Important words and concepts from Chapter 23, Campbell & Reece, 2002 (3/25/2005):
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(1) Chapter title: The Evolution of Populations
(a) "An organism exposes its phenotype--its physical traits, metabolism, physiology, and behavior--not its genotype, to the environment. Acting on phenotypes, selection indirectly adapts a population to its environment by increasing or maintaining favorable genotypes in the gene pool." (p. 430)
(b) "One obstacle to understanding evolution is the common misconception that individual organisms evolve, in the Darwinian sense, during their lifetimes. In fact, natural selection does act on individuals; their characteristics affect their chances of survival and reproductive success. But the evolutionary impact of this natural selection is only apparent in tracking how a population of organisms changes over time... Thus, it is the population, not its individuals, that evolves, as some heritable variation becomes more common at the expense of others." (p. 416)
(c) ["To the people gathered there, most of whom had no more than a first- or second-grade education, some genetic principles seemed to make intuitive sense, whereas others did not. No one had trouble, for instance, understanding that traits can be inherited. But the fact that the probability of inheriting a trait is unrelated to the previous births was more difficult to grasp. If one parent has the Alzheimer's mutation, there is a 50 percent risk that each child will have it too. But, just as parents who have had three girls in a row may expect their chance of having a boy to increase, the villagers endorsed a logical fallacy. One man announced to the assembled group: 'We the families in which there are only a few affecteds must be grateful to those families with many affecteds.' Local ideas of guilt and collective burden were deeply ingrained, and clashed with the principles of population genetics." p. 15 of Kenneth S. Kosik, 1999, The fortune teller, The Sciences 39:13-17]
MICROEVOLUTION TOOLS AND OVERVIEW
(2) Population genetics (see also population genetics)
(3) Modern Synthesis (see also Modern Synthesis)
(b) That is, evolution is a genetic phenomenon so cannot be fully (or even well) understood without an understanding of Mendelian genetics
(c) This synthesis between Darwinism and Mendelian genetics did not occur until the 1930s (recall that Darwinism and Mendelian genetics both came into being during the mid to late 1800s)
(e) "The modern synthesis emphasizes the importance of populations as the units of evolution, the central role of natural selection as the most important mechanism of evolution, and the idea of gradualism to explain how large changes can evolve as an accumulation of small changes occurring over long periods of time."
(f) ["...the Modern Synthesis is a theory about how evolution works at the level of genes, phenotypes, and populations whereas Darwinism was concerned mainly with organisms, speciation and individuals. This is a major paradigm shift and those who fail to appreciate it find themselves out of step with the thinking of evolutionary biologists. Many instances of such confusion can be seen here in the newsgroups, in the popular press, and in the writings of anti-evolutionists." (Talk.Origins)]
(4) Population (see also population)
(a) The term population is more complex than you may realize
(b) However we will delay our discussion of the complexity inherent in the term population until our considerations of speciation
(c) For now, consider a population to be a localized group of interbreeding individuals (with lots of emphasis on interbreeding)
(5) Species (see also species)
(b) For now, consider a species to be a group of populations whose members are capable of interbreeding
(6) Gene pool (see also gene pool)
(c) Recall that diploid individuals possess two alleles at each locus
(b) We would describe the frequency of a fixed allele within a gene pool as 1.0
(c) We would describe the frequency of all other alleles as 0.0 (i.e., they are not present)
(d) An allele with a frequency of 0.0 is said to be extinct
(b) We describe this frequency as allele frequency or, less correctly but more commonly, as gene frequency
(c) Remember that gene (or allele) frequency refers to the frequency of alleles in an entire gene pool, not in single individuals
(9) Genotype frequency (see also genotype frequency)
(b) Thus, three alleles (or many more) can exist in a population (with associated allele frequencies) but only up to two alleles at a time can exist within a given individual
(c) The frequency of genotypes within a population is dependent on the frequency of alleles (and vice versa, actually)
(d) It is only within genotypes that evolution acts on alleles
(f) That is, make sure the following makes sense to you:
(ii) genotypes underlie phenotypes
(iii) alleles underlie genotypes
(10) Genetic structure (supplemental concept) (see also genetic structure)
(b) Evolution may be defined as change over time of a population's genetic structure
(c) "Evolution is a generation-to-generation change in a population's frequencies of alleles and genotypes--a change in a population's genetic structure."
(b) The frequency of an allele within a population is equal to the number of alleles of a given type within the population divided by the total number of alleles found at a given locus
(c) Thus, if 200 A alleles and 400 a alleles are found within a given population, then the frequency of A alleles is 200 / (200 + 400) = 1/3 = 0.33.
(d) If this is a diploid population, how many individuals are in this population? (answer: 300... make sure that these ideas and calculations make sense to you)
(a) Note that very often one knows (or can infer) genotype frequency
(b) If so, then genotype frequency information can be used to calculate allele frequency. How?
(c) If a population has 100 Aa individuals, 200 aa individuals, and 300 AA individuals then the number of A alleles is 100*1 + 300*2 = 700; the number of a alleles is 100*1 + 200*2 = 500; the frequency of A therefore is 700 / (500 + 700) = 7/12 = 0.58
CALCULATING GENOTYPE FREQUENCIES FROM ALLELE FREQUENCIES
(a) Calculating genotype frequencies from allele frequencies is also possible, but requires quite a bit of fudging
(b) In fact, much of this chapter deals with this fudging
(d) Assume that the frequency of allele A is 0.4 and that the frequency of allele a is 0.6; What is the frequency of genotypes AA, Aa, and aa?
(i) Frequency AA = 0.4 * 0.4 = 0.16
(ii) Frequency aa = 0.6 * 0.6 = 0.36
(iii) Frequency Aa = 0.4 * 0.6 + 0.6 * 0.4 = 0.48
(e) Remember that there are two paths by which the heterozygote may be constructed, A from mom and a from dad, or a from mom and A from dad (make sure that this idea makes sense to you)
(f) Now, substitute the letter p for the frequency of A (i.e., in this example p = 0.4) and the letter q for the frequency of a (i.e., in this example q = 0.6); what is the frequency of the genotypes AA, Aa, and aa?
(i) Frequency AA = p * p = p2
(ii) Frequency aa = q * q = q2
(iii) Frequency Aa = p * q + q * p = 2pq
(i) p2 + 2pq + q2 = 1 = (p + q)2
(h) In addition, of course, keep in mind that
(i) p = 1 -- q
(ii) q = 1 -- p
(iii) 1 = p + q
(i) Again, make sure that these ideas and generalizations make sense to you, particularly to the point where you are able to apply these ideas
(a) Genotype frequencies do not necessarily coincide with phenotype frequencies (e.g., as a consequence of complete dominance) so calculating genotype frequencies from phenotype frequencies is not necessarily straightforward
(b) However, if the frequency of the recessive allele is q then
(i) the frequency of the recessive homozygote is q2
(ii) the frequency of the dominant homozygote is (1 - q)2
(iii) the frequency of the heterozygote is 2 * q * (1 - q)
(iv) (these ideas and concepts should eventually make intuitive sense to you and you should be working towards that point, so make sure that these ideas makes sense to you to this point, before you move on, such that you are at least able to recapitulate and then utilize the underlying logic, e.g., why is the frequency of the dominant homozygote equal to (1 - q)2?)
(c) Thus, if the recessive allele, a, has a frequency of 0.01, then
(i) Frequency AA = 0.99 * 0.99 = 0.98
(ii) Frequency Aa = 2 * 0.99 * 0.01 = 0.02
(iii) Frequency aa = 0.01 * 0.01 = 0.0001
(d) (do you know where the above numbers come from? if you don't, then you don't understand the concept so go back and try again)
(e) In other words, in this example there are 200 times more heterozygotes carrying the recessive allele than there are recessive homozygotes carrying the recessive allele--rare recessive alleles are hidden in populations within heterozygotes (where does "200 times" come from? you should be able to understand this... if you don't then go back and try again)
(f) "The rarer the recessive allele, the greater the degree of protection afforded by heterozygosity."
(g) That is, as recessive alleles become more and more rare, many, many more carriers of this allele will be heterozygotes (who are asymptomatic in the case of complete dominance, i.e., are hidden recessives) rather than homozygotes
(15) The Hardy-Weinberg theorem (see also Hardy-Weinberg theorem)
(a) The above calculations are stated more formally as the Hardy-Weinberg theorem
(b) "The theorem states that the frequencies of alleles and genotypes in a population's gene pool remain constant over the generations unless acted upon by agents other than Mendelian segregation and recombination of alleles." (p. 447, Campbell & Reece, 2002)
(c) "The system operates somewhat like shuffling a deck of cards: No matter how many times the deck is reshuffled to deal out new hands, the deck itself remains the same. Aces do not grow more numerous than jacks. And the repeated shuffling of a population's gene pool over the generations cannot, in itself, increase the frequency of one allele relative to another." (p. 448, Campbell & Reece, 2002)
(d) In the Hardy-Weinberg theorem it is assumed that matings between individuals within a population occur randomly and that no evolution is occurring within the population
(e) Under such conditions genotype frequency may be calculated from allele frequency information as described above (i.e., p2 + 2pq + q2)
(f) The existence of this calculation given these assumptions is termed the Hardy-Weinberg theorem
(g) See Figure, The Hardy-Weinberg theorem
(i) "The Hardy-Weinberg theorem is important conceptually and historically because it shows how Mendel's theory of inheritance plugs a hole in Darwin's theory of natural selection... The Hardy-Weinberg theorem explains how Mendelian inheritance preserves genetic variation from one generation to the next." (p. 449, Campbell & Reece, 2002)
(16) Hardy-Weinberg equilibrium (see also Hardy-Weinberg equilibrium)
(c) Furthermore, so long as these conditions stay the same, then genotype frequency will remain the same, as calculated above (this is true because genotype frequencies under these conditions are not a function of genotype frequencies so much as allele frequencies, and allele frequencies we are assuming are not changing)
(d) The constant genotype frequencies in the absence of evolution and given Hardy-Weinberg conditions is called Hardy-Weinberg equilibrium
(e) That this is an equilibrium is implied by the absence of change over time (particularly change in genotype frequency since a lack of change in allele frequencies is, in fact, one of our assumptions)
(f) Remember that, given the appropriate conditions (above), it takes only a single generation to generate a Hardy-Weinberg equilibrium
(g) ["The discrete genes Mendel discovered would exist at some frequency in natural populations. Biologists wondered how and if these frequencies would change. Many thought that the more common versions of genes would increase in frequency simply because they were already at high frequency. Hardy and Weinberg independently showed that the frequency of an allele would not change over time simply due to its being rare or common." (Talk.Origins)]
(b) "If the frequencies of alleles or genotypes deviate from values expected from Hardy-Weinberg equilibrium, then the population is evolving... If we track allele and genotype frequencies in a population over a succession of generations, some loci may be at equilibrium, while frequencies of alleles at other loci may be changing."
(c) More specifically, Hardy-Weinberg conditions assume an absence of microevolutionary forces
(d) To accomplish this, Hardy-Weinberg conditions include
(i) Very large (infinite) population sizes
(ii) Isolation from other populations
(iii) No net mutations
(iv) Random mating
(v) No natural selection
(e) These conditions correspond to the five mechanisms of microevolution
(i) Genetic drift
(iv) Nonrandom mating
(f) "...we do not really expect a natural population to be in Hardy-Weinberg equilibrium. And a deviation from the stability of a gene pool--and from Hardy-Weinberg equilibrium--usually results in evolution." (p. 449, Campbell & Reece, 2002)
(a) "Of all the causes of microevolution, only natural selection generally adapts a population to its environment. The other agents of microevolution are sometimes called non-Darwinian because of their usually non-adaptive nature."
(c) That is, only natural selection is always an agent of positive change (at least over the short term and in the sense of adapting a population to its local environment); all other mechanisms can be agents of positive change, but are not necessarily so
(d) Only natural selection represents Darwinian evolution, all other mechanism of microevolution may be termed non-Darwinian evolution
(19) Genetic Drift (see also genetic drift)
(a) Genetic drift is sampling error
(c) This problem increases in magnitude as population sizes become smaller
(d) Sampling error affects the transfer of alleles from one generation to the next, resulting in a random increase or decrease in the frequency of a given allele
(e) This latter effect is known as genetic drift
(g) Again, this problem only increases with smaller population sizes
(h) See Figure, Genetic drift
(i) Two situations in which the effects of genetic drift are particularly dramatic include
(ii) Founder effect
(j) ["Sharp drops in population size can change allele frequencies substantially. When a population crashes, the alleles in the surviving sample may not be representative of the precrash gene pool. This change in the gene pool is called the founder effect, because small populations of organisms that invade a new territory (founders) are subject to this. Many biologists feel the genetic changes brought about by founder effects may contribute to isolated populations developing reproductive isolation from their parent populations. In sufficiently small populations, genetic drift can counteract selection. [genetic drift: a random change in allele frequencies] Mildly deleterious alleles may drift to fixation." (Talk.Origins)]
(20) Bottleneck effect (genetic bottleneck) (see also bottleneck, genetic)
(a) When a population is reduced in size by some non-microevolutionary means (e.g., via a natural disaster), sampling error results in the allele frequencies of the new population not likely matching what were the allele frequencies in the old population
(b) See Figure, The bottleneck effect: an analogy
(d) Furthermore, the longer a population remains at a reduced size, the greater the effect of genetic drift on allele frequency
(f) Genetic bottlenecks can lead to the fixing of maladaptive alleles (i.e., genetic defects)
(21) Founder effect (see also founder effect)
(b) An alternative means by which population size may be decreased is via the transplanting of part of a population to a new locale
(c) This new population is smaller than its parent population and therefore is subject to the effects of sampling error
(d) (Consequently, new populations tend to possess a different genetic structure than their parent populations)
(e) Consequently, new populations tend to possess different allele frequencies than their parent populations
(f) This effect is enhanced with smaller founder populations
(g) This effect is also enhanced by (but are not identical to) bottleneck effects that result from the new population remaining small over many generations
(h) The net effect is for new populations to not resemble parent populations in terms of allele frequencies (and genetic structure)
(i) Founder effects probably play relevant roles in speciation since they set it up so that two populations are genetically dissimilar essentially from the start
(a) The degree to which two populations resemble each other depends on the degree of gene flow between those two populations
(b) Gene flow is essentially the movement of alleles into and out of populations
(c) Of course, these alleles are carried within individuals who are doing the actual moving (migration) between populations
(d) Depending on the degree of gene flow between populations, allele frequencies of populations will be dissimilar to different degrees: the more gene flow, the more similar, the less gene flow, the less similar
(e) Note that migration is a microevolutionary event since the movement of an allele into or out of a population automatically changes allele frequency (either increasing or decreasing allele frequency)
(23) Mutation (see also mutation)
(b) For example, a mutation involves the conversion of one allele into another allele
(c) Typically mutation does not play a big, direct role in changing allele frequency because mutation rates per loc tend to be low
(d) However, indirectly mutation is absolutely essential to microevolutionary processes because all allelic variation ultimately has a mutational origin
(e) That is, mutations make the new alleles that then either increase or decrease in frequency via the other microevolutionary forces
(f) However, keep in mind that mutations are not only rare but also often represent random changes in highly evolved (i.e., information laden) nucleotide sequences
(g) As a consequence, mutation typically results in a loss in gene (product) function--that is, adaptations are lost (though this loss is limited to those organisms carrying the mutation)
(h) "Organisms are the refined products of thousands of generations of past selection, and a random change is not likely to improve the genome any more than firing a gunshot blindly through the hood of a car is likely to improve engine performance."
(i) Consequently, most mutations are recessive
(k) "On rare occasions, however, a mutant allele may actually fit its bearer to the better and enhance the reproductive success of the individual. This is not especially likely in a stable environment, but becomes more probable when the environment is changing and mutations that were once selected against are now favorable under the new conditions."
(a) "An organisms exposes its phenotype--its physical traits, metabolism, physiology, and behavior--not its genotype, to the environment. Acting on phenotypes, selection indirectly adapts a population to its environment by increasing or maintaining favorable genotypes in the gene pool." (p. 458, Campbell & Reece, 2002)
(d) That is, natural selection serves to reduce certain genotypes relative to others in terms of their contribution of alleles to the gene pool
(e) Natural selection acting at the haploid stage serves to reduce allelic frequency directly
(f) Note that in either case the effect of natural selection is to reduce (not to increase) the absolute number of genotypes or alleles
(g) That is, mutation places alleles into a gene pool, other microevolutionary forces can serve to increase the frequency of the allele, but selection acts to selectively remove maladaptive alleles (mutation in, selection out)
(h) Natural selection is differential reproductive success: in the absence of natural selection an organism contributes x to the next generation; in the presence of natural selection an organism contributes <x gametes to the next generation
(i) "Of all agents of microevolution that change a gene pool, only selection is likely to be adaptive. Natural selection accumulates and maintains favorable genotypes in a population. If the should change, selection responds by favoring genotypes adapted to the new conditions. But the degree of adaptation can be extended only within the realm of the genetic variability present in the population."
(j) Natural selection serves to increase the information content contained within the genomes of the organisms of a population; more specifically, it increases the prevalence of information which has been time-tested to allow the increased survival and reproduction of genotypes within the environment in which a population resides
(25) Darwinian Fitness (see also Darwinian fitness)
(a) "Darwinian fitness is the contribution an individual makes to the gene pool of the next generation relative to the contributions of other individuals." (p. 457, Campbell & Reece, 2002)
(b) Darwinian fitness is the allelic contribution an individual makes to the next generation
(c) Thus, the more likely an individual is to survive and reproduce (i.e., to contributes its alleles to the next generation), the higher that individual's Darwinian fitness
(d) Note that the Darwinian fitness is a quantity equal to the average reproductive output associated with a given genotype
(e) Thus, Darwinian fitness is an environment-specific quantity (i.e., it may change depending on environment)
(f) Darwinian fitness is often simply called fitness
(26) Relative fitness (see also relative fitness)
(a) "In a more quantitative approach to natural selection, population geneticists define relative fitness as the contribution of a genotype to the next generation compared to the contributions of alternative genotypes for the same locus... The relative fitness of the most reproductively successful variants is set at 1 as a basis for comparison." (pp. 458-459, Campbell & Reece, 2002)
(c) Typically these fitnesses are presented as relative quantities rather than as absolutes
(d) Typically the genotype with the highest Darwinian fitness is given a relative fitness value of 1.0
(e) All other genotypes, i.e., those with lower than the highest Darwinian fitness, then have relative fitness values of less than 1.0
(f) If one genotype produces on average 4 progeny per generation and another produces on average 1 progeny per generation, then what is the relative fitness of the latter genotype? The former? (answer: 0.25 and 1.0, respectively)
(g) Relative fitness and the "selection coefficients" employed when mathematically following the impact of selection on a population are essentially identical concepts
(i) "Survival alone does not guarantee reproductive success. Relative fitness is zero for a sterile plant or animal, even if it is robust and outlives other members of the population. But, of course, survival is a prerequisite for reproducing, and longevity increases fitness if it results in certain individuals leaving more descendants than other individuals leave." (p. 458, Campbell & Reece, 2002)
(a) "Survival alone does not guarantee reproductive success. Relative fitness is zero for a sterile plant or animal even if it is robust and outlives other members of the population. But, of course, survival is a prerequisite for reproducing, and longevity increases fitness if it results in certain individuals leaving disproportionately high numbers of descendants. Then again, an individual that matures quickly and becomes fertile at an early age may have a greater reproductive potential than individuals that live longer but mature late. Thus, the components of selection are the many factors that affect both survival and fertility."
(b) In following a population through generations, one that is undergoing natural selection but is otherwise adhering to Hardy-Weinberg conditions, A population will go through the following contortions (note typical animal sexual cycle):
(ii) Natural selection can reduce the frequency of certain genotypes relative to others; note that this happens formally by multiplying genotype frequency by relative fitness and then recalculating genotype frequencies (do you know how to do this/understand what I mean?)
(iii) Natural selection can also act at the level of generation; obviously an individual who can't make gametes has a Darwinian fitness (and relative fitness) of zero
(iv) An individual fails to fertilize if an individual fails to mate (or if an individual dies before reaching sexual maturity...)
(c) "A genotype at a particular locus may have multiple effects, especially if it influences the development or growth of the organism. This ability of genes to influence many phenotypic characters is called pleiotropy. The overall fitness of a genotype depends on whether its positive effects outweigh any harmful effects it may have on the survival and reproductive success of the organism... The finished organism subjected to natural selection is an integrated composite of its many phenotypic features, not a collage of individual parts. The relative fitness of a genotype at any one locus depends on the entire genetic context in which it works." --in other words, things get very complicate, very fast, and organisms are always at best compromises between competing selective forces
MANY MODES/TYPES OF NATURAL SELECTION
(b) However, natural selection is considered to display different modes depending on what is being edited out
(c) Consider a character that is controlled by many loci and whose associated traits span a spectrum such as from short to tall (for the character height) or light to dark (for the character hair color), etc.
(d) In such a case, depending on where on a given spectrum natural selection acts most strongly, selection may be classified as
(iii) Diversifying selection
(e) See Figure, Modes of selection
(29) Stabilizing selection (see also stabilizing selection)
(b) Thus, stabilized populations tend to be reasonably well adapted to their environments
(c) (what does that statement mean? It means that we can infer, minimally, that the extreme phenotypes are less well adapted to the environment than the intermediate phenotypes. Why? Because natural selection is selectively removing the extreme phenotypes rather than the now by-definition better-adapted intermediate phenotypes. If those intermediate phenotypes were not reasonably well adapted to their environment, then the population would be in fairly rapid decline and therefore, in all likelihood, either not be observed or be only briefly observed)
(30) Directional selection (see also directional selection)
Directional Selection (in Macroevolution)
The fossil lineage of the horse provides a remarkable demonstration of directional succession. The full lineage is quite complicated and is not just a simple line from the tiny dawn horse Hyracotherium of the early Eocene, to today's familiar Equus. Overall, though, the horse has evolved from a small-bodied ancestor built for moving through woodlands and thickets to its long- legged descendent built for speed on the open grassland. This evolution has involved well- documented changes in teeth, leg length, and toe structure.
(b) The net effect of directional selection is to increase or decrease the character along the spectrum of its possible expression (i.e., taller, shorter, etc.)
(a) In diversifying selection it is the intermediate form that is selected against
(b) Diversifying selection can result in balanced polymorphisms
(32) Sexual selection (sexual dimorphism, secondary sexual characteristics) (see also sexual selection)
(a) Males and females often differ phenotypically other than in their possessing different sexual organs
(b) Such differences are referred to as sexual dimorphisms or secondary sexual characteristics
(c) For example, human males generally are taller, heavier, and hairier than human females
(d) Sexual dimorphisms often are involved in mate procurement
(e) We can distinguish sexual selection into an intrasexual and intersexual selection
(a) "Intrasexual selection is a direct competition among individuals of one sex (usually the males in vertebrates) for mates of the opposite sex. Males may use secondary sexual equipment such as antlers to battle competitors. This is especially common in species where a single male garners a harem of females. These males may gain their status by defeating smaller, weaker, or less fierce males in combat; more often, they are the victors in ritualized displays that discourage would-be competitors." (p. 460, Campbell & Reece, 2002)
(b) The better fighter typically is the fighter that gains preferred access to the female and, of course, genes can underlie fighting ability
(a) Any trait that increases the attractiveness of an individual to sexually mature members of the opposite gender will confer a selective advantage to the bearer because this attractiveness will increase the bearer's likelihood of either
(i) depositing its gametes in the gene pool or
(ii) having its gametes fertilize the gametes of an individual possessing a preferred genotype
(b) This can all get very complicated since just what a preferred genotype is can depend on just what a preferred genotype is (i.e., positive feedback)
(c) Regardless, the alleles that lead to an increase an individual's ability to either secure a mate or to secure the mate of one's choice are selected, at least in part, by a form of natural selection known as sexual selection
(d) "In intersexual selection, also called mate choice, individuals of one sex (usually females) are choosy in selecting their mates from individuals of the other sex. Apparently, males with the most impressive masculine features are the most attractive to females. A peacock strutting in front of hens with his tail feathers spread into a showy fan is an example of this 'choose me' statement. What intrigued Darwin about such behavior is that some of the features that appear to help attract mates do not seem to be adaptive in any other way and may in fact pose some risk in natural environments [i.e., negatively impact on survival]. For example, showy plumage may make male birds more visible to predators. But if such secondary sexual characteristics help a male gain a mate, then they will be reinforced over the generations for the most Darwinian of reasons--because they enhance reproductive success. Every time a female chooses a mate based on a certain appearance or behavior, she perpetuates the alleles that caused her to make that choice and allows a male with a particular phenotype to perpetuate his alleles." (p. 461, Campbell & Reece, 2002)
NATURAL SELECTION'S RAW MATERIAL
(a) "Heritable variation is at the heart of Darwin's theory of evolution, for variation provides the raw material--the substrate--on which natural selection works."
(c) Note that in practice polymorphism tends to mean that one allele does not overwhelmingly dominates a given locus (such that all other alleles are very rare)
(d) Finally, the term polymorphism is derived from the idea that a population consists of individuals having two or more distinct morphologies; this concept has since been extended to the broader idea of more than one phenotype (or even more than one genotype); at the level of molecules, phenotypes vary dependent on variations in alleles; consequently, a locus that possesses more than a single allele across a single gene pool is said to be polymorphic, regardless of the effects of the individual alleles on morphology
(e) In general, there is a lot more polymorphism in wild populations than one might otherwise expect
(f) Heritable variation within a population is synonymous with polymorphism (if only a single allele exists at a given locus, then by definition there is no heritable variation at that locus)
(i) Therefore, the raw material of natural selection are polymorphisms
(ii) Therefore, the fewer polymorphisms, the less ably a population can respond to environmental change (i.e., the population is less able to adapt)
(iii) Therefore, the less polymorphism, the more likely a population will go extinct given environmental change
(v) Lack of adaptation to environmental change further reduces population size which further reduces polymorphism
(vi) The effect of man on the environment generally is to reduce population sizes while simultaneously effecting environmental change (guess what comes next)
(g) Note that "Polymorphism applies only to discrete characters, not to characters such as human height, which varies among people in a continuum." (p. 453, Campbell & Reece, 2003)
(36) Hiding deleterious recessives
(a) "The diploid nature of most eukaryotes hides a considerable amount of genetic variation from selection in the form of recessive alleles in heterozygotes. Recessive alleles that are less favorable than their dominant counterparts, or even harmful in the present environment, can persist in a population through their propagation by heterozygous individuals. This latent variation is exposed to selection only when both parents carry the same recessive allele and combine two copies in one zygote. This happens only rarely if the frequency of the recessive allele is very low. The rarer the recessive allele, the greater the degree of protection from natural selection [using the Hardy-Weinberg theorem concepts, do you understand why?]. Heterozygote protection maintains a huge pool of alleles that may not be suitable for present conditions but that could bring new benefits when the environment changes." (p. 456, Campbell & Reece, 2002)
(b) Note that this hiding of alleles from natural selection is not the same as a balanced polymorphism; based on your understanding of balanced polymorphism (defined below) do you understand why?
(b) Recessive alleles are more difficult to eliminate than are dominant alleles because the former tend to be tied up in phenotypically dominant
(c) A number of additional mechanisms tend to preserve polymorphisms
(ii) Hybrid vigor
(iv) Neutral variation
(d) A stably persisting polymorphism is known as a balanced polymorphism
(e) The existence of a balanced polymorphism implies a lack of allele fixation and, furthermore, the existence of a mechanism or mechanisms that inhibits the fixation of a given allele
MECHANISMS FOR MAINTAINING POLYMORPHISMS
(a) In certain circumstances the is better adapted than either
(b) In such circumstances, the greater adaptedness of the heterozygote prevents the extinction of one or the other allele
(c) An example is sickle-cell disease where the heterozygote is more resistant to malaria than either homozygote while the affected homozygote dies young from sickle-cell disease, but the allele is nevertheless maintained in areas experiencing high incidences of malaria
(d) ["Balancing selection is rare in natural populations. [balancing selection: selection favoring heterozygotes] Only a handful of other cases beside the sickle-cell example have been found. At one time population geneticists thought balancing selection could be a general explanation for the levels of genetic variation found in natural populations. That is no longer the case. Balancing selection is only rarely found in natural populations. And, there are theoretical reasons why natural selection cannot maintain polymorphisms at several loci via balancing selection." (Talk.Origins)]
(a) Hybrid vigor is related to heterozygous advantage
(c) This occurs in part due to heterozygous advantage and also due to a simple masking of deleterious recessives (do you understand the difference? Essentially heterozygous advantage is a product of a codominant relationship between alleles while the masking of deleterious recessives is a product instead of a dominant-recessive relationship)
(d) Hybrid vigor is best exemplified in the production of hybrid horticultural varieties, e.g., hybrid corn
(e) Note that the concept of hybrid vigor makes the most sense particularly when considering the formation of a heterozygote across more than one locus
(a) Frequency-dependent selection occurs in situations where the advantage of possessing an allele increases with a decreasing frequency of that allele (i.e., increasing rarity); that is, there is more survival and increases in reproductive success as a genotype gets rarer, thereby interfering with the elimination of the underlying alleles from the population
(b) Rarity tends to be a factor when an allele is involved in combating an enemy
(c) For example, frequency-dependent selection is found among butterflies who mimic other, foul-tasting butterflies--the more prevalent the mimic, the less likely the predator (a bird) will worry about accidentally consuming a foul-tasting species; this places a natural cap on the mimic's population size, thus resulting in an advantage associated with mimicking a different-looking foul-tasting species (i.e., employing a different, rarer morphology)
(d) Major histocompatibility proteins (the killer T-cell, etc., receptors found on normal body cells) also are the product of frequency-dependent selection; different alleles result in different abilities to recognize different pathogens (particularly viruses); individuals with common alleles are susceptible to viruses which have evolved to evade alleles common to the rest of the population
(e) Parasites, similarly, may be subject to frequency dependent selection as hosts develop resistance to more common parasite phenotypes
(f) See Figure, Frequency-dependent selection in a host-parasite relationship
(b) Such neutral mutations tend, by definition, not to be eliminated from populations by natural selection
(c) Thus, in populations that are large enough to display minimal genetic drift, neutral variation can be very abundant
(d) Note that neutral variation by definition need be neutral only within the context of the environment in which an organism resides
(e) Transfer to a new environment may increase or decrease the selective advantage associated with an allele; thus, neutral alleles serve as a reservoir of allelic variation
(f) "There is no consensus among evolutionary biologists on how much genetic variation is neutral or even if any variation can be considered truly neutral. Variations that appear to be neutral may in fact influence survival and reproductive success in ways that are difficult to measure. It is possible to show that a particular allele is detrimental, but it is impossible to demonstrate that an allele brings no benefits at all to an organism. Furthermore, a variation may be neutral in one environment but not in another. We can never know the degree that even if only a fraction of the extensive variation in a gene pool significantly affects the organisms, that is still an enormous reservoir of raw material for natural selection and the adaptive evolution it causes." (p. 457, Campbell & Reece, 2002)
NATURAL SELECTION'S LIMITATIONS
(a) No! Why not?
(b) "An organism's phenotype is constrained by its evolutionary history"
(i) Some snakes may be able to glide, but it's unlikely one will ever flap a wing
(c) "Adaptations are often compromises"
(i) Any engineer knows the truth that optimizing one aspect of a design inevitably compromises another
(ii) That is why you might be able to take out all of your friends in your mom's minivan, but you'll never beat a motorcycle in a drag race with it
(d) "Not all evolution is adaptive"
(ii) If it ain't broke, don't fix it
(e) "Selection can only edit variations that exist"
(i) In part this is continuation of the first point
(ii) Also, it is an indication that it is tough to get all of the right components of an adaptation into a single individual, then keep them there in descendants
(f) Environments change
(i) Even if a perfect organism existed, it would only remain perfect so long as its environment remained unchanged (i.e., the one to which it is perfectly adapted)
(ii) Environments change all the time, not necessarily catastrophically, but change nonetheless
(g) Environments vary over even individual life spans
(i) To make matters worse, environments even change over single individual's life spans
(ii) Thus, the environment to which the hypothetical perfectly adapted organism is adapted tends to always be a moving target
(a) "Natural selection is usually thought of as an agent of change, but it can also act to maintain the status quo. Stabilizing selection probably prevails most of the time, resisting change that may be maladaptive. Evolutionary spurts occur when a population is stressed by a change in the environment, to a new place, or a change in the genome. When challenged with a new set of problems, a population either adjusts through natural selection or becomes extinct. The fossil record indicates that extinction is the more common outcome."
NONRANDOM MATING (AND CONSEQUENCES)
(b) I typically like to think of the pool very literally as a well-mixed tub of randomly colliding sperm and eggs
(c) Anything that interferes with this nonrandom fertilization constitutes structure within the gene pool
(e) Anything that interferes with the random mating between individuals (now think of a well-mixed bowl of males and females randomly . . . oh, never mind) is nonrandom mating
(g) Two aspects of nonrandom mating are
(ii) Assortative mating
(45) Inbreeding (supplemental discussion) (see also inbreeding)
(a) Inbreeding typically results from individuals nonrandomly mating over geographical distances
(b) Basically, in a population which is not well mixed (i.e., not highly mobile) individuals more likely mate with neighbors than with non-neighbors (the guy next door versus the guy 8,000 miles down the road)
(c) This nonrandom mating and minimal movement means that, with time, individuals are more likely to mate with relatives than with non-relatives (more precisely: with closer relatives than with more distant relatives)
(d) Inbreeding requires effectively small population sizes (i.e., mating within an artificially constrained gene pools) so is a mechanism associated with genetic drift (e.g., inbreeding results from bottleneck and founder effects) though is not a mechanism of genetic drift (associated here meaning found occurring under the same circumstances)
(e) Thus, inbreeding tends to be associated with the expression of rare recessive alleles (in a homozygous state) and even a local fixing of alleles of alleles that are otherwise rare in larger populations
(46) Assortative mating (supplemental discussion) (see also assortative mating)
(a) Assortative mating is where an individual chooses a mate based on how that mate resembles the individual
(b) For example (and I'm not exactly sure how I pulled this off), I married a girl who looks like my mother
(d) That is, one major consequence of inbreeding is a decline in heterozygosity
(e) Note, however, that in an infinite population with no selection, no migration, and no mutation, assortative mating will not have an impact on allele frequency because decreasing heterozygosity only results in changes in allele frequency given the existence of natural selection
(f) Assortative mating will certainly impact on genotype frequency, however (Why? If you understand assortative mating, genotype frequency, and the impact of the various Hardy-Weinberg assumptions, then the answer should be obvious)
STRATEGIES FOR SOLVING HARDY-WEINBERG PROBLEMS
(a) General strategies to employ when attempting Hardy-Weinberg problems
(i) Think of these problems as puzzles and then keep telling yourself that it's only a puzzle or a game; that is, just go with the flow; stressing yourself out at any juncture in life is counterproductive
(ii) For introductory problems one can usually assume one locus, two allele, diploid genetics; if this is not the case, often one will be told so with the exception of questions that ask for speculation as to the number of loci, alleles, or the ploidy involved
(iii) Always assume Hardy-Weinberg equilibrium unless information contradicts that assumption; you can always reject this hypothesis down the road
(b) Work with decimals
(i) Decimals typically are easier to work with than percentages, fractions, or absolute numbers. Consequently:
· Always convert percentage information into decimal information (i.e., frequencies; 97% --> 0.97)
· Always convert fractions into decimals
· Always convert absolute information (e.g., numbers of individuals) into decimal information (e.g., frequencies of phenotypes)
(c) Convert phenotypes to genotypes
(i) Always look for how you might convert phenotype information into genotype information, and then do so; remember, solving Hardy-Weinberg problems is a game; whenever you see phenotype frequencies, you should start looking forward to deducing genotype frequencies
(ii) Remember, frequencies must add up to one
(iv) When phenotypes do not map onto genotypes one-to-one, then try to figure out the phenotype frequency of one homozygote, and then assume Hardy-Weinberg equilibrium (unless you have reason not to)
(v) Remember, again, frequencies must add up to one
(d) Convert genotypes to alleles
(i) When you have genotype frequencies, use that information to calculate allelic frequency; remember again that solving Hardy-Weinberg problems is only a game; whenever you see phenotype frequencies, you should start looking forward to deducing genotype frequencies
(ii) If you have Hardy-Weinberg equilibrium and have the frequency of one homozygote, then you can calculate at least one allele's frequency as the square root of the homozygote's frequency.
(iii) If you don't know allelic frequencies but do know genotype frequencies then you can calculate allelic frequencies by multiplying the frequency of each genotype by a coefficient equal to the number of alleles of one type in each genotype, then divide the quantity by 2 (e.g., f(A) = (f(AA)*2 + f(Aa)*1 + f(aa)*0)/2)
(iv) If you have not yet calculated genotype frequencies, but do know the absolute number of each genotype, then it is possible to skip a step and calculate allelic frequencies directly from absolute genotype numbers; just multiplying absolute numbers by the coefficient, as above, and then divide by twice the sum of the population size (i.e., the sum of the absolute numbers of genotypes)
(v) Remember, frequencies must add up to one
(e) Convert alleles to genotypes
(ii) Remember, frequencies must add up to one
(iii) Remember that you can generate genotype frequencies using the Hardy-Weinberg equation only if Hardy-Weinberg conditions apply.
(f) Incorporating selection
(i) Incorporating selection into Hardy-Weinberg problems complicates things somewhat
(ii) Selection is doable, however, so long as you keep in mind that the effect of selection is to reduce absolute genotype/phenotype/allele numbers
(iii) Operationally this may be accomplished by multiplying frequencies (typically genotype frequencies) by a selection coefficient
(iv) Remember that by following such a procedure the resulting "frequencies" will no longer add to one, but must be re-calculated such that genotype frequencies following selection are presented as decimals which do add up to one
(i) As in much of life, the key to success is practice and dedication
(ii) Anything that you can do to make a difficult task an enjoyable one will always serve to make that task (and your life) easier; so lighten up and learn to enjoy doing population genetics
(iii) Remember, it's only a game
(48) Vocabulary [index]
(b) Allele frequency
(o) Fixed allele
(p) Fixed locus
(q) Founder effect
(s) Gene frequency
(t) Gene flow
(u) Gene pool
(w) Genetic drift
(cc) Hidden recessives
(ee) Hybrid vigor
(ii) Mate choice
(ll) Modern synthesis
(oo) Natural selection
(pp) Neutral variation
(qq) No evolution
(ss) Nonrandom mating
(vv) Population genetics
(ww) Relative fitness
(yy) Sexual dimorphism
(zz) Sexual selection
(bbb) Stabilizing selection
(a) The study of allele and genotype frequencies within populations is called what?
(b) A plant population consists of two flower morphs, white and red, controlled by a single locus and two alleles. The white morph represents the recessive homozygote. The red morph consists of some combination of heterozygotes and dominant homozygotes. Assume that 50% of the population has red flowers. What are the frequencies of all three genotypes assuming Hardy-Weinberg equilibrium?
(c) A population of 40 guinea pigs undergoing natural selection is reduced to 20 individuals in only five generations. At this point genotype frequencies are 0.25, 0.5, and 0.25 for the genotypes AA, Aa, and aa, respectively. Assume that natural selection continues to act on this population. Is the population in Hardy-Weinberg equilibrium?
(d) Given a locus with three alleles and allele frequencies of 0.4, 0.4, and 0.2, what is the frequency of the least prevalent heterozygote?
(e) Given a population that up to now had been in Hardy-Weinberg equilibrium. Assume two alleles, one locus, p = 0.5, and distinctly different (and unambiguous) phenotypes associated with each genotype. Now assume internal fertilization and that all matings over one generation are 100% assortative with regard to the trait in question. What are the genotype frequencies before this round of assortative mating? What are the genotype frequencies in the generation that follows this round of assortative mating? Note: To answer this question you must know what assortative mating is and consequently understand the structural impact of assortative mating on the gene pool.
(f) What is a balanced polymorphism?
(g) Relative fitnesses that vary as a function of genotype frequency is an example of what?
(h) You have a population that, before selection, consists of 0.5 AA individuals, 0.25 Aa individuals, and 0.25 aa individuals. The relative fitnesses associated with each of these three genotypes are 0.3, 0.5, and 1.0, respectively. Define p, the frequency of A, (i) before selection and (ii) following one round of selection.
(i) Given a population with genotype frequencies of 0.6, 0.2, and 0.2 for genotypes AA, Aa, and aa, what should be the genotype frequencies be if the population were in Hardy-Weinberg equilibrium?
(j) What is assortative mating and what does it do to a population's gene pool?
(k) You have a haploid population (hey, a bunch of T4 phage!) and one locus, two allele genetics. 50% of the A individuals die per round of replication but all of the a individuals survive. Survivors reproduce at the same rate, independent of genotype. You begin with a population in which the frequency of A (i.e., p) is equal to the frequency of a (i.e., q). What is the ratio of genotypes following one round of selection?
(l) The B allele is dominant to the b allele. The phenotype associated with the former is brown eyes, while blue eyes is the phenotype associated with the latter. The brown eye allele is present in the population at a frequency of 0.2. Given Hardy-Weinberg equilibrium and no differences in allele frequencies between genders, what is the probability that a blue-eyed woman will marry a brown-eyed man?
(m) Given a one locus, two allele system in which the relative fitness of AA is 0.5, Aa is 1.0, and aa is 0.0, this is an example of what?
(n) Draw a population of 10 giraffes following strong (i.e., highly effective) diversifying selection. Try to avoid being ambiguous in your drawings.
(o) The integration of Darwinism with Mendelian genetics is called the _________.
(p) What is the maximum number of alleles that a diploid individual can have at each locus? Consider only loci found on autosomal chromosomes.
(q) A population is in Hardy-Weinberg equilibrium. Consider only a single locus and two alleles found at that locus. If the frequency of the a allele is 0.4, what is the frequency of all of the possible genotypes at this locus? Call the other allele A. Assume that these organisms are diploid.
(r) A population consists of 200 aa individuals and is in Hardy-Weinberg equilibrium. Assuming one-locus, two-allele genetics, what is the frequency of the a allele if the population consists of a total of 1,000 individuals? What if the 200 aa individual population consists of a total of 10,000 individuals?
(s) A population is in Hardy-Weinberg equilibrium. The frequency of the dominant phenotype is 0.99. What fraction of individuals that carry at least one recessive allele are homozygous at this locus? Assume one-locus, two-allele genetics.
(t) Distinguish genetic bottleneck from founder effects.
(u) Inbreeding and assortative mating are both examples of what?
(v) In a hypothetical population of 2500 people, 2275 people have brown eyes and 225 people have blue eyes (the homozygous-recessive phenotype). If there are 4000 children produced by this generation, how many (i.e., what number) of the children would be expected to be heterozygous for eye color? Assume Hardy-Weinberg equilibrium.
(w) Describe, in terms of heritable variation, a population lacking in polymorphisms.
(x) How does heterozygous advantage contribute to the maintenance of polymorphisms, i.e., balanced polymorphisms?
(y) What characteristic of the two parent populations is typically a necessary prerequisite for the occurrence of hybrid vigor?
(z) In stabilizing selection, what categories of phenotypes is selection "editing out" of the population?
(aa) In many human societies both genders are responsible for the care of offspring though with the duties typically separated such that the female is more responsible for meeting the physical needs of offspring while the male is more responsible for meeting the economic needs of offspring (obviously there exists a great deal of variation both within and between societies). As a consequence of these shared responsibilities toward raising offspring, human males, unlike those of many species, are often as picky about choosing their long-term mate as human females are about picking theirs. Perhaps consequently, both human genders, at sexual maturity, divert much time and energy away from survival and growth and instead toward self grooming, presumably to enhance their attractiveness to the other gender. Those humans most successful at such grooming display an edge in the procurement of the most desirable mates. One could even argue that such grooming represents a means of fooling prospective mates into believing that the groomer is healthier or otherwise more desirable as a mate than otherwise might be the case. In evolutionary terms, what form of natural selection is likely responsible for the evolution of such grooming behavior as exhibited by both human males and human females?
(cc) What is assortative mating?
(dd) Considering eye color, if B is the brown-eye allele and b is the blue-eye allele, given a population consisting of the following, 323 BB, 23 Bb, and 45 bb, what are the frequencies of allele B and of allele b? Is this population in Hardy-Weinberg equilibrium? Quantitatively justify your answer (i.e., calculate the expected Hardy-Weinberg genotype frequencies and absolute genotype numbers, then compare these numbers to those observed in the populations).
(ee) Paleontology, taxonomy, biogeography, and population genetics were combined during the 1940s resulting in a significant advance in our understanding of evolutionary principles, a process since dubbed the "__________".
(ff) Which manifestation (mode) of natural selection is thought to be most prevalent within wild populations of organisms, particularly well-established large populations of organisms that are already well adapted to their environments?
(i) Artificial selection
(ii) Directional selection
(iii) Disruptive selection
(iv) Diversifying selection
(v) Stabilizing selection
(gg) What must occur for increased longevity to correlate with increased Darwinian fitness?
(hh) Why do we employ the concept of relative fitness particularly when considering competition between conspecifics, i.e., organisms of the same species?
(ii) What is neutral variation?
(jj) Two individuals are from two different populations, A and B. All individuals within each population are significantly inbred because of ongoing genetic bottlenecks and thus are very similar within populations, though, in fact, genotypically dissimilar between the two populations. Romeo comes from population A and Juliet from population B. Shakespeare got it wrong and, in fact, they married and then had a number of children. Though raised in an environment that was essentially identical to that in which their parents were raised, all of Romeo and Juliet's children seemed stronger, healthier, and smarter than their parents, indeed better fit and seemingly better adapted to their environment. What is the technical term we give to this manifestation of what is, at least in part, heterozygous advantage?
(kk) What is a balanced polymorphism, i.e., define the term?
(ll) If it is natural selection that removes alleles from a gene pool, what ultimately is responsible for putting alleles into gene pools?
(mm) Which of the following does not impact on the frequency of heterozygotes within a population?
(i) Assortative mating
(ii) Heterozygote advantage
(iii) Hybrid vigor
(iv) Neutral variation
(v) All of the above impact on the frequency of heterozygotes
(vi) None of the above impact on the frequency of heterozygotes
(nn) Give one (good) reason that evolution has trouble fashioning a "perfect" organisms.
(oo) What comes between an organism's genotype and its environment thereby setting things up so that natural selection acts only indirectly on genotypes? Note: I'm looking for the general answer, not a bunch of specific examples.
(pp) What word or phrase do we use to describe (i.e., call) a localized group of interbreeding individuals? (and no, subspecies is not the answer that I am looking for)
(qq) What phrase do we use to describe a gene that consists of only a single allele within an entire population?
(rr) A population possesses 200 AA individuals, 100 AB individuals, 100 BB individuals, 100 AO individuals, 200 BO individuals, and 100 OO individuals. What are the frequencies of the three alleles?
(ss) A population possesses 200 AA individuals, 100 AB individuals, 100 BB individuals, 100 AO individuals, 200 BO individuals, and 100 OO individuals. What are the frequencies of the three alleles?
(tt) Need an "Is the pop in H-W equilibrium?" question.
(uu) Principally, the Modern Synthesis represented an integration of what with what? (i.e., what two major aspects of biology?)
(vv) What is a fixed locus?
(ww) If an individual had three alleles at each locus, then what ploidy would you expect this individual would be?
(xx) If three alleles exist at a given locus within the diploid individuals found within a population, then how many different genotypes (different combinations of these three alleles) are possible?
(yy) If, within a population, a given locus has a total of two alleles present, A and a, the number of AA individuals is 300, the number of aa individuals is also 300, and the total number of individuals is 1000 (all diploid), then what is the frequency of the A allele within the population?
(zz) Red flower color is completely dominant to white. If there are 90 red-flowered and 10 white-flowered plants, then what is the frequency of the red allele within this population if we assume random mating and no evolution?
(aaa) Given a frequency of a dominant allele of 0.09 (=9%), what is the frequency of the dominant phenotype assuming Hardy-Weinberg equilibrium and only two alleles within the population?
(bbb) Even given Hardy-Weinberg equilibrium, phenotype frequencies can vary (i.e., change) over time. Given your understanding of Hardy-Weinberg equilibrium, what does this statement say about the relationship between genotype and phenotype?
(ccc) Of all of the Hardy-Weinberg assumptions, only one can have an impact (in its violation) on genotype frequencies without impacting on allelic frequencies. Which one?
(i) Very large populations
(ii) No mutation
(iii) No selection
(iv) No migration
(v) Random mating
(ddd) Darwinian evolution is particularly associated with violation of which Hardy-Weinberg assumption?
(i) Very large populations
(ii) No mutation
(iii) No selection
(iv) No migration
(v) Random mating
(eee) If a genetic bottleneck follows a founder effect, then what does that tell you about what property of a population over time (other than simply that the population is subject to genetic drift)?
(fff) Which of the following is least associated with some aspect of local population size?
(i) Absolute mutation rate within population
(ii) Founder effect
(iii) Genetic drift
(iv) Natural selection
(v) Non-random mating
(ggg) What is assortative mating?
(hhh) What agent of microevolution is most likely to lead to adaptation to new conditions?
(iii) Need additional H-W questions.
(jjj) Which of the following tends not to contribute to the maintenance of balanced polymorphisms?
(i) Founder effect
(ii) Frequency-dependent selection
(iii) Heterozygous advantage
(iv) Hybrid vigor
(v) Neutral variation
(kkk) While heterozygous advantage may contribute to some aspects of hybrid vigor, of greater relevance is the __________ afforded by the well-outcrossed diploid condition. (this more than a single-word answer)
(lll) Frequency-dependent selection typically means that possessing such an allele is particularly advantageous when that allele is __________.
(mmm) In population genetics the quality equal to the average reproductive output associated with a given genotype is called __________.
(nnn) USE AS BONUS: A diploid population consists of 30% A and 70% a alleles. Assume Hardy-Weinberg equilibrium for this population at birth. However, later in life the population is subject to selection such that one-half of the AA individuals die before reproducing while the Aa and aa individuals are not similarly reduced in number. What is the frequency of the A allele in this population following one round of selection? What are the genotype frequencies in the generation following this one round of selection?
(ppp) Phenotypic distinctions between males and females of the same species are thought, in part, to be a consequence of _________.
(i) Artificial selection
(ii) Disruptive selection
(iii) Gender bias
(iv) Sexual selection
(v) Stabilizing selection
(qqq) True or False, Natural selection, acting upon populations of individuals well adapted to the unchanging environments tends to select for changes in common characters.
(rrr) Which of the following is most likely to result in a balanced polymorphism?
(i) Directional selection
(ii) Diversifying selection
(iii) Sexual Selection
(iv) Stabilizing selection
(v) All have a similar impact
(sss) Darwinian fitness is a measure of what?
(ttt) In the concept of "Neutral variation," variation is neutral with regards to what?
(uuu) In frequency-dependent selection, what is it that is being selected?
(i) Common alleles
(iv) Rare alleles
(vvv) Hybrid vigor refers in part to the masking of deleterious alleles that can occur when two unrelated individuals mate. In addition, hybrid vigor can result from heterozygous advantage. What is heterozygous advantage?
(www) What does the term "polymorphism" mean?
(xxx) What is "Assortative mating?"
(yyy) When populations are not well mixed there is a tendency for individuals to mate non-randomly as a function of geographic distance, i.e., matings occur between individuals that live closer rather than farther apart. Even in the absence of assortative mating, lack of mixing of populations can result in __________ and an associated expression of recessive alleles that are otherwise rare in the larger population.
(zzz) Founder Effects and Genetic Bottlenecks can give rise to __________, a violation of one of the five criteria required for the establishment of Hardy-Weinberg equilibrium.
(aaaa) Give three mechanisms of Non-Darwinian evolution (hint, these are all violations of conditions required for the establishment of Hardy-Weinberg equilibrium).
(bbbb) The Modern Synthesis represented a melding (i.e., a bring together) of two key biological concepts. What were these two concepts? A: Darwinian evolution/natural selection with Mendelian genetics
(cccc) "The __________ emphasizes the importance of populations as the units of evolution, the central role of natural selection as the most important mechanism of evolution, and the idea of gradualism to explain how large changes can evolve as an accumulation of small changes occurring over long periods of time." A: Modern synthesis
(dddd) What is the frequency of an allele that may be described as "fixed" within a population? A: 1.0
(eeee) The genetic structure of a population refers to two frequencies of entities within that population. What are those two entities? A: allele frequencies and genotype frequencies
(ffff) What are the five mechanisms of microevolution? A: mutation, natural selection, genetic drift, migration, and non-random mating
(gggg) Of the five mechanisms of microevolution, only one is consistently an agent of "positive" change. Which mechanism of microevolution gives rise to this positive change? A: Natural selection
(hhhh) When the main population of a species is reduced in size for one or more generations, thus giving rise to sampling error as alleles are passed from one generation to the next, we call this process __________, which is one form of genetic drift. A: genetic bottleneck, bottleneck; not founder effect
(iiii) Of the five microevolutionary mechanisms, one is absolutely essential for the occurrence of microevolution but nevertheless does not play a larger, direct role in changing allele frequencies. Which mechanism is this? A: Mutation
(jjjj) What is "Darwinian fitness" a measure of? A: reproductive output associated with a given genotype
(kkkk) Graphically indicate what it means for a population to be undergoing stabilizing selection. A: there should be some sort of indication that the extremes are being selected against
(llll) Indicate what intrasexual selection is. A: intrasexual selection is competition within genders; contrast with intersexual selection which is competition for the favor the opposite gender
(mmmm) What is a balanced polymorphism? Be sure to define both "balanced" as it applies to polymorphisms and "polymorphism." A: A balanced polymorphism is a stably maintained presence within a population of more than one allele at a given locus, particularly beyond that numbers of non-prevalent alleles expected to be present in a population as a consequence of mutation alone
(nnnn) The raw material for natural selection is variation. Another term that we use to describe the presence of variation within populations, particularly at specific loci, is __________. A: polymorphism
(oooo) True or False, one route towards balanced polymorphism is dominant-recessive relationships between alleles where recessive alleles are maintained within populations because they are not expressed
(pppp) What is frequency-dependent selection? A: it means that rarity increases the fitness of an allele, thereby making it difficult to eliminate rare alleles from populations; i.e., in frequency-dependent selection, selection acts against the extinction of rare alleles
(qqqq) A botanist is investigating a population of plants whose petal color is controlled by a single gene whose two alleles are codominant. She finds 170 plants that are homozygous brown, 340 plants that are homozygous purple and 21 heterozygous plants whose petals are purple-brown. Is this population in Hardy-Weinberg equilibrium? Justify your answer. A: No, f(B) = (2*170 + 21) / 2 * (170+340+21) = 361 / 1062 = 0.34 = p; q = 0.66; p2 = 0.12 à f(BB) à 64 (= 0.12 * 531) homozygous brown individuals, which is clearly different from the 170 seen in the population (adapted from http://science.kennesaw.edu/~rmatson/Biol%203380/PROBLEMS.html)
(rrrr) Phenylketonuria is a severe form of mental retardation due to a rare autosomal recessive allele. About 1 in 10,000 newborn Caucasians are affected with the disease. Calculate the frequency of carriers (i.e., heterozygotes). A: 1 / 10,000 = the frequency of the homozygous recessive individuals = q2 à q = 0.01; p = 0.99; 2pq = 2*0.01*0.99 = 0.0198 = f(carriers) (adapted from http://science.kennesaw.edu/~rmatson/Biol%203380/PROBLEMS.html)
(ssss) The compound phenylthiocarbamide (PTC) tastes very bitter to most persons. The inability to taste PTC is controlled by a single recessive gene. In the American white population, about 70% can taste PTC while 30% cannot (are non-tasters). Estimate the frequencies of the Taster (T) and nontaster (t) alleles in this population as well as the frequencies of the diploid genotypes. A: q2 = 0.30; q = 0.55 = f(t); p = 0.45 = f(T); f(TT) = p2 = (0.45)2 = 0.20; f(Tt) = 2pq = 2*0.55*0.45 = 0.50; f(tt) = q2 = 0.30; note that f(TT) + f(Tt) = 0.70 à 70% (adapted from http://science.kennesaw.edu/~rmatson/Biol%203380/PROBLEMS.html)
(tttt) You have created an artificial population containing 300 plants with red flowers (AA) and 300 plants with white flowers (aa). Assuming that all the conditions of the Hardy-Weinberg Equilibrium are true, what will be the genotype frequencies of the next generation? A: 0.25, 0.5, and 0.25 (adapted from http://www.csupomona.edu/~jcclark/classes/bio213/hardy-weinberg.pdf)
(a) population genetics
(b) the frequency of a is 0.707 (the square root of 0.5); the frequency of A is 0.293 (= 1 - 0.707); the frequency of aa is 0.5, the frequency of AA is 0.086; the frequency of Aa is 0.414 (note that I had to use three significant figures to avoid rounding error)
(c) No, it is being subjected to natural selection and does not have a large size
(e) AA parents are 25% of population and produce only AA children; aa parents are 25% of the population and produce only aa children; Aa parents are 50% of the population and produce children who are 25% AA, 50% Aa, and 25% aa. Since these latter children make up only 50% of the population, the final frequencies are: AA = 0.25 + (0.25 * 0.5) = 0.375; aa = 0.375; and last, but surely not least, the frequency of the heterozygote is 0.5 * 0.5 = 0.25. 0.375 + 0.375 + 0.25 = 1.0. Note that assortative mating has decreased the frequency of heterozygotes in the population.
(f) a stably-existing polymorphism
(g) frequency dependent selection
(h) p = 0.625 prior to selection and [(0.5 * 0.3 * 2) + (0.25 * 0.5 * 1)] * 1 / [(0.5 * 0.3 * 2) + (0.25 * 0.5 * 2) + (0.25 * 1.0 * 2)] = (.3 + 0.125) / (0.3 + 0.25 + 0.5) = 0.425 / 1.05 = 0.405 after selection
(i) p = 0.7; q = 0.3; p2 = 0.49, 2pq = 0.42, q2 = 0.09
(j) It is non-random mating in which phenotypically similar individuals preferentially mate. It subdivides the population into more than one gene pool; alternatively, you might want to think of assortative mating's effect on the gene pool as one of subdividing by parent phenotype the vat into which we bestow our germ cells.
(k) p = 0.5; following selection the p = (0.5 * 0.5) / [(0.5 * 0.5) + 0.5] = 0.33; the ratio is either 0.33 or 3. If 70% of A died then p = (0.5 * 0.7) / [(0.5 * 0.7) + 0.5].
(l) p = 0.2; q = 0.8; p2 = 0.04; 2pq = 0.32; q2 = 0.64; the frequency of brown-eyed people (men or women) is 0.04 + 0.32 = 0.36; the frequency of blue-eyed people (men or women) is 0.64; the probability that a brown-eyed man will marry a blue eyed woman therefore is 0.36 * 0.64 = 0.23. That is, 23% of all marriages, assuming random marrying, will be between blue-eyed women and brown-eyed men (another 23% will be between blue-eyed men and brown-eyed woman, 41% will consist of all blue-eyed people, and 13% will be between all brown-eyed people.
(m) heterozygote advantage
(n) the giraffes should be distributed into two, preferably quantitative phenotypes such as with one set of giraffes having short necks and the other group having long necks
(s) 1-0.99 = frequency of the recessive homozygote = 0.01; The frequency of the recessive allele is 0.1; the frequency of the heterozygote therefore is 2 * 0.1 * (1-0.1) = 0.18; the fraction of individuals that carry the recessive alleles that are homozygous for this allele therefore is 0.01 / (0.18 + 0.01) = 0.056 or approximately one in 18
(t) genetic bottlenecks result from a reduction in the size of a population or the maintenance of a population at a low population size; founder effects result when new populations are founded by relatively few individuals. Founder effects may be followed or preceded by genetic bottlenecks but are not necessarily so (i.e., the subpopulation that is doing the founding could be derived from a population that is relatively small or could fail to increase in number following the founding event thus resulting in an extended genetic bottleneck in addition to the founding effect.
(v) 225 / 2500 = 0.09 = the frequency of the blue-eye allele individuals; (0.09)1/2 = 0.3 = the frequency of the blue-eye allele; 2 * (0.3) * (1 - 0.3) = 0.42 = the frequency of the heterozygote; 0.42 * 4000 = 1680 = number children of 4000 that would be expected to be heterozygous for eye color
(w) A population lacking heritable variation would also be lacking in polymorphisms, i.e., each locus would be associated with only a single allele
(x) with heterozygous advantage, two different alleles are required to display the phenotype/genotype with the greatest associated fitness. Thus, selection favors the maintenance of two alleles per that locus and the maintenance of two or more alleles per given locus is the definition of balanced polymorphism
(y) Inbreeding or, at least, the fixing of deleterious alleles not shared with the other parental population such that masking of deleterious alleles in the offspring may occur
(aa) sexual selection
(bb) random mating between individuals
(cc) Assortative mating is the choosing a mate on the basis of resemblance to the choosing individual
(dd) frequency of B is equal to [(323 * 2) + (23 * 1) + (45 * 0)] / [(323 * 2) + (23 * 2) + (45 * 2)] = 669 / 782 = 0.855; frequency of b is equal to 1 - 0.855 = 0.145; f(BB) = (0.855)2 = 0.73, f(Bb) = 0.25, f(bb) = 0.021, which corresponds to actual numbers of 391*0.73»285, 391*0.25»98, 391*0.021»8 for BB, Bb, and bb, respectively
(ee) Modern synthesis
(ff) Stabilizing selection
(gg) Increased longevity must correlate with increased product production or increased progeny survival/fitness
(hh) Because the important thing in intraspecific competition is relative success, i.e., relative survival and relative reproductive output; why? Because if we are comparing two individuals within a population and asking who made the most babies, we can answer that question both absolute (Bob has three children and Mary only two) or relatively (Bob has 50% more children than Mary)... assuming a population of constant size through time, then all that really matters, to an individual who is in that population is its relative success
(ii) Neutral variation are mutations that are effectively not distinguishable from wild-type or parental alleles in terms of natural selection, i.e., even in large populations genetic drift has a greater impact on their frequency than natural selection
(jj) Hybrid vigor
(kk) A balanced polymorphism is two or more alleles retained within a population at a given locus each at relatively high frequencies; that is, balanced polymorphism is any equilibrium situation at a given locus other than allele fixation (fixed allele)
(ll) Mutation puts new alleles into gene pools
(mm) (v) all of the above impact on the frequency of heterozygotes (as does just about everything talked about in this chapter)
(nn) See list above
(pp) A population
(rr) f(A) = 200 * 2 + 100 + 100 / 800 * 2 = 600 / 1600 = 0.375; f(B) = 100 * 2 + 200 + 100 / 800 * 2 = 500 / 1600 = 0.313; f(O) = 100 * 2 + 200 + 100 = 400 / 1600 = 0.313
(ss) f(A) = 200 * 2 + 100 + 100 / 800 * 2 = 600 / 1600 = 0.375; f(B) = 100 * 2 + 200 + 100 / 800 * 2 = 500 / 1600 = 0.313; f(O) = 100 * 2 + 200 + 100 = 400 / 1600 = 0.313
(uu) Darwinian evolution and Mendelian genetics
(vv) A fixed locus is a monomorphic one, that is, one in which only one allele is present at that locus within a population
(ww) (iii) Triploid
(xx) six: AA, AB, BB, BC, CC, CA
(yy) 2*300 + 1*400 / 2*1000 = 0.5
(zz) q = [10/(90+10)]½ = 0.316; p = 1 - q = 0.68
(aaa) (0.09)2 + 2*0.09*(1-0.09) = 0.0081 + 0.1638 = 0.1719 = 1 -- (1-0.09)2 = 0.1719
(bbb) It says that phenotypes can vary without underlying genotypes also varying
(ccc) (v) Random mating
(ddd) (iii) No selection
(eee) It says that the population has remained small over more than one generation
(fff) (iv) Natural selection
(ggg) Assortative mating is mating between phenotypically similar individuals
(hhh) Natural selection
(jjj) (i) Founder effect
(kkk) masking of mildly deleterious recessive alleles
(lll) Rare (uncommon)
(mmm) Darwinian fitness (basically, fitness)
(nnn) A: Before selection: f(A) = p = 0.3; f(a) = q = 0.7; f(AA) = p2 = 0.09; f(Aa) = 2pq = 0.42; f(aa) = q2 = 0.49; To incorporate selection: 0.09 * 0.5 + 0.49 * 1.0 + 0.42 * 1.0 = 0.045 + 0.49 + 0.42 = 0.955; f(AA) = 0.09 * 0.5 / [0.045 + 0.49 + 0.42] = 0.045 / 0.955 = 0.0471; f(Aa) = 0.42 * 1.0 / [0.045 + 0.49 + 0.42] = 0.42 / 0.955 = 0.440; f(aa) = 0.49 * 1.0 / [0.045 + 0.49 + 0.42] = 0.49 / 0.955 = 0.513; 0.0471 + 0.513 + 0.440 = 1.000; following selection:f(A) = 2*0.0471 + 1*0.440 / 2 = 0.267 (note that it had been 0.3 before selection); f(AA) = 0.2672 = 0.071 (note that it had been 0.09); f(Aa) = 2 * 0.267 * (1 -- 0.267) = 0.391 (note that it had been 0.42); f(aa) = (1 -- 0.267)2 = 0.537 (note that it had been 0.49); thus, the answers are f(A) = 0.267, f(AA) = 0.071, f(Aa) = 0.391, and f(aa) = 0.537 (and 0.071 + 0.391 + 0.537 = 0.999 ~ 1.000)
(ooo) Directional selection
(ppp) (iv) Sexual selection
(rrr) (ii) Diversifying selection
(sss) Reproductive success
(ttt) Natural selection (Darwinian fitness)
(uuu) (iv) Rare alleles
(vvv) Heterozygous advantage is a greater fitness associated with the heterozygote relative to either homozygote
(www) A polymorphism is the existence, within a population, of more than one allele at a given locus
(xxx) Assortative mating is the pairing off of like-phenotyped individuals
(zzz) Genetic drift (sampling error)
(aaaa) Mutation, Genetic Drift, Migration (non-random mating)
(bbbb) REST OF QUESTIONS SHOULD BE HARDY-WEINBERG QUESTIONS
(51) Practice questions (additional) [index]
(a) Questions from p. 259-261 of Campbell, 1996:
(b) In a population with two alleles for a particular locus, B and b, the allele frequency of B is 0.7. What would be the frequency of heterozygotes if the population is in Hardy-Weinberg equilibrium? [PEEK]
(c) In a population that is in Hardy-Weinberg equilibrium, 16% of the individuals show the recessive trait. What is the frequency of the dominant allele in the population? [PEEK]
(d) Levy and Levin (1975) used electrophoresis to study the phosphoglucose isomerase-2 locus in the evening primrose Oenothera biennis. . . They observed two alleles affecting electrophoretic mobility of the enzyme, PGI-2a and PGI-2b. In 57 strains, they observed 35 PGI-2a/PGI-2a, 19 PGI-2a/PGI-2b, and 3 PGI-2b/PGI-2b. . . Calculate the expected numbers of the three genotypes . . . assuming that the genotypes occur in Hardy-Weinberg proportions. [PEEK]
(e) Kelus (cited in Mourant et al., 1976) reports a study of 3100 Poles, of which 1101 were MM, 1496 were MN and 503 were NN. Calculate the allele frequencies of M and N (and) the expected numbers of the three genotypic classes. [PEEK]
(f) Mourant et al. (1976) cite data on 400 Basques from Spain, of which 230 were Rh+ and 170 were Rh-. Calculate the allele frequencies of D (i.e., the allele which in homozygous form results in the Rh+ phenotype) and d (the allele which in homozygous form results in the Rh- phenotype; recall that the phenotype of Dd is Rh+). How many of the Rh+ individuals would be expected to be heterozygous? [PEEK]
(g) Phenylketonuria is a severe form of mental retardation due to a rare autosomal recessive. About one in 10,000 newborn Caucasians are affected with the disease. Calculate the frequency of the carriers (heterozygotes). [PEEK]
(h) The IA "allele" for the ABO blood groups actually consists of two subtypes, IA1 and IA2, either being considered "IA". In Caucasians, about 3/4 of the IA alleles are IA1 and 1/4 are IA2 (Cavalli-Sforza and Edwards, 1967). Among individuals of genotype IAIO, what fraction would be expected to be IA1IO? What fraction IA2IO? What would be the expected proportions of IA1IA1, IA1IA2, and IA2IA2 among IAIA individuals? [PEEK]
(i) If the frequency of the "green" form of red-green color blindness (due to an X-linked locus) is 5 percent among males, what fraction of females would be affected? What fraction of females would be heterozygous? [PEEK]
(j) Imagine an autosomal locus with four alleles, A1, A2, A3, and A4, at frequencies .1, .2, .3, and .4, respectively. Calculate the expected random mating frequencies of all possible genotypes. [PEEK]
(k) Consider a locus with two alleles (A1 and A2) and another locus with three alleles (B1, B2, B3). Let p1 = .3 be the allele frequency of A1, q1 = .2 be that of B1, and q2 = .3 be that of B2. Calculate the frequencies of all possible gametes, assuming that the loci are in linkage equilibrium. [PEEK]
(l) Suppose genotypes AA, Aa, and aa have frequencies in zygotes of 0.16, 0.48, and 0.36, respectively, and relative viabilities of w11 = 1.0, w12 = 0.8, and w22 = 0.6, respectively. Calculate the genotype frequencies in the zygotes in the next generation. [PEEK]
(m) Questions from pp. 253 of Sinnott et al., 1958:
(n) The frequencies in per cent of the blood group alleles in a Scottish population were computed to be IA = 20.62, IB = 7.56, and i = 71.83 (i.e., these are the ABO blood groupings where IA is the frequency of the "A" allele, IA is the frequency of the "B" allele, and "i" is the frequency of the O allele). What are the expected phenotype frequencies in this population, on the assumption of random mating? [PEEK]
(o) In a Chinese population, 99 per cent of all persons tested were Rh-positive (D+). What are the frequencies of the three genotypes DD, Dd, and dd expected on the assumption of random mating? What proportion of matings in this population would be subject to the risk of having a baby with erythroblastosis due to D incompatibility? [PEEK] (note: to answer this question you absolutely, positively must be aware of when and how erythroblastosis occurs)
(p) If mating is at random and red-green color blindness (which is sex/X linked) does not affect survival or fertility, what should be the proportion of color-blind women in a population at (Hardy-Weinberg) equilibrium in which 8 per cent of the men are color blind? [PEEK]
(q) Questions from p. 484-485 of Hartl, 1983:
(r) Among a sample of 1000 Britishers, the number of individuals with each of the MN blood group phenotypes was as follows M: 298, MN: 489, N: 213. What is the M allele frequency? What is the N allele frequency? What number of each of the genotypes would be expected with random mating? [PEEK]
(s) A certain randomly mating population has a frequency of Rh- blood types of 16 percent. What is the frequency of the d allele (i.e., the Rh- allele)? What the frequency of the D allele (i.e., the Rh+ allele)? What are the expected genotype frequencies? [PEEK]
(t) The dry type of ear cerumen ("wax") is due to homozygosity for a simple Mendelian recessive. Among American Indians the frequency of dry-cerumen individual is 66 percent. What is the frequency of the recessive allele? What is the overall frequency of heterozygotes? Among individuals with the wet type of cerumen, what is the frequency of heterozygotes? (hint: to answer this question you must assume that the population is in Hardy-Weinberg equilibrium) [PEEK]
(u) In Zurich, Switzerland, the allele frequencies of IA, IB, and IO are 0.27, 0.06, and 0.67, respectively. What are the expected frequencies of blood types A, B, AB, and O? [PEEK]
(52) Practice question answers (additional) [index]
(a) Questions from p. 259-261 of Campbell, 1996:
(b) (iv) 0.42 = 2 * 0.7 * 0.3 = 2 * 0.7 * (1 - 0.3) = 2 * p * q = 2 * p * (1 - p).
(c) (iii) 0.6; the frequency of the recessive phenotype is given. This phenotype can only be achieved in the homozygote. Therefore you know what the frequency of the recessive homozygote is. This frequency is equal to q2 where q is the frequency of the recessive allele. The square root of 0.16 is 0.4 which is the value of q. The frequency of the dominant allele, p is simply 1 - q = 1 - 0.4 = 0.6.
(d) Make p the frequency of PGI-2a and q the frequency of PGI-2b. The frequency of PGI-2a is equal to 35/57 + 0.5*19/57 = 0.78. Thus, p = 0.78 and q = 1 - 0.78 = 0.22. Given Hardy-Weinberg proportions, the expected frequency of PGI-2a/PGI-2a = p2 = 0.61, of PGI-2a/PGI-2b = 2pq = 0.34, and of PGI-2b/PGI-2b = q2 = 0.05. As a check, 0.61 + 0.34 + 0.5 do indeed equal 1.0. 0.61 * 57 = 35, 0.34 * 57 is a little greater than 19, and 0.05 * 57 is a little less than 3. Though they didn't ask, you probably would, to a first approximation (i.e., it's always good form to do the statistics even on the obvious), assume that this population is in Hardy-Weinberg equilibrium.
(e) This question is answered in the same manner above. That is, the frequency of allele M is equal to (1101 + 0.5 * 1496)/3100 = 0.60. Therefore the frequency of N is 0.40, of MM 0.36, of MN 0.48, and 0.16 for NN assuming Hardy-Weinberg equilibrium. Expected numbers are 0.36 * 3100 = 1116, 0.48 * 3100 = 1488, and 0.16 * 3100 = 496, respectively, which, of course, are pretty similar to the observed numbers.
(f) Since Rh- is the phenotype of the homozygous recessive, the d allele frequency is equal to the square root of 170/400 = 0.65. The expected frequency of heterozygotes is equal to 2 * 0.65 * (1 - 0.65) = 0.46 which is 182 individuals of 400.
(g) The frequency of the homozygous recessive is 1 in 10,000 = 0.0001 (= 10-4). Assuming simple genetics (e.g., all homozygotes are born and counted at the same rate as non-affected individuals), the frequency of the recessive allele is the square root of this, 0.01. From there the simple answer is about one in 50. Why, because when the recessive is sufficiently rare, the dominant allele is sufficiently close to 1 that the expression 2pq is essentially equal to 2q. Since q = 0.01, 2q = 0.02 = 1 / 50. Note that if you prefer to do things without taking short cuts, the answer would be 2 * 0.01 * (1 - 0.01) = 0.0198. Basically 0.02.
(h) This question is of a type that may be categorized as almost unfairly easy. That is because it is actually so simple that one wants to read far more into it than there actually is, and thus distracts oneself maximally, or at least reach unwanted levels of anxiety. The answers are: 3/4, 1/4, 9/16, 6/16, and 1/16. Why? First, the question was made ridiculously easy simply by asking only for answers which are frequencies among individuals already carrying IA. Thus, among IAIO individuals, the fraction with the IA1 has to be the same (on average, of course) as its fraction in the entire population, which is 3/4. Similarly, the fraction of IA2 has to be equal to the frequency of this allele in the total population, which is 1/4. What is the fraction of the genotypes made up of only the IA1 and IA2 alleles, among IAIA individuals? Again, this is a far simpler question than what is the fraction of these genotypes among the total population? and is calculated simply using the familiar p2, 2pq, and q2 from the Hardy-Weinberg equation where p is the frequency of IA1 and q is the frequency of IA2, which are 3/4 and 1/4, respectively.
(i) The frequency of the phenotype among males is 0.05. Recall that males are haploid for the X chromosome. Therefore the rate at which they carry an X-linked allele is equal to the frequency of the allele in the population, which therefore is also 0.05. The probability that a female will carry one copy of this relatively rare allele is actually a little less than twice the allelic frequency, or a little less than 0.10. Particularly, nearly twice the male probability because the female has two chances of carrying the allele, i.e., one chance for each X chromosome she carries, but, since the allele is relatively rare, a relatively low chance of picking up both alleles (the latter chance is part of the reason this value is a little less than twice the male rate, i.e., the odds of picking up one allele is some value less the odds of picking up two alleles). In fact, the more precise calculation of the frequency of the heterozygote in this case is simply 2pq or 2 * 0.05 * (1 - 0.05) which equals 0.095. The probability of female affliction is equal to the frequency of the homozygous recessive, q2 or 0.052 = 0.0025. Note, for the sake of checking these answers, that the rate at which females are neither afflicted nor carriers is p2 or (1 - 0.05)2 = 0.9025. These values should all add up to one and they do: 0.095 + 0.0025 + 0.9025 = 1.000.
(j) Answering this question is conceptually easy, but a lot of work in practice. First figure out the possible genotypes, then multiply out the allele frequencies for each allele of a given genotype, then check yourself by making sure that frequencies add up to 1.0 (did you remember to multiply the frequency of all of the heterozygotes by 2, i.e., as in 2pq?). Thus:
(i) A1A1, 0.1 * 0.1 = 0.01
(ii) A1A2, 0.1 * 0.2 * 2 = 0.04
(iii) A1A3, 0.1 * 0.3 * 2 = 0.06
(iv) A1A4, 0.1 * 0.4 * 2= 0.08
(v) A2A2, 0.2 * 0.2 = 0.04
(vi) A2A3, 0.2 * 0.3 * 2 = 0.12
(vii) A2A4, 0.2 * 0.4 * 2 = 0.16
(viii) A3A3, 0.3 * 0.3 = 0.09
(ix) A3A4, 0.3 * 0.4 * 2 = 0.24
(x) A4A4, 0.4 * 0.4 = 0.16
(k) Stating that the loci are in linkage equilibrium simply means that we are assuming that there are no biases in allele combinations. It is very important in answering this question that you keep in mind that what we are looking for are gamete frequencies, not diploid frequencies! Here, then, the frequency of any given gamete is equal to the product of the frequencies of the constituting alleles (which also, by the way, need to be calculated to answer this question: p2 = 1 - p1 = 1 - 0.3 = 0.7 and q3 = 1 - q1 - q2 = 1 - 0.2 - 0.3 = 0.5). However, unlike above, we are not calculating heterozygote frequencies so avoid multiplying by 2! Finally, as usual, check yourself by making sure that all of the frequencies add up to 1.0. Thus:
(i) A1 B1, 0.3 * 0.2 = 0.06
(ii) A1 B2, 0.3 * 0.3 = 0.09
(iii) A1 B3, 0.3 * 0.5 = 0.15
(iv) A2 B1, 0.7 * 0.2 = 0.14
(v) A2 B2, 0.7 * 0.3 = 0.21
(vi) A2 B3, 0.7 * 0.5 = 0.35
(l) Don't let the notation throw you. w11 is just the relative fitness of AA, w12 the relative fitness of Aa, etc., though note that here relative fitness is being described solely in terms of survival. Regardless, multiply frequencies by relative viabilities: (0.16)(1.0) = 0.16, (0.48)(0.8) = 0.384, and (0.36)(0.6) = 0.216. These sum to 0.76 and these numbers thus translate to frequencies of 0.211, 0.505, and 0.284 for AA, Aa, and aa, respectively. The question specifically asked for zygote frequencies. These are just allelic frequencies. So 0.211 + 0.505/2 = 0.464 is the frequency of the A gamete and 0.536 the frequency of the a gamete. Assuming Hardy-Weinberg-like reestablishment of the next generation's zygotes (i.e., random mating, large population, no additional evolutionary change in allele frequency) this implies frequencies of AA, Aa, and aa of (0.464)2, 2(0.464)(0.536), and (0.536)2 or 0.215, 0.497, and 0.287, respectively.
(m) Questions from pp. 253 of Sinnott et al., 1958:
(n) The frequency of IAIA is 0.2062 * 0.2062 = 0.0425. The frequency of IBIB is 0.0756* 0.0756 = 0.0057. The frequency of II is 0.7183 * 0.7183 = 0.5160. The frequency of IAIB is 2 * 0.2062 * 0.0756 = 0.0312. The frequency of IAI is 2 * 0.2062 * 0.7183 = 0.2962. The frequency of IBI is 2 * 0.0756 * 0.7183 = 0.1086. 0.0425 + 0.0057 + 0.5160 + 0.0312 + 0.2962 + 0.1086 = 1.0002 which is close enough to one (assuming rounding error) to assume that I have not only listed all of the possible genotypes but have properly determined their frequencies assuming Hardy-Weinberg conditions. The frequency of the A phenotype is equal to the sum of the frequencies of the IAIA and IAI genotypes = 0.0425 + 0.2962 = 0.3387. The frequency of the B phenotype is equal to the sum of the frequencies of the IBIB and IBI genotypes = 0.0057 + 0.1086 = 0.1143. The frequency of the AB phenotype is equal to the frequency of the IAIB genotypes = 0.0312. The frequency of the O phenotype is equal to the frequency of the II genotypes = 0.5160. Once again, check to make sure that the frequencies add up to one. This will only happen with high likelihood if you have done all of the calculations correctly: 0.3387 + 0.1143 + 0.0312 + 0.5160 = 1.0002.
(o) THE FOLLOWING CALCULATIONS START OFF WITH AN ERROR AND SHOULD BE DISREGARDED UNTIL THIS ERROR IS CORRECTED; MY APPOLOGIES. The frequency of D is 0.99 and 0.01 for d. The frequencies of DD, Dd, and dd would be 0.9801, 0.0198, and 0.0001, respectively. Erythroblastosis only occurs if the baby is Rh-positive and the mother Rh-negative. If the mother is Rh-negative, then the odds of the baby being Rh-positive are equal to the odds of the father being DD plus the frequency of the father being Dd divided by 2 which is 0.9801 + 0.0198/2 = 0.9900. The odds that the mother in any given mating is Rh-negative are 0.0001. Thus, the odds that an Rh-positive baby will be carried by an Rh-negative mother are 0.9900 * 0.0001 = 0.000099 (or almost every baby born to an Rh-negative mother in this population). However, that is not what the question asked (and do you ever get the feeling that perhaps the authors of question such as these put twists like that in their questions perhaps inadvertently?). Instead it asked about what the odds of any women having a baby who is affected by erythroblastosis, and this condition only occurs if a second Rh-positive baby is carried by an Rh-negative woman. Thus, the probability is dependent on how many babies these women have. If we assume that they have two babies, no more, no less, then the probability of having a baby which is affected by erythroblastosis are equal to the odds of any woman being Rh-negative and carrying an Rh-positive child, times the odds that an Rh-negative woman's second child will also be Rh-positive (since the woman stays constant in this exercise, she doesn't get refactored into the equation; if you asked the question, what are the odds of two woman-child pairs being picked at random where the woman is Rh-negative and the child is Rh-positive in this population, then you would square 0.000099 instead of multiplying it by 0.99), i.e., 0.000099 * 0.99 = 0.000098. This isn't a very high incidence in the population, but note that it means that 98 out of every 100 Rh-negative women who mate randomly in this population (though not necessarily with more than one man) and has two children will face this problem.
(p) Because male's are haploid for the X chromosome, q = 0.08. Since females are diploid for the X chromosome, their rate of color blindness in this population would be q2 = 0.0064 or 0.64%.
(q) Questions from p. 484-485 of Hartl, 1983:
(r) Note that since the frequency of the three phenotypes equals 1.0 (i.e., 298 + 489 + 213 = 1000) that this implies that either this is a 1 locus, 2 allele system, or that this population is not in Hardy-Weinberg equilibrium (i.e., if there were a third, recessive allele, it apparently is not found in this population in the homozygous state). In addition, it would appear that the two alleles display codominance. Thus, the three genotypes associated with the three phenotypes, M, MN, and N, are MM, MN, and NN. The allelic frequency of M is (298 + 0.5 * 489) / 1000 = 0.5425. The allelic frequency of N is (213 + 0.5 * 489) / 1000 = 0.4575 = 1 - 0.5425. Given Hardy-Weinberg equilibrium, the expected genotype frequencies of MM, MN, and NN are 0.54252, 2 * 0.5425 * 0.4575, and 0.45752, respectively, which translates to 0.29, 0.50, and 0.21, respectively. These add up to 1.0. The associated numbers given a population size of 1000 are 290, 500, and 210, respectively, which his pretty close to the numbers observed.
(s) Given that this is a standard autosomal recessive allele, the frequency of d is the square root of 0.16 which is 0.4. Thus the frequency of D must be 0.6. The three possible genotypes are DD, Dd, dd and though the problem didn't state it, we will assume the null state and calculate the frequencies of these genotypes assuming Hardy-Weinberg equilibrium which are 0.36, 0.48, and, of course, 0.16 respectively. 0.36 + 0.48 + 0.16 = 1.0.
(t) The frequency of the recessive allele is simply the square root of 0.66 = 0.81. The frequency of heterozygotes must therefore be 2 * 0.81 * (1 - 0.81) = 0.30. 0.66 + 0.30 + (1 - 0.81)2 = 1.0. The last question is the tough one since it is not asking for the overall frequency but instead the frequency among a subgroup. Individuals with wet type cerumen include the homozygous dominant and the heterozygotes. Thus, the frequency of the heterozygotes among individual with wet type cerumen is equal to the frequency of heterozygotes divided by the sum of the frequency of heterozygotes and the frequency of homozygous dominants: 0.30 / (0.30 + 0.035) = 0.90, or 90 per cent.
(u) The frequency of type A blood = IA2 + 2 * IA * IO = 0.4347. The frequency of type B blood = IB2 + 2 * IB * IO = 0.084. The frequency of type AB blood = 2 * IA * IA = 0.0324. The frequency of type O blood = IO2 = 0.4489. 0.4347 + 0.084 + 0.0324 + 0.4489 = 1.000.
Blue x Blue
Brown x Blue
Brown x Brown
(i) Working out the genotypes from phenotypes
· Since almost exactly half [317/(317+316)] the offspring from brown x blue parents are blue eyed we can assume all brown offspring are heterozygous brown (Bb) (why? Because one parent was blued-eyed)
· 25 blue eyed individuals result from both brown eyed parents, so both the parents must also be heterozygous brown which gives assumed progeny genotype rations of 25 bb, 50 Bb and 25 BB. This leaves 7 offspring (i.e., 82-3*25) whose parents must be Bb x BB or BB x BB. The proportions of the 7 individuals are most likely 0.333 Bb and 0.666 BB, or approximately ~ 2 Bb and 5 BB. This gives you 52 Bb individuals (i.e., 50 + 2) and 30 BB individuals (i.e., 25 + 5). [these ratios come from an assumption that the allelic ratio, B:b, is 1:1, thus there are twice as many Bb x BB matings as BB by BB matings, but only half of the former but none of the later mating's progeny are Bb, hence a ratio of ½ to (½ + ½)]
(ii) We can now find the allelic frequencies:
· b = ((2 x 625) + (2 x 317) + 1 x 316 + (2 x 25) + 1 x 52) / 2730 = 0.843
· B = (1 x 316 + 52 + (2 x 30)) / 2730 = 0.157
(iii) Calculation of Hardy-Weinberg equilibrium
· bb = (0.843 x 0.843) = 0.711
· BB = (0.157 x 0.157) = 0.025
· Bb = 2 x (0.843 x 0.157) = 0.264
bb 970.5 (0.711 x 1365)
BB 34.1 (0.025 x 1365)
Bb 360.4 (0.264 x 1365)
BB 30 (calculated genotypes)
Bb 368 (calculated genotypes)
bb = 967 / 1365
b = 0.841
B = 0.159
BB = 0.025
Bb = 0.267
bb 966.4 (0.708 x 1365)
BB 34.1 (0.025 x 1365)
Bb 364.5 (0.267 x 1365)
1) Yes, the population is in Hardy-Weinberg equilibrium.
2) With regard to the blue and brown phenotypes, the data appears to be reliable (observed and expected numbers are similar).
(a) Campbell, N. A. (1996). Biology. Fourth Edition. Benjamin/Cummings Publishing, Menlo Park, California. pp. 434-435.
(b) Hartl, D. L. (1980). Principles of Population Genetics. Sinauer Ass., Inc., Sunderland, Massachusetts. pp. 78, 137-139.
(c) Hartl, D.L. (1983). Human Genetics. Harper & Row, Publishers, New York. pp. 484-485.
(d) Sinnott, E.W., Dunn, L.C., Dobzhansky, T. (1958). Principles of Genetics. Fifth Edition. McGraw-Hill Book Co., Inc. New York. p. 253.
(bonus = 1/15th of available points) You suspect that a local population of Delphinium is highly selfing. In order to test your hypothesis, you collect maternal plants and four seeds from each plant. You would like to have all the seeds associated with their maternal plants, however your lab partner threw all 1200 seeds in one bag! Despite this setback, you proceed with an analysis of allozyme variation (F = Fast and S = Slow Alleles) that yields the following results. Do these results support your hypothesis that this population is highly selfing? Why or why not? (bonus points are available only for answering both parts correctly) (from: http://www.bio.utk.edu/ecology/courses/eeb431/hardy.htm)
() In sheep, the allele for dark fleece D is dominant to the allele for light fleece d. A small population on an island consists of 25 DD, 50 Dd, and 25 dd (p = q = 0.5 and this population is in Hardy-Weinberg equilibrium, is it not?). A farmer brings in 25 light-fleeced sheep from a neighboring island. What is the new frequency of the d allele? (from http://biology.soton.ac.uk/bs202/extra.html)
A: f(a) = 2*(25+25) + 1*50 / [2*(25 + 50 + 25 + 25)] = 150/250 = 0.60 (Chapter 23)
(v) This question is E. O Carter's Human Heredity: Eye colour data was collected by Winge (1921) in Denmark:
Blue x Blue
Brown x Blue
Brown x Brown
(i) Is the population in Hardy-Weinberg equilibrium?
This is how Peter Fisher solved this problem:
· Ignore the Greyish or Bluish-green column.
· Assume blue eye colour is homozygous recessive (bb).
· Assume there is a second system (locus) of brown eye colour that is homozygous dominant (B1B1) and hypostatic (enhances the phenotype associated with another locus) to the first system of brown eye colour (explains the brown eyed offspring from two blue eyed parents, i.e., a B1B1 individual has brown eyes regardless of the genotype at the other locus).
· You need to remove the effects of the second system from the first.
(iii) Working - modification of the phenotypes
· First calculate the frequency of the homozygous dominant brown genotype (B1B1); this can be done by looking at the children of Blue x Blue parents
· Note this genotype only affects blue-eyed individuals changing their eye colour to brown (brown eyed individuals remain brown eyed).
· 12 / (12+625) = 0.0188 = fraction of brown eyed children produced by blue-eyed parents; this is also an estimation of the fraction of individuals in the population with the B1B1 genotype
· For both blue eyed parents subtract the number of affected blue eyed offspring from brown eyed offspring, i.e., 12 (12-12=0)
· For brown x blue parents calculate the number of affected offspring = 0.0188 x (317+322) = 12.0132 ~ 12 (i.e., fraction that we expect to have the B1B1 genotype times the total number of offspring of parents of these phenotypes)
· approximately half the offspring are blue eyed so subtract 6 (the proportion of affected blue eyed individuals) from the brown eyed offspring (i.e., 322-6=316)
· For both brown eyed parents calculate the number of affected offspring: 0.018 x (25+82) = 2.0116 ~ 2
· Since the proportion of blue eyed offspring is 2/82 = 0.234 (x2) is less than 0.5 (so rounds to zero) then changes are needed this number (i.e., 82-0)
· Modified table
The following are from Spring, 2003, bio 114:
(#) What consists of the total of all alleles at all gene loci in all individuals found within a population?
A: A gene pool (chapter 23)
(#) What is a fixed locus?
A: A fixed locus is a locus for which only (or nearly only) a single allele exists for an entire gene pool (chapter 23)
(#) What are the three mechanisms of non-Darwinian evolution (more precisely, non-Darwinian microevolution)? Note, non-random mating is not one of the answers
A: genetic drift, migration, and mutation (chapter 23)
(#) Another name for the movement of alleles between populations in the course of organism migration is __________.
A: Gene flow (chapter 23)
(#) What is Darwinian fitness?
A: "Darwinian fitness is the contribution an individual makes to the gene pool of the next generation relative to the contributions of other individuals;" Darwinian fitness is the allelic contribution an individual makes to the next generation; Darwinian fitness is a quantity equal to the average reproductive output associated with a given genotype; Darwinian fitness is a measure of reproductive success; etc. (chapter 23)
(#) Label (a), (b), and (c) as Directional selection, Diversifying, or Stabilizing selection:
A: (a) Stabilizing, (b) Directional, and (c) Diversifying (chapter 23)
(#) What is Intersexual selection?
A: Mate choice, i.e., natural selection that is based on the ability of organisms to attract and then mate with the opposite sex (chapter 23) à also pull H&W question from text, the one with Sickle Cell and odds of offspring getting it if brothers have it
(#) In a population that is in Hardy-Weinberg equilibrium, 16% of the individuals show the recessive trait. What is the frequency of the dominant allele in the population?
A: 0.6 = 1 -- square-root of 0.16 (chapter 23)
(#) How does hybrid vigor contribute to the existence of balanced polymorphisms. Note, don't just define hybrid vigor.
A: Because, with hybrid vigor, heterozygotes display greater fitness than either homozygote, there is selection for the continued existence of a polymorphism, i.e., the retention of more than one allele at a given locus (chapter 23)
(#) What is the term used to describe the mechanism giving rise to a balanced polymorphism whereby there is an occurrence of more than one allele at a given locus within a population, but members of this population nevertheless display very similar Darwinian fitness regardless of whether the locus is found in a homozygous or heterozygous state?
A: Neutral variation (chapter 23)
(#) Even if a perfect organism existed, it would remain perfect only so long as its __________ remained unchanged. (assume that we are talking about a single organism that neither ages, dies, mutates, and even varies phenotypically in a non-adaptive manner--that is, the intrinsic perfection of this organism does not waver)
A: environment (chapter 23)
(#) You have a population of sardines (small marine fish) that vary in the coloration of their fins. Silver fins are more common (84 fish have them), but there are 16 fish with black fins. You know three important facts. First, that the fin color is controlled by a single gene with two alleles. Second, that the black allele is recessive. Third, that the population is in Hardy-Weinberg equilibrium. How many heterozygotes are there in your sardine population? (from http://mendel.bio.indiana.edu:16080/courses/L111-Bever/Homework/pop%20genetics%20exercise.htm)
A: q = (0.16)1/2 = 0.4; p = 0.6; frequency of heterozygotes = 2*0.4*0.6 = 0.48; since the population consists of 100 individuals, that means that there are 48 heterozygotes. (chapter 23)
(#) After graduation, you and 19 friends, all brown eyed, build a raft, sail to a deserted island, and start a new population, totally isolated from the rest world. Two of your friends carry (that is, are heterozygous for) the recessive b allele, which in homozygotes gives rise to blue eye color.
Assuming that the frequency of the b allele does not change as the population grows nor has any impact on survival or reproduction, what will be the expected frequency of blue-eyed individuals on your island 100 years hence? (from http://science.nhmccd.edu/biol/hwe/hwefrm4.html)
A: The initial allelic frequency is 2/40 (40 = you + 19 friends times 2); therefore the expected frequency of heterozygotes should be 2*38*2/(40*40) = 0.10 = 0.095 (chapter 23)
(#) A rancher decided to raise cattle in an isolated valley and bought 1000 head which he transported to the valley to establish a randomly mating population. When released, the animals consisted of 130 white-coated beasts, 330 red, and 540 roan (this latter color represents the heterozygote). (from http://www.pstcc.cc.tn.us/mfhicks/biol2120/hardyweinbergproblems.html)
A: f(A) = (2*130 + 1*540)/2000 = 0.4; number of AA expected) = 0.42 * 1000 = 160, so: A. No, B. 160 white, 360 red, and 480 roan, C. Yes (chapter 23)
(#) Because a nurseryman finds that his customers generally prefer antirrhinum flowers that are red or pink (the red-red homozygote and heterozygote, respectively), he plans that the seeds provided for sale shall contain as few seeds for white flower as possible. He samples his antirrhinum plot, which has been established for some years, pollinates randomly, and finds that 9% of the plants have white flowers (the white-white homozygote). He uproots these plants. Next year the remaining red and pink flowers pollinate freely and he collects their seed for marketing. What proportion of the seeds he sells will subsequently produce plants with white flowers? (from http://www.pstcc.cc.tn.us/mfhicks/biol2120/hardyweinbergproblems.html)
A: (0.09)1/2 = 0.3, which is the initial frequency of the recessive allele; This means that the population initially had a frequency of 0.49 of dominant homozygotes (red flowers) and a frequency of 0.42 of the pink flowers (note that 0.49 + 0.42 = 0.91 = 1 -- 0.09); if all whites are killed (that is, all white phenotypes and genotypes, not all white alleles), then the resulting frequencies are red = 0.42 / (42+0.49) = 0.46 and pink = 0.49 / (0.42+0.49) = 0.54; frequency of the white allele therefore will be 0.49 / 2 = 0.25 (roughly); the frequency of white flowers therefore should be about 0.06 = 0.252; calculations such these, by the way, represented the biological flaw in the philosophies of the eugenics movements of the early twentieth century à it simply is not all that easy to get rid of alleles from populations by culling homozygotes only (chapter 23)
(#) A botanist is investigating a population of plants whose petal color is controlled by a single gene whose two alleles are codominant. She finds 170 plants that are homozygous brown, 340 plants that are homozygous purple and 21 plants whose petals are purple-brown. Is this population in Hardy-Weinberg Equilibrium?
A: Absolutely no way, there is no way you can be in equilibrium with an excess of both homozygotes relative to the heterozygote (chapter 23)
(#) Among a group of 730 Australian aborigines, the following blood types (i.e., phenotypes) were determined for the M-N blood group: M = 22, MN = 216, and N = 492. This group has three blood types (phenotypes), M, N and MN, which are caused by a single locus with two codominant alleles, LM and LN. Individuals homozygous for LM are blood type M; homozygotes for LN are blood type N; heterozygotes express both alleles and are blood type MN. Using these data, calculate the frequency of the LM and LN alleles in this population.
A: f(LM) = (2*22 + 1*216) / 2*(22+216+492) = 260 / 1460 = 0.18; f(LN) = 0.82 (chapter 23)
(bonus) 7. An investigator finds that a group of people meets the conditions of the Hardy-Weinberg Law. She tells you that there are twice as many persons with the genotype B/B as there are heterozygotes. What is the frequency of the B allele? (assume that only two alleles are found at this locus) (from http://www.radford.edu/~rsheehy/genetics/problems/popgenprobset3.html)
A: This requires a little algebra: (# B homozygotes) = 2*(heterozygotes); given H.W. equilibrium, this means that p2 = 2*2pq; Note that q = 1 -- p so therefore p2 = 2*2p(1 -- p); multiplying out: p2 = 4p -- 4p2; solving for p we find that p = 4/5 = 0.8; f(B homozygotes) = 0.82 = 0.64; f(heterozygotes) = 2*0.8*0.2 = 0.32, which satisfies the conditions stated (chapter 23)
The following are from Spring, 2002, bio 114:
(#) The table refers to a three-allele locus in a Hardy-Weinberg population. Fill in the
blank boxes with the appropriate quantity if there is sufficient information, or else
just leave the question mark if there is not.
0.0625 + 0.150 + 0.225 + 0.09 + 0.270 + 0.203 = 1.01 [H14 from http://www.wisc.edu/genetics/CATG/courses/G620/problems/HardyWeinberg.pdf] (chapter 23)
(#) Suppose genotypes AA, Aa, and aa have frequencies in zygotes of 0.16, 0.48, and 0.36, respectively, and relative viabilities of w11 = 1.0, w12 = 0.8, and w22 = 0.6, respectively. Calculate the genotype frequencies in the zygotes in the next generation.
A: Don't let the notation throw you. w11 is just the relative fitness of AA, w12 the relative fitness of Aa, etc., though note that here relative fitness is being described solely in terms of survival. Regardless, multiply genotype frequencies by relative viabilities: (0.16)(1.0) = 0.16, (0.48)(0.8) = 0.384, and (0.36)(0.6) = 0.216. These sum to 0.76 and these numbers thus translate to frequencies of 0.211, 0.505, and 0.284 for AA, Aa, and aa, respectively. The question specifically asked for zygote frequencies. These are just allelic frequencies. So 0.211 + 0.505/2 = 0.464 is the frequency of the A gamete and 0.536 the frequency of the a gamete. Assuming Hardy-Weinberg-like reestablishment of the next generation's zygotes (i.e., random mating, large population, no additional evolutionary change in allele frequency) this implies frequencies of AA, Aa, and aa of (0.464)2, 2(0.464)(0.536), and (0.536)2 or 0.215, 0.497, and 0.287, respectively. (chapter 23)
(#) In humans, the inability to tolerate caffeine is an autosomal recessive trait (t), while the ability to tolerate caffeine is dominant (T). In a certain remote country, 84% of the people can tolerate caffeine. What are the frequencies of T and t in that population? Assume that the alleles are at Hardy-Weinberg frequencies.
A: 1 -- 0.84 = 0.16 = q2; q = 0.4; p = 0.6 from http://depts.washington.edu/genetics/courses/genet371b-aut00/public_html/problems/371B_practice_11.html (chapter 23)
(#) In a Caucasian population of 9000 individuals, the frequency of the allele (B) for male pattern baldness is 0.3 (call the allele for lack of male-pattern baldness H for Hair). What are the expected genotypes and their frequencies if the population is in Hardy-Weinberg equilibrium? The baldness allele is recessive in females but dominant in males. What are the expected phenotype frequencies in males and females?
from http://depts.washington.edu/genetics/courses/genet371b-aut00/public_html/problems/371B_practice_11.html (chapter 23)
(#) Suppose the 32 flowers are red, 42 pink, and 51 white. Assume codominance between R (for red) and r alleles underlying these phenotypes (such that RR is red, Rr is pink, and rr is white). What are the frequencies of R and r?
A: f(R) = (2*32 + 1*42 + 0*51) / 2*(32 + 42 + 51) = 106 / 250 = 0.424; f(r) = 1 -- f(R) = 0.576 (chapter 23)
(#) If 9% of an African population is born with a severe form of sickle-cell anemia (ss), what percentage of the population will be more resistant to malaria because they are heterozygous(Ss) for the sickle-cell gene?
A: 9% =.09 = ss = q2 ; (¦)s = q = Square root of .09 = .3 ; p = 1 - .3 = .7 ; 2pq = 2 (.7 x .3) = .42 = 42% of the population are heterozygotes (carriers) [from http://science.nhmccd.edu/biol/hwe.html] (chapter 23)
A: f(R) = (2*32 + 1*42 + 0*51) / 2*(32 + 42 + 51) = 106 / 250 = 0.424; f(r) = 1 -- f(R) = 0.576 (chapter 23)
The following are from Spring, 2004, bio 114:
(#) In humans, the inability to tolerate caffeine is an autosomal recessive trait (t), while the ability to tolerate caffeine is dominant (T). In a certain remote country, 84% of the people can tolerate caffeine. What are the frequencies of T and t in that population? Assume that the alleles are at Hardy-Weinberg frequencies.
A: 84% à 0.84 = dominant type; 1 -- 0.84 = 0.16 = recessive type; square root of 0.16 = 0.4, which is the frequency of the recessive allele (t); 1 -- 0.4 = 0.6 is the frequency of the dominant allele (T) (chapter 23)
(bonus) In humans, the inability to tolerate caffeine is an autosomal recessive trait (t), while the ability to tolerate caffeine is dominant (T). In a certain remote country, 84% of the people can tolerate caffeine. In a strange turn of events, a fringe group (whose slogan is "Starbucks Everywhere™") overthrows the government and decrees that henceforth, caffeine-intolerants will not be allowed to have children. What will be the frequencies of T and t after one generation under this hyperactive regime?
A: 84% à 0.84 à f(tt) = 1 -- 0.84 = 0.16 à f(t) = 0.4 à f(T) =1 -- 0.4 = 0.6 à f(Tt) = 2*0.6*0.4 = 0.48 à f(TT) = 1 -- 0.48 -- 0.16 = 0.36 à following selection: f(TT) = 0.36*1 /(0.36*1 + 0.48*1) = 0.43; f(tt) = 0; f(Tt) = 1 -- 0.43 = 0.57 à f(T) = (0.43*2 + 0.57) / 2 = 0.72; f(t) = 0.28 (chapter 23)
(#) The frequency of a recessive allele in the population is 0.2. Assuming that the dominant and recessive alleles are at Hardy-Weinberg frequencies, predict the probability of a mating between a heterozygote and a homozygous recessive individual.
A: (chapter 23)
(#) Genetic testing reveals that in a small population, the number of individuals homozygous normal (AA) for PKU is 660, the number of heterozygotes (Aa) is 280, and the number of homozygous recessive (aa) individuals is 60. What are the frequencies of the wild type and the PKU allele in this population?
A: f(A) = (660*2 + 280) / 2*(660 + 280 + 60) = 1600/2000 = 0.8; f(a) = 1 -- 0.8 = 0.2 (chapter 23)
(bonus) You choose to examine the aesthetic appeal of the common Seattle slug. Aesthetic appeal in the slug is determined by a single autosomal locus "Slimy", at which there are three alleles. The alleles are Icky (Si), Yucky (Sy), and Gross (Sg). Icky is dominant over both yucky and gross. Yucky is dominant over gross. After a long walk through the rain, you observe that the phenotypes of the slugs occur in the following proportions: 50% are icky, 30% are yucky, and 20% are gross. Assuming that the alleles are at Hardy-Weinberg proportions, what are the allele frequencies f(Si), f(Sy), and f(Sg)? Hint: the correct solution to the equation, 0 = x2 + x0.8944 -- 0.30, is x = 0.2599.
A: f(Sg) = square root of 0.20 = 0.4472; for f(Sy) à 0.30 = f(Sy)*(f(Sy)+ 2*f(Sg)) à 0 = f(Sy)2 + f(Sy)*2*0.4472 -- 0.30 à f(Sy) = 0.3680; f(Si) = 1 -- 0.4472 -- 0.2599 = 0.2929; f(Icky) = 0.29292 + 2*0.2929*0.4472 + 2*0.2929*0.2599 = 0.0858 + 0.2620 + 0.1522 = 0.50 (chapter 23)
(#) The following numbers of allozyme (protein) genotypes at a shell deposition locus of the barnacle (Semibalanus balanoides) were identified in a sample of 1000 barnacles from coastal Rhode Island before a hurricane hit: 90 FF, 420 FS and 490 SS individuals (F stands for fast migrating protein allele, S = slow migrating allele in gel electrophoresis). Are the barnacles in Hardy-Weinberg equilibrium? Show your work.
A: f(F) = (90*2 + 420) / 2*1000 = 600/1000 = 0.6; f(S) = 1 -- 0.6 = 0.4; Assuming HW equilibrium: f(FF) = 0.6*0.6 = 0.36; that would be 360 individuals; since actual number is 90, we can be pretty certain that the population is not in H-W equilibrium; f(FS) = 2*0.6*0.4 = 0.48 à 480, which is fairly close to 420; f(SS) = 0.4*0.4 = 1.6 à 160, which is a lot different from 490; clearly there is an over representation of S-allele-containing individuals (chapter 23)
(#) What percentage of apparently healthy Welsh Springer Spaniels (WSS) are potential producers (carriers) of epilepsy? Previous research in the UK and Holland showed the "simple autosomal recessive" model almost fits the pedigree data we have for epilepsy in the WSS. Numbers from the Dutch club's study of epilepsy suggested about 3 % of WSS are epileptic. Assume Hardy-Weinberg equilibrium.
A: f(ee) = 0.03; f(e) = 0.1732; f(Ee) = 2*0.1732*(1-0.1732) = 2*0.1732*0.8268 = 0.2864, which means that about 29% of the population are carriers (chapter 23)
(#) In Zurich, Switzerland, the allele frequencies of IA, IB, and IO are 0.25, 0.35, and 0.40, respectively. What are the expected frequencies of blood types A, B, AB, and O?
A: f(IAIA) = 0.25*0.25; f(IAIO) = 2*0.25*0.40 à 0.0625 + 0.2 = 0.2625 = f(A blood type); f(IBIB) = 0.35*0.35; f(IAIO) = 2*0.35*0.40 à 0.1225 + 0.28 = 0.4025 = f(B blood type); f(O blood type) = 0.40*0.40 = 0.16; f(AB blood type) = 2*0.25*0.35 = 0.1750; 0.2625 + 0.4025 + 0.16 + 0.1750 = 1.00 (chapter 23)
(#) If mating is at random and red-green color blindness (which is sex/X linked) does not affect survival or fertility, what should be the proportion of color-blind women in a population at Hardy-Weinberg equilibrium in which 10 per cent of the men are color blind?
A: Because male's are haploid for the X chromosome, q = 0.1. Since females are diploid for the X chromosome, their rate of color blindness in this population would be q2 = 0.01 or 1%. (chapter 23)
(#) Which aspect of microevolution is non-Darwinian, does not require more than one population, and does not serve as the ultimate source of genetic variation in populations?
A: Genetic drift (chapter 23)
(#) The contribution an individual makes to the gene pool of the next generation relative to the contributions of other individuals we describe as that individual's __________.
A: Relative fitness, Darwinian fitness, fitness (chapter 23)
(#) Natural selection is not always directional. What do we call natural selection that is selection against the most-common type?
A: disruptive selection or frequency-dependent selection or diversifying selection (chapter 23)
(#) Describe intrasexual selection.
A: This competition among same genders for mates (chapter 23)
(#) What is heterozygous advantage?
A: The heterozygote is better adapted than either homozygote (chapter 23)
(#) What does it mean for variation to be neutral?
A: It means that the variation is not distinguished by natural selection (chapter 23)