okay so in this final segment of the lecture I'm going to introduce two critical Concepts in quantitative genetics heritability um which is to determine the extent to which genetic factors cause resemblance among individuals and the Breeders equation which is where we can use heritability to predict the potential for evolutionary change so what is heritability well heritability is arguably one of the most widely estimated and indeed discussed parameters in quantitive genetics heritability simply defined as the proportion of phenotypic total phenotypic variance that's VP that we described in that previous section that can be that can be attributed to genetic causes put differently this is the relative importance of gen of genetic variance in determining phenotypic variance and there are two types of heritability to consider here the simplest is what we term Broad sense heritability which is given as the ratio of total genotypic variance over phenotypic variance it's a ratio now importantly if you're paying attention to those pre the previous section you'll know that um VG itself encompasses both additive and non-additive genetic variants therefore this sort of um estimate of heritabilities is much more useful um for organisms where we don't um have to worry about non- adive genetic variance so for instance in species where um Offspring or parents and Offspring genotypes are virtually identical EG for instance in clonal or self- fertilizing species where there's no outcrossing the second type of heritability that we consider and one that we're much more interested in if we work on species where we do see outcrossing is what we term Narin heritability and this is much more appropriate for outbreeding species and given as the ratio of additive genetic variance of va over total phenotypic variance or VP and this describes the proportion of total phenotypic variance that can be attributed to the additive effect of genes IE the proportion of genetic variation that confers evolutionary change in out Crossing species so in the next lecture we'll learn about many of the methods that we use to estimate heritability using the principles discussed here for now um I want to introduce um a second important um concept and that is um how we predict responses to selection and there are two basic requirements um that we need for evolution to happen first of all we need to see that there is actually phenotypic variation in the trait of interest and more importantly this variation has to have some kind of Fitness implication so for instance um individuals of certain um phenotypes might exhibit differential survival or reproductive success so selection has to be able to operate on the variance that we see and another and of course critical um requirement for evolutionary change is there must be underlying additive genetic variance for the trait and interest in other words heritability or naron heritability given as that h squ symbol needs to be significantly greater than zero and we can formalize these two um processes here this requirement for selection and also there to be added to genetic variance into a single equation um which it we term the Breeders equation here R refers to the response to selection so this is what we're interested in actually predicting s in the equation is the selection differential okay this is this requirement that there's phenotypic variation that's linked to Fitness okay so selection differential is the difference in the means between the selected group okay so the parents for instance and the mean of the whole population I'll go into this a little bit more in the next slide and heritability as we've just described is in this case the narison heritability heritability and it should be fairly obvious in this simple equation that r that is the response to selection critically depends on there being heritable variation in the trait of Interest so now let's EXP explore the relationship between naris and heritability and the response to selection so pictured here is a very simple theoretical relationship that I've taken from um the book from allendorf and lukart which I'll give you at the end of this lecture and this diagram very clearly shows how the response to selection are depends on the heritability underlying heritability of the trait so here we've got the selection differential which we can see given as s which is the difference between the mean of the selected so it might be something that you select on as an animal breeder for instance something like yield meat yield in your um catalog Dairy yields for instance and so you picking from one side of the distribution that would give you high values of that that's your selection differential so that's a difference between your selected parents and the underlying um average of the population and as you can see if the mean of the selected progeny is equal to the mean of the parents so the progeny that comes out of those parents we could say that heritability equals one okay which is given on that right hand Arrow at the bottom whereas if a trait knows shows no response to selection so in other words um the mean of the selected progeny is still equal to the mean of the population um and unaffected by the mean of the parents then we would have a heritability of zero and of course generally um the mean of selected progeny assuming there is a herble genetic basis to that trait will be somewhere between zero and one okay let's stay with this concept now this idea of relating the response to selection and in heritability um uh and think about this a little bit more from the P perspective for instance of an animal breeder let's say for instance that an animal breeder selects for a particular trait let's say milk yield in dairy cattle so in the figure the breeder selects for the trait from the Shaded area of the graph the distribution at the top graph here the top bell curve so that be from individuals with high milk yields obviously he wants to ensure that his population increases in value in terms of milk yields that it produces and what this figure shows you is two generations of artificial selection for that trait which has a heritability in this case of 33 so the breeder selects by truncating the population and uses only individuals above a certain threshold as breeders are where the selection differential differential is positive and the mean of the progeny would then move onethird of the distance from the population mean to the mean of the selected parents each generation of selection with a heritability of three so it's very very simple mathematics here one thing to really um that's quite important to note here is that the total phenotypic variation is reduced as selection continues and this is because as I've already said before in the absence of this sort of genotype by environment interaction scenario I've set up is that continuous directional sele on a trait should eventually erode the variance that's in that trait in the population I want to now very briefly explore some frequent misconceptions about heritability so an important point about heritability is that it's a ratio of variances okay and this is important for a couple of reasons first of all the measure of heritability is frequently misinterpreted as the degree of genetic determination of a trait we might want to think about why is this wrong well it's wrong because the low side that determine a trait can be fixed and therefore exhibit absolutely no variation at all which in turn would generate a zero estimate of heritability for a trait that's is entirely determined by genes so if we think about for instance genes that control the number of eyes in humans we expect them to be fixed okay we all have two eyes number of legs in dogs is the same thing they would have zero variance and therefore would exhibit zero heritability so we can't think of narison heritability as a measure of the degree of genetic termination traits under strict genetic control might have very low values of heritability and a second problem is that heritability is also misinterpreted as a measure of evolvability so in other words how much potential for evolution is our population showing and again we might want to consider why this is misleading well let's goes back to the fact that heritability is a ratio of variances and this has two very important implications first of of all um the total phenotypic variance which is the denominator in the equation for arance heritability includes environmental variance okay which makes heritability specific to the environment in which it's measured if you have high environmental variance um you might have a great deal of variance in your trait which is determined by that variance and therefore ultimately a low heritability for that trait would come out because of that very high denominator in the equation and also you need to remember that um because genotype by environment interaction the measure of additive genetic variance which is the numerator of our equation can be sensitive to the environment in which it's measured now both of these things um mean that environment can critically determine the level of heritability of your trait irrespective of any underlying differences and add genetic variance between the populations of Interest now I want to explore that very briefly in this final slide as I mentioned earlier um when we were talking about um the concept of gbes I'd end this lecture by briefly exploring how measures of heritability can be highly sensitive to environmental effects which very much speaks to what I've just um put into that last slide so I'm going to use this empirical example on wild radish um to illustrate this which is um a nice paper because it simultaneously in illustrates how sensitive estimates of H2 can be to environmental effects because of the way the environment affects both the numerator and the denominator of those ratios that of that ratio that makes up Nance heritability so in the table that's here um which comes from a paper by Connor and his colleagues uh where they were studying um wild radish Straits um the uh Columns of interest um to make this point about heritability are the three on the right hand side okay the estimates of um VP total phenotypic VAR you've got CVA there which is uh means coefficient of additive genetic variance and uh this is effectively a size standardized estimate of the additive genetic variants that we're interested in and also then in the final column is the value of heritability okay which is obviously the ratio of additive genetic variance to Total phenotypic variance so for each of these traits that are listed on the left hand side of this table the authors estimated um their PHP values for the same genetic if you like population but under Greenhouse conditions and in the field now in the greenhouse we have very controlled environmental conditions whereas in the field where they're growing of course the authors have no control over environments you have a lot more environmental variation so if we first concentrate on that column of VP we can see generally I've just highlighted them there and for the greenhouse estimates we tend to see um much higher estimates of total phenotypic iic um values in the uh field estimates which are underneath the greenhouse estimates than in the greenhouse so basically as we would expect levels of phenotypic variation for the trait of Interest tend to be higher in the field because of course those factors like temperature rain sunlight Etc are not controlled as they could be in in a greenhouse now here are the um corresponding estimates of additive genetic variance um under those two conditions Greenhouse and estimates and note that CVA so the coefficient of additive genetic variance is generally higher in those greenhouse estimat and this is good evidence that we've got genotype bi environment interaction because if you remember the definition of that the level of attitud genetic variance can depend on the environment in which it's measured and if we now look at the ensuing patterns of heritability for those field and Greenhouse samples we see something quite interesting overall we see that heritability is generally um lower in the field estimates but the important point to to note here is that this is due to both the inflation of phenotypic variance in those field estimates and genotype bi environment interaction now it's important to remember these heritability estimates come from the same species but they're measured in different environments and this raises a fundamental question how useful is heritability as a measure of evolvability as I said to you in the last passage we really need to understand that heritability is only relevant for the environment in which it's measured okay so I want to finish the lecture by just suggesting some further reading which I think you'll find useful um to accompany this lecture so the um book by um Connor and Har a primer of ecological genetics gives a really nice uh Foundation to quantitative genetics that you may find of interest um also your um textbook on uh by uh Ridley on Evolution will be useful and if you want a more of a conservation perspective so for instance some of those relationships between responses to selection inheritability that I showed you in the final part of this lecture um can be found in the book by allendorf and lukart thanks very much and I'll talk to you in the next lecture