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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]
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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 

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