We will now address the last assumption of H W Equilibrium
Non-random mating
Non-random mating with respect to genotype occurs in population where the mating individuals are more closely or less closely related than those drawn by chance from the population
Reprise of random mating
Remember, H W Principle assumes that mates find each other through a fair lottery process
Chose one individual at random from population
Chose another individual at random and mate the two
Anyone has equal chance of being picked in each draw
It’s possible that these two individuals will be related to one another
But, in a large population the chance will be low
Non-random mating means that the lottery isn’t “fair”
Some pairings are more likely than others
We’ve already discussed two types of non-random mating
One in which mates are less related to one another than expected by chance
This was the example of the Hutterites (and also mice), in which matings were more likely between individuals of different MHC genotype
This creates disassortative mating
Mates tend to be more different in their phenotypes than expected by chance
What do you think disassortative mating will do to genotype frequencies?
Increase heterozygosity above that predicted by H W Principle
Actually, working out the effects of disassortative mating for more than two alleles is really messy
Let’s consider one simple example
Special example of disassortative mating: single locus with two alleles
Yields three genotypes: AA, Aa, and aa
Suppose that matings are assortative in the following fashion
AA x aa and Aa x aa
Real-world example
Distylous plants (draw picture on board, explain biology)
Suppose that you have a population consisting of all three genotypes
|
AA |
Aa |
aa |
|
Long style |
Long style |
Short style |
Pollinators then visit flowers and distribute pollen
Because of the flower morphology, only successful matings occur between
AA x aa and Aa x aa
What will genotypes of progeny generation be?
Progeny from AA x aa = Aa only
Progeny from Aa x aa = Aa and aa
There will be no more AA genotypes
All individuals in the population will now be
Aa long styled
or aa short styled
And successful matings will occur only between Aa and aa
Leading to equal number of each kind of progeny in the third generation
This is a stable state, a 1:1 ratio of Aa long style and aa short style individuals
Same thing happens with ordinary sex-determining system
XX and XY
Again leading to stable 1:1 polymorphism
Two sexes is the stable result of disassortative mating according to the polymorphic sex chromosome controlling sex
And, another kind of non-random mating in which mates are more related to one another than expected by chance
This was the problem in which there was a morning glory population with a flower color polymorphism and on each day, pollinators chose to visit only plants of one flower color
Thus,
White flowered plants mated only with other white flowered plants
Plants with light colored flowers mated only with other light colored flowered plants
Plants with dark colored flowers mated only with their own “kind”
This creates assortative mating
A type of inbreeding with respect to the flower color phenotype
What did we find that assortative mating according to flower color did to genotype frequencies?
Increased homozygosity above that predicted by H W Principle
In fact, in this type of assortative mating, heterozygosity in the population (i.e. the frequency of heterozygotes) declines by this rate:
Where, p = allele frequency, t = time, in generations, and H0 = frequency of heterozygotes (= heterozygosity) in a randomly mating population (i.e. one at H W equilibrium)
What did it do to allele frequencies?
Did not, by itself, change allele frequencies
So, changed H W ratios between allele and genotype frequencies
However, different kinds of systems of inbreeding will create different effects on allele and genotype frequencies
When particular types of matings are more likely (i.e. a systematic bias in the mating lottery), this creates what is called a “mating system”
e.g. selfing is a mating system, common in plants, wherein individuals mate with themselves
sib mating is a mating system in which sibs always mate with each other
There has been particular interest in mating systems that produce inbreeding
Inbreeding
Inbreeding is a kind of assortative mating
Mating between genetically related individuals
As such, it does the same thing to heterozygosity as does assortative mating
e.g. Self-fertilization
An extreme form of inbreeding
See figure 23-10
Selfing causes continual erosion of heterozygosity (flip side = excess homozygosity)
But no change in allele frequency
So, like perfect assortative mating, it does not by itself cause evolutionary change
However, as we shall see, it does have important evolutionary implications
Loss of heterozygosity is because genetically related individuals are more likely to share the same alleles
Which causes the progeny to be homozygous for that shared allele
Why is this of interest?
Because it’s not such a good thing for populations
Of course, one of the things we learned from our study of selection processes and mutation selection balance is that many deleterious recessive alleles “lurk” in populations at low frequency
Inbreeding causes these to end up in homozygous situations more frequently than by chance alone
So, phenotypes of rare deleterious recessive alleles are more likely to be seen in inbred populations
To better quantify this problem, need amore general way of considering inbreeding
More general way of considering inbreeding
Mathematical theory of inbreeding was developed by Sewell Wright, who did most of his pioneering population genetics research on guinea pigs (tell guinea pig at the chalkboard story)
Wright had a personal interest in inbreeding because he was himself inbred, being the son of a double first cousin marriage
An important concept for inbreeding theory is identity by descent
Two alleles are identical only if one descended from the other
Thus, if two alleles produce the same phenotype, but arose from two different mutation events, and hence descended from different ancestors
Then they are not identical by descent
They could have the same DNA base-pair sequence yet still not be identical by descent
The reason for this restricted definition
Individuals that inherit genes that are identical by descent must themselves be related
E.g.
Thus, identity by descent is a kind of bookkeeping strategy for keeping track of genetic relationships among individuals
Could use pedigrees, but they become unwieldy very rapidly
A population that has an inordinately large number of individuals that share identical alleles (defined in this narrow sense) is likely to be inbred
Have more related individuals than expected
Therefore, we can determine the level of inbreeding in a population by the extent to which individuals share identical alleles
A relative concept, needs standardization
Even in a completely randomly outbreeding population
There will be individuals that share alleles by descent
e.g. parents and their offspring, siblings, etc.
So, need a statistic with which to measure excess inbreeding
Wright devised this statistic and called in the inbreeding coefficient
Inbreeding coefficient
F = average inbreeding coefficient of a population
F = probability that a random individual inherited two alleles that are identical by descent relative to the probability that this would happen under purely random mating
What does it mean for an offspring to inherit two alleles that are identical by descent?
One allele comes from mom, and one from dad
Thus, if both mom and dad contribute the same identical allele
It means that mom and dad both acquired this allele from a common ancestor
Back sometime in their pedigree, they are related
It’s called an average inbreeding coefficient because it’s averaged over all the offspring in the population
The value of F ranges from
0 = purely random mating, to
1 = all individuals are homozygous for alleles that are identical by descent
After working out the theory of inbreeding in sexually reproducing organisms, Sewell Wright calculated his own inbreeding coefficient
It was 0.063
About 100 times the average for a human population in the
U.S.
But, he doesn’t seem to have suffered from inbreeding depression
Having sired children and then go on to publish his last paper at the age of 99!
Incorporating inbreeding coefficient into Hardy Weinberg analysis
Back to the usual population with two alleles, A and a, at a single locus
When they are ready to mate, they release gametes into the common gene pool
Each zygote represents a random draw of two gametes
In a population at H-W equilibrium
Just by random processes, occasionally the two gametes will be related (that is, share alleles that are identical by descent)
This is the rate at which identical alleles unite to form zygotes when F = 0
When F is larger than zero
It means that more zygotes are formed from unions of identical gametes than expected by this random process
And, it means that there will be more homozygous zygotes than expected by this random process
How do we incorporate this excess relatedness into our H W analysis?
First draw one gamete at random from the gene pool
But, for the second draw, think of the gamete pool as consisting of two fractions
The fraction (F) that is identical by descent to our chosen gamete
The fraction (1 – F) that is not identical by descent to our chosen gamete
Think about each genotype at a time
AA genotype probability
First, random draw of an A egg from the whole gamete pool (probability p)
Once you have an A egg, there are two ways of getting an AA homozygote
Simply by chance, getting an A sperm from the fraction of the gamete pool that is unrelated
Probability = fraction of gene pool that is not identical by descent x frequency of A in that fraction = (1 – F) p
So, probability of AA homozygote this way is
Probability of A egg x probability of non-identical A sperm = p x (1 – F) p = p2 (1 – F)
Getting a sperm that is A because it is identical by descent
An event with Probability = F
Probability of getting AA homozygote in this way is
Probability of A egg x probability of identical A sperm = p F
So, total probability of getting AA homozygote is
P2 (1 – F) + p F
Aa genotype probability
First, random draw of an A egg from the whole gamete pool (probability p)
Once you have an A egg, there is only one way of getting an Aa heterozygote
Simply by chance, getting an a sperm from the fraction of the gamete pool that is unrelated
Probability = fraction of gene pool that is not identical by descent x frequency of a in that fraction = (1 – F) q
So, probability of Aa homozygote this way is
Probability of A egg x probability of non-identical a sperm = p x (1 – F) q = pq (1 – F)
Note: can’t get a sperm that is identical by descent
Because A and a are different alleles and can’t be identical by descent!
But, there’s another way of getting a heterozygote, which is to first draw an a egg from the whole gamete pool (probability q)
Once you have the a egg, there is only one way of getting an Aa heterozygote
Simply by chance, getting an A sperm from the fraction of the gamete pool that is unrelated
Probability = fraction of gene pool that is not identical by descent x frequency of a in that fraction = (1 – F) p
So, probability of Aa homozygote this way is
Probability of a egg x probability of non-identical A sperm = q x (1 – F) p = pq (1 – F)
So, total probability of getting AA homozygote is sum of these two probabilities
2pq (1 – F)
aa homozygote
First, random draw of an a egg from the whole gamete pool (probability q)
Once you have an a egg, there are two ways of getting an aa homozygote
Simply by chance, getting an a sperm from the fraction of the gamete pool that is unrelated
Probability = fraction of gene pool that is not identical by descent x frequency of a in that fraction = (1 – F) q
So, probability of aa homozygote this way is
Probability of a egg x probability of non-identical a sperm = q x (1 – F) q = q2 (1 – F)
Getting a sperm that is a because it is identical by descent
An event with Probability = F
Probability of getting aa homozygote in this way is
Probability of a egg x probability of identical a sperm = q F
So, total probability of getting aa homozygote is
q2 (1 – F) + q F
Homework problems (see pg 162 of your text)
Try using these new versions of the H W equation to show that it returns to the good old simple H W when mating is random (i.e., when F = 0)
Also, try using it to examine the effects of generations of selfing on heterozygosity
Define heterozygosity as HF
= H0 (1 – F) (same
equation as in text, they use Het instead of H
Inbreeding depression
What effects does inbreeding have on populations?
Can increase phenotypic variance in population
When heterozygote phenotype is intermediate to homozygotes (co-dominance), then
Inbreeding increases phenotypic variance
Simply because of the increase in the number of extreme (homozygote) phenotypes
Can decrease mean fitness of population: inbreeding depression
See how this happens
Use our H W equations modified for inbreeding to derive a quantitative expression for inbreeding depression
Calculate mean fitness, 
The first term is the mean fitness in the absence of inbreeding
The second term measures the change in fitness due to inbreeding
Thus,
Inbreeding depression can be defined as the difference in fitness between a randomly bred and an inbred population
Notice that inbreeding depression is a function of:
The allelic frequencies
The fitness relationships
And a linear function of the inbreeding coefficient, F
Suppose that a population has a polymorphic locus in which the rare allele is present at low frequency (strong directional selection against the deleterious recessive)
Then fitnesses are:
|
AA |
Aa |
aa |
|
1 |
1-hs |
1-s |
