Download PopGen4: Assortative mating

PopGen4: Assortative mating
Introduction
Although random mating is the most important system of mating in many natural populations, non-random
mating can also be an important mating system in some populations. Non-random mating results in changes in
the genotype frequencies in the population, i.e., how the alleles are put together into genotypes, but it does NOT
change the allele frequencies themselves. Since genotype frequencies will be affected, non-random mating
results in a deviation from Hardy-Weinberg equilibrium.
For the purpose of this course we will divide mating systems into four broad categories.
Mating system
Random
Mate choice is independent of both phenotype and
genotype
Positive assortment
Mate choice is based on similarity of phenotype
Negative assortment
Mate choice is based on dissimilarity of phenotype
Inbreeding
Mating with relatives at a rate greater than expected
by chance
The topic of these notes is ASSORTATIVE MATING, the non-random mating system where mates are chosen by
their phenotypes.
Positive assortative mating
Under a system of POSITIVE ASSORTATIVE MATING individuals choose mates that are phenotypically like
themselves. Note that under random mating there will always be some fraction of the population that mate with
phenotypically similar individuals. So when we say positive assortment, we mean that the mating of
phenotypically similar individuals is occurring at a frequency that is greater than expected by chance.
We can look to ourselves, humans, for an example of positive assortative mating. It has been shown that there
is significant assortment according to phenotypes such as height, IQ score and race. There is assortment for
certain socioeconomic traits. Interestingly, in the US, one of the highest correlations is found between the
numbers of rooms in the homes of the parents of married couples.
To consider the effect of positive assortment on genotype frequencies, let:
AA
Aa
aa
Genotype
P1
P2
P3
Frequency
Note: We are NOT assuming HW frequencies here
Even though we do not assume HW equilibrium, we still compute p and q as before:
p = P1 + (1/2)P2
q = P3 + (1/2)P2
Now consider that the frequency of positive assortment in a population is equal to α:
α = the frequency of AA x AA, Aa x Aa and aa x aa in addition to random mating
and
(1 - α) is the random mating fraction
Remember that the three types of mating under positive assortment yield the following:
AA x AA
Aa x Aa
aa x aa
=
=
=
100% AA
(1/4)AA + (1/2)Aa + (1/4)aa
100% aa
The frequencies of AA, Aa, and aa in the next generation (P1’ P2’ and P31) are as follows:
P1' = (1 − α ) p 2 + α (P1 + (1 / 4 )P2 )
1424
3 1442443
Freq of AA under
random mating
P2' = (1 − α )2 pq +
14243
Freq of Aa under
random mating
Freq of AA under positive
assortment has two sources:
100% from AAxAA, and
1/4 from AaxAa
α ((1 / 2)P2 )
14243
Freq of Aa under positive
assortment has one source:
1/2 from AaxAa matings
P3' = (1 − α )q 2 + α (P3 + (1 / 4)P2 )
1
424
3 1442443
random mating
component
positive assortment
component
Note that when α > 1, the frequencies will no longer sum to 1. To get the population frequencies you need to
standardize by the sum P1’ + P2’ + P31.
We can look at the effect on heterozygosity under this system of mating (plot A below). Remember that we have
assumed a very simplistic scenario as heterozygotes can be distinguished from homozygotes, so no AA × Aa
mating will occur for this locus. The second plot below (B) shows the effect of dominance [formula not shown].
A. Effect of complete (α = 1) and partial
(α = 0.75) positive assortative mating on
heterozygosity
B. Effect of positive assortative mating
(α = 1) on heterozygosity under complete
dominance
Frequency of heterozygotes
Frequency of heterozygotes
0.6
p = q = 0.5
0.5
0.4
0.3
α = 0.75
0.2
0.1
α = 1.0
[Formula not shown]
0.6
p = q = 0.5
0.5
0.4
0.3
α = 1.0 + dominance
0.2
0.1
0
0
1
3
5
7
9
11
13
15
17
1
19
3
5
7
9
11
13
15
17
19
generation
generation
When there is no dominance effect the frequency of heterozygote genotypes in the population declines very
rapidly. The frequency will rapidly go to zero when the effectiveness of positive assortment is 100% (α = 1).
When positive assortment is not complete (e.g., α = 0.75) The population heterozygosity declines quickly until
is reaches an equilibrium value (in the case above equilibrium is about 0.21).
Dominance slows the rate to equilibrium considerably by the effect of dominance. In the example above the
frequency of heterozygotes will eventually, for all practical purposes, go to zero; P’2 = 0.005 after 198
generations.
In example A above p = q = 0.5. Genotype frequencies at generation zero and after 20 generations are as
follows.
Generation
0
20 (α = 0.75)
AA
0.250
0.396
Genotype frequencies
Aa
0.5
0.208
Check for yourself; before and after 20 generations p = q = 0.5
aa
0.250
0.396
21
Positive assortative mating and the process of speciation
We do not cover the topic of speciation in this course. However, it is worth noting the potentially important role
that positive assortative mating could have in the process of speciation. There are many hypotheses about the
causes of speciation. One hypothesized mechanism is called REINFORCEMENT. Under reinforcement, natural
selection acts to favour the process of positive assortative mating. The idea is based on the premise that mating
between individuals from populations that have diverged will result in offspring with reduced fitness; hence,
selection will favour positive assortment because reproductive effort will not be wasted on producing less-fit
“hybrid” offspring. Under these circumstances assortative mating could lead to increased reproductive isolation
and eventually the final stages of the speciation process. The type of selection that would lead to reinforcement
is called DISRUPTIVE SELECTION; a selective pressure for divergence into two populations into ecologically distinct
types.
Until now I have relied on your intuitive sense of what a species is. A discussion of species concepts is well
beyond the scope of this course, so for the purpose of our discussion we will assume a species is an
independent evolutionary lineage, and we are interested in what role positive assortative mating might play in
the process of splitting one interbreeding population into two independent evolutionary lineages.
The consensus opinion is that the process of reinforcement is
probably rare. However, recent examples, many coming from
lakes filled with closely related fish species, is leading many
biologists to think that reinforcement is worth a closer look.
Pied flycatcher colour polymorphism
A good example of positive assortative mating and reinforcement
of a species barrier was presented by Sætre et al. (1998) for
species of flycatcher. The power of this example comes from
studying mate choice in two populations (or close species) where
the two ranges overlap (SYMPATRY), and comparing the patterns
with those occurring in regions where the two populations occur
singly (ALLOPATRY).
The pied flycatcher (Ficedula hypoleuca) is typically black and
white over much of its distribution. However, in parts of Central
and Eastern Europe the pied flycatcher is sympatric with another
species, the collared flycatcher (F. albicollis), and in the areas of
sympatry, the males are a dull brown rather than black and whites.
Allopatric type
Sympatric type
Adapted from Butlin and Tregenza 1998
In Central and Eastern Europe, where the Pied flycatcher is sympatric with the
collared flycatcher, the two species exhibit distinct colour differences
Collared Flycatcher
(F. albicollis)
Pied Flycatcher
(F. hypoleuca)
Sympatry
Allopatry
Allopatry
Sætre et al. (1998) Four points:
1. Between species matings are more rare than expected, and hybrids have reduced fitness
2. Phylogenetics indicated that plumage polymorphism is derived.
3. Females of sympatric populations/species prefer males that have the sympatric colouring rather than the
allopatric colouring (positive assortment).
4. Pied females exhibit the opposite preference (for dull brown males) than is exhibited in most other
populations; in most populations the preference is for striking black and white males.
Mate preferences of female flycatchers
Adapted from Sætre et al. (1998)
It is likely that the genetic basis of colour polymorphism in Pied flycatchers is more complicated than our single
locus model above. Moreover the flycatcher case involves interbreeding between two populations and our
model is based on a single random mating population. Nevertheless our model does provide some sense of
positive assortative mating for change in genotype frequencies in a population, and the Pied flycatcher provides
an example of the relevance of such non-random mating systems to evolution.
Positive assortment keynotes:
•
Increases homozygosity, thereby preventing HW equilibrium
•
Does not affect allele frequencies
•
Affects only those genes related to the phenotype by which mates are chosen. The other loci can be in
HW equilibrium
•
Results in gametic phase disequilibrium because it prevents equilibrium of allele frequencies between
the locus subject to assortment and other loci in the genome
•
Dominance dilutes the effect of positive assortment
Negative assortative mating
NEGATIVE ASSORTATIVE MATING is the avoidance of mating with phenotypically similar individuals. This is also
called DISASSORTATIVE MATING. Of course there will be a certain frequency of mating among dissimilar individuals
in a random mating population; so we are interested in the cases where the frequency of disassortment is
greater than expectations under random mating.
Negative assortative mating is an important breeding pattern in plants. In fact plants have evolved a diverse
collection of assortative systems. Systems of self incompatibility mechanisms can be divided into two
categories: (i) gametophytic and (ii) sporophytic. GAMETOPHYTIC incompatibility derives from failure of pollen with
an allele in common with the maternal plant to fertilize that plant; i.e., it is based on allelic incompatibility.
SPOROPHYTIC incompatibility works at the level of the genotype; diploid plants must have different genotypes for
successful fertilization.
Drosophila show an unusual type of negative assortative mating called RARE MALE ADVANTAGE. Here, the female
Drosophila prefers to mate with males with the rarest phenotypes.
It should be obvious that negative assortative mating will result in an excess of heterozygotes.
Negative assortment keynotes:
•
Yields an excess of heterozygotes, as compared with HW equilibrium
•
Does not affect allele frequencies (An exception is the rare male advantage phenomenon in Drosophila,
because of greater reproductive success of rare males. Under “normal” cases of negative assortative
mating, all males have equal mating success)
•
Loci not subject to negative assortative mating can be in HW equilibrium
•
Dominance dilutes the effect of negative assortment
•
Increases the rate to equilibrium of alleles among loci because linkage phases are disrupted by
recombination in double homozygotes.
Final note: Although assortative mating on its own does not affect allele frequencies, when it is combined with
natural selection they can have a significant affect on the rate of change in the allele frequencies at the locus
subject to assortative mating.