Biomedical subjects

William J Reed

Publications and source records attributed to William J Reed.

4 recordsLinked to original sources

PubMed2004

A model explaining the size distribution of gene and protein families.

This article deals with the theoretical size distribution of gene and protein families in complete genomes. A simple evolutionary model for the development of such families in which genes in a family are formed or selected against independently and at random, and in which new families are formed by the random splitting of existing families, is used to derive the resulting size distribution. Mathematically this turns out to be the distribution of the state of a homogeneous birth-and-death process after an exponentially distributed time, which it is shown will under certain conditions exhibit the power-law behaviour observed for gene and protein family sizes.

Algorithms↗

PubMed2003

Stochastically evolving networks.

We discuss a class of models for the evolution of networks in which new nodes are recruited into the network at random times, and links between existing nodes that are not yet directly connected may also form at random times. The class contains both models that produce "small-world" networks and less tightly linked models. We produce both trees, appropriate in certain biological applications, and networks in which closed loops can appear, which model communication networks and networks of human sexual interactions. One of our models is closely related to random recursive trees, and some exact results known in that context can be exploited. The other models are more subtle and difficult to analyze. Our analysis includes a number of exact results for moments, correlations, and distributions of coordination number and network size. We report simulations and also discuss some mean-field approximations. If the system has evolved for a long time and the state of a random node (which thus has a random age) is observed, power-law distributions for properties of the system arise in some of these models.

Journal Article↗

PubMed2002

From gene families and genera to incomes and internet file sizes: why power laws are so common in nature.

We present a simple explanation for the occurrence of power-law tails in statistical distributions by showing that if stochastic processes with exponential growth in expectation are killed (or observed) randomly, the distribution of the killed or observed state exhibits power-law behavior in one or both tails. This simple mechanism can explain power-law tails in the distributions of the sizes of incomes, cities, internet files, biological taxa, and in gene family and protein family frequencies.

Journal Article↗

PubMed2002

On the size distribution of live genera.

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 function of the distribution is derived and solved and a recurrence relation for computing the probabilities in the distribution presented. Some properties of the distribution, including asymptotic behaviour, are examined and the distribution of the time since establishment of a genus of a given size derived. Fitting the distribution to empirical taxon size distributions by maximum likelihood is discussed and two examples are presented.

Animals↗