# A Devonian Fish Tale: A New Method of Body Length Estimation Suggests Much Smaller Sizes for Dunkleosteus terrelli (Placodermi: Arthrodira)

## Abstract

**:**

^{2}= 0.947, PE

_{cf}= 17.55%), and accurately predicts body size in arthrodires known from complete remains. Applying this method to Dunkleosteus terrelli results in much smaller sizes than previous studies: 3.4 m for typical adults (CMNH 5768) with the largest known individuals (CMNH 5936) reaching ~4.1 m. Arthrodires have a short, deep, and cylindrical body plan, distinctly different from either actinopterygians or elasmobranchs. Large arthrodires (Dunkleosteus, Titanichthys) were much smaller than previously thought and vertebrates likely did not reach sizes of 5 m or greater until the Carboniferous.

## 1. Introduction

#### Introducing Orbit-Opercular Length

**Figure 1.**Heads of (

**A**), an osteichthyan (Micropterus dolomieu, CMNH Teaching Collection); (

**B**), a chondrichthyan (Carcharhinus obscurus; modeled after specimen in [37]); (

**C**), a coccosteomorph arthrodire (Coccosteus cuspidatus, after [15]); and (

**D**), Dunkleosteus terrelli (CMNH 6090), showing how orbit-opercular length was measured accounting for different arrangements of the gill skeleton in different lineages. Dotted line in (

**C**,

**D**) shows how the cranio–thoracic joint in arthrodires exceeds (in

**C**) or is equivalent to (in

**D**) the level of the posterior gill margin.

**Figure 2.**Elongate-bodied (

**A**,

**C**), and compressiform (

**B**,

**D**) acanthopterygian (

**A**,

**B**) and non-acanthopterygian (

**C**,

**D**) fishes, showing how short fishes have short heads and long fishes have long heads. (

**A**), Acanthocybium solandrei (Scombridae), drawn from FSBC 6267. (

**B**), Catoprion abscondidus (Serrasalmidae), modified from Bonani Mateussi et al. [43]. (

**C**), Esox lucius (Esocidae), modified from Casselman et al. [44]. (

**D**), Argyrops spinifer (Sparidae), modified from Randall [45]. Drawings by Russell Engelman.

## 2. Materials and Methods

#### 2.1. Institutional Abbreviations

**AA.MEM.DS**, Université Cadi Ayyad, Marrakech, Morocco;

**ANSP**, Academy of Natural Sciences, Philadelphia, PA, USA;

**AMNH FF**, American Museum of Natural History fossil fish collection, New York City, NY, USA;

**CMNH**; Cleveland Museum of Natural History, Cleveland, OH, USA;

**FMNH**, the Field Museum, Chicago, IL, USA;

**FSBC**, Florida Biodiversity Collection, Florida Fish and Wildlife Research Institute, St. Petersburg, FL, USA;

**LDUCZ**, Grant Museum of Zoology, University College, London, U.K.;

**MNHM**, Musée d’Histoire Naturelle de Miguasha, Quebec, Canada;

**MZL**; Musée Cantonal de Zoologie, Lausanne, Switzerland;

**NHMUK**, the Natural History Museum, London, U.K.;

**NMS**, National Museum of Scotland, Edinburgh, UK;

**OSUM**, Ohio State University Museum of Biological Diversity, Columbus, OH, USA;

**ROM**, Royal Ontario Museum, Toronto, Ontario, Canada.

#### 2.2. Model Assumptions

- The dataset must include a wide variety of fishes, including fishes spanning the possible range of body sizes for Dunkleosteus. This is necessary to avoid errors from data extrapolation, which if not controlled for can lead to errors in body size estimation [30,35,36]. Related to this, it is important to include taxa that phylogenetically bracket the extinct taxa of interest, in order to increase confidence in the applicability of the model [48]. For arthrodires, this phylogenetic bracket would encompass extant gnathostomes (chondrichthyans, osteichthyans), lampreys (Petromyzontiformes), and other arthrodires for which complete remains are known (Figure 3). Lampreys are not the closest relative to gnathostomes among jawless fish groups (cephalaspidomorphs are closer), but were chosen here because lampreys can be measured from modern specimens and thus be measured more precisely.
- The model must accurately estimate body size in fishes regardless of phylogeny. If a model only predicts body length in one group of fishes like sharks or bony fishes but cannot be applied more broadly, it is unlikely to be accurate in arthrodires. Similarly, a measurement may strongly correlate with total length in fishes but different groups of fishes may follow different regression lines. If this is the case, an additional variable would be needed to adjust for clade-specific differences in slope and intercept. However, such a model would be almost useless for estimating body size in arthrodires, as the additional coefficients for arthrodires would be calculated based on a narrow subset of taxa spanning a limited range of sizes.
- The model must accurately estimate total length in the few arthrodire taxa known from complete remains. If a method works for extant gnathostomes (which are universally regarded as more closely related to each other than to arthrodires; [5,49]) but fails to predict length in Arthrodira, it cannot be reasonably applied to Dunkleosteus. One potential issue is that most arthrodires for which complete remains are known are either coccosteomorphs (e.g., Coccosteus, Millerosteus, Watsonosteus) or more basal arthrodire lineages (Africanaspis, Holonema). Amazichthys trinajsticae is the only exception in this regard [21]. However, given the distribution of taxa considered in this study (Figure 3), if a model accurately predicts body length in lampreys, coccosteomorphs, basal arthrodires, Amazichthys, and extant jawed fishes it can be assumed it will also accurately predict body length in Dunkleosteus terrelli and other “pachyosteomorph” arthrodires (Dunkleosteoidea and Aspinothoracidi).
- The anatomical proxy for total length must be measurable in fossils of Dunkleosteus terrelli. If a measurement is highly correlated with size but is not measurable in Dunkleosteus specimens (e.g., snout-vent length) or is based on anatomical landmarks that cannot be reliably recognized in arthrodires (e.g., prebranchial length, given the branchial region of arthrodires cannot be easily distinguished from the rest of the skull [50,51]), then it is useless for estimating the body size of D. terrelli.

#### 2.3. Data and Measurements

**Figure 4.**Reconstruction of a juvenile Dunkleosteus terrelli, showing the measurements used in this study. Abbreviations: SnL, snout length; OOL, orbit-opercular length.

#### 2.4. Statistical Analysis

^{2}values, percent error (%PE), percent standard error of the estimate (%SEE), Akaike information criterion (AIC; [106]), Bayesian Information criterion (BIC; [107]), and log likelihood (logLik). The r

^{2}value, also known as the correlation coefficient, is the traditional support statistic of choice in the ichthyological literature, but has several key statistical deficiencies that are covered by the other methods used here. Specifically, r

^{2}cannot directly determine how accurate the resulting model is at predicting new values [108,109]. The r

^{2}value is also very sensitive to the range of sizes spanned by the data. As the magnitude of sizes spanned by the data increases r

^{2}unilaterally increases, even when prediction accuracy is very low [40,109]. Thus, even models where prediction error is so high as to make the model uninformative can have an r

^{2}greater than 0.99 if data spans a wide enough range of sizes [109]. This problem is magnified in log-transformed datasets (i.e., most analyses of biological data), because the spread of the data is compressed by log-transformation and r

^{2}tends to overestimate confidence in prediction accuracy. The r

^{2}value measures the correlation between the log-transformed data, when the value of interest is how accurately the model predicts data on the original untransformed scale. Thus, %PE and %SEE, which measure how well the model predicts new data on a log-detransformed scale, were used as the primary measures of model accuracy.

#### 2.4.1. Estimating the Length of the Largest Dunkleosteus

#### 2.4.2. Body Mass of Dunkleosteus

^{2}= 0.996). Precaudal length and girth were used to create a regression model estimating the body mass of Dunkleosteus. This model takes the form of:

^{2})×length + girth×length + girth

^{2}+ girth + length + length×head length + “presence of swim bladder?” + (“is tail heterocercal” × caudal fin length)

^{2})

^{0.9267}

^{2}; [124,125]). Using these values for bone density, which were calculated based on terrestrial tetrapods, seems reasonable, given histological studies of arthrodire plates show cancellous and cortical layers similar to terrestrial tetrapods [126]. This is distinctly unlike either the pachyostotic bones of most aquatic tetrapods [127,128] or the acellular bone typical of euteleosts [129,130]. This method was used to provide a conservative estimate of by how much the body armor of Dunkleosteus would be expected to bias body mass estimates based on non-armored taxa.

## 3. Results

#### 3.1. Results of Model

#### 3.1.1. OOL in Extant Fishes

_{cf}) for the model is relatively low (17.55%). That is, on average OOL without any additional parameters will predict the body length of a given fish within +/−17.55% of the actual value (Table 1). 88% of all sampled fishes have estimated lengths within +/−33% of their actual value, whereas roughly 2/3 have their length estimated within +/−20% (Supplementary File S3: Section S5.7). Taxa outside this interval are mostly those with very extreme body shapes that are not typical for fishes (e.g., highly anguilliform taxa).

^{2}~0.8; Supplementary File S3: Section S3). In other words, the general observation that short fishes have short, deep heads and elongate fishes have elongate heads is generally true (see also [46]). However, the model shows residual variation significantly correlated with body shape (t = 287.22, p < 0.001; Supplementary File S3: Section S7.2.3). Anguilliform and macruriform fishes show the greatest underestimates of body length, elongate-bodied fishes slightly less so, fusiform fishes show residuals close to zero, and compressiform fishes show positive residuals and overestimates of body length (Supplementary File S3: Figure S7). However, these differences are only differences in intercept, not slope (Supplementary File S3: Section S7.2). Slopes of different shape categories are non-significantly different except for elongate fishes, which may be due to under-sampling of small-bodied elongate fishes.

#### 3.1.2. Outliers in the OOL Model

#### 3.1.3. Effects of Snout Length

_{cf}(14.6% versus 17.6%), AIC, and BIC compared to the OOL model without snout length (Supplementary File S3: Section S12.1). However, when applied to arthrodires of known length, this model resulted in systematically smaller lengths for arthrodires. In some cases this resulted in lower error rates, but in others including snout length resulted in systematic and sometimes substantial underestimates of actual body length (Supplementary File S3: Table S12). Examination of the data finds arthrodires have shorter snouts relative to their body size than other fish clades. This is true whether snout length is measured relative to head length (t = −7.325, p < 0.001; Supplementary File S3: Figure S12 and Section S12.5) or relative to total length (t = −3.836, p < 0.001; Supplementary File S3: Figure S12 and Section S12.5). This may be due to the fact that most bony fishes have prognathic mouthparts that extend anterior to the neurocranium (Figure 8), whereas arthrodires either have subterminal mouths (e.g., Coccosteus; Figure 8B) or mouthparts that extend to the anterior level of the neurocranium (e.g., Dunkleosteus, see Figure 1D).

#### 3.1.4. Body Size of Arthrodires

#### 3.2. Body Size of Dunkleosteus terrelli

#### 3.2.1. Length of Dunkleosteus terrelli

_{cf}= 12.40) and lowest values of AIC (−2310) and BIC (−2237). The only model that produced comparable values was considering shape as the only additional variable (%PE

_{cf}= 12.03, AIC = −2846, BIC = −2785), but this model is not favored as it has issues when predicting length in large fishes. Specifically, because the largest fishes in this study are primarily lamnids, megachasmids, or echinorhinids which are fusiform but have very short trunks and long branchial regions (Supplementary File S3: Figure S10), this results in the model considering only body shape to be biased towards smaller lengths at larger body sizes. Thus, the latter model’s inability to distinguish lamnids from other fusiform fishes makes it less ideal for estimating shape in Dunkleosteus.

#### 3.2.2. The Largest Dunkleosteus

#### 3.2.3. Weight of Dunkleosteus terrelli

^{2}= 0.992; %PE

_{cf}= 21.97). This is a much higher error than in length–weight models in other studies of fishes (e.g., ~10% PE; [161]), and much higher than the error of 1% reported by Ault and Luo [118]. However, this higher error is to be expected given this study is using an interspecific model with fishes of different body shapes, whereas most length–weight equations focus on a single taxon or a few closely related taxa of similar body shape. Another source of error is many fishes considered here had their weight estimated via standard length–weight models, which may not be sensitive to intraspecific variation in girth due to body condition. Given these limitations a model error of only 20% is rather good, especially as prediction errors for body mass in other vertebrate groups (e.g., mammals; [40,101]) are rarely below 33%. The model based on only large, pelagic fishes has a higher accuracy rate (%PE

_{cf}= 9.8) but a lower r

^{2}(0.990) due to the smaller range of body sizes in these data (see Materials and Methods).

^{3}. Assuming an average density for whole bone (1.2–1.3 g/cm

^{2}, [124,125]), this suggests the bony armor of this individual weighed ~30 kg, only 7.5% of the animal’s predicted armor-free body mass (see Supplementary File S3: Section S16.6). These results are consistent even under different methods of estimating bone density (see Supplementary File S3: Table S16). This is much less than the carapace contributes to body mass in extant armored animals, such as nine-banded armadillos (Dasypus novemcinctus, 16% body mass; [163]) or turtles (≥16.7% body mass; [164]).

## 4. Discussion

#### 4.1. Head–Body Proportions in Fishes

^{2}= 0.95, %PE

_{cf}= 17.55; Table 1) as well as the aspect ratios of the head and body (r

^{2}= 0.80–0.88; Supplementary File S3: Table S3). Although other studies have noted that head length and total length are often correlated in fishes [168], the idea that these proportions are this strongly correlated across such a wide diversity of fishes is unexpected. Knapp et al. [169] find a similar correlation between head (= neurocranium) and body fineness ratio in Scombriformes, but the present study suggests that this pattern extends to all “fishes”. The close relationship between head and trunk elongation in fishes (both in terms of total head length and OOL), used here to predict length in Dunkleosteus, occurs across such a great phylogenetic, morphological, and ecological breadth of fishes that it calls for a biological explanation. For example, one would expect a much poorer correlation between head and body proportions if a similar study was performed on tetrapods.

#### 4.2. Body Shape of Arthrodires

**Figure 11.**Reconstructions of (

**A**) Coccosteus cuspidatus (modeled after [15,200]), (

**B**) Dunkleosteus terrelli, and (

**C**) Amazichthys trinajsticae (proportions modeled after [21]), scaled to the same head length. The shorter lengths for Dunkleosteus terrelli in the present study better agree with the locations of the pelvic girdle/posterior end of the ventral armor and caudal peduncle in other arthrodires. A. trinajsticae also shows a more elongate body plan than other arthrodires (especially if scaled based on OOL rather than head length, as here). Missing elements of Amazichthys modeled after Draconichthys, Gymnotrachelus, Stenosteus, and Trachosteus. Drawings by Russell Engelman.

**Figure 12.**Silhouettes of a tuna ((

**A**), Thunnus thynnus), Dunkleosteus terrelli (juvenile) (

**B**), and carcharhinid shark ((

**C**), Carcharhinus obscurus), all scaled to ~150 kg, showing differences in body shape of actinopterygians, arthrodires, and elasmobranchs at the same body mass. Proportions of (

**A**) modeled after Rivas [203] and Russell [96]; (

**B**) from present study and Engelman [115], based on CMNH 7424 and CMNH 6090;

**C**modeled after 3.2 m individual in Garrick [37]. Note tunas are unusually wide for actinopterygians, the figured individual of C. obscurus is comparatively deep-bodied for Carcharhinus, and the length of D. terrelli might be a slight overestimate if arthrodires show ontogenetic allometry similar to actinopterygians. Thus, these three specimens understate the differences in body shape between the three major clades. Drawings by Russell Engelman.

#### 4.3. Body Size of Dunkleosteus terrelli

#### 4.4. Body Size Evolution in Paleozoic Vertebrates

## 5. Conclusions

## Supplementary Materials

**A**), Coccosteus cuspidatus (ROM VP52664, from collections.rom.on.ca); (

**B**), Watsonosteus fletti (NMS G.1995.4.2, courtesy of M. J. Newman); (

**C**), Incisoscutum ritchei (WAM 03.3.28, modified from Trinajstic et al. [273]); (

**D**), Amazichthys trinajsticae (AA.MEM.DS.8, modified from Jobbins et al. [21]). Scale = 5 cm, no scale available for

**C**. Supplementary File S7. Silhouette of a small juvenile individual of Dunkleosteus terrelli, modeled after CMNH 7424. This image is needed to rerun the R code in Supplementary File S3. Supplementary File S8. Silhouette of a late-stage juvenile of Dunkleosteus terrelli, modeled after CMNH 6090 and 7424. This image is needed to rerun the R code in Supplementary File S3. Supplementary File S9. Silhouette of an adult individual of Dunkleosteus terrelli, modeled after CMNH 5768. This image is needed to rerun the R code in Supplementary File S3.

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 5.**CMNH 5768, the largest complete individual of Dunkleosteus terrelli in oblique left lateral (

**A**) and left lateral (

**B**) view. Some of the thoracic plates are reconstructed but the skull and ventral armor are entirely real. The proportions of the reconstructed plates closely resemble other specimens of Dunkleosteus. Note (

**B**) is taken at a slightly oblique angle because a camera could not be placed in perfectly lateral view. Scale = 30 cm, but only applies to (

**B**), (

**A**) is scaleless.

**Figure 6.**Inferognathal of Dunkleosteus terrelli (CMNH 5698, reversed), showing the measurements of this bone used to estimate the length of CMNH 5936. Definitions of JM1-JM5 follow Ferrón et al. [12].

**Figure 7.**Plot of log

_{10}orbit-opercular length against log

_{10}total length in fishes. Solid and dashed blue lines represents best-fit regression line and 95% confidence intervals for all species, respectively.

**Figure 8.**X-ray of Hydrocynus forskahlii ((

**A**), CAS SU 63349; [144]) and Coccosteus cuspidatus ((

**B**), modified from [15]) scaled to the same neurocranial length, showing how arthrodires have proportionally shorter snouts than other fishes. Note how the neurocranium of the two taxa is similar in shape but the head of H. forskahlii is slightly longer due to the more prognathic mouthparts of this taxon. Scale = 3 cm.

**Figure 9.**CMNH 5936, a left inferognathal fragment pertaining to the largest currently known individual of Dunkleosteus terrelli. Scale = 10 cm.

**Figure 10.**Graph of total length versus body mass for all specimens of sharks and tunas (Thunnini) in which weight was directly recorded, compared to estimated weights for arthrodires in this study.

**Figure 13.**Reconstruction of the largest known specimen of Dunkleosteus terrelli (CMNH 5936, proportions primarily from the slightly smaller but more complete CMNH 5768), compared to one of the largest reliably measured specimens of Carcharodon carcharias (MZL 23981; [166]). A 175 cm tall human for scale (from NASA). Drawings by Russell Engelman.

**Table 1.**Regression equations and support statistics for some of the best-fitting models. All equations reported here are for models using individual specimens, not species averages. Additional statistical information, including models fitted using species averages, can be found in Supplementary File S3. Note more complex multivariate equations are listed in Supplementary File S3 due to space constraints. Abbreviations: TL, total length; OOL, orbit-opercular length; HDL, head length; SNL snout length.

Model | N | Equation | r^{2}_{adj} | AIC | BIC | %PE | CF | %PE_{cf} | %SEE |
---|---|---|---|---|---|---|---|---|---|

All species | 3169 | Ln(TL) = 0.9962 × Ln(OOL) + 1.9008 | 0.947 | −463 | −445 | 17.83 | 1.019 | 17.55 | 25.21 |

Fusiform and elongate taxa | 2660 | Ln(TL) = 0.9836 × Ln(OOL) + 1.9622 | 0.962 | −1164 | −1147 | 15.38 | 1.011 | 15.26 | 21.44 |

With shape as covariate | 3398 | See Supplementary Information | 0.974 | −2846 | −2785 | 12.10 | 1.009 | 12.03 | 17.23 |

Fusiform species only | 1741 | Ln(TL) = 0.9713 × Ln(OOL) + 1.9121 | 0.980 | −1562 | −1545 | 11.98 | 1.008 | 11.88 | 16.69 |

Including body depth as covariate | 2845 | See Supplementary Information | 0.950 | −761 | −737 | 16.26 | 1.023 | 16.17 | 23.56 |

Including snout length as covariate | 3169 | Ln(TL) = 0.7482 × Ln(OOL) − 0.2301 × Ln(SNL) + 2.124 | 0.961 | −1451 | −1426 | 14.82 | 1.018 | 14.62 | 21.21 |

Pelagic species only | 638 | Ln(TL) = 0.9677 × Ln(OOL) + 2.0373 | 0.953 | −256 | −242 | 16.65 | 1.009 | 16.56 | 21.83 |

Fusiform and elongate non-acanthopterygians | 2394 | Ln(TL) = 0.9902 × Ln(OOL) + 1.8915 | 0.960 | −687 | −670 | 16.47 | 1.017 | 16.26 | 23.3 |

Sharks only | 540 | Ln(TL) = 0.8852 × Ln(OOL) + 2.1809 | 0.962 | −544 | −531 | 11.57 | 1.012 | 11.51 | 15.69 |

With shape, allowing variable slope for Chondrichthyes | 3169 | See Supplementary Information | 0.971 | −2310 | −2237 | 12.45 | 1.015 | 12.40 | 18.27 |

Head length | 3169 | Ln(TL) = 0.9717 × Ln(HDL) + 1.5688 | 0.963 | −1579 | −1561 | 14.55 | 1.018 | 14.37 | 20.75 |

**Table 2.**Length estimates for arthrodires known from whole-body fossils using OOL from the all taxa, individual specimen equation. Selected representatives for each taxon are given in cases where more than one individual was measured for the sake of space, a complete listing of all results can be found in Supplementary File S3: Section S8. Abbreviations: PE, percent error; P.I., prediction interval. All measurements in cm.

Taxon | Specimen | Actual Length | Estimated Length | +/−PE | 95% P.I. | PE |
---|---|---|---|---|---|---|

Millerosteus minor | FMNH PF 1089 | 13.7 | 13.87 | (11.4–16.3) | (8.9–21.6) | 1.1 |

Millerosteus minor | Composite (see Methods) | 15.0 | 16.04 | (13.2–18.9) | (10.3–24.9) | 6.8 |

Africanaspis dorissa | Reconstruction in [17] | 23.0 | 24.45 | (20.2–28.7) | (15.7–38.0) | 5.9 |

Incisoscutum ritchei | Reconstruction in [55] | 30.3 | 31.62 | (26.1–37.2) | (20.4–49.1) | 4.3 |

Coccosteus cuspidatus | NMS 1893.107.27 | 29.6 | 35.10 | (28.9–41.3) | (22.6–54.5) | 15.6 |

Coccosteus cuspidatus | FMNH PF 1673 | 37.1 | 36.51 | (30.1–42.9) | (23.5–56.7) | −1.7 |

Coccosteus cuspidatus | Reconstruction in [15] | 39.4 | 43.94 | (36.2–51.7) | (28.3–68.3) | 10.3 |

Coccosteus cuspidatus | ROM VP 52664 | 37.5 | 42.52 | (35.1–50.0) | (27.4–66.1) | 11.8 |

Plourdosteus canadensis | MNHM 2-177 | 37.5 | 51.40 | (42.4–60.4) | (33.1–79.9) | 27.0 |

Dickosteus threiplandi | NMS 1987.7.118 | 43.7 | 56.13 | (46.3–66.0) | (36.1–87.2) | 22.2 |

Holonema westolii | Reconstruction in [16] | 60.6 | 51.18 | (42.2–60.2) | (32.9–79.5) | −18.5 |

Watsonosteus fletti | NMS G.1995.4.2 | 56.6 | 65.30 | (53.8–76.8) | (42.0–101.5) | 13.3 |

Amazichthys trinajsticae | AA.MEM.DS.8 | 89.7 | 78.02 | (64.3–91.7) | (50.2–121.2) | −15.0 |

**Table 3.**Length estimates of the largest complete individual of Dunkleosteus terrelli (CMNH 5768) under a variety of different models and starting assumptions. Abbreviations as in Table 2. All measurements in cm.

Individual Specimens | Species Averages | |||||
---|---|---|---|---|---|---|

Model | Estimate | +/−PE | 95% P.I. | Estimate | +/−PE | 95% P.I. |

All fishes | 352.6 | (290.7–414.5) | (226.8–548.1) | 338.9 | (278.4–399.4) | (214.0–536.7) |

Fusiform and elongate fishes | 353.8 | (299.8–407.8) | (241.7–518.0) | 343.0 | (289.9–396.1) | (229.7–512.1) |

With shape as covariate | 324.8 | (285.8–363.9) | (237.8–443.7) | 320.1 | (279.8–360.3) | (229.9–445.6) |

Fusiform taxa only | 319.7 | (281.7–357.6) | (236.1–432.8) | 313.9 | (278.6–349.3) | (234.1–421.1) |

With body depth as covariate | 335.4 | (281.1–389.6) | (221.4–508.0) | 344.1 | (283.6–404.6) | (221.8–536.6) |

Including snout length as a separate integer | 336.8 | (284.9–388.7) | (231.1–492.7) | 328.5 | (276.1–380.9) | (219.8–493.2) |

Pelagic taxa | 357.5 | (298.3–416.7) | (242.4–527.2) | 328.8 | (276.7–380.9) | (222.4–486.1) |

Fusiform and elongate non-acanthopterygians | 340.5 | (285.1–395.9) | (225.7–513.7) | 318.5 | (279.3–357.7) | (234.0–433.5) |

Sharks | 298.5 | (264.2–332.9) | (224.1–397.8) | 299.6 | (268.0–331.2) | (227.9–393.9) |

With shape and variable slope for Chondrichthyes | 340.7 | (298.4–382.9) | (245.1–473.6) | 328.6 | (284.4–372.9) | (226.9–476.0) |

Head length | 266.7 | (228.3–305.0) | (184.2–386.0) | 262.3 | (221.3–303.2) | (176.0–390.9) |

Other methods of estimating length | ||||||

Scaling from Coccosteus in [15], head length | 341 | — | — | |||

Scaling from Coccosteus in [15], length of mediodorsal (sensu [64]) | 223 | — | — | |||

Scaling from Coccosteus in [15], greatest external length of mediodorsal | 297 | — | — | |||

Scaling from Coccosteus in [15], greatest length of posteroventrolateral | 388 | — | — | |||

Scaling from Coccosteus in [15], inferognathal length | 523 | — | — | |||

Scaling from Coccosteus in [15], body depth | 614 | — | — | |||

Entering angle (sensu [150]) | 347 | — | — | |||

Approximate location of pelvic girdle on body | ~340 | — | — |

**Table 4.**Estimated lengths (in cm) of the largest known specimen of Dunkleosteus terrelli (CMNH 5936) using the best-performing models in this study. Abbreviations as in Table 2. All measurements in cm.

Measurement | Model | Data Type | Estimated Length | +/−PE | 95% P.I. |
---|---|---|---|---|---|

JM3 | All specimens | Individual Data | 409.4 | (337.6–481.3) | (263.4–636.5) |

All specimens | Species Averages | 392.7 | (322.6–462.8) | (248.0–622.0) | |

Fusiform fishes only | Individual Data | 369.8 | (325.9–413.7) | (273.1–500.7) | |

Fusiform fishes only | Species Averages | 362.7 | (321.9–403.6) | (270.4–486.7) | |

Variable slope for chondrichthyans | Individual Data | 395.4 | (346.4–444.5) | (284.4–549.8) | |

Variable slope for chondrichthyans | Species Averages | 339.4 | (293.7–385.1) | (179.0–643.6) | |

JM5 | All specimens | Individual Data | 423.5 | (349.2–497.8) | (272.4–658.4) |

All specimens | Species Averages | 406.0 | (333.6–478.5) | (256.4–643.1) | |

Fusiform fishes only | Individual Data | 382.2 | (336.8–427.6) | (282.3–517.5) | |

Fusiform fishes only | Species Averages | 374.8 | (332.6–417.0) | (279.4–502.9) | |

Variable slope for chondrichthyans | Individual Data | 409.0 | (358.3–459.7) | (294.2–568.6) | |

Variable slope for chondrichthyans | Species Averages | 350.5 | (303.3–397.7) | (183.7–668.8) |

**Table 5.**Estimated body masses of Dunkleosteus terrelli and their 95% prediction intervals in kg. Prediction intervals not available for Carcharodon length–weight equation. Length calculated using the model including information from body shape and varying slope level for Chondrichthyans. CMNH 6090 and 7054 are almost identical in size, but the thoracic armor of 6090 is slightly deeper, hence the discrepancy in length and weight. Body proportions of CMNH 5396 were calculated assuming isometry with CMNH 5768. Additional details of how these masses were calculated can be found in Supplementary File S3.

Specimen | Estimated Total Length (cm) | Ellipsoid Model, All Fishes | Ellipsoid Model, Large Pelagic Fishes | Carcharodon Length–Weight Equation |
---|---|---|---|---|

CMNH 7424 | 188.9 | 106.7 (60.5–188.4) | 166.7 (120.7–230.1) | 136.0 |

CMNH 6090 | 283.2 | 391.7 (221.1–693.9) | 561.3 (401.8–784.2) | 423.9 |

CMNH 7054 | 295.5 | 381.4 (215.5–675.0) | 545.0 (393.0–755.8) | 413.2 |

CMNH 5768 | 340.6 | 1008.4 (564.6–1801.0) | 1204.1 (833.1–174053) | 941.5 |

CMNH 5936 | 406.5 | 1763.9 (982.1–3168.0) | 1731.6 (1175.9–2549.8) | 1494.2 |

**Table 6.**Broad-scale differences in body proportions between the three major fish clades considered in this study. Note Chondrichthyes here almost exclusively refers to Elasmobranchii as extant holocephalians and batoids have heavily modified body plans (though extinct chondrichthyans like Cladoselache are generally similar in body shape to extant elasmobranchs), and Osteichthyes almost exclusively refers to actinopterygians due to low availability of data for sarcopterygians.

Clade | Arthrodira | Chondrichthyes (Elasmobranchii) | Osteichthyes (Actinopterygii) |
---|---|---|---|

Body cross-section in anterior view | Circular | Circular | Mediolaterally narrow |

Anteroposterior length relative to thoracic girth | Short | Elongate | Variable, generally intermediate |

Body height relative to anteroposterior length | Deep | Shallow | Deep |

**Table 7.**Previous length estimates of Dunkleosteus terrelli arranged in chronological order and their methodology. “Unstated” refers to estimates where the methodology used to calculate these length estimates is undefined and no citation is made to length estimates in prior studies.

Study | Length Estimate | Method of Estimation |
---|---|---|

Newberry [206]: p. 24 | 4.5–5.5 m (“15 to 18 feet”) | Extrapolated from Coccosteus cuspidatus |

Newberry [210]: p. 24 | 4.5 m (“15 feet in length”) | Unstated (implied correlation with Coccosteus) |

Dean [211]: p. 130 | 3 m (“10 feet”) | Unstated |

Hussakof [116]: pp. 32–34 | 1.67 m (juvenile) ^{1}2.43 m (“8 feet”, juvenile) ^{1}3.79 m (extrapolated CMNH 5768) | “Entering angle” of body (sensu Dean [150]). |

Anonymous [212] | 7.6 m (“25 feet”) | Unstated ^{2} |

Hyde [213] | 4.5–6 m (“15 to 20 feet”) | Unstated |

Romer [214]: p. 49 | 9 m (“may have reached a length of 30 feet”) | Unstated |

Colbert [215]: p. 36 | 9 m (“30 feet”) | Unstated |

Denison [61]: p. 88 | 6 m | Unstated |

Williams [216] ^{3} | 5 m | Unstated |

Maisey [217]: pp. 80–81 | 4 m (figured specimen) 5–6 m (typical adult) | Unstated |

Janvier [218]: p. 12 | 6–7 m | Unstated ^{4} |

Young [7] | “6 m, with evidence that some individuals may have doubled that length” | Unstated |

Anderson and Westneat [8] | 6 m | Unstated |

Anderson and Westneat [9] | 10 m | Unstated |

Carr [11] | 4.5–6 m | Unstated |

Long [6]: pp. 88–90 | 4–8 m | Unstated ^{5} |

Sallan and Galimberti [32] | 8 m | Stated to be from Denison [61], but cited length disagrees with latter study. |

Ferrón et al. [12] | 6.88 m (CMNH 5768), 8.79 m (maximum) | Upper jaw perimeter |

Long et al. [219]: p. 13 | 6–8 m | Unstated ^{4} |

Johanson et al. [29] | ~3 m (juvenile) ^{6}~7.1 m (extrapolated CMNH 5768) ^{6} | Unstated |

Present Study | 3.4 m (typical adult = CMNH 5768), 3.9–4.1 m (maximum) | Orbit-opercular length |

^{1}Estimate based on an individual of “Dinichthys intermedius” (=juvenile D. terrelli) in the AMNH (specimen number unknown) with an inferognathal 31 cm long and a skull roof 27 cm long. Adult length extrapolated assuming similar head–body proportions for CMNH 5768, length estimated based on entering angle in CMNH 5768 can be found in Table 3.

^{2}Publication date (1923) and context suggest that this is a field estimate referring to one of the mounted Dunkleosteus specimens at the CMNH or USNM.

^{3}Semi-popular account but treated as primary reference in Hansen [220], so considered here.

^{4}Mentions specimens with “carapaces” (head and thoracic armor) over 2 m long, significantly larger than any specimen in the collections of the AMNH, CMNH, or NHMUK (~75% of the hypodigm), but do not provide specimen numbers.

^{5}Mentions specimens “with headshields over a meter long”, significantly larger than any specimen of D. terrelli in the collections of the AMNH, CMNH, or NHMUK (~75% of the hypodigm), but do not provide specimen numbers. It is possible this estimate is referring to Denison [61] or Janvier [218], but this is unclear.

^{6}Authors suggest length of ~3 m for studied specimen. Assuming similar head–body proportions this would produce length of 7.1 m for CMNH 5768.

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**MDPI and ACS Style**

Engelman, R.K.
A Devonian Fish Tale: A New Method of Body Length Estimation Suggests Much Smaller Sizes for *Dunkleosteus terrelli* (Placodermi: Arthrodira). *Diversity* **2023**, *15*, 318.
https://doi.org/10.3390/d15030318

**AMA Style**

Engelman RK.
A Devonian Fish Tale: A New Method of Body Length Estimation Suggests Much Smaller Sizes for *Dunkleosteus terrelli* (Placodermi: Arthrodira). *Diversity*. 2023; 15(3):318.
https://doi.org/10.3390/d15030318

**Chicago/Turabian Style**

Engelman, Russell K.
2023. "A Devonian Fish Tale: A New Method of Body Length Estimation Suggests Much Smaller Sizes for *Dunkleosteus terrelli* (Placodermi: Arthrodira)" *Diversity* 15, no. 3: 318.
https://doi.org/10.3390/d15030318