Re: Does anybody want to proofread and criticize a 7000 plus word
- From: "rev.goetz" <jimgoetz316@xxxxxxxxx>
- Date: 17 Jul 2006 19:11:41 -0700
John Harshman wrote:
[snip]
It got very ugly. Your line length is too long and you have hard returns[snip]
that leave an extra blank line after every one. Reformat. The equations
seem fine, though.
All subscripts and italics are lost, but i think it is mostly
understandable.
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 (10^80). 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 evelopmental 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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