Evolution ❮ 145
the two alleles? Remember that it is not 0.16 and 0.84 because there are also the heterozy-
gotes to consider!
In a problem like this, it is important to determine the value of qfirst because we
know that all individuals with the recessive phenotype must be aa (q^2 ). You cannot begin
by calculating the value of pbecause it is not true that all the individuals with the domi-
nant phenotype can be lumped into p^2. Some folks displaying the dominant phenotype
are heterozygous Aa (pq).
We know that q^2 =0.16, so we find qby calculating Now
remember that they do not let you use a calculator. So these problems will give numbers
that are fairly easy to work with. Do not despair.
What about p? Since p+qis 1, and we know q=0.40, then pmust equal 1 −0.40 or
0.600.
You may also be asked to go a step further and give the percentages of the homozygous
dominant and heterozygous conditions (remember, we know that the recessive condition
is 16 percent—all these individuals must be aa in order to express the recessive trait). This
is simple—just plug in what you know about pandq:
2 pq=(2) (0.6) (0.4) =0.48 or 48%
p^2 =(0.6) (0.6) =0.36 or 36%
Now check your math: do the frequencies add up to 100 percent?
16 + 48 + 36 = 100
Why do we ever use the Hardy-Weinberg equation if it rarely applies to real populations?
This can be an excellent tool to determine whether a population is evolving or not; if we
find that the allele frequencies do not add up to one, then we need to look for the reasons
for this (perhaps the population is too small and genetic drift is a factor, or perhaps one of
the alleles is advantageous and is therefore being selected for and increasing in the popula-
tion). Therefore, although the Hardy-Weinberg equilibrium is largely theoretical, it does
have some important uses in evolutionary biology.
The Evidence for Evolution
Support for the theory of evolution can be found in varied kinds of evidence:
- Homologous characters.Traits are said to be homologous if they are similar because their
host organisms arose from a common ancestor (which implies that they have evolved).
For example, the bone structure in bird wings is homologous in all bird species.
- Embryology.The study of embryos reveals remarkable similarities between organisms at
the earliest stages of life, although as adults (or even at birth) the species look completely
different. Human embryos, for example, actually have gills for a short time during early
development, hinting at our aquatic ancestry. Darwin used embryology as an important
piece of evidence for the process of evolution. In 1866, the scientist Ernst Haeckel
uttered the phrase, “Ontogeny recapitulates phylogeny.” Ontogenyis an individual’s
development;phylogenyis a species’evolutionary history. What Haeckel meant was
that during an organism’s embryonic development, it will at some point resemble the
adult form of all its ancestors before it. For example, human embryos at some point look
a lot like fish embryos. The important conclusion from this is that Haeckel and others
thought that embryologic similarity between developing individuals could be used to
0 16→=q 0 400...
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