In 1856 an Augustinian friar began experiments on pea plants in the Abbey's greenhouse.
His discoveries came to be known as Mendel's laws of heredity,
and the man himself Gregor Johann Mendel, became known as the father of genetics.
By using simple probability models, Mendel showed the power
of statistics and mathematics in genetics.
He crossed pea plants producing only yellow seeds with plants producing only green seeds.
The first generation hybrid seeds were all yellow.
He then crossed those seeds and the second generation were 75 percent yellow
and 25 percent green.
Mendel showed that each plant carries a pair of hereditary factors
for each character, one factor from each parent.
One factor is dominant and one recessive.
In this case the F1 seeds yg are phenotypically yellow.
Mendel's two factors are a form of a single gene and we call them alleles of the single gene.
A blueprint of genes an individual carries is called a genotype.
The expressed character of an individual is called a phenotype.
Common examples are human hair colour, eye colour and blood types.
The familiar ABO blood system is an interesting genetic model in itself
because there are three different alleles.
Basically, the A, B and O allele.
The A and the B allele are equally dominant and the O is recessive.
I'm Melanie Bahlo.
I'm a laboratory head at the Walter and Eliza Hall Institute
which is a biomedical research institute in Australia.
I have a PhD in Statistics.
I work a lot on genetic mapping, finding genes that cause disease in humans
but I've done quite a lot of work in mouse genetics as well like for example,
genes that determine coat colour in mice.
The mice that we're crossing here is a white mouse and a black mouse.
Now even though we've just got two coat colours there, what is actually hidden
in this cross are three colours and that's because of the two genes that are involved
and they're on different chromosomes and these two give the genetic information
that determines the coat colour in this particular cross.
To work at the genetic level, they used mouse blood samples.
In genetics, a locus , plural loci, is the specific location
of a gene or DNA sequence on a chromosome.
A list of loci in a known order, separated
by known genetic distances, is called the genetic map.
For each parent of course you get 2 alleles, one from one locus and one from the other locus,
so that means that you can get 4 by 4 different genotypic combinations or allelic combinations
and that will determine the outcome of the coat colour and that's most easily explained
in a Punnett square which is a very typical way of writing
out the genetic combinations of alleles.
If you have two copies of the capital A allele, that's the agouti allele, you will be agouti,
the browny colour and if you've got two copies of the capital C allele
which is the wild type allele at the albino locus then you will not be albino.
So albino is recessive, so you need two copies of the little c allele to make you white,
and then the complication is that the albino locus masks whatever is going
on at the agouti locus.
So therefore it whites out everything if the mouse is albino.
Now considering all the possible matings between the male
and female mouse you have 16 different outcomes.
In the top left hand corner you've got a double dose of the agouti allele,
the white type allele, at the agouti locus and a double dose
of the c allele the wild type allele at the albino locus.
So therefore the mouse is agouti and not albino.
In contrast the albino mouse as you can see is actually capital A capital A
which would be agouti if you could see it but because they're little c little c they're albino
and therefore that masks the agouti or black colour whatever it is.
So it's brown underneath but you never see it because it's masked by the albino allele.
So mating the black and the white mouse together produces a brown agouti.
And then when you get to the F2 which is what's called an inter-cross,
so here you're mating the brothers and sisters offspring, the F1s so all the agouti mice
with each other, you can now see the entire phenotypic spectrum:
black, white and agouti mice.
What's important here is the ratio which we've worked out from our Punnett square
of the outcomes of these coat colours, considering the 16 outcomes is 9 to 3 to 4
of agouti to black to albino and that is the first bit of maths down there.
A genetic marker is a variable locus in the DNA sequence with a known location on a chromosome.
So here you can see a map of 156 genetic markers,
so at each location we get a genotype for that marker.
And the aim of the game is to correlate the genetic outcomes of the genetic markers
with the coat colour expressions in terms of mathematics.
All the chromosomes are now stacked up one after each other we've added them together
so we're basically scanning the genome for what's called linkage
between the coat colour trait here and the genetic marker loci.
On the Y axis is our statistical measure here called the LOD score.
A LOD score of about three is considered statistically significant and you can see
that we've identified two coat colour loci so we were easily able to map the agouti locus
to chromosome 2 where we know it resides, and similarly the albino locus
to chromosome 7 where we also know it resides.
So maths and stats are incredibly vital in genetics.
In my particular area we're assessing relationships between traits.
We're interested in identifying diseases running in families, and the methodology
that I've displayed here with regards to identifying the loci
for the coat colours that's exactly the same methods that we use.
The mathematical machinery is the same, so we use this technique all the time
and it's a very powerful technique.