What
is the Source of Heritable Variation?
Biometricians Discontinuous /Mendelians
Darwin
- Blending Inheritance Huxley
- sports
Fleming
Jenkins - Blending flawed
<-
Galton – Develops Regression ->
Weldon
- correlations and data Bateson
- neo-Mendelian
Pearson
- refined correlations de
Vries - Mutations
Johannsen,
Jensen, Pearl
Pure Line
Theory
Sound
Empirical data:
1) Castle 1911) - selection on
continuous characters is effective
2) Nelsson-Ehle (1908) &
East (1910) mendelian inheritance could explain continuous variation
3) Morgan - mendelian traits
with small effects
Theory:
1) Yule (stable 1:2:1 ratio)
2) Hardy (1908) & Weinberg
(1908) - variation preserved (Pearson 1904)
3) Punnet (selection on mimicry)
4)
Fisher - Synthesized Biometrics & Mendelism in early work (1918)
"The Correlation between Relatives on the Supposition of Mendelian
Inheritance".
Fisher,
Wright, and Haldane -- all three developed mathematical treatments of evolution
yet they differed in emphasis of key features of the theory
Fisher
1) Synthesized
Biometrics & Mendelism in early work (1918) "The Correlation between
Relatives on the Supposition of Mendelian Inheritance".
2) Fundamental
theorem of natural selection in The Genetical Theory of Natural Selection,
1930: "The rate of
increase in fitness of any organism at any time is equal to its genetic
variance in fitness"
3) selection on
variation in large populations most effective since variation is high compared
to small inbred populations
4) genetic
interactions are negligible
5) Mass selection of
small single gene effects in large pops.
6) Theory of
dominance (1928):
i) Large pops,
long periods of time, small selection pressures.
ii) Most mutations
are deleterious but occur at a finite rate
iii) Mutant becomes fixed at
very low frequency (mutation-selection balance).
iv) Initially heterozygote
is intermediate in expression & fitness.
v) Because Aa occurs
at high frequency in a population than aa (AA wild type of higher fitness),
selection would tend to preserve those heterozygotes which because of modifiers
more closely resemble wild type AA.
vi) Slow selection on
modifiers causes Aa to resemble AA over a long period of time.
Wright
1) path analysis
"Correlation and causation", 1921
2) applied to
systems of mating: inbreeding and assortative
3) Epistasis (e.g.,
inter-gene interactions) and inbreeding (e.g., small pops) are key features of
his theory. Selection on
interaction systems is most effect.
4) Random genetic
drift important in creating novel interaction systems upon which natural
selection acts
5) Theory of
dominance (1929):
i) Fisher's
theory depends on lack of genic interaction
ii) allelomorphs
represent the presence or absence of something
iii) Thus one does of an
entity would resemble two doses more than it would resemble no doses (one does
good enough)
iv) Mutations are most
frequently in the direction of inactivation, and inactivation should
behave as a recessive
v) However,
dominance is a phenomenon of epistasis.
In one genetic background A1
is dominant to A2, in another, A2 is dominant to A1.
6) Shifting
balance theory (1931). Fisher
large populations would change very slowly because change is limited by
mutation rates. More favorable
conditions for evolutionary change would be found in a large population broken
up into imperfectly isolated strains (inbreeding uncovers novel
interactions). In this case, rate
of evolutionary change depends on balance between effective population size in
a local strain and migration (not limited by mutation rates). Rapid differentiation of local strains,
selective increase or decrease & migration. Rapid advance of species as a whole.
Haldane
1) A Mathematical
Theory of Natural and Artificial Selection, 1924-1932; The Causes of Evolution,
1932.
2) places tremendous
importance on selective importance of large single gene effects (rather than
lots of small gene effects of Fisher)
3)
Works out many
selection scenarios including cases in which selection is tied to mortality
rates, also linkage.
4) Independently
derives a theory of evolution in small populations. Works on the selection on interaction effects (and
emphasizes the importance of small populations). However, believes such conditions not very common in nature.
5) Theory of Dominance
(1930).
i) Same
argument as Wright regarding recessive Loss of Function alleles.
ii) But why should
there be this safety margin so Aa is almost as capable as AA (e.g., in
enzymatic activity, etc.)
iii) Selection on
allelomorphs not modifiers.
iv) If A1A1
can just oxidize all of a certain substance as fast as it is formed, then its
inactivation produces a zygote A1a
which can only oxidize at half the rate.
If A1 mutates to A2 which can oxidize at 2X or 3X the rate
of A1 then A1A2 same as A2A2 or A1A1.
v) However, the
inactivation mutant A2a will also be
normal but A1a will be deficient and
A2a is selected over A1a.
vi) Selection for mutations
of large effect, which differs from Fishers view of Selection for Gain
of Function.
All
of this is quite complicated, how can we simplify the concepts
Maynard
Smith and Price come up with Game Theory, which is closely related to John
NashÕs game theory concepts (Nash just obtained the Nobel Prize, 1996)
A game can be defined as a means of reaching a
decision in a conflict situation in which one contestant wins at the expense of
another. Von Neumann and Morgenstern (1953) developed game theory to explain
human behavior in conflict situations. The Nobel Laureate James Nash developed
the key concept of a Nash equilibrium,
which is the stance a rationale player should take in contests. Maynard Smith
and Price (1973) came up with a similar concept, which we call the ESS or Evolutionarily Stable Strategy. Game theory was developed as a way to explain costs
and benefits that arise from economic decisions.
Which strategy is the winner in the long-term? For a strategy to be an Evolutionarily
Stable Strategy or an ESS, two conditions must be met.