Philosophy of Biology

(Tuis.) #1
The Development of Population Genetics 327

The other important component in the analogy with gas theory was the fact that
the distribution of the frequency ratio for different Mendelian factors was calculable
from the fact that the distribution was stable in the absence of selection, random
survival effects and so forth. Again, the source was the velocity distribution law
in gas theory. Just as the formulation of this law assumed an independence of
molecules in the gas, so too, Fisher assumed the independence of various hereditary
factors from each other and their independence from the effects of selection and
random survival. The important difference was that he specified a population
in which he could first calculate the distributions without selection, mutation
and random survival, and then he used those results to go on and determine
how the effects of selection operated in different contexts. To do that Fisher
considered the cases of uniform genetic selection in the absence of dominance and
genotypic selection with complete dominance. From those distributions he was
able to calculate the amount of mutation needed to maintain the variability given
a specific amount of selection. To maintain variability in the case of equilibrium
in the absence of selection, the rate of mutation had to be increased by a very
large quantity. So the presence of even the slightest amount of selection in large
populations had considerably more influence in keeping variability in check than
did random survival. Consequently, the assumption of genotypic selection balanced
by occasional mutations fit the facts deduced from the correlations of relatives in
humans.


So, by making simplifying assumptions about the large size of the population
and its high degree of genetic variability, Fisher was able to demonstrate how
his stochastic distributions led to the conclusion that natural selection acting on
single genes (rather than mutation, random extinction, epistasis etc.) was the
primary determinant in the evolutionary process. He found that mutation rates
significantly higher than any observed in nature could be balanced by very small
selection rates. The distribution of the frequency ratios for different factors was
calculated from the assumption that the distribution was stable. The kind of
statistical independence that figured prominently in the velocity-distribution law
was applicable to the effects of selection in Mendelian populations.


As more variables were added, the mathematics Fisher used became intractable,
a situation that led to the development of his famous “fundamental theorem of
natural selection”, published in 1930 inThe Genetical Theory of Natural Selection.
The theorem states that the rate of increase in fitness for any organism at any time
is equal to its genetic variance in fitness at that time. The meaning of the theorem
and what it implies has been the subject of great controversy in the literature
since its publication. It is now widely thought that the correct interpretation of
the theorem has been given by Price [1972] and Ewens [1989]. I will not go into
the details of the technicalities here but instead will simply give an overview of the
theorem so that the reader can have some appreciation of its importance. Perhaps
the first thing that needs to be mentioned is that although the theorem refers to
the fitness of an organism Fisher intended this to refer to the mean fitness of the
species conceived of as an idealised panmictic population. Secondly, the genetic

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