Document Type
Article
Publication Date
1-14-2026
Abstract
Background
Tyrannosaurus rex, one of the most iconic non-avialan dinosaurs, remains a central focus of paleobiological research. Growth modeling suggests T. rex exceeded 8,000 kg within two decades and had a lifespan approaching 30 years. However, this understanding of T. rex growth dynamics is dependent on single-point histological sampling of multiple skeletal elements and lacks specimens encompassing the earliest growth states.
Methods
We present the most comprehensive histological analysis of Tyrannosaurus ontogeny to date, based on transverse diaphyseal sections of femora and tibiae from 17 individuals ranging from small juveniles to large adults. Four alternative statistical models were tested, differing in the treatment of cortical growth marks, including annulus-like birefringent bands visible only in cross-polarized light. Due to high intraspecies morphological variability, the taxonomic status of many Tyrannosaurus specimens is debated, prompting use of the term “Tyrannosaurus rex species complex” to describe our dataset.
Results
The best-supported model incorporated all visible growth marks, produced the narrowest confidence bands, and indicated lower maximum growth rates and a delayed attainment of asymptotic size (~35–40 years) compared with earlier estimates. We also find that two immature specimens within the Tyrannosaurus rex species complex are not statistically compatible with the other growth series. Our approach is the first in dinosaur skeletochronology to simultaneously estimate the position of the earliest preserved growth mark across specimens, while fitting sigmoidal curves with simultaneous confidence bands. We find the inclusion of double growth marks and those visible only with cross polarized light provide better statistical model fits and this may have implications for modeling other taxa. Additionally, we find no strong link from extant vertebrates to support the idea that the growth inflection point is biologically significant and corresponds to sexual maturity. Our results suggest that the Tyrannosaurus rex species complex grew more gradually and over a longer lifespan than indicated by prior models, with a protracted period of subadult development.
Recommended Citation
Woodward HN, Myhrvold NP, Horner JR. 2026. Prolonged growth and extended subadult development in the Tyrannosaurus rex species complex revealed by expanded histological sampling and statistical modeling. PeerJ 14:e20469 https://doi.org/10.7717/peerj.20469
Figure_S1.png (340 kB)
Six Tyrannosaurus specimens did not exhibit growth marks visible only in cross polarized light (XPL). Note that the NoX variant is therefore identical to NoXM, and NoM is identical to A, so only NoXM and A variants are plotted. Cortical growth mark (CGM) count on the x-axis, CGM circumference on the y-axis. DOI: 10.7717/peerj.20469/supp-1
Figure_S2R1.png (569 kB)
Seven Tyrannosaurus growth series displayed some cortical growth marks (CGM) only visible with cross polarized light (XPL). Counts for each class of CGM are in table S1. Note that Tibia CGM V33.1.15 has no multiplet CGM so its NoX variant is identical to NoXM, and A is identical to NoM. Cortical growth mark (CGM) count on the x-axes, CGM circumference on the y-axes. DOI: 10.7717/peerj.20469/supp-2
Figure_S3R1.png (528 kB)
Individual Tyrannosaurus growth series for dataset Trex1, A and NoM variants. Cortical growth mark (CGM) count on the x-axis, CGM circumference on the y-axis. DOI: 10.7717/peerj.20469/supp-3
Figure_S4R1.png (500 kB)
Individual Tyrannosaurus growth series for dataset Trex1, NoX and NoXM variants. Cortical growth mark (CGM) count on the x-axis, CGM circumference on the y-axis. DOI: 10.7717/peerj.20469/supp-4
Figure_S5R1.png (440 kB)
Individual Tyrannosaurus growth series for dataset Trex2 (BMRP specimens removed), A and NoM variants. Cortical growth mark (CGM) count on the x-axis, CGM circumference on the y-axis. DOI: 10.7717/peerj.20469/supp-5
Figure_S6R1.png (428 kB)
Individual Tyrannosaurus growth series for dataset Trex2 (BMRP specimens removed), NoX and NoXM variants. Cortical growth mark (CGM) count on the x-axis, CGM circumference on the y-axis. DOI: 10.7717/peerj.20469/supp-6
Figure_S7.png (213 kB)
Individual Gorgosaurus libratus growth series, A and NoM variants. Data for FMNH PR 2211 obtained from Cullen et al. (2021). Cortical growth mark (CGM) count on the x-axis, CGM circumference on the y-axis. DOI: 10.7717/peerj.20469/supp-7
Figure_S8.png (200 kB)
Individual Gorgosaurus libratus growth series, A and NoM variants. Data for FMNH PR 2211 obtained from Cullen et al. (2021). Cortical growth mark (CGM) count on the x-axis, CGM circumference on the y-axis. DOI: 10.7717/peerj.20469/supp-8
Figure_S9.png (127 kB)
The first step of least squares clustering is projecting overlapping growth series onto one another. CGM growth series are said to overlap if the range of circumferences for the series overlap. In that case the (cgmci, sizei) points for each overlapping series are “projected” onto all the other overlapping series. Dashed arrows show the projections. All are calculated assuming piecewise linear interpolation between the (cgmci, sizei) points of the series being projected upon. The least squares clustering algorithm then minimizes the sum of the square of the projection lengths (i.e. length of the arrows) for all overlaps, varying the starting age of each growth series. Cortical growth mark (CGM) count on the x-axis, CGM circumference on the y-axis. DOI: 10.7717/peerj.20469/supp-9
FigureS10R1.png (497 kB)
Tyrannosaurus dataset Trex1 growth series clustered by least squares, for A and NoM variants. For each specimen, the starting cortical growth mark (CGM) age is estimated using least squares minimization, and the numerical values are found in the inset table in the column labeled “1st”. All ages are in years relative to the starting age of the smallest CGM circumference in Tibia MOR 1189. DOI: 10.7717/peerj.20469/supp-10
FigureS11R1.png (505 kB)
Tyrannosaurus dataset Trex1 growth series clustered by least squares, for NoX and NoXM variants. For each specimen, the starting cortical growth mark (CGM) age is estimated using least squares minimization, and the numerical values are found in the inset table in the column labeled “1st”. All ages are in years relative to the starting age of the smallest CGM circumference in Tibia MOR 1189. DOI: 10.7717/peerj.20469/supp-11
Figure_S12R1.png (490 kB)
Tyrannosaurus dataset Trex2 growth series clustered by least squares, for A and NoM variants. . For each specimen, the starting cortical growth mark (CGM) age is estimated using least squares minimization, and the numerical values are found in the inset table in the column labeled “1st”. All ages are in years relative to the starting age of the smallest CGM circumference in Tibia MOR 1189. DOI: 10.7717/peerj.20469/supp-12
Figure_S13R1.png (435 kB)
Tyrannosaurus dataset Trex2 growth series clustered by least squares, for NoX and NoXM variants. For each specimen, the starting cortical growth mark (CGM) age is estimated using least squares minimization, and the numerical values are found in the inset table in the column labeled “1st”. All ages are in years relative to the starting age of the smallest CGM circumference in Tibia MOR 1189. DOI: 10.7717/peerj.20469/supp-13
FigureS14R1.png (654 kB)
Tyrannosaurus growth modeling for dataset Trex1, A and NoM variants. The 95% simultaneous confidence bands (CB) and best fit equations are shown, in this case the arctan 3 function for variant A and the laplace 3 function for variant NoM. All ages are in years relative to the starting age of the smallest cortical growth mark (CGM) circumference in Tibia MOR 1189. DOI: 10.7717/peerj.20469/supp-14
FigureS15R1.png (649 kB)
Tyrannosaurus growth modeling for dataset Trex1, NoX and NoXM variants. The 95% simultaneous confidence bands (CB) and best fit equations are shown, in this case the laplace 3 function for variant NoX and the arctan 3 function for variant NoXM. All ages are in years relative to the starting age of the smallest cortical growth mark (CGM) circumference in Tibia MOR 1189. DOI: 10.7717/peerj.20469/supp-15
Figure_S16R1.png (595 kB)
Tyrannosaurus growth modeling for dataset Trex2, A and NoM variants. The 95% simultaneous confidence bands (CB) and best fit equations are shown, in this case the extreme value 3 function for both variants. All ages are in years relative to the starting age of the smallest cortical growth mark (CGM) circumference in Tibia MOR 1189. DOI: 10.7717/peerj.20469/supp-16
Figure_S17R1.png (595 kB)
Tyrannosaurus growth modeling for dataset Trex2, NoX and NoXM variants. The 95% simultaneous confidence bands (CB) and best fit equations are shown, in this case the extreme value 3 function for both variants. All ages are in years relative to the starting age of the smallest cortical growth mark (CGM) circumference in Tibia MOR 1189. DOI: 10.7717/peerj.20469/supp-17
Figure_S18.png (100 kB)
Residuals to best fitting growth models for variants of Trex2 dataset. The residuals from the data series are plotted, along with their 0.025, 0.5 (median) and 0.975 quantiles. DOI: 10.7717/peerj.20469/supp-18
Figure_S19.png (722 kB)
Comparison of arithmetic and log-transformed growth models for Trex2, A and NoM variants. All ages are in years relative to the starting age of the smallest cortical growth mark (CGM) circumference in Tibia MOR 1189. DOI: 10.7717/peerj.20469/supp-19
Figure_S20.png (712 kB)
Comparison of arithmetic and log-transformed growth models for Trex2, NoX and NoXM variants. All ages are in years relative to the starting age of the smallest cortical growth mark (CGM) circumference in Tibia MOR 1189. DOI: 10.7717/peerj.20469/supp-20
Figure_S21.png (657 kB)
Synthetic linear growth series for testing compatibility. . Each panel shows a different variant (A, NoM, NoX, NoXM). The black growth series is Tibia BMRP 2006.4.4. The colored lines show linear growth series of the same length, but with constant linear growth rate ranging from 2 mm/year (bottom most line) to 30 mm/year (topmost line). Cortial growth mark (CGM) count on the x-axes, CGM circumference on the y-axes. DOI: 10.7717/peerj.20469/supp-21
Figure_S22.png (203 kB)
Confidence band (CB) area and CB area/length for trials with synthetic growth series at different linear growth rates. The plots show the total CB area (top panel) and CB area divided by length of CB (bottom panel) for different variants of the Trex2 dataset, plus one synthetic data series with linear growth at the specified rate. Each area (or area/length) curve reaches a minimum value at the black points. Minimum values indicate the linear growth rate that is the most compatible (of those simulated) with the given variant of the Trex2 data series. DOI: 10.7717/peerj.20469/supp-22
FigureS23R1.png (331 kB)
BMRP 2002.4.1 and BMRP 2006.4.4 growth series for each variant. Cortical growth mark (CGM) count on the x-axes, CGM circumference (mm) on the y-axes. DOI: 10.7717/peerj.20469/supp-23
FigureS24.png (165 kB)
BMRP 2002.4.1 and BMRP 2006.4.4 growth series annotated. The A variant of the growth series contains all of the observed cortical growth marks (CGM). CGM marked M are multiplets which would not be present in the NoM, or NoMX variants. Those marked X are XPL CGM and would be present in the NoX and NoXM variants. DOI: 10.7717/peerj.20469/supp-24
Table_S1R1.xlsx (58 kB)
Specimen raw data. Individual specimen tabs provide raw data tables for each growth series. DOI: 10.7717/peerj.20469/supp-25
Table_S2.docx (15 kB)
Count of cortical growth marks (CGM) visible in cross polarized light (XPL) and those comprising a multiplet (M). CGM which are only visible in cross polarized light are counted in the column XPL count. CGM which are omitted from variants NoM and NoXM on the basis that they are members of multiplets are counted in column “M count”. DOI: 10.7717/peerj.20469/supp-26
Table_S3.docx (16 kB)
Arithmetic scale models fit to growth data. This table is primarily composed of sigmoidal models, but simple linear and quadratic models are also included. For the sigmoidal models the parameter is always the maximum asymptotic size, is always a location parameter that determines where on the time axis the sigmoid is located. The parameter is related to the slope (growth rate) of the model in its intermediate growth phase. DOI: 10.7717/peerj.20469/supp-27
Table_S4.docx (16 kB)
Models fit to log-transformed growth data. The models fit to conventional (arithmetic scale) data are modified for fitting to log-transformed data, in which the circumference values are log-transformed. Here we use log to mean natural logarithm. Parameter interpretation is as described for arithmetic scale models. The Laplace 3 model (Table S2) is not included because it has algorithmic issues in fitting. DOI: 10.7717/peerj.20469/supp-28
Table_S5.docx (21 kB)
Trex2 model parameters and their 95% confidence intervals (CI). The model, parameter values and 95% CI for the parameter values are shown in the table, with the CI expressed both in a high/low, and as a percentage variation on the median value. The parameters are for the sigmoidal model shown. The parameters for each of the specimen names are the estimated ages to be added to the 1 st CGM in the growth series for the specimen (in years). DOI: 10.7717/peerj.20469/supp-29
Table_S6.docx (21 kB)
Trex2 model parameters and their 95% confidence intervals (CI). The model, parameter values and 95% CI for the parameter values are shown in the table, with the CI expressed both in a high/low, and as a percentage variation on the median value. The parameters are for the sigmoidal model shown. The parameters for each of the specimen names are the estimated age to be added to the 1 st CGM in the growth series for the specimen (in years). DOI: 10.7717/peerj.20469/supp-30
Six Tyrannosaurus specimens did not exhibit growth marks visible only in cross polarized light (XPL). Note that the NoX variant is therefore identical to NoXM, and NoM is identical to A, so only NoXM and A variants are plotted. Cortical growth mark (CGM) count on the x-axis, CGM circumference on the y-axis. DOI: 10.7717/peerj.20469/supp-1
Figure_S2R1.png (569 kB)
Seven Tyrannosaurus growth series displayed some cortical growth marks (CGM) only visible with cross polarized light (XPL). Counts for each class of CGM are in table S1. Note that Tibia CGM V33.1.15 has no multiplet CGM so its NoX variant is identical to NoXM, and A is identical to NoM. Cortical growth mark (CGM) count on the x-axes, CGM circumference on the y-axes. DOI: 10.7717/peerj.20469/supp-2
Figure_S3R1.png (528 kB)
Individual Tyrannosaurus growth series for dataset Trex1, A and NoM variants. Cortical growth mark (CGM) count on the x-axis, CGM circumference on the y-axis. DOI: 10.7717/peerj.20469/supp-3
Figure_S4R1.png (500 kB)
Individual Tyrannosaurus growth series for dataset Trex1, NoX and NoXM variants. Cortical growth mark (CGM) count on the x-axis, CGM circumference on the y-axis. DOI: 10.7717/peerj.20469/supp-4
Figure_S5R1.png (440 kB)
Individual Tyrannosaurus growth series for dataset Trex2 (BMRP specimens removed), A and NoM variants. Cortical growth mark (CGM) count on the x-axis, CGM circumference on the y-axis. DOI: 10.7717/peerj.20469/supp-5
Figure_S6R1.png (428 kB)
Individual Tyrannosaurus growth series for dataset Trex2 (BMRP specimens removed), NoX and NoXM variants. Cortical growth mark (CGM) count on the x-axis, CGM circumference on the y-axis. DOI: 10.7717/peerj.20469/supp-6
Figure_S7.png (213 kB)
Individual Gorgosaurus libratus growth series, A and NoM variants. Data for FMNH PR 2211 obtained from Cullen et al. (2021). Cortical growth mark (CGM) count on the x-axis, CGM circumference on the y-axis. DOI: 10.7717/peerj.20469/supp-7
Figure_S8.png (200 kB)
Individual Gorgosaurus libratus growth series, A and NoM variants. Data for FMNH PR 2211 obtained from Cullen et al. (2021). Cortical growth mark (CGM) count on the x-axis, CGM circumference on the y-axis. DOI: 10.7717/peerj.20469/supp-8
Figure_S9.png (127 kB)
The first step of least squares clustering is projecting overlapping growth series onto one another. CGM growth series are said to overlap if the range of circumferences for the series overlap. In that case the (cgmci, sizei) points for each overlapping series are “projected” onto all the other overlapping series. Dashed arrows show the projections. All are calculated assuming piecewise linear interpolation between the (cgmci, sizei) points of the series being projected upon. The least squares clustering algorithm then minimizes the sum of the square of the projection lengths (i.e. length of the arrows) for all overlaps, varying the starting age of each growth series. Cortical growth mark (CGM) count on the x-axis, CGM circumference on the y-axis. DOI: 10.7717/peerj.20469/supp-9
FigureS10R1.png (497 kB)
Tyrannosaurus dataset Trex1 growth series clustered by least squares, for A and NoM variants. For each specimen, the starting cortical growth mark (CGM) age is estimated using least squares minimization, and the numerical values are found in the inset table in the column labeled “1st”. All ages are in years relative to the starting age of the smallest CGM circumference in Tibia MOR 1189. DOI: 10.7717/peerj.20469/supp-10
FigureS11R1.png (505 kB)
Tyrannosaurus dataset Trex1 growth series clustered by least squares, for NoX and NoXM variants. For each specimen, the starting cortical growth mark (CGM) age is estimated using least squares minimization, and the numerical values are found in the inset table in the column labeled “1st”. All ages are in years relative to the starting age of the smallest CGM circumference in Tibia MOR 1189. DOI: 10.7717/peerj.20469/supp-11
Figure_S12R1.png (490 kB)
Tyrannosaurus dataset Trex2 growth series clustered by least squares, for A and NoM variants. . For each specimen, the starting cortical growth mark (CGM) age is estimated using least squares minimization, and the numerical values are found in the inset table in the column labeled “1st”. All ages are in years relative to the starting age of the smallest CGM circumference in Tibia MOR 1189. DOI: 10.7717/peerj.20469/supp-12
Figure_S13R1.png (435 kB)
Tyrannosaurus dataset Trex2 growth series clustered by least squares, for NoX and NoXM variants. For each specimen, the starting cortical growth mark (CGM) age is estimated using least squares minimization, and the numerical values are found in the inset table in the column labeled “1st”. All ages are in years relative to the starting age of the smallest CGM circumference in Tibia MOR 1189. DOI: 10.7717/peerj.20469/supp-13
FigureS14R1.png (654 kB)
Tyrannosaurus growth modeling for dataset Trex1, A and NoM variants. The 95% simultaneous confidence bands (CB) and best fit equations are shown, in this case the arctan 3 function for variant A and the laplace 3 function for variant NoM. All ages are in years relative to the starting age of the smallest cortical growth mark (CGM) circumference in Tibia MOR 1189. DOI: 10.7717/peerj.20469/supp-14
FigureS15R1.png (649 kB)
Tyrannosaurus growth modeling for dataset Trex1, NoX and NoXM variants. The 95% simultaneous confidence bands (CB) and best fit equations are shown, in this case the laplace 3 function for variant NoX and the arctan 3 function for variant NoXM. All ages are in years relative to the starting age of the smallest cortical growth mark (CGM) circumference in Tibia MOR 1189. DOI: 10.7717/peerj.20469/supp-15
Figure_S16R1.png (595 kB)
Tyrannosaurus growth modeling for dataset Trex2, A and NoM variants. The 95% simultaneous confidence bands (CB) and best fit equations are shown, in this case the extreme value 3 function for both variants. All ages are in years relative to the starting age of the smallest cortical growth mark (CGM) circumference in Tibia MOR 1189. DOI: 10.7717/peerj.20469/supp-16
Figure_S17R1.png (595 kB)
Tyrannosaurus growth modeling for dataset Trex2, NoX and NoXM variants. The 95% simultaneous confidence bands (CB) and best fit equations are shown, in this case the extreme value 3 function for both variants. All ages are in years relative to the starting age of the smallest cortical growth mark (CGM) circumference in Tibia MOR 1189. DOI: 10.7717/peerj.20469/supp-17
Figure_S18.png (100 kB)
Residuals to best fitting growth models for variants of Trex2 dataset. The residuals from the data series are plotted, along with their 0.025, 0.5 (median) and 0.975 quantiles. DOI: 10.7717/peerj.20469/supp-18
Figure_S19.png (722 kB)
Comparison of arithmetic and log-transformed growth models for Trex2, A and NoM variants. All ages are in years relative to the starting age of the smallest cortical growth mark (CGM) circumference in Tibia MOR 1189. DOI: 10.7717/peerj.20469/supp-19
Figure_S20.png (712 kB)
Comparison of arithmetic and log-transformed growth models for Trex2, NoX and NoXM variants. All ages are in years relative to the starting age of the smallest cortical growth mark (CGM) circumference in Tibia MOR 1189. DOI: 10.7717/peerj.20469/supp-20
Figure_S21.png (657 kB)
Synthetic linear growth series for testing compatibility. . Each panel shows a different variant (A, NoM, NoX, NoXM). The black growth series is Tibia BMRP 2006.4.4. The colored lines show linear growth series of the same length, but with constant linear growth rate ranging from 2 mm/year (bottom most line) to 30 mm/year (topmost line). Cortial growth mark (CGM) count on the x-axes, CGM circumference on the y-axes. DOI: 10.7717/peerj.20469/supp-21
Figure_S22.png (203 kB)
Confidence band (CB) area and CB area/length for trials with synthetic growth series at different linear growth rates. The plots show the total CB area (top panel) and CB area divided by length of CB (bottom panel) for different variants of the Trex2 dataset, plus one synthetic data series with linear growth at the specified rate. Each area (or area/length) curve reaches a minimum value at the black points. Minimum values indicate the linear growth rate that is the most compatible (of those simulated) with the given variant of the Trex2 data series. DOI: 10.7717/peerj.20469/supp-22
FigureS23R1.png (331 kB)
BMRP 2002.4.1 and BMRP 2006.4.4 growth series for each variant. Cortical growth mark (CGM) count on the x-axes, CGM circumference (mm) on the y-axes. DOI: 10.7717/peerj.20469/supp-23
FigureS24.png (165 kB)
BMRP 2002.4.1 and BMRP 2006.4.4 growth series annotated. The A variant of the growth series contains all of the observed cortical growth marks (CGM). CGM marked M are multiplets which would not be present in the NoM, or NoMX variants. Those marked X are XPL CGM and would be present in the NoX and NoXM variants. DOI: 10.7717/peerj.20469/supp-24
Table_S1R1.xlsx (58 kB)
Specimen raw data. Individual specimen tabs provide raw data tables for each growth series. DOI: 10.7717/peerj.20469/supp-25
Table_S2.docx (15 kB)
Count of cortical growth marks (CGM) visible in cross polarized light (XPL) and those comprising a multiplet (M). CGM which are only visible in cross polarized light are counted in the column XPL count. CGM which are omitted from variants NoM and NoXM on the basis that they are members of multiplets are counted in column “M count”. DOI: 10.7717/peerj.20469/supp-26
Table_S3.docx (16 kB)
Arithmetic scale models fit to growth data. This table is primarily composed of sigmoidal models, but simple linear and quadratic models are also included. For the sigmoidal models the parameter is always the maximum asymptotic size, is always a location parameter that determines where on the time axis the sigmoid is located. The parameter is related to the slope (growth rate) of the model in its intermediate growth phase. DOI: 10.7717/peerj.20469/supp-27
Table_S4.docx (16 kB)
Models fit to log-transformed growth data. The models fit to conventional (arithmetic scale) data are modified for fitting to log-transformed data, in which the circumference values are log-transformed. Here we use log to mean natural logarithm. Parameter interpretation is as described for arithmetic scale models. The Laplace 3 model (Table S2) is not included because it has algorithmic issues in fitting. DOI: 10.7717/peerj.20469/supp-28
Table_S5.docx (21 kB)
Trex2 model parameters and their 95% confidence intervals (CI). The model, parameter values and 95% CI for the parameter values are shown in the table, with the CI expressed both in a high/low, and as a percentage variation on the median value. The parameters are for the sigmoidal model shown. The parameters for each of the specimen names are the estimated ages to be added to the 1 st CGM in the growth series for the specimen (in years). DOI: 10.7717/peerj.20469/supp-29
Table_S6.docx (21 kB)
Trex2 model parameters and their 95% confidence intervals (CI). The model, parameter values and 95% CI for the parameter values are shown in the table, with the CI expressed both in a high/low, and as a percentage variation on the median value. The parameters are for the sigmoidal model shown. The parameters for each of the specimen names are the estimated age to be added to the 1 st CGM in the growth series for the specimen (in years). DOI: 10.7717/peerj.20469/supp-30
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This article was originally published in PeerJ, volume 14, in 2026. https://doi.org/10.7717/peerj.20469