okay welcome to the second of my four lectures this one on quantitative genetic methods okay so as for the previous lecture this lecture is going to be split into three segments and set the segment so the first one is going to be exploring and some basic methods that we use to estimate heritability usually under laboratory settings in the second segment are then introduced a method of quantitative genetic analysis that we tend to use when working on natural populations a much more powerful method that enables us to calculate heritabilities and other quantitative kinetic parameters in the wild which selection actually occurs and in the third segment I'm going to introduce a bit of a problem if you like the quantitative geneticists up until now and during this electron will be constantly talking to you about how we partition sources of variants in an individual population phenotype into its genetic component on what today I'm going to show you how assumptions that we make about the genetic mechanics and sometimes still be compromised by environmental effects so I'll introduce you to one case study that exposes this problem further okay so let's first start by introducing some basic methods that we used to estimate heritability in laboratory populations so as I've emphasized in my first lecture one of the key goals of quantitative genetics genetics is to quantify the degree of resemblance among relatives so that we can estimate the amount of additive genetic variants that underlies those traits but also so that we can then calculate the right parameters such as ferris ability or evolvability etc so an obvious place to start looking for these similarities among family members might be for instance through the similarity that parents share with their offspring so here for example some Hollywood legends where we which the phases between the parents in this case on the electrical side we've got black Donna and her daughter gwyneth paltrow and on the right we've got Sutherlands we've got Kieffer and his father Donald and as you can see there's striking resemblance really between parents and their offspring typically there is okay so how do we actually quantify that extensive resemblance in order to derive something that's useful for us as quantitative janessa's in this case here it's busy so the method I want to consider here is one of the simplest methods that we use to explore patterns of family resemblance using the relationship between traits from offspring and their parents so we call this of course parent-offspring regression this is a statistical technique as is all of quantitative genetics where we explore the relationship between traits in parents offspring and The Offspring themselves so to do this sort of thing we would very simply set up a number of monogamous pairings between for instance you know males and females south of our population they might just once we then measure the traits of interests both in the offspring from those traits and from the parents okay so we need to make sure that we measure those traits the same kind of time let's imagine we're talking about body size for instance we've measure body size in the adult parents so we wait until the offspring from those parents were at the same developmental stage or age and we've measure those traits in the offspring we can then regrets the means for the family from each of those pairs of males and females on to what we call the mid parent values that means the average of the traits for the two parents alternatively we could choose just one of those parents to regress those on every particular interested in patterns of for instance maternal or paternal inheritance first race and then we use the familiar linear regression which is y equals a plus B X a is the intercept for that relationship and being is the slope of that relationship so it describes the rate of change in the trait which is X as we move along the way as we move along the x-axis okay what's pretty useful about the sort of design is that the slope that is B gives the sourcing indication of the degree of resemblance between the parents and their offspring and so therefore it gives us an estimate of the additive genetic effects that's the effects of the genes that are transferred to offspring for the tray of interest in there but we can calculate or estimate heritability from that relationship so in a real example for instance in Birds this is a study by Weems and colleagues they looked at the relationship between mid parent as this length that this is the length of part of the lake which is used generally as an estimate of body sizing birds and you can see that along the x-axis just here and pointing with a mouse and on the y-axis we can see the offspring classes link so there the average families average values for the families that are aggressed on the parent values and here we can see the slope of that relationship so if this was our regression equation that we derived in that simple relationship we can see that the slope here is point 5 and that gives us a direct measure of the heritability of the traitor the narrow sense heritability of that trait would be point 5 that means half of the variance that we see in the ostmen can be explained by the additive genetic effect of genes it means of course that we can't explain the other half which is probably due to environmental effects which we discussed in the first lecture and non additive effects which were also considering that lecture so another very popular method permission with degree of family resemblances actually explore the similarity among half siblings and in particular paternal half siblings and this method is proved to be a really powerful one for assessing the additive effect of genes and the basic principle behind this sort of analysis is simple we're now to provide no resources to females reproduction other than course genes any phenotypic similarity among his offspring from different females must be due to fear and sharing the same paternal genes because we're all out any effects of females okay so this has proved as I say very powerful men to petition the additive effect of genes which of course is responsible for those similarity effects that we see in offspring and all his offspring in this case paternal hofstra offsprings and the basic principle is that males provide very low levels of if you like environmental variance because in effect by transferring melee sperms females in many cases there's very little scope for males to influence their offspring other than through genetic and faxes slow let's just use the little cartoon hypothetical example to explain exactly how this paternal half-sibling works this imagine lyst sky here we're calling Bob and Joe he makes who he mates throughout his reproductive life went to different climates okay and he has children with both those two different partners if we then look at the offspring resemblance in the office in the oxen from both of those females let's explore the one at the bottom here if we for instance to look at the similarity in the trait among those three offspring that I've now circled it's not surprising that we've see some very striking similarities among them okay they share the same parents so of course they're going to say a lot of the same genes but don't forget they also share a lot of environmental factors that might also derive those similarities among the offspring those full sibling offspring from that particular female let's explore what those might be for instance they all share the same intrauterine environment they were born from the same mother so of course they would have had similar levels of resources devoted to them during pregnancy they probably live in the same house and therefore had the same diet and would have share very similar environment than schooling etc so the sort of similarities which see between four siblings can't really be attributed purely to genes because of course environment plays a really important role in also determining and how offspring ultimately develop but now let's explore the relationship if you're like all the similarities across half-siblings now in this case if we choose little boy in the middle we can see looks very very similar okay almost identical puff from the clothes that is wearing okay now of course we can't now say this has anything to do with the mothers genotype because these these two boys come from different parents different mothers so any similarity between these two really has to do with the fact that they share genes from the father so in effect these paternal half siblings share some allows you simply through genetics now it's probably fair to say that they grow up in different households they certainly developed in different ones and the extent that the father himself doesn't get too much involved in the parental care of those offspring in the two different families it's fair to say that environmental flex couldn't possibly drive any similarities between these two these two individuals so as you can see the paternal half-sibling design is a really nice way of teasing apart those environmental effects and really narrowing it down to the effects of genes and very little else so that's the basis of the design I want to talk about so how better to illustrate this them with a real example some of you may not be familiar with this guy Steve Tyler from the band Aerosmith more my generation perhaps than yours but for all accounts he was pretty prolific with the amount of women he had that probably wouldn't be surprising for rock stars of his sort of caliber and here are just a handful of the women that he's been associated with him probably mated with no doubt now it happens that he has several offspring and in this case two of these pictured here so to these offspring come from different mothers but the same father I think it's fair to say there's a pretty striking resemblance both between the two girls themselves or one of course is Liv Tyler who would all seen in the in the in the movies that she's been in but also between her half-sister here so those similarities and the similarities they share with their father of course could only come about through their shared paternal inheritance okay so you should now have a pretty good idea of how the paternal obstacle in design works let's now see a more formal representation of that design so here as an experiments are in the lab we would set up what we call here of course the nested paternal half-sibling design okay this is where we make mouths which we typically call size in a quantitative genetics sort of framework we make them to a number of females which we turn dance okay in this case this is a paternal half-sibling design involving three dams per side okay these are the factors in our analysis and i'll come back to the analysis that we derive from this sort of design shortly we then would allow each of those females to produce offspring and we would measure the traits of interest in all of those offspring of course across those three paternal half-sibling families okay and then we would look at the covariance in the traits traits of interest for instance that could be the body size and birds we've already considered it could be any trait of interest to the quantitative geneticists we measure those and we can then derive an estimate of the absa genetic effects from the covariance across those paternal half-sibling and families and of course like any decent experiment we need to replicate this so this would be replicated ideally 50 or 100 times that you have quite literally thousands of offspring in your analysis and this sort of thing is really important from quantitative genetics because often the effects that we're trying to detect a very very subtle and we need large sample sizes to detect them so once we've done our experiment we've measured the trace of interest when then in positions start thinking about partitioning the variance in this trait among these different causal or observational variance components okay and to do that we can use simple analysis of variance in this case of nested analysis of advantage because in each case the Dan so the three dams that we make to each sire in a statistical sense and nested within each sire so we would then collect data for our offspring from those four and five cific families across all those different side groups and we would come up or derive three different observation variance components and that analysis the first we will consider is the one we're very interested in from the point of view of estimating the additive effects of genes and that is to explore the covariance among paternal half siblings which we will call the sire component okay that's if you like the factor attributable to size that we put into our next to deliver in the first place we then get a second component which we're going to call the damn component this is actually the nested term that we put into our model and this describes the differences among progeny or females makes it to the same male okay so that's we can call V D or the damn component and finally we need some sort of error term in our model and this is described by the differences among individual offspring of the same female so these the four siblings that are measured in each one in effect this is like an error in any standard another model and we'll call that within fortunately component or V W now a very useful property of the paternal half-sister sign is that we can directly estimate the Addison genetic variants from that side component it so happens that the side component is a quarter of the value of V a so in order to derive a measure of additive genetic variance VA we simply multiply the side component by four there are assumptions in this calculation which are probably a little bit to complicate to go into this lecture but some of the reading I suggest at the very end of the lecture will help you understand the theory that sets up that simple calculation now total phenotypic variance of course is really important if we're going to calculate heritability because of course it's the ratio of the additive genetic variance to the total phenotypic variance that gives us and there are some serviceability and that's very simple to calculate that's simply the sum of these three variance components that is BS plus BD + VW is equal to VP total tips total phenotypic variance and to get narrow sense heritability as I've already said you simply take the ratio of VA to VP okay so so far we've focused on half sip designs and they're fantastic for many model organisms for instance things like Joseph ler or internal fertilizers where we need to make females and soy males to a number of different females but for some organisms we can actually use what we call cross classified or factorial breeding designs where individuals or indeed genetic lines can be crossed in all combinations and I'll explain why that's a neat little learn feature of these designs in a moment so I'm going to go here into detail about something that's called the north carolina to design and here we simply cross in all combinations number of sires and a number of dams to produce the number that the the factorial number of those quater so in this case we've got four size most four different damn so we will generate 16 families okay there be the combinations here that we would see in our design now this designers a number of advantages over the basic paternal half-sibling design first of all we can explore the covariance of course paternal half siblings to estimate the additive genetic effects now that's no difference than the half sip design because if you think about it where this arrow points down here with the mouse ok this is effectively just a nested model that we already did this sigh for made it to four different Dan's ok but what we also get here which important to the mouse here along here is we get an estimate of maternally derived permits in Austin because we also have the covariance cross and eternal assets now one particularly useful feature of this design is that this design enables us to actually calculate the amount of non-genetic maternal inheritance that contributes towards the traits of interest in offspring and the reason for that is because of course males and females produce or contribute exactly the same amount of genetic variance to each of their offspring so if we mean take the difference between the variance components between the paternal and the maternal half-zip factors in our model what's left over of course environmental effect that could be reversible for instance two females producing larger or smaller eggs that might influence the covariance across their progeny from different desires okay there's another particularly useful feature of the design as well not only can we get estimates of paternal and maternal half-sibling covariance but we can also look at the way that male and female genotypes interact in order to influence or swim fitness so we can look if you like at the compatibility of those males and females so for instance if offspring from certain size only do well when they make with certain females but not others we've got evidence for a compatibility effect now informally in the model that would come out through an interaction between the sire effect and the dam effect on the track of interest so any sort of interaction will be indicative of some sort of compatibility based effect on offspring now for those of you that are thinking very deeply about this design or see that of course it's not particularly amenable to all organisms how for instance can you get offspring how can you get sorry females to mate with a four different mouths simultaneously ok that's effectively what the society saying well of course you could let them make sequentially but that brings in things like time effects female effects and all sorts of other noise that would injure a sort of confound our estimates of genetic variation but the design is particularly useful for animals that release eggs and sperm externally where we can split the eggs and sperm into experimental batches so I think of external fertilizers for instance pictured here or a chins and also externally fertilizing fish we could in the lab take experts from a female and split them for this particular design across all these different males and we could do the same thing for each of those females in each of those Mouse so that each can be crossed in a unique combination and that's exactly what this design doesn't it's exactly where this design is best applied so it's particularly useful for externally fertilizing broadcast warning species such as these okay so you now have a sort of idea of the breeding designs that we can apply it to a laboratory setting but what about where selection actually occurs in the wild how could we apply these sorts of designs to species or two populations I should say that a living out where selection actually happens to consider that in the second part of this lecture I'm going to talk about a very special and type of quantitative genetic analysis that specifically design so that we can make it applicable to natural populations and we consider that in the next segment