during part of the year (Fig. 2). Dark gray bands bound the 25th–75th percentiles of model results. Lighter gray bands bound the 5th–95th percentiles. Sinusoidal δ18O variability resolvable beyond typical instrumental precision (± 0.1 ‰ 2SD) would not be unambiguously detected in slow swimmers from many locations but could potentially be detected in fast swimmers at mid- or high-latitude locations where strong seasonal controls of temperature structure of the water column are present

Fig. 4
figure 4

Model δ18Oaragonite results for 500 simulations a fixed growth rate and swimming velocity with three time-averaging treatments for the Upwelling location. The black line is the mean value for all model runs. Dark gray band delimitation of 25th and 75th percentiles. Light gray bands are the 5th and 95th percentiles. Increased time averaging reduces the expected measured δ18Oaragonite range of these data much like increased swimming speeds (Fig. 3). This result suggests independent constraints on growth will be necessary to unambiguously interpret δ18Oaragonite in cephalopods

Fig. 5
figure 5

Model δ18Oaragonite results for 500 simulations with a fixed growth rate, time averaging, and swimming speed of 10 m/h for different depth limits at the Eastern North American location. As the depth limit shallows, the expected variability in δ18O decreases and the mean pattern is more sinusoidal

Fig. 6
figure 6

Serially sampled δ18Oaragonite for previously published ammonites overlain on predicted δ18Oaragonite variability due solely to temperature at different locations, 25 m/h swimming speed, and 7 days time averaging per analysis. Published oxygen isotope values are adjusted to set the simulated mean and measured mean to be equal and points are published point order multiplied by 8 to scale to near 1 year. Baculites compressus (Fatherree et al. 1998) is overlain on the prediction derived from modern temperatures at 51.5 N, 170.5 W. Nowakites savini (Lukeneder et al. 2010) is overlain on the prediction from 33.5 N, 170.5 W. Grantziceras affine (Zakharov et al. 2011) overlays 70.5 N, 15.5 E


Sensitivity to swimming speed and location


The modeled water column location (Fig. 1) and therefore water temperature (Fig. 2) has the strongest control on the δ18Oaragonite results of this model. Mean δ18Oaragonite is not found to change within environments across swimming velocities (< 0.1  ‰, Table 1).

Table 1 Summary of modeled δ18Oaragonite data distributions for Fig. 3 at each location (Figs. 1, 2) with different vertical swimming velocities


As swimming velocity changes from the slowest modeled value (5 m/h) to the highest (100 m/h), expected variability (summarized as 1 standard deviation, Table 1) in δ18Oaragonite decreases across all environments (Fig. 3, Table 1). The largest reduction is in the equatorial environment with a well-developed thermocline and minimal seasonal temperature change (Figs. 2, 3, Table 1). The smallest change is observed in the WestMed environment with a uniform water column temperature below 100 m (Figs. 2, 3, Table 1).


Skew of the distribution was also found to vary with swimming speed across environments with faster swimmers having a smaller magnitude of skew. Overall, the magnitude of skew is largest in the Mediterranean environment and smallest in the equatorial environment (Table 1).


The expected range of δ18Oaragonite also changes with swimming velocity but is also strongly controlled by the thermal characteristics of the water column at specific locations (Fig. 3, Table 1). Faster swimmers are generally expected to have smaller ranges in the measured δ18Oaragonite across all environments (Fig. 3, Table 1).

Sensitivity to time averaging

When the model is run to average less time per sample, the variability and range of the faster swimming model output increases across all environments (Fig. 4, Table 2). The 25 m/h model (Fig. 4) has similar characteristics to the 5 m/h model (Fig. 3, Table 1) when time averaging is decreased. Increased time averaging reduces the variability produced by the model (Fig. 4). Mean values and data skew do not change with time averaging (Table 2).

Table 2 Summary of modeled δ18Oaragonite data distributions at each time averaging step (Fig. 4) with uniform vertical swimming velocity and at the upwelling location

Sensitivity to depth limits

When the model is run keeping swimming velocity and time averaging constant but increasing the depth limits for the model, the range and variability increases and the sinusoidal character of the mean through the year decreases (Fig. 5, Table 3). Skewness of the distributions increases as the depth limit increases, and the expected range of δ18O also increases (Table 3).

Table 3 Summary of modeled δ18Oaragonite data distributions at each depth limit step (Fig. 5) with uniform vertical swimming velocity and time averaging at the Eastern North American location


Model assumptions

Four major assumptions underpin the implementation of this model and should therefore be examined in greater detail.

  1. (1)

    Growth is modeled as continuous and uniform. In living organisms, continuous, invariant growth rates are unlikely to occur. The growth rate of bivalves often varies with temperature and is fastest in a window of optimum temperature [e.g. Judd et al. 2018]. In cephalopods, statolith growth rate is influenced by both temperature and food availability (Zumholz et al. 2006; Aguiar et al. 2012). Growth in modern Nautilus macromphalus appears to be continuous across a wide range of temperatures, but daily rates vary (Linzmeier et al. 2016). Varying the amount of time averaging also indicates that faster growing individuals would have more variability than slower growing individuals with the same swimming velocity (Figs. 3, 4, Table 1). Variation in daily growth rate is unlikely to impact the model results because individual depth trajectory is random, and therefore individuals will not be at the same depth at the same time from day to day. Growth rate dramatically varying with temperature could influence these results but would likely cause reduced variability across all environments and swimming speeds.

  2. (2)

    Continuous activity is possible. It is unlikely that any individual was swimming at these sustained velocities every hour throughout a whole year; however, the random walk is modeled as a normal distribution, so the average hourly vertical swimming velocity is zero. This approach, however, leaves periods of rest at depths and different modes of depth migration to discuss. Modern cuttlefish appear to have resting periods that may indicate sleep (Frank et al. 2012). Telemetry of modern Nautilus suggests that swimming can happen at any point in a day although it is often concentrated at dawn and dusk (Ward et al. 1984; Dunstan et al. 2011). Because time averaging in this model encompasses days to weeks of growth, any resting period of less than 50% of the time would be unlikely to influence the variance structure for a bound-random walk style depth migration. Additionally, unless resting occurs at a specific depth and time and is not done opportunistically in response to external stimuli, it is unlikely to influence these results and would instead make the faster swimming simulations look more like the slower swimming.

  3. (3)

    Vertical swimming is possible. In modern Nautilus, depth change is coupled to along-bottom swimming in an environment with a steep forereef (Ward et al. 1984; Dunstan et al. 2011). If fossil groups were similarly constrained by a long-bottom swimming, both epeiric seaway and passive margin settings would greatly reduce the potential for depth change (Landman et al. 2018a). It is unknown, however, if fossil cephalopod groups were similarly constrained and vertical velocity components to many shell morphologies have been hypothesized (Westermann 1996).

  4. (4)

    Shell δ18Oaragonite is driven by temperature rather than δ18Owater change. In much of the modern ocean, temperatures vary vertically by 5 °C within the top 100 m. This condition was also potentially present to some extent for most of the Cretaceous (Huber et al. 2018). The δ18Owater of seawater varies by ~ 4‰ across the surface ocean, with most of the difference being present in the Arctic Ocean and ~ 1‰ with depth (LeGrande and Schmidt 2006). The magnitude of the δ18O gradient expected in carbonates precipitated in δ18O equilibrium with water can have up to 25% attributed to the water composition rather than temperature component of the surface water. Further development of this model can explicitly test the influence of these assumptions on the modeled δ18Oaragonite variability using more advanced oceanographic data products.

Broad patterns of variability and swimming velocity

In locations with a strong, stable thermocline (e.g. Equatorial and Upwelling examples) δ18Oaragonite variability is large (2–4‰) and continuous through the year. Variability approaches the surface-depth range in the modeled slow swimmers (Figs. 2, 3, 4). Faster swimmers, perhaps counterintuitively, would be expected to have reduced δ18Oaragonite variability across all environments given time-averaged sampling (Figs. 3, 4). This reduced variability is caused by the more uniform sampling of the water column through the time-averaged sample. Similar expansion and reduction of variance is coupled to growth rates (Figs. 3, 4). In modern Nautilus, time-averaged δ18Oaragonite measurements have little variance over the lifetimes of individuals (Landman et al. 1994; Auclair et al. 2004; Zakharov et al. 2006) even though depth migration behavior has been documented by telemetry (Carlson et al. 1984; Ward et al. 1984; Dunstan et al. 2011) and high spatial resolution δ18Oaragonite by SIMS (Linzmeier et al. 2016).

In locations with a thermal profile that becomes nearly uniform in value seasonally, clustering of δ18Oaragonite variability is expected (Fig. 3, WestMed or EastNA). Samples from these locations would be most likely to produce sinusoidal variability in bulk sampling, but not all individuals from these locations would be expected to have sinusoidal variability present because individuals may swim to different depths at different times (Helser et al. 2018; Linzmeier et al. 2018). Instead of simple sinusoidal variability, individuals are expected to have clusters of higher or lower variability δ18Oaragonite. Therefore, if interpreting years of growth, years could be identified as the distance between the middle of high variance areas of the shell rather than local minima or maxima as is commonly done in bivalves (Ivany 2012).

Reinterpretation of bulk data


Potential variation within individuals and across populations is predicted by this modeling. For some locations and swimming speeds, large ranges in δ18Oaragonite (~ 4‰) are possible (Fig. 3). Individual serially sampled ammonites may have any trajectory within this modeled range. Recent serially sampled ammonites that lived in similar water column conditions show divergent patterns of δ18O (Landman et al. 2018b; Linzmeier et al. 2018) and recent otoliths show similar patterns (Helser et al. 2018). Population-scale sampling of multiple individuals would have individual-to-individual variability approaching that range as well, assuming that sampling is random with respect to time within each shell. This would mean for instance, if Sphenodiscus, Baculites, and Discoscaphites from the Owl Creek Formation (Maastrichtian, Mississippi, USA) had similar growth rates, Sphenodiscus would have had the fastest and Discoscaphites the slowest vertical swimming speeds based on interpretation of population-level variability (Sphenodiscus 0.75‰ 1SD N = 8 and Discoscaphites 0.24‰ 1SD N = 78, Sessa et al. 2015). The skew of the distributions reported (+ 0.3 and + 0.4) was not reproduced from temperature alone but could potentially be due to freshwater influence coupled to temperature seasonality (Sessa et al. 2015). Other populations of Baculites also show similarly variable δ18Oaragonite although some are apparently coupled to methane seep ecosystems and preclude migration along the bottom and far from the seep (Landman et al. 2018b).


Considering these model results, published records of δ18Oaragonite in ammonites can likely be reinterpreted to incorporate both seasonality and local thermocline conditions (Fig. 6). To do this reinterpretation, paleolatitudes for sample collection sites of three serially sampled ammonites (Baculites compressus, Nowakites savini, and Grantziceras affine, from (Fatherree et al. 1998; Lukeneder et al. 2010; Zakharov et al. 2011), respectively) were found using Gplates (Wright et al. 2013), modern representative locations near to those latitudes were picked from the World Ocean Atlas Dataset focusing on open-ocean data with complete annual coverage (Locarnini et al. 2013). For each representative location, a single swimming velocity (25 m/h) and time averaging (7 days/analysis) were calculated. The entire measured individual datasets were  scaled to fit within the window of a single year and the measured values were adjusted to have an equal mean δ18Oaragonite to simulated data.

The modeled context provides some additional insight into the interpretation of these data. The Baculites compressus (Campanian, Upper Cretaceous; Pierre Shale, South Dakota, USA, Fatherree et al. 1998) shows a partial sinusoid with greater variance than expected from temperatures alone (Fig. 6). Because the Western Interior Seaway is thought to be a very dynamic environment with freshwater input (Dennis et al. 2013; Petersen et al. 2016; Linzmeier et al. 2018) and seasonal thermal stratification (Kump and Slingerland 1999), it is possible the representative water column does not adequately capture this variation. Small amounts of variation in δ18Owater could explain the portion of the δ18O not explained by temperature (Dennis et al. 2013; Petersen et al. 2016). The Nowakites savini (Santonian, Upper Cretaceous; Edelbachgraben, Austria, Lukeneder et al. 2010) could be interpreted as a single year combining of swimming and seasonal modulation of swimming-induced variance rather than a strict ontogenetic habitat change (Fig. 6). The Grantziceras affine (Albian, Lower Cretaceous; Matanuska River Basin, Alaska, USA, Zakharov et al. 2011) may not show any annual variability in δ18O and could just show behavior of this individual during a portion of the year (Fig. 6).


These model results also help to explain why in Nautilus, a known depth migrator, δ18O variance from bulk samples is low (Taylor and Ward 1983; Landman et al. 1994; Moriya et al. 2003; Auclair et al. 2004; Ohno et al. 2015). Comparison of the slowly precipitating septa (Westermann et al. 2004) to shell wall that grows much faster (Martin et al. 1978) has recently been interpreted as a depth bias of septal growth (Moriya 2015) or disequilibrium precipitation of septa (Ohno et al. 2015). Perhaps the time-averaging difference between samples, as modeled here, could explain this difference (Fig. 4). Higher temporal resolution sampling of the outer shell wall of Nautilus macromphalus reveals a larger amount of variability in δ18Oaragonite (Linzmeier et al. 2016) compared to traditional bulk sampling (Auclair et al. 2004). Higher spatial sampling of the septa also reveals δ18O variability that bulk analysis does not (Oba et al. 1992).

Future model development

This preliminary model simplifies both the complicated nature of coastal oceanography (Sobarzo et al. 2007; van Leeuwen et al. 2015) and potential behavioral differences between groups based on location (Ward et al. 1984; Dunstan et al. 2011). Future development will correct these simplifications to provide better quantitative constraints on the expected δ18O variability within individuals and populations of free-swimming fossil groups. Additionally, because the biological pump creates a gradient in δ13C across the depths of interest (Hain et al. 2014) incorporation of this phenomena into the model would be useful, although the contribution of respired carbon may be variable as an organism swims (McConnaughey and Gillikin 2008; Landman et al. 2018b). Application of inverse methods (e.g. Passey et al. 2005; Sakamoto et al. 2018) on these data may provide additional insight into growth rates, behaviors, and palaeoceanographic conditions including water column seasonality. Irrespective of the direction future modeling takes, it is clear that additional large stable isotope datasets from modern and fossil populations and individuals will be necessary for testing future model development.

Determining growth rates in fossil cephalopods

This modeling suggests that when attempting sclerochronological growth rate determination in fossil cephalopods, both morphological characteristics and environmental characteristics will be important for sample selection and data interpretation. In modern ocean, higher latitude locations on the Western continental margins have stronger seasonal variation throughout the water column when compared to low latitude locations (Figs. 1, 2). Additionally, locations adjacent to seasonally varying ocean currents (e.g. Gulf Stream) may have strong seasonal signals (Figs. 1, 2). The broad distribution of these characteristics that affects seasonality can be assessed with comparison to paleogeographic reconstructions (Scotese 1991; Wright et al. 2013). Ammonites that are likely slower swimmers (e.g. serpenticones) from middle latitudes may contain clusters of δ18O variance caused by seasonally variable water column rather than simple sinusoids (Fig. 3). If potentially faster swimmers (e.g. oxycones) lived in locations with strong seasonal variation throughout the water column, sinusoidal variability may be expected. Groups confined to the shallowest water due to implosion (Hewitt 2000) may also show variability (Fig. 5). Growth rate estimates using isotope sclerochronology will require serially sampling multiple individuals (Ellis and Tobin 2019) from the same location if possible (Landman et al. 2018b). These methods must also be coupled with calculations derived from chamber evacuation (Bucher et al. 1996; Lukeneder 2015) and comparison to shell internal growth banding (Barbin 2013) analyzed with robust time series analysis methods (Meyers et al. 2001; Meyers 2014). Comparison of ammonites to cooccurring obligate benthic mollusks will provide a minimum estimate for expected seasonal δ18O variation within ammonites and provide insight into the potential of swimming behavior or migrations.


Expected patterns of shell δ18O within individual free-swimming organisms such as ammonites is complicated to interpret because of the combined effects of the thermocline, swimming speeds, and growth rate (Fig. 7). Quantitative and predictive frameworks based on modern, climate model, or comparative isotope analyses are necessary to disentangle the various conditions that influence any geochemical system that varies on timescales comparable to growth rates. It is clear that δ18Oaragonite variability is expected to be higher than instrumental precision for bulk analyses across many environments and therefore individuals may show unique trajectories through ontogeny, and reproducibility between individuals is not necessarily expected (Fig. 7). Variability measured in existing datasets reinterpreted in this quantitative framework and suggests similar vertical swimming velocities or different growth rates in some instances between co-occurring ammonites. Analysis of poorly streamlined ammonites (e.g. serpenticones) from locations that are likely to have strong seasonality may provide evidence for ammonite growth rates and water column structure. Future development of this model and more extensive δ18O sampling of ammonite material may yet disentangle growth rates and swimming behavior of the ammonites, but interpretation of bulk sampling alone may still be ambiguous and therefore more high temporal resolution sampling by SIMS may be required to use δ18Oaragonite records from ammonites to understand either habitat change or growth rates.

Fig. 7
figure 7

Summary of the effects of growth rate, swimming speed, and seasonal stratification on δ18Oarg variability in free swimming organisms. Each panel has a summary kernel density plot on the right axis to illustrate the total distribution of δ18Oaragonite in each modeled field and represents the expectation for a population-level distribution where serial sampling was not done. With increasing swimming speed or faster growth rate, δ18Oarg variability is expected to decrease (right panels). Seasonal water column variability is expected to skew δ18Oarg toward more positive values with occasional low values (bottom panels)


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I would like to thank G.L. Wolfe, R. Hoffmann, S.E. Peters, J.L. Schnell, B.B. Sageman, and A.C. Denny for discussion of this project and the model. I am also indebted to Neil Landman and Alexander Lukeneder for their thoughtful reviews of this manuscript. This project was partially supported by the University of Wisconsin—Madison Department of Geoscience through teaching assistantships and by a postdoctoral fellowship through the Ubben fund at Northwestern University. The code for this model is available as a supplemental file.

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Linzmeier, B.J. Refining the interpretation of oxygen isotope variability in free-swimming organisms. Swiss J Palaeontol 138, 109–121 (2019).

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  • Modeling
  • Stable isotopes
  • Sclerochronology
  • Seasonality
  • Growth rates