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Factorizing the rate of evolution

In this section discrepancies between the corridor simulations and predictions of one character quantitative genetic theory are partitioned into three factors: deviations from the predicted selection differential, the selection response and the asymptotic genetic variance.

Standard quantitative genetic theory predicts that the rate of change due to directional selection can be modeled as a two stage process. First selection acts on the phenotypic distribution of the parental generation, which produces the selection differential, and second the transmission to the next generation. The selection differential is the difference between the population mean value before and after selection , . In the simulations the selection intensity was measured by , the standardized selection differential. Hence the realized selection differential is

The expected selection differential depends on the phenotypic variance of the parental population and the strength of the directional selection. If the phenotyic values are normally distributed, the strength of the directional selection is given by , for a single character which is under the influence of the fitness function . The expected selection differential therefore is , and we measure the relative realized selection differential by:

The selection response is the difference between the character mean values before selection in the first generation and the following generation, . The expected selection response is the product of the selection differential and the heritability, . Note that in analysing the simulations, both the heritability and the selection differential are observed values. The prediction only concerns the functional relationship between the selection response and the selection differential and the heritability. The

Table A,



Table B,



Table C,



realized average selection response in our simulation is measured as . Hence, we measure the relative response to selection as

Finally the asymptotic rate of evolution depends on how much genetic variation for the character can be maintained under selection, mutation and drift. For the case without pleiotropic effects the prediction of Hill (1982) is . The relative amount of genetic variation in our simulations is calculated by

The relative rate of evolution can be reconstructed from these three factors: . In table 6 the three factors influencing the relative rate of evolution are listed. In the low mutation rate scenario it is obvious that the selection differential has the smallest impact on the relative rate of evolution. The realized selection differential is between 88 and 99% of the expected. Clearly the stationary amount of genetic variation has the strongest impact on the observed relative rate of evolution. The relative magnitude of the selection response is only important in cases where the stabilizing selection is strong () and the directional selection is weak or moderate ( or ). In the high mutation rate scenario, the only significant factor influencing the relative rate of evolution is the stationary amount of genetic variance.



next up previous
Next: An approximate analytical Up: Finite Population Model Previous: The rate of

Tue Apr 9 13:43:34 EDT 1996