i'm dr d dr d dr d dr d dr d dr d dr d explain stuff hey everyone dr d here and in this video we are going to be covering chapter 3 from our genetics essentials concepts and connections fourth edition textbook this chapter deals with the basic principles of heredity and when you think of heredity the name that should pop to mind is gregor mendel now recall that we've covered a lot of gregor mendel's seminal work in biology 1406 including the monohybrid cross and the dihybrid cross and how you know those led to the principles of segregation of alleles and the principle of independent assortment and how that ultimately led to our understanding of heredity and how that led to our understanding of how heredity is linked to meiosis events in meiosis dictate heredity the concept of dominant alleles and recessive alleles so on and so forth and how all that ultimately led to pun and square analysis and and all of that is covered in biology 1406 so if you need a refresher from biology 1406 there's this link right here i'll also throw a card up above so that you can get access to that from this video um again if anything from this chapter is fuzzy with regard to the monohybrid dihybrid cross those concepts i just mentioned this is a nice refresher video for you but let's go ahead and get started and see what we can cover here gregor mendel known as the father of modern genetics he did a lot of studies with pea plants and those pea plants gave insights to how heredity works he used a model organism remember we talked about model organisms in chapter one and his model organism was pi some sativa the pea plant and it was a wonderful organism to use because it's very easy to grow there's many different let me show you there's many different phenotypes you can have yellow pod color green pod color inflated pods constricted pods you can have flowers at the axial location you could have flowers at the terminal location tall plant short plant seed coat color you can have gray coat around the seed or a white coat around the seed seed shape round or wrinkly you could have seed colors yellow and green do you see the the vast array of variety here between types and phenotypes and also what really helped him was the the fact that a lot of these tended to have a clear dominant and a clear recessive allele and they also tended to be on different uh chromosomes so you could have independent assortment working properly so he used the proper experimental model he used the proper uh genetic model organism and because of that he was able to unravel the mystery of heredity again this should be evidence of how just how important these model organisms are these genetic model organisms are okay so he used an experimental approach and analyzed results mathematically he this is actually understated a lot of times how important it was that he used math and his understanding of statistics in order to make these uh stu to do these studies uh what mendel understood because he studied at the university of vienna and he he studied under some famous physicists he actually even studied other christian doppler you know the the doppler radar fame the the guy who came up with the whole concept of the doppler effect you know which led to the doppler radar uh he he studied under these uh brilliant minds at university of vienna at the time and he uh knew what a good mathematical study was a good experimental study with a high n number you know what n number means number of uh uh subjects in the study so he didn't stop at one plant and then make conclusions he did this hundreds of times and got thousands of offspring and then from having a high enough n number he was able to make statistically sound observations and come up with this one to two to one genotypic ratio or is three to one phenotypic ratios etc you cannot come up with those ratios if you're only doing a couple of plants you know so the math he he was using the statistics he was using were sound and that's how we got our clear cut ratios that we know and he studied uh easily differentiated characteristics it was very easy to see if there's yellow pods or green pods etc and guess what the best perk of all the best perk of all he got to eat his results right i mean how many scientists get to go ahead and make pea soup at the end of the day and eat their results so let's move on again this should all be review but you should know what a gene is you should know what an allele is locus genotype heterozygote homo homozygote phenotypic trait uh the characteristics or character but uh again this is review that you should definitely know from biology 1406 so please go ahead and brush up on this i i will briefly touch on this even though we shouldn't have to but let's go ahead and briefly touch up on this a gene an inherited factor so that that helps determine a characteristic a gene is not an not an interchangeable term with allele i want you to know that allele is a type of gene allele let's look at the proper definition one of two or more alternative forms of a gene does that make sense so if the gene is eye color an allele would be brown or blue or green does that make sense allele and gene are not interchangeable terms allele is a alternative form of a gene okay locus locus is the specific place on the chromosome where the allele lives where that particular gene lives a genotype is the set of alleles possessed by an individual the set so allele is brown or blue but what is my genotype my genotype could be brown brown brown blue blue blue does that make sense genotype means what set do i have what alleles did i inherit from my parents i got a brown from my dad and a blue from my mom that's my genotype brown blue so you see genotype and allele are not the same thing and then heterozygote heterozygous means an individual with two different alleles so if if i'm a heterozygote for eye color i have a brown eye color allele and a blue eye color allele so that means my genotype is brown blue does that make sense homozygote is the opposite i have two of the same allele i inherited brown eye color from my mom and brown eye color from my dad so my genotype is brown brown so homozygote okay phenotype phenotype is what you see it's the appearance or manifestation of the characteristic what you see so if i have brown eyes that's my phenotype even if i carry a blue eye allele you can't tell because the the brown eye color is is dominant to the to the recessive uh blue eye color and the characteristic the characteristic is an attribute or feature possessed by an organism so uh the characteristic could be eye color right so again here's an example of alleles this is the concept of the allele if this is let's say chromosome 3 uh from my mom i might have gotten allele r so let's say brown eyes if this is chromosome 3 which would be known as the homologous chromosome from my dad it would have allele r as well so this is the lower the recessive version so that might be blue eyes uh allele from my dad does that make sense now concept check time what is the difference between a locus and an allele well think about it we just covered that on that table earlier a locus is the position of the allele on the chromosome you see so you see the locus would be here on the chromosome so if this is chromosome 3 i would say allele ours locus is at this spot on chromosome 3. does that make sense whereas an allele is an alternative version of the gene and then what is the difference between genotype and phenotype genotype again is the set of chromosomes i have my genotype could be brown brown it could be brown blue but phenotype is what you see you see brown eyes now just because you see brown eyes does not mean that you know my genotype does it because my genotype could be brown brown or my genotype is brown blue but you don't know my genotype simply by looking at my phenotype do you so phenotype is what you see a genotype is what you have you're the set of chromos of alleles you have right does that make sense now sometimes you can tell the genotype if you see the phenotype but that's only if someone's showing the recessive phenotype so if i'm showing blue eyes then you could pretty much guess that my alleles are blue blue because that's the recessive allele and the only way i would be showing blue eyes is if i have two recessive alleles so sometimes you can guess an organism's genotype from the phenotype and sometimes you can't guess an organism's genotype from its phenotype it depends if you're looking at the recessive phenotype or if you're looking at the dominant phenotype if that makes sense now remember from biology 1406 what can you do if you see the the phenotype but you want to determine the genotype that's a test cross you have to cross that organism with a recessive organism and then depending on the results of that test cross you can tell whether it was a heterozygote or a homozygous dominant organism so that's all uh what we answered here so let's hop into the monohybrid cross this was again one of mendel's seminal work where he showed the principle of segregation of alleles by doing the monohybrid cross and what is the minor hobbit cross it's a cross between two parents that differ in a single characteristic so conclusion one one character is encoded by two genetic factors conclusion two was two genetic factors or alleles separate when gametes are formed conclusion three the concept of dominant recessive alleles and conclusion four two alleles separate with equal probability into gametes these were four very very important conclusions of mendel's studies post monohybrid cross analysis so when mendel did his monohybrid cross these were four very important conclusions uh that were accurate conclusions that he made okay so let's go into the monohybrid cross and how the monohybrid cross work so what you would have to do is start with two parents these are parents and it was very important to start with homozygous parents so you would start with one parent that is one parent that is a homozygous dominant and one parent that is homozygous recessive for the particular trait okay so in this case it looks like they were looking at wrinkly versus round uh peas so one of these parents was homozygous for wrinkly peas one of these parents was homozygous for round peas and then what you do is you take a paintbrush you pick up some pollen from the stigma oh i'm sorry you pick up some pollen from the anther the male parts of this flower you pick up the pollen from the anther which is essentially the sperm and then you deposit that pollen on the stigma of another plant and this is called cross fertilization you're taking pollen from this homozygous plant and you're depositing on this homozygous plant this female flower so you got the male flowers pollen to the female flower anther and there you go uh you check out the embryos each pea serves as an embryo which you can then plant uh and once that once that embryo grows once it germinates and grows up into a new flower into a new plant you can then study the peas from those plants so what did we find the parents were homozygous the parents were homozygous for round and the other parent was homozygous for wrinkly you did the cross fertilization in the f1 generation the the offspring of this p generation you found that all of the p's were round so what should that tell you about the uh the the dominance and recessiveness of of round well round was the dominant allele round is the dominant allele the f1 generation will show you which one is the dominant allele now remember that these this was a homozygous for round so this p plant contained capital r capital r right two alleles for round and this pea plant contained two alleles for wrinkly which means when this pea plant made sperm the sperm contained one copy of big r when this when this p made eggs it contained one copy of little r and so when the big r sperm met the little r egg these are all what's called uh the hybrids or the heterozygotes all of these are heterozygotes they're also known as the hybrid that's where the monohybrid cross got its name these are all considered hybrids so each one of these p's is going to be big r little r and because big r is round and it's dominant uh then they all show the round trait now the next step was to self fertilize each of these plants self-fertilize and then once you self-fertilize you you then plant these peas and you study the offspring and the offspring were uh look like 304 five thousand four hundred and seventy four round seeds eighteen hundred and fifty wrinkly seeds and see because you did it thousands of times because mendel did it thousands of times he was able to get accurate ratios so he figured that there was actually a three to one ratio of round to wrinkly in the f2 generation in the grandchildren essentially of the parent generation and you saw that yes the the recessive allele comes back or i should say the recessive phenotype comes back and it always comes back in a three to one ratio when you have a clear-cut mendelian um allele or mendelian trait uh in the f2 generation so conclusion the traits of the parent plants do not blend remember the blending hypothesis from chapter one how i told you that's a false hypothesis you didn't get some wrinkly smooth wrinkly round plant peas you got either round or wrinkly traits do not blend so the parent that there's no blending going on so right there mendel disproved the blending hypothesis and then it says although the f1 plants display the phenotype of one parent they must have had the genetic information from the other parent otherwise how did the wrinkly come back in the f2 generation both traits are passed on to the f2 progeny in a three to one ratio so because of this study he was able to determine that each individual organism has two bits of information for any one trait you know two two now we know them as two alleles for every gene right uh he would have called it two uh variety of every characteristic right very interesting stuff so again what does this mean if i have two variety if i have two bits of information for my trait i can either pass on this one or that one right so uh my alleles segregate when i form the sperm or the egg when i have progeny my project my let's say for example i'm brown eye blue eye for my eye color and brown eye blue eye for my eye color right that's my genotype let's say that well i either pass on to my child brown eye information or i pass on to my child blue eye information but not both right does that make sense so my alleles get segregated to my progeny does that make sense and that's what the monohybrid cross taught us look at this the monohybrid cross taught us the principle of segregation of alleles that's mendel's first law you see each individual diploid organism possesses two alleles i have brown eye blue eye for any particular characteristic like eye color these two alleles segregate when gametes are formed so my sperm either gets brown eye information or blue eye information not both right and one allele goes to each gamete right you see that how powerful that is just by studying this humble pea plant he was able to make this powerful powerful conclusion and then the concept of dominance too he was able to derive the concept of dominant recessive alleles from this study as well two powerful conclusions from one study with the humble pea plant it's amazing when two different alleles are present in a genotype only the trading encoded by one of them which is called the dominant allele like brown eye color is observed in the phenotype isn't that powerful so again what did the monohybrid cross teach us it taught us the principle of segregation of alleles and the concept of dominant recessive alleles so here this is a figure showing mendel's monohybrid cross revealed the principle of segregation and the concept of dominance again it's it's a it's essentially what we've already covered but let's look at it one more time so in the parent generation again i told you that you in order to make this cross work in order to do the monohybrid cross properly you have to start with uh homozygous parents look you have to start with a homozygous round for instance round pea color plant and you have to cross it with a homozygous recessive a homozygous recessive p color plant so this would be a wrinkly plant if you don't start with homozygous plants your ratios are going to be off and your results don't make any sense and that's why it was so important that actually before mendel knight had come along ta knight i believe and he had shown that you have to start with what are called true breeders true breeder organisms if you're going to do a monohybrid cross study you have to start with true breeders and what does a true breeder mean it means you have to start with a homozygous plant pea plant that means one that has two of the same allele and you have to cross that with another homozygous that has two of the same recessive allele and that's the only way to get these ratios to work properly does that make sense so again mendel crossed the plant homozygous for round with a plant homozygous for wrinkles if you don't start with homozygous aka true breeder parents you're not going to get the right results okay and uh by the way uh big r big r means that you're a diploid organism right you see this big r big r means that you're a diploid organism look here let me show you something just gonna hop back look if if i'm big r big r one big r is on my dad's chromosome three one big r is on my mom's chromosome three for instance does that make sense but do you guys remember the concept of meiosis that we talked about in meiosis when the sperm or the egg are formed do my sperm or egg get both of these alleles these are homo these are homozygous i'm sorry homologue these are homologous chromosomes does that make sense this is my dad's chromosome 3. this is my mom's chromosome 3 that i inherited right does my sperm cell get both of these no my sperm cells are haploid i'm diploid i have two chromosome threes but my sperm is going to be haploid it's either going to get this chromosome 3 or this chromosome 3. does that make sense you guys follow me so that's why you see here this parent is big r big r but it's gamete uh let's say the sperm for instance is gonna be big r or big r it can't have two big r's you can't have two of the same allele in one sperm so the sperm can only be big r or big r that's it you can't have a sperm that's big r big r because that would suggest that the sperm is diploid and the sperm is not diploid it's haploid right you only have one of every allele because you only get one uh homologous chromosome hopefully this makes sense so the sperm from this organism is going to be big r this the eggs from this organism are going to be little r so what that means is when you cross this guy with this one you your offspring are guaranteed to be big r little r does that make sense because the big r sperm is going to meet the little r egg or vice versa okay so if a big r sperm meets a little r egg that means each and every one of your offspring is going to be big r little r its genotype is going to be big r little r and if we know that big r it means uh round seeds and little r means wrinkly then what is going to be the phenotype of this particular p that's right it's going to be round because whatever the dominant allele is that's going to express itself into the phenotype it's going to show in the phenotype so a hundred percent of the f1 generation is going to be big r little r and it's going to have the phenotype round right so this and by the way in the f1 generation this is called the hybrid this is called the hybrid so if you're wondering why is it called the mono hybrid cross mono means one trait uh it refers to one trait you're looking at just in this case p shape round or wrinkle right one shape uh one trait all right um hybrid means this guy this is the hybrid it's the big r little r hybrid it's a hybrid of the round and the wrinkly right this is the hybrid now what you really care about well actually the f1 generation is is informative because it tells you which one of the alleles is the dominant allele right in this case the round is the dominant allele but what you care about now is the f2 generation what happens when i take this p and i this pea plant and i self fertilize it self fertilize it remember um flowering plants are special because you can self fertilize them they make the pollen and the egg they make the sperm and the egg so you can you can self fertilize pea plants so if i took this plant and i fertilized itself not cross fertilized with another plant but fertilized itself that means this guy makes the sperm and the eggs does that make sense this plant makes the sperm and the egg and what could be in the sperm when look during gamete formation what could be in the sperm let's say this is the sperm well the sperm i can remember the sperm can either get this r or this r you can't have both r's because they are on homologous chromosomes does that make sense that would uh you're going from diploid to haploid right so the sperm could have a big r right so some sperm are going to have a big r and then half of the sperm are going to have a little r does that make sense and if you're not just the the the male but you're also the female that means your eggs are also going to get a big r or a little r you see that so now now so what that means is this organism if it self fertilizes it can make sperm that are big r or little r it can make eggs that are big r or little r so then we need to solve so think about it this big r sperm could fertilize this big r egg giving you big r big r this big r sperm could fertilize this little r egg giving you big r little r or what else could happen this little r sperm could fertilize this big r egg giving you big r little r this little r egg could fertilize this little this little r sperm could fertilize this little r egg and give you little r little r so all of those are equally probable aren't they all of those events could happen and that's exactly what you see when you cross these sperm with these eggs these are the possible combinations you could get if this sperm met that egg you would end up with big r big r offspring round offspring homozygous dominant is what they call them homozygous dominant offspring that are round if this sperm met that egg that's equally likely to happen that's big r little r isn't it big r little r which is equally likely to happen and that's going to give you a round round p but it's going to be a heterozygote if this little r met that big r that's going to be little r big r and that's going to give you again a round around seed and that's equally likely to happen but it's also a heterozygote or you know another thing that's equally likely to happen is this little r sperm could fertilize this little r egg and that is another equally likely event but in this case you would end up with little r little r um genotype offspring and that would be a wrinkly offspring so again this is how you end up with your three to one ratio look uh a quarter uh a quarter of these are big r big r a quarter r big r little r a quarter r little r big r so actually actually three quarters three quarters are going to be round does that make sense and only one quarter is wrinkly so that means there's a three to one ratio of round to wrinkly so one quarter is homozygous dominant one half are going to be heterozygous and one quarter is going to be recessive and that's where your one to two to one ratio of genotype comes from you guys remember so this is actually very important for you guys to understand so maybe i'll you know what i'm going to do i'm going to walk you through this real quick in a in a in a genotypic let me show you something this is very important for you to understand in in the monohybrid cross what did we see the phenotype phenotypic ratio what was the phenotypic ratio we just talked about three dominant two one recessive right but then the i might also ask you what is the genotypic ratio what is the genotypic ratio of the monohybrid cross that's a different question isn't it think about it uh the phenotype means how many rounds versus how many wrinkle in the f2 generation but the genotypic ratio means how many are big r big r how many are big are little are how many are little are little are right does that make sense uh in that case how many big our big r do we get one quarter right how many big r little r's do we have and by the way this one is considered big r little r uh i usually like to write the capital letter first right so how many big r little r's do we have it looks like one quarter plus one quarter which would be two quarters right does that make sense um or one half and then how many little are little r's did we get look here that's right we got one so you need to know this a hundred percent you need to know that in the f2 generation of a monohybrid cross uh you're going to end up with a three to one phenotypic ratio of dominant to recessive but a one to two to one ratio genotypically which means one homozygous dominant big r big r two heterozygotes big r little rs and one homozygous recessive little r little r okay i hope that makes sense uh i i know it is a lot to take in but hopefully it's a lot of review from biology 1406. so this is showing you in a f2 generation right what happens if you self-fertilize these and then move on to the f3 generation right so we're not going to touch on that so much but now you know at least how to read the the the genotypic ratios how to read the phenotypic ratios how the phenotypes work how the genotypes work how the how those genes are passed on how gametes are formed you know which is very very powerful stuff and again like i said if anything seems confusing go back to this link i have at the beginning to the biology 1406 review of the monohybrid and dihybrid cross it's it's going to go into all this detail again step by step so that you understand so let's do a quick concept check and then take a break um and we will come back with more so concept check time how did mendel know that each of his pea plants carried two alleles encoding a characteristic this was his powerful powerful observation isn't it the principle of segregation of alleles that every individual has two alleles for every trait well didn't didn't he see in the in the hybrid in the f1 generation didn't he see just one phenotype but then in the f2 generation the recessive phenotype reappeared this suggested that the f1 hybrid even though it was round it still had wrinkly information right so let's see what they say the traits encoded by both alleles appeared in the f2 progeny even though they one of them disappeared the recessive one disappeared in the f1 progeny and in the f1 does that make sense so very very important stuff again let's take a quick break time with gizmo and wicket and we'll come back strong to finish off this chapter what do you say [Music] all right welcome back from break time with gizmo and wicked let's go ahead and get started so believe it or not mendel did all of this work not knowing anything about the importance of chromosomes the importance of genes this was all pre uh sutton right so sutton came along and brought us a chromosomal theory of heredity that the inheritable material this the genes as essentially the genetic material is found on the chromosomes the chromosome is the heredity material right and our understanding of meiosis allowed us to make sense mechanistically of mendel's findings so now knowing how meiosis works with you know meiosis one meiosis ii how there's crossing over happening how there's independent assortment happening by knowing that now we can make sense of mendel's findings so let's take a look here inside this cell the two alleles of genotype rr are located on homologous chromosomes so this would be your uh you know parent cell your parent cell has uh two homologous chromosomes with allele big r and allele little r so this would be like the hybrid of mendel's study the f1 hybrid and then during chromosome replication you know s phase all of the chromosomes are copied so now you have sister chromatids big r big r sisters little our little are sisters then during prophase one those separate you know the cell splits and you end up with two haploid cells right two haploid cells and then you have anaphase one or you have crossing over during prophase then you have anaphase one where independent assortment happens and then you have anaphase two and you've split all the alleles from one another and this is how you end up with the segregation of alleles you say you see you started with a parent that had two different alleles a big r and a little r and you ended up with gametes that have either big r or little r did you see that so now we can make sense of the principle of segregation of alleles by looking at meiosis and understanding what is happening with the process of meiosis how you go from a diploid parent to haploid gametes the gametes are haploid they only have one allele for every trait for every characteristic and the reason for that is they're haploid they've only in the the the gametes only carry one uh homologue right does that make sense again the parent big r little r after s phase you've copied all the chromosomes during prophase one you have crossing over occurring so there's some genetic variability here and then you separate those uh homologs from one another during anaphase one during anaphase one the homologs separate from one another and then anaphase ii the sisters crumb the the non-identical sister chromatids separate from one another and this results in the product of the monohybrid cross which is the segregation of alleles right this is why i might have brown eye blue eye but my gametes are going to have either brown eyes or blue eyes now after mendel published his seminal findings reginald punnett was able to take these concepts and adapt them to what he called the punnett square where now to simplify things we could take the gamete the gamete types of one parent and place them on top of a square like this and the gamete combinations from the other parent and place them on the other part of the square like this to form what's known as the punnett square so if we have let's say a tall plant and this plant has the genotype big t little t so it appears to be heterozygous for tall big t little t and cross it with a short plant which is homozygous recessive for short little t little t you could predict the outcomes of this cross using what's known as the punnett square the way you conduct a punnett square is pretty straightforward you have to figure out what are the gamete combinations from this plant so that would be this plant is big t little t so what kind of gametes could this plant make you could say well the gametes could have either a big t or a little t because again the gametes are haploid and then you would write these combinations you would write the big t on one side of the square and the little t on the same side of the square so this would be one parent's gamete combination on this side of the square you do the same thing with the other parent the other parent is little t little t so uh the only combination uh that could be in the eggs are little t so you write little t or little t on the other side of the square so this parent's genetic contribution on this side of the square this parent's gamete genetic combination on this type of square then you solve the square if this sperm for instance or to meet this egg then you would get a offspring that's big to your little t so you could solve the square if this sperm met that egg same thing big t little t if this sperm were to beat that egg little t little t if this sperm were to meet that egg little t little t uh so in this case i would say that thanks to the punnett square i was able to quickly determine that the offspring of this cross this p generation cross the offspring would be half tall and half short phenotypically so the phenotype ratio is one tall to one short which means half half half half or you could say two tall to two short one tall to one short either way it's half half it's a one to one one to one ratio genotypically it's also a one to one ratio because it's half big t little t and half little t little t does that make sense so that makes it a one to one genotypic ratio and a one to one phenotypic ratio now let's talk a little bit about probability because sometimes you want to know how how likely is it for an event to occur or how likely is it for an event to occur multiple times in a row you know and to do that we need to understand this concept of the addition rule and the multiplication rule again it's used in genetics to predict the outcome of genetic crosses so the multiplication rule let's start with this one if you were to roll a die and a dice has six sides what are the odds that you'll get a four well that's very easy right it's a one and six chance you have a one in six opportunity a one and six probability of rolling a four now if you roll the dice again if you roll the dice again your probability of getting the four again is one and six right but what are what is the odds of getting a four twice in a row what would what would be your chance of getting a a four twice in a row well that's where the multiplication rule comes in so the probability of getting a four on two sequential roles is one over six times one over six and when you multiply fractions essentially you're multiplying the denominator and the numerator so you're getting 36 right does that make sense so 1 times 1 is 1 6 times 6 is 36. so the odds of getting a 4 twice in a row is one in 36 chances right now but what if you want what if you wanted to know something different what if you wanted to know what are the odds of getting a three or a four when i roll the dice when right when i roll my dice i want to get a three or a four on that roll on that roll you know that in that case i would use what's known as the addition rule if you roll a dice and you want to know if you get a three or a four remember the three is a one and six chance the four is a one and six chance well in this case you would add them together right because you want to get a three or a four on a single row so the probability of getting either a three or a four is one over six plus one over six which equals two over six or one third you have a one third chance one in three chance of getting a three or a 4 on a single dice roll so let's apply this to a genetics problem right the probability of being blood type a is 1 in one in eight people one at eight and the probability of blood type o is one half so what is the probability of being either a or o okay so what does this sound like does this sound like a multiplication rule or an addition rule probability problem well it sounds like an addition rule doesn't it because it's either a or o right so what was a one and eight chance what was o one and a half chance so how do we do that well we have to add well you have to make the numerators the same if you're gonna add so one over eight plus how how can we make this one half out of eight you know something out of eight one over eight plus what about four over eight right if we change the one half to four over eight isn't that the same thing as one half four over eight so one over eight plus four over eight equals five over eight so that makes sense the odds of u being a or o is five over eight now uh there are other there are other aspects to these crosses that i'm not going to touch on this time and that is the test cross i think i briefly mentioned a test cross earlier and that's when you see a dominant phenotype and you want to figure out the genotype then you could apply what's known as the test cross to figure out the genotype of that phenotype but we're not going to you know go into that too much in this course but i will share with you some ratios of simple crosses real briefly here's just a table that you could review on your own of some of the phenotypic ratios for simple genetic crosses like when you get a three to one ratio or a one to 1 ratio and here's some of the genotypic ratios of these simple genetic crosses as well when do you get a one to two to one genotypic ratio when do you get a one to one genetic ratio it's just good handy dandy you know a shortcut sheet for you to take a look at but now let's go ahead and hop into the dihybrid cross and why the dihybrid cross of mandel was so important remember i said earlier that the reason uh his dihybrid cross was so important is because it shed light on how different characteristics are inherited and how different traits are inherited and it really uh made sense of how different traits are separated independently from one another you know during gamete formation and obviously this was called the principle of independent assortment how different traits separate from one another uh randomly so let's look at how you know what what question he was asking and how he showed these results so again it's called the dihybrid cross because he's looking at two different traits not just uh p shape but in this case p shape plus p color right so you're looking at two different traits at once so let's take a look here uh in this case he was looking at a true breeder that means homozygous dominant a true breeder for shape which is round and color which is yellow and he crossed that he did a cross fertilization with a true breeder for wrinkle and green peas and what kind of gametes what kind of gametes could this uh round yellow seed or round yellow pea plant make well it looks like it only has big r so big r could go into a sperm cell and big y could go into the sperm cell are there any other gamete combinations that this parent could make no that's it big r big y and then this parent here is little r little r little y little y what kind of gametes could this parent make again it's little r little y right so if you were to make a punnett square you would have one part of the it would just it would be the simplest square in the world it would be a one by one square this sperm carrying big r big y would have to fertilize this egg little r little y to give you what offspring all of the offspring would be big r little r big y little pie now you might be asking me but dr d you just said the the the gametes are haploid why are there two different why are there two letters inside of this gamete well remember haploid means uh one of the homologous chromosomes both of these r's are on different chromosomes they're on homologs right so you can either get this allele or this allele but not both but either way you can have two different alleles you can have an r and a y because those are completely different alleles does that make sense you can't have two of the same letters in the same gamete but you can have two different letters because the different letters represent different alleles and a lot of times when you're talking about these simple crosses they're going to be on different chromosomes too if that makes any sense so all of the offspring are going to be heterozygotes this would be your your hybrid organism big r little r big y little y this is your hybrid offspring and they are all 100 gonna have the same phenotype which is round and yellow and they are all going to have 100 the same genotype which is big our little i uh big big r little r big y little y and then what's the second part of these crosses what do you have to do now that's right you have to self fertilize you have to self fertilize this you know itself right now to do that what do you need to do first of all you need to figure out what kind of gametes these are the gametes what kind of gametes could this parent make well think about it what are the different combinations of r and y that could go into the gametes well couldn't you have a gamete with a big r and a big y yeah so one of the let's say sperm it could be egg or sperm one of the sperm could have a big r and a big y correct and isn't it equally likely that a sperm could get a big r and a little y uh this one a big r and a little y yes and isn't it equally likely that you could have a little r with a big y and isn't it equally likely that you could get a little r with a little y so would you agree that this parent this uh f1 generation could make sperm that are either big or big y little r little y big r little y or little r big y and all of those are equally likely yes and so if you were to make a punnett square wouldn't you put all these different sperm on one side of the square and that's exactly what you do you take those combinations i just told you on one side of the square and if you're the mom and the dad you put the same combinations on the other side of the square you see what i'm saying so these would be let's say the eggs these would say b let's say the sperm and so then you solve if a big if a big r big y sperm met a big r big y egg what would be the result big our big r big y big y and then you just keep solving if a big r big y sperm met a little r little y egg you would get big r little r big y little y and you just keep solving and you solve the whole square you see and then you could determine okay what did i get here what is my phenotypic ratio and once you've solved the whole square you'll see that there's a very distinct ratio that occurs and you need to write this down because you're going to get how you want to count and say how many of these are round and yellow that means dominant for both traits so let's count them together how many are round and yellow which means dominant for both traits one two three four five six seven eight nine nine of them are round and yellow so nine round yellow now ask how many are round and green which means dominant for the first trait recessive for the second tray so how many are round and green one two three okay so three round greens so now we have a nine to three ratio of those two now how many are wrinkly but yellow that means recessive for the first trait dominant for the second trait wrinkly yellows look look uh one two wrinkly yellows three one two three yeah yeah one two three there's three wrinkly yellows okay and how many are recessive for both traits recessive for both traits which would mean one what wrinkly and green look at it only one's wrinkly green so what is your phenotypic ratio it should be nine three three one does that make sense so the that's exactly what you get with the with the dihybrid cross you got a 9331 ratio now before i move on i want to show you why this was so important why did mendel even do this you know why was he even curious to try this experiment you know what did it even show us let's look let me tell you so what mendel was trying to figure out was are different traits linked okay are different traits linked so look at this this parent was round and yellow correct and this parent was green and wrinkly so what his question was are are these traits linked together which means if you get a round pea plant does it also have to be yellow is yellow linked to round and if you have a green wrinkly does green and wrinkly have to be linked or or could you get combinations or do they do these traits are they linked or do they assort independently independently um if it's independent you could end up with yellow wrinkly or round green does that make sense if the traits are independent you could get new combinations that you don't see in these parents if they're linked you're not going to get new combinations you're going to get either wrinkly green or round yellow does that make sense that's why he did this cross he was curious do traits assort independently or do traits different traits a sort in a linked fashion and what would you say from his results here what would you say just look at the results here are the traits for shape and color are the traits linked or are the traits independently assorting well i would argue they're independent you know why because i'm seeing new combinations here i didn't see a wrinkly yellow before and i didn't see a round green before either the fact that i'm seeing those now suggests that these are traits that are you know independently assorting and that's exactly what his conclusion was after this study was that the traits are independently assorting so the dihybrid cross showed us what the principle of independent assortment and now we know we could link that to meiosis and what happening during meiosis you remember during metaphase one how the tetrads line up in a random fashion and uh because of metaphase one uh that's why we know that you know this is happening now we can make sense of mendel's studies gametes located on different chromosomes will sort independently okay lucky for mendel shape and color of peace were on alleles on different chromosomes if here's the thing if shape and color were on the same chromosome he would have got different results it wouldn't have quite worked that way and we're going to talk about that in the next chapter we're going to talk about what happens if alleles are on the same chromosome are you going to see independent assortment and the answer is no because they're on the same chromosome but lucky for mendel shape and color were on different chromosomes and different chromosomes do independently assort during metaphase one of meiosis so concept check time how are the principles of segregation and the independent assortment related and how are they different well obviously they're both related in that they are explained by meiosis in meiosis you see the principle of segregation because you start with a diploid cell and you end up with haploid cells at the end of meiosis independent assortment is a part of that process it occurs during metaphase one of that same meiosis event um the fact that those tetrads line up independently of one another during metaphase one uh is the explanation behind independent assortment and the fact that you go from diploid cell to haploid gametes is the def is the explanation for the principle of segregation of alleles and that's explained right here so here's exactly what we're seeing with uh once we've learned about meiosis and chromosomes and alleles you know now we can make sense of mendel's studies again you start with a diploid cell this cell contains two pairs of homologous chromosomes here's like chromosome one for instance and here's chromosome two and then you copy all the dna so you have now the sister chromatids then during anaphase one this is where you've segregated or i should say this is where you've done the independent assortment independent assortment occurs at metaphase one and then those homologs are separated during anaphase one and then during anaphase ii you end up with the segregation of the alleles you end up with the haploid gametes all right let's pick up here with uh chi-square goodness of fit so what if you do a cross like this what if you do a monohybrid cross for instance and you want to check whether the the phenotypic ratios that result are they match your expected ratios or if they might deviate from the expected ratios how could you test that statistically for instance from a monohybrid cross wouldn't you expect a three to one ratio of f2 progeny phenotypically the answer is yes now what if you see numbers that aren't exactly three to one what if they're a little bit off uh wouldn't it be nice if there was an equation or something that you could plug into to determine whether the numbers you're getting are off due to chance or they're off because they're really actually do deviate significantly from that three to one ratio that you expect that's where this chi-square analysis comes into play and why it's useful for geneticists it indicates the probability that the difference between the observed and the expected values is due to chance or not right so let's take a look here let's say i do a simple cross a simple monohybrid cross where i take a purple flower plant that's a true breeder and i cross that with a white flower plant that's a true breeder and in my f1 generation i see a hundred percent purple flowers that's to be expected because this is my hybrid and the purple flower color must be the dominant flower color but then what do i do remember i self-fertilize this plant i self-fertilize and i would expect to see a three to one ratio right i want to see a 3 to 1 ratio but let's say i do my study and i don't have a lot of time to work with i see 105 purple to 45 white and that kind of appears to be a three to one ratio but not exactly now i want to determine statistically with mathematics i want to determine whether this is deviating from three to one in a due to chance or if it really is significantly different from a true three to one ratio so in that case i could use this equation this equation here that i'm outlining this equation is called the chi-square equation and this equation will allow me to plug in and to quickly determine whether the ratios i'm seeing the values i'm seeing match my expected outcomes of three to one or if it's not due to chance if it is actually different from a three to one ratio so hopefully this all makes sense so let's take a look again what did i see i saw 105 purple i saw 45 white and that gives me a grand total of 150 right so that's what i observed that's what i observed what did i expect to see i expected three-fourths of these to be purple so what's three-fourths of my total 150 three-fourths of 150 is the same thing as saying 75 percent of 150 and so that would be 112.5 112.5 is what i expected should have been purple does that make sense and only one quarter should have been uh white so a quarter of the 150 or 37.5 should have been white uh that's what i expected to see so again i expected if it was a if it was exactly a three to one ratio uh i should have seen 112.5 purple and 37.5 white what did i actually see what did i actually observe 105 purple 45 white now i'm going to plug into my chi-square equation to determine whether or not that value those values that i found are statistically significant or just different these are different 45 is different than 37 due to chance or is 105 different from 112.5 due to chance that's what this this equation is going to teach me so let's let's think about this real quick what is this this is chi-square my chi-square equals the sum of sigma means the sum of my observed values minus my expected squared divided by my expected so let me show you how this would work let's plug in my chi square equals uh what is my observed for dominant my observed is 105 minus the expected what was my expected 112.5 uh put that in the parentheses squared over expected what was my expected 112.5 so here you go here's the first part of my equation now for the recessive what was my observed 45 what was my expected 37 over expected 37. so here's my my my completed equation let's solve when you solve you get 56.25 over 112.5 plus 56.25 over one 37 point and when we solve all that we get 0.5 plus 1.5 that equals 2. so our chi-square is 2. our chi-square is 2. that doesn't tell us anything until we plug it into our chi-square table for degrees of freedom this is our critical values of the chi-square distribution which plots the the p-values p-values mean significance values over uh the degrees of freedom what are degrees of freedom let me show you something up so if you have two traits if you have two uh values you're looking at your degrees of freedom are uh you have to subtract one you subtract one from the number of values you have i guess that's the simplest way of putting it so if i have two values i'm looking at i subtract one my degrees of freedom are one does that make sense so when i go back to this table i look at my degrees of freedom i go over until i get to my chi-square value what was my chi-square value wasn't it 2 so i'm about here my chi-square was 2 so i'm actually not quite here this is 2.7 but i'm higher than here so i'm somewhere between 0.5 and 0.1 does that make sense my p value my prob my probability is between 0.5 and 0.1 so my p my chi-square is right here why is this important well i need you to understand that in statistics a p-value is only significant at .05 or lower you see this here p-value is .05 you see the little asterisks that's because that's where significance occurs p05 is where a value is significant where does r value lie is it higher than .05 with our chi-square with with our degrees of freedom or is it lower than .05 with our chi-square well like i said we had the value of two so we're somewhere over here we're well above the point zero five threshold of significance so you see what it says here r chi-square because our chi-square is between 0.1 and 0.5 indicating a high probability that the difference between observed and expected values is due to chance it's not significant unless we got a p-value of .05 or less because our p-value was higher than .05 according to our chi-square analysis we can say that our conclusion should be there is no significant difference between observed and expected values so again our chi squared was two our degrees of freedom are n minus one so two minus one uh um not this chi square our degrees of freedom are based on the number of observations we made two minus one and so we plugged in and we saw no difference so this this tells us that um our our observation of 105 purple flowers and 45 white flowers the only reason it's not exactly what we expected to see was just due to chance it wasn't because this is some special variant of mendel's principles and it really truly is different it's not really truly uh it does it's not deviating from what we expected because it's truly different it's deviating from what we expected because it just was random chance now think about this this is something to uh mull around your head a little bit how could we get our observed values how could we how could we redo this and get our observed values closer to our expected values think about that for a second that will show me that you truly understand this concept how could we redo this experiment and get our observed values closer to our expected values what do you think anyone taking statistics in the past what would a statistician tell you well we know it doesn't deviate due to significant difference it deviates it deviated due to chance think about it this way if you were to flip a coin if you were to flip a penny ten times would you get five and five every time five heads and five tails every time now what if you were to flip that coin a million times wouldn't that get you closer to a 50 50 ratio so what a statistician will always tell you is that more is better more values is better more end more uh counting more flowers not just 105 plus 45 150 but what if we did this with 1 500 better yet what if we did this with 15 000. better yet what if we did this with 150 thousand plants right now we're going to get closer to our expected value does that make sense so one way to get our observed value closer to our expected value is to use large numbers i think the only reason uh we we didn't get our close to our expected values and this is because for such a study 150 uh observe observations is actually kind of low and you're going to get some variability there so hopefully that all makes sense and uh you have an appreciation for the the importance of a chi-square analysis and um you could use this in the future to to to to determine whether the results of your cross are due to chance or due to significant difference so let's do a concept check real quick a chi-square test comprising oh sorry comparing observed and expected numbers of progeny is carried out and the probability associated with the calculated chi-square value is 0.72 what does this probability represent what happens if you have a p-value of 0.72 now the first thing you should think about is is 0.72 higher like greater or less than 0.05 0.05 is the only probability value you really need to understand because .05 means that a value is significantly different it's significant is 0.75 larger than .05 yes 0.72 is larger so that means that oh i gave away the answer let's just go right to the answer it wants to do it anyway the probability that the difference between the observed and expected numbers could be due to chance the reason they observed and expected values are different is because chance it's not because they're actually significantly different hopefully that makes sense now if the value was .007 well then it would be that the observed values are significantly different than the expected values so something must be going on causing that result to be different than what you expected and then that would require you to do more investigation as to well what why is that going on right so now let's jump to another concept here uh the final concept of the chapter which is this concept of pedigree analysis there's a whole field of study on pedigrees if you're trying to trace a disease throughout your family tree it you know there's a whole field of study on this uh you could get you could specialize in family counseling you could become a genetic counselor and genetic counselors a big part of their job is to determine for example what are the odds that your children might uh you know what are the odds that your children might have a particular genetic disorder based on maybe a genetic disorder that runs in your family for instance if sickle cell anemia were to run in your family you would maybe consult with a genetic counselor to see what are the odds that my child might have sickle cell what are the odds because maybe my great grandfather had it and then my mom had it and then on the other side on my spouse's side you know does it run in my spouse's side then there's even more chance of your children having it so uh pedigree analysis makes those types of heredity analysis of gene transmission from generation to generation easy to do so let's look at it a pedigree is essentially a pictorial representation of a family history a family tree that outlines the inheritance of one or more characteristics and when i'm when we're looking at them remember that the the pro band pro band refers to the person from whom the pedigree is initiated so the great grandpa generations ago that had the disorder you know or the trait that you know we're tracing down it doesn't have to be a disorder you might be tracing brown eye color throughout your pedigree uh you know blue eye color or whatever you're trying to whatever genetic trait that you're you're following throughout a family tree now here's a a pictorial representation of uh kind of what we usually see the symbols that we usually see associated with pedigree so a an empty box a clear box is an unaffected person squares are males circles are females and diamonds are sex unknown now when you see a shaded in like this one's shaded in with red when you see shaded in uh squares circles and diamonds these are affected persons so let's say a person with the sickle cell anemia someone with a dot inside uh this would be an obligate carrier someone that carries the gene but does not have the trait right away what does this say about that that trait what right away what what would this say about that trait if there's such thing as a carrier someone that has the gene but doesn't show the disorder what right away what do you know about that that allele you should know that if you if you're a carrier then it must be a trait that is recessive does that make sense so um albinism for example is recessive uh i could have an allele for albinism and not be albino right so i could be a carrier there there are no carriers there are no carriers if you're talking about a dominant dominant disease trait does that make sense now then you have an asymptomatic carrier unaffected at this time but may later exhibit the trait that's when you see this split symbol so for example if it's a if it's a if it's a genetic disorder that could that could present later in life like alzheimer's or dementia then you could have the little line here because we don't know if it's going to present itself or not and it's you know pretty uncertain until later in life heart disease things like this multiple persons would have a number inside deceased person has a diagonal line the pro band which means the first affected family member coming to attention of the geneticist a lot of times you'll have a little p with an arrow that means the first person in your family tree to have that particular disorder and then family history of unknown a person unknown so you have unknown people a lot of times you say oh i had a great uncle who you know i didn't know much about that would be a question mark here here's some more here's some more legends uh some more ways of understanding these trees so family parents and three children so here you have a male parent and a female parent the the horizontal lines mean mating and the vertical lines lead to offspring so these are the parents they had three children these are siblings these are siblings one boy they had one boy and two girls does that make sense so these parents there's mating there's three children one boy two girls and do any of these have a disease no because it's not shaded in right adoption adoption uh you have the brackets enclosed adopted persons so if you have a brackets around that's an adopted person so the adopted person had their own parents so this boy had uh their his own parents and then there was they were adopted he was adopted into this family so this would indicate that you know you really can't take those genetics uh in you can't really look at the the adoptive parents as contributing to him because he's from a whole another family tree twins twins uh if they're identical twins you've got not just the you've got kind of a branch with a line across non-identical twins you've got the branch with no line across remember these are like fraternal twins uh identical twins there is a big difference there and then unknown whether the twins are identical or unknown that could be a question mark here consanguinity this is mating between related persons so here you have parents who had offspring those offspring had children and then those cousins made it so this is a first cousin here from the this this uh aunt uh the aunt of this person uh married the um the daughter they the but the aunt now the aunt of this person had uh this boy and then the uncle of this boy had this daughter and these cousins these first cousins uh made it so this this here is an example of inbreeding so let's take a look at some of these pedigrees you can have autosomal recessive traits these would be things like albinism which is a recessive trait and then you can have autosomal dominant traits as well these are diseases that are passed on in a dominant fashion so let's take a look let's start with a recessive trait you have the parents this is the great grandpa great grandpa and great grandma they had three three children two females and a and a son it looks like number three was an affected person number three was an affected person number two and number four were non-affected or did not present the disease so you know what that tells me right away is that this is a recessive trait because it didn't appear in the parents i know it's a recessive trait and you know what else i know i know that the the the father and the mother were carriers that means that um this this person had a normal or wild type and a mutant or disease allele and this mom had a normal wild type and a disease uh trait uh allele as well and then uh so the other two um the this this female and this male appear normal appear wild type but they could very well be carriers does that make sense they could very well be carriers i'm not sure why they didn't draw in the carrier you know they should have drawn drawn in that they're carriers but maybe they didn't know for instance maybe you know there wasn't any information so they're trying to figure it out so anyway this son married someone and had two children a male and a female this daughter married someone and had three children a male and two females this this person's not hasn't had any children yet and then the cousins married the cousins uh mated right the cousins married this male married first cousin and they had four children and it looks like one of their children has the disease trait one of their children has the disease trait so what does this tell you about these two first cousins it should tell you that they're both carriers does that make sense they are both carriers which means that both of them are heterozygous for this particular trait now this is why uh uh inbreeding is not you know something that's that's usually healthy for a population because a lot of times your family tree might have a recessive disorder a recessive genetic disorder and as long as you're marrying outside of your family the chances of your recessive disorder being you know complementing your spouse is lower than if you make within your family the chances of your uh recessive disorder being complemented by the same recessive disorder and presenting itself in your children is much higher does that make sense so the odds of having children with genetic disorders is much higher with inbreeding for example mating with a cousin or a sibling or something it's much much more common to have genetic disorders present themselves because of these recessive alleles whereas mating outside it's much less likely and it's much more you have much more robust populations this is why in zoos as well you know zoos go out of their way to mate let's say they're polar bears or their panda bears with distantly related polar bears and panda bears so that they can have a robust uh diversity of genes there and you're not inbreeding them over because again remember what i said in chapter two the best way to go extinct is to limit the gene pool the best way to go extinct is to decrease genetic variability in the population more genetic variability gives you bigger resistance and persistence of life less genetic variability is easier to you know end up with extinction so let's look at a dominant trait dominant traits you only need one copy of the diseased allele in order to show the diseased phenotype so this mom uh this this great grandma uh had this disorder married the grandpa who did not they had uh how many children one two three four children two of them have the allele these two can be pretty sure that they don't have the allele at all because it's a dominant trait which means if you show it you have even one one allele so then they go on to have kids have their kids have it have their kids and and so that's kind of how this works um if you if you have the the phenotype of this dominant disorder you have a 50 chance of your kids getting it because you have you know like i said you have one healthy allele one mutant allele your gametes will get one or the other your offspring have a 50 50 chance of having this disorder does that make sense now uh here's an example weinberg's uh syndrome which is marked by uh it's a it's a autosomal dominant trait characterized by deafness fair skin visual problems and this this white forelock that that appears in the hair so it's a it's a autosomal dominant so if you have one copy it's going to present itself here's here's great grandma deceased great grandpa and it looks like they only had two children but both of them got this uh syndrome and then it goes on and you can see it it's pretty pretty consistent with half of the children getting this disorder because again it's a dominant disorder and that means that half of the children will have it through time right so it basically mimics the the inheritance found here with this with this uh framework of dominant autosomal trait uh so again hopefully it all makes sense um thank you for joining me uh this was chapter three let's get let's get going right into chapter four and and finish it strong dr d dr d dr d dr d dr d dr d [Music] d