2. Genetic Drift: The Effect of Non-infinite Population Size
It's quite simple, really. There is really no such thing as an infinitely large population.
And even in a large population, only a small subset of possible gametes will make it into the next generation.
The number of genetically unique gametes an individual can make is equal to 2n
n = the number of different genes the organism has.
The average mammal (you) has about 20,000 genes
That means you are capable of generating 220000 genetically unique gametes.
But will each of your 220000 unique gametes make it into the next generation? That's where Genetic Drift comes in.
Genetic Drift: Genetic Change due to Sampling Error
The smaller the population, the less genetic diversity it has.
In a very small population, alleles can be lost from one generation to the next, simply due to sampling error.
When a population evolves only because sampling error, then GENETIC DRIFT is taking place.
There are two basic "flavors" of genetic drift:
Founder Effect: a small sample of breeding
individuals from a large population colonizes a new area and stops breeding with the original "source" population.
Bottleneck Effect: a
large population is almost wiped out due to something that randomly kills individuals, such as a hurricane, volcanic
eruption, or other catastrophe. Only a few lucky
individuals survive to become the progenitors of the new population. This small subset of the original population is more subject to sampling error, which will be reflected in the future generations.
Consider the effects of inbreeding and outbreeding on homozygosity and heterozygosity.
Small, isolated populations (such as island populations separated from the mainland) will eventually consist of members who are related to one another. This leads to inbreeding.
Inbreeding greatly increases the likelihood of homozygosity at multiple loci.
In a small population with only two alleles for a given gene, one or the other allele can be lost entirely, and the population will become fixed at that allele. Only a mutation of that gene (creating a new allele) will provide new genetic variability.
IN GENERAL, A SMALL, ISOLATED POPULATION WILL EVOLVE MUCH MORE RAPIDLY THAN A LARGE POPULATION DUE TO GENETIC DRIFT.
Here's an overview of genetic drift and its consequences. These links should help clarify the concepts.
Genetic Drift is likely a major force in microevolution and, ultimately, macroevolution.
While this is especially true in small, genetically isolated populations, random sampling error contributes to evolution in any non-infinite population.
3. Random Mating
If a population is mating randomly, then the alleles at a given gene locus should combine with the same frequency predicted by their relative frequency in the population. This can be predicted by the Product Rule:
If two events (in this case, the occurence of two different alleles) are independent of one another, then the probability of their occurring together (i.e., ending up as part of the same zygote) is the product of their probability of occurring in the population (i.e., their relative frequency).
Let's create an imaginary population in which a dominant allele (A) represents 60% (0.6) of the alleles and a recessive allele makes up the remaining 40% (0.6) at a given locus.
If the population is not evolving, then, according to the Hardy-Weinberg Principle (which we'll review shortly) the predicted relative genotype frequencies should be:
0.6 x 0.6 = 0.36 for AA
2(0.6 x 0.4) = 0.48 for Aa
0.4 x 0.4 = 0.16 for aa
Using the Product Rule, one can determine that the likelihood of an AA individual mating with an Aa individual is:
0.36 x 0.48 = 0.17
This means that 17 out of 100 matings in the population should be AA x Aa, if mating is completely random.
If there is significant deviation from this prediction, then non-random mating is occurring.
Non-random mating can change the relative genotype frequencies of AA, Aa and aa.
If non-random mating is occurring, then the next interesting question should be...WHY?.
Assortative mating can work two ways (with respect to a trait):
positive assortative mating: individuals of similar genotype/phenotype mate together significantly more often than predicted by their relative frequencies in the population. This will result in a greater homozygosity.
negative assortative (=disassortative)mating: individuals of dissimilar genotype/phenotype mate together significantly more often than predicted by their relative frequencies in the population. This will result in greater heterozygosity.
Non-random Mating: Inbreeding vs. Outbreeding
inbreeding occurs in a population when matings between closely related individuals occurs more frequently than would be predicted by their relative frequency in the population. That is, individuals preferentially mate with relatives.
outbreeding occurs in a population when matings between unrelated individuals occurs more frequently than would be predicted by their relative frequencies in the population. That is, individuals preferentially mate with non-relatives.
Inbreeding can change allele frequencies, as can be seen in this diagram
of a brother/sister mating
Gene A has four alleles (A1, A2, A3 and A4)
The unrelated parents (Bob and Alice) are heterozygous and genetically dissimiliar: Bob is A1A2, and Alice is A3A4.
The chance that Bob will contribute either allele (A1 or A2) to his offspring is 1/2 (0.5).
The chance that Alice will contribute either of her alleles to her offspring is
also 1/2 (0.5).
In this example, Bob has bequeathed the A1 allele to both his offspring, Jethro and Ellie May.
The Product Rule (The combined probability of any two independent events occurring together is equal to the product of their individual probabilities.) tells us that the probability that both Jethro and Ellie May inherited the A1 allele from Bob is
0.5 x 0.5, or 0.25 (25%)
If Jethro and Ellie May reproduce together, then the chance of both of them passing the A1 allele to an offspring is the combined probability of both of them having inherited the A1 allele:
0.25 x 0.25 (0.0625, or 6.25%)
Now let's say that A1 is a relatively rare allele in this population: only one in every thousand individuals carries it. That means
If either Jethro or Ellie May mated with a random non-relative, the likelihood of the offspring receiving A1 from each parent would be
0.25 x 0.001 (0.00025, or 0.025%)
But if a Jethro x Ellie May mated with a each other, the likelihood of their offspring receiving A1 from each of them would be
0.25 x 0.25 (0.0625, or 0.6.25%)
The relative (hee haw) probability/risk of homozygosity is greater with inbreeding.
If the allele happens to be deleterious...well...you can see why there are taboos in human society against inbreeding.
Note that small, isolated populations will much more quickly come to consist of members
who are related to one another than a very large population. Small populations are much more likely to lose one allele and become fixed at the other for a given locus, simply due to random sampling error.
Small populations and inbreeding can greatly increase the rate of evolution at any given gene locus.
Criterion 4. No Migration
Loss or addition of alleles from immigration or
emigration will change the allele frequency in the population under
Gene Flow is the process by which movement of genes takes place
between populations or demes.
gene flow spreads novel alleles that have arisen via mutation
gene flow has a homogenizing effect if a recipient population is small
relative to a donor population.
gene flow increases the effective size of a population.
lack of gene flow may eventually lead to speciation, but the rate at
which this occurs depends on the species.
A species whose demes tend not to become reproductively isolated is known as a cohesive species. There is no simple explanation as to why a particular species is cohesive or not.
Red-winged Blackbird Agelaius phoeniceus) populations in
California and Florida do not migrate between those populations. The birds are physically indistinguishable and have the same mating behaviors. Despite lack of gene
flow, they are not reproductively isolated.
The Coyote (Canis latrans) and Timber Wolf (Canis lupus)
occasionally hybridize, producing fertile offspring--yet their lineages
have remained separate for two million years.
Black Cottonwood (Populus trichocarpa) and Balsam Poplar (Populus
balsamifera) occasionally hybridize to produce fertile offspring. Yet, the fossil record indicates that they have been recognizably separate species (morphologically)
for 12 million years.
On the other hand, Hawaiian Drosophila species are varied in appearance and
behavior, and many are reproductively isolated from one another. Genetically, however,
they are very similar.
Forces that Drive Evolution: Redux
If you're paying close attention, you will notice...
Forces #2, #3 and #4 are essentially about...population size.
#2: Small population size means more likelihood of a non-representative sample of genes in the next generation.
#3: Assortative mating segregates subsets of genes into smaller, interbreeding populations.
#4: Lack of migration results in smaller population size. Migration restores large population size, at least in terms of gene flow.
These forces all result in (populational) genetic changes that are not direct responses to natural selection. Of all the forces that drive evolution, only natural selection results in organisms that are better suited to live and reproduce in their environment.
A mutation can be one of three things to the organism that inherits it:
beneficial (helps the organism in some way) --> adaptive
deleterious (harms the organism in some way) --> maladaptive
neutral (does not affect the organism) --> neutral
In the "contest" of natural selection, organisms do not compete
against their predators, parasites or pathogens. They compete against
The individuals in any given species who are best
suited to leave the most offspring in a given environment are the
"winners" of that round of natural selection. But note that a form well-suited to one environment may be completely inappropriate in another. A trait that's adaptive in one set of circumstances can become neutral or maladaptive if the environment changes.
It's all about context.
Unlike genetic drift, evolution via natural selection cannot be considered random change. It is directed change in gene frequencies due to the interaction of organisms with each other and with their environment.
Recall the tenets of Evolution by Natural Selection:
No genotype confers a reproductive advantage over another genotype.
Remember Darwin's four tenets of Evolution by Natural Selection:
1. Organisms are capable of producing huge numbers of offspring (OVERPRODUCTION)
2. Those offspring are physically variable, and the variation is heritable (VARIABILITY)
3. Those offspring must compete for limited resources, from food to nesting sites to mates (COMPETITION)
4. Those whose phenotypic characters allow them to best exploit those limited resources will leave the most genes to succeeding populations. (DIFFERENTIAL REPRODUCTION)
An individual's Darwinian (evolutionary) fitness is a measure of the proportion of
genes it contributes to succeeding generations. Evolutionary fitness is defined by the environment. A phenotype
conferring fitness in a particular environment could be a liability if the environment changes.
Quantifying Relative Darwinian Fitness: Fitness and Selection Coefficients
In a population where individuals expressing a particular genotype have a selective advantage over those expressing a different genotype, certain coefficients can give an indication of just how much selective pressure is operating on each genotype.
The fitness coefficient (W) is an expression of the adaptive value of a particular genotype relative to other genotypes. The genotype that produces the most offspring in a given population
is assigned a fitness value of 1.0.
Example: There are three genotypes, AA, AA' and A'A' in a population. Over their lifetimes, the three genotypes produce the following numbers of offspring:
AA --> 10 offspring
AA' --> 5 offspring
A'A' --> 2 offspring
The fitness coefficents for each genotype are measured relative to the most successful genotype.
AA: W = 10/10 = 1.0
AA': W = 5/10 = 0.5
A'A': W = 2/10 = 0.2
The AA genotype has the highest fitness for this gene locus in this environmental/selective context.
Conversely, the selection coefficient (s) is a measure of selective pressure
against a particular genotype, relative to the other genotypes in the
population. It is calculated as 1 - W.
In our example, for each of our genotypes:
AA: s = (1.0 - 1.0) = 0 (no selection against this genotype)
AA': s = (1.0 - 0.5) = 0.5 (50% more selection against this genotype than against AA)
A'A': s = (1.0 - 0.2) = 0.8 (80% more selection against this genotype than against AA)
Selection pressure is highest against the A'A' genotype, relative to the
Sexual selection is a special case of natural selection based upon an individual's relative ability to attract and mate with members of the opposite sex. Individuals exhibiting characters that make them more likely to gain mating opportunities gain a selective advantage. Sexual selection is most likely to change allele frequencies when there is competition for mates.
Sexual selection can result in sexual dimorphism.
Sexual selection can operate in two ways:
Members of one sex compete against each other for mates, thereby creating a reproductive differential among themselves. If those members of the population having heritable characteristics that contribute to their winning more mates reproduce more than those lacking those traits, then natural (sexual) selection is occurring.
Members of one sex prefer a particular trait in the members of the opposite sex, creating a reproductive differential in the other sex. If members of the population having a heritable trait that makes them more attractive to the opposite sex than those lacking the trait, they will out-reproduce them. Natural selection (of the sexual kind) is occuring.
Classic examples of traits molded by sexual selection, with a few surprises.
Carotenoid production in birds - parasite load can depress the production of red/orange/yellow carotenoid pigments; females who choose brightly colored males are getting an "honest signal" of health, and genetic quality.
The Sexy Son Hypothesis - a female who chooses a mate based on his attractive male traits may have sons who share their father's attractiveness, and have increased reproductive success.
At the start of a "selection cycle" the population is usually made up of
individuals expressing a particular trait along a continuum, which can
be expressed as a bell-shaped curve
stabilizing selection: selective forces at work on
a population favor greatest reproduction by individuals exhibiting
the average state of a particular character. In this instance,
the composition of the population doesn't change.
directional selection: the individuals at one extreme
or the other of the bell shaped curve have a reproductive advantage
over the rest.
(e.g., in drought years in the Galapagos, insects
become scarce and seeds relatively abundant. Finches with deep,
thick bills have an advantage in that they can more effectively
crack seeds. The narrow-billed birds die out or have lower reproductive
success because of the scarcity of food.)
disruptive (= diversifying) selection:
individuals at the average point on the curve are at a selective
disadvantage; individuals with either extreme have a reproductive
Why Can't Polar Bears Just Evolve Gills?
You've probably heard the bad news that polar bears will likely be extinct before the end of the century, largely because climate change is drastically changing their habitat.
(Click on the image, and then click on "THREATS")
So why can't polar bears just evolve gills and get over it?
As you probably have figured out, evolution doesn't work that way.
Natural Selection Does not Make Perfect Organisms
Though natural selection results in populations that are evolutionarily adapted to a their particular environment, there are plenty of examples of a lack of "intelligent design." Why?
Natural Selection acts only on polymorphism that already exists.
Mutations do not necessarily generate ideal traits. Natural selection acts only upon what a population currently has to work with. Mutations are random. Traits don't evolve because organisms need them.
Natural Selection works only on traits that already exist.
Apple seeds grow into apple trees, and manatees give birth to manatees. Modifications to their body plans are based on what is historically there in the genes. Mutation do not generate complex structures de novo. It conscripts existing structures for new functions.
Natural Selection results in traits that are sometimes compromises.
The traits we have may be well adapted for our ecological niche. But there are constraints placed on our evolution by the multi-tasking we must do in our lives.
example: Some body forms just work better in water than on land, though the animal might be able to live in either habitat.
Random events govern evolution, too.
A hundred thousand years ago, a Super Frog was born. He had the best mating call anyone in the swamp had ever heard. His colors were perfect. Every female wanted him.
But just as he was getting ready for his First Big Mating Call, SPLAT!! A broken branch from the tree over his rock squashed him flat. His fantastic mutations died with him.
You might have the most fantastic mutation lurking in one of your thousands of gametes. But given that you will actually use one or two of them in your lifetime (if you are a smart and environmentally sensitive person), that fantastic mutation might just never see the light of day.
These four constraints mean that evolution doesn't necessarily build ideal organisms.
We're just as good as we can be, given the circumstances. And that's...okay.
Population Genetics: Measuring Evolutionary Change
In an idealized, model population that is not evolving, none of the five factors we have just examined are
at work, and allele frequencies for a given locus will not change over time.
Such idealized populations rarely, if ever, exist in nature.
By monitoring changes in allele and genotype frequencies over generations, the population geneticist can quantify microevolutionary change.
The population geneticist translates evolution into precise, genetic terms by studying
composition of populations
the forces that determine and change that genetic composition.
Genetic variability can exist:
within a population
between geographically close populations (example: Liguus, the Florida Tree Snail, on Everglades Hammock islands)
between geographically distant populations (geographic variation, as in these House Finches from Michigan (left) and Mexico (right)
clinal variation (example: gradations in human skin color by geographic region)
Microevolution involves change in the relative frequency of the various alleles of gene loci in a population.
How can we tell if this is happening?
A measure of genetic variabity in populations is heterozygosity: the proportion of genes in the genome that are present in heterozygous condition.
Genetic variability in a population can be quantified as average heterozygosity: the average percent of loci that are heterozygous in that population.
We examine the genes of a population of frogs in Yeehaw Pond
This species of frog has 30,000 genes (= loci) (two copies of each, if diploid)
We discover that in the average frog, 10,000 of those gene loci are heterozygous
This means that the frog population is--on average--33% heterozygous and 67% homozygous at all the gene loci in its genome.
The Hardy-Weinberg Equation: Testing Whether a Population is Evolving
In 1908, Godfrey H. Hardy, a British mathematician, and Wilhelm Weinberg, a German
...independently reported a mathematical rule that predicts relative genotype
frequencies--given starting frequencies of two alleles--in a population that is not evolving.
It's an expansion of the binomial equation, (p + q)2
For a population segregating two alleles at a particular locus in which A
is the dominant allele and a is the recessive allele
the total frequency of all alleles, A + a = 1.0.
The total number of either allele is equal to [the number of the allele (A or a)] divided by [the total number of alleles in the population]
The frequency of A is represented as p.
The frequency of a is represented as q.
Hence, p + q = 1.0
Hardy and Weinberg independently noted that
at any given point in time and
at any given starting point of relative allele frequencies
the expected relative genotype frequencies (AA, Aa and aa) in an idealized, non-evolving population could be predicted by the equation:
p2 + 2pq + q2
p2 = predicted frequency of homozygous dominant individuals q2 = predicted frequency of homozygous recessive individuals 2pq = predicted frequency of heterozygous individuals
The model assumes...
genotype frequencies are predicted by allele frequencies
there is no change in allele frequencies between generations
The equilibrium is neutral: small changes in frequency
revert to the original frequency within one generation of random mating, as
long as certain requirements (to be enumerated below) are met.
If a population's relative genotype frequencies (at a particular locus) match those predicted by the HW equation, the population is NOT EVOLVING at that locus. It is said to be in Hardy Weinberg equilibrium with respect to that locus.
If relative genotype frequencies are significantly different from the prediction, or if they change significantly over generations, then the population IS EVOLVING at that locus, and is NOT in Hardy-Weinberg equilibrium.
Why do these numbers make sense?
If the dominant allele (A) is present in known frequency (p) in both eggs
and sperm, then its likelihood of being inherited from both an egg and
sperm by the next generation can be expressed by the Product Rule (The probability of two independent events happening is the product of their individual probabilities):
p x p = p2
The same is true for the recessive allele:
q x q = q2
And Product Rule also gives us the expected frequency of heterozygotes in the
multiplied frequency of both alleles (p x q)(p x q):
(Each offspring inherits two alleles for a given locus, and each of these two "inheritance events" will give either A or a).
Hence, given any initial relative starting frequencies of A (p) and a (q), the three genotypes should be present in the predicted relative frequencies in the next generation:
p2 : 2pq : q2
...as long as the five conditions are met:
there is no mutation at the locus in question
the population is infinitely large
individuals of the population mate randomly
no individuals emigrate from or immigrate into the population
no genotype has a reproductive advantage over another (no natural selection)
A Sample Hardy-Weinberg calculation
Species: Sciurus carolinensis (Grey Squirrel)
Gene Locus: A
Alleles: A (dominant; wild type agouti fur) and a (recessive; melanistic black fur)
We are studying a population of 1000 squirrels. Of these, 60 (60/1000, or 0.06)
If each of these melanistic squirrels carries two recessive alleles, we can use this to calculate the expected frequency of q, since q2 is the frequency of the alleles in the homozygous recessive individuals.
The square root of q2 is equal to q. (duh)
In our example, the square root of 0.06 = .25.
Since p + q = 1.0, you can now solve for p
1 - 0.25 = 0.75
Our predicted frequencies, based on the assumption that the squirrel population is in HW equilibrium, are p = 0.75 and q = 0.25
plug these values into the HW equation to calculate expected relative genotype frequencies:
0.752 + 2(0.75)(0.25) + 0.252
This means that if our population of 1000 squirrels is in HW equilibrium, then
p2 = 0.56 - (0.56 x 1000, or 560 squirrels should be AA)
2pq = 0.38 - (0.38 x 1000, or 380 squirrels should be Aa)
q2 = 0.06 - (0.06 x 1000, or 60 squirrels should be aa)
(Notice that these three frequencies add up to 1.0, 100% of the 1000 squirrels in the population.)
Heterozygosity and Deleterious Alleles
Can you think of reasons why it might be advantageous to be heterozygous, rather than homozygous for a particular trait?
Recall the example of Sickle Cell Anemia.
Here's another example.
The major histocompatibility complex The MHC, or Major Histocompatibility Complex is a relatively large gene family found in most vertebrates. The MHC genes encode MHC polypeptides, which are constructed into important players in the immune system.
The significantly longer survival of MHC heterozygotes over MHC homozygotes is another bit of evidence that heterozygosity at certain gene loci can be adaptive. The more heterozygous the individual, the longer that patient staves off full-blown AIDS.
This trend is seen not only in HIV+ human patients, but also in other species.
Captive big cats exposed to feline parvovirus (cause of feline distemper)
Hybrid individuals usually exhibit a high degree of heterozygosity, which results in HYBRID VIGOR.
The more closely related parents are (i.e. the more inbred the offspring), the LESS heterozygous their offspring are likely to be.
While inbreeding does not always produce misfit offspring, it often does result in reduced vigor of the products of inbreeding.
Reduction in biological (as opposed to evolutionary) fitness in an inbred organism is known as inbreeding depression (<-- required link).
Humans' breeding of animals for specific traits has led to some striking examples of inbreeding depression. Meet Kenny the White Tiger.
(click on pic)
You might reasonably ask:
How can "bad" genes stay in a population? Why are they not "selected out"?
There are several possible reasons.
Though an allele might be deleterious (harmful) in homozygous condition, some harmful alleles can confer a selective advantage in heterozygous condition. (e.g., sickle-cell anemia)
Some locations on the DNA can be mutational "hot spots" that mutate with relative frequency. Even though the harmful alleles may be "weeded out" by natural selection, new mutations at that locus maintain the mutation.
An allele that is harmful in one environmental context may not be harmful in another. If a deleterious allele continuously enters a population where it is harmful because of migration into that population from a neighboring area where that mutation is not harmful, the mutation may continually be found in the location where it is disadvantageous.
natural selection is not instantaneous
In a changing environment, a deleterious allele may not always be so harmful that it is immediately removed from a population. Natural selection may take longer to remove some alleles than others.
allele expressed too late for natural selection to act
Some genes or alleles exhibit age-dependent expression, and are expressed at a particular stage of development in the organism. If a harmful allele is expressed only after an organism has reproduced, then it will escape the jaws of natural selection.