INBREEDING

1
INBREEDING
Double first cousin
Sib mating
Self-fertilization
These graphs compare the decay of heterozygosity
under inbreeding and genetic drift. Compare the
scales on the x-axes of the two graphs ---
heterozygosity decays much more rapidly with
inbreeding. This is true even with double first
cousin matings, the mildest form of inbreeding
shown.
GENETIC DRIFT
The entire graph shown in A would fit between
the origin and this point.
2
MIGRATION AND GENE FLOW
GENETICALLY EFFECTIVE MIGRATION OR GENE FLOW
REDUCES GENIC DIVERGENCE AMONG POPULATIONS
(CAUSED BY SELECTION AND/OR DRIFT). SOME
BIOLOGISTS THINK OF IT AS THEGLUE THAT HOLDS
THE POPULATIONS OF A SPECIES TOGETHER.
m fraction of breeding individuals in a
population that are genetically effective
migrants. or fraction of gametes in the
population that come from migrant
individuals.
3
In dealing with migration/gene flow, we will
assume that all migration is genetically
effective. A migrant organism arrives and is
(almost) immediately able to interbreed with the
local population and to compete successfully for
mates. This assumption is necessary to keep the
math simple, but it is obviously naïve. From
what little biologists have been able to observe
of the process of migration, it seems that many
migrants arrive in poor condition, and it is
unlikely that they would be able to interbreed
with the local population. In addition to the
effects of a rigorous journey, a migrant
frequently has to deal with social and ecological
problems as well. Consequently, it is likely
that much (or even most) migration is not
genetically effective.
4

• Evolutionary biologists have defined several
  different simple
• models of (sub)population structure to study the
  effects of
• migration/gene flow
• Island/continent one way migration from
  continent to island.
• Island random migration among all islands
  regardless of
• their proximity.
• Stepping stone Most migration occurs among
  adjacent
• populations, much less among nonadjacent
  ones. Can be
• 2D or 3D.
• Note As the stones get smaller and
  closer, the stepping stone
• model becomes another important one
  Isolation by Distance
• in a continuous population.

5
Simple mainland vs island model as shown in the
text. MIGRATION FROM MAINLAND TO
ISLAND ONLY pi island gene frequency pc
mainland gene frequency m individuals arrived
from the mainland 1-m individuals born on the
island pi(1) (1-m)pi(0) mpc ?pi (pi(1) -
pi(0) ) m(pc - pi) Change in gene frequency
depends on m and the difference in gene
frequencies between mainland and island.
6
Example The frequency of an allele on the
mainland is 0.8, and on and adjacent island it is
0.2. How much change takes place in a
generation if the migration rate is 5? What is
pi at that point? ?pi m(pc - pi)
.05(.8 - .2) .05(.6) .003 pi(1)
0.2 .003 .203
7
pi(1) (1-m)pi(0) mpc is the equation we
derived earlier for the new gene frequency on
the island. If we are interested in m we can
conveniently rewrite this equation
m (pi(1) - pi(0))/ (pc - pi(0))
Example After a generation of migration, the
frequency of an allele on an island is 0.2.
The starting frequency was 0.15. The
frequency of the same allele on the mainland is
0.4. What is the effective genetic migration
rate, m? m (pi(1) - pi(0))/ (pc -
pi(0)) (0.2-0.15)/(0.4 - 0.15)
.05/0.25 0.2

8
The analysis that follows is controversial and
some students will be uncomfortable with it. I
apologize for the discomfort, but I believe
that the logic and the data are sound. As a
scientist, my main job is the objective
evaluation of data. But I feel strongly that
when the science I do can contribute in a
potentially meaningful way to important social
issues, it is my responsibility to make that
contribution. In other words, yes, I do have
an agenda here, and I would think myself a
lesser human being if I did not, and so would
most of you The culture we share has an
unfortunate history of slavery and racial
discrimination. It is undisputed that, under
those conditions, black women were uniquely
vulnerable to exploitation. We are not able to
directly measure the moral, personal and social
effects of that exploitation. But we can measure
its reproductive and genetic consequences.
And we can reasonably make the argument that
such measurements might index the less tangible
but more important factors that we cannot
measure.
BRUCE J. TURNER
9
The migration formula we derived earlier can be
used to measure gene flow between human
populations. The continent/island model lends
itself well to doing this when we have a
(partially) isolated, geographically coherent
population (the island) surrounded by a much
larger one (the continent), and, for cultural
reasons, most of the gene flow is from the
continent to the island. This question is
especially importance when the island
population is in a negative political, cultural,
or economic position relative to the continent
population. Put more simply, how much
genetic/reproductive exploitation
accompanies oppression?
West African Population
Claxton Blacks Claxton Whites Rh1
0.62 (pi(0)) 0.45(
pi(1)) 0.03 ( pc) m (pi(1) -
pi(0))/ (pc - pi(0)) (0.45 - 0.62)/ (0.03 -
0.62) 0.17/.59 0.29
In this case, the gene flow has taken place over
about 10 generations. It is straightforward to
compute it for one generation (1-M)10 (1-.29)
so 10 log (1-M) log .71 log(1-M) log.71/10
-.0149 1-M 0.97, M .03 per generation.
Claxton, GA, where this research was done.
10
To put our results in a more social context, we
have just determined that in the Black
population of Claxton about 3 of the infants
born every generation likely had a White
father. This does not seem like much until one
realizes that over 10 generations, very nearly a
third of the infants born had a white
father. Even if only half of these babies
resulted from intercourse fostered in some way
by social inequality rather than direct consent,
this represents reproductive and sexual
exploitation on a large scale.
11
The island model of migration and gene flow
In the island model, each island population
receives individuals (or gametes) from all other
populations, so that the immigrant gene
frequency is essentially the average frequency,
p. In this model, the gradual convergence of
different gene frequencies toward a common mean
is especially apparent.
12
MUTATION
Mutations are the ultimate source of ALL genetic
variation, and thus of all evolutionary change.
Viewed from a long-term perspective, they are an
evolutionary force of unquestioned importance.
Mutations, however, are generally rare events
(another way of saying this is that they occur
at low rates per generation). Their effects on
gene frequencies in one or a few generations are
likely to be small, and probably imperceptible.
As observed in our text, they can change the
frequencies of genes only slowly.
13
Models of the mutation process in natural
populations
Much like migration, there are several
different models of the dynamics of mutations
in natural populations. In part, this stems
from lack of knowledge of the process. In part,
it also reflects progressive increases in our
knowledge of the structure and nature of genes
themselves. Not surprisingly, as our knowledge
became more detailed, our views of the nature
of mutation changed accordingly. This is an
area where there is still a lot to be discovered.
We will briefly consider only the two most
different models. They are the recurrent
model which is the oldest one, and the infinite
alleles model, which is more recent.
As you learn these models, contrast them and see
if you can decide which is more likely to be
correct... Both are fairly straightforward. Unfor
tunately, our text is strangely silent about
models of mutation.
14
The recurrent model of mutations in natural
populations A gene has two alleles, A and
a. A encodes the wildtype phenotype,
while a (in homozygous form) encodes the
mutant phenotype. During gamete formation,
A mutates to a at some rate, u or
A a (u) u is
generally considered to be about 10 -6 per gene
per cell division. (Note that this implies that
this mutation happens repeatedly). a also
backmutates to A at some rate, v.
a A (v)
usually about 10-8 or 10-9
15
We can use some formulas in the text to calculate
how u can influence gene frequencies (see Box
5.9)
p1 p0 - up0 p2 p1 - up1 (p0 -
up0) - u (p0-up0) Pn p0e-un
Here is an example. Suppose p0 was 0.9, and u is
10 -6, What is p100? Ans. p100 0.9 e -.0001
0.9 (.99999) 0 .899. What about p10,000?
Ans. 0.891 These examples show us that as
mutation is not a powerful way of changing gene
frequencies.
16
The case of the equilibrium that isnt In the
recurrent model, we can calculate the combined
effects of forward and back mutation on any gene
frequency pt pt-1 (1-u)
(1-pt-1)v We can imagine an equilibrium where p
doesnt change, because the copies of A lost
by forward mutation are exactly replaced by
those gained by back mutation. At this
equilibrium, pt pt-1. With some algebra, it
can be shown that pequil v/(uv)
17
However, there is a small problem, shown in the
graph below. It will take so long to establish
this equilibrium that it cannot be
biologically significant! The math works nicely,
but it has no relevance