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- Electron
microscopic
observations
on the meiotic
karyotype of
diploid and
tetraploid
Saccharomyces
cerevisiae.: Proceedings of
the National
Academy of
Sciences of
the United
States of
America, Vol.
72, No. 12.
(December
1975), pp.
5056-5060.Cert
ain strains of
Saccharomyces
cerevisiae
contain
visible
segments of
synaptonemal
complex which
are apparent
components of
bivalents in
pachytene of
meiotic
prophase. The
synaptonemal
complex has
the typical
width in the
frontal plane
but is
unusually thin
in the
sagittal
plane, thus
accounting for
its poor
visibility.
Amorphous
densities
situated
adjacent to
the central
element occur
at intervals
suggesting
their
coincidence
with sites of
crossing over.
Reconstruction
of the
synaptonemal
complex from
serial
sections has
permitted
karyotypic
analysis. The
number of
segments of
synaptonemal
complex and
the
distribution
of their
legths is
consistent
with the
genetic map.
Two, possibly
three,
segments enter
the nucleolus
as if bearing
sequences
encoding
ribosomal RNA.
Reconstruction
of tetraploid
nuclei reveals
an approximate
doubling of
the diploid
chromosome
number and
confirms the
pattern of
nucleolar
entry.
Quadrivalent
pairing is
evident
between the
pairs of
synaptonemal
complex
segments in
the tetraploid
nuclei.B
Byers, L
Goetsch
Source: Proceedings of the National Academy of Sciences of the United States of America, Vol. 72, No. 12. (December 1975), pp. 5056-5060. - PROBABILITY OF
FIXATION AND
MEAN FIXATION
TIME OF AN
OVERDOMINANT
MUTATION: Genetics, Vol.
74, No. 2. (1
June 1973),
pp.
371-380.The
probability of
fixation of an
overdominant
mutation in a
finite
population
depends on the
equilibrium
gene frequency
in an infinite
population (m)
and the
product (A) of
population
size and
selection
intensity. If
m < 0.5
(disadvantageo
us
overdominant
genes), the
probability is
generally much
lower than
that of
neutral genes;
but if m is
close to 0.5
and A is
relatively
small, it
becomes
higher. If m >
0.5
(advantageous
overdominant
genes), the
probability is
largely
determined by
the fitness of
heterozygotes
rather than
that of mutant
homozygotes.
Thus,
overdominance
enhances the
probability of
fixation of
advantageous
mutations. The
average number
of generations
until fixation
of an
overdominant
mutation also
depends on m
and A. This
average time
is long when m
is close to
0.5 but short
when m is
close to 0 or
1. This
dependence on
m and A is
similar to
that of
Robertson's
retardation
factor.Masatos
hi Nei, AK
Roychoudhury
Source: Genetics, Vol. 74, No. 2. (1 June 1973), pp. 371-380. - Long-term
stability from
fixation
probabilities
in finite
populations:
New
perspectives
for ESS theory: Theoretical
Population
Biology, Vol.
68, No. 1.
(July 2005),
pp. 19-27.For
mixed
strategies in
finite
populations,
long-term
stability is
defined with
respect to the
probability of
fixation of a
mutant. Under
weak
selection,
necessary and
sufficient
conditions are
obtained using
a diffusion
approximation
of the
Wright-Fisher
model or exact
solutions for
the Moran
model. These
differ from
the usual ESS
conditions if
the strategies
affect
fertility
instead of
viability,
leading to a
game matrix
depending on
the population
size, or if
the mutant
mixed strategy
uses a new
pure strategy.
In this case,
the mutant
deviation must
not exceed
some threshold
value
depending on
the population
size. In a
diploid
population,
long-term
stability may
not occur
unless there
is partial
dominance. In
the case of
sex
allocation,
continuous
stability of
an even sex
ratio is
ascertained.
If sex
allocation is
random, an
evolutionary
decrease of
the variance
is
predicted.Sabi
n Lessard
Source: Theoretical Population Biology, Vol. 68, No. 1. (July 2005), pp. 19-27. - Discrete
polymorphisms
due to
disruptive
selection on a
continuous
trait--I: The
one-locus case: Theoretical
Population
Biology, Vol.
69, No. 3.
(May 2006),
pp. 283-295.We
have
investigated,
numerically
and
analytically,
long-term
evolution
under
frequency-depe
ndent
disruptive
selection of a
continuous
trait varying
in a finite
range and
controlled by
one diploid
mendelian
locus. We
found that
evolution
converges
towards a
unique
long-term
equilibrium
where only two
extreme
phenotypes are
present with
frequencies
identical to
those of the
mixed strategy
that would be
the unique ESS
of the game
defined by the
basic fitness
function of
the model. As
long as this
precise
phenotypic
composition is
preserved, any
genetic
configuration
of the
polymorphism
is equally
acceptable
(selectively
neutral) at
the
equilibrium.
Thus the
number of
alleles and
their
dominance
pattern may
vary
considerably
among
different
equilibrium
populations.
If genetic
expression of
the trait is
variable but
the amount of
variability is
genetically
modifiable,
disruptive
selection,
acting on such
modifiers,
produces a
steady
increase of
expression
variability
before the
equilibrium is
attained. In
this case a
population at
the long-term
equilibrium
might even be
genetically
monomorphic,
with the
phenotypic
dimorphism
resulting from
purely random
individual
variation.Carl
o Matessi,
Alexander
Gimelfarb
Source: Theoretical Population Biology, Vol. 69, No. 3. (May 2006), pp. 283-295. - Complex
dynamical
behaviour of
frequency-depe
ndent
viability
selection: An
example: Journal of
Theoretical
Biology, Vol.
130, No. 2.
(21 January
1988), pp.
167-173.The
model of
viability
selection
based on a
one-locus,
two-allele
diploid
population is
considered.
Frequency
dependence is
introduced
through the
fitnesses of
three
phenotypes
(strategies)
exhibited by
the
population.
Both discrete
and continuous
dynamics are
analyzed and
contrasted
with the
classical
results of
frequency-inde
pendent
selection and
with the more
recent results
of
frequency-depe
ndent
selection
based on
two-phenotype
multi-allele
systems.
Cycling and
chaotic
behaviour are
shown to be
easily
obtained in
the discrete
model.
Intuitive
biological
conditions for
stability are
shown to fail
as well at
general
equilibria of
the continuous
model.R
Cressman
Source: Journal of Theoretical Biology, Vol. 130, No. 2. (21 January 1988), pp. 167-173. - A dynamic game
theory model
of a diploid
genetic system: Journal of
Theoretical
Biology, Vol.
129, No. 2.
(21 November
1987), pp.
243-255.The
dynamic game
theory model
developed
previously for
asexual
organisms is
extended to
randomly
mating diploid
populations
where the
strategy used
is determined
by a single
locus. Any
number of
strategies may
be considered
in the model,
but only the
case of
hierarchical
dominance is
treated. An
algorithm is
given for
determining
all equilibria
in any given
game, and for
checking these
equilibria for
local
stability.
Many of the
stability
properties
found in our
previous paper
for asexual
populations
also apply to
diploid
populations,
but, in
contrast to
asexual
populations,
diploid
populations
with no
evolutionarily
stable points
(ESPs) can
exhibit stable
oscillations.G
lenn Rowe
Source: Journal of Theoretical Biology, Vol. 129, No. 2. (21 November 1987), pp. 243-255. - Separation of
time scales,
fixation
probabilities
and
convergence to
evolutionarily
stable states
under
isolation by
distance: Theoretical
Population
Biology, Vol.
69, No. 2.
(March 2006),
pp. 165-179.To
a first order
of
approximation,
selection is
frequency
independent in
a wide range
of family
structured
models and in
populations
following an
island model
of dispersal,
provided the
number of
families or
demes is large
and the
population is
haploid or
diploid but
allelic
effects on
phenotype are
semidominant.
This result
underlies the
way the
evolutionary
stability of
traits is
computed in
games with
continuous
strategy sets.
In this paper
similar
results are
derived under
isolation by
distance. The
first-order
effect on
expected
change in
allele
frequency is
given in terms
of a measure
of local
genetic
diversity, and
of measures of
genetic
structure
which are
almost
independent of
allele
frequency in
the total
population
when the
number of
demes is
large. Hence,
when the
number of
demes
increases the
response to
selection
becomes of
constant sign.
This result
holds because
the relevant
neutral
measures of
population
structure
converge to
equilibrium at
a rate faster
than the rate
of allele
frequency
changes in the
total
population. In
the same
conditions and
in the absence
of demographic
fluctuations,
the results
also provide a
simple way to
compute the
fixation
probability of
mutants
affecting
various
ecological
traits, such
as sex ratio,
dispersal,
life-history,
or
cooperation,
under
isolation by
distance. This
result is
illustrated
and tested
against
simulations
for mutants
affecting the
dispersal
probability
under a
stepping-stone
model.Francois
Rousset
Source: Theoretical Population Biology, Vol. 69, No. 2. (March 2006), pp. 165-179. - Evolutionarily
Stable
Strategy in a
Sex- and
Frequency-Depe
ndent
Selection
Model: Journal of
Theoretical
Biology, Vol.
204, No. 2.
(21 May 2000),
pp. 191-200.In
this paper, a
sex-dependent
matrix game
haploid model
is
investigated.
For this
model, since
the phenotypes
of female and
male
individuals
are determined
by alleles
located at a
single locus
and are sex
dependent, any
given genotype
corresponds to
a strategy
pair. Thus, a
strategy pair
is an ESS if
and only if
the allele
corresponding
to this
strategy pair
cannot be
invaded by any
mutant allele.
We show that
an ESS
equilibrium
must be
locally
asymptotically
stable if it
exists.TAO Yi,
Sabin Lessard,
Mathieu Lemire
Source: Journal of Theoretical Biology, Vol. 204, No. 2. (21 May 2000), pp. 191-200. - Evolutionary
limits to the
frequency of
aggression
between
related or
unrelated
conspecifics
in diploid
species with
simple
mendelian
inheritance: Journal of
Theoretical
Biology, Vol.
93, No. 1. (7
November
1981), pp.
97-124.Game
theory has
been used by
some authors
to analyse
evolutionary
limits to the
expression of
aggression in
theoretical
haploid
parthenogeneti
c species.
Others have
examined
frequency
dependent
selection, of
which
aggression may
be a case, by
applying
population
genetic models
to diploid
species. A
model is
presented
which attempts
to combine
these two
approaches.
Game theory is
used to
determine
evolutionarily
stable
strategies and
corresponding
stable
polymorphisms
for a
two-strategy
game played by
members of a
diploid sexual
species, when
choice of
strategy is
determined by
two alleles at
a single
locus. Results
are given for
dominant,
co-dominant
and recessive
determination
of choice of
the more
aggressive of
two
strategies,
for two levels
of
relationship:
unrelated
players and
sibs. It is
found that for
a range of
models of
single locus
inheritance
the
evolutionarily
stable
strategy (ESS)
determined for
haploid
species
remains the
stable
population
strategy for
diploid sexual
species, when
players are
unrelated. In
sibling
contestants
aggression is
reduced. The
mixed strategy
haploid ESS
underestimates
, but the pure
strategy
haploid ESS
provides a
good
indication of
the degree to
which
relatedness
lessens
aggression in
diploid
species. For
both haploid
and diploid
species there
may be a
considerable
advantage to
confining
conflicts to
kin.Michel
Treisman
Source: Journal of Theoretical Biology, Vol. 93, No. 1. (7 November 1981), pp. 97-124. - Evolutionary
dynamics in
frequency-depe
ndent
two-phenotype
models: Theoretical
Population
Biology, Vol.
25, No. 2.
(April 1984),
pp.
210-234.Genera
l
frequency-depe
ndent
selection
models based
on two
phenotypic
classes are
analyzed with
underlying
one-locus
multiallele
phenotypic
determination
systems in
diploid
populations.
It is proved
that the mean
phenotypic
fitnesses tend
to equality
over discrete
generations
and genetic
mutations if a
phenotypic
polymorphism
is to be
maintained.
The exact
conditions are
examined. The
present
results are
valid for a
wide class of
models
whenever
random
groupings or
assortative
patterns based
on phenotype
and affecting
fitness,
linearly or
not, are
independent of
sex, mating
preferences,
or kinship.
They can also
be applied to
two-sex
haploid
models.Sabin
Lessard
Source: Theoretical Population Biology, Vol. 25, No. 2. (April 1984), pp. 210-234.
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