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Volumn 283, Issue 5406, 1999, Pages 1310-1314

Evolutionary and preservational constraints on origins of biologic groups: Divergence times of eutherian mammals

Author keywords

[No Author keywords available]

Indexed keywords

EVOLUTION;

EID: 0033605215     PISSN: 00368075     EISSN: None     Source Type: Journal    
DOI: 10.1126/science.283.5406.1310     Document Type: Article
Times cited : (208)

References (87)
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    • We evaluate divergence times rather than branching topology. We are not concerned with determining whether the relative order of hypothesized origins is consistent with observed first appearances [M. A. Norell and M. J. Novacek, Science 255, 1690 (1992); J. P. Huelsenbeck, Paleobiology 20, 470 (1994); P. J. Wagner, ibid. 21, 153 (1995); R. Hitchin and M. J. Benton, ibid. 23, 20 (1997)]. Rather, we are interested in cases in which the absolute timing of postulated origins and of observed origins are already known to disagree.
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    • note
    • n-j if p ≠ q The last equation is a correction of equation (A18) from (9). Let P(≥ n, t, a) be the probability that diversity is greater than or equal to n lineages at time t, given that it is equal to a lineages at t = 0. Then (equation presented) Let t and T be two points in time such that t < T, and let the group have diversity equal to one lineage at t = 0. Let P(n, t, s, T) be the probability that diversity is exactly equal to n lineages at time t, given that the group survives at least until time T. Let P(n,t,N,T) be the probability that diversity is exactly equal to n lineages at time t, given that diversity is exactly equal to N lineages at time T. And let P(n,t ≥ N, T) be the probability that diversity is exactly equal to n lineages at time t, given that diversity is greater than or equal to N lineages at time T. Then, by the rules of conditional probability, P(n,t,s,T) = P(n,t,1) · P(s,T - t,n)/P(s,T,1); P(n.t.N,T) = P(n,t,1) · P(N,T - t,n)/P(N,T,1); and P(n,t, ≥ N,T) = P(n,t,1) · P(≥ N,T - t,n)/P(≥ N,T,1) The corresponding expected (mean) diversities at time t are given by (equation presented) and (equation presented)
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    • We thank J. Alroy, R. J. Asher, J. Flynn, D. Jablonski, C. R. Marshall, R. R. Rogers, P. J. Wagner, and J. R. Wible for discussion, and R. H. De Simone, D. Jablonski, C. R. Marshall, D. M. Raup, and two anonymous referees for reviews. This research was supported by NSF (grant EAR-9506568) and NASA (grant NAGW-1693).


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