Philippa Kaur

Monitoring sites and speciesThe monitoring survey was conducted at five sites in Fukushima Prefecture (sites 1–4 and A1) and at one site in Ibaraki Prefecture (site 5), Japan (Fig. 1). Sites 1, 2, and A1 are located in Kawauchi Village, site 3 in Otama Village, site 4 in Tadami Town, and site 5 in Ishioka City. Monitoring at sites 1–5 was started in 2011 or 2012, and site A1 was additionally monitored since 2017. The tree species, age, mean diameter at breast height, initial deposition density of 137Cs, and sampling year of each sample at each site are listed in Table 1. The dominant tree species in the contaminated area, namely, Japanese cedar (Cryptomeria japonica [L.f.] D.Don), Japanese cypress (Chamaecyparis obtusa [Siebold et Zucc.] Endl.), konara oak (Quercus serrata Murray), and Japanese red pine (Pinus densiflora Siebold et Zucc.) were selected for monitoring. Japanese chestnut (Castanea crenata Siebold et Zucc.) was supplementally added in 2017. The cedar, cypress, and pine are evergreen coniferous species, and the oak and chestnut are deciduous broad-leaved species. Sites 1 and 3 each have three plots, and each plot contains a different monitoring species. Site A1 has one plot containing two different monitoring species, and the remaining sites each have one plot with one monitoring species, giving ten plots in total.Figure 1Locations of the monitoring sites and initial deposition densities of 137Cs (decay-corrected to July 2, 2011) following the Fukushima nuclear accident in Fukushima and Ibaraki Prefectures. Open circles indicate the monitoring sites and the cross mark indicates the Fukushima Dai-ichi Nuclear Power Plant. Data on the deposition density were provided by MEXT19,20 and refined by Kato et al.21. The map was created using R (version 4.1.0)22 with ggplot2 (version 3.3.5)23 and sf (version 1.0–0)24 packages.Full size imageTable 1 Description of the sampled trees and monitoring sites.Full size tableSample collection and preparationBulk sampling of bark and wood disks was conducted by felling three trees per year at all sites during 2011–20168,25 and at sites 3–5 and A1 during 2017–2020. Partial sampling from six trees per year was conducted at sites 1 and 2 during 2017–2020 (from seven trees at site 2 in 2017) to sustain the monitoring trees. All the samples were obtained from the stems around breast height. During the partial sampling, bark pieces sized approximately 3 cm × 3 cm (axial length × tangential length) were collected from four directions of the tree stem using a chisel, and 12-mm-diameter wood cores were collected from two directions of the tree stem using an automatic increment borer (Smartborer, Seiwa Works, Tsukuba, Japan) equipped with a borer bit (10–101-1046, Haglöf Sweden, Långsele, Sweden). Such partial sampling increases the observational errors in the bark and wood 137Cs concentrations in individual trees26. To mitigate this error and maintain an accurate mean value of the 137Cs concentration, we increased the number of sampled trees from three to six. The sampling was conducted mainly in July–September of each year; the exceptions were site-5 samples in 2011 and 2012, which were collected irregularly during January–February of the following year. The collected bark pieces were separated into outer and inner barks, and the wood disks and cores were split into sapwood and heartwood. The outer and inner bark samples during 2012–2016 were obtained by partial sampling of barks sized approximately 10 cm × 10 cm from 2–3 directions on 2–3 trees per year.The bulk samples of bark, sapwood, and heartwood were air-dried and then chipped into flakes using a cutting mill with a 6-mm mesh sieve (UPC-140, HORAI, Higashiosaka, Japan). The pieces of the outer and inner bark were chipped into approximately 5 mm × 5 mm pieces using pruning shears, and the cores of the sapwood and heartwood were chipped into semicircles of thickness 1–2 mm. Each sample was packed into a container for radioactivity measurements and its mass was measured after oven-drying at 75 °C for at least 48 h. Multiplying this mass by the conversion factor (0.98 for bark and 0.99 for wood)8 yielded the dry mass at 105 °C.Radioactivity measurementsThe radioactivity of 137Cs in the samples was determined by γ-ray spectrometry with a high-purity Ge semiconductor detector (GEM20, GEM40, or GWL-120, ORTEC, Oak Ridge, TN). For measurements, the bulk and partial samples were placed into Marinelli containers (2.0 L or 0.7 L) and cylindrical containers (100 mL or 5 mL), respectively. The peak efficiencies of the Marinelli containers, the 100-mL container, and the 5-mL container were calibrated using standard sources of MX033MR, MX033U8PP (Japan Radioisotope Association, Tokyo, Japan), and EG-ML (Eckert & Ziegler Isotope Products, Valencia, CA), respectively. For the measurement of the 5-mL container, a well-type Ge detector (GWL-120) was used under the empirical assumption that the difference in γ-ray self-absorption between the standard source and the samples is negligible27. The measurement was continued until the counting error became less than 5% (higher counting errors were allowed for small or weakly radioactive samples). The activity concentration of 137Cs in the bark (whole) collected by partial sampling was calculated as the mass-weighted mean of the concentrations in the outer and inner barks; meanwhile, the concentration in the wood (whole) was calculated as the cross-sectional-area-weighted mean of sapwood and heartwood concentrations. The activity concentrations were decay-corrected to September 1, 2020, to exclude the decrease due to the radioactive decay.Trend analysesThe yearly representative values (true states) of 137Cs activity concentration in each stem part in each plot were estimated using a DLM, a state-space model in which the noise follows a normal distribution and the relationship between variables is linear. One basic DLM is the local linear trend model defined by the following equations:$$Y_{t} = mu _{t} + varepsilon _{t} ,quad quad quad varepsilon _{t} sim Normal left( {0,sigma _{varepsilon }^{2} } right)$$
(1)
$$mu_{t} = mu_{t – 1} + beta_{t – 1} + eta_{t} ,quad quad quad eta_{t} sim Normal left( {0,sigma_{eta }^{2} } right)$$
(2)
$$beta_{t} = beta_{t – 1} + zeta_{t} ,quad quad quad zeta_{t} sim Normal left( {0,sigma_{zeta }^{2} } right)$$
(3)
where Yt, μt, and βt are the observation values, level (true state), and slope, respectively, and εt, ηt, and ζt denote their corresponding noises. The subscript t is the time index. The noises εt, ηt, and ζt follow normal distributions with a mean of 0 and variances of ({sigma }_{varepsilon }^{2}), ({sigma }_{eta }^{2}), and ({sigma }_{zeta }^{2}), respectively. To detect relatively long-term trends, we employed the smooth local linear trend model28 (also called the smooth trend model, integrated random walk model, or second-order trend model), which is obtained by considering that μt and βt are driven by the same noise. The trend changes are assumed to be smoother in this model than in the local linear trend model28,29. Combining Eqs. (2) and (3), μt in the smooth local linear trend model is finally obtained as$$mu_{t} = 2mu_{t – 1} – mu_{t – 2} + eta_{t} ,quad quad quad eta_{t} sim Normal left( {0,sigma_{eta }^{2} } right)$$
(4)
The parameters μt, ({sigma }_{eta }^{2}), and ({sigma }_{varepsilon }^{2}) of each stem part in each plot were determined by Bayesian estimation with a Markov chain Monte Carlo (MCMC) method. The Bayesian estimation was performed in R (version 4.1.0)22 with the rstan package (version 2.21.2)30. Uninformative prior distributions were used for μ1, μ2, ({sigma }_{eta }^{2}), and ({sigma }_{varepsilon }^{2}). The log-transformed values of the 137Cs activity concentration (decay-corrected to September 1, 2020) were given as Yt (the observed values of multiple individuals in each year were passed via the segment function of Stan). MCMC sampling was conducted for four chains of 50,000 iterations (the first 25,000 were discarded as warmup), obtaining 100,000 MCMC samples for each parameter. The MCMC was judged to have converged when the maximum value of Rhat was less than 1.05 and the divergent transitions after warmup were fewer than 1,000 (i.e., less than 1% of the MCMC sample size). On the datasets of the outer and inner barks from site-3 oaks and all stem parts from site-A1 pines and chestnuts, the MCMC converged poorly owing to the small number of monitoring years. Thus, the temporal trends in these datasets were not analyzed (the observational data at site A1 are shown in Supplementary Fig. S1 and Table S1).To detect decadal trends rather than yearly variations, we determined the temporal trends in the true state (μ) by setting 2–4 delimiting years and examining whether μ varied significantly from one delimiting year to the next. As the delimiting years, we selected the initial and final years of monitoring and the years in which the median µ was highest (µ-max year) and lowest (µ-min year). When the µ-max year and/or the µ-min year coincided with the initial year and/or final year of monitoring, the number of delimiting years reduced from four to two or three. The trend in µ between two delimiting years was determined to be increasing and decreasing when the 95% credible interval of µ2nd delimiting year − µ1st delimiting year (obtained from the MCMC samples) was higher and lower than zero, respectively. A flat trend (no significant variation) was detected when the 95% credible interval included zero. If the 3rd and 4th delimiting years existed, the trends between the 2nd and 3rd delimiting years and between the 3rd and 4th delimiting years were determined in the same manner.The 137Cs CRs of outer bark/inner bark, heartwood/sapwood, and inner bark/sapwood were also subjected to the above trend analyses. On datasets with less than five years of monitoring, the MCMC did not converge so the trend analysis was not attempted. More

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Constant contacts modelWe assume the affected population is composed of two risk-groups, a fraction p of the population is composed of risk-takers (RT) and the remaining fraction (1-p) are risk-evaders (RE). We differentiate the RT and RE subpopulations by assuming the RE population face a reduced likelihood of infection due to adopting precautionary behaviors. On the other hand, we assume RT do not follow public health recommendations, thus facing a higher risk of infection, relative to the RE population. Political or ideological reasons, economic stress, the lack of reasonable alternatives, epidemic politicization or the lack of trust in public health authorities are some of the documented factors that potentially lead the population to risk the dangers of COVID-19 infection44, 45.Previous mathematical models consider complex within-host disease dynamics46 or the impact of exogenous factors on the COVID-19 transmission dynamics47. In this study, we focus on incorporating individual heterogeneous adaptive behavioral responses, based on group-specific infection risk perceptions. Our model of disease progression assumes that individuals in each behavioral group may show the following health status: Susceptible (S), infectious Exposed (E), Infectious symptomatic (I), infectious Asymptomatic (A), and Recovered (R). We consider a pre-symptomatic infectious health status (E), following evidence suggesting that exposed individuals exhibit a period of viral shedding38, 48,49,50,51. RT susceptible individuals ((S_1)) can get infected by making contacts with either: symptomatic ones (I) with a baseline per-contact likelihood of disease transmission (beta), exposed individuals ((E_1) and (E_2)) with reduced per-contact likelihood of infection (rho beta) , or asymptomatic individuals ((A_1) and (A_2)) with reduced per-contact likelihood of infection (alpha beta). Similarly RE susceptible individuals ((S_2)) may get infected by making contacts with symptomatic, exposed or asymptomatic individuals at respective likelihoods, (epsilon beta), (rho epsilon beta), and (alpha epsilon beta), where (0 More

Sample collection and hydrographySampling was conducted aboard the University of Victoria’s MSV John Strickland either weekly, biweekly or monthly between 11 March 2010 and 15 November 2017 in Saanich Inlet at 48.59°N, 123.50°W (Fig. 1). To standardize measurements and due to biological significance, seawater was collected from the euphotic zone. Sampling depths corresponded to approximately 100, 50, 15, and 1% of the photosynthetically active radiation (PAR) at the surface (Io). These “light” depths were either determined using a CTD-mounted PAR sensor or a Secchi disk. CTD profiles were performed prior to each seawater cast to measure depth, temperature and conductivity of the water column, and PAR, fluorescence, and dissolved oxygen (when available).Seawater from each light depth was collected using Niskin or GO-FLO bottles on either a rosette sampler or an oceanographic wire. When possible, individual samples were collected directly from the Niskin or GO-FLO bottles. When time was not sufficient to allow direct sampling, bulk samples of seawater from each depth were collected into acid-washed polyethylene carboys, kept cold in the dark, and homogenized before sub-sampling for the individual measurements.Dissolved nutrientsFor the measurements of nitrite (NO2−), nitrate and nitrite (NO3− + NO2−), phosphate (PO43−) and Si(OH)4, seawater samples from each light depth were syringe-filtered through a combusted 0.7 µm (nominal porosity) glass fibre filter into acid-washed 30-mL polypropylene bottles and immediately frozen. All nutrient samples were stored at −20 °C until analysis. Concentrations of NO2−, NO3− + NO2−, PO43−, and Si(OH)4 were determined using an Astoria Nutrient Autoanalyzer (Astoria-Pacific, OR, USA) following the methodology of Barwell-Clarke and Whitney22. During 2014 and 2015, samples for the measurement of Si(OH)4 were collected separately from those for the other nutrients, filtered with a 0.6 µm polycarbonate membrane filter and stored at 4 °C. During this period, Si(OH)4 concentrations were determined manually using the molybdate blue colorimetric methodology23. Replicate (2 or 3) nutrient samples were taken at each depth; average data are presented in the published dataset and the figures (Fig. 2).Fig. 2Dissolved macronutrient concentrations in the euphotic zone of Saanich Inlet from March 11, 2010 to November 15, 2017. Left panels show depth-integrated concentrations (black bars on top) and time-series profiles (filled contour/scatter plots on bottom) for (A) nitrate plus nitrite (NO3− + NO2−), (B) phosphate (PO43−) and (C) silicic acid (Si(OH)4). In the time-series profiles, 2012–2013 data are not interpolated due to single-depth sampling. Grey shaded regions in top panels indicate the phytoplankton growing seasons considered for this study (March 1st – October 30th). Right panels show monthly-averaged depth profiles for the entire 8-year period, illustrating euphotic zone seasonality for each nutrient. The color scale bars on the far right apply to both the time-series vertical profiles and the 8-year seasonal plots. Sampling depths are indicated by round symbols. The year labels are positioned under the tick marks corresponding to January.Full size imageSuspended particulate matterTotal chlorophyll-aChlorophyll-a (Chl-a) was used as a proxy for phytoplankton biomass (Fig. 3A). For total Chl-a analysis, seawater samples (0.25–1 L) were gently vacuum filtered onto 0.7 µm (nominal porosity) glass fiber filters, which were then stored at −20 °C until analysis. Chl-a concentrations were determined using the acetone extraction and acidification method24,25. Acidification of samples decreased the likelihood of overestimation of Chl-a concentrations due to the presence of chlorophyll degradation products26. Filters were submerged in 10 mL of 90% acetone, sonicated for 10 minutes in an ice bath, and left to extract at −20 °C for 22 h. Following the extraction period, samples were allowed to equilibrate to room temperature (~2 h). Fluorescence of the acetone solution containing the extracted Chl-a was measured before and after acidification with 1.2 N hydrochloric acid using a Turner 10-AU fluorometer. The final concentrations of total Chl-a were calculated from measurements made before (Fo) and after (Fa) acidification using Eq. (1)25. The coefficient (τ) of Eq. (1), adapted from Strickland and Parsons25, was derived from a calibration of the Turner 10-AU fluorometer with known pure chlorophyll standards (Table 2).$${rm{C}}{rm{h}}{rm{l}} mbox{-} {rm{a}}(mu g,{L}^{-1})=frac{tau }{tau -1}ast ({rm{F}}{rm{o}}-{rm{F}}{rm{a}})ast 0.814ast left(frac{{rm{V}}{rm{o}}{rm{l}}.{rm{A}}{rm{c}}{rm{e}}{rm{t}}{rm{o}}{rm{n}}{rm{e}},{rm{e}}{rm{x}}{rm{t}}{rm{r}}{rm{a}}{rm{c}}{rm{t}}{rm{e}}{rm{d}}}{{rm{V}}{rm{o}}{rm{l}}.{rm{S}}{rm{e}}{rm{a}}{rm{w}}{rm{a}}{rm{t}}{rm{e}}{rm{r}},{rm{f}}{rm{i}}{rm{l}}{rm{t}}{rm{e}}{rm{r}}{rm{e}}{rm{d}}}right)$$
(1)
Fig. 3Biological particulate concentrations in the euphotic zone of Saanich Inlet from March 11, 2010 – November 15, 2017. Left panels show time-series profiles (filled contour/scatter plots) of (A) total chlorophyll-a (Total Chl-a), (B) particulate carbon (PC), (C) particulate nitrogen (PN), and (D) particulate biogenic silica (bSiO2). The 2012–2013 data are not interpolated due to single-depth sampling. In A, the bar plot in the top panel shows percent contribution of different size fractions to total Chl-a. In (B–D), black bars in top panels show depth-integrated concentrations. Grey shaded regions in bar plots indicate phytoplankton growing seasons considered for this study (March 1st – October 30th). Right panels show monthly-averaged depth profiles for the entire 8-year period, illustrating euphotic zone seasonality for each particulate. The color scale bars on the far right apply to both the time-series vertical profiles and the 8-year seasonal plots. Sampling depths are indicated by round symbols. The year labels are positioned under the tick marks corresponding to January.Full size imageSize fractionated chlorophyll-aTo determine the percent contributions of “pico” (0.7–2 µm), “small nano” (2–5 µm), “large nano” (5–20 µm) and “micro” ( >20 µm) phytoplankton to total Chl-a, seawater samples (0.25–1 L) separate from those used for total Chl-a) were consecutively filtered through 20, 5 and 2 µm polycarbonate membrane filters and 0.7 µm (nominal porosity) glass fiber filters. Between 2013 and 2017, the “pico” and “small nano” size classes were collected as one fraction (0.7–5 µm). Analysis of Chl-a concentrations for each size fraction followed the same procedure outlined for total Chl-a.Particulate carbon and nitrogenParticulate C and N measurements were obtained from seawater samples incubated for carbon (ρC) and nitrate uptake (ρNO3) rates (see section on “Uptake rates of carbon and nitrate” for methodology) (Fig. 3B,C). PC and PN measurements presented in this dataset were taken at the end of ρC and ρNO3 incubations; however, original (‘ambient’) values can be back calculated by subtracting the amount of C and N taken up during the incubation period from the final PC and PN values. The differences between after-incubation PC and PN data and back-calculated ambient values were not significantly different than the measurement error.Particulate biogenic silicaParticulate biogenic silica was used as a proxy for siliceous phytoplankton biomass (Fig. 3D). Seawater samples (0.5–1 L) from each depth were gently vacuum filtered through 0.6 µm polycarbonate membrane filters. Filters were folded and placed in polypropylene centrifuge tubes, dried for 48 h at 60 °C, and then stored in a desiccator at room temperature until analysis. Filters were digested with 4 mL of 0.2 M NaOH for 30–45 min in a water bath at 95 °C27. After digestion, samples were neutralized with 0.1 N HCl and cooled rapidly in an ice bath. Samples were centrifuged to separate out the undissolved lithogenic silica, and colorimetric analysis was performed on the supernatant. The transmittance of the samples, standards, and reverse-order reagent blanks were read at 820 nm using a Beckman DU 530 ultraviolet-visible (UV/Vis) spectrophotometer27,28.Uptake rates of carbon and nitrateSeawater samples (~0.5–1 L) were gently collected into clear polycarbonate bottles. One additional sample was collected from the 100% light depth, into a dark polycarbonate bottle, which did not allow light penetration. After the addition of the isotopic tracers (see below), bottles were placed into an acrylic incubator with constant seawater flow to maintain surface seawater temperature. Three acrylic tubes wrapped in colored and neutral density photo-film (to obtain 50, 15, and 1% of surface PAR) were used to incubate sample bottles under the same in-situ light conditions from which samples were collected. Samples from the 100% light level were placed inside the same acrylic incubator, but outside of the film-covered tubes. A LI-COR® LI-190 Quantum sensor was installed next to the incubator and continuously recorded incoming PAR for the entire incubation period. During sampling in 2010 and 2011, all experiments were performed using a shipboard incubator. For sampling from 2012 onwards, all experiments were done using an incubator on land (University of Victoria Aquatic Facility), which was connected to a seawater system maintained at local surface seawater temperature (approximately 9–12 °C depending on the time of year).Rates of C (ρC) and NO3 (ρNO3) uptake were determined using a stable isotope tracer-technique29,30 (Fig. 4). A single seawater sample from each light depth received a dual spike, with NaH13CO3 (99% 13C purity, Cambridge Isotope Laboratories) for the determination of ρC and Na15NO3 (98 + % 15N purity, Cambridge Isotopes Laboratories) for the determination of ρNO3. Isotope additions were made at approximately 10% of ambient dissolved inorganic carbon (DIC) and NO3− concentrations.Fig. 4Carbon and nitrate uptake rates in the euphotic zone of Saanich Inlet from March 11, 2010 – November 15, 2017. Left panels show depth-integrated rates (black-bars on top) and time-series profiles (filled contour/scatter plots below) of (A) carbon (ρC) and (B) nitrate (ρNO3) uptake rates. In the time-series profiles, 2012–2013 data are not interpolated due to single-depth sampling. Grey shaded regions in depth-integrated plots indicate phytoplankton growing seasons for this study (March 1st – October 30th). Right panels show monthly-averaged depth profiles for the entire 8-year period, illustrating euphotic zone seasonality for carbon and nitrate uptake. The color scale bars on the far right apply to both the total time-series vertical profiles and the 8-year seasonal plots. Sampling depths are indicated by round symbols. The year labels are positioned under the tick marks corresponding to January.Full size imageSpiked seawater samples were incubated for 24 h, except from 2010 to 2013 when the incubation period was 4 to 6 hr. After incubation, the entire sample was gently vacuum filtered onto a combusted 0.7 µm (nominal porosity) glass fibre filter. Filters were dried for 48 h at 60 °C and kept in a desiccator at room temperature until analysis. Filters were packed into pellets and sent to the Stable Isotope Facility at the University of California (UC) Davis for analysis of 13C and 15N enrichment, and total C and N content by continuous flow isotope ratio mass spectrometry and elemental analysis, respectively. For these measurements, UC Davis uses either an Elementar Vario EL Cube or Micro Cube elemental analyzer (Elementar Analysensysteme GmbH, Hanau, Germany) interfaced to either a PDZ Europa 20–20 isotope ratio mass spectrometer (Sercon Ltd., Cheshire, UK) or an Isoprime VisION IRMS (Elementar UK Ltd, Cheadle, UK).Carbon and NO3− uptake rates were calculated using Eq. 3 of Hama et al.29, and Eq. 3 and 6 of Dugdale and Wilkerson30, respectively.For samples incubated for less than 24 h, the daily C or NO3− uptake rates (ρX) were calculated using a PAR extrapolation method shown in Eq. (2):$$rho X(mu mol,{L}^{-1}da{y}^{-1})=left(rho X(mu mol,{L}^{-1}h{r}^{-1})divleft(frac{PAR,during,incubation}{Total,Daily,PAR}right)right)ast 24$$
(2)
Additionally, to account for NO3− uptake occurring under no light, ρNO3− was measured in dark bottles and this rate was added to the ρNO3− of each sample incubated for less than 24 h. The ρNO3− DARK was calculated following Eq. (3):$$rho N{O}_{3}DARK(mu mol,{L}^{-1}da{y}^{-1})=left(rho N{O}_{3}DARK(mu mol,{L}^{-1}h{r}^{-1})divleft(frac{Total,Daily,PAR-PAR,during,incubation}{Total,Daily,PAR}right)right)ast 24$$
(3)
PAR data used in Eqs. (2) and (3) came from the LI-COR® LI-190 Quantum sensor that was mounted beside the incubator. The seawater DIC value for each sample was calculated using a regression equation relating water density to DIC for Saanich Inlet31. Ambient NO3− concentrations were measured as described above. More

Virtual hydrostatic model parametersVarious morphological characteristics were held constant in order to isolate and manipulate the variable of conch shape. A CT-scanned Nautilus pompilius conch was essentially morphed into ammonoid-like conch shapes, populating the Westermann morphospace22 while holding constant septal morphology, septal spacing, and shell/septal thicknesses (Fig. 9). Furthermore, body chamber proportions were determined by iteratively computing soft body volumes that yield Nautilus-like chamber liquid (~ 12% of the phragmocone volume retained)67,68. Septal spacing was measured as the angle from the ventral attachment of the current and previous septa, and the spiraling axis of the conch. Because septal spacing differs in early ontogeny (Fig. S11), only measurements from the 7th to 33rd (terminal) septum were considered. The average angle of 23.46° ± 3.32° (standard deviation) was rounded to 23° and held constant throughout the ontogeny of the hydrostatic models.Figure 9Hydrostatic models of theoretical planispiral cephalopods. These models were constructed by morphing a Nautilus pompilius conch into ammonoid shapes (see “Methods”): (a) oxycone, (b) serpenticone, (c) sphaerocone, and (d) morphospace center. The centers of buoyancy and mass are denoted by the tips of the blue (upper) and red (lower) cones. Prime symbols (′) refer to transparent, transverse views of each respective conch shape. (e) Westermann morphospace22 showing relative positions of these conch shapes. All models were rendered in MeshLab76.Full size imageShell and septal thicknesses were measured with digital calipers from a physical specimen of Nautilus pompilius (Table S13). These measurements were recorded as a ratio of inner whorl height (measured from the ventral point on the current whorl to the ventral point on the previous whorl). These ratios were used in the theoretical models to define shell and septum thicknesses (3.1% of inner whorl height for shell thickness and 2.1% of inner whorl height for septal thickness; Table S13).Hydrostatic model constructionThe near-endmember models were constructed from representative ammonoid specimens (Sphenodiscus lobatus and S. lenticularis—oxycone; Dactylioceras commune—serpenticone; Goniatites crenistria—sphaerocone). Lateral and transverse views were measured from figured specimens for the oxycone (Fig. 5 of Kennedy et al.69), serpenticone (Fig. 2 of Kutygin and Knyazev70), and sphaerocone (Figs. 17 and 20 of Korn and Ebbighausen71). These models were constructed with array algorithms similar to earlier hydrostatic models9,35,72, which were used in a piecewise manner to account for allometric changes in coiling throughout ontogeny (Table S14). These arrays replicated the adult whorl section backwards and translated, rotated, and scaled each successive one. These whorl sections were bridged together to create a single tessellated surface representing the outer interface of the shell. Shell thickness was defined by shrinking the original whorl section so that the thickness between the two was equal to 3.1% of the inner whorl height (Table S13), then using the same array to build the internal interface of the shell. The morphospace center was constructed from previously used conch measurements18 and averaging the whorl section shape in blender (Fig. S12). The corresponding Westermann morphospace parameters (Fig. S13) for each morphology are reported in Table S15.Virtual models of the septa were derived from the CT-scan of Nautilus pompilius (Fig. S14). A single septum was isolated from the adult portion of the phragmocone then smoothed to delete the siphuncular foramen. This septum was placed within the whorl section of each theoretical model and stretched in the lateral directions until it approximately fit. The “magnetize” tool in Meshmixer (Autodesk Inc.) was used to attach the septal margin to the new whorl section so that the Nautilus suture was transferred to the new whorl section. The septum was then smoothed to reconcile the first order curves with the new location of the septal margin. The respective septum for each theoretical model was then replicated with the same array instructions used to build the shell. Because each replicated object was rotated one degree (Table S14), 22 septa were deleted in between every two so that the septal spacing was equal to 23° (Fig. S11).For each theoretical model, the septa were unified with the model of the shell using Boolean operations in Netfabb (Autodesk Inc.). To perform hydrostatic calculations, virtual models must be created for each material of unique density. The virtual model of the shell constrains the shape of the soft body (within the body chamber) and chamber volumes (within the phragmocone). These internal interfaces were isolated from the model of the shell, then their faces inverted for proper, outward-facing orientations of their normals. A conservative soft body estimate was created, aligning with previously published reconstructions64,65,73. The profile shape of this soft body was scaled and maintained between each model. External interfaces of the shell and soft body were also isolated to create a model of the water displaced by each theoretical cephalopod. Each of these models are necessary for hydrostatic calculations (buoyancy and the distribution of organismal mass).Each hydrostatic model is stored in an online repository (Dataset S1; https://doi.org/10.5281/zenodo.5684906). The hydrostatic centers of each virtual model and their volumes and masses are listed in Tables S16 and S17.Hydrostatic calculationsEach theoretical model was scaled to have equal volume (near one kilogram; 0.982 kg–a result of arbitrarily scaling the sphaerocone model to 15 cm in conch diameter). An object is neutrally buoyant when the sum of organismal mass is equal to the mass of water displaced (the principle of Archimedes). The percentage of chamber liquid can be computed to satisfy this condition.$${Phi } = frac{{left( {frac{{{text{V}}_{{{text{wd}}}} {uprho }_{{{text{wd}}}} – {text{V}}_{{{text{sb}}}} {uprho }_{{{text{sb}}}} – {text{V}}_{{{text{sh}}}} {uprho }_{{{text{sh}}}} }}{{{text{V}}_{{{text{ct}}}} }}} right) – left( {{uprho }_{{{text{cl}}}} } right)}}{{left( {{uprho }_{{{text{cg}}}} – {uprho }_{{{text{cl}}}} } right)}}$$
(1)
where Vwd and ρwd are the volume and density of the water displaced, Vsb and ρsb are the volume and density of the soft body, Vsh and ρsh are the volume and density of the shell, ρcl is the density of cameral liquid, ρcg is the density of cameral gas, and Vct is the total volume of all chambers. A soft body density of 1.049 g/cm3 is used based on bulk density calculations of Nautilus-like tissues74, a seawater-filled mantle cavity, and thin calcitic mouthparts21. A shell density of 2.54 g/cm374, cameral liquid density of 1.025 g/cm375, and cameral gas density of 0.001 g/cm3 are adopted from recent hydrostatic studies.Other hydrostatic properties depend on the relative positions of the centers of buoyancy and mass. The center of buoyancy is equal to the center of volume of water displaced. This center and the centers of each virtual model of unique density were computed in the program MeshLab76. The individual centers for each organismal model (soft body, shell, cameral liquid and cameral gas) were used to compute the total center of mass, with an average weighted by material density:$$M = frac{{sum left( {L*m_{o} } right)}}{{sum m_{o} }}$$
(2)
where M is the total center of mass in a principal direction, L is the center of mass of a single object measured with respect to an arbitrary datum in each principal direction, and (m_{o}) is the mass of each object with unique density. Equation 2 was used in the x, y, and z directions to compute the 3D coordinate position of the center of mass. The centers of mass for the chamber contents (liquid and gas) were set equal to the center of volume of all chambers, a minor assumption considering the capillary retention of liquid around the septal margins in the living animals62.The hydrostatic stability index (St) is computed from the relative location of the centers of buoyancy (B) and mass (M), normalized by the cube root of volume (V) for a dimensionless metric that is independent of scale:$$S_{t} = frac{{ sqrt {left( {B_{x} – M_{x} } right)^{2} + left( {B_{y} – M_{y} } right)^{2} + left( {B_{z} – M_{z} } right)^{2} } }}{{sqrt[3]{V}}}$$
(3)
where the subscripts correspond to the x, y, and z components of each hydrostatic center.Apertural orientations were measured in blender after orienting each model so that the center of buoyancy was vertically aligned above the center of mass. Apertural angles of 0° correspond to a horizontally facing soft body, while angles of + 90° and − 90° correspond to upward- and downward-facing orientations, respectively.Thrust angles were measured from the hyponome location (ventral edge of the aperture) to the midpoint of the hydrostatic centers, with respect to the horizontal. Thrust angles of 0° infer idealized horizontal backward transmission of energy into movement, while thrust angles of + 90° and − 90° infer more efficient transmission of energy into downward and upward vertical movement, respectively.Biomimetic robot constructionTo isolate the variable of shell shape on swimming capabilities, only the external shape, and static orientation of each virtual hydrostatic model were used to build physical, 3D printed robots. That is, each model has artificially high hydrostatic stability (Tables S3) to nullify the effect of the thrust angle (the angle at which thrust energy passes through the hydrostatic centers and most efficiently transmits energy into movement; Table S4). Less stable morphotypes (e.g., serpenticones and sphaerocones) are more sensitive to the constraints imposed by this hydrostatic property.Space constraints inside each model were determined by first constructing a propulsion system and electronic components that operate the motor. The models use impeller-based water pumps (Figs. 1d and 10a) driven by a brushed DC motor. This system creates a partial vacuum by centrifugal acceleration, drawing water from a “mantle cavity” and expelling it out of a “hyponome”. This system was optimized by iteratively designing models in Blender77, then testing 3D-printed, stand-alone water pumps. After three iterations, a four-blade impeller and gently tapering hyponome (inner diameter at distal end = 6.7 mm) were chosen. The electronic components used to drive the motor consist of an Arduino Pro Micro microcontroller, a motor driver, and two batteries (Fig. 10). A 3.7 V battery operates the microcontroller, and a larger 7.4 V battery supplies power to the motor. Communication is achieved via infrared, allowing specification of the jet pulse duration, number of pulses, and the power level of the motor (using pulse-width modulation; PWM). Each of these electronic components fold into a compact cartridge capable of being plugged into 3D-printed models of each investigated shell shape (Figs. 2 and 10). Each model was designed with brackets to hold the electronics cartridge in place. The sphaerocone had the most severe space constraints, with low conch diameter to volume ratio. After determining the space required for the electronics (Fig. 10) this model was scaled to 15 cm, and all other models were scaled to have similar volumes (with subtle volume differences due to minor differences in soft body shape compared to the hydrostatic models).Figure 10Biomimetic cephalopod robot components. (a) Ventral view of the sphaerocone biomimetic robot (before covering the pump and mantle cavities) with assembled electronics cartridge to the right. (b) View of electronic components that fit into the cartridge. (c) Electronics cartridge placed in robot. These two halves are fit together with wax to create a water-tight seal. Each model component is denoted by letters in circles: A = Arduino microcontroller, B = microcontroller charger / voltage regulator, C = motor driver, D = infrared sensor, E = indicator LED, F = microcontroller battery (3.7 V), G = motor battery (7.4 V), H = brushed motor, I = impeller and water pump cavity, J = electronics cartridge. The colors of annotations correspond to components depicted in Figs. 1 and 2.Full size imageIn addition to having a propulsion system, biomimetic cephalopod robots must also be capable of neutral buoyancy, while assuming the proper orientation in the water. These robots, and their once-living counterparts, each have differing material densities and associated mass distributions for each component. To reconcile these differences, the total mass and total centers of mass for each model were manipulated by controlling the volume and 3D distribution of the 3D-printed PETG (polyethylene terephthalate glycol) thermoplastic. That is, the shape of this material holds each model component in place while correcting for these differences in hydrostatics. The PETG mass required for neutral buoyancy was found by subtracting the mass of every other model component from the mass of the water displaced by the model (i.e., electronics cartridge, bismuth counterweight, liquid, motor, batteries, electronic components, and self-healing rubber; Table S1). This model configuration also allows buoyancy to be fine-tuned in water, compensating for potential density differences between the virtual water and the actual water in the experimental settings. That is, each virtual model accounts for ~ 9 g of internal liquid, but the actual volume of this liquid can be adjusted in the physical robot with a syringe through a self-healing rubber valve (Table S1; Fig. 1).The 3D position of the total center of mass was manipulated by accounting for the local centers of mass of each material of unique density. Materials like the batteries, motor, and electronic components were each assigned bulk density values because they are made up of composite materials. While this is an approximation, their contributions to the total center of mass are low because they account for small fractions of the total model mass (Tables S1 and S2). These components, like all others, were digitally modeled in Blender77 and their volumes and centers of mass were computed in the program MeshLab76. A dense, bismuth counterweight was also modeled, and positioned to artificially stabilize each model (pulling the z component of the total center of mass downward, while maintaining the horizontal components). The virtual model of this counterweight was used to make a 3D-printed mold, allowing a high heat silicone mold to be casted. The bismuth counterweight was cast from this silicone mold and filed/sanded to the dimensions of its virtual counterpart. Hyponomes were oriented horizontally, to yield movement in this direction. To maintain the same static orientation as the virtual model (same x and y center of mass components), the PETG center of mass was computed with the following equation:$$D_{PETG} = frac{{Mmathop sum nolimits_{i = 1}^{n} m_{i} – mathop sum nolimits_{i = 1}^{n} (D_{i} m_{i} )}}{{left( {m_{PETG} } right)}}$$
(4)
where DPETG is the location of the PETG center of mass from an arbitrary datum in each principal direction. M is the total center of mass in a particular principal direction, mi is the mass of each model component, Di is the local center of mass of each model component in a particular principal direction and mPETG is the mass of the PETG required for a neutrally buoyant condition. See Tables S1 and S2 for a list of model components and measurements.Each model was 3D printed with an Ultimaker S5 3D printer using clear (natural) PETG in separate parts, allowing the internal components to be implanted (i.e., brushed DC motors and bismuth counterweights). Each model part was chemically welded together with 100% dichloromethane, with minor amounts of cyanoacrylate glue used to fill seams (e.g., the water pump lid; Fig. 10a). Each final model consists of the main body (housing the water pump, motor, and counterweight), and a “lid” with brackets that house the electronics cartridge (Figs. 2 and 10). The main body and lid were fused together before each experiment by placing wax (paraffin-beeswax blend) along a tongue and groove seam, heating it with a hairdryer, then vigorously squeezing each part together. Surplus wax extruded from the seam was removed and smoothed, producing a water-tight seal.Thrust calibrationEven though each model was designed to have equal mantle cavity and pump cavity volumes, they produced slightly different thrusts. These differences were likely due to variable degrees of friction between the impellers and the surrounding water pumps. To correct for these differences, the thrust produced by each model was measured with a Vernier Dual-Range Force Sensor (0.01 N resolution). Each robot was attached at the hyponome location, through a series of pulleys, and to the sensor with fishing line (Fig. S1; similar to the methods used for living cephalopods78). Force was recorded for 30-s intervals at a sample rate of 0.05 s. During this time, each model was recorded jetting with a 6-s pulse for 15 trials (Fig. S2A). Each trial had initial noise from setting up the model, then peaked randomly when the fishing line became taught, then stabilized after some period of oscillation. Only the stabilized portion of the thrust profile was used to record thrust at 100% voltage for each model (Fig. S2B). The true zero datum was also subtracted from each of these trials. The lowest thrust from each of the models was used as a baseline (serpenticone and oxycone). Each model was recorded again for 15 trials by lowering the motor voltage in increments of 5% until they yielded similar thrusts (0.3 N) to the original serpenticone and oxycone trials (Fig. S2C). The final power levels were then determined for each model and adjusted with pulse-width modulation (PWM) through the microcontroller: serpenticone (100%), oxycone (100%), sphaerocone (95%), and morphospace center (85%).The peak thrust measured for 1 kg extant Nautilus is around 2 N16. The time-averaged thrust during each pulse is around 23% of this value (0.46 N16). This computed value slightly overpredicts observed maximum velocities for this animal (33 cm/s instead of 25 cm/s), so the appropriate time-averaged thrust is probably slightly lower. The motor in the robots quickly reaches its maximum thrust (~ 0.3 N) once initiated then quickly declines after shutting off (Fig. S2). Therefore, the thrust produced by the robots can be treated as a conservative Nautilus-like jet thrust close to the behavior of escape jetting. One-second pulse and refill intervals are also on par with values reported for extant Nautilus16.Robot buoyancyEach of the models were made near neutrally buoyant by adjusting the allotted ~ 9 g of internal liquid with a syringe through a self-healing rubber valve. The single-pulse experiments were performed in an external pool (ranging ~ 23.5 to 26.5 °C). The three-pulse and maneuverability experiments were performed in an internal pool (the Crimson Lagoon at the University of Utah). This internal pool had slightly higher temperatures (~ 28 °C), yielding lower ambient water densities than the virtual water. These conditions required slightly less internal liquid (~ 2–5 g). These differences in internal liquid masses produced negligibly small shifts in mass distributions because they are very small proportions of total robot masses (Table S1).Perfect neutral buoyancy cannot be practically achieved, but this condition can be closely approached. Each of the biomimetic robots experience subtle upward or downward movements of the course of their 5–15 s long trials due to slightly positive or negative buoyancies. Because these differences in buoyancy influence the vertical component of movement, only the horizontal components are considered for discussion. However, a comparison of velocities computed from full, 3D movement (Eq. 5) and restricted 2D components (Eq. 6) reveals that these differences are minor (Figs. S7 and S8). These comparisons demonstrate that model buoyancy did not substantially influence kinematics other than gross trajectories (Figs. 4 and S9).3D motion trackingAfter adjusting buoyancy, each model was positioned underwater with a grabber tool. This tool was fitted with a bundle of fiber-optic cable (Fig. S4) attached to an infrared remote control. Arduino code (Dataset S2) was uploaded to the microcontroller in the robot allowing jet pulse duration, number of pulses, and power to be adjusted with this remote control. After an infrared pulse is received, the motor activates, and activity is indicated by a green LED that illuminates the model from the inside. This light is used to determine time-zero for each trial of motion tracking.After sending an infrared signal, the movement of each model was recorded with a submersible camera rig fitted with two waterproof cameras (Fig. 3). Each of the four models were monitored during a single, one-second jet for at least 9 trials each. Additionally, the laterally compressed morphotypes (serpenticone and oxycone) were monitored during three, one-second pulses for 10 trials each. The inflated morphotypes (sphaerocone and morphospace center) were not able to be monitored over longer distances because they had the tendency to rotate about the vertical axis, obscuring views of the tracking points. In addition to horizontal movement, turning efficiency (maneuverability about the vertical axis) was monitored by directing the cameras with a top-down view of each model. A 90° elbow attachment for the hyponome was fit to each model to investigate the ease or difficulty of rotation. Each model was designed to spin counter-clockwise when viewed from above so that the influence of the motor’s angular momentum was consistent between models.Footage was recorded with two GoPro Hero 8 Black cameras at 4K resolution and 24 (23.975) frames per second, with linear fields of view. Motion tracking was performed with the software DLTdv879 to record the pixel locations of each tracking point (Figs. 1c and S4). These coordinates were transformed into 3D coordinates in meters using the program easyWand580. The tracking points on each model were used for wand calibration because the distances between these sets of points were fixed. Standard deviations of the reproduced tracking point distances of less than 1 cm were considered suitable.The 3D position datasets allowed velocity, acceleration, rocking, to be computed for each experiment. Additionally angular displacement and angular velocity was of interest for the rotation experiments about the vertical axis. Velocity was computed under two scenarios: (1) using the 3D movement direction between each timestep (Eq. 5), and (2) only considering the horizontal movement direction between each time step (Eq. 6). The latter scenario was preferred to nullify the influences of model buoyancies, which were not perfectly neutral and caused some degree of vertical movement.$$V_{i} = frac{{sqrt {left( {x_{i} – x_{i – 1} } right)^{2} + left( {y_{i} – y_{i – 1} } right)^{2} + left( {z_{i} – z_{i – 1} } right)^{2} } }}{{left( {t_{i} – t_{i – 1} } right)}}$$
(5)
$$V_{i} = frac{{sqrt {left( {x_{i} – x_{i – 1} } right)^{2} + left( {y_{i} – y_{i – 1} } right)^{2} } }}{{left( {t_{i} – t_{i – 1} } right)}}$$
(6)
where V and t are velocity and time, and the subscripts i and i −1 refer to the current and previous time steps, respectively. Coordinate components are denoted by x, y, and z at each timestep. The averaged 3D location of both tracking points was used for each model (i.e., midpoints). Note that Eq. (5) uses the 3D form of the Theorem of Pythagoras, whereas Eq. (6) uses the 2D version. Time zero for each trial was defined as the frame where the robot was illuminated by the internal LED, indicating motor activity. Acceleration was modeled by fitting a linear equation to the datapoints during the one-second pulse interval(s) using the curve fitting toolbox in MATLAB R2020A.The artificially high hydrostatic stability of each model was designed to nullify rocking during movement. This behavior was computed for each model during the one-pulse experiments with the following equation:$$theta_{dv} = cos^{ – 1} left( {frac{{left( {z_{2} – z_{1} } right)}}{{sqrt {left( {x_{2} – x_{1} } right)^{2} + left( {y_{2} – y_{1} } right)^{2} + left( {z_{2} – z_{1} } right)^{2} } }}} right) – theta_{tp}$$
(7)
where (theta_{dv}) is the angle deviated from true vertical and (theta_{tp}) is the angle of the tracking points measured from the vertical in a static setting. The subscripts 1 and 2 of the x, y, and z coordinates refer to the anterior and posterior tracking points, respectively.Maneuverability about the vertical axis was determined by computing the angle between the horizontal components of each tracking point. The net angle from the starting angle for each trial was tabulated. Angular velocity was determined by dividing the change in angle between each frame by the frame duration (1/23.975 fps).Links to example motion tracking footage, and robotic models are deposited in an online repository60,61,63 (Dataset S2; https://doi.org/10.5281/zenodo.6180801). More

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