Re: Does anybody want to proofread and criticize a 7000 plus word
- From: "rev.goetz" <jimgoetz316@xxxxxxxxx>
- Date: 17 Jul 2006 13:05:38 -0700
John Harshman wrote:
rev.goetz wrote:
Does anybody want to proofread and criticize a 7000 plus word review of
molecular evolution?
Everything is standard science up till the discussion. Then I consider
the possibility of teleology.
The formating for some of the equations will not hold in a copy and
paste to the newsgroup. So if anybody is interested, I will have to
email the text in an rtf document.
Post it with the equations removed, or reformatted, or merely described.
Generally a review article doesn't deal with equations, so I'm puzzled
as to what they might be.
This could look ugly. I tried to use "^" for all exponants. I hope that
I caught all of them.
Statistical Probability in the Evolution of Mendelian Populations
By James Goetz
Abstract
The evolution of Mendelian populations has some mechanics that have a
high statistical probability while
other mechanics have a low statistical probability, where a high
probability is equal to or greater than .95
while a low probability is equal to or less than .05 (an arbitrary
decision). The high probability mechanics
include the occurrence of mutations in new generations, purifying
selection, the selection of slightly
advantageous mutations that frequently recur, the selection of highly
advantageous mutations, biased gene
conversion, and some elements of neutral molecular evolution. The low
probability mechanics include the
drift of specific neutral mutations, the selection of slightly
advantageous mutations that rarely recur, and
polygenic Mendelism. A review of these mechanics and statistical
probabilities suggest that assuming the
origin of animals, then the evolution of new animal phenotypes was
likely while no or few animal
phenotypes in particular were likely.
1. Introduction
This paper reviews the mechanics of molecular evolution in Mendelian
populations while focusing on the
respective statistical probability. Some evolutionary mechanics have a
high statistical probability while
other mechanics have a low statistical probability, where a high
probability is equal to or greater than .95
while a low probability is equal to or less than .05 (an arbitrary
decision). The high probability mechanics
include the occurrence of mutations in new generations, purifying
selection, the selection of slightly
advantageous mutations that frequently recur, the selection of highly
advantageous mutations, biased gene
conversion, and some elements of neutral molecular evolution. The low
probability mechanics include the
drift of specific neutral mutations, the selection of slightly
advantageous mutations that rarely recur, and
polygenic Mendelism. Additional mechanics include the rate of adaptive
evolution in relation to the rate of
molecular evolution, geographical variation, major changes of
environment, and prerequisite accumulation.
2. High Probability Mechanics of Molecular Evolution
2.1 Mutations in New Generations
Deoxyribonucleic acid (DNA) mutations will occur in each new generation
with a probability nearly equal to
1. Examples include both point substitutions and indels related to
highly repeated sequences such as
transposable elements (Smith et al., 2002; Hardison et al., 2003). And
various types of mutations have
respective mutation rates.
2.2 Slightly Advantageous Substitutions
High probability in positive directional selection may have involved
slightly advantageous mutations that
frequently recurred such as specific substitutional point mutations.
And the dynamics of the number of the
effective diploid population size (Ne) and the window-time-unit of
opportunity (T) influenced the probability
of fixation (P) for new advantageous mutations that arose more than
once (Fisher, 1930; Haldane, 1932).
For hypothetical example, mutant allele A2 was derived from a specific
transitional substitution with the
selective advantage (s) = 2% and the gene had a statistically random
mutation rate for point substitutions
per site per year = 1.5 x 10^-9 for a hominid species that existed for
1 million years (MY). In theory, A2
would have arisen an average of 10 times if Ne = 10,000 or 100 times if
Ne = 100,000. Likewise, P = .34
or .98, respectively (Table 1). Additionally, a set of various
mutations may cause the same phenotype
(Weiss and Buchanan, 2000), which would increase the number of
mutations and P for the positive natural
selection of a slightly advantageous monogenic trait.
2.3 Highly Advantageous Mutations
Extreme possibilities of high probabilities in adaptive fixations
include highly advantageous positive
natural selection such as P = .99 when s = 250% (Table 1). Such highly
advantageous selection would
literally tear through a large population. According to a classical
calculation for average fixation time,
(1) mt = (2/s)LN(2Ne) generations when s ≠ 0
where mt is the mean fixation time and LN denotes the natural logarithm
(Kimura and Ohta, 1969;
Maruyma and Kimura, 1974). For hypothetical example, a new mutation
with s = 250% when Ne =
1,000,000 would fix in an average of a mere 12 generations.
2.4 Biased Gene Conversion
In some cases, concerted evolution from biased gene conversion caused
highly probable mutations and
fixations that resulted in the homogenization of paralogous genes (Lamb
and Helmi, 1982; Nagylaki and
Petes, 1982; Walsh, 1985). In other words, an advantageous fixation in
one gene sometimes determined
the same fixed mutation in another gene.
2.5 Neutral Mutations and Drift
The drift of specific neutral mutations typically has low
probabilities, but the drift also has highly probable
outcomes. For example, Kimura (1968, 1983) discovered that the drift of
allele frequencies in neutral
mutations produces a fascinating constant that enables some crude
estimations of phylogeny and
mutation rates; regardless of Ne,
(2) K = µ
where K is the rate of neutral fixation and µ is the rate of neutral
mutation. A simple mathematical
explanation for Equation 2 involves assuming that Ne = N, where N is
the number of the diploid population
size (Li and Graur, 1991). For example, this calculation works from
chance because in the case of neutral
mutations,
(3) P = the allele frequency
(If a neutral mutation has an allele frequency = 20%, then P = .2 from
chance.), so by definition a new
neutral mutation in a diploid population has
(4) the allele frequency = 1/(2N) = 1/(2Ne)
and
(5) P = 1/(2N) = 1/(2Ne)
and
(6) 2Neµ = µp
where µp is the rate of neutral mutation per population. Equations 3-6
lead to the calculation that K = µ
regardless of Ne because Ne has an inverse correlation to P. An
increase in Ne reduces P while a
decrease in Ne increases P. The molecular evidence of this phenomenon
led Zuckerkandl and Pauling
(1962, 1965) to propose a steady relative rate of DNA divergence called
the molecular clock, but some
calculate that the clock is only local instead of universal (Gillespie,
1991; Graur and Li, 2000).
Neutral mutations and drift has also helped to determine that genome
size will expand for many species.
For example, many highly repeated sequences have neutrally inserted
with comparably less deletion. And
as long as the mutation rate for the number of neutral nucleotide site
insertions exceeds the fixation rate for
all nucleotide site deletions, genome sizes will expand over
evolutionary time. This appears to be the rule
for many multicellular species and may explain the existence of a
putative vast amount non-transcribing
DNA that lacks evolutionary conservation. For example, roughly 97% of
DNA in humans and mice is
non-transcribing DNA with no known evolutionary constraints (Frazer et
al., 2001; Nobrega et al., 2004;
Goetz, in review). And drift had a major role in many gene duplications
(Lynch and Conery, 2000).
2.6 Purifying Selection
Purifying selection, the elimination of unfit genotypes, is the most
consistent high probability mechanic in
natural selection (Ohno, 1970; Nei, 1987). For example, if a
deleterious mutation has a selective
disadvantage = .1% with Ne = 10,000, then P ≈ 10-18. In some cases,
however, slightly deleterious
mutations with P nearly equal to P for a neutral mutation might have
fixed (Ohta, 1973, 1995).
3. Low Probability Mechanics of Molecular Evolution
3.1 Revisiting the Neutralist-Selectionist Debate
Neutral mutations are subject to drift and the Neutralist-Selectionist
debate. In some cases, the controversy
was more about rhetoric than data because some people feared that
Kimura was going to make natural
selection second place to drift in regards to morphological evolution.
For example, Gillespie (1997: 19)
supports the Selectionist side and writes,
The neutral theory states that much of molecular variation is due to
the interaction of drift and mutation. This
theory, one of the great accomplishments of population genetics because
it is the first fully developed
theory to satisfy the Great Obsession, has remained controversial
partly because it has been difficult to
test and partly because of its outrageous claim that most of evolution
is due to genetic drift rather than
natural selection, as Darwin imagined.
The above quote leads us to doubt that Gillespie (1991, 1997) is
comparing oranges with oranges. First,
Gillespie appears to say that Neutralists claim to have satisfied the
“Great Obsession” of formulating a
complete theory of evolution, but most Neutralists typically focus on
analyzing amino acid evolution without
relating it to morphological evolution. Second, Charles Darwin
primarily focused on morphological
adaptations and paid comparatively trivial attention to the following
two concepts: 1) variation with no effect
on fitness, 2) variation of fitness with no effect on morphology.
I admit that in the naive days of my molecular research I associated
the fixation of most adaptations with
neutral molecular evolution, but that, by far, is not a necessary
conclusion of neutral theory. In fact, Nei
(1983: 189) appears to have made an accurate prediction, “Only a
small proportion of mutations are
advantageous, and that is sufficient for adaptive evolution.” For
hypothetical example, there might have
been roughly 20,000,000 fixed mutations (both point substitutions and
indels) during the last 700,000
generations of wise human ancestry, which roughly equals 1 fixed
mutation per .0065 nucleotide sites. This
equals an average fixation rate of 1 per .035 generations. Both sides
of the debate, however, typically
address only amino acid evolution from point substitutions, but they
must recognize that they are not
addressing all of the genetic elements that effect phenotypes because
many mutations in non-coding
functioning DNA had a profound effect on phenotypes (Enard et al.,
2002). And we should not merely look
at molecular evolution from point substitutions because some indels and
large-scale mutations possibly
had an effect on phenotypes. But for the sake of simplicity, we will
work with a model of amino acid
substitutions. For instance, we will use an estimate of 10,000,000
amino acid sites in the human genome.
If .2% of the amino acid sites had fixed substitutions during the last
700,000 generations of wise human
ancestry, then there have been 200,000 fixed amino acid substitutions.
This equals an average of 1
fixation per 3.5 generations.
If “Haldane’s Dilemma” was off by 2 orders of magnitude higher,
then the fastest realistic average rate of
adaptive fixation equals 1 per 3 generations (Haldane, 1957; Maynard
Smith, 1968). This extreme gives
some room for the Selectionist side, but we need to consider other
elements. First, paleontologists have
never attempted to model the number of adaptive fixations in Homo
sapiens ancestry, and we conjecture
that paleontologists would not come close to realistically estimating
an average of 1 adaptive fixation per 3
generations during the last 700,000 generations of Homo sapiens
ancestry. Second, an average fixation
time of 3 generations with the number of the effective population size
equal to 10,000 requires a selective
advantage equal to 600% while an average fixation time of 30
generations in the same population
requires a selective advantage equal to 67% (Equation 1), and such
rigorous advantageous selection
might never have occurred in hominid history. Third, no evidence
supports effective population size
bottlenecks less than 10,000 in recent wise human ancestry (Takahata et
al., 1995; Sherry et al., 1997;
Clark et al., 1998), which may suggest a moderate “cost of natural
selection” with a moderate rate of
adaptive molecular evolution. Forth, 1 adaptive fixation per 3
generations for a prolonged period of time
would leave numerous evidences of selective sweeps throughout the
genome (Hudson et al., 1987;
Hudson, 1991), but nothing close to this magnitude of evidence has ever
materialized. Fifth, the
Selectionist side predicts that balancing selection caused most
heterozygosity and there are some
significant measurements of balancing selection (Hughes and Nei, 1988,
1989; Hughes, 1999), but most
heterozygosity in humans exhibits a pattern that is consistent with
neutral theory (Cargill et al., 1999). Sixth,
if adaptation dominated the evolution of amino acids during the last
700,000 generations of wise human
ancestry, then most exons in humans would be dominated with the
proportion of nonsynonymous
substitution exceeding the proportion of synonymous substitution
(Kimura 1977, 1983), but only sparse
examples of such candidate positive directional selection in human
exons have been significantly
measured (Hughes, 1999; Wyckoff et al., 2000; Johnson et al., 2001).
Additionally, all human zygotes have
a unique genome that would cause a unique phenotype as defined by Mayr
(1982), but all of these
phenotypes in former generations have never repeated from zygote
formation so we cannot invoke natural
selection as the primary cause of these phenotypes. In sum, numerous
lines of evidence in human genetics
point to neutral theory.
The implications of neutralist theory in human amino acid evolution may
point to the evolutionary
importance of indels in exons and all mutations in non-coding
regulatory elements. In other words,
assuming that the evidence of adaptations in humans indicates a history
of molecular adaptation, then little
evidence of adaptive point substitutions in exons may suggest that
molecular adaptations involved indels
in exons or mutations in other genome regions. And if there were few
molecular adaptations of any type,
then some morphological adaptations might have been abrupt.
The Selectionist side, however, raises important issues. For example,
the evolution of nonsynonymous
sites in several mammalian genes have the Index of Dispersion (R) that
is inconsistent with neutral theory,
where R is the ratio of the variance to the mean for the number of
point substitutions in a gene lineage that
is compared to at least two other lineages with the same gene (Ohta and
Kimura, 1971; Gillespie, 1989).
The Selectionist side claims that calculations of R that indicate
significant overdispersion in mammalian
gene lineages have disproved neutral theory (Gillespie, 1997; Zeng et
al., 1998; Hey, 1999). However, the
claim to victory needs further evaluation.
First, the Selectionist side did not prove that the majority of
mammalian gene lineages are significantly
overdispersed. For hypothetical example, if more than 50% of mammalian
gene lineage dispersion is
consistent with neutral theory, then the Neutralist side wins.
Second, significant evidence of overdispersion may indicate that
positive natural selection acted on a
gene lineage, but the overdispersion does not indicate that natural
selection caused most of the amino
acid evolution in the respective gene lineage. In a hypothetical case,
a gene lineage had a brief episode of
positive natural selection that preceded a long period of neutral
molecular evolution, and only a third of the
amino acid evolution in the lineage resulted from positive natural
selection while the gene lineage
indicated significant evidence of overdispersion. In this case, the
majority of the gene lineage evolved from
neutral evolution.
Third, particular lineages of a gene may be overdispersed while the
other lineages of the gene may be
consistent with neutral theory. In a hypothetical case, a gene lineage
in the ancestor of primates had an
episode where all of the amino acid evolution resulted from positive
natural selection. But the respective
gene had only neutral evolution throughout primate evolution. In this
case, the gene exhibited positive
natural selection throughout the ancestral lineage while the gene
exhibited neutral evolution throughout the
primate lineages.
We conjecture that the Selectionist side will never discover evidence
that indicates at least 50% of all
amino acid evolution in mammals resulted from positive natural
selection. And we will continue to discover
pervasive molecular evidence of both neutral evolution and positive
natural selection.
An interesting twist to the Neutralist-Selectionist debate involves
amino acid codon bias in Drosophila
genes (Kreitman, 1996; Zeng et al., 1998; Hey, 1999). Amino acid codon
bias is a contradiction to neutral
theory that may indicate positive natural selection. And perhaps in the
case of Drosophila amino acid
evolution, the Selectionist side will prevail to indicate that at least
50% of amino acid evolution resulted
from positive natural selection.
Incidentally, the Neutralist-Selectionist debate still has unbroken
ground. For example, we need to analyze
the roles of neutral evolution and positive natural selection in the
following: indels in exons, all mutations in
non-coding regulatory elements, and all mutations in non-coding DNA
that lacks evolutionary conservation.
And we noted in Section 2.5 that roughly 97% of the DNA in humans and
mice is non-transcribing DNA
with no known evolutionary constraints.
3.2 Slightly Advantageous Mutations that Rarely Recur
Many specific indels and large-scale mutations rarely recur. And
slightly advantageous mutations that
rarely recur have a low probability of fixation from positive natural
selection compared to slightly
advantageous mutations that frequently recur (Table 1). This section
outlines mutation rates and allele
frequencies that relate to fixation while focusing on mutations that
rarely recur.
Here is a hypothetical mutation rate for a particular gene: the gene
has a mean point substitutional
mutation rate (µ) equal to 3 x 10^-9 per nucleotide site per year.
This article, however, focuses on specific
mutations. For instance, the above gene has a statistically random
mutation rate and the x nucleotide has
the i-th nucleotide (adenine) mutate to the j-th nucleotide (guanine)
with µx(ij) = 10^-9 per year.
Now we will examine hypothetical mutation rates of specific insertions.
Due to technical constraints, we
have yet to see a study that directly estimates the mutation rates for
the arising of any specific insertion of
functioning DNA. On the other hand, Lynch and Conery (2000) analyzed
eukaryotic lineages and estimate
that each gene on average generates a fixed duplicative insertion at a
rate of 1 per 100 MY. Since most of
these gene duplications eventually ceased to express or never expressed
at all, the above rate may mostly
represent neutral insertions so the fixation rate may roughly equal the
mutation rate. Regardless, the above
rate does not address specific “haploid set locations,” where the
haploid set location of an insertion is the
specific location in the chromosomes of a gamete. A hypothetical
mutation rate for the arising of a specific
insertion follows: µx(i) is the mean rate of the i-th sequence
inserting into the x haploid set location per
year. For hypothetical example, a specific sequence that contains an
exon is inserted into a haploid set
location with µx(i) = 10-36 per year.
Here is a hypothetical breakdown of possible insertions with sequences
ranging from 100 to 100,000
nucleotide sites in a haploid set of 10 chromosomes that contain 108
nucleotides per piece. In such a
haploid set, there could be 1014 unique sequences ranging from 100 to
100,000 nucleotide sites. And
each sequence has approximately 109 possible insertion locations so the
total number of different specific
insertions with the above range approximately equals 1023.
More than one specific insertion, however, could cause the same
phenotype. For example, the insertion of
exon sequences can have multiple possibilities that cause the same
phenotype for at least four reasons: 1)
an intron may have numerous locations that could incorporate a specific
exon while many of the
possibilities cause the same phenotype; 2) the insertion of a sequence
that contains an exon may have
various breakpoints with differing amounts of intron sequence at the
5’ and 3’ ends while many of the
possibilities cause the same phenotype; 3) multiple paralogous exons in
the same class may be similar
enough so that any of them could insert into a gene at the same
location while each of the possibilities
cause the same phenotype; 4) subject to regulatory constraints and
phase limitations, a set of paralogous
genes may be similar enough so that a specific exon sequence could
insert into any of them at a
paralogous location while each of the possibilities cause the same
phenotype. For instance, the above
example of the sequence that contained an exon with µx(i) = 10-36 per
year could have the same
phenotype with the x set of haploid set locations and the i-th set of
sequences, which makes µx(i) = 10^-27
per year. Similarly, subject to regulatory constraints, the above
concepts of various breakpoints, various
paralogous sequences, and various locations describes how multiple
possibilities of duplicative gene
insertions could cause the same phenotype.
Due to genetic mechanisms, some types of insertions have a higher
fixation rate than others, which
suggests that some specific insertions have a higher µx(i) compared to
others. For examples, 1) many
insertions of genes were in a tandem array because of unequal crossing
over; 2) most insertions of exons
were internal gene duplications instead of exon insertions that created
chimeric genes (Graur and Li,
2000).
Concerning allele frequencies, the arising of new mutations can lead to
allele frequencies, and many
estimates of allele frequencies refer to alleles generated by point
substitutions. For hypothetical example,
a population of 100,000 hominids had 30,000 copies of a mutant allele
and 170,000 copies of the wild
type (the relatively original gene), so the mutant allele frequency
equaled 15%. The same concept for allele
frequencies also applies to indels and large-scale mutations because
many of these mutations originated
from a single germ cell-line and survived as a polymorphism until
fixation. Here are hypothetical examples
of allele frequencies for an insertion and two types of large-scale
mutations: 1) the above hominid
population had a specimen with a new gene insertion, and eventually the
new locus had 10,000 copies
divided between 9,000 heterozygote hominids and 500 homozygote hominids
while the population size
remained the same, so the allele frequency for the new locus equaled
5%; 2) a hominid population had 48
diploid chromosomes per specimen, but a mutation fused 2 chromosomes
for a gamete so the haploid set
had 23 chromosomes; this gamete helped to produce a heterozygous
hominid specimen with 47
chromosomes, and eventually the allele frequency for the fusion equaled
100% when all of the hominid
population was homozygous with 46 diploid chromosomes; 3) a Xenopus (a
genus of toads that are
commonly called clawed frogs) population had 18 diploid chromosomes per
specimen, but a mutation
resulted in a duplicated haploid set for a gamete so the gamete had 18
chromosomes; this gamete helped
to produce a heterozygous Xenopus specimen with 27 chromosomes, and
eventually the allele frequency
for the duplication in an isolated population equaled 100% when all of
the Xenopus population was
homozygous with 36 chromosomes.
This explanation of mutation rates and allele frequencies helps to show
how many rare mutations have
fixed. And some of these rare fixed mutations were vital for
evolutionary history. For example, a review by
Patthy (1999) suggests that the rise of exon shuffling coincides with
the origins of metazoan phyla.
Additionally, rare events of gene creation resulted from series of
insertions and horizontal gene transfer
(Brosius, 1999; Courseaux and Nahon, 2001; The International Human
Genome Sequencing Consortium,
2001; Hardison et al., 2003). In sum, the fixation for many of these
vital insertions resulted from a single
trial that had a low probability of fixation (Table 1).
3.3 Polygenic Mendelism and Evolution
Independent assortment with recombination is a remarkable system of
shuffling in diploid sexual
reproduction that facilitates the formation of new functioning DNA
combinations and a population-wide
accumulation of adaptations. For example, without recombination, entire
chromosomes instead of
functioning DNA loci would be the object of natural selection and
drift.
Concerning the facilitation of new DNA combinations, from independent
assortment alone each human
with 23 pairs of chromosomes has 223 ≈ 8 x 10^6 possible DNA
combinations for gametes while a
mating pair has approximately 7 x 10^13 possible DNA combinations for
zygotes (assuming that no pair of
chromosomes is identical). When recombination is considered, a human
has more possible DNA
combinations for gametes than the estimated number of neutrons and
protons in the observed universe
(1080). For example, Cargill et al. (1999) estimate that the typical
human is a heterozygote at
24,000-40,000 nonsynonymous sites, which also means that humans are a
heterozygote at roughly the
same amount of amino acid sites. This indicates that each human has
approximately 10^7,200-10^12,000
possible combinations of amino acid sequences from recombination during
gamete development, so only
a trivial fraction ever occur.
The trivial fraction of recombination that did occur, however, might
have helped to form new polygenic
traits. For hypothetical example, a hominid population had 6 specimens
originate a neutral mutation while
each mutation was at a different locus, but from drift the 6 mutations
eventually combined in a specimen
while the 6 mutations together created a polygenic trait that had a
selective advantage. Likewise, Mayr
(1982: 57) states, “… by recombination, a new gene pool is
organized in each generation, and hence a
new and unpredictable start is made for the selection procedure of the
next generation.”
On the other hand, the new unpredictable start for each new generation
also means that new
advantageous DNA combinations have to overcome the Regression to the
Mean in each new generation.
For hypothetical example, a specimen with the above polygenic trait
from 1 copy of each of the 6
mutations had mated with a specimen with just 1 copy of 2 of the
mutations so on average only 3.5% of
their F1 offspring inherited the polygenic trait (excluding the
possibility of a heterozygote advantage). This
example suggests that each mutation that was vital for an advantageous
polygenic trait must have
individually fixed while each of the fixations depended upon drift if
the mutations were originally neutral.
Likewise, this example indicates that in such cases the Regression to
the Mean can cause the loss of an
advantageous polygenic trait.
4. Additional Mechanics of Evolution
4.1 Adaptive Evolution
Molecular evolution is relatively independent of adaptive evolution
while adaptive evolution is relatively
independent of morphological evolution. And adaptations that involved
increased morphological
complexity appear to be the exception in natural history (Eldridge and
Gould, 1972; King and Wilson,
1975; Wilson, 1975; Gould and Eldridge, 1977, 1993; Gould and Lewontin,
1979; Nei, 1987; Gould, 1989;
Gilbert et al., 1996; Li, 1997; Hall, 1998; Wolpert et al., 2002,
Gilbert, 2003). For example, the last
650,000 generations in modern human ancestry included the evolutionary
development of hominid
bipedalism, exceptional manual dexterity, remarkably increased
encephalization relative to body stature,
and neocortex wiring that enables the development of scientific theory
and religious practice (Newberg et
al. 2001), but during the same time the lineages of the other extant
African hominoids encountered
comparatively little morphological and intellectual development
(Conroy, 1990, 1997; Fleagle, 1999;
Stauffer et al., 2001). And most of the ancestry that preceded the
origin of animals involved miniscule
developmental evolution such as an estimated 3 plus billion years
divided between a prokaryotic lineage
and a unicellular eukaryotic lineage.
Morphological adaptations are also relatively independent of
physiological adaptations. For example,
several studies of metazoan genes measure significant evidence of
directional molecular adaptation while
all of the respective known gene functions relate to recognition or
reproduction, which improved the fitness
of the physiology in the particular lineages but had no known effect on
the morphology in the lineages
(Hughes, 1999; Hellberg et al., 2000; Hughes et al., 2000; Wyckoff et
al., 2000; Zhang and Nei, 2000;
Johnson et al., 2001; Swanson and Vacquier, 2002; Zhang et al., 2002;
Zhu et al., 2004). Likewise, many
physiological adaptations have no effect on morphology.
The above trend of adaptive studies may help to explain the fossilized
evidence of stasis according the
hypothesis of Punctuated Equilibrium (Eldridge and Gould, 1972; Gould
and Eldridge, 1977, 1993). The
hypothesis of Punctuated Equilibrium claims that a repeated pattern in
metazoan evolution involved long
periods of stasis despite significant environmental changes, and the
stasis was interspersed with relatively
punctuated changes in metazoan morphology. The fossilized evidence of
evolutionary stasis maintained
during significant environmental changes, however, might have involved
morphological stasis while many
important physiological adaptations occurred with no impact on
morphology.
On the other hand, the paleontological observation of punctuated
evolutionary development is due in part
to incomplete preservation of the fossil record but might also have
involved occasional adaptations from
mutations related to regulation, and an irregular evolutionary
developmental tempo might in part have
resulted from the relative independence of molecular and morphological
evolution. Perhaps the most
documented case of relatively rapid evolutionary development that
involved possible large morphological
adaptations from single mutations is the purported descent of maize
from teosinte (a wild grass) in 4 or 5
mutational steps (Beadle, 1981; Doebley, 2001).
4.2 Environmental Factors
Geographical variation influenced the percent of selective advantage
for an advantageous mutation during
a species existence (Simpson, 1953). For hypothetical example, a
hominid species existed for 1 MY, but
part of the population lived in a forest environment and the other part
lived in a savanna environment.
Mutant allele A2 had been neutral in the forest subpopulation but
advantageous in the savanna
subpopulation so the forest environment and the forest subpopulation
decreased the probability of fixation
for allele A2 compared to the savanna environment and the savanna
subpopulation.
Other environmental factors that influenced natural selection included
major environmental changes. For
example, since Early Cambrian, life history triumphed through twelve
major extinctions while seven of them
preceded major adaptive radiations. As with the case of the Late
Cretaceous extinction of many
Dinosauria taxa followed by the Early Tertiary radiation of Eutheria,
the causes of the extinctions of former
niche domineers might have enabled many adaptive radiations that might
never have occurred otherwise.
4.3 Prerequisite Accumulation
Evolutionary events are typically dependent upon previous evolutionary
events (Simpson, 1953). For
example, a selective advantage for mutations could have depended on the
accumulation of other fixations.
In this hypothetical case, a hominid species had the fixation of 10 new
slightly advantageous homeotic
gene alleles in 1 MY, and the alleles are respectively named A2 through
J2. Biochemical complexities,
however, caused J2 to have a disadvantageous fitness prior to the
accumulation of A2 through I2 with J2
having an advantageous fitness after the accumulation of A2 through I2.
Though the hominid species
existed for 1 MY, J2 might have been advantageous for only 100,000
years. Additionally, in some cases,
series of amino acid adaptations have depended upon the low
probabilities of the mutation and fixation of
gene duplications (Goodman et al., 1975; Hughes, 1999; Wyckoff et al.,
2000; Hughes et al., 2000; Zhang
and Nei, 2000; Johnson et al., 2001; Zhang et al., 2002; Zhu et al.,
2004).
5. Discussion
This paper reviews the probabilities of mechanics in the molecular
evolution of Mendelian populations.
And we see both high probability mechanics and low probability
mechanics. And we conclude that the
history of molecular evolution included numerous cases of positive
natural selection that involved low
probabilities (Sections 3.2 & 4.3).
First, we acknowledge the role of high probability mechanics in
molecular evolution: A) mutations provided
a consistent supply of physiological variation (Section 2.1), and a
small proportion of these mutations had
a physiological advantage for the respective specimen, and a small
proportion of these physiologically
advantageous mutations resulted in fixed adaptations, and a small
proportion of these fixed adaptations
caused morphological adaptations; B) many specific mutations that
frequently recurred, such as slightly
advantageous point substitutions and biased gene conversion, had a
nearly determinate probability for
fixation (Sections 2.2 & 2.4); C) neutral mutations and drift were a
consistent cause of molecular evolution
(Section 2:5); D) purifying selection typically maintained adaptations
(Section 2.6).
On the other hand, many foundational mutations that caused exon
shuffling and gene duplications rarely
recurred (Sections 3.2). And there is little evidence of highly
advantageous mutations that had a high
probability of fixation with a single trial (Section 2.4). And though
neutral mutations are a high probability
cause of molecular evolution, adaptive evolution is relatively
independent of molecular evolution (Section
4.1). And regardless of which side wins the Neutralist-Selectionist
Debate (Section 3.1), most
advantageous mutations that rarely recurred had a low probability of
fixation from positive natural
selection. And many of these low probability fixations were
prerequisites for most advantageous mutations
that frequently recurred and had a high probability of fixation from
positive natural selection (Section 4.3).
And the Regression to the Mean could cause the extinction of
advantageous polygenic traits (Section 3.3).
Additionally, environmental factors influenced the direction of natural
selection (Section 4.2).
The evidence in this review indicates that both molecular evolution and
positive natural selection involved
numerous occasions that involved low probabilities. And this suggests
that assuming the origin of animals,
then the evolution of new animal phenotypes was likely while no or few
animal phenotypes in particular
were likely.
The many low probabilities in molecular evolution and positive natural
selection may also support a
perspective of the late Stephen Jay Gould, which says that the natural
emergence of intelligent life in the
universe was unlikely (Gould, 1989; Conway Morris and Gould, 1998;
Goetz, in review). And for the
purpose of this paper, intelligent life is a species that can invent
scientific theories and practice religion
(Newberg et al., 2001) while it has manual dexterity and deft
locomotion that enables the species to act
upon its intelligence, which gives a selective advantage to the
intelligence.
Let us look at a brief probability study about the only known species
of intelligent life, which is Homo
sapiens. For example, if since the origin of animals there were at
least 12 vital events of mutation and
selection in H. sapiens ancestry that had a .01 probability, including
any possible multiple trials and various
pathways that could lead to a similar end, then H. sapiens most likely
would not have emerged in our
universe with roughly 10^22 stars. And to make any relevance of this
probability study, we need to take a
hard look at “various pathways that could lead to a similar end.”
For hypothetical examples of various pathways that could lead to a
similar end, we conjecture that the H.
sapiens phenotype could result from various synonymous karyotypes. For
instance, perhaps the H.
sapiens phenotype could have had a chromosome number other than 46.
And beyond synonymous karyotypes, other various pathways that could
lead to a similar end could have
involved convergent evolution that could have produced other forms of
intelligent life. For example, Conway
Morris (2003) compiles ubiquitous evidence of evolutionary convergence
in predators while he argues that
assuming abiogenesis the origin of predatorily intelligent life on
earth was inevitable.
Conway Morris (2003) also proposes that teleology helped to make the
evolutionary emergence of
predatorily intelligent life inevitable in our universe. And Denton and
colleagues (Denton, 1998; Denton and
Marshall, 2001; Denton et al., 2002; Denton et al., 2003) have a
similar perspective while proposing that
all teleology in evolutionary history was contained in the initial
conditions of the universe. On the other hand,
I (Goetz, in review) propose that the low probabilities in natural
evolutionary mechanics coupled with the
time constraints of multigenerational stars in the universe suggest
that teleology in the history of adaptive
evolution included occasional intervention from outside the initial
conditions.
In this discussion, we briefly cited various conclusions related to the
low probabilities in the history of
molecular evolution and natural selection. The various conclusions
follow: 1) the natural emergence of
intelligent life was unlikely while the emergence of intelligent life
occurred regardless; 2) the ubiquitous
evidence of convergent evolution indicates that the natural emergence
of intelligent life was likely; 3)
according to various models of teleology, evolution included an unknown
teleological factor so the
emergence of intelligent life was inevitable. Some of these conclusions
may overlap. And at this point in
the history of thought in empirical research, any of the above
conclusions would be a conjecture.
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Table 1. Probability in Advantageous Fixation.1
Selective Number of trials
advantage
1 10 100
1% 0.02 0.18 0.87
2% 0.04 0.34 0.98
3% 0.06 0.46 1.00
4% 0.08 0.57 1.00
5% 0.10 0.65 1.00
10% 0.18 0.86 1.00
15% 0.26 0.95 1.00
20% 0.33 0.98 1.00
25% 0.39 0.99 1.00
30% 0.45 1.00 1.00
35% 0.50 1.00 1.00
50% 0.63 1.00 1.00
100% 0.87 1.00 1.00
150% 0.95 1.00 1.00
200% 0.98 1.00 1.00
250% 0.99 1.00 1.00
1. P = 1 - (1 - π)^n, where P is the probability for fixation
including multiple trials (1 - the proportion of 0
successes) and π is the proportion of fixation for a single mutation
(π also equals P for a single mutation)
and n is the number of trials; π = 1-e^-2s when Nes ≥ 2 (minimum Nes
value is an arbitrary decision),
where s is the percent of selective advantage and Ne is the number of
the effective diploid population size
and Ne is also equal to the diploid population size for the sake of
mathematical simplicity (Fisher, 1930;
Wright, 1931; Kimura, 1962; Crow and Kimura, 1970; Hedrick, 1983; Li
and Graur, 1991); n = 2 NeTµ,
where T is the window-time-unit of opportunity and µ is the rate for a
specific mutation (or the rate for a set
of mutations that cause the same phenotype when calculating P for an
advantageous monogenic trait) per
haploid set per year.
.
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