Instructor: Dr. Martha B Reiskind AEC 550: Conservation Genetics Spring 2017 We will talk more about about D and R 2 and here s some additional information. Lewontin (1964) proposed standardizing D to the maximum possible value it can take: D = D/Dmax Recall Dmax is the value of D at the given allele frequencies. Dmax is equal to the lesser of p A q b or p B q a if D is positive or the lesser of p A p B or q a q b if D is negative. Note that all of these numbers will be positive, so when you divide the lesser of two into the negative D, make sure you take the absolute value, not the negative value. Here s an example. D varies between 0 and 1 and allows us to assess the extent of linkage disequilibrium relative to the maximum possible value it can take. Hill and Robertson (1968) proposed the following measure of linkage disequilibrium: R 2 = D2 /[p A p B q a q b ] R 2 varies between 0 and 1. As for D, the maximum value of R 2 depends on the allele frequencies and one can determine a R value which is the square root of R 2. This is the correlation coefficient of alleles between loci within the gamete. Factors that cause linkage or gametic disequilibrium: There are five processes that can produce linkage disequilibrium in a population: epistatic natural selection (alleles at different loci produce a phenotype that is favored by selection), mutation, random drift, genetic hitchhiking, and gene flow. Although natural selection is the most important some of the others (notably gene flow) can create substantial levels of disequilibrium. Mutation. Similar to its weak effects on allele frequency change, the process of mutation does not lead to any substantial disequilibrium. Recurrent mutation will certainly produce nonrandom associations between alleles at different loci. However, recombination typically occurs at higher levels than mutation and it will 1
break apart any non-random associations of alleles. Furthermore, recurrent mutations are not expected to be associated with the same alleles at other loci. However, in non-recombining regions of the genome (such as part of the human Y chromosome) mutation can form linkage disequilibrium between loci that will not decay and can increase in frequency by drift or selection. Genetic drift. Non-random associations between alleles at different loci may be produced by random drift. In any one population, the magnitude of linkage or gametic disequilibrium may indeed be substantial. In a finite population with effective population size N E and a rate of recombination, r, between loci the expected value of R 2 is E(R 2 ) 1/[1 + 4N E r] This equation shows that if 4N E r is small, the expected value of R 2 approaches 1.0. As 4N E r increases in magnitude, the expected value of linkage disequilibrium approaches 0, at which point you have gametic or linkage equilibrium. When 4N E r is large, the expectation becomes: E(R 2 ) 1/4N E r Here, 4Ner is called the population recombination rate (similar to 4NEµ being the population mutation rate, you will see shortly). This relationship has attracted the attention of population geneticists because if one knows the rate of recombination for a region in the genome then it is possible to estimate N E. Gene flow. Gene flow can produce significant levels of linkage or gametic disequilibrium in a population. However, this will occur only when the frequencies of alleles at both loci differ between the populations. The greater the allele frequency differences, the greater the linkage or gametic disequilibrium produced by gene flow. If there is linkage disequilibrium between loci in the source populations then this will contribute even further to the non-random associations of alleles. Population subdivision has the effect of reducing the rate of decay of linkage disequilibrium. If gene flow is small, then the rate of decay is determined by the magnitude of m, the proportion of migrants. If gene flow is more extensive, then the decay is determined by the recombination rate. Inbreeding slows the decay of linkage or gametic disequilibrium. Intuition tells us that inbreeding should slow the decay of linkage disequilibrium because it reduces the frequencies of double heterozygotes. It is through recombination in these double heterozygotes that disequilibrium is altered. The effect of inbreeding on the decay of disequilibrium has been studied for partially selfing species. If selfing levels are high, the decay of linkage disequilibrium is slowed substantially simply because inbreeding reduces the conduit (i.e., double heterozygotes) by which linkage or gametic disequilibrium is eliminated. The evolution of supergenes. Natural selection can create linkage disequilibrium between genes by favoring specific combinations of alleles at different loci. If particular combinations of alleles function better as a group (than being randomly 2
assembled) then natural selection can act to push the different loci physically together into what is called a supergene. The tight linkage acts to reduce recombination between individual genes in the supergene. Recombination in the region of surrounding the supergene can also be reduced to further maintain the strong linkage disequilibrium between genes. One of the best studied examples of a supergene occurs in the land snail Cepaea nemoralis. This snail is highly polymorphic for its shell coloration and banding patterns. Shell color ranges from yellow to pink to brown with various shades of each. Shell color is controlled by several alleles at a single locus. Brown is dominant over yellow and pink. In turn, pink is dominant over yellow. The shells of Cepaea are also banded to varying degrees. The number of bands can range from 0 (dominant) to 5 (or sometimes 6). Modifier loci also exist that control the number of bands and how they are expressed. The loci controlling shell color, banding, and all the modifier genes that act on these traits are tightly linked as a supergene. Low levels of recombinants are detected in lab crosses but the genes effectively behave as one single locus. Why did this supergene evolve? Many studies conducted in both England and France suggested that spatially varying selection favors certain combinations of alleles. Selection acting on the shell phenotypes is related to predation and thermal biology. Other good examples of supergenes include the genes for heterostyly in several plants and those controlling mimicry in some butterflies. The same principles apply for the coadaptation of genes locked within chromosomal inversions. We will talked about admixture and population subdivision. Your book discusses how to calculate D for subdivided populations. I think they do an excellent job discussing this and I ll highlight this in the context of the speciation event in blue rockfish during class. 3
QUANTITATIVE TRAIT LOCI From Darwin's time onward, it has been widely recognized that natural populations harbor a considerably degree of genetic variation. Darwin came to this conclusion from the experience of animal and plant breeders of his day and he relied on it heavily when developing his theory of evolution by natural selection. The form of variation envisaged by Darwin to be of fundamental importance for evolutionary change was continuous or what we know call polygenic or quantitative. The statistical approach to studying such traits is referred to as quantitative genetics. "Polygenic" simply means that there are a number of genes affecting the trait. The vast majority of morphological, physiological, and behavioral characters are quantitative and thus understanding this class of variation is fundamental for evolutionary biologists. For conservation geneticists, we want to know what genes are involved in local adaptation so we can better understand how populations will change with environmental change. Quantitative traits that are influenced by both genes and the environment commonly exhibit a normal distribution. Early in the course we talked about continuous versus discrete traits. Many of the traits that we are interested in as conservation geneticists are these continuous traits that are controlled by many loci (quantitative traits). Above is an example or length frequency data from pink salmon females and males. There are three types of quantitative traits: (1) continuous traits that have a normal distribution in populations (e.g., weight, height, beak length ), (2) meristic traits that have an integer (e.g., clutch size, number of vertebrae, gill rakers ), and (3) threshold traits that have discrete states (e.g., alive or dead, sick or well). All of these typically have many genes that control them. For many traits we know there are more than two genes, but don t know how many there are. In addition, we may have variance in the contribution of the genes, there may be weak or strong effect genes which we refer to as major and minor effect genes, respectively. What is the nature of the genes affecting quantitative characters? Quantitative geneticists believe that they are no different from any other genes they may possess multiple alleles, exhibit varying degrees of dominance, mutate, and undergo 4
changes in allele frequencies as we ve discussed so far in class. Understanding the total number of genes controlling a quantitative character and determining the relative roles of major and minor effect genes is referred to as understanding the genetic architecture of the trait. A quantitative genetics model. In order to construct this model we need to decompose phenotypic values into genetic and environmental components. The model includes these variables. Remember that understanding the quantitative genetic architecture of a trait is essential for predicting genetic changes VP = VE + VG In words, the phenotypic variation of a quantitative trait breaks down into the components of genetic variation and environmental variation. The environmental variation is the phenotypic variance among individuals caused by the fact they are exposed to different environments, while the genetic variation is variance in phenotype among individuals caused by different genotypes. In the equation above we want to understand what part of the genetic variation is heritable. We can further break down genetic variation as follows: VP = VE + (VA + VD + VI) Genetic variation breaks down to contributions from additive genetic variation (VA), dominance variation (VD), and epistatic variation (VI). VD is the variance in dominance deviations. There is a certain amount of variation that occurs at an individual locus that is due to the alleles interacting, but this interaction is NOT heritable. VI accounts for the variation that occurs due to loci interactions, or alleles at different loci interacting and it is NOT heritable, recombination breaks this apart. Additive genetic variation, VA, is variance caused by an allele s affect on the phenotype, not interactions among alleles or among loci. The full model also includes an interaction term that accounts for interactions between genotype and environment (VGXE). VP = V E +V A + V D + V I + V GXE The interaction term drops out if there is no association between genotypes and environment. We will look at an example of this in class. There is an obvious and not so obvious point here. First, the obvious point is that genetic variation confers phenotypic variation for selection to change the frequency of that trait. NO variation, NO change. The not so obvious is that certain types of genetic variation are heritable and therefore changes in that trait can occur over generations and some genetic variation is not 5
heritable and cannot be influenced by selection. There are two types of heritability: Broad sense heritability: HB = VG/VP Narrow sense heritability: HN = VA/VP What is additive gene action? In this case we can assign value to each of the alleles at a locus. For example A1 = +10g, A2 = +20g, the following genotypes have different sizes: A1A1 = 20 grams A1A2 = 30 grams A2A2 = 40 grams Alleles that act in an additive fashion exhibit no dominance. Heterozygotes thus fall exactly intermediate between the two alternate homozygotes. Genes that act in an additive fashion allow populations to evolve far beyond the current limit of phenotypic variation. Here is an example of additive gene action at two loci: B1B1 B1B2 B2B2 A1A1 2 3 4 A1A2 4 5 6 A2A2 6 7 8 It is the narrow sense heritability that is important in determining both the rate and the response to selection. The expression of heritability is complicated it depends on the number of genes influencing the trait, the frequencies of alleles at these loci, and the extent of dominance and epistasis. There is another fundamental problem with the concept of heritability it is specific to the population and environment in which it was measured. If populations differ in the types and frequencies of alleles controlling quantitative traits then narrow sense heritability may differ. If exactly the same alleles are present at the same frequencies in two populations, then narrow sense heritability can differ if the environmental conditions differ. These problems severely limit the generality of estimates of heritability. Estimating heritability. How do we typically measure heritability? There are three main ways: 1. Reduction/elimination of variance components 2. Resemblance among relatives 3. Realized heritability Resemblance among relatives. Suppose we are interested in obtaining an estimate of heritability for growth rate for a salamander. One way to do this would be to perform pair matings between different individuals and then rear the progeny of these crosses under similar conditions (to hold the environmental effect constant 6
among families). We allow the progeny of these matings to reach the same age as the parents. We then take the mean of each pair of parents - this is called the midparent value. We then take the mean of each set of progeny - we can call this the offspring value. Cross Midparent (cm/day) Offspring (cm/day) F1 x M2 2.34 3.65 F3 x M4 3.56 2.89 F2 x M1 2.03 2.45 We can then estimate heritability by regressing the offspring values against the midparent values. The slope of this regression line is an estimate of heritability. Other comparisons are possible that give rise to modified estimates of narrow sense heritability. Comparison Midparent-offspring Parent-offspring Half-sibs First cousins Correlation HN 1/2HN 1/4HN 1/8HN When comparisons are undertaken among individuals that are more distantly related, the precision of the heritability estimate is reduced. Realized heritability. We can obtain an estimate of what is called realized heritability by estimating the response to selection. Consider the following example. Suppose we wanted to estimate the heritability of body size in mice. Our starting population had a mean size of 124.5 g and exhibited a normal distribution. Suppose we selected the top 15% of the population as parents for the next generation and the mean of this group was 168.4 g. We breed the individuals in this selected group and rear the mice in the same environment as the parents until they reach the same age. Suppose the offspring had a mean size of 154.2 g. The realized heritability can be estimated from the relative response of the selected group Realized heritability = HN= R/S 7
Where R is the response to selection and S is called the selection differential. The response to selection (R) is the difference in the mean between the progeny generation and the whole population. While the selection differential (S) is the differences in the means between the selected parents and the whole population. In this example S = 168.4 124.5 = 43.9 R = 154.2 125.4 = 28.8 thus HN = 28.8/43.9 = 0.656 This tells us that 65.6% of the variance in the starting population was attributable to additive genetic variation. This realized heritability allows us to predict how the population will respond to further selection (at least in the short term). What about the long-term response? Will the population continue to evolve under the imposed selection regime or will the genetic variation become depleted? What maintains genetic variation for quantitative characters? Accounting for the persistence of genetic variation underlying quantitative traits remains controversial. Many models have been proposed. One of the most influential is Russ Lande s, which postulated the existence of a mutation- selection balance at these genes. According to this model, the amount of variation affecting the trait reflects an equilibrium balance between the erosion of variation by stabilizing selection and the input of variation by mutation. The overall balance depends on four parameters: 1. the strength of selection on the trait s 2. the number of loci involved n 3. the mutation rate per locus µ 4. the average effect of an allele on the phenotype. a The adequacy of this model has been the topic of many studies and is widely recognized as being inaccurate in its most important postulates, namely, the ability of mutation to replenish variation lost by either drift or stabilizing selection. Another model first developed by Michael Turelli postulates equilibrium between the effects of mutation introducing variation and its loss by drift this is mutationdrift equilibrium. This idea may seem rather silly it is unlikely that most quantitative traits are neutral. However, the model has been useful in showing that over macroevolutionary time periods, the rate of evolution of these characters is generally slow. So slow, in fact, that divergence of the trait by random drift cannot be excluded. A number of factors have been proposed to account for the maintenance of genetic variation in quantitative traits. Unfortunately, there is little empirical evidence to evaluate their relative importance. The list includes: 8
1. Overdominance - there is little support that overdominance is so widespread to maintain variation of this magnitude. 2. Pleiotropy The idea here is that a genotype at a certain locus may be beneficial for quantitative trait A and bad for trait B. Another genotype would have imparted a high fitness for trait B and low fitness for trait A. Although there is some evidence suggesting life-history characters may trade-off in an antagonistic fashion, there is no evidence that genotypes at any locus do the same. Furthermore, the circumstances allowing antagonistic pleiotropy to operate are rather restrictive. 3. Epistasis In theory epistatic interactions among genotypes at different loci can maintain variation. Although historically there has been little support for epistasis, there is growing evidence that it could play some role in maintaining variation for quantitative traits. 4. Variable selection Fluctuations in the optimal phenotype from one generation to the next can certainly delay the loss of variation. However, random fluctuations in selection will eventually result in the loss of the variation and thus this explanation cannot account for the long-term persistence of polygenic variation. 5. Gene flow Gene flow between populations that differ in optimum phenotypes can maintain variation in each population. Even if the same optimum phenotype is favored in the two populations, the genes contributing the trait may differ and the frequencies of alleles at the same loci may differ. Thus, gene flow can maintain allelic variation underlying polygenic traits. As for epistasis, there is little empirical support for this possibility. What does this mean for changes in allele frequencies? The equation above is summed over all loci and a is the mean phenotype of the AA and aa or homozygous alleles and d is any deviation from additive allele frequency variation due to allele interactions at that locus (i.e. dominance or epistatic variation). Without allele interactions, changes in allele frequencies will cause changes in additive genetic variance. As selection drive alleles to fixation, there is a loss of heritability. Remember that the amount of additive genetic variation influences phenotypic variation and is heritable, but once you ve lost that variation due to divergent or directional selection, there is not as much genotypic or phenotypic variation at that locus in the population. Therefore, lower frequency alleles are more heritable compared to high frequency alleles. For example traits with a high effect on fitness, such has life-history traits, have low narrow sense heritability versus meristic traits that have low fitness effect will have high narrow sense heritability. As traits go to fixation, the additive genetic variation is used up, so 9
to speak, so the greater the effect on fitness, the lower additive genetic variance and the lower the heritability. You may have low narrow sense heritability but still have high broad sense heritability from other types of genetic variation. Divergence among populations. For quantitative traits, we can measure the differential effects of natural selection acting on heritable traits can measure the effects of local adaption. We can measure this: GST = VGB/(2VGW + VGB) In this equation VGB is variation due to differences in additive genetic variation among populations while VGW is mean additive genetic variance within populations. QST = FST if FST is estimated from the allele frequencies at the loci affecting the quantitative trait under investigation. Qst is a measure of differential directional selection on a trait, while Fst is just due to population subdivision and depends on a drift and gene flow balance. If Qst < Fst then natural selection favors the same quantitative trait s phenotype in different populations. If Qst > Fst then selection favors different quantitative traits between different populations. We ve already talked a bit about why different types of markers are important for conservation, those associated with quantitative traits and those that are neutral. We can talk about this some more next class period. FINDING QUANTITATIVE TRAIT LOCI: There are two approaches to finding quantitative traits, top-down and a bottom-up approaches. The top-down approach usually involves finding candidate genes. With candidate genes we usually you have prior knowledge of the function of the gene or that the function of the gene may affect the trait we are interested in. We refer to this as top down, because we begin with the phenotype effects and then look for associations in differences in that gene with phenotypic differences. We look for amino acid protein differences in the alleles that may result in different structural proteins to explain the phenotypic differences. There are certain pros and cons with this approach. First, it allows you to focus your research on the actual gene effect and produce interpretable results that relate to physiology. In addition, you can measure this in natural samples. The cons include a lot of preliminary work and the physiological pathway must be figured out or defined previously. This also means that you may miss out on other loci that we don t have this information for. In fact your candidate gene may only be a minor effect gene or a false correlation. The bottom-up approach involves QTL mapping. Traditionally, there have been two ways to estimate the numbers of genes underlying quantitative traits. One has been to examine the response to selection experiment. Making a few (questionable) assumptions that the effects of all loci are equal and that there is no linkage or epistasis, one can estimate the number of loci underlying a selection response. For 10
example, Dudley and Lambert (2004) estimated that 56 genes were contributing to the response to selection on oil content in corn. Alternatively, one can examine the phenotypic variation in the F2 generation after crossing two parental lines (P1 and P2). A statistical estimate of the effective number of loci underlying the trait is: ne = (P 1 P 2 ) 2 /8V Here P 1 and P 2 are the phenotypic means of the two parents and V is the difference in the genetic variance between the F1 and F2 populations (V = VF1 VF2). New insights are being provided by the ability to map QTL's, or "quantitative trait loci." This is done by melding traditional breeding experiments of quantitative genetics with fine resolution linkage maps. A linkage map is a detailed "map" of the location of genetic markers dispersed throughout the genome of the species. Identifying and characterizing QTL loci is going to dominate the field of quantitative genetics for many years to come. Mapping QTL s in non-model organisms is now possible with new methodologies, but often requires ability to breed the populations in the laboratory. To perform QTL mapping you need a high-resolution linkage map of the target species. These markers can be either microsats, SNPs or even AFLPs. Developing a high-resolution map for a species is a considerable undertaking, it requires the developing and mapping of hundreds to thousands of polymorphisms. To map QTLs one also needs to generate linkage disequilibrium between the markers and the quantitative traits of interest. Why is this? Well, if the QTLs are in linkage equilibrium with the markers our ability to identify their numbers and locations is impossible! To generate linkage disequilibrium, it is common to cross lines that have been made homozygous by inbreeding. These are crossed to form F1 and F2 populations that have highly significant levels of linkage disequilibrium. The premise of identifying QTLs is based on what is called a LOD score. A LOD score is the likelihood ratio of the probability of having an association between a marker and a QTL assuming genetic linkage (with a recombination rate between the genes of r ), divided by the probability of having an association assuming no linkage: L = Pr (association r = r ) Pr (association r = 0.5) This ratio is also called the odds. The LOD score is the logarithm of the odds. A LOD score of 3 or greater is considered as statistically significant evidence for linkage between a marker and a QTL. A LOD score of 2 or less is significant evidence of no linkage. 11