the goal of genetic analysis is to determine how phenotypes or traits such as the color of flowers or the yield of crops or human diseases are inherited or transmitted through generations is a particular trait dominant or recessive or is it autosomal or x-linked when we are working with plants or animals that are models for the study of genetics in the in the lab then we can figure out the the inheritance of crates by picking individuals with particular phenotypes and then crossing those or meeting those individuals and determining the frequency of various phenotypes in in the progeny as we have done before however this method is not possible when we are trying to determine the inheritance of human traits especially human disease traits so geneticists use what's known as human pedigree analysis where you study the result of meetings or or the phenotypes of progeny produced by meetings after the fact by building pedigrees or family trees that show the um the relationships between individuals as well as the phenotypes that those individuals have often this kind of analysis is done with respect to human diseases and so phenotypes are usually whether they are affected or have the disease or they don't have the disease it is important that you familiarize yourself with the different symbols that are used in drawing these pedigrees for example males are represented as squares females circles a mating between a male and female is indicated with a horizontal line connecting the two individuals that are affected so in the context of a disease if they have the disease or have a particular phenotype or trait are shown as filled squares or circles whereas unaffected individuals are shown as open squares or circles heterozygotes for autosomal recessive traits or carriers of diseases are indicated by half filled squares or circles sometimes if you have a carrier of a sex-linked recessive trait they are indicated as a circle with a dot inside it note that only females can be carriers of sex-linked recessive alleles since if um a male had the affected x chromosome they would always have the phenotype or the disease finally individuals who have uh who are not alive are indicated by putting a diagonal slash on the square or the circle as the case may be next let us use an example to practice human pedigree analysis and before we dive into the problem let me just say that there are two basic types of pedigree analysis problems type one is what i would call deductive problems where you have been given how the the trait or the disease is inherited so you have already been told it's recessive it's autosomal x-linked and so on and the goal is to use logical reasoning deductive reasoning to determine the genotypes of the individuals in the pedigree and and the probabilities of individuals having a trait or not having a trait and so on type two problems are what i would call inductive problems and i call them inductive because they require inductive reasoning where you are presented with a pedigree but you haven't been told how the trait is inherited and the goal of the problem is to determine whether this trait is dominant or recessive or x-linked or autosomal and so on okay a recessive allele inherited in a mendelian manner causes the disease cystic fibrosis a phenotypically normal man whose father had cystic fibrosis marries a phenotypically normal woman from outside the family and the couple have a child who has cystic fibrosis the couple is considering having a second child what is the probability that this child would have cystic fibrosis now in these problems the very first thing to do is to start drawing the pedigree and let's go ahead and do that and so we have a phenotypically normal man and so we will draw a little square and this individual had a father who has cystic fibrosis so the father is of course a square but it's a phil square because this individual had cystic fibrosis and obviously there is a mom and we don't yet know what her phenotype is and then this man goes ahead and marries another phenotypically normal woman and so they marry and so we'll use an open circle to represent his wife uh who's phenotypically normal and then the child uh the the couple have a child who has cystic fibrosis and when you don't know the sex of an individual you use a rhombus to represent that individual okay and now the couple is going to have or are considering having a second child and the question is what is the probability that this child would have cystic fibrosis if the first step was drawing the pedigree our second step should be to write down as many genotypes of these individuals as we can so let's go ahead and choose some symbols and i'm going to say f1 is normal this is really arbitrary i like the subscript like f sub 1 and f sub 2 as symbols rather than big f and little f because the big f and little f can get confusing especially with letters like c so f2 is you have the disease you have cystic fibrosis and we've been told that cystic fibrosis is recessive and therefore f1 over f2 the heterozygote would be phenotypically normal all right the easiest genotypes to write down would be that of the grandfather and the first child that is affected by cystic fibrosis because it's recessive they must both be f2 over f2 what about the man and the woman well they're phenotypically normal as indicated by the opens uh square and circles and they could be either f1 over f1 uh homozygous for the f1 allele or they could be heads f1 over have f2 and since we don't know we can indicate that uncertainty by writing f1 over hyphen or f1 over dash and this notation will become very useful later on in the course however we would need to determine the exact genotypes of the man and the woman in order to be able to compute the probability that the second child has cystic fibrosis now the man must be a heterozygote f1 over f2 since his father is homozygous for the f2 allele and therefore this man must have at least one f2 allele what about the the woman his wife well she must also be a heterozygote she must have the f2 allele because their son has two f2 alleles and must be getting one from the father and the other from the mother what about the grandmother do we need to know her genotype and in this case we don't really need to know her genotype in order to determine the probability that the second child will have cystic fibrosis since we know the exact genotypes of both the man and the woman all right let's go ahead and compute that probability and there are at least two ways of doing this one is of course the old familiar punnett square and you can go ahead and work out the punnett square of the cross between the man and the woman and determine the the proportion of the progeny that will have that will be homozygous for the f2 allele which would be a quarter as we have worked out before but i also want to demonstrate to you the use of the product rule here so the probability of having cystic fibrosis is the probability of being homozygous for the f2 allele and therefore two events have to happen which is the child must get the one f2 allele from father and he must also get the other f2 allele from the mother and these are independent events because the probability of getting uh an f2 sperm is not dependent on the probability of getting the an f2 egg and therefore we can go ahead and multiply them to determine the probability of getting an f2 from both the father and the mother so there's the and clause here and the probability of getting f2 from the father is a half because the father is a heterozygote so half the sperm carry the f1 allele and half the sperm carry the f2 allele similarly the probability of getting f2 from the mother is a half and therefore the probability of the second child having cystic fibrosis is one quarter next let's um consider a type 2 problem where we are given a pedigree and we have to infer the mode of inheritance of the trait whether it's dominant or recessive and so on now strictly speaking you cannot infer the the mode of inheritance of a trait unless you have looked at the phenotype in large numbers of progeny and determine their ratios however we can look at hallmarks of different traits in in pedigrees and we could make pretty good guesses about how the trait must be inherited but these are not going to be slam dunk conclusions of the sort you can make when you do crosses with model organisms in the lab so one thing you see with recessive traits is that they tend to skip generations and the reason is that the the progeny of homozygous individuals are heterozygous and do not show the trait however the trait will reappear in the children of the heterozygotes because you will start to get individuals who are homozygous for the recessive allele in contrast dominant traits tend to appear every generation since you just need the one dominant allele in order to show the phenotype recessive traits tend to be relatively rare and so you will have sparse pedigrees or you know the there are fewer affected individuals since the probability of getting two of the the uh two of the same allele is going to be lower than the probability of getting just one allele as is the case in dominant rates and therefore dominant rates tend to be more common there are some hallmarks for x-linked recessive traits as well one key hallmark is that more males are affected in x-linked recessive traits and that's because in females you would need to have two of the affected x chromosomes in order to show the phenotype whereas males need only one x since they are x y um in autosomal recessive traits by contrast males and females are affected equally and that makes sense since the the trait is not linked to the sex chromosomes um other hallmarks of excellent recessive traits are that sons of affected mothers are always affected and that's because an affected mother is homozygous for the affected x chromosome and the sun gets their x chromosome from their mother then therefore the probability that they will have an affected x chromosome and have the trait is 100 percent another hallmark or another inference you can make about x-linked recessive traits is that unaffected daughters of affected fathers are carriers and that's because these daughters will receive one of their x chromosomes from the father and since if it's an affected father then that means they have the x uh chromosome that carries the allele for the particular trait now let's use these hallmarks to try and infer the mode of inheritance of um the the these particular pedigrees so in the first pedigree we see that the trait seems to appear in every generation that suggests that the trait is dominant rather than recessive again as i said before this is not slam dunk you can't prove that it's dominant however the fact that it comes in every generation is highly suggestive that this is a dominant trait and the next thing we would need to decide is whether this trait is autosomal or is it an x-linked trait and the hallmark we may want to look here or look for is the ratio of affected female to affected males and it appears that um the equal numbers are um yeah exactly equal numbers of males and females are affected and that would make us lean towards deciding that this is an autosomal trait rather than an x-linked one we should also try and write down the genotypes of as many individuals as possible for practice and i'm going to say that z1 is the dominant allele and z2 is the recessive allele now since this is a dominant trait all the open circles must be z2 over z2 what about the affected individuals well the affected individuals are at least z1 over dash because they are showing the phenotype for some of these individuals we may be able to say a little bit more um than um z1 over dash for instance this individual is the progeny of an affected individual with an um a recessive a homozygous uh an individual who's homozygous for the recessive allele and therefore this individual must be z1 over z2 now let's look at the other trait which appears to be a recessive trait since there are so few affected individuals furthermore both the affected individuals are progeny of unaffected parents and that can clearly only happen in a recessive trade we must also decide whether this is an autosomal trait or an x-linked trait there are two affected males but no affected females and that suggests that this is in fact an x-linked or a sex-linked trait rather than an autosomal one let's also go ahead and write down as many genotypes as we can first we should choose some symbols i'm going to say xn is the dominant normal allele of the x chromosome and x a for x affected is the um the the affected individual on the affected x chromosome that gives the affected phenotype so the male of uh genotypes are really easy to write down um if if you are affected then you must be xa y and if you are not affected then you must be x and y for all of them females it will be hard to it will be harder to infer the genotypes we can certainly say that females must be x n over dash since none of the females are affected over here so they're either x n over x n or x n over x a um for the mothers of affected males we can go a step further and say that they must be xn over xa since males get their x chromosomes for their from their mothers their mothers must be carriers or heterozygous for the x-linked trait