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How does selection affect allele frequency?

How does selection affect allele frequency?



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Question

People who are carriers for Blooms Syndrome have developed a selective advantage. How would this affect the allele frequency of the disease allele?

My thoughts

Natural selection will occur, only the carrier is selected and the affected will be selected against, leading to an imbalance of the Hardy-Weinburg equilibrium.


Question

People who are carriers for Blooms Syndrome have developed a selective advantage. How would this affect the allele frequency of the disease allele?

Your answer

Natural selection will occur [… ]

This is correct. Anytime you have a fitness differential among different genotypes, selection will affect allele frequencies.

[… ] [l]eading to an imbalance of the hardy-weinburg equilibrium.

Hard-Weinberg equilibrium describes the relationships between allele frequencies and genotype frequencies. Selection can sure affect this relationship at some stage of life but it will not affect this relationship just after fecundation.

In any case, the question does not seem to expect you to talk about that. The question is asking about allele frequency only.

If you want to understand Hardy-Weinberg, you should definitely have a look at Solving Hardy Weinberg problems.

What I would answer

Not assuming any extra knowledge, the only simple, logic answer is to say that the frequency of the allele coding for the Blooms Syndrome will likely increase in frequency in the population, eventually reaching fixation. This increase in allele frequency would yield to an increase in the frequency of carriers of Blooms Syndrome.

Of course, if there is heterozygote advantage (aka. overdominance for fitness), then in an infinite population, the allele should never fully reach fixation.

If we were to know more about the genetics of the Blooms Syndrom or the specific selection advantage (and eventually many other things one may want to consider) one could formulate a more quantitative answer.


Antagonistic Interspecific Coevolution

Positive Directional Selection: Arms Race Coevolution

Under directional selection , relative fitness increases as the value of a trait increases (positive directional selection) or decreases (negative directional selection). Dawkins and Krebs (1979) argued that reciprocal positive directional selection exerted by coevolving hosts and parasites could lead to a situation where hosts continually become more resistant to parasitism while parasites respond by becoming more virulent or evolving new mechanisms of evading host immunity.

Unlike negative frequency-dependent selection, this so-called ‘Arms Race coevolution’ does not generate a rare advantage per se. Instead, host resistance and parasite ‘virulence’ are inherent properties of the individual genotype and do not depend on the frequency of the other genotypes. In this scenario, repeated selective sweeps favoring resistant hosts and virulent parasites will lead to the evolution of reciprocal host and parasite adaptations that, once overcome by a counter-adaptation, will not again incur resistance/virulence ( Figure 1(b) Woolhouse et al., 2002 Burdon et al., 2013 ). Another important distinction between Red Queen and Arms Race coevolution is that the latter, in favoring traits that counter adaptations in the biological antagonist, has a high potential for evolutionary innovation (e.g., Kerns et al., 2008 reviewed in Daugherty and Malik, 2012 ).


Microevolution versus Macroevolution

Evolution is a continuous process, but major evolutionary changes are rare events. Major evolutionary changes distinguish one population from another and result in the creation of a new species. Evolutionary changes that mark the appearance of a new species (or genera and higher) are macroevolutionary events.

However, evolution can occur within a species. Think about the human allele for sickle-cell disease populations living in areas with high incidences of malaria are better adapted because of the high frequency of this allele. Hence, evolution of human populations has occurred in the past, is occurring today, and will continue to occur. Changes that lead to alterations in allele frequencies are microevolutionary events. At the most basic level, evolution is a change in allele frequencies and genotype frequencies in a population from generation to generation. A population is evolving even if allele frequencies are fluctuating at just one chromosomal location. At the population level, therefore, evolution is a nearly continuous process.

We have discussed how natural selection adapts organisms to their environment. As you learned from the example of the sickle-cell allele, this adaptation results in a change in allele frequency. As you will soon learn, however, natural selection is only one mechanism that can change allele frequencies.


Darwin

Charles Darwin was 22 years old when he accepted an unpaid position aboard the H.M.S. Beagle. The Beagle sailed on a surveying expedition, primarily to chart the South American coastline. Among other things, Darwin observed many plant and animal species on the Galapagos Islands (off the coast of Ecuador) that exist nowhere else in the world. The species on these islands exhibit great diversity, the most notable being the finches of the Galapagos. The differences in feeding adaptations among these finches led Darwin to describe how such adaptations arise in species. Darwin's observations from the voyage later supported his theory of natural selection in The Origin of Species. In this work, Darwin described two processes. In one process, "descent with modification," Darwin suggested that all life descended from one original form and that diversity was the result of adaptations. Toward the end of The Origin of Species, he used the word evolution. The other process he described was natural selection. We will discuss these processes in the remainder of this tutorial.

At some point, you should consider reading Darwin's book. Although written over 150 years ago, it is still relevant and it is easy to read.


How does selection affect allele frequency? - Biology

Mutation, Migration, Inbreeding, & Genetic Drift in natural populations How do mutation, migration, inbreeding, and genetic drift interact with selection?
Do they maintain or reduce variation?
Can they maintain variation at a high level?
What is their significance in population (short-term) & evolutionary (long-term) biology?

(1) Mutation / selection equilibrium

Deleterious alleles are maintained by recurrent mutation.
A stable equilibrium (where q = 0) is reached
when the rate of replacement (by mutation)
balances the rate of removal (by selection).

µ = frequency of new mutant alleles per locus per generation
typical µ = 10 -6 : 1 in 1,000,000 gametes has new mutant
_____
then =(µ / s) [see derivation]

Ex.: For a recessive lethal allele (s = 1) with a mutation rate of µ = 10 -6
then = û = (10 -6 / 1.0) = 0.001

mutational genetic load
Lowering selection against alleles increases their frequency.
Medical intervention has increased the frequency of heritable conditions
in Homo (e.g., diabetes, myopia)
Eugenics : modification of human condition by selective breeding
'positive eugenics': encouraging people with "good genes" to breed
'negative eugenics': discouraging people with 'bad genes'' from breeding
e.g., immigration control, compulsory sterilization
[See: S. J. Gould , " The Mismeasure of Man "]

Is eugenics effective at reducing frequency of deleterious alleles?
What proportion of 'deleterious alleles' are found in heterozygous carriers?

(2pq) / 2q 2 = p/q 1/q (if q << 1)

if s = 1 as above, ratio is 1000 / 1 : most of variation is in heterozygotes,
not subject to selection

(2) Migration / selection equilibrium

Directional selection is balanced by influx of 'immigrant' alleles
a stable 'equilibrium' can be reached iff migration rate constant.

Consider an island adjacent to a mainland, with unidirectional migration to the island.
The fitness values of the AA, AB, and BB genotypes differ in the two environments,
so that the allele frequencies differ between the mainland (qm) and the island (qi).


AA AB BB
W0 W1 W2 q
Island 1 1-t 1-2t qi 0
Mainland 0 0 1 qm 1

B has high fitness on mainland, and low fitness on island.
[For this model only, allele A is semi-dominant to allele B,
so we use t for the selection coefficient to avoid confusion]

m = freq. of new migrants (with q m) as fraction of residents (with q i)
if m << t qi = (m / t)(qm) [see derivation]

Gene flow can hinder optimal adaptation of a population to local conditions.

Ex: Water snakes (Natrix sipedon) live on islands in Lake Erie ( Camin & Ehrlich 1958 )
Island Natrix mostly unbanded on adjacent mainland, all banded.
Banded snakes are non-cryptic on limestone islands, eaten by gulls
Suppose A = unbanded B = banded [AB are intermediate]
Let qm = 1.0 ["B" allele is fixed on mainland]
m = 0.05 [5% of island snakes are new migrants]
t = 0.5 so W2 = 0 ["Banded" trait is lethal on island]
then qi = (0.05/0.5)(1) = 0.05
and Hexp = 2pq = (2)(0.95)(0.05) 10%
i.e, about 10% of snakes show intermediate banding, despite strong selection

=> Recurrent migration can maintain a disadvantageous trait at high frequency.

(3) Inbreeding / selection

Inbreeding is the mating of (close) relatives
or, mating of individuals with at least one common ancestor
F ( Inbreeding Coefficient ) = prob. of " identity by descent ":
Probability that two alleles are exact genetic copies of an allele in the common ancestor
This is determined by the consanguinity (relatedness) of parents.

Inbreeding reduces Hexp by a proportion F
(& increases the proportion of homozygotes). [see derivation]

f(AB) = 2pq (1-F)
f(BB) = q 2 + Fpq
f(AA) = p 2 + Fpq

Inbreeding affects genotype proportions,
inbreeding does not affect allele frequencies.

Inbreeding increases the frequency of individuals
with deleterious recessive genetic diseases by F/q [see derivation]

Ex.: if q = 10 -3 and F = 0.10 , F/q = 100
=> 100-fold increase in f(BB) births

Inbreeding coefficient of a population can be estimated from experimental data:

F = ( 2pq - Hobs ) / 2pq [see derivation]

Ex.: Selander (1970) studied structure of Mus house mice living in chicken sheds in Texas

Variation at Est-4 locus
obs exp
AA 0.226 0.181
AB 0.400 0.489
BB 0.374 0.329

since p = 0.226 + (1/2)(0.400) = 0.426
& q = 0.374 + (1/2)(0.400) = 0.574

Then F = (0.489 - 0.400) / (0.489) = 0.182
which is intermediate between Ffull-sib = 0.250
& F1st-cousin = 0.125

=> Mice live in small family groups with close inbreeding
[This is typical for small mammals]


Paradoxes of inbreeding:
Inbreeding is usually thought of as "harmful":
inbreeding increase the probability that deleterious recessive alleles
will come together in homozygous combinations
"Harmful" alleles are reinforced
Inbreeding depression : a loss of fitness in the short-term due to
difficulty in conception, increased spontaneous abortion, pre- & peri-natal deaths
Ex.: First-cousin marriages in Homo
Two-fold increase in spontaneous abortion & infant mortality
Every human carries 3

4 "lethal equivalents"
NatSel Exercise #3

However, in combination with natural selection, inbreeding can be "advantageous":
increases rate of evolution in the long-term (q 0 more quickly)
deleterious alleles are eliminated more quickly.
increases phenotypic variance (homozygotes are more common).
advantageous alleles are also reinforced in homozygous form

(4) Genetic Drift / selection

Genetic Drift is stochastic q [unpredictable, random]
(cf. deterministic q [predictable, due to selection, mutation, migration)

Sewall Wright (1889 - 1989): " Evolution and the Genetics of Populations "

Stochastic q is greater than deterministic q in small populations:
allele frequencies drift more in 'small' than 'large' populations.

Drift is most noticeable if s 0, and/or N small (< 10) [N 1/s]

q drifts between generations (variation decreases within populations over time) [ DEMO ]
eventually, allele is lost (q = 0) or fixed (q = 1) (50:50 odds)

Ex: NatSel Laboratory Exercise #4
[Try: q = 0.5, W0 = W1 = W2 = 1.0, and N = 10, 50, 200, 1000]

q drifts among populations (variation increases among populations over time)
eventually, half lose the allele, half fix it.

**=> Variation is 'fixed' or 'lost' & populations will diverge by chance <=**

Evolutionary significance:
"Gambler's Dilemma" : if you play long enough, you win or lose everything.
All populations are finite: many are very small, somewhere or sometime.
Evolution occurs on vast time scales: "one in a million chance" is a certainty.
Reproductive success of individuals in variable: "The race is not to the swift . "

What happens in the really long run?

Effective Population Size (Ne)
= size of an 'ideal' population with same genetic variation (measured as H)
as the observed 'real' population.
= The 'real' population behaves evolutionarily like one of size Ne :
the population will drift like one of size Ne
loosely, the number of breeding individuals in the population

Consider three special cases where Ne < or << Nobs [the 'count' of individuals]:

Ne = (4)(Nm)(Nf) / (Nm + Nf)
where Nm & Nf are numbers of breeding males & females, respectively.

"harem" structures in mammals (Nm << Nf)
Ex.: if Nm = 1 "alpha male" and Nf = 200
then Ne = (4)(1)(200)/(1 + 200) 4
A single male elephant seal (Mirounga) does most of the breeding
[Elephant seals have very low genetic variation]

eusocial (colonial) insects like ant & bees (Nf << Nm)
Ex.: if Nf = 1 "queen" and Nm= 1,000 drones
then Ne = (4)(1)(1,000)/(1 + 1,000) 4
Hives are like single small families

(2) Unequal reproductive success
In stable population, Noffspring/parent = 1
"Random" reproduction follows Poisson distribution (N = 1 1)
(some parents have 0, most have 1, some have 2 or 3 or more)

X Ne = Reproductive strategy
1 1 Nobs Breeding success is random
1 0 2 x Nobs A zoo-breeding strategy
1 >1 < Nobs K-strategy, as in Homo
1 >>1 << Nobs r-strategy, as in Gadus

(3) Population size variation over time

Ne = harmonic mean of N = inverse of arithmetic mean of inverses
[a harmonic mean is much closer to lowest value in series]
n
Ne = n / [ (1/Ni) ] where Ni = pop size in ith generation
i=1

Populations exist in changing environments:
Populations are unlikely to be stable over very long periods of time
10 -2 forest fire / 10 -3 flood / 10 -4 ice age

Ex.: if typical N = 1,000,000 & every 100th generation N = 10 :
then Ne = (100) / [(99)(10 -6 ) + (1)(1/10)] 100 / 0.1 = 1,000

Founder Effect & Bottlenecks:
Populations are started by (very) small number of individuals,
or undergo dramatic reduction in size.

Ex.: Origin of Newfoundland moose (Alces):
2 bulls + 2 cows at Howley in 1904
[1 bull + 1 cow at Gander in 1878 didn't succeed].

Population cycles: Hudson Bay Co. trapping records (Elton 1925)
Population densities of lynx, hare, muskrat cycle over several orders of magnitude
Lynx cycle appears to "chase" hare cycle

The effect of drift on genetic variation in populations

Larger populations are more variable (higher H) than smaller
if s = 0: H reflects balance between loss of alleles by drift
and replacement by mutation

Ex.: if µ = 10 -7 & Ne = 10 6 then Ne µ = 1 and Hexp = (0.4)/(0.4 + 1) = 0.29

But typical Hobs 0.20 which suggests Ne 10 5
Most natural populations have a much smaller effective size than their typically observed size.

Ex.: Gadus morhua in W. Atlantic were confined to Flemish Cap during Ice Age 8

10,000 YBP
mtDNA sequence variation occurs as "star phylogeny":
most variants are rare and related to a common surviving genotype
Carr et al. 1995 estimated Ne = 3x10 4 as compared with Nobs 10 9
Effective size is ca. 5 orders of magnitude smaller than observed

Stochastic effects may often be more important than deterministic processes in evolution.


You can easily conjure an image of a tiger, but it’s harder to define a species just by its physical and behavioral traits. Thus, evolutionary biologists define a species by the equilibrium of alleles in its population. Alleles rise and fall in the course of a species’ history. But periods of stability exist. The equilibrium of alleles allows the species to have a certain level of stability and fitness in its environment. Evolution is the guiding force that moves wavy, fluctuating allele pools to tranquil, stable ones.

Darwin’s theory of evolution became a redefining force in the field of biology before biologists had an understanding of genes or alleles. Hence, to a biologist of yesteryear, evolution was a concept unrelated to allele frequency. But today’s biologists know that alleles can explain everything Darwin described. Darwin knew that every generation of species contained offspring with random changes, but he did not know how such a phenomenon occurred. Today, biologists know the mechanisms that allow for such evolution: changes in alleles.


Discussion

Methodology

Several statistical methods have been developed to scan large numbers of loci across many individuals and link patterns of genetic variation to environmental variation (Holderegger et al., 2008 Schoville et al., 2012 Pannell and Fields, 2014). These methods identify outlier loci – loci with stronger differentiation in allele frequencies between populations than can be expected to occur due to random processes only, and which are, therefore, assumed to have been under selection. Statistically significant associations between genetic variation in outlier loci and variation in environmental variables indicate a role of the outlier loci in local adaptation. Adaptive outlier loci may represent new beneficial mutations that have increased in frequency and eventually become fixed in the population (hard sweeps). Alternatively, outlier loci represent alleles or haplotypes that have increased in frequency, but where some polymorphism is maintained (soft sweeps) (Barrett and Schluter, 2007). Soft sweeps can occur when selection on standing variation acts on multiple haplotypes in the genome simultaneously. Studies of local adaptation usually compare populations that have been exposed to contrasting conditions over many generations, and, in spite of migration, have evolved through repeated cycles of recombination and selection (e.g., Freeland et al., 2010 Turner et al., 2010 Gould et al., 2014). In some cases, such studies include replicates of populations that have started out from a common pool and been exposed to the same conditions these replicates can be used to separate consistent signs of selection from random changes like genetic drift (Wiberg et al., 2017). The present study is different from these studies in the way that we characterize the selection (mortality/survival) that occurs within one generation only, with no reproduction or migration occurring. This allows for the use of a simple FST-based test of changes in allele frequencies resulting from selection. We show that in spite of a large proportion of random mortality/survival, the use of several replicate survivor populations, sampled from replicate plots in a field experiment, improves the power of the test substantially, and makes it possible to remove these random effects and identify loci that have been under selection in all replicates. In study 1, BayeScan identified one of the SNP outliers identified by the simple FST-based method, after combining the 3H and 5H replicates. In contrast, in study 3, where a higher number of individuals were pooled in each population sample and the differentiation between populations was larger than in study 1, BayeScan identified more potential outliers than the simple FST-based method. Testing these SNPs further with analysis of variance made it possible to identify differential selection due to stand type and/or seeding density. In study 3, all outliers identified by the simple FST-based method were included among those identified by BayeScan.

In order to be able to detect all loci with differences in allele frequency, it is necessary to have a sufficient coverage of the genome, i.e., a sufficiently high SNP density. A high SNP density can be achieved by using a restriction enzyme in the GBS protocol which is a frequent cutter (i.e., ApeK1, which we used), combining several restriction enzymes, and by sequencing to a sufficient read depth to be able to call SNPs and determine allele frequencies for the majority of restriction sites. The required SNP density depends on the linkage disequilibrium (LD) of the population. The lower the LD, the higher the SNP density needed in order for all genes to be in some degree of linkage with at least one nearby SNP. Red clover has a relatively small genome (approximately 420 Mb), facilitating good read depth relative to the sequencing effort, but varieties tend to have limited LD. The LD along the different chromosomes in the original population studied here has previously been characterized by De Vega et al. (2015), who found that the average LD, measured as R 2 , at distances of 100 Kb, ranged between 0.19 and 0.25 for the different chromosomes. At 500 Kb LD had decayed completely to background levels (R 2 0.02𠄰.05). The likelihood of detecting a locus with significantly different allele frequency in different populations depends on the magnitude of the allele frequency difference, the distance between the gene conferring the effect on survival and a linked SNP, and the LD in that specific region. Here, we obtained an average density of one SNP per 85 kb or 37 kb in study 1 and in study 3, respectively. The studied variety is a synthetic population with several possible haplotypes at any given chromosomal segment, thus all nearby SNPs might not necessarily be diagnostic, that is, distinguish between alleles with different effects on survival. Therefore, with the SNP densities obtained in our study, we are likely to pick up a substantial amount of loci affecting survival, but not all, particularly not in study 1.

Pooling of individual DNA samples, or of individual leaf samples prior to DNA extraction, can increase the allele frequency information obtained per sequencing effort, and allow for comparison of a large number of populations (Turner et al., 2010 Byrne et al., 2013 Wiberg et al., 2017). While sequencing of individuals requires a certain read depth in order to call SNPs and distinguish between homozygotes and heterozygotes, sequencing pools requires an even higher read depth for allele frequencies to be estimated accurately. Moreover, information about haplotypes and population structure is lost when sequencing pools. In our study, a very good correlation was obtained between allele frequencies obtained from a DNA pool of 88 individuals and allele frequencies obtained from genotyping of individuals (Figure 4 and Table 3). Read depth was increased only 7 times in the pool relative to the 88 individual samples (i.e., >10x reduction in sequencing effort), and a similar number of SNPs were obtained. At a MAF > 0.05 and a read depth in pools of 100-499, R 2 was 0.97, while it was somewhat lower at lower and higher read depth. At the same MAF and read depth range, pooling of leaves of 100 plants prior to DNA extraction led to an average correlation of 0.87 and 0.90 in two sets of three replicates. This is slightly lower than that reported by Byrne et al. (2013), who obtained a correlation of R = 0.91 (R 2 = 0.93) at MAF > 0.05 and read depth above 20x in replicate samples of leaves from around 200 perennial ryegrass seedlings. Pooling of individual leaf samples prior to DNA extraction reduces costs, but the accuracy of the allele frequency estimates is also reduced. Estimates could possibly have been improved if we had used more uniform leaf material and taken more care in sampling equal amounts of tissue from each individual. However, the use of several replicate populations compensates to some extent for the reduced accuracy of allele frequency estimates. The replicate samples from two of the populations in study 3 showed that there was considerable sampling error in our method. This could be overcome by sampling more individuals and/or by including replicate samples or populations in the study.

Selection Occurring in the Field Within One Generation

The 88 plants in the original population sample represent the sown populations while the survivor populations represent subsets remaining in each plot after selection (survival) during 2.5 years of exposure to the prevailing field conditions and management. Such selection within one generation represents the environmental flexibility that the genetic variation within populations of outcrossing species can provide (Charles, 1964 Crossley and Bradshaw, 1968). Some alleles may contribute to yield in some environments, while other alleles contribute in other environments, making the population or cultivar robust to environmental variation. Our analyses of the genetic variation in the survivor populations as compared to the original population that was sown (study 1) showed that the survivor populations in four different plots had diverged from the original population in different directions. Thus, although the first PC-axis separated the two harvesting regimes (Figure 1), most of the allele frequency variation was random. This may reflect a response to unintended variation in the environment among plots, random selection of alleles at the majority of loci, or sampling error. The original population had only a very weak genetic structure, which remained in the survivor populations, indicating that there was no selection acting on the structure (Figure 2). In study 3, the first PC-axis separated Ps from Ms, and within Ps it separated the two seeding densities, suggesting that differential selection had occurred due to the different treatments (Figure 5).

If the original population has high genetic diversity and low LD (typical of forage cultivars), it cannot be expected that selection acting on a relatively limited number of loci will affect average genetic distance measured across the genome. In order to identify such selection, each individual locus must be considered. Indeed, by looking for allelic shifts of individual SNPs in several replicate survivor populations we identified loci that had been systematically selected under the prevailing conditions in the investigated field experiment (Figure 3). These are candidate loci for establishment success or persistence. In study 1, 12 SNPs, representing 11 loci, had significantly altered allele frequencies, measured as FST, in Ps survivor populations (high seeding rate) relative to the original population. These SNPs represent loci with alleles conferring a higher likelihood for survival under the conditions that are common to all four plots. They may be related to, e.g., establishment, competition in Ps, winter survival and the general environmental and management conditions. The absolute average allele frequency changes detected ranged from 0.22 to 0.09. Tp3_5909984 was the SNP with the largest allele frequency shift from the original population to the survivor populations in study 1. It is located in the middle of the proximal half of Tp3. Interestingly, this is also the approximate location of the only QTL for persistence detected in a red clover mapping population of red clover by Herrmann et al. (2008).

In study 3, survivor populations were not compared with the originally sown population. Instead, survivors from Ps populations were compared to survivors from Ms populations, and survivors from populations sown at high seeding density was compared to survivors from populations sown at low density. A number of loci with allele frequencies indicating differential selection in Ps and Ms were identified. The absolute allele frequency changes detected were up to 0.36, suggesting that stand type exerted a relatively strong differential selection pressure. Red clover in mixture with perennial ryegrass and tall fescue experience earlier competition for light and possibly other resources, as the grasses grow and elongate earlier in the summer. Indeed, we have previously shown that offspring of survivor populations from Ms have earlier stem elongation than offspring from survivor populations from Ps (Ergon and Bakken, 2016), suggesting differential selection for earliness. Later in the summer, red clover plants are likely to experience stronger competition in Ps than in Ms, as individual red clover plants grow very large. Another condition that may vary between Ps and Ms is a stronger dependence of red clover plants on nitrogen fixation in Ms, as grasses have a more efficient nitrogen uptake and less is left for the clover.

Breeding, variety testing and seed multiplication of red clover occurs in Ps. Although seeding rates used usually are much lower (2𠄴 kg ha -1 ) than those in our experiment, our results suggest that unintended selection occurring in Ps during breeding and seed multiplication may not necessarily be in favor of good persistence in practical farming, were Ms are used.


How does selection affect allele frequency? - Biology

Activity 1: Breeding Bunnies

In this activity, you will examine natural selection in a small population of wild rabbits. Evolution, on a genetic level, is a change in the frequency of alleles in a population over a period of time. Breeders of rabbits have long been familiar with a variety of genetic traits that affect the survivability of rabbits in the wild, as well as in breeding populations. One such trait is the trait for furless rabbits (naked bunnies). This trait was first discovered in England by W.E. Castle in 1933. The furless rabbit is rarely found in the wild because the cold English winters are a definite selective force against it.

Note: In this lab, the dominant allele for normal fur is represented by Fand the recessive allele for no fur is represented by f.Bunnies that inherit two Falleles or one Fand one fallele have fur, while bunnies that inherit two fs have no fur.

Procedures Part A: Part Title -->

Print the Gene Frequency Data form (pdf) and the Discussion Questions (pdf), or get them from your teacher. Fill in the hypothesis section of the data form and specific predictions based on that hypothesis.

Your teacher may assign you to a working group and distribute the materials. If you are working alone, proceed on your own.

The red beans represent the allele for fur, and the white beans represent the allele for no fur. The container represents the English countryside, where the rabbits randomly mate.

Label one dish FF for the homozygous dominant genotype. Label a second dish Ff for the heterozygous condition. Label the third dish ff for those rabbits with the homozygous recessive genotype.

Place the 50 red and 50 white beans (alleles) in the container and shake up (mate) the rabbits. (Please note that these frequencies have been chosen arbitrarily for this activity.)

Without looking at the beans, select two at a time, and record the results on the data form next to "Generation 1." For instance, if you draw one red and one white bean, place a mark in the chart under "Number of Ff individuals." Continue drawing pairs of beans and recording the results in your chart until all beans have been selected and sorted. Place the "rabbits" into the appropriate dish: FF, Ff, or ff. (Please note that the total number of individuals will be half the total number of beans because each rabbit requires two alleles.)

The ff bunnies are born furless. The cold weather kills them before they reach reproductive age, so they can't pass on their genes. Place the beans from the ff container aside before beginning the next round.

Count the F and falleles (beans) that were placed in each of the "furred rabbit" dishes in the first round and record the number in the chart in the columns labeled "Number of F Alleles" and "Number of fAlleles." (This time you are really counting each bean, but don't count the alleles of the ff bunnies because they are dead.) Total the number of Falleles and falleles for the first generation and record this number in the column labeled "Total Number of Alleles."

Place the alleles of the surviving rabbits (which have grown, survived and reached reproductive age) back into the container and mate them again to get the next generation.

Repeat steps five through nine to obtain generations two through ten. If working as a team, make sure everyone in your group has a chance to either select the beans or record the results.

Determine the gene frequency of F and f for each generation and record them in the chart in the columns labeled "Gene Frequency F" and "Gene Frequency f." To find the gene frequency of F, divide the number of F by the total, and to find the gene frequency of f, divide the number of f by the total. Express results in decimal form. The sum of the frequency of F and f should equal one for each generation.

If you are doing this activity at school, record your group's frequencies on the board so your classmates can see them.

Graph your frequencies. Prepare a graph with the horizontal axis as the generation and the vertical axis as the frequency in decimals. Plot all frequencies on one graph. First, plot your own data. Use a solid line for Fand a dashed line for f. Then, if you are at school, plot the class totals. Use the same symbols for each group but a different color. If you are at home, you may wish to go through the activity again and see how your graphs compare.

Complete the Discussion Questions form with your group.

Adapted with permission from a 1994 Woodrow Wilson Biology Institute Laboratory "Evolution and Gene Frequencies: A Game of Survival and Reproductive Success," by Joseph Lapiana.


Directional selection

This extension of the infinitesimal model immediately leads to a remarkably general expression for the effect of epistasis on the limits to directional selection on standing variation (Paixao and Barton, 2016). (Note that here, I use directional selection to refer to an exponential relation between fitness and trait other forms of selection—for example, truncation selection—will select on the variance as well as the mean). Under the infinitesimal model, the additive variance, VA, decreases by a factor (1−1/(2Ne)) per generation, whereas the mean increases by βVA, where β is the selection gradient. Therefore, the total change in mean sums to 2Neβ which is just 2Ne times the change in the first generation (V 0 A being the initial additive variance). Robertson (1960) showed that this result can be derived by considering the slight increase in fixation probability of favourable alleles because of selection—a derivation that makes clear that the infinitesimal model implicitly assumes selection on individual alleles, s, to be weaker than drift (that is, Nes<<1).

The same argument applies with epistasis: classical quantitative genetics gives expressions for the conversion of epistatic variance into additive variance because of the changes in additive effects of alleles as the genetic background changes (Hill et al., 2006). The total response to directional selection β of a haploid population is Neβ, V 0 G which only depends on the total initial genotypic variance V 0 G. Because the change in mean in the first generation, β, is proportional only to the additive component of the genetic variance, the response to selection is slower in the presence of epistasis (for a given total variance, V 0 G). It is remarkable that the ultimate change in trait mean, which may take the phenotype far beyond its initial range, can be predicted simply from the components of variation in the original population.

Epistatic variance makes a bigger contribution to the ultimate response of a diploid population: the increase in mean is , where V 0 A(k) is the initial kth order variance component. However, it is still unlikely that higher-order variance components can be substantial, for two reasons. First, for biallelic loci with allele frequencies p, q, VA(k) is proportional to (2pq) k , and as the product of allele frequencies pq is less than one-fourth, we expect 2 k−1 VA(k) to decrease with k, especially when the contributing alleles are rare (Maki-Tanila and Hill, 2014). Second, for the additive variance to be much smaller than epistatic variance, the marginal effects of alleles must be small—as, for example, for variation in fitness components that is maintained by balancing selection. However, such special situations are sensitive to allele frequency, and any change in allele frequencies will generate additive variance. In addition, balancing selection is likely to act on a small number of loci with relatively large effect that would be rapidly fixed by strong directional selection (an exception is where recessive lethals increase a selected trait when heterozygous see, for example, Yoo, 1980). Such extreme cases cannot be common, as artificially selected traits usually do not revert when selection is relaxed (Weber, 1996).

Epistatic variance makes a relatively larger contribution to selection response in diploids than in haploids, as represented by the factor 2 k−1 in the above formula. This is because an allele has twice the effect in a homozygote as in a heterozygote, and hence the ultimate effect of interaction among a set of k alleles is greater by a factor 2 k , compared with their effect when segregating as heterozygotes. We have ignored dominance here, but note that rare recessives can inflate additive variance when they become common, and that this ‘conversion’ of dominance to additive variance may be much larger than the conversion of epistatic variance (Hill et al., 2006). However, there must still be a systematic bias towards favourable effects of rare recessives to increase the expected selection response.

The connection between the components of initial standing variation and the ultimate selection response is very general: it applies for any form of epistasis, provided that interactions are not strongly biased with respect to the selected trait, and provided that genetic variance is dissipated primarily by sampling drift rather than by selection. It applies even when the fitness landscape is ‘rugged’, so that large populations would be trapped at local ‘adaptive peaks’. This is simply because when selection on individual alleles is weak relative to drift, populations can readily cross between such peaks. As I argue in the following, selection is, in some sense, most efficient in this ‘infinitesimal’ regime.

How does epistasis affect the response to directional selection in the opposite case of a very large population? Now, the initial variance components are not directly relevant, because very rare alleles, which initially make hardly any contribution to the variance components, can increase to determine the ultimate response. Nevertheless, we can compare the total change in mean with that what would be achieved under the corresponding additive model, in which the effects of alleles on the original genetic background remain constant. Of course, if epistasis is systematically positive, there will be an accelerating response, and a much larger total change than with the original additive effects conversely, systematically negative epistasis leads to a smaller selection response (Hansen, 2013).

If epistatic interactions are random with respect to the marginal effects on the trait, and if the optimal genotype is the same under the epistatic and the corresponding additive models, then epistasis has no expected effect (Paixao and Barton, 2016). However, if epistasis is sufficiently strong, the marginal effects of alleles will change sign as allele frequencies change, so that a different optimal genotype will be reached. Now, epistasis does increase the expected response, even when interactions are random with respect to fitness. The magnitude of this effect can be predicted if interactions among different sets of genes are independent of each other, and matches simulations of random pairwise epistasis well. Overall, however, the effect of epistasis on selection response is modest (Paixao and Barton, 2016 Figure 3).

The effective dimension of trait variation in short versus long term. Left: the fraction of variance explained by the largest 1, 2, …, eigenvectors for 10, 100, 1000 traits (black, blue, red, top to bottom), measured in the final generation. Right: the same, but for a population that contains all mutations that fixed over 50 000 generations (that is, an F2 between the ancestral and derived population). An additive infinite sites model was simulated, with free recombination, stabilising selection exp(−|z| 2 /(2Vs)), Vs=100, N=100 haploid individuals, and mutation rate U=0.1 per genome per generation. Mutations have magnitude |α| drawn from an exponential with mean 1 with random direction. In these simulations, the variance of each trait mean around the optimum is close to the predicted Vs/(2N)=0.5, causing a loss of fitness 1/(4N)=0.0025 per trait. A full colour version of this figure is available at the Heredity journal online.

These arguments apply to the initial response to selection because of standing variation. Over longer timescales (>50 generations, say Hill, 1982), mutation makes a significant contribution, increasing additive variance by V A m per generation. Under the standard infinitesimal model, the additive variance approaches an equilibrium between mutation and random drift of 2NeV A m, and the mean will change under directional selection in proportion to this variance. In the short term, mutation generates negligible epistatic variance, unless mutations have large effect, as it introduces alleles at low frequency (Hill and Rasbash, 1986). However, epistasis makes additive effects conditional on genotype, so that the effect of new mutations may change with the mean. In the long term, the genetic variance will evolve unpredictably, as new alleles introduced by mutation become common enough to interact with each other. Nevertheless, as mutational variance is ubiquitous (Houle et al., 1996 Lynch and Walsh, 1998), an indefinite response to directional selection is expected.

When multiple traits are selected, the mean changes in proportion to the additive genetic covariance matrix (termed the ‘G matrix’) that in turn is proportional to the mutational covariance in the infinitesimal limit. The G matrix has received much attention on the grounds that it constrains adaptation. However, artificial selection has proved successful even when deliberately applied to trait combinations that show minimal variance (see, for example, Weber et al., 1999 Hill and Kirkpatrick, 2010 Marchini et al., 2014): as long as there is some additive variance in the direction of selection, selection can change the mean. Of course, the G matrix has very high dimension, and some directions may have zero variance (that is, there may be some zero eigenvalues). Even then, however, the G matrix does not necessarily constrain adaptation in the long term: it inevitably changes as new mutations arise, with effects in different directions. Imagine that traits may be influenced by a very large number of sites, n, of which only a much smaller number, 1<< ns<< n, are segregating at any one time any allele potentially has random effects on all k traits. At any time, G will have dimension ns, but as alleles are lost or fixed, in the long run adaptation can occur through the whole space of dimension n >> ns. Thus, evolution is constrained by the total number of sites that could affect the traits, and not by the number segregating at any particular time. Therefore, observation of the G matrix at any one time would not inform us about constraint on long-term evolution. This is illustrated in Figure 3. The left panel shows that in any one generation, most variance is explained by <50 dimensions, regardless of the number of traits under stabilising selection. In contrast, the right panel shows that over 50 000 generations, variance is spread over a number of dimensions proportional to the number of traits. Thus, each trait is kept close to the optimum, regardless of how many traits are being selected.


How does selection affect allele frequency? - Biology

Unit Four. The Evolution and Diversity of Life

14.10. Sickle-Cell Anemia

Sickle-cell disease is a hereditary disease affecting hemoglobin molecules in the blood. It was first detected in 1904 in Chicago in a blood examination of an individual complaining of tiredness. You can see the original doctor’s report in figure 14.25. The disorder arises as a result of a single nucleotide change in the gene encoding b-hemoglobin, one of the key proteins used by red blood cells to transport oxygen. The sickle-cell mutation changes the sixth amino acid in the b-hemoglobin chain (position B6) from glutamic acid (very polar) to valine (nonpolar). The unhappy result of this change is that the nonpolar valine at position B6, protruding from a corner of the hemoglobin molecule, fits nicely into a nonpolar pocket on the opposite side of another hemoglobin molecule the nonpolar regions associate with each other. As the two-molecule unit that forms still has both a B6 valine and an opposite nonpolar pocket, other hemoglobins clump on, and long chains form as in figure 14.26a. The result is the deformed “sickle-shaped” red blood cell you see in figure 14.26b. In normal everyday hemoglobin, by contrast, the polar amino acid glutamic acid occurs at position B6. This polar amino acid is not attracted to the nonpolar pocket, so no hemoglobin clumping occurs, and cells are normal shaped as in figure 14.26c.

Figure 14.25. The first known sickle-cell disease patient.

Dr. Ernest Irons's blood examination report on his patient Walter Clement Noel, December 31, 1904, described his oddly shaped red blood cells.

Figure 14.26. Why the sickle-cell mutation causes hemoglobin to clump.

Persons homozygous for the sickle-cell genetic mutation in the b-hemoglobin gene frequently have a reduced life span. This is because the sickled form of hemoglobin does not carry oxygen atoms well, and red blood cells that are sickled do not flow smoothly through the tiny capillaries but instead jam up and block blood flow. Heterozygous individuals, who have both a defective and a normal form of the gene, make enough functional hemoglobin to keep their red blood cells healthy.

The disorder is now known to have originated in Central Africa, where the frequency of the sickle-cell allele is about 0.12. One in 100 people is homozygous for the defective allele and develops the fatal disorder. Sickle-cell disease affects roughly two African Americans out of every thousand but is almost unknown among other racial groups.

If Darwin is right, and natural selection drives evolution, then why has natural selection not acted against the defective allele in Africa and eliminated it from the human population there? Why is this potentially fatal allele instead very common there?

The Answer: Stabilizing Selection

The defective allele has not been eliminated from Central Africa because people who are heterozygous for the sickle-cell allele are much less susceptible to malaria, one of the leading causes of death in Central Africa. Examine the maps in figure 14.27, and you will see the relationship between sickle-cell disease and malaria clearly. The map on the left shows the frequency of the sickle-cell allele, the darker green areas indicating a 10% to 20% frequency of the allele. The map on the right indicates the distribution of malaria in dark orange. Clearly, the areas that are colored in darker green on the left map overlap many of the dark orange areas in the map on the right. Even though the population pays a high price—the many individuals in each generation who are homozygous for the sickle-cell allele die—the deaths are far fewer than would occur due to malaria if the heterozygous individuals were not malaria resistant. One in 5 individuals (20%) are heterozygous and survive malaria, while only 1 in 100 (1%) are homozygous and die of sickle-cell disease. Similar inheritance patterns of the sickle-cell allele are found in other countries frequently exposed to malaria, such as areas around the Mediterranean, India, and Indonesia. Natural selection has favored the sickle-cell allele in Central Africa and other areas hit by malaria because the payoff in survival of heterozygotes more than makes up for the price in death of homozygotes. This phenomenon is an example of heterozygote advantage.

Figure 14.27. How stabilizing selection maintains sickle-cell disease.

The diagrams show the frequency of the sickle-cell allele (left) and the distribution of falciparum malaria (right). Falciparum malaria is one of the most devastating forms of the often fatal disease. As you can see, its distribution in Africa is closely correlated with that of the allele of the sickle-cell characteristic.

Stabilizing selection (also called balancing selection) is thus acting on the sickle-cell allele: (1) Selection tends to eliminate the sickle-cell allele because of its lethal effects on homozygous individuals, and (2) selection tends to favor the sicklecell allele because it protects heterozygotes from malaria. Like a manager balancing a store’s inventory, natural selection increases the frequency of an allele in a species as long as there is something to be gained by it, until the cost balances the benefit.

Stabilizing selection occurs because malarial resistance counterbalances lethal sickle-cell disease. Malaria is a tropical disease that has essentially been eradicated in the United States since the early 1950s, and stabilizing selection has not favored the sickle-cell allele here. Africans brought to America several centuries ago have not gained any evolutionary advantage in all that time from being heterozygous for the sickle-cell allele. There is no benefit to being resistant to malaria if there is no danger of getting malaria anyway. As a result, the selection against the sickle-cell allele in America is not counterbalanced by any advantage, and the allele has become far less common among African Americans than among native Africans in Central Africa.

Stabilizing selection is thought to have influenced many other human genes in a similar fashion. The recessive cf allele causing cystic fibrosis is unusually common in northwestern Europeans. People that are heterozygous for the cf allele are protected from the dehydration caused by cholera, and the cf allele may provide protection against typhoid fever too. Apparently, the bacterium causing typhoid fever uses the healthy version of the CFTR protein (see page 80) to enter the cells it infects, but it cannot use the cystic fibrosis version of the protein. As with sickle-cell disease, heterozygotes are protected.

Key Learning Outcome 14.10. The prevalence of sickle-cell disease in African populations is thought to reflect the action of natural selection. Natural selection favors individuals carrying one copy of the sickle-cell allele, because they are resistant to malaria, common in Africa.