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

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

A Burgessian critique of nominalistic tendencies in contemporary mathematics and its historiography

We analyze the developments in mathematical rigor from the viewpoint of a Burgessian critique of nominalistic reconstructions. We apply such a critique to the reconstruction of infinitesimal analysis accomplished through the efforts of Cantor, Dedekind, and Weierstrass; to the reconstruction of Cauchy's foundational work associated with the work of Boyer and Grabiner; and to Bishop's constructivist reconstruction of classical analysis. We examine the effects of a nominalist disposition on historiography, teaching, and research.Comment: 57 pages; 3 figures. Corrected misprint

Ten Misconceptions from the History of Analysis and Their Debunking

The widespread idea that infinitesimals were "eliminated" by the "great triumvirate" of Cantor, Dedekind, and Weierstrass is refuted by an uninterrupted chain of work on infinitesimal-enriched number systems. The elimination claim is an oversimplification created by triumvirate followers, who tend to view the history of analysis as a pre-ordained march toward the radiant future of Weierstrassian epsilontics. In the present text, we document distortions of the history of analysis stemming from the triumvirate ideology of ontological minimalism, which identified the continuum with a single number system. Such anachronistic distortions characterize the received interpretation of Stevin, Leibniz, d'Alembert, Cauchy, and others.Comment: 46 pages, 4 figures; Foundations of Science (2012). arXiv admin note: text overlap with arXiv:1108.2885 and arXiv:1110.545

The Impact of the Species–Area Relationship on Estimates of Paleodiversity

Estimates of paleodiversity patterns through time have relied on datasets that lump taxonomic occurrences from geographic areas of varying size per interval of time. In essence, such estimates assume that the species–area effect, whereby more species are recorded from larger geographic areas, is negligible for fossil data. We tested this assumption by using the newly developed Miocene Mammal Mapping Project database of western North American fossil mammals and its associated analysis tools to empirically determine the geographic area that contributed to species diversity counts in successive temporal bins. The results indicate that a species–area effect markedly influences counts of fossil species, just as variable spatial sampling influences diversity counts on the modern landscape. Removing this bias suggests some traditionally recognized peaks in paleodiversity are just artifacts of the species–area effect while others stand out as meriting further attention. This discovery means that there is great potential for refining existing time-series estimates of paleodiversity, and for using species–area relationships to more reliably understand the magnitude and timing of such biotically important events as extinction, lineage diversification, and long-term trends in ecological structure

Habitable Zones in the Universe

Habitability varies dramatically with location and time in the universe. This was recognized centuries ago, but it was only in the last few decades that astronomers began to systematize the study of habitability. The introduction of the concept of the habitable zone was key to progress in this area. The habitable zone concept was first applied to the space around a star, now called the Circumstellar Habitable Zone. Recently, other, vastly broader, habitable zones have been proposed. We review the historical development of the concept of habitable zones and the present state of the research. We also suggest ways to make progress on each of the habitable zones and to unify them into a single concept encompassing the entire universe.Comment: 71 pages, 3 figures, 1 table; to be published in Origins of Life and Evolution of Biospheres; table slightly revise

Regional Environmental Breadth Predicts Geographic Range and Longevity in Fossil Marine Genera

Geographic range is a good indicator of extinction susceptibility in fossil marine species and higher taxa. The widely-recognized positive correlation between geographic range and taxonomic duration is typically attributed to either accumulating geographic range with age or an extinction buffering effect, whereby cosmopolitan taxa persist longer because they are reintroduced by dispersal from remote source populations after local extinction. The former hypothesis predicts that all taxa within a region should have equal probabilities of extinction regardless of global distributions while the latter predicts that cosmopolitan genera will have greater survivorship within a region than endemics within the same region. Here we test the assumption that all taxa within a region have equal likelihoods of extinction.We use North American and European occurrences of marine genera from the Paleobiology Database and the areal extent of marine sedimentary cover in North America to show that endemic and cosmopolitan fossil marine genera have significantly different range-duration relationships and that broad geographic range and longevity are both predicted by regional environmental breadth. Specifically, genera that occur outside of the focal region are significantly longer lived and have larger geographic ranges and environmental breadths within the focal region than do their endemic counterparts, even after controlling for differences in sampling intensity. Analyses of the number of paleoenvironmental zones occupied by endemic and cosmopolitan genera suggest that the number of paleoenvironmental zones occupied is a key factor of geographic range that promotes genus survivorship.Wide environmental tolerances within a single region predict both broad geographic range and increased longevity in marine genera over evolutionary time. This result provides a specific driving mechanism for the spatial and temporal distributions of marine genera at regional and global scales and is consistent with the niche-breadth hypothesis operating on macroevolutionary timescales

Earliest Triassic microbialites in the South China Block and other areas; controls on their growth and distribution

Earliest Triassic microbialites (ETMs) and inorganic carbonate crystal fans formed after the end-Permian mass extinction (ca. 251.4 Ma) within the basal Triassic Hindeodus parvus conodont zone. ETMs are distinguished from rarer, and more regional, subsequent Triassic microbialites. Large differences in ETMs between northern and southern areas of the South China block suggest geographic provinces, and ETMs are most abundant throughout the equatorial Tethys Ocean with further geographic variation. ETMs occur in shallow-marine shelves in a superanoxic stratified ocean and form the only widespread Phanerozoic microbialites with structures similar to those of the Cambro-Ordovician, and briefly after the latest Ordovician, Late Silurian and Late Devonian extinctions. ETMs disappeared long before the mid-Triassic biotic recovery, but it is not clear why, if they are interpreted as disaster taxa. In general, ETM occurrence suggests that microbially mediated calcification occurred where upwelled carbonate-rich anoxic waters mixed with warm aerated surface waters, forming regional dysoxia, so that extreme carbonate supersaturation and dysoxic conditions were both required for their growth. Long-term oceanic and atmospheric changes may have contributed to a trigger for ETM formation. In equatorial western Pangea, the earliest microbialites are late Early Triassic, but it is possible that ETMs could exist in western Pangea, if well-preserved earliest Triassic facies are discovered in future work

Hierarchy Theory of Evolution and the Extended Evolutionary Synthesis: Some Epistemic Bridges, Some Conceptual Rifts

Contemporary evolutionary biology comprises a plural landscape of multiple co-existent conceptual frameworks and strenuous voices that disagree on the nature and scope of evolutionary theory. Since the mid-eighties, some of these conceptual frameworks have denounced the ontologies of the Modern Synthesis and of the updated Standard Theory of Evolution as unfinished or even flawed. In this paper, we analyze and compare two of those conceptual frameworks, namely Niles Eldredge’s Hierarchy Theory of Evolution (with its extended ontology of evolutionary entities) and the Extended Evolutionary Synthesis (with its proposal of an extended ontology of evolutionary processes), in an attempt to map some epistemic bridges (e.g. compatible views of causation; niche construction) and some conceptual rifts (e.g. extra-genetic inheritance; different perspectives on macroevolution; contrasting standpoints held in the “externalism–internalism” debate) that exist between them. This paper seeks to encourage theoretical, philosophical and historiographical discussions about pluralism or the possible unification of contemporary evolutionary biology