- School of Mathematics and Statistics - Research Publications
School of Mathematics and Statistics - Research Publications
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ItemTheoretical size distribution of fossil taxa: analysis of a null modelReed, WJ ; Hughes, BD (BIOMED CENTRAL LTD, 2007)BACKGROUND: This article deals with the theoretical size distribution (of number of sub-taxa) of a fossil taxon arising from a simple null model of macroevolution. MODEL: New species arise through speciations occurring independently and at random at a fixed probability rate, while extinctions either occur independently and at random (background extinctions) or cataclysmically. In addition new genera are assumed to arise through speciations of a very radical nature, again assumed to occur independently and at random at a fixed probability rate. CONCLUSION: The size distributions of the pioneering genus (following a cataclysm) and of derived genera are determined. Also the distribution of the number of genera is considered along with a comparison of the probability of a monospecific genus with that of a monogeneric family.
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ItemThe density of the time to ruin for a Sparre Andersen process with Erlang arrivals and exponential claimsDICKSON, D. ; HUGHES, B. ; ZHANG, L. ( 2005)