Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-23T18:33:01.723Z Has data issue: false hasContentIssue false
  • English
  • Français

A mathematical model for long-term patterns of evolution: effects of environmental stability and instability on macroevolutionary patterns and mass extinctions

Published online by Cambridge University Press:  20 May 2016

Satoshi Chiba
Satoshi Chiba*
Affiliation:
Institute of Biology and Earth Science, Shizuoka University, 836 Oya, Shizuoka, 422 Japan. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

A simple mathematical model to examine the relationships between environmental instability and long-term macroevolutionary trends is presented. The model investigates the evolutionary changes that occur in certain population characters in an environment with physical disturbance. These quantitative genetic characters are related to intrinsic growth rates and mean carrying capacity. The model assumes that individual fitness is determined by these characters. I examine the likelihood of extinction under different degrees of environmental instability and for rapid change of environmental instability. The model suggests that characters that promote a high intrinsic growth rate and a low carrying capacity tend to evolve in the most unstable environments. This suggests that small body size, high fecundity, and simple forms evolve in unstable environments. The extinction probability of a population is the lowest for taxa possessing K-selected characters in the most stable environment. However, the extinction probability of a species (metapopulation) becomes lowest for r-selected species living in the most unstable environment and for the K-selected species living in the most stable environment, and it becomes the highest for taxa living in a moderately unstable environment. Increasing environmental instability changes the extinction probabilities of different taxa in different ways, due to differences in phenotypes and environments. The effect of environmental change is most serious for the K-selected taxa in the most stable environment. This also suggests that a continuously stable environment increases the extinction probability of taxa when environmental change occurs. Although catastrophic changes in environments are not presumed, these results are consistent with the existence of two “macroevolutionary regimes” in which a taxon's extinction rate and its characters differ for mass extinction and normal extinction. Mass extinction can occur as a result of long-term adaptation to a stable environment following a minor change of environment without catastrophes.

Type
Articles
Information
Paleobiology , Volume 24 , Issue 3 , Summer 1998 , pp. 336 - 348
Copyright
Copyright © The Paleontological Society 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Literature Cited

Allmon, W. D. 1992. A causal analysis of stage in allopatric speciation. Oxford Surveys in Evolutionary Biology 8: 219–257.Google Scholar
Brasier, M. D. 1982. Sea level changes, facies changes and the Late Precambrian-Early Cambrian evolutionary explosion. Precambrian Resarch. 17: 105–123.Google Scholar
Bulmer, M. G. 1985. The mathematical theory of quantitative genetics. 2d edition. Oxford University Press, Oxford.Google Scholar
Burger, R. and Lynch, M. 1995. Evolution and extinction in a changing environment: a quantitative genetic analysis. Evolution 49: 151–163.Google Scholar
Burger, R. G., Wagner, G., and Stettinger, F. 1989. How much heritable variation can be maintained in a finite population by mutation selection balance? Evolution 43: 1748–1766.Google Scholar
Calder, W. A. 1984. Size, function, and life history. Harvard University Press, Cambridge.Google Scholar
Caughley, G. 1994. Directions in conservation biology. Journal of Animal Ecology 63: 215–244.Google Scholar
Falconer, D. S. 1989. Introduction to quantitative genetics. 3d edition. Longman, New York.Google Scholar
Foley, P. 1992. Small population genetic variability at loci under stabilizing selection. Evolution 46: 763–774.CrossRefGoogle ScholarPubMed
Goel, N. S. and Richter-Dyn, N. 1974. Stochastic models in biology. Academic Press, New York.Google Scholar
Gould, S. J. 1977. Ontogeny and phylogeny. Harvard University Press, Cambridge.Google Scholar
Grime, J. P. 1977. Evidence for the existence of three primary strategies in plants and its relevance to ecological and evolutionary theory. American Naturalist 111: 1169–1194.Google Scholar
Grime, J. P. 1979. Plant strategies and vegetation processes. Wiley, Chichester.Google Scholar
Gurney, W. S. C. and Nisbet, R. M. 1978. Single species population fluctuations in patchy environments. American Naturalist 112: 1075–1090.Google Scholar
Hallam, A. 1978. How rare is phyletic gradualism? Evidence from the Jurassic bivalves. Paleobiology 4: 16–25.Google Scholar
Hallam, A. 1984. Pre-Quaternary sea level changes. Annual Review of Earth and Planetary Sciences 12: 205–243.Google Scholar
Hallam, A. 1987. End-Cretaceous mass extinction event: argument for terrestrial causation. Science 238: 1237–1242.Google Scholar
Hallam, A. 1990. Biotic and abiotic factors in the evolution of Early Mesozoic marine molluscs. pp. 249–269in Ross, R. M., Allmon, W. D. eds. Cause of evolution: a paleontological perspective. University of Chicago Press, Chicago.Google Scholar
Hanski, I. 1989. Metapopulation dynamics: Does it help to have more of the same? Trends in Ecology and Evolution 4: 113–114.Google Scholar
Hanski, I. and Gilpin, M. 1991. Metapopulation dynamics: brief history and conceptual domain. Biological Journal of the Linnean Society 42: 3–16.Google Scholar
Hanski, I., Moilanen, A., and Gyllenberg, M. 1996. Minimum viable metapopulation size. American Naturalist 147: 527–541.Google Scholar
Harvey, P., Nee, S., Mooers, A., and Partridge, L. 1993. These hierarchical views of life: phylogenies and metapopulations. pp. 123–137in Crawford, T., Hewitt, E. eds. Genes in evolution. Blackwell Scientific, Oxford.Google Scholar
Houle, D. 1989. The maintenance of polygenic variation in finite populations. Evolution 43: 1767–1780.Google Scholar
Iwasa, Y. 1990. Introduction to mathematical biology. HBI Publication, Tokyo. [In Japanese.].Google Scholar
Iwasa, Y. and Pomiankowski, A. 1994. The evolution of mate preferences for multiple sexual ornament. Evolution 48: 853–967.Google Scholar
Iwasa, Y., Pomiankowski, A., and Nee, S. 1991. The evolution of costly mate preference. II. The handicap principle. Evolution 45: 1431–1442.Google Scholar
Jablonski, D. 1986a. Causes and consequences of mass extinctions. pp. 183–229in Eliott, D. K. ed. Dynamics of extinction. Wiley, New York.Google Scholar
Jablonski, D. 1986b. Background and mass extinctions: the alteration of macroevolutionary regimes. Science 231: 129–133.Google Scholar
Jablonski, D. 1989. The biology of mass extinction: a paleontological view. Philosophical Transactions of the Royal Society of London B. 24: 357–368.Google Scholar
Jablonski, D. and Lutz, R. A. 1983. Larval ecology of marine benthic invertebrates: paleobiological implications. Biological Review 58: 21–89.Google Scholar
Kimura, M. 1983. The neutral theory of molecular evolution. Cambridge University Press, Cambridge.Google Scholar
Kirkpatrik, M. 1985. Evoluton of female choice and male parental investment in polygynous species: the demise of the sexy son. American Naturalist 125: 788–810.Google Scholar
Kirkpatrik, M. 1986. The handicap mechanism of sexual selection does not work. American Naturalist 127: 222–240.Google Scholar
Kitchell, J. A. and Karr, T. R. 1985. Nonequilibrium model of diversification: faunal turnover dynamics. pp. 277–310in Valentine, J. ed. Phanerozoic diversity patterns. Princeton University Press, Princeton, N.J.Google Scholar
Lande, R. 1979. Quantitative genetic analysis of multivariate evolution, applied to brain, body size allometry. Evolution 33: 402–416.Google Scholar
Lande, R. 1980. Genetic variation and phenotypic evolution during allopatric speciation. American Naturalist 116: 463–479.Google Scholar
Lande, R. 1981. Models of speciation and sexual selection on polygenic traits. Proceedings of the National Academy of Sciences USA. 78: 3721–3725.Google Scholar
Lande, R. 1982. A quantitative genetic theory of life history evolution. Ecology 63: 607–615.Google Scholar
Lande, R. 1993. Risks of population extinction from demographic and environmental stochasticity, and random catastrophes. American Naturalist 142: 911–927.Google Scholar
Levin, R. 1969. The effect of random variations of different types on population growth. Proceedings of the National Academy of Sciences USA. 62: 1061.Google Scholar
Ludwig, D. 1996. The distribution of population survival times. American Naturalist 147: 506–526.Google Scholar
Lynch, M. 1994. Neutral models of phenotypic evolution. pp. 86–108in Real, L. A. ed. Ecological genetics Princeton University Press, Princeton, N.J.Google Scholar
Lynch, M. and Hill, W. G. 1986. Phenotypic evolution by neutral mutation. Evolution 40: 915–935.Google Scholar
Lynch, M. and Lande, R. 1993. Evolution and extinction in response to environmental change. pp. 234–250in Kareiva, P. M., Kingsolver, J. G., Huey, R. B. eds. Biotic interactions and global change. Sinauer, Sunderland, Mass.Google Scholar
Lynch, M., Gabriel, W., and Wood, A. M. 1991. Adaptive and demographic responses of plankton populations to environmental change. Limnology and Oceanography 36: 1301–1312.CrossRefGoogle Scholar
MacArthur, R. H. and Wilson, E. O. 1967. The theory of island biogeography. Princeton University Press, Princeton, N.J.Google Scholar
McKinney, M. L. 1986. Ecological causation of heterochrony: a test and implications for evolutionary theory. Paleobiology 12: 282–289.Google Scholar
McKinney, M. L. 1989. Periodic mass extinctions: product of biosphere growth dynamics? Historical Biology 2: 273–287.Google Scholar
McKinney, M. L. and Allmon, W. D. 1995. Metapopulation and disturbance: from patch dynamics to biodiversity dynamics. pp. 123–183in Erwin, D. H., Anstey, R. L. eds. New approaches to speciation in the fossil record. Columbia University Press, New York.Google Scholar
McNamara, K. J. 1990. Evolutionary trends. University of Arizona Press, Tucson.Google Scholar
McNamara, K. J. 1994. Diversity of Cenozoic marsupiate echinoids as an environmental indicator. Lethaia 27: 257–268.Google Scholar
Pianka, E. R. 1970. On r and K selection. American Naturalist 104: 592–597.Google Scholar
Pianka, E. R. 1972. r and K selection or b and d selection. American Naturalist 106: 581–588.Google Scholar
Pianka, E. R. 1978. Evolutionary ecology. 2d ed.Harper and Row, New York.Google Scholar
Nussbaum, R. A. 1987. Parental care and egg size in salamanders: an examination of the safe harbor hypothesis. Research on Population Ecology 29: 27–44.Google Scholar
Nussbaum, R. A. and Schultz, D. L. 1989. Coevolution of parental care and egg size. American Naturalist 133: 591–603.Google Scholar
Plotnick, R. E. and McKinney, M. L. 1993. Ecosystem organization and extinction dynamics. Palaios. 8: 202–212.CrossRefGoogle Scholar
Roff, D. A. 1992. The evolution of life histories: theory and analysis. Chapman and Hall, London.Google Scholar
Roughgarden, J. 1971. Density dependent natural selection. Ecology 52: 453–468.Google Scholar
Roughgarden, J. 1979. Theory of population genetics and evolutionary ecology: an introduction. Macmillan, New York.Google Scholar
Roughgarden, J. 1983. Coevolution between competitors. pp. 383–403in Futuyma, D. J., Slatkin, M. eds. Coevolution. Sinauer, Sunderland, Mass.Google Scholar
Rummel, J. and Roughgarden, J. 1985. A theory of faunal buildup for competition communities. Evolution 39: 1009–1033.Google Scholar
Sepkoski, J. J. Jr. 1984. A kinetic model of Phanerozoic taxonomic diversity. III. Post-Paleozoic families and extinctions. Paleobiology 10: 246–267.Google Scholar
Shaffer, M. L. 1981. Minimum population size for species conservation. Bioscience 31: 131–134.Google Scholar
Sheehan, P. M. 1985. Reefs are not so different—they follow the evolutionary pattern of level-bottom communities. Geology 12: 46–49.Google Scholar
Sheldon, P. R. 1993. Making sense of microevolutionary patterns. pp. 19–41in Lees, D. R., Edwards, D. eds. Evolutionary patterns and processes. Linnean Society Symposium 14 Academic Press, London.Google Scholar
Slatkin, M. 1987. Heritable variation and heterozygosity under a balance between mutation and stabilizing selection. Genetic Research 50: 53–62.Google Scholar
Soulé, M. E. 1980. Thresholds for survival: maintaining fitness and evolutionary potential. pp. 111–124in Soulé, M. E., Wilcox, B. A. eds. Conservation biology: an evolutionary ecological perspective. Sinauer, Sunderland, Mass.Google Scholar
Stanley, S. M. 1987. Extinctions. Scientific American Library, New York.Google Scholar
Stanley, S. M. 1990. Delayed recovery and the timing of mass extinctions. Paleobiology 16: 401–414.Google Scholar
Stearns, S. C. 1976. Life-history tactics: a review of the ideas. Quarterly Review of Biology 51: 3–47.Google Scholar
Stearns, S. C. 1992. The evolution of life histories. Oxford University Press, Oxford.Google Scholar
Taper, M. L. and Case, T. J. 1985. Quantitative genetic model for the coevolution of character displacement. Ecology 66: 355–371.Google Scholar
Turelli, M. 1984. Heritable genetic variation via mutation-selection balance: Lerch's zeta meets the abdominal bristle. Theoretical Population Biology 25: 138–193.Google Scholar
Turjapurker, S. 1989. An uncertain life: demography in random environment. Theoretical Population Biology 35: 227–294.Google Scholar
Vermeij, J. G. 1987. Evolution and escalation. Princeton University Press, Princeton, N.J.CrossRefGoogle Scholar
Ward, P. D. and Signor, P. W. 1983. Evolutionary tempo in Jurassic and Cretaceous Ammonites. Paleobiology 9: 183–198.Google Scholar