Important words and concepts from Chapter 23,
Campbell & Reece, 2002 (3/25/2005):
by Stephen T. Abedon (abedon.1@osu.edu)
for Biology 113 at the Ohio State University
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(1) Chapter title: The Evolution of
Populations
(a)
"An organism exposes its phenotype—its
physical traits, metabolism,
physiology, and behavior—not its genotype, to the environment. Acting
on phenotypes, selection indirectly adapts a population to its environment by
increasing or maintaining favorable genotypes in the gene pool."
(p. 430)
(b)
"One obstacle to understanding evolution is the common
misconception that individual organisms evolve, in the Darwinian sense, during
their lifetimes. In fact, natural selection
does act on individuals; their characteristics affect their chances of survival
and reproductive success. But the evolutionary impact of this natural selection
is only apparent in tracking how a population of organisms changes over time…
Thus, it is the population, not its individuals,
that evolves, as some heritable variation becomes more common at the expense of
others." (p. 416)
(c)
["To the people gathered there, most of whom had no more than a
first- or second-grade education, some genetic principles seemed to make
intuitive sense, whereas others did not. No one had trouble, for instance,
understanding that traits can be inherited. But the fact that the probability
of inheriting a trait is unrelated to the previous births was more difficult to
grasp. If one parent has the Alzheimer's mutation, there is a 50 percent risk
that each child will have it too. But, just as parents who have had three girls
in a row may expect their chance of having a boy to increase, the villagers
endorsed a logical fallacy. One man announced to the assembled group: ‘We the
families in which there are only a few affecteds must be grateful to those
families with many affecteds.’ Local ideas of guilt and collective burden were
deeply ingrained, and clashed with the principles of population genetics."
p. 15 of Kenneth S. Kosik, 1999, The fortune teller, The Sciences 39:13-17]
(d)
[the evolution of populations
(Google Search)] [population evolution and
speciation (BSC Courseware)] [index]
MICROEVOLUTION TOOLS AND
OVERVIEW
(a)
Population genetics is essentially the study of allele and genotype frequencies within populations of
organisms
(b)
[population genetics
(Google Search)] [DNA technology in forensic
science (welcome to applied population genetics) (Committee on DNA
Technology in Forensic Science)] [index]
(a)
The ultimate triumph of Darwinism required its integration with Mendelian genetics
(b)
That is, evolution is a genetic phenomenon so cannot be fully (or even
well) understood without an understanding of Mendelian genetics
(c)
This synthesis between Darwinism and Mendelian genetics did not occur
until the 1930s (recall that Darwinism and Mendelian genetics both came into
being during the mid to late 1800s)
(d)
The combination of Darwinism and Mendelian genetics is called the
modern synthesis (of Darwinism and Mendelian genetics as well as paleontology, taxonomy, biogeography, and population genetics)
(e)
"The modern synthesis emphasizes the importance of populations as
the units of evolution, the central role of natural selection as the most important
mechanism of evolution, and the idea of gradualism to explain how large changes
can evolve as an accumulation of small changes occurring over long periods of
time."
(f)
["…the Modern Synthesis is
a theory about how evolution works at the level of genes, phenotypes, and
populations whereas Darwinism was concerned mainly with organisms, speciation
and individuals. This is a major paradigm shift and those who fail to
appreciate it find themselves out of step with the thinking of evolutionary
biologists. Many instances of such confusion can be seen here in the
newsgroups, in the popular press, and in the writings of anti-evolutionists."
(Talk.Origins)]
(g)
[modern synthesis, the modern synthesis of genetics
and evolution (Google Search)] [index]
(a)
The term population is more complex than you may realize
(b)
However we will delay our discussion of the complexity inherent in the term
population until our considerations of speciation
(c)
For now, consider a population to be a localized group of interbreeding
individuals (with lots of emphasis on interbreeding)
(d)
[interbreeding population
(Google Search)] [index]
(a)
The term species is also fraught with complexity
which will be considered more fully when we discuss speciation
(b)
For now, consider a species to be a group of populations whose
members are capable of interbreeding
(c)
Species and populations possess certain properties (or
characteristics) such as their location that we will discuss in more detail
when considering population ecology
(d)
One property is that the population's underlying a species may undergo
different degrees of gene exchange ranging from very little (an
isolated population) to quite a bit
(e)
[species (Google Search)] [index]
(a)
In a population
genetics
sense, a population or species consists of a gene pool
(b)
A gene pool "consists of all alleles at all gene
loci in all individuals in a population."
(c)
Recall that diploid individuals possess two alleles at
each locus
(d)
[gene pool (Google Search)] [index]
(7)
Fixed locus (fixed
allele)
(a)
A locus for which only a single allele exists for an entire gene pool is
considered to be fixed, i.e., a fixed locus
(b)
We would describe the frequency of a fixed allele within a gene pool as
1.0
(c)
We would describe the frequency of all other alleles as 0.0 (i.e., they
are not present)
(d)
An allele with a frequency of 0.0 is said to be extinct
(e)
["fixed locus" and
genetics, "fixed locus" and
evolution, fixed allele, fixed alleles (Google Search)] [index]
(8)
Gene frequency (allele
frequency)
(a)
All alleles at not-fixed loci possess a frequency that is somewhere between 0.0 and 1.0
(b)
We describe this frequency as allele
frequency or, less correctly but more commonly, as gene frequency
(c)
Remember that gene (or allele) frequency refers to the frequency of
alleles in an entire gene pool, not in single individuals
(d)
Remember that each diploid individual
has two alleles at each locus
(e)
[gene frequency, gene frequencies, allele frequency, allele frequencies
(Google Search)] [index]
(a)
Remember that any one individual may be homozygous for only one allele of the one
or more present in the population (at a given locus) or a given individual may be heterozygous at that locus
(b)
Thus, three alleles (or many more) can exist in a population (with
associated allele frequencies) but only up to two alleles at a time can exist
within a given individual
(c)
The frequency of genotypes within a
population is dependent on the frequency of alleles (and visa versa, actually)
(d)
It is only within genotypes that evolution acts on alleles
(e)
Consequently, to understand evolution and evolutionary change, it is
usually important to keep track of allele frequencies and to keep track of genotype frequencies
(f)
That is, make sure the following makes sense to you:
(i)
natural selection acts on phenotypes
(ii)
genotypes underlie phenotypes
(iii)
alleles underlie genotypes
(g)
[genotype frequency
(Google Search)] [index]
(10)
Genetic structure (supplemental concept)
(a)
Genetic structure is a population genetics term used to refer to a population’s
allele and genotype frequencies
(b)
Evolution may be defined as change over time of a population's genetic
structure
(c)
"Evolution is a generation-to-generation change in a population's
frequencies of alleles and genotypes—a change in a population's genetic
structure."
(d)
[genetic structure (Google Search)] [index]
(11) Calculating
allele frequencies
(a)
Remember that a diploid organism has two (not necessarily
different) alleles at each locus
(b)
The frequency of an allele within a population is equal
to the number of alleles of a given type within the population divided by the
total number of alleles found at a given locus
(c)
Thus, if 200 A alleles and
400 a alleles are found within a
given population, then the frequency of A
alleles is 200 / (200 + 400) = 1/3 = 0.33.
(d)
If this is a diploid population, how many individuals are in this
population? (answer: 300… make sure that these ideas and calculations make
sense to you)
(e)
[calculating allele frequencies,
determining allele frequencies
(Google Search)] [index]
(12) Calculating
allele frequencies from genotype frequencies
(a)
Note that very often one knows (or can infer) genotype frequency
(b)
If so, then genotype frequency information can be used to calculate allele
frequency. How?
(c)
If a population has 100 Aa individuals, 200 aa
individuals, and 300 AA individuals
then the number of A alleles is 100*1 + 300*2 = 700; the number of a alleles is 100*1 + 200*2 = 500; the
frequency of A therefore is 700 /
(500 + 700) = 7/12 = 0.58
(d)
Remember, diploid individuals contribute two alleles
from each locus to the gene pool (hence
the *2 in the above calculations); How many diploid individuals are present in
the above example?
(e)
[Calculating allele frequencies
from genotype frequencies (Google Search)] [index]
CALCULATING GENOTYPE
FREQUENCIES FROM ALLELE FREQUENCIES
(13) Calculating
genotype frequencies from allele frequencies
(a)
Calculating genotype frequencies from allele
frequencies is also possible, but requires quite a bit of fudging
(b)
In fact, much of this chapter deals with this fudging
(c)
However, the calculations are simple: One assumes simply that alleles are picked at random from the gene pool to
assemble genotypes
(d)
Assume that the frequency of allele A
is 0.4 and that the frequency of allele a
is 0.6; What is the frequency of genotypes AA,
Aa, and aa?
(i)
Frequency AA = 0.4 * 0.4 =
0.16
(ii)
Frequency aa = 0.6 * 0.6 =
0.36
(iii)
Frequency Aa = 0.4 * 0.6 +
0.6 * 0.4 = 0.48
(e)
Remember that there are two paths by which the heterozygote may be constructed, A from mom and a from
dad, or a from mom and A from dad (make sure that this idea
makes sense to you)
(f)
Now, substitute the letter p
for the frequency of A (i.e., in this
example p = 0.4) and the letter q for the frequency of a (i.e., in this example q = 0.6); what
is the frequency of the genotypes AA,
Aa, and aa?
(i)
Frequency AA = p * p
= p2
(ii)
Frequency aa = q * q
= q2
(iii)
Frequency Aa = p * q
+ q * p = 2pq
(g)
Note that for a locus for which only two alleles are
present in a population:
(i)
p2 + 2pq + q2 = 1 = (p
+ q)2
(h)
In addition, of course, keep in mind that
(i)
p = 1 – q
(ii)
q = 1 – p
(iii)
1 = p + q
(i)
Again, make sure that these ideas and generalizations make sense to
you, particularly to the point where you are able to apply these ideas
(j)
[(Google Search)] [index]
(a)
Genotype frequencies do not necessarily
coincide with phenotype frequencies (e.g., as a
consequence of complete dominance)
so calculating genotype frequencies from phenotype frequencies is not
necessarily straightforward
(b)
However, if the frequency of the recessive allele is q then
(i)
the frequency of the recessive homozygote is q2
(ii)
the frequency of the dominant homozygote is (1 - q)2
(iii)
the frequency of the heterozygote is 2 * q * (1 - q)
(iv)
(these ideas and concepts should eventually make intuitive sense to you
and you should be working towards that point, so make sure that these ideas
makes sense to you to this point, before you move on, such that you are at
least able to recapitulate and then utilize the underlying logic, e.g., why is
the frequency of the dominant homozygote equal to (1 - q)2?)
(c)
Thus, if the recessive allele, a,
has a frequency of 0.01, then
(i)
Frequency AA = 0.99 * 0.99 =
0.98
(ii)
Frequency Aa = 2 * 0.99 *
0.01 = 0.02
(iii)
Frequency aa = 0.01 * 0.01 =
0.0001
(d)
(do you know where the above numbers come from? if you don’t, then you
don’t understand the concept so go back and try again)
(e)
In other words, in this example there are 200 times more heterozygotes carrying the recessive allele than there are
recessive homozygotes carrying the recessive allele—rare recessive alleles are hidden in populations
within heterozygotes (where does “200 times” come from? you should be able to
understand this… if you don’t then go back and try again)
(f)
"The rarer the recessive allele, the greater the degree of
protection afforded by heterozygosity."
(g)
That is, as recessive alleles become more and more rare, many, many
more carriers of this allele will be heterozygotes (who are assymptomatic in
the case of complete dominance, i.e., are hidden recessives) rather than
homozygotes
(h)
[hidden recessives, hidden recessive (Google Search)] [index]
(15) The
Hardy-Weinberg theorem
(a)
The above calculations are stated more formally as the Hardy-Weinberg
theorem
(b)
“The theorem states that the frequencies of alleles and genotypes in a
population’s gene pool remain constant over the generations unless acted upon
by agents other than Mendelian segregation and recombination of alleles.” (p.
447, Campbell & Reece, 2002)
(c)
“The system operates somewhat like shuffling a deck of cards: No matter
how many times the deck is reshuffled to deal out new hands, the deck itself
remains the same. Aces do not grow more numerous than jacks. And the repeated
shuffling of a population’s gene pool over the generations cannot, in itself,
increase the frequency of one allele relative to another.” (p. 448, Campbell
& Reece, 2002)
(d)
In the Hardy-Weinberg theorem it is assumed that matings between
individuals within a population occur randomly and that no evolution
is occurring within the population
(e)
Under such conditions genotype frequency
may be calculated from allele frequency information as described above (i.e., p2 + 2pq + q2)
(f)
The existence of this calculation given these assumptions is termed the
Hardy-Weinberg theorem
(g)
See Figure 23.3, The
Hardy-Weinberg theorem
(h)
(i)
“The Hardy-Weinberg theorem is important conceptually and historically
because it shows how Mendel’s theory of inheritance plugs a hole in
(j)
[Hardy-Weinberg theorem
(Google Search)] [Hardy-Weinberg Equilibrium (a guide to teaching H-W at the pre-college
level) (see also…) (Judith Stanhope)] [population genetics, Hardy-Weinberg equilibrium, and
the modes of evolution (a lecture) (Rebecca Irwin)] [model construction and the
Hardy-Weinberg equilibrium (model construction and hypothesis
testing using Hardy-Weinberg as example) (Biomathematics -- Sally Otto)] [index]
(16) Hardy-Weinberg
equilibrium
(a)
Note that so long as no evolution is occurring within a population
then allele frequencies are not changing within that population
(b)
So long as allele frequencies are not changing, then genotype frequencies may be calculated using the Hardy-Weinberg theorem
(c)
Furthermore, so long as these conditions stay the same, then genotype
frequency will remain the same, as calculated above (this is true because
genotype frequencies under these conditions are not a function of genotype
frequencies so much as allele frequencies, and allele frequencies we are
assuming are not changing)
(d)
The constant genotype frequencies in the absence of evolution and given
Hardy-Weinberg conditions is called Hardy-Weinberg equilibrium
(e)
That this is an equilibrium is implied by the absence of change over
time (particularly change in genotype frequency since a lack of change in
allele frequencies is, in fact, one of our assumptions)
(f)
Remember that, given the appropriate conditions (above), it takes only
a single generation to generate a Hardy-Weinberg equilibrium
(g)
["The discrete genes
Mendel discovered would exist at some frequency in natural populations.
Biologists wondered how and if these frequencies would change. Many thought
that the more common versions of genes would increase in frequency simply
because they were already at high frequency. Hardy and Weinberg independently
showed that the frequency of an allele would not change over time simply due to
its being rare or common." (Talk.Origins)]
(h)
[Hardy-Weinberg equilibrium,
the Hardy-Weinberg equilibrium
simulator, Hardy-Weinberg problems
(Google Search)] [population genetics, Hardy-Weinberg equilibrium, and
the modes of evolution (Biology 391: Organic Evolution)] [index]