The fossil record of evolution: Data on diversification and extinction

Understanding of the evolution of complex life, and of the roles that changing terrestrial and extraterrestrial environments played in life's history, is dependent upon synthetic knowledge of the fossil record. Paleontologists have been describing fossils for more that two centuries. However, much of this information is dispersed in monographs and journal articles published throughout the world. Over the past several years, this literature was surveyed, and a data base on times of origination and extinction of fossil genera was compiled. The data base, which now holds approximately 32,000 genera, covers all taxonomic groups of marine animals, incorporates the most recent taxonomic assignments, and uses a detailed global time framework that can resolve originations and extinctions to intervals averaging three million years in duration. These data can be used to compile patterns of global biodiversity, measure rates of taxic evolution, and test hypotheses concerning adaptive radiations, mass extinctions, etc. Thus far, considerable effort was devoted to using the data to test the hypothesis of periodicity of mass extinction. Rates of extinction measured from the data base have also been used to calibrate models of evolutionary radiations in marine environments. It was observed that new groups, or clades of animals (i.e., orders and classes) tend to reach appreciable diversity first in nearshore environments and then to radiate in more offshore environments; during decline, these clades may disappear from the nearshore while persisting in offshore, deep water habitats. These observations have led to suggestions that there is something special about stressful or perturbed environments that promotes the evolution of novel kinds of animals that can rapidly replace their predecessors. The numerical model that is being investigated to study this phenomenon treats environments along onshore-offshore gradients as if they were discrete habitats. Other aspects of this investigation are presented

The fossil record of evolution: Data on diversification and extinction

The two principle efforts include: (1) a compilation of a synoptic, mesoscale data base on times of origination and extinction of animal genera in the oceans over the last 600 million years of geologic time; and (2) an analysis of statistical patterns in these data that relate to the diversification of complex life and to the occurrence of mass extinctions, especially those that might be associated with extraterrestrial phenomena. The data base is unique in its taxonomic scope and detail and in its temporal resolution. It is a valuable resource for investigating evolutionary expansions and extinctions of complex life

Dynamics of clade diversification on the morphological hypercube

Understanding the relationship between taxonomic and morphological changes is important in identifying the reasons for accelerated morphological diversification early in the history of animal phyla. Here, a simple general model describing the joint dynamics of taxonomic diversity and morphological disparity is presented and applied to the data on the diversification of blastozoans. I show that the observed patterns of deceleration in clade diversification can be explicable in terms of the geometric structure of the morphospace and the effects of extinction and speciation on morphological disparity without invoking major declines in the size of morphological transitions or taxonomic turnover rates. The model allows testing of hypotheses about patterns of diversification and estimation of rates of morphological evolution. In the case of blastozoans, I find no evidence that major changes in evolutionary rates and mechanisms are responsible for the deceleration of morphological diversification seen during the period of this clade's expansion. At the same time, there is evidence for a moderate decline in overall rates of morphological diversification concordant with a major change (from positive to negative values) in the clade's growth rate.Comment: 8 pages, Latex, 2 postscript figures, submitted to Proc.R.Soc.Lond.

Entropic Sampling and Natural Selection in Biological Evolution

With a view to connecting random mutation on the molecular level to punctuated equilibrium behavior on the phenotype level, we propose a new model for biological evolution, which incorporates random mutation and natural selection. In this scheme the system evolves continuously into new configurations, yielding non-stationary behavior of the total fitness. Further, both the waiting time distribution of species and the avalanche size distribution display power-law behaviors with exponents close to two, which are consistent with the fossil data. These features are rather robust, indicating the key role of entropy

A model of macro-evolution as a branching process based on innovations

We introduce a model for the evolution of species triggered by generation of novel features and exhaustive combination with other available traits. Under the assumption that innovations are rare, we obtain a bursty branching process of speciations. Analysis of the trees representing the branching history reveals structures qualitatively different from those of random processes. For a tree with n leaves, the average distance of leaves from root scales as (log n)^2 to be compared to log n for random branching. The mean values and standard deviations for the tree shape indices depth (Sackin index) and imbalance (Colless index) of the model are compatible with those of real phylogenetic trees from databases. Earlier models, such as the Aldous' branching (AB) model, show a larger deviation from data with respect to the shape indices.Comment: 16 pages, 8 figures, 1 table, v2: minor corrections and addition

Rank Statistics in Biological Evolution

We present a statistical analysis of biological evolution processes. Specifically, we study the stochastic replication-mutation-death model where the population of a species may grow or shrink by birth or death, respectively, and additionally, mutations lead to the creation of new species. We rank the various species by the chronological order by which they originate. The average population N_k of the kth species decays algebraically with rank, N_k ~ M^{mu} k^{-mu}, where M is the average total population. The characteristic exponent mu=(alpha-gamma)/(alpha+beta-gamma)$ depends on alpha, beta, and gamma, the replication, mutation, and death rates. Furthermore, the average population P_k of all descendants of the kth species has a universal algebraic behavior, P_k ~ M/k.Comment: 4 pages, 3 figure

The fossil record of early tetrapods: worker effort and the end-Permian mass extinction

It is important to understand the quality of the fossil record of early tetrapods (Tetrapoda, minus Lissamphibia and Amniota) because of their key role in the transition of vertebrates from water to land, their dominance of terrestrial faunas for over 100 million years of the late Palaeozoic and earlyMesozoic, and their variable fates during the end−Permian mass extinction. The first description of an early tetrapod dates back to 1824, and since then discoveries have occurred at a rather irregular pace, with peaks and troughs corresponding to some of the vicissitudes of human history through the past two centuries. As expected, the record is dominated by the well−sampled sedimentary basins of Europe and North America, but finds from other continents are increasing rapidly. Comparisons of snapshots of knowledge in 1900, 1950, and 2000 show that discovery of new species has changed the shape of the species−level diversification curve, contrary to earlier studies of family−level taxa. There is, however, little evidence that taxon counts relate to research effort (as counted by numbers of publications), and there are no biasing effects associated with differential study of different time intervals through the late Palaeozoic and Mesozoic. In fact, levels of effort are apparently not related to geological time, with no evidence that workers have spent more time on more recent parts of the record. In particular, the end−Permian mass extinction was investigated to determine whether diversity changes through that interval might reflect worker effort: it turns out that most records of early tetrapod taxa (when corrected for duration of geological series) occur in the Lower Triassic

A soluble model of evolution and extinction dynamics in a rugged fitness landscape

We consider a continuum version of a previously introduced and numerically studied model of macroevolution (PRL 75, 2055, (1995)) in which agents evolve by an optimization process in a rugged fitness landscape and die due to their competitive interactions. We first formulate dynamical equations for the fitness distribution and the survival probability. Secondly we analytically derive the $t^{-2}$ law which characterizes the life time distribution of biological genera. Thirdly we discuss other dynamical properties of the model such as the rate of extinction and conclude with a brief discussion.Comment: 6 pages LaTeX source with 2 figures. Submitted to PRL (Jan. 97

The influence of environmental forcing on biodiversity and extinction in a resource competition model

In this paper, we study a model of many species that compete, directly or indirectly, for a pool of common resources under the influence of periodic, stochastic, and/or chaotic environmental forcing. Using numerical simulations, we find the number and sequence of species going extinct when the community is initially packed with a large number of species of random initial densities. Thereby, any species with a density below a given threshold is regarded to be extinct