Evolutionary and Preservational Constraints on Origins of Biologic Groups: Divergence Times of Eutherian Mammals

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Science  26 Feb 1999:
Vol. 283, Issue 5406, pp. 1310-1314
DOI: 10.1126/science.283.5406.1310


Some molecular clock estimates of divergence times of taxonomic groups undergoing evolutionary radiation are much older than the groups' first observed fossil record. Mathematical models of branching evolution are used to estimate the maximal rate of fossil preservation consistent with a postulated missing history, given the sum of species durations implied by early origins under a range of species origination and extinction rates. The plausibility of postulated divergence times depends on origination, extinction, and preservation rates estimated from the fossil record. For eutherian mammals, this approach suggests that it is unlikely that many modern orders arose much earlier than their oldest fossil records.

The molecular clock hypothesis (1) sometimes yields estimated times of origin of major biologic groups that substantially predate their oldest known occurrences in the fossil record, especially when massive evolutionary radiations have occurred (2–7). A large discrepancy between a group's origin and its oldest observed fossil occurrence may imply an extraordinarily incomplete fossil record (3). If lineages continually branch, with few daughter branches surviving for tens of millions of years (8–10), much more diversity may be missing than suggested by a simple tally of gaps between postulated origins and oldest fossil appearances of lineages extant today (Fig. 1). Thus, postulated early divergence times may implicitly require much lower rates of origination and extinction than measured in the fossil record or unusually low rates of preservation during certain intervals of geologic time. To test divergence times, we must therefore have good estimates of rates of taxonomic evolution and of fossil preservation. Here we build upon the standard birth-death model (8, 9) that has been applied to a range of paleobiological problems (9,11–13). To test the specific case of eutherian (placental) mammals, we use conservative hypotheses of diversity history, assuming monotonic increase in species diversity from the postulated time of origin of the taxonomic group to the time it is first observed in the fossil record (Fig. 2), but the approach is more general.

Figure 1

Hypothetical illustration of the missing diversity problem. Species 1 through 5 comprise the extant part of the group of interest, whose outgroup is O. Solid lines show the known fossil record. (A) Relatively even distribution of branching events. (B) Clustering of some branching events, as is often thought to occur in the early stages of an evolutionary radiation (41). In both cases, the tree topology, the length of the known fossil record, and the age of the common ancestor to the outgroup and the group of interest are the same. In (B), however, the interval of missing history is shorter and the sum of missing species durations is lower.

Figure 2

Comparison of expected diversity in models (13), illustrated with q = 0.25 Lmy−1, T = 50 My, N = 10 species, and p = q +ln(N)/T, values similar to those in the empirical case we examine. Dotted line is exponential growth. Short-dashed line is diversity before time T conditioned upon survival of group to time T. Long-dashed line is diversity before time T conditioned upon diversity exactly equal to N at time T. Solid line is diversity before time T conditioned upon diversity greater than or equal to N at time T.

The question of interest is to estimate how low the rate of fossil preservation must be for all species of a group to escape detection over a specified interval of geologic time. To incorporate incomplete preservation of fossil taxa into our branching model, we treat preservation as a time-homogeneous Poisson process (14–17). Because the branching model explicitly considers only the divergence of species, not their morphological evolution, we assume that morphological divergence occurs soon enough after lineage splitting so that daughter species, if discovered, would be recognized as distinct from their ancestors. We contrast two alternatives: total lack of preservation and preservation at least once. We consider a hypothesis of missing diversity plausible if the probability of complete nonpreservation of the group is at least 0.5. This is a conservative value.

We estimate the sum of missing species durations implied by a hypothesized divergence time. This sum increases with (i) the length of missing history, (ii) the diversity at the end of this interval, and (iii) the extinction rate in most diversity models (Fig. 3) (13, 18). Increases in all three parameters demand more extinct species evolving before the time that the group is first observed. Because the length of missing history and the minimal diversity at the group's first fossil appearance are given by the hypothesized time of origin and by observed fossils, the parameters that need to be constrained are extinction rate and preservation rate. For a group's summed species durations to be unobserved, the extinction rate, the preservation rate, or both must fall below some threshold (Fig. 3). We can thus place upper probabilistic bounds on the rates consistent with the hypothesis of early origins and unobserved diversity.

Figure 3

Analysis of the hypothesis that many lineages of modern eutherians originated before the Tertiary (4,13, 17). T is taken to be 64 My,N is taken to be 9 species, and q is taken to be 0.25 Lmy−1 (see text). (A to C) Exponential diversity model; (D to F) diversity before time T conditioned upon minimal diversity ofN at time T; other diversity models yield results between these extremes. (A and D) Variation in T withN = 9 species and q = 0.25 Lmy−1. (B and E) Variation in N withT = 64 My and q = 0.25 Lmy−1. (C and F) Variation in q withT = 64 My and N = 9 species. Left-hand ordinate (solid line), expected sum of species durations, S(13). Right-hand ordinate (dashed line), preservation rate required to yield a probability of complete nonpreservation exactly equal to 0.5 (17). Shaded area beneath corresponds to probabilities of nonpreservation greater than 0.5, and thus to combinations of preservation rate and value of abscissa for which the corresponding amount of missing diversity is plausible. For example, in (D), q = 0.25 Lmy−1 and N= 9 species. If T = 40 My, then S = 918 Lmy. This value of T implies thatr max = −ln(0.5)/918 = 0.0008 Lmy−1. For this value of r, any value ofT less than 40 My yields a probability of nonpreservation of the group greater than 0.5 (the shaded region), and, for this value ofT, any value of r less thanr max yields a probability of nonpreservation of the group greater than 0.5. As T increases so doesS, and thus an ever smaller value of r is required to make group nonpreservation likely. The same is true for an increase in N with T and q fixed (B and E) or an increase in q with T andN fixed (C and F).

The known fossil record of modern eutherian mammals has a concentration of ordinal first appearances during the early Tertiary (19–21). There are no unequivocal, pre-Tertiary occurrences of modern eutherian orders or supraordinal groupings (22), and the low resolution of morphological and molecular phylogenies (19, 23) suggests that the orders arose within a short period of time, whether within or before the Tertiary. Some molecular clock calculations nevertheless suggest ordinal origins at widely spaced times during the Cretaceous, as much as 129 ± 18.5 million years (My) ago (4). This implies a missing history of 64 My for the group and a minimal diversity of nine species (the number of orders or supraordinal groupings) at the end of this interval (Table 1 and Fig. 3). Nine species is an absolute lower bound, as it treats each major lineage as if it consisted of a single species. If the extinction rate were on the order of 0.1 per lineage-million-years (Lmy), a low value for mammals (14, 24, 25), then summed species durations would be on the order of 1000 Lmy (13). This large a sum of missing durations demands a preservation rate on the order of 7 × 10−4 Lmy−1 or lower (17). If we take the nine lineages individually and assume no extinction or origination, then we have the absolutely minimal sum of missing durations of these lineages (the sum of postulated gaps), or 346 Lmy. This still requires a preservation rate of 2 × 10−3 Lmy−1 or lower. Other treatments of the hypothesis, including several in which we minimized summed species durations by assuming no extinction and several in which we accepted that the modern eutherian fossil record starts at 85 My ago, which implies fewer than nine lineages at the start of the fossil record (4, 26), yield comparable results (Table 1 and Fig. 3).

Table 1

Analysis of the hypothesis that many modern eutherian lineages arose before the Tertiary (4,13, 17). N is the minimal number of species present at the time the group is first found in the fossil record, T is the time between the postulated origin of the group and its first fossil appearance, q is the extinction rate, S is the expected summed species durations,r max is the preservation rate that yields a probability of 0.5 that S will completely escape preservation, and P is the probability that Swill completely escape preservation if r = 0.03 Lmy−1 (see text) (that is, P =e −0.03 S). For the bottom part of the table, S is the grand sum of summed species durations of the individual lineages. See (13) for exponential (E) and conditional (C) diversity models; the latter conditions upon minimal diversity of N at time T. Results of the other models (13) are within these extremes. We do not consider the “star phylogeny” model, in which all extant lineages diverge at the origin of the group, because it is inconsistent with the hypothesis we are testing. That model yields even greater summed species durations than those we present.

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Estimated preservation rates for Cenozoic mammals (14,24) are at least two orders of magnitude higher than those required by the early-origins hypothesis, but one could expect that Cenozoic rates overestimate Cretaceous values: Cretaceous mammals were small (mostly under ∼2 kg in body mass), whereas many Cenozoic species were larger (27). We therefore used known Late Cretaceous mammals to measure preservation rate. Because there are no unequivocal modern eutherians in the Cretaceous, we measured preservation and extinction rates for Late Cretaceous species in all other mammal groups known. We estimate that the extinction rate for Late Cretaceous mammals is ∼0.25 ± 0.034 Lmy−1, lower than observed Cenozoic rates (14, 24,25), and that the preservation rate is ∼0.03 ± 0.0038 to ∼0.06 ± 0.0086 Lmy−1 (28).

This preservation rate is lower than similarly derived estimates for Cenozoic mammals (14, 24, 29) but is higher than the rates required by the hypothesis of missing eutherian diversity (Table 1). Even with the most generous treatment of the hypothesis, the preservation rate required is about an order of magnitude lower than our estimates, and the probability of complete nonpreservation is only 0.02 (Table 1). We therefore find it difficult to support an extensive missing history of modern eutherians. Only if most of the divergences occurred within the last few million years of the Cretaceous, implying a long lag after the postulated origin of modern eutherians (4), could one support pre-Tertiary divergences of modern eutherian lineages (30) (Figs. 1B and 3D).

Several hypotheses could explain the discrepancy between our results and the postulate of missing eutherian history: (i) Cretaceous members of the modern eutherian orders are preserved and described, but they are not recognized because they are so primitive and lack most diagnostic features (3). This requires both that morphological evolution be largely decoupled from lineage splitting and molecular evolution and that eutherians experienced much lower rates of morphological change through the Cretaceous than during the Cenozoic, two conditions that may be testable. (ii) Modern eutherian lineages existed through the Cretaceous, but their preservation rates were generally lower than those of species in other mammal groups. This difference in preservation rates would have to be more than an order of magnitude, for which we can offer no support (31). (iii) Modern eutherian lineages diversified in regions that have no known Late Cretaceous mammals (such as Africa, Australia, and Antarctica) and suddenly dispersed widely during the early Tertiary. This “Garden of Eden” hypothesis is testable with intensive exploration of the fossil record of the regions in question (32). (iv) The hypothesis of extensive missing history is wrong, because rates of molecular evolution are heterogeneous among lineages (33,34) or, more importantly, over time (7,33–37). If, as sometimes suggested, molecular evolutionary rates speed up during times of evolutionary radiation (7,33, 36, 37), then divergences during a Tertiary radiation might spuriously appear to have occurred earlier, especially if, as in (4), the molecular clock is calibrated with lineages that diverged long before the Tertiary (synapsids and diapsids), in what appears not to have been a remarkable radiation. This possibility, which is testable (38), is consistent with Kumar and Hedges's (4) analysis of major vertebrate lineages, which shows that estimated divergence times and oldest fossil occurrences agree fairly well for many gradually diversifying higher taxa but not for the rapidly diversifying, extant eutherian orders.

Our branching model approach is readily applicable to other cases, such as the postulated origins of a number of animal phyla some half-billion years before the Cambrian (2, 3) and the postulated origins of extant groups of flowering plants tens of millions of years before their oldest fossils (6,7). The main value of this approach is that it maps out a field of preservation rates and rates of taxonomic evolution that can be measured and compared to hypothesized divergence times. Because these rates can be estimated directly with empirical data from the fossil record (14, 16, 24,25), one can explicitly test an evolutionary hypothesis and its implications regarding rates of morphological, molecular, and taxonomic evolution.

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