Biogeographical basis of recent phenotypic divergence among birds: a global study of subspecies richness.

Theory predicts that biogeographic factors should play a central role in promoting population divergence and speciation. Previous empirical studies into biogeography and diversification have been relatively restricted in terms of the geographical area, phylogenetic scope, and the range of biogeographic factors considered. Here we present a global analysis of allopatric phenotypic divergence (measured as subspecies richness) across more than 9600 bird species. The main aim of this study was to examine the extent to which biogeographical factors can explain patterns of phenotypic divergence. Analysis of the taxonomic distribution of subspecies among species suggests that subspecies formation and extinction have occurred at a considerably faster rate than has species formation. However, the observed distribution departs from the expectation under a random birth-death model of diversification. Across 19 phylogenetic trees, we find no significant linear relationship between species age and subspecies richness, implying that species age is a poor predictor of subspecies richness. Both subspecies richness and subspecies diversification rate are found to exhibit low phylogenetic signal, meaning that closely related species do not tend to possess similar numbers of subspecies. As predicted by theory, high subspecies richness was associated with large breeding range size, island dwelling, inhabitation of montane regions, habitat heterogeneity, and low latitude. Of these factors, breeding range size was the variable that explained the most variation. Unravelling whether species that have invaded previously glacial areas have more or fewer subspecies than expected proves to be complicated due to a covariation between the postglacial colonization, latitude, geographic range size, and subspecies richness. However, the effect of postglacial colonization on subspecies richness appears to be small. Mapping the distribution of species' subspecies richness globally reveals geographical patterns that correspond to many of the predictions of the statistical models, but may also reflect geographical variation in taxonomic practice. Overall, we demonstrate that biogeographic models can explain about 30% of the global variation in subspecies richness in birds.

Theoretical size distribution of fossil taxa: analysis of a null model.

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.

A stochastic model for the spread of a sexually transmitted disease which results in a scale-free network.

A stochastic model for the spread of a sexually transmitted disease (STD) is presented. To reflect varying degrees of promiscuity among individuals it is assumed that the infectivity of any infected individual is proportional to the number of previous contacts the individual has had with other infected individuals. In both the simple single-sex model and in the more complex two-sex model, the tree graphs of the infection exhibit scale-free network behaviour (i.e. power-law behaviour in the upper tail of the degree distribution). The distributions of the size of the infection and of the ring number (distance from the original source of the infection) are determined.

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.

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.

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.

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.