A MATHEMATICAL-MODEL FOR LONG-TERM PATTERNS OF EVOLUTION - EFFECTS OFENVIRONMENTAL STABILITY AND INSTABILITY ON MACROEVOLUTIONARY PATTERNSAND MASS EXTINCTIONS

A simple mathematical model to examine the relationships between envir onmental instability and long-term macroevolutionary trends is present ed. The model investigates the evolutionary changes that occur in cert ain 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 f itness is determined by these characters. I examine the likelihood of extinction under different degrees of environmental instability and fo r rapid change of environmental instability. The model suggests that c haracters that promote a high intrinsic growth rate and a low carrying capacity tend to evolve in the most unstable environments. This sugge sts that small body size, high fecundity, and simple forms evolve in u nstable environments. The extinction probability of a population is th e lowest for taxa possessing K-selected characters in the most stable environment. However, the extinction probability of a species (metapop ulation) becomes lowest for r-selected species living in the most unst able environment and for the K-selected species living in the most sta ble environment, and it becomes the highest for taxa living in a moder ately unstable environment. Increasing environmental instability chang es the extinction probabilities of different taxa in different ways, d ue to differences in phenotypes and environments. The effect of enviro nmental change is most serious for the K-selected taxa in the most sta ble environment. This also suggests that a continuously stable environ ment increases the extinction probability of taxa when environmental c hange occurs. Although catastrophic changes in environments are not pr esumed, these results are consistent with the existence of two ''macro evolutionary regimes'' in which a taxon's extinction rate and its char acters differ for mass extinction and normal extinction. Mass extincti on can occur as a result of long-term adaptation to a stable environme nt following a minor change of environment without catastrophes.