Chi-square Step 1 - Calculating Expected Ratios and Class Numbers in F2s

Deana Namuth-Covert Author

01/13/2019 Added

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Tutorial clip demonstrating how to calculate expected F2 ratios and individuals in classes for a chi-square analysis.

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[00:00:00.040]Hello everyone this is Dr. Deana and today I'm going to be walking you through the first step
[00:00:14.280]of a chi-square analysis in this video tutorial. We're going to be looking at how we actually
[00:00:21.040]calculate two different expected numbers. The first we're going to be looking at how we calculate our
[00:00:28.360]expected ratios for our different classes. This is based on the experiment that we're
[00:00:35.760]conducting. Once we have the ratios figured out, we can convert that then to the number
[00:00:42.360]of individuals that we expect to see in each of our classes. What we're going to do is
[00:00:51.160]follow along with our lesson, which is looking at our bacterial spot disease in tomato, and
[00:00:58.160]so here on the left, we have our breeding line OH88119, okay, and it is true breeding
[00:01:16.160]susceptible, okay, with regards to the bacterial spot disease. Now it has many of the other
[00:01:26.160]traits that we're interested in as far as, like,
[00:01:27.160]a cultivated variety,
[00:01:28.160]So that's why we're using it. What we're going to do is cross it with another breeding line.
[00:01:34.160]And this particular one is 6.8068.
[00:01:43.160]And this breeding line came from a wild germplasm.
[00:01:49.160]Okay, so it doesn't have all the qualities we're looking for in a variety, but it does have resistance to bacterial spot.
[00:01:59.160]Okay, so that's what we want to do is transfer then that bacterial spot resistance into our other line here in the end.
[00:02:08.160]So when we cross these two together [6.8068 X OH88119], we get an F1.
[00:02:12.160]And in this F1 generation, we found that all of the plants were resistant.
[00:02:19.160]Okay, so think back to your introductory genetics course, and what does this tell us?
[00:02:34.160]Well, for a hypothesis, we can guess then that bacterial spot resistance is due to a dominant gene, since all of the F1 were showing that.
[00:02:45.160]So let's give it a big R.
[00:02:48.160]And then we can say then that our resistant parental line here was big R, big R.
[00:02:55.160]And then that would make our susceptible line little r, little r.
[00:03:03.160]So then our F1 generation would all be big R, little r.
[00:03:10.160]Okay, so now what we're going to do is allow these F1s to self-pollinate.
[00:03:17.160]So we're going to have a big R, little r times a big R, little r in our F2 generation.
[00:03:24.160]So let's go ahead and clean this slate here. [blank screen appears]
[00:03:27.160]Let's go ahead and draw out a Punnett square for those of you that it's been a while since you've had genetics.
[00:03:33.160]So we've got big R, little r, or if this is your first class of genetics.
[00:03:39.160]Okay, so in our F2 generation then it's going to come from a big R, little r times a big R, little r.
[00:03:46.160]And so we want to figure out what ratios we're going to expect for resistant to susceptible.
[00:04:00.160]Okay, in our F2s.
[00:04:04.160]So that's what we're trying to calculate.
[00:04:07.160]Okay, so what we're going to do, we'll do a quick little Punnett
[00:04:11.080]square here. We'll put the gametes for one on the top, so we'll have a big R and a
[00:04:22.270]little r, and the gametes for the other [side] would be a big R little r. Okay, so we've
[00:04:29.890]got the pollen gametes on one line and then the egg gametes on the other. So we
[00:04:34.490]fill in the Punnett square, we're gonna have a big R big R here in this square [top left].
[00:04:39.050]Going across we'll see a big R little r [top right]. Coming down here we also see a big R
[00:04:46.630]little r [bottom left]. Then our final square here will be a little r little r [bottom right]. Okay, so
[00:04:53.110]since our hypothesis is that resistance is due to a single gene and that gene is
[00:04:59.130]showing dominance inheritance, then we can say we've got, we're going to be
[00:05:04.470]expecting three [circles all but the bottom left little r, little r square]
[00:05:07.690]plants here are going to show resistance. So that'll be a three and then we have
[00:05:14.510]just this one box here [bottom right] which is showing susceptibility. So on our f2 we will be
[00:05:22.650]expecting a three to one ratio where three fourths of the plants will be
[00:05:27.030]resistant and one fourth will be susceptible. Now when we're using chi
[00:05:31.290]squared we have to convert these ratios then to actual numbers. Okay, so
[00:05:36.330]how do we do that? Well in our example we have an F2 population with a total
[00:05:42.510]of 197 plants. Okay, so we have 197 F2 plants. So how many of those 197 plants
[00:05:58.970]do we expect to be resistant? Okay, so let me see if I can get the cursor over here.
[00:06:06.170]All right, so what we simply do is take that 197 from our total population and
[00:06:18.110]multiply that times 3/4 because we expected three out of four plants up
[00:06:26.990]here [from our Punnett square] to be resistant in our ratio. So if you take 197 times 3/4 that will give you
[00:06:36.010]the 147.75 that were expected in our F2 to be resistant and that's what we
[00:06:50.890]had in the text. Okay, now you can't have 3/4 of a plant, this 0.75, so you may
[00:06:56.950]want to go ahead and round that up to 148, so it's kind of up to you. Then
[00:07:01.750]similarly if we're going to calculate how many individuals we expected to be
[00:07:05.850]susceptible, we take the total number in our population, 197, times 1/4, because
[00:07:13.590]this time 1 out of 4 of those Punnett square boxes were susceptible, and then
[00:07:19.370]that gives us a total value of 49.25. Now if you want to double check your math,
[00:07:31.170]what you do is you add these two numbers together, and that should come up
[00:07:35.690]with your 197 total plants that were in your F2 generation.
[00:07:42.930]Okay, so this is step 1 in chi-squared, how you calculate your expected ratios,
[00:07:48.410]and then convert your ratios to the actual number of plants or individuals.
[00:07:52.930]In this particular example, we were just looking at a disease resistance,
[00:07:57.190]which was due to what we think is single dominance, so single gene with
[00:08:01.490]complete dominance inheritance. So obviously, if you're looking at inheritance
[00:08:05.530]of two traits, it gets more complicated. But this kind of shows you the idea of
[00:08:09.950]how you calculate ratios and individuals.
[00:08:12.150]♪ ♪
[00:08:15.150]♪ ♪

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Chi-square Step 1 - Calculating Expected Ratios and Class Numbers in F2s

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