Phanerozoic marine biodiversity follows a hyperbolic trend

doi:10.1016/j.palwor.2007.01.002

Palaeoworld

Volume 16, Issue 4, December 2007, Pages 311-318

https://doi.org/10.1016/j.palwor.2007.01.002 Get rights and content

Abstract

Changes in marine biodiversity through the Phanerozoic correlate much better with hyperbolic model (widely used in demography and macrosociology) than with exponential and logistic models (traditionally used in population biology and extensively applied to fossil biodiversity as well). The latter models imply that changes in diversity are guided by a first-order positive feedback (more ancestors, more descendants) and/or a negative feedback arising from resource limitation. Hyperbolic model implies a second-order positive feedback. The hyperbolic pattern of the world population growth arises from a second-order positive feedback between the population size and the rate of technological growth. The hyperbolic character of biodiversity growth can be similarly accounted for by a feedback between the diversity and community structure complexity. The similarity between the curves of biodiversity and human population probably comes from the fact that both are derived from the interference of the hyperbolic trend with cyclical and stochastic dynamics.

Section snippets

Introduction: mathematical modeling of biodiversity dynamics

Mathematical modeling of fossil biodiversity dynamics is essential for understanding general trends of biotic evolution. Among diverse models that were used to describe and interpret the changes in global marine biodiversity through the Phanerozoic, the exponential and logistic models and their combinations are the most popular (Sepkoski, 1991a, Benton, 1999). The exponential, or expansionist, model implies simple positive feedback between the diversity (N) and its growth rate (more ancestors

Materials and methods

We used Sepkoski's compendium of fossil marine animal genera (available online at http://strata.ummp.lsa.umich.edu/jack/). We considered only genera dated with substage or stage-level precision. We used absolute datings from Gradstein et al. (2004). In order to estimate how the changes in absolute geochronology can influence the results, we also applied an older scale for comparison (Harland et al., 1982). The results were practically the same (data not shown). The best-fit parameters for the

Results

Exponential model describes Phanerozoic marine biodiversity better than linear model; however, simple hyperbolic model (dN/dt = kN²) fits much better to empirical data than exponential model (Fig. 1a–c). The latter explains only 46–54% of total macrovariation, while the former explains 85.4%. Notably, it is not necessary to divide the Phanerozoic into segments in order to achieve good correlation; the whole Phanerozoic history of biodiversity fits well to a single hyperbolic trend.

Reliability of the fossil record

The fossil record provides important insights into the quantitative patterns of evolution, although the degree of reliability and adequacy of this source of data is disputable. The skeptics mention, for instance, differential incompleteness of various parts of the record and ‘the pull of the recent’ effect (Raup, 1979). By the end of the 20th century, however, most authors had agreed that the paleontological record is representative and robust enough to adequately reveal the main quantitative

Conclusions

Generally, the paleontological data confirm the idea that there was an increase in the complexity and stability of marine communities throughout the Phanerozoic. These changes can be accounted for through the existence of the second-order positive feedback in the course of biodiversity growth that reveals itself in the hyperbolic character of the latter. Biodiversity growth facilitated the increase in the communities’ complexity and stability, and this, in turn, resulted in the increasing

Acknowledgements

We thank Arnold Miller and the anonymous reviewer for useful suggestions for improving the manuscript. The work was supported by the Program 25 of the Presidium of the Russian Academy of Sciences “Biosphere origin and evolution” and the Russian Science Support Foundation.

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According to Korotayev and Markov, the hyperbolic character of biodiversity growth can be similarly accounted for by a feedback between the diversity and community structure complexity. They suggest that the similarity between the curves of biodiversity and human population probably comes from the fact that both are derived from the interference of the hyperbolic trend with cyclical and stochastic dynamics (Refs. [10] and [11]). This author was struck by the following Fig. 10 (taken from the above-mentioned Wikipedia site) showing the increase, but not monotonic increase, of the number of Genera (in thousands) during the 541 million years making up for the Phanerozoic.
Ray Kurzweil's famous 2006 book “The Singularity Is Near” predicted that the Singularity (i.e. computers taking over humans) would occur around the year 2045. In this paper we prove that Kurzweil's prediction is in agreement with the “Evo-SETI” (Evolution and SETI)” mathematical model that this author has developed over the last five years in a series of mathematical papers published in both Acta Astronautica and the International Journal of Astrobiology.
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Actually, some general patterns exhibited by complex ecosystems over evolutionary time scales, such as community rebuilding after a major extinction event are closely related to some phenomena occurring at short, ecological time scales, such as ecological succession (Solé et al., 2002; Solé and Bascompte, 2006). This hyperbolic growth model has been used to model the dynamics of marine biodiversity through the Phanerozoic (Markov and Korotayev, 2007). Mass extinctions have received considerable attention from paleontologists, evolutionary biologists and others over the past several decades (see Jablonski, 2005 and references therein).
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Research paperPhanerozoic marine biodiversity follows a hyperbolic trend

Abstract

Section snippets

Introduction: mathematical modeling of biodiversity dynamics

Materials and methods

Results

Reliability of the fossil record

Conclusions

Acknowledgements

Palaeogeogr. Palaeoclimatol. Palaeoecol.

Physica A

Paleolatitudinal sampling bias, Phanerozoic species diversity, and the end-Permian extinction

Geology

Effects of sampling standardization on estimates of Phanerozoic marine diversification

Proc. Natl. Acad. Sci. U.S.A.

Species richness in marine benthic habitats through the Phanerozoic

Paleobiology

Anatomical and ecological constraints on Phanerozoic animal diversity in the marine realm

Proc. Natl. Acad. Sci. U.S.A.

Diversification and extinction in the history of life

Science

The history of life: large databases in palaeontology

Quality of the fossil record through time

Nature

Did alpha diversity increase during the Phanerozoic? Lifting the veils of taphonomic, latitudinal, and environmental biases

J. Geol.

The Demographic Transition: Stages, Patterns, and Economic Implications

Population growth and earth's carrying capacity

Science

Random walks in the history of life

Proc. Natl. Acad. Sci. U.S.A.

Absolute measures of the completeness of the fossil record

Nature

A Geologic Time Scale 2004

A Geologic Time Scale 1982

Mass extinctions and macroevolution

Paleobiology

Measuring past biodiversity

Science

Introduction to Social Macrodynamics: Compact Macromodels of the World System Growth

Introduction to Social Macrodynamics: Secular Cycles and Millennial Trends

Population growth and technological change: One million B.C. to 1990

Quart. J. Econ.

Evolutionary consequences of niche construction and their implications for ecology

Proc. Natl. Acad. Sci. U.S.A.

Taxonomic level as a determinant of the shape of the Phanerozoic marine biodiversity curve

Am. Nat.

Research paper
Phanerozoic marine biodiversity follows a hyperbolic trend