Hi. It's Mr. Andersen and in this podcast I am going to talk about population
modeling. We're going to start by talking about what a population is. And before we
can do that let's talk about what an individual is. And so let's say this is an oak tree.
Well, you probably know that an oak tree starts life as an acorn. So that acorn will germinate,
a little tree grows out of that. Eventually it's going to produce pollen and make more
seeds and eventually we're going to have more acorns. And so since we are talking about
populations, a population is a group of organisms living in the same place at the same time.
So let's say this is a group of oak trees that are living together. And so since we're
talking population life cycles, it's easiest to start with humans. And so you know a little
bit about humans. You know that we start as adults, we going to produce sex cells and
those sex cells are eventually going to fertilize one another and that's going to create babies.
And so let's use biology terms. And so that's going to be adults creating gametes. Those
gametes are then fertilizing eggs and those are making what are called zygotes. And then
finally we have juveniles. And this is a cycle, so let's put that in a cycle. So adults are
producing gametes, which produce zygotes which produce juveniles which produce more adults
again. And so if we were to just generalize for all of life we have adults producing gametes.
Those produce zygotes, juveniles and then it goes again, over and over and over again.
So this is the life cycle. And we could apply this to humans or oak trees or oysters or
squirrels. Whatever, they're going to go through a life cycle. And so since we're talking about
a population, remember a population if we look at all the genes in that population,
we call that a gene pool. And that gene pool should remain unchanged through time unless
we violate one of these five rules of Hardy-Weinberg Equilibrium. In other words, we have to have
a population that's big enough, we have to have random mating we have to have no mutations,
no gene flow and then no selection. And if we do that it will remain the same. And so
basically I want to ask you a quick question, and so if we have this life cycle for all
of life, the size of this life cycle is going to be related to the large population, but
what I'd like you to do is pause the video and think for a moment, where would you put
random mating? Would you put it here, would you put it here, would you put it here or
here? And like wise for mutations, gene flow and selection? So I am going to stop for a
second, that's good and then I am going to show you where they should go. So if we start
with random mating, that would actually go here, between the gametes and the zygotes.
If we're talking about mutations, where are most mutations going to occur, that's going
to be between adults and the formation of the gametes. If we talk about gene flow, remember
that's emigration and immigration that's going to go between the juveniles and the adults.
And then if we talk about selection most of that is going to occur between the zygote
and the juveniles. And so again if we can keep all five of these the same, in other
words, no mutations, random mating, no selection, no gene flow the population should remain
the same, as long as we have a large enough population. And so basically in this podcast,
what we're going to do is we're going to play around with modeling of a population. And
especially we are going to focus on this large population side. So we're going to be using
a spreadsheet. And a spreadsheet is very important to biologists. And the reason why is that
you can gather, well first of all we can gather a lot of data and we can put that into a spreadsheet
and we can analyze the data. But we can also produce models, so mathematical models and
we can use those within our spreadsheet to do studies, to do experiments. And we don't
have to do that in the wild and we don't have to take the time for animals to reproduce
and so we can generate a huge amount of data really really quickly. And so we're going
to be using this spreadsheet right here. Basically what happens is you're going to start with
allele frequencies that you put in. Remember that's going to be the frequency of one gene
and another. In this case we'll start with 0.5 and 0.5. We'll then use our spreadsheet
to generate gametes. Those gametes are going to fertilize and form zygotes and that's eventually
going to make juveniles. So we're going through this life cycle, but we're going through it
using a spreadsheet. So I'm going to launch a spreadsheet program and so we are going
to us numbers, but you can use excel or google docs to do this. And I'll try to put a link
to the spreadsheet that I'm using down below video so you can try it on your own. And so
let's start right here. So right up here we're going to start with a population where the
frequency is 0.50 and 0.50. And so this is, you can think of this almost like the gene
pool. These are the adults and let's say that that generation one, the frequency of those
two genes is going to be the same. Next they're going to produce gametes, zygotes and juveniles.
But let me show you how the spreadsheet is actually producing these gametes. So if I
click right here on this gamete right here, it's kind of hard for you to see, but i'll
zoom in, basically this is the equation of this cell. And when we're talking about spreadsheets
and I talk about cells, basically what is a cell? It's going to be one of these boxes
in the spreadsheet. And so if you've ever played Battleship before you know that this
right here, this cell right up here is going to be cell B,1. You can read it off. Or this
right here would be A,5. And so if we go right here to C,5 and we look what's in that cell,
there is an equation. And so basically this formula, I should say, says if a random number
is less than or equal to what's in B,1, and so B,1 is what's going to be in this cell
right here, display the gene A. But if it's not, then display the gene B. And so right
now think of a decimal between zero and one and try to include two numbers in that. So
maybe you're thinking of 0.23, that's what I'm thinking of. And so let's say a random
number is generated right here, I'll say right here. So it's going to generate a random number
and we chose 0.23. And so is 0.23 less than what's in B,1. And in this case what's in
B,1 is going to be 0.50. So since 0.23 is less than 0.50, then it's going to display
the gene A. If it wasn't, let's say you chose 0.79, then it would display B. And so each
of these cells right here has the same exact formula in it, but each of them are going
to generate a different random number. And therefore each of them are going to generate
a different gene. Those genes will combine to form a zygote and then we are going to
compile the different types of zygotes that we have to eventually make the juvenile. And
so in this case we've got a gene A from one gamete a gene B from another one so we have
AB. So we could say that right here. And so that would be one of the seven ABs that we're
going to have in the population. And so the neat thing about a spreadsheet is I can set
the allele frequencies to 0.50 and 0.50 and now I can just click on this mate over here
and look what's happening to the data down below. It's basically doing generation after
generation after generation. So each time I click this it's going to make a brand new
generation. Now you'll find that also if I could just hit enter on one it will make a
new generation as well. And so the neat thing about that is we're gathering a huge amount
of data. So we're modeling a huge amount data. And so if we start with 0.50 and 0.50, let's
look and see what happens to our gene frequencies at the end. If we look way down at the bottom,
you'll see that in this mating that I just did, we're actually going to have a p and
a q value of 0.47 and 0.53. In other words this one generation, this one turn through
the life cycle, what's happened? Well, you can see right here that we've got a lot of
those that are AB, a few that are AA and a few that are BB, but the frequencies have
changed. In other words the frequencies of the gene pool that we had at the start are
different then the ones that we have at the end. And the reason why, since we're not doing
mutations or selection. We're doing random mating and then we're also doing no gene flow,
basically the one thing that's causing this change is going to be small population size.
And so this in science is called genetic drift. And so let's just do a quick experiment. So
let's say I start with 0.50 and 0.50 and let me do a quick mating. And so I'm going to
put my generation 1 right up here, 0.50 and 0.50. So let's say this is generation 1, now
let's do a quick mating. So I'm going to click on the mate and it's going to do one quick
mate and if you look down at the bottom you'll see that the new p and q values are 0.41 and
0.59. Well, let's put those in here and use that to set the next generation. In other
words, let's us these juveniles to set the next generation. So I'm going to remember
that. It's 0.41 and 0.59. And so let's put those up here as well, 0.41 and 0.59 and now
let's just do another mating and see what happens. So right now it has changed again
to 0.44 and 0.56. And so if we put those values in here, so again, 0.44 and 0.56, we've got
allele frequencies that are changing. And that's just do to chance. And so I'm going
to just speed up the video and I'm going to gather the next, it looks like five generations
and then we'll go look at the results. Okay. So I just finished doing those matings and
you can see the allele frequencies have changed. And I've organized those on the next sheet
of the spreadsheet so we can look at them. And so basically what happened was our p generation
started to drop and our q generation started to increase. And if we were to graph that,
what have we seen? Well, we've seen an increase in the q generation and a decrease in the
p generation. And so they started at 0.5 and 0.5 and then they've changed away from that
equilibrium. And so what's causing that? Well that's just randomness, that's just random
change due to a small population size. And how small is our population size? It's just
15 individuals right here. And so what you could do is you could play around with this
spreadsheet and you can vary different things. Right here we're just looking at population
size. And then you can see the results. And so what we've created is a model to study
populations. And we could make that model even more complex to add selection and we
could add random mating. And so that's kind of up to you. So again, I'll put a link to
this spreadsheet at the bottom and that is population and modeling and I hope that's
helpful.