3.
Non-Random Mating:
As we've seen, equilibrium can only occur if ALL of the assumptions are met. If they are not met, then the population will evolve. We are now going to look at each assumption, and consider what happens when each assumption is violated. This will show us how evolution can occur by each of these different agents of evolutionary change.
1. Mutation
Although large scale mutations like polyploidy can cause instantaneous speciation, what we are talking about here are substitution mutations that change one allele into another, or make a new allele. Although such changes are very important sources of new variation, they do not change the genetic structure of a population very much at all, even when they occur: these mutations are rare, usually occurring at a rate of 1 x 10-4 to 1 x 10-6.
Consider a population with:
f(A) = p = 0.6
f(a) = q = 0.4
Suppose 'a' mutates to 'A'
at a realistic rate of: µ = 1 x 10-5 . How will this rate of
mutation change gene frequencies? Not much: 'a' will decline by: qm = .4 x 0.00001
= 0.000004
'A' will increase by the same amount. So, the new gene frequencies will be:
p1 = p + µq = .600004, and q1 = q - µq = q(1-µ) = .399996.
So, mutation is a very important source of new alleles, but it doesn't change
the gene frequencies in a population very much.
2. Migration
Consider a resident population in which p = 0.6 and q = 0.4. Suppose immigrants migrate into this population, bringing A and a alleles into the population at these frequencies: p =0.8 and q = 0.2. The effect of this influx will depend on the number of immigrants relative to the number of residents. 100 immigrants may not change the genetic structure of a population containing 1 million residents, but they could have a dramatic effect on a population of 100 residents. We measure this relative effect by quantifying the proportion of the total combined population that are immigrants. So, in our example, suppose so many immigrants move in that they represent 10% of the new, combined population. We calculate new p as a weighted average based on fraction of immigrants and residents:
So, p1 = (0.6)(0.9) + (0.8)(0.1)
= 0.54 + 0.08 = 0.62
residents contribute p at a rate of 0.6, and they represent 90% of the combined
population. Immigrants contribute p at a rate of 0.8, and they are 10%
of the population.
q1 = (0.4)(0.9) + (0.2)(0.1)
= 0.36 + 0.02 = 0.38, so we have done our math right because 0.62 + 0.38 = 1.0
There are two possible evolutionary effects. First, migration will make two populations similar to one another; particularly if the rate of immigration is high or the process is continuous over time. Migration can also introduce new alleles into a population, but again this effect will be correlated with the abundance of immigrants relative to the number of residents.
3.
Non-Random Mating:
a. Positive Assortative Mating
There are many ways that non-random mating can occur. We will look at a couple. The first example is called "positive assortative mating". This is where mates 'sort' themselves with others of the same genotype. This can be thought of as "like mates with like". So, consider our old four o'clock plants with incomplete dominance. A population might contain red, pink, and white flowers. Suppose the red flowers open in morning, and are pollinated just by hummingbirds (that prefer red flowers). Suppose the white flowers open at night, and are pollinated by moths. And suppose the pink flowers open in the afternoon, and are pollinated by bees and butterflies. In this case, "like mates with like" for flower color (and time of opening). So, a plant with red flowers will only mate with another plant having the same genotype for (red) flower color. Now, it is IMPORTANT to realize that plants are only positively assorting for flower color and opening time in this case. One red flowering plant may be tall while the other is short; one may have hairy leaves while the other has smooth leaves. Indeed, the plants may be mating at random with respect to all other traits.
When AA individuals mate only with each other, all their offspring will be AA, as well. So, if 20% of the population is AA (intial genotypic frequency = 0.2), and if there is no difference in reproductive success (because we are only violating the assumption of random mating so there is no selection), then these parents will make 20% of the offspring and they will all be AA. The same goes for aa individuals only mating with other aa individuals - all their offspring are aa. However, when Aa heterozygotes only mate with one another, they produce AA, Aa, and aa offspring in a 1/4:1/2:1/4 ratio. If 60% of the population is heterozygous, then they will make 60% of the offspring... but these offspring won't all be heterozygous; only 1/2 - or 30% will be heterozygous. 15% will be AA and 15% will be aa. So, the total frequency of AA offspring in the F1 will be 35%; 20% had AA parents and 15% had Aa parents.
As a consequence of positive assortative mating, the frequency of heterozygotes will decline and the frequency of homozygotes will increase. Curiously, the gene frequencies won't change, so in the F1, f(A) = .35 + 0.30/2 = 0.5... just as it was in the orginal population (f(A) = 0.2 + 0.6/2 = 0.5). The genes are just being 'dealt' to offspring in a non-random manner, affecting the genotypic frequencies at this locus.
So, suppose we observed the F1 population in nature, and wanted to know if it was in HWE. We would calculate the gene frequencies (A = 0.5, a = 0.5), and then estimate what the frequencies of the genotypes would be IF the population was in HWE: p2 = 0.25, 2pq = 0.5, q2 = 0.25. We would compare our real population's genotypic array with this HWE expectation, and see that they are not the same. And we could see one thing more... we would see that the ACTUAL OBSERVED frequency of heterozygotes (0.30) is LESS THAN the expected frequency of heterozygotes under the HWE hypothesis (0.5). And we would see that the observed frequency of both homozygotes is greater than expected. Knowing that positive assortative mating can cause this pattern, we would have a working hypothesis regarding the agent of evolution at work in this population.
b. Inbreeding: Mating with a Relative
Inbreeding is mating with a relative. It is similar to positive assortative mating, except that the two mates are not just similar at one locus, but they are probably similar at MANY loci because they are related and got their genes from the same ancestors. Siblings share, on average, half their genes. Matings between siblings, then, will tend to reduce heterozygosity at MANY loci, not just one.
The most extreme example is "obligate self-fertilization". This is where a hermaphrodite ONLY mates with themselves. This is not asexual reproduction - they produce gametes by meiosis and get all the benefits of producing variable gametes that occurs in sexual reproduction; but they only fertilize their own gametes. This has a profound effect on the genetic structure of the population. Think about it: when an organism mates with themselves, they are mating with an organism that has the SAME genotype at EVERY locus. So, there will be a decrease in heterozygosity across the entire genome, with a 50% reduction in heterozygosity each generation. This is the most rapid loss possible. Siblings are only related, on average, by 50%, so the loss of heterozygosity will only occur 1/2 as fast.... but it will still occur at all loci across the genome.
Inbreeding often reduces reproductive
success, because there is an increase in homozygosity - and this means that
deleterious recessives are going to be expressed more frequently and exert their
negative effects on the offspring. A deleterious allele may be rare in a population,
but inbreeding will increase the probability that it occurs in the homozygous
condition and is expressed. Because inbreeding can reduce the survivorship of
offspring and thus reduce reproductive success of the parent, it is often selected
against. Selection favors different strategies that reduce the likelihood of
inbreeding, like "self-incompatibility" in some plants, like lions who push
male cubs out of a pride when they mature (thus they don't breed with their
sisters), or like humans who have a variety of cultural taboos against breeding
with relatives. However, inbreeding is also a mechanism for purging deleterious
alleles from the population. If a population can get through the first
few generations in which homozygote recessive are produced and selected against,
the net effect will be to eliminate these deleterious alleles from the population.
That can be a good thing in the long run.
4. Populations of Finite Size and Sampling Error/"Genetic
Drift"
The genetic structure of a population can change from generation to generation
just by chance - through a process statisticians call "sampling error"
and geneticists call "genetic drift". Think about it this way: suppose
we have a very large population in which p = 0.3 and q = 0.7, and the population
is in HWE to start; so the f(AA) = 0.09, f(Aa) = 0.21, and f(aa) = 0.49. Now,
suppose only 4 individuals mate, and suppose those four are just 'lucky' - they
don't mate because they are better adapted in any way, they just got lucky.
It is very unlikely that these four individuals will have the same genetic structure
as the whole population; small samples are notoriously unrepresentative and
variable. Indeed, all four may be 'aa', and the population will have changed
dramatically, losing the 'A' allele. This is why, to have confidence in any
observed pattern, you want a large sample. So, a population's genetic structure
may change just due to chance.
There are two important patterns that result from this effect:
First, small samples will tend to differ more from the original population than large samples. Second, since the direction of this change is random, multiple small samples will tend to vary more from one another, on average, than multiple large samples. So, small populations will diverge more rapidly from one another, due to drift, than large populations.
There are two biological situations where these effects are particularly important. The first is called a "Founder Effect", where a small number of colonists establish a new population that is isolated from the original population. Because this population of "founders" is small, it is likely to differ dramatically from the original population.... and because it is small, it will also chance quickly just due to drift, as the simulations in lab showed.
The second important instance in which drift is important is called the "bottleneck effect". This is when a large population is reduced in size. Typically this reduction is caused by predation, a pathogen, or an environmental change. The survivors usually make it because of selection at certain loci. For instance, survivors of a pathogenic infection may be resistant to the pathogen. However, at other loci, the reduction in population size causes genetic change due to drift.
So, CHANCE can be an agent of evolutionary
change. CHANCE, especially in small populations, can cause changes in
the genetic structure of a population. This is NOT selection - selection is
"non-random reproductive success" - the organisms that breed are "better" than
the others. Here, in Genetic Drift, the breeders are just LUCKY, not better.
It is random change. And, as the computer modes demonstrate, populations will
tend to become different genetically 'simply by chance', because these chance
changes are unlikely to be the SAME changes, or in the same direction, from
population to population. So, we can't STOP populations from evolving, really
- they will all change over time, even just do to random sampling error, and
they will tend to become different from other populations of the same species.
Of course, if the populations are very large, these random patterns of divergence
will be very slow.... but since no population is infintie in size, these random
changes will necessarily occur over time.
Study Questions:
1. Consider a population with p = 0.8 and q = 0.2. If the mutation rate of A--> a = 4.0 x 10-6, what will the new gene frequencies be in the next generation?
2. Consider a population, p = 0.8 and q = 0.2. If migrants enter this population with p = 0.1 and q = 0.9, such that immigrants comprise 15% of the total population, what will the new gene frequencies be?
3. If the population below undergoes positive assortative mating, what will the genotype frequencies be in the next generation?
| AA | Aa | aa |
| 0.3 | 0.4 | 0.3 |
4. How can the decimation of a population by overhunting cause changes in a population due to both selection and drift?