Two inbred lines of sunflowers (P₁and P₂) produce different total...

Question

Two inbred lines of sunflowers (P₁and P₂) produce different total weights of seeds per flower head. The mean weight of seeds (grams) and the variance of seed weights in different generations are as follows. Generation Mean Weight/Head (g) Variance P₁ 105 3.0 P₂ 135 3.8 F₁ 122 3.5 F₂ 125 7.4 Use the information above to determine VG, VE, and VP for this trait.

Table showing mean yield and variance for sunflower generations W1, W2, F1, and F2.

Accepted Answer

Hi, everyone. Welcome back. Let's look at our next problem. It says two in bread lines of wheat, W one and W-2 produce different average grain yields per plot. The mean yield in pounds and the variance of yields in different generations are as follows. And we have a table for two different inbred strains W one W- and then two following generations F one and F two for each strain or generation we have in the second column, the generation mean yield for each and in the third column, the plot variants in pounds. Then our question says, what is the phenotype phenotypic variances V subscript P for grain yield in this case, choice? A 12 point oh two B 13 point oh two C 10.62 or D 11.87. So when we think about phenotypic variants, so the distribution about the mean of a certain phenotypic value. So in this case, the phenotypic value we're looking at is green yield in the form of the average yield per plot. And we want to know what's that phenotypic variances? How are yields distributed about the mean? Well, phenotypic variances is made up of two different types of factors. So V subscript P is equal to V G plus V E. Um All these letters are actually subscripts. Did I say superscript? They're all subscripts. But I'm just going to say V PVG V E rather than saying the word subscript all the time. But so we know that's how they're being written with subscripts there as different types of variants. V being the main letter there. So V G there being the genetic variants and V E the environmental variants. So phenotypic variants due to genetic factors versus environmental factors. Well, genetic factors, you have two different things that can be in going into play here. So V G can be further broken down to VA plus V D. Again, the A MD beings subscripts. And in this case, we can recall B A is the additive variants. And in that case, that refers to variants due to inheritance of different alleys. So looking overall at different genotypes, the plants could have inherited and what's the variance caused by just inheriting different genes. But that's not a simple additive thing. Sometimes sometimes you have masking effects if one gene is dominant and one recessive, your recessive trait might be in be completely or incompletely masked by the expression of the dominant trait. So we do need to take into effect that dominant variation. So that would be dominance and that would be due to I'll just write masking to help us remember. So we're going to be looking at in the end, our sort of master equation we're looking at is V P that we're looking for is equal to. And then our V G is broken down into VA plus V D plus V E the environmental variants. So we had our genetic variants due to inheriting different genes and how those genes interact, alls interact with each other and environmental variants. What is the effect of differences in the amount of water differences in the amount of sunlight differences in the type of soil and how to what extent can that affect the phenotype? So obviously, you aren't going to have some sort of infinitely small or infinitely large grain yield. Again, variants being that distribution around the mean. So we recall that variant equals distribution around the meme with that in mind, let's calculate the three values we need. So we'll start with va that additive variants. And in this case, we just focus on our values for W one and W-2. We don't want to mix in F one and F two, which should be the result of crossing F one, crossing W one and W-2 and then F two, the result of crossing F one individuals. So that will be taken into account in our V D because we'll look at how do these two alleles interact with each other. Here, we just want to look at what are the for lack of a better word, extremes of variants just caused by those all in their pure form. So we'll look at the difference in the yield of the two strains. So in parentheses, that would be the W-2 mean yield uh in this case, that's just chosen because it's the larger we're looking for an absolute value difference um overall. So just pick the one that's larger. So the W-2 mean yield minus the W one mean yield. And then, because we're looking for both an absolute value and we're looking for distribution about, I mean, we'll take that difference and divide the whole amount in parentheses by two. So that means when we plug in our values, our W-2 mean yield is then minus sine W one mean yield is 50. That difference divided by two will give us 10, divided by two will equal five. So our va equals five. Now let's move on to V D. Well, we don't have enough information to calculate this directly, but we can estimate it. So instead of equals, I'm going to put approximately equal to and I can do that by looking at the differences. Now, I just now I will just look at my two crossed generations, F one and F two, look at the differences in their mean yields. And then I'm going to subtract that va that I calculated because I want to just look at the interaction of the alleys in crossbred generations. So is one dominant over the other. So I'm going to subtract the effect of the pure alls themselves. So in parentheses, again, I want just larger, minus smaller. So I'll have a look at the difference there. So in this case, F two mean yield minus F one mean yield. So there's my crossbred generations and then I will subtract out va to account for that additive variances that I'm already going to be putting in there. And then again, I will be dividing by two. Since again, I'm looking at distribution around me. So in this case, that would mean in parentheses minus 9 55 minus sign five, that's va that whole expression divided by two. So we end up with two, divided by two, which equals one. So we estimate R V D as one. And finally, we are on to V E the environmental variants. Well, how would we calculate that? Well, if we looked at genetically identical plants and then said, how much variance is there in the crop yield of a whole field full of genetically identical plants? And I will be left with variants due to environmental factors, the genes have been held constant. I'm just looking at environmental factors, we can make this number a little more accurate because we have four different strains to look at four different genotypes to look at W one W-2 F one and F two. So let's just find the mean of the variants of all those different strains to come up with this V E. So that means we will add together. So I'll put in parentheses, the sum of the variants of W one, W-2 F one and F two. And we're finding the mean value here so that some will be divided by four, the number of total strains we had. So that will equal and in parentheses five point oh plus sign six point oh plus sign 5.5 plus sign 7.0, close parentheses divided by two. And when we calculate that all out, round it off to the first decimal point will give us 5.9 clear there. So now we have all three values that we need for our final calculation. Going to scroll up just a little bit to make room for that. So we're ready to calculate V P phenotypic variants, which as we know is equal to the sum of VA V D and V E. So we have those three values that we've calculated or estimated. So that will be five plus sign one plus sign 5.9. And when we add those all up, we end up with 11.9, we go back to our answer choices and we see that we have our very close choice. D 11.87. Of course, we did a little rounding off. So 11.9 11.87, our answer here calculating the phenotypic variants for grain yield with these different strains of wheat and their cross bread generations this choice. D 11.87. See you in the next video.

Key Concepts

Genetic Variance (VG)

Environmental Variance (VE)

Phenotypic Variance (VP)

Watch next