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Stochastic processes in genetics and evolution : computer experiments in the quantification of mutation and selection
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Title
Stochastic
processes
in
genetics
and
evolution
:
computer
experiments
in the
quantification
of
mutation
and
selection
Creator
Mode, Charles J., 1927
Contributors
Sleeman, Candace K.
World Scientific (Firm)
DescriptionAbstract
The
scope
of this
book
is
the
field
of
evolutionary
genetics
. The
book
contains
new
methods
for
simulating
evolution
at the
genomic
level
.
It
sets
out
applications
using
up
to
date
Monte
Carlo
simulation
methods
applied
in
classical
population
genetics
, and
sets
out
new
fields
of
quantifying
mutation
and
selection
at the
Mendelian
level
. A
serious
limitation
of
WrightFisher
process
, the
assumption
that
population
size
is
constant
,
motivated
the
introduction
of
self
regulating
branching
processes
in this
book
.
While
providing
a
short
review
of the
principles
of
probability
and its
application
and
using
computer
intensive
methods
whilst
applying
these
principles
, this
book
explains
how
it
is
possible
to
derive
new
formulas
expressed
in
terms
of
matrix
algebra
providing
new
insights
into the
classical
WrightFisher
processes
of
evolutionary
genetics
. Also
covered
are the
development
of
new
methods
for
studying
genetics
and
evolution
,
simulating
nucleotide
substitutions
of a
DNA
molecule
and on
self
regulating
branching
processes
.
Components
of
natural
selection
are
studied
in
terms
of
reproductive
success
of
each
genotype
whilst
also
studying
the
differential
ability
of
genotypes
to
compete
for
resources
and
sexual
selection
. The
concept
of the
gene
is
also
reviewed
in this
book
and
it
provides
a
current
definition
of a
gene
based
on
very
recent
experiments
with
microarray
technologies
. A
development
of
stochastic
models
for
simulating
the
evolution
of
model
genomes
concludes
the
studies
in this
book
.
Deserving
of a
place
on the
book
shelves
of
workers
in
biomathematics
,
applied
probability
,
stochastic
processes
and
statistics
, as
well
as in
bioinformatics
and
phylogenetics
,
it
will also be
relevant
to those
interested
in
computer
simulation
, and
evolutionary
biologists
interested
in
quantitative
methods
.
DescriptionTable Of Contents
1
. An
introduction
to
mathematical
probability
with
applications
in
Mendelian
genetics
.
1.1
.
Introduction
.
1.2
.
Mathematical
probability
in
Mendelian
genetics
.
1.3
.
Examples
of
finite
probability
spaces
.
1.4
.
Elementary
combinatorial
analysis
.
1.5
. The
binomial
distribution
.
1.6
. The
multinomial
distribution
.
1.7
.
Conditional
probabilities
and a
Bayesian
theorem
.
1.8
.
Expectations
and
generating
functions
for
binomial
and
multinomial
distributions
.
1.9
.
Marginal
and
conditional
distributions
of the
multinomial
distribution
.
1.10
. A
law
of
large
numbers
and the
frequency
interpretation
of
probability
.
1.11
. On
computing
Monte
Carlo
realizations
of a
random
variable
with a
binomial
distribution
.
1.12
. The
betabinomial
distribution

2
.
Linkage
and
recombination
at
multiple
loci
.
2.1
.
Introduction
.
2.2
.
Some
thoughts
on
constructing
databases
of
DNA
markers
from
sequenced
genomes
of
relatives
.
2.3
.
Examples
of
informative
matings
for the
case
of
two
loci
.
2.4
.
General
case
of
two
linked
loci
.
2.5
.
General
case
of
three
linked
loci
.
2.6
.
General
case
of
four
or
more
linked
loci
.
2.7
.
Theoretical
calculations
in
statistical
and
population
genetics

3
.
Linkage
and
recombination
in
large
random
mating
diploid
populations
random
mating
diploid
populations
.
3.1
.
Introduction
.
3.2
. The
one
locus
case
.
3.3
. The
case
of
many
autosomal
loci
with
arbitrary
linkage
.
3.4
.
Sex
linked
genes
in
random
mating
populations
.
3.5
.
Comments
and
historical
notes

4
.
Two
allele
WrightFisher
process
with
mutation
and
selection
.
4.1
.
Introduction
.
4.2
.
Overview
of
Markov
chains
with
stationary
transition
probabilities
.
4.3
.
Overview
of
WrightFisher
perspective
.
4.4
.
Absorbing
Markov
chains
with a
finite
state
space
.
4.5
.
Distributions
of
first
entrance
times
into an
absorbing
state
and their
expectations
and
variances
.
4.6
.
Quasistationary
distribution
on the
set
of
transient
states
.
4.7
.
Incorporating
mutation
and
selection
into
two
allele
WrightFisher
processes
.
4.8
.
Genotypic
selection
with
no
mutation
and
random
mating
.
4.9
. A
computer
experiment
with the
WrightFisher
neutral
model
.
4.10
. A
computer
experiment
with
WrightFisher
selection
model
.
4.11
. A
computer
experiment
with
WrightFisher
genotypic
selection
model
.
4.12
. A
computer
experiment
with a
WrightFisher
model
accommodating
selection
and
mutation

5
.
Multitype
gamete
sampling
processes
,
generation
of
random
numbers
and
Monte
Carlo
simulation
methods
.
5.1
.
Introduction
.
5.2
. A
WrightFisher
model
with
multiple
types
of
gametes

Mutation
and
selection
.
5.3
.
Examples
of
multiple
alleles
and
types
of
gametes
involving
two
chromosomes
.
5.4
. A
genetic
theory
for
inherited
autism
in
man
.
5.5
. An
evolutionary
genetic
model
of
inherited
autism
.
5.6
.
Multitype
gamete
sampling
processes
as
conditioned
branching
processes
.
5.7
. On the
orderly
pursuit
of
randomness
underlying
Monte
Carlo
simulation
methods
.
5.8
.
Design
of
software
and
statistical
summarization
procedures
.
5.9
.
Experiments
in the
quantification
of
ideas
for the
evolution
of
inherited
autism
in
populations
.
5.10
.
Comparative
experiments
in the
quantification
of
two
formulations
of
gamete
sampling
models
.
5.11
. An
experiment
with a
three
allele
neutral
model
.
5.12
.
Rapid
selection
and
convergence
to a
stationary
distribution
. ;
8
6
.
Nucleotide
substitution
models
formulated
as
Markov
processes
in
continuous
time
.
6.1
.
Introduction
.
6.2
.
Overview
of
Markov
jump
processes
in
continuous
time
with
finite
state
spaces
and
stationary
laws
of
evolution
.
6.3
.
Stationary
distributions
of
Markov
chains
in
continuous
time
with
stationary
laws
of
evolution
.
6.4
.
Markov
jump
processes
as
models
for
base
substitutions
in the
molecular
evolution
of
DNA
.
6.5
.
Processes
with
preassigned
stationary
distributions
.
6.6
. A
numerical
example
for a
class
of
twelve
parameters
.
6.7
.
Falsifiable
predictions
of
Markov
models
of
nucleotide
substitutions
.
6.8
.
Position
dependent
nucleotide
substitution
models
.
6.9
. A
retrospective
view
of a
Markov
process
with
stationary
transition
probabilities

7
.
Mixtures
of
Markov
processes
as
models
of
nucleotide
substitutions
at
many
sites
.
7.1
.
Introduction
.
7.2
.
Mixtures
of
Markov
models
and
variable
substitution
rates
across
sites
.
7.3
.
Gaussian
mixing
processes
.
7.4
.
Computing
realizations
of a
Gaussian
process
with
specified
covariance
function
.
7.5
.
Gaussian
processes
that
may
be
computed
recursively
.
7.6
.
Monte
Carlo
implementation
of
mixtures
of
transition
rates
for
Markov
processes
.
7.7
.
Transition
rates
based
on
logistic
Gaussian
processes
.
7.8
.
Nucleotide
substitution
in a
three
site
codon
.
7.9
.
Computer
simulation
experiments

8
.
Computer
implementations
and
applications
of
nucleotide
substitution
models
at
many
sites

Other
nonSNP
types
of
mutation
.
8.1
.
Introduction
.
8.2
.
Overview
of
Monte
Carlo
implementations
for
nucleotide
substitution
models
with
N
sites
.
8.3
.
Overview
of
genographic
research
project

studies
of
human
origins
.
8.4
.
Simulating
nucleotide
substitutions
in
evolutionary
time
.
8.5
.
Counting
back
and
parallel
mutations
in
simulated
data
.
8.6
.
Computer
simulation
experiments
With a
logistic
Gaussian
mixing
process
.
8.7
.
Potential
applications
of
many
site
models
to the
evolution
of
protein
coding
genes
.
8.8
.
Preliminary
notes
on
stochastic
models
of
indels
and
other
mutations

9
.
Genealogies
,
coalescence
and
selfregulating
branching
processes.9.1
.
Introduction
.
9.2
.
One
type
stochastic
genealogies
.
9.3
.
Overview
of the
GaltonWatson
process
.
9.4
.
Selfregulating
GaltonWatson
processes
.
9.5
.
Fixed
points
and
domains
of
attraction
.
9.6
.
Probabilities
of
extinction
.
9.7
.
Stochastic
genealogies
in the
multitype
case
.
9.8
.
Multitype
GaltonWatson
processes
.
9.9
.
Selfregulating
multitype
processes
.
9.10
.
Estimating
the
most
recent
common
ancestor
.
9.11
. The
deterministic
model
and
branching
process
.
9.12
.
Realizations
of a
Poisson
random
variable

10
.
Emergence
,
survival
and
extinction
of
mutant
types
in
populations
of
self
replicating
individuals
evolving
from
small
founder
populations
.
10.1
.
Introduction
.
10.2
.
Experiments
with the
evolution
of
small
founder
populations
with
mutation
but
no
selection
.
10.3
.
Components
of
selection

Reproductive
and
competitive
advantages
of
some
types
.
10.4
.
Survival
of
deleterious
and
beneficial
mutations
from a
small
founder
populations
.
10.5
.
Survival
of
mutations
with
competitive
advantages
over
an
ancestral
type
.
10.6
.
Chaotic
embedded
deterministic
model
with
three
types
.
10.7
.
Self
regulating
multitype
branching
processes
in
random
environments
.
10.8
.
Simulating
multitype
genealogies
and
further
reading
. ;
8
11
.
Two
sex
multitype
self
regulating
branching
processes
in
evolutionary
genetics
.
11
.
Introduction
.
11.2
.
Gametes
,
genotypes
and
couple
types
in a
two
sex
stochastic
population
process
.
11.3
. The
parameterization
of
couple
formation
processes
.
11.4
. An
example
of
couple
formation
process
with
respect
to an
autosomal
locus
with
two
alleles
.
11.5
.
Genetics
and
offspring
distributions
.
11.6
.
Overview
of a
selfregulating
population
process
.
11.7
.
Embedding
nonlinear
difference
equations
in the
stochastic
population
process
.
11.8
. On the
emergence
of a
beneficial
mutation
from a
small
founder
population
.
11.9
. An
alternative
evolutionary
genetic
model
of
inherited
autism
.
11.10
.
Autism
in a
population
evolving
from a
small
founder
population
.
11.11
.
Sexual
selection
in
populations
evolving
from a
small
founder
population
.
11.12
.
Two
sex
processes
with
linkage
at
two
autosomal
loci

12
.
Multitype
selfregulatory
branching
process
and the
evolutionary
genetics
of
age
structured
two
sex
populations
.
12.1
.
Introduction
.
12.2
. An
overview
of
competing
risks
and
semiMarkov
processes
.
12.3
.
Age
dependence
and
types
of
singles
and
couples
.
12.4
.
Altruism
and
semiMarkovian
processes
for
evolution
of
single
individuals
.
12.5
. On an
age
dependent
couple
formation
process
.
12.6
. A
semiMarkovian
model
for
deaths
,
dissolutions
and
transitions
among
couple
types
.
12.7
.
Gamete
,
genotypic
and
offspring
distributions
for
each
couple
type
.
12.8
.
Overview
of
stochastic
population
process
with
two
sexes
and
age
dependence
.
12.9
.
Overview
of
nonlinear
difference
equations
embedded
in the
stochastic
population
process
.
12.10
. A
two
sex
age
dependent
population
process
without
couple
formation
.
12.11
.
Parametric
latent
risk
functions
for
death
by
age
.
12.12
.
Sexual
selection
in an
age
dependent
process
without
couple
formation
.
12.13
.
Population
momentum
and
emergence
of a
beneficial
mutation
.
12.14
.
Experiments
with a
version
of the
age
dependent
model
with
couple
formation

13
. An
overview
of the
history
of the
concept
of a
gene
and
selected
topics
in
molecular
genetics
.
13.1
.
Introduction
.
13.2
. A
brief
history
of the
definition
of a
gene
.
13.3
.
Transcription
and
translation
processes
.
13.4
.
Preprocessing
messenger
RNA
.
13.5
.
Difficulties
with
current
gene
concepts
.
13.6
.
Acronyms
in
tiling
array
technology
.
13.7
.
Genome
activity
in the
ENCODE
project
.
13.8
.
Interpreting
tiling
array
experiments
.
13.9
. A
tentative
updated
definition
of a
gene
.
13.10
.
ABO
blood
group
genetics
in
humans
.
13.11
.
Duffy
blood
group
system
in
man
.
13.12
.
Regulation
of the
Shh
locus
in
mice

14
.
Detecting
genomic
signals
of
selection
and the
development
of
models
for
simulating
the
evolution
of
genomes
.
14.1
.
Introduction
.
14.2
.
Types
of
selection
and
genomic
signals
.
14.3
.
DNA
sequence
evolution
in
large
genomic
regions
.
14.4
.
Statistics
used
in
genome
wide
scans
.
14.5
.
Detecting
signals
of
natural
selection
.
14.6
.
Simulated
genomic
data
in
statistical
tests
.
14.7
.
Species
and
gene
trees
from
mammalian
genomic
data
.
14.8
.
Overview
of
Markovian
codon
substitution
models
.
14.9
.
Simulating
genetic
recombination
.
14.10
.
Modelling
gene
conversion
.
14.11
.
Nucleotide
substitutions
during
meiosis
.
14.12
.
Simulating
insertions
and
deletions
.
14.13
.
Simulating
copy
number
variation
.
14.14
.
Simulating
mutational
events
and
genetic
recombination

15
.
Suggestions
for
further
research
,
reading
and
viewing
.
15.1
.
Introduction
.
15.2
.
Suggestions
for
further
research
on
selfregulating
branching
processes
.
15.3
.
Suggestions
for
continuing
development
of
stochastic
models
of
genomic
evolution
.
15.4
. A
brief
list
of
references
on
genetics
and
evolution
for
further
study
.
Publisher
World Scientific Pub. Co.
Subject
Evolutionary genetics  Computer simulation.
Evolutionary genetics  Mathematics.
Molecular genetics  Computer simulation.
Molecular genetics  Mathematics.
Stochastic programming.
Identifier
9789814350686
(electronic
bk.)
;
9814350672
;
9789814350679
;
http://www.worldscientific.com/worldscibooks/10.1142/8159#t=toc
Language
eng
Type
Electronic books.
FormatExtent
xxviii, 666 p. : ill. (some col.)
Date
c2012
.
OCLC number
874497768
CONTENTdm number
352
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