Extinction and the loss of evolutionary history

Science

Volumn 278, Issue 5338, 1997, Pages 692-694

  Nee, Sean ^a   May, Robert M ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

DNA;

EVOLUTION; EVOLUTIONARY HISTORY; EXTINCTION; SPECIES LOSS;

ADAPTATION; ALGORITHM; ARTICLE; EVOLUTION; PHYLOGENY; PRIORITY JOURNAL; SPECIES DIFFERENTIATION; TAXONOMY;

ANIMALS; ECOSYSTEM; EVOLUTION; MATHEMATICS; POPULATION DENSITY;

EID: 0030680940     PISSN: 00368075     EISSN: None     Source Type: Journal    
DOI: 10.1126/science.278.5338.692     Document Type: Article

References (35)

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11. All four equations are derived by fixing the times between nodes at the mean times for the appropriate probability distributions. The random sampling models exploit coalescence theory of gene genealogies from population genetics to provide the probability distributions of the times between nodes in the tree. For a random sample from a tree that has been growing exponentially, this probability distribution is implicit in a simulation algorithm presented by M. Slatkin and R. Hudson [Genetics 129, 555 (1991)] and made explicit by S. Nee, R. M. May, and P. H. Harvey [Philos. Trans. R. Soc. London Ser. B 349, 25 (1994)]. The expression for the maximizing algorithm treats the exponentially growing population as a birth process. The expressions for the constant size models are derived in a natural way by using the well-known distribution of coalescence times from population genetics, for example, J. Felsenstein, Genet. Res. Cambridge 59, 139 (1992), which is discussed in a macroevolutionary context, most relevant for our purposes, in (4), and by J. Hey [Evolution 46, 627 (1992)]. Hence, Eqs. 1 and 3 are derived as follows. For both the entire tree with n species and for the pruned tree of k randomly chosen species, the amount of time between nodes i and i + 1 is proportional to 1/i(i + 1). (The constants of proportionality all cancel so are not made explicit.) As there are i + 1 lineages between these nodes, this interval contributes an amount (i + 1)/i(i + 1) to the total evolutionary history. So the total amount of evolutionary history of the pruned tree is (Formula Presented) In exactly the same fashion, we find that the total amount of evolutionary history of the entire tree is ln (n - 1) + C. Equation 1 in the text now follows immediately. For the derivation of Eq. 3, recall that the optimizing algorithm selects the first k - 1 nodes of the tree, defining the k species to be saved. The amount of evolutionary history contained in the pruned tree consists of the sum of (i) the amount of evolutionary history contained in the tree from its root up to the appearance of the k + 1 lineage and (ii) k multiplied by the amount of time between this event and the present. That is, (Formula Presented) The expression in the text now follows immediately.
12. All four equations are derived by fixing the times between nodes at the mean times for the appropriate probability distributions. The random sampling models exploit coalescence theory of gene genealogies from population genetics to provide the probability distributions of the times between nodes in the tree. For a random sample from a tree that has been growing exponentially, this probability distribution is implicit in a simulation algorithm presented by M. Slatkin and R. Hudson [Genetics 129, 555 (1991)] and made explicit by S. Nee, R. M. May, and P. H. Harvey [Philos. Trans. R. Soc. London Ser. B 349, 25 (1994)]. The expression for the maximizing algorithm treats the exponentially growing population as a birth process. The expressions for the constant size models are derived in a natural way by using the well-known distribution of coalescence times from population genetics, for example, J. Felsenstein, Genet. Res. Cambridge 59, 139 (1992), which is discussed in a macroevolutionary context, most relevant for our purposes, in (4), and by J. Hey [Evolution 46, 627 (1992)]. Hence, Eqs. 1 and 3 are derived as follows. For both the entire tree with n species and for the pruned tree of k randomly chosen species, the amount of time between nodes i and i + 1 is proportional to 1/i(i + 1). (The constants of proportionality all cancel so are not made explicit.) As there are i + 1 lineages between these nodes, this interval contributes an amount (i + 1)/i(i + 1) to the total evolutionary history. So the total amount of evolutionary history of the pruned tree is (Formula Presented) In exactly the same fashion, we find that the total amount of evolutionary history of the entire tree is ln (n - 1) + C. Equation 1 in the text now follows immediately. For the derivation of Eq. 3, recall that the optimizing algorithm selects the first k - 1 nodes of the tree, defining the k species to be saved. The amount of evolutionary history contained in the pruned tree consists of the sum of (i) the amount of evolutionary history contained in the tree from its root up to the appearance of the k + 1 lineage and (ii) k multiplied by the amount of time between this event and the present. That is, (Formula Presented) The expression in the text now follows immediately.
13. All four equations are derived by fixing the times between nodes at the mean times for the appropriate probability distributions. The random sampling models exploit coalescence theory of gene genealogies from population genetics to provide the probability distributions of the times between nodes in the tree. For a random sample from a tree that has been growing exponentially, this probability distribution is implicit in a simulation algorithm presented by M. Slatkin and R. Hudson [Genetics 129, 555 (1991)] and made explicit by S. Nee, R. M. May, and P. H. Harvey [Philos. Trans. R. Soc. London Ser. B 349, 25 (1994)]. The expression for the maximizing algorithm treats the exponentially growing population as a birth process. The expressions for the constant size models are derived in a natural way by using the well-known distribution of coalescence times from population genetics, for example, J. Felsenstein, Genet. Res. Cambridge 59, 139 (1992), which is discussed in a macroevolutionary context, most relevant for our purposes, in (4), and by J. Hey [Evolution 46, 627 (1992)]. Hence, Eqs. 1 and 3 are derived as follows. For both the entire tree with n species and for the pruned tree of k randomly chosen species, the amount of time between nodes i and i + 1 is proportional to 1/i(i + 1). (The constants of proportionality all cancel so are not made explicit.) As there are i + 1 lineages between these nodes, this interval contributes an amount (i + 1)/i(i + 1) to the total evolutionary history. So the total amount of evolutionary history of the pruned tree is (Formula Presented) In exactly the same fashion, we find that the total amount of evolutionary history of the entire tree is ln (n - 1) + C. Equation 1 in the text now follows immediately. For the derivation of Eq. 3, recall that the optimizing algorithm selects the first k - 1 nodes of the tree, defining the k species to be saved. The amount of evolutionary history contained in the pruned tree consists of the sum of (i) the amount of evolutionary history contained in the tree from its root up to the appearance of the k + 1 lineage and (ii) k multiplied by the amount of time between this event and the present. That is, (Formula Presented) The expression in the text now follows immediately.
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35. S.N. acknowledges the Biotechnology and Biological Sciences Research Council (grant G04872). R.M.M. acknowledges the Royal Society of London. We thank D. Erwin for his stimulating comments.