On the size distribution of live genera.

@article{Reed2002OnTS,
  title={On the size distribution of live genera.},
  author={William J. Reed and Barry D. Hughes},
  journal={Journal of theoretical biology},
  year={2002},
  volume={217 1},
  pages={
          125-35
        }
}
  • W. Reed, B. Hughes
  • Published 7 July 2002
  • Mathematics
  • Journal of theoretical biology
This article deals with the theoretical size (number of species) distribution of live genera, arising from a simple model of macroevolution in which speciations and extinctions are assumed to occur independently and at random, and in which new genera are formed by the random splitting of existing genera. Mathematically, the distribution is that of the state of a homogeneous birth-and-death process after an exponentially distributed time. An ordinary differential equation for the generating… 

Figures from this paper

Taxon Size Distribution in a Time Homogeneous Birth and Death Process
The number of extant individuals within a lineage, as exemplified by counts of species numbers across genera in a higher taxonomic category, is known to be a highly skewed distribution. Because the
The Distribution of Family Sizes Under a Time-Homogeneous Birth and Death Process
TLDR
It is proposed that the probability distributions of lineage size may have a number of relevant applications to biological problems such as the coalescence of genetic lineages and in predicting the number of species in living and extinct higher taxa, as these systems are special instances of the underlying process analyzed in this article.
Evolutionary dynamics of taxonomic structure
TLDR
Application to living marine molluscs of New Zealand shows that bivalves have a higher relative rate of genus origination than gastropods, and suggests that analysis of living taxonomic distributions may allow inference of macroevolutionary dynamics even without a fossil record.
An Asymptotic Result in a Pure Birth Stochastic Process
The F1 2 hypergeometric function appears in a wide variety of applications in probability and statistics. This article is motivated from an important application that arises in stochastic processes.
POWER-LAW DISTRIBUTIONS FROM EXPONENTIAL PROCESSES : AN EXPLANATION FOR THE OCCURRENCE OF LONG-TAILED DISTRIBUTIONS IN BIOLOGY AND ELSEWHERE
TLDR
This work considers both tree-like networks, appropriate in biological applications, and networks in which closed loops can appear, which model communication networks and networks of human sexual interactions, and a randomly growing network, with the state of a random node observed.
Model for macroevolutionary dynamics
TLDR
Fitted extinction rates for large clades are close to speciation rates, consistent with high rates of species turnover and the relatively slow change in diversity observed in the fossil record, and the SEO model generally supports the consistency of generic boundaries based on morphological differences between species and provides a comparator for rates of lineage splitting and morphological evolution.
Modern and Cretaceous–Cenozoic Diversification of Angiosperms
TLDR
The performed modeling of the S/G ratio in families has shown a satisfactory correspondence between the observed and calculated number of species within a wide iteration range only when the dynamic factor of extinction was applied.
New Analytic Results for Speciation Times in Neutral Models
TLDR
An analytic way—as opposed to the common simulation approach—for calculating the speciation times in a reconstructed phylogenetic tree is developed, which is useful for the model with extinction, since simulations of birth-death processes which are conditioned on obtaining n extant species today are quite delicate.
On the need to renew the taxonomic system of the candoninae (non-marine Ostracoda, Crustacea). Reflexions from an analysis of data using the Yule Process
TLDR
The taxonomic system currently accepted for that subfamily must be renewed including: the re-examination of the diagnostic criteria used a restatement of the taxonomic meaning of the species-rich lineages endemic to ancient lakes, the increased cooperation between neontologists and palaeontologists to produce common-based taxonomic criteria, the addition of new sources of taxonomic information (morphometric, molecular, etc.) and the adoption of ideas and/or methods specific to phylogenetic systematics.
...
1
2
3
...

References

SHOWING 1-10 OF 23 REFERENCES
Mathematical models of cladogenesis
TLDR
This work states that the most useful equations based on the homogeneous model, which provides a framework for describing the history of taxonomic diversity (clade shape) and other aspects of larger evolutionary patterns, are those that specify change, regular or episodic, in speciation and extinction probabilities.
A simple explanation for taxon abundance patterns.
  • J. Chu, C. Adami
  • Environmental Science
    Proceedings of the National Academy of Sciences of the United States of America
  • 1999
TLDR
The model predicts-with no free parameters-the rank-frequency distribution of the number of families in fossil marine animal orders obtained from the fossil record and finds that near power law distributions are statistically almost inevitable for taxa higher than species.
The fractal geometry of evolution.
TLDR
This study shows that the fractal geometry of taxonomic systems (Burlando, 1990) reflects self-similar evolutionary pattern, thus limiting the importance of species within the evolutionary context in favour of a more comprehensive view of life diversification.
The Fractal Dimension of Taxonomic Systems
Stochastic models and descriptive statistics for phylogenetic trees, from Yule to today
TLDR
A probabilist’s musings on what dominates the macroevolutionary process (adaptive radiation; “neutral” evolution) and how a simple stochastic model predicts the observed pattern of imbalance.
Extinction: bad genes or bad luck?
  • D. Raup
  • Environmental Science
    New scientist
  • 1991
TLDR
If extinction is selective, the time homogeneous model suggests that trilobites had species durations 14 to 28 percent shorter than normal for Paleozoic manne invertebrates, which may be because extinction is, in fact, selective.
On the times of births in a linear birthprocess
If Sj,, S2, . . . are the times of successive births in a pure birth-process with linear birthrate and i > 0 individuals initially, then given that there are k > 0 births in (0, /), the random
Large-scale processes and the Asian bias in species diversity of temperate plants
TLDR
The most probable cause of the EAS-ENA anomaly in diversity is the extreme physiographical heterogeneity of temperate eastern Asia, especially compared with eastern North America, which in conjunction with climate and sea-level change has provided abundant opportunities for evolutionary radiation through allopatric speciation.
A comparative summary of genetic distances in the vertebrates from the mitochondrial cytochrome b gene.
TLDR
There is rather poor equivalency of taxonomic rank across some of the vertebrates, by the yardstick of genetic divergence in this mtDNA gene, as well as genetic distances in allozymes.
THE NAME OF THE ROSE: A REVIEW OF IDEAS ON THE EUROPEAN BIAS IN ANGIOSPERM CLASSIFICATION.
TLDR
It is concluded that, to a remarkable degree, practising taxonomists ignore conceptual or philosophical difficulties and are able to co-operate, although their leisurely and arcane procedures may not measure up to the'information explosion'.
...
1
2
3
...