Tyrannosaur Life Tables: An Example of Nonavian Dinosaur Population Biology

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Science  14 Jul 2006:
Vol. 313, Issue 5784, pp. 213-217
DOI: 10.1126/science.1125721


The size and age structures for four assemblages of North American tyrannosaurs—Albertosaurus, Tyrannosaurus, Gorgosaurus, and Daspletosaurus—reveal a pronounced, bootstrap-supported pattern of age-specific mortality characterized by relatively high juvenile survivorship and increased mortality at midlife and near the maximum life span. Such patterns are common today in wild populations of long-lived birds and mammals. Factors such as predation and entrance into the breeding population may have influenced tyrannosaur survivorship. This survivorship pattern can explain the rarity of juvenile specimens in museum collections.

Little is known about the population biology of nonavian dinosaurs. Did these animals show survivorship patterns akin to extant living dinosaurs—the birds, like the dinosaurs' cousins the crocodilians, or were they similar to more distantly related ecological analogs? Here, we use the age and size distribution from a death assemblage of the North American tyrannosaur Albertosaurus sarcophagus to produce an age-standardized ecological life table for a nonavian dinosaur population.

We analyzed specimens from a monospecific assemblage found in 1910 by Brown (1) in sediments from the Horseshoe Canyon Formation along the Red Deer River, near Dry Island Buffalo Jump Provincial Park, Alberta, Canada. Renewed excavation of the site by the Royal Tyrrell Museum of Palaeontology, Drumheller, shows that 22 individuals are represented at the site (Table 1), making it the largest known aggregation of nonavian theropods from the Cretaceous Period and second only to the Cleveland Lloyd allosaur quarry (n = 40+) for a large species (2). Taphonomic analysis (1, 3) reveals that the assemblage represents an attritional sampling (i.e., it is not representative of standing crop; fig. S2) from the local population (a group of coexisting individuals of the same species, whether a pack or individuals drawn from the area). The animals succumbed over a short period of time, perhaps through drought or starvation.

Table 1.

Life table for Dry Island A. sarcophagus. TMP, Royal Tyrrell Museum of Palaeontology, Drumheller, Alberta, Canada; AMNH, American Museum of Natural History, New York City. Specimen numbers reflect elements definitively attributed to separate individuals from the assemblage. Mean length of life = 16.60 years. lx values are the proportion of individuals alive at the beginning of each age class.

Specimen numberAge (years)dx (proportion dying)lx (proportion surviving)qx (interval mort. rate)qx(year) (annual mort. rate)View inline
TMP 2002.5.46View inline 2 0.0455 1.000 0.0455 0.0455
(Age not represented) 3 0.0241
TMP 2000.45.15 4 0.0455 0.9545 0.0477 0.0241
(Age not represented) 5 0.0254
TMP 1999.50.19 6 0.0455 0.9090 0.0501 0.0254
(Age not represented) 7 0.0267
AMNH 5229View inline 8 0.0455 0.8635 0.0527 0.0267
TMP 2000.45.7 9 0.0455 0.8180 0.0556 0.0556
(Age not represented) 10 0.0299
AMNH 5233View inline 11 0.0455 0.7725 0.0589 0.0299
TMP 1999.50.28 12 0.0455 0.7270 0.0626 0.0626
TMP 1999.50.26 13 0.0455 0.6815 0.0668 0.0668
TMP 2004.56.43, 2001.45.60 14 0.0909 0.6360 0.1429 0.1429
AMNH 5234,View inline AMNH 5218i 15 0.0909 0.5451 0.1668 0.1668
TMP 2001.45.49 16 0.0455 0.4542 0.1002 0.1002
AMNH 5235,View inline 5228 17 0.0909 0.4087 0.2224 0.2224
AMNH 5218ay 18 0.0455 0.3178 0.1432 0.1432
AMNH 5232,View inline 5231 19 0.0909 0.2723 0.3338 0.3338
AMNH 5218ac 20 0.0455 0.1814 0.2508 0.2508
TMP 1999.50.2 21 0.0455 0.1359 0.3348 0.3348
(Age not represented) 22 0.2952
TMP 2000.45.9 23 0.0455 0.0904 0.5033 0.2952
(Age not represented) 24 to 27
TMP 2004.56.48 28 0.0455 0.0449 1.000 1.000
  • View inline* Specimens for which longevity was directly determined from growth line counts.

  • View inline Values for the missing cohorts (ages 3, 5, 7, 10, 22) were calculated assuming constant annual mortality over the interval spanning missing ages (3).

  • We selected fibulae and/or metatarsals from individuals representing 27% of the assemblage and used growth line counts to estimate ages at death (36). The smallest individual was included, as were some of the largest (Table 1). A regression of these data, along with age estimates for four other A. sarcophagus specimens from nearby sites within the formation (7) on femoral length, yielded Age(years) = 0.033(Femoral length(mm)) – 9.765, r2 = 0.919 (fig. S1). The ages of the remaining individuals from the bone bed were estimated from this equation. Femoral lengths ranged from 0.32 to 1.16 m, and corresponding total lengths ranged from 2.2 to 10.1 m (table S1). Estimated ages for the dinosaurs spanned 2 to 28 years (Table 1). A life table (Table 1) (3, 8) was constructed using these data, and a graph of age (x) versus survivorship (log lx) was made (Fig. 1). We found a convex pattern of survivorship, with annual mortality (qx(year)) varying between 2 and 7% (mean = 3.7%) from ages 2 through 13, and between 10 and 33% (mean = 22.9%) from ages 14 through 23. (Note: 14 years is a plausible estimate for the typical age of sexual maturation in this taxon; see below.) Individuals surviving to 2 years of age had an average life expectancy of 16.60 years [6207 days divided by the 374 days in an early Maastrichtian year (9)]. A 90% confidence interval based on 10,000 bootstrap samples of these data supports the convex shape of the survivorship curve (Fig. 1 and fig. S4) (3).

    Fig. 1.

    Survivorship curve for a hypothetical cohort of 1000 Albertosaurus sarcophagus individuals, based on the Dry Island assemblage. Hypothesized neonate mortality is 60%. A period of relatively low mean mortality rates (q̄x(year)) followed by a period of higher rates is indicated by the shaded regions. The progressive entrance of individuals into the breeding population may be reflected by the initial increases. A possible second increase in mortality late in development is denoted by dashed lines. Skeleton sizes during development at 2, 13, and 28 years are drawn in relative proportions to the maximal adult size of 10.1 m. The equation for the Gompertz curve is nx = n0 exp{(0.0073/0.1870)[1 – exp(0.1870x)]}, r2 = 0.996, where nx is the number of individuals alive at year x. Triangles show the 90% confidence interval based on 10,000 bootstrap samples of these data.

    Given that wild vertebrate populations, including carnivores, show high neonate mortality rates [e.g., a range of 50 to 80% per year is common in living crocodilians (10), birds (11), and mammals (12, 13) despite major life history differences], this suggests similar rates in Dry Island A. sarcophagus and their complete survivorship curve resembling the sigmoidal type B1 pattern (14) [a blend of Deevey type I and type III survivorship (15)] in which high neonate mortality gives way to high juvenile survivorship followed by increased rates of attrition later in development. Of the major survivorship patterns used to characterize populations for heuristic purposes (Fig. 2), types II and III can be ruled out as competing hypotheses in that they show linear and concave patterns, respectively. The remaining type I pattern is convex but is untenable because it occurs only in captive animals and humans from developed countries, where medical care and an absence of predation yield low neonate mortality.

    Fig. 2.

    Albertosaurus survivorship compared with patterns in living mammals, archosaurian relatives, and outgroup tyrannosaurs. The data are standardized according to ecological convention, with survivorship plotted on a logarithmic scale with respect to percent of maximum life span (12, 13, 15). (A) The shaded backgrounds show hypothetical ecological extremes used to characterize and contrast survivorship patterns (15). The convex type I pattern seen in some captive animals and in humans from developed countries (8, 15) shows relatively low initial mortality followed by massive, senescence-driven die-offs as maximal life span is approached. The diagonal type II pattern [characteristic of small, short-lived birds, mammals, and lizards (8, 11, 15)] occurs in animals whose mortality is relatively constant throughout life. Populations showing the concave type III pattern [approached in crocodilians (10, 18) and other large, long-lived reptiles (17)] experience high, early attrition; the few survivors that reach threshold sizes are likely to experience low mortality and to reach maximal life span. Long-lived, typically moderate to large birds (22) and mammals (12)—and presumably the tyrannosaur—show a sigmoidal type B1 (14) pattern with high initial mortality rates, subsequent lower mortality, and increased mortality before extinction of the cohort. Note: Midlife, non–senescence-driven increases in mortality rates (arrows) often correspond to the onset of sexual maturity and breeding competition (12, 16, 26). (B) Survivorship in outgroup tyrannosaurs from multipopulation samples. All three outgroup species show bootstrap-supported (3) patterns of survivorship like that of the Dry Island A. sarcophagus population. Gompertz equation (nx = n0 exp{(a/g)[1 – exp(gx)]}) parameter values and fits: for A. sarcophagus, a = 0.0073, g = 0.1870, r2 = 0.9961; for Daspletosaurus sp., a = 0.0018, g = 0.2006, r2 = 0.9669; for G. libratus, a = 0.0059, g = 0.2072, r2 = 0.9944; and for T. rex, a = 0.002, g = 0.2214, r2 = 0.9822.

    The observed Dry Island A. sarcophagus survivorship pattern may be characteristic of tyrannosaurs as a whole, or it may reflect adaptation to local selective factors. Similar-sized single-population aggregations are not available for comparison. However, we surveyed a number of tyrannosaur fossils collected throughout specific North American formations (multipopulation sampling) and constructed composite life tables for these populations for comparison (tables S2 to S4) (3). Survivorship curves were constructed for Tyrannosaurus rex (n = 30) from the Hell Creek, Scollard, Willow Creek, and Frenchman formations; Gorgosaurus libratus (n = 39) from the Dinosaur Park and Two Medicine formations; and Daspletosaurus (n = 14) from the Dinosaur Park, Two Medicine, Oldman, and Lower Kirtland formations (3). As for the A. sarcophagus analysis, age was determined from growth line counts for 23% of the T. rex (n = 7), 13% of the G. libratus (n = 5), and 21% of the Daspletosaurus specimens (n = 3).

    Like the Dry Island albertosaur population, survivorship in the outgroup tyrannosaurs—including T. rex, an animal with five times the body mass of A. sarcophagus (7)—was characterized by a convex pattern (Fig. 2). Postneonate mortality rates averaging 2.5% (range 2.4 to 2.7%) were followed by increases in mortality averaging 20.9% (range 15.2 to 30.0%) before the demise of the cohorts. Maximum life span was 28 years for T. rex, 22 years for G. libratus, and 26 years for Daspletosaurus. Bootstrapped confidence intervals supported the convex pattern in each taxon (fig. S4). Hence, it is unlikely that these samples could have come from populations with survivorship characteristics different from those of Dry Island A. sarcophagus, and this pattern appears to be characteristic of the entire group.

    The ecological factors that contribute to the expression of type B1 survivorship in extant vertebrate populations are well understood (11, 12, 1416). High neonate mortality rates due to predation alone (disease, starvation, accidents, adverse climatic conditions, etc., also contribute) subside once a threshold size is reached. It appears that such a threshold was reached by age 2 in A. sarcophagus, when these animals had attained total lengths of 2 m, rivaling all other carnivorous theropods (deinonychosaurs, oviraptors, and ornithomimosaurs) in the Horseshoe Canyon Formation. It is here that A. sarcophagus survivorship diverged from patterns exhibited by their living archosaurian relatives, the crocodilians (Fig. 2), as well as other large ectothermal reptiles (17). Crocodilians, unlike nonavian dinosaurs such as tyrannosaurs (6, 7), grow slowly, and their young remain susceptible to predation relatively late into development (10, 18). Poor survivorship is further attenuated in crocodilians by rampant cannibalism that does not subside until they approach adult size (10). The relatively earlier decline in mortality and the evidence for gregariousness in tyrannosaurs (1, 19), along with the rarity of postcranial bite marks from tyrannosaurs feeding on other tyrannosaurids (20), suggest that the rampant cannibalism seen in some theropods (21) was not a major factor in A. sarcophagus attrition. The A. sarcophagus survivorship pattern is also unlike that of most small birds, which do not show precipitous declines in mortality with attainment of adult size. This is because they remain highly susceptible to predation throughout life (15). In addition, adult size is often reached in a fraction of a year, so high neonate mortality rates contribute minimally to the first-year survivorship pattern (11, 15). The hypothesized type B1 survivorship pattern of tyrannosaurs is, however, similar to that seen in long-lived, typically large birds and mammals (1113, 15, 16, 22), which reach threshold sizes more rapidly than do ectothermal reptiles because of their relatively rapid growth rates (23), rates that are shared by tyrannosaurs (7).

    The relatively low mortality rates among postneonate A. sarcophagus were maintained through about the 13th year of life, at which point they reached total lengths of ∼6 m or 60% of their maximum recorded size (Fig. 1). A consequence of such low attrition is that ∼70% of the animals surviving to 2 years of age were still alive at age 13. The taphonomic implications of this are intriguing. Neonate dinosaur remains are rarely recovered, either because they go unnoticed in the field or because their bones were consumed in their entirety or were completely broken down by the environment, hence they were unlikely to survive the vagaries of diagenesis to become fossilized (12, 13, 15). It seems unlikely that such considerations apply to the relatively large juveniles and subadults of North American tyrannosaurs, and yet their remains (even partial remains) are rare (tables S2 to S4) (24, 25). Some have speculated, on the basis of an implicit assumption of a constant rate of mortality, that tyrannosaurs must have rocketed to adult size in a few years or less (25), thereby leaving only a small fraction of development from which juveniles could have contributed to the fossil record. However, this notion is inconsistent with our growth curve (7). Instead, we suggest that these young animals simply had low mortality, just like older juveniles and subadults of most large terrestrial mammals today.

    Midlife increases in mortality rate among extant vertebrates are not uncommon (8, 12, 13, 15). Some of these increases reflect intermittent adverse environmental perturbation or human intervention. Those reflecting life history often coincide with the onset of sexual maturity and/or entrance into the breeding population, at which time the physiological demands of oviposition and fasting, increased injuries and stress from agonistic activity in competition for mates, and heightened exposure to predators take their toll. Notable examples of decreased survival associated with attainment of sexual maturity include some birds (11), large ungulates (12, 26), and marine mammals (16). Given these considerations, it is plausible that the doubling of interval mortality rates and the quadrupling of annual mortality rates predicted between ages 11 and 15 reflect one or more of these same selective factors (Table 1). Horrific cranial bite scars attest that agonistic encounters with conspecifics were commonplace in tyrannosaurs (19). Schweitzer et al. (27) have found medullary bone deposits indicating sexual maturity in a young T. rex. The corresponding developmental stage in A. sarcophagus occurs at 14 to 16 years (fig. S3), approximately the age at which growth rates begin to slow in A. sarcophagus in association with somatic maturity (7). Slowing of somatic growth also signals the onset of sexual maturity in living reptiles (28).

    If A. sarcophagus typically matured no later than 14 to 16 years of age, the survivorship curve indicates that ∼25% of A. sarcophagus hatchlings reached reproductive maturity; the proportion that successfully reproduced is indeterminable. Among this group, few would have had long reproductive life spans because mortality rates escalated thereafter to greater than 23% per year.

    In most long-lived vertebrates, mortality rates accelerate late in life. Such acceleration may reflect the debilitating effects of physiological senescence that promote greater susceptibility to disease, predation, and injury (29, 30). Substantial declines in survival late in life are difficult to document because large sample sizes are required and few older individuals remain to be sampled. Although our samples contained only one or two large individuals, the largest and oldest known T. rex—the 28-year-old FMNH PR 2081—derives from a late (stationary) developmental stage (7) and shows numerous signs of senescence in the form of age-related disease (31). Similarly, the giant 10.1-m A. sarcophagus individual in our analysis is the largest (and presumably oldest) known for the taxon. It also was in the late stationary phase of development (7) and, like FMNH PR 2081, appears to be an outlier in the size distribution (fig. S2) and thus may have been of similar physiological condition at the time of its demise. As is true for the paucity of subadult specimens in museums, the estimated survivorship curve also provides a possible explanation for the rarity of such giants; just 2% of the population lived long enough to attain maximal size and age for the species.

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    Figs. S1 to S4

    Tables S1 to S4


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