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In 1856 an Augustinian friar began experiments
on pea plants in the Abbey's greenhouse.

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His discoveries came to be known
as Mendel's laws of heredity,

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and the man himself Gregor Johann Mendel,
became known as the father of genetics.

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By using simple probability
models, Mendel showed the power

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of statistics and mathematics in genetics.

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He crossed pea plants producing only yellow
seeds with plants producing only green seeds.

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The first generation hybrid
seeds were all yellow.

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He then crossed those seeds and the
second generation were 75 percent yellow

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and 25 percent green.

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Mendel showed that each plant
carries a pair of hereditary factors

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for each character, one factor from each parent.

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One factor is dominant and one recessive.

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In this case the F1 seeds yg
are phenotypically yellow.

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Mendel's two factors are a form of a single gene
and we call them alleles of the single gene.

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A blueprint of genes an individual
carries is called a genotype.

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The expressed character of an
individual is called a phenotype.

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Common examples are human hair
colour, eye colour and blood types.

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The familiar ABO blood system is an
interesting genetic model in itself

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because there are three different alleles.

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Basically, the A, B and O allele.

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The A and the B allele are equally
dominant and the O is recessive.

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I'm Melanie Bahlo.

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I'm a laboratory head at the
Walter and Eliza Hall Institute

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which is a biomedical research
institute in Australia.

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I have a PhD in Statistics.

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I work a lot on genetic mapping, finding
genes that cause disease in humans

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but I've done quite a lot of work in
mouse genetics as well like for example,

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genes that determine coat colour in mice.

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The mice that we're crossing here
is a white mouse and a black mouse.

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Now even though we've just got two coat
colours there, what is actually hidden

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in this cross are three colours and that's
because of the two genes that are involved

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and they're on different chromosomes and
these two give the genetic information

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that determines the coat colour
in this particular cross.

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To work at the genetic level,
they used mouse blood samples.

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In genetics, a locus , plural
loci, is the specific location

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of a gene or DNA sequence on a chromosome.

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A list of loci in a known order, separated

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by known genetic distances,
is called the genetic map.

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For each parent of course you get 2 alleles,
one from one locus and one from the other locus,

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so that means that you can get 4 by 4 different
genotypic combinations or allelic combinations

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and that will determine the outcome of the
coat colour and that's most easily explained

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in a Punnett square which is
a very typical way of writing

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out the genetic combinations of alleles.

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If you have two copies of the capital A allele,
that's the agouti allele, you will be agouti,

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the browny colour and if you've got
two copies of the capital C allele

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which is the wild type allele at the
albino locus then you will not be albino.

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So albino is recessive, so you need two copies
of the little c allele to make you white,

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and then the complication is that the
albino locus masks whatever is going

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on at the agouti locus.

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So therefore it whites out
everything if the mouse is albino.

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Now considering all the possible
matings between the male

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and female mouse you have 16 different outcomes.

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In the top left hand corner you've got
a double dose of the agouti allele,

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the white type allele, at the
agouti locus and a double dose

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of the c allele the wild type
allele at the albino locus.

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So therefore the mouse is agouti and not albino.

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In contrast the albino mouse as you
can see is actually capital A capital A

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which would be agouti if you could see it but
because they're little c little c they're albino

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and therefore that masks the agouti
or black colour whatever it is.

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So it's brown underneath but you never see
it because it's masked by the albino allele.

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So mating the black and the white
mouse together produces a brown agouti.

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And then when you get to the F2 which
is what's called an inter-cross,

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so here you're mating the brothers and sisters
offspring, the F1s so all the agouti mice

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with each other, you can now see
the entire phenotypic spectrum:

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black, white and agouti mice.

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What's important here is the ratio which
we've worked out from our Punnett square

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of the outcomes of these coat colours,
considering the 16 outcomes is 9 to 3 to 4

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of agouti to black to albino and that
is the first bit of maths down there.

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A genetic marker is a variable locus in the DNA
sequence with a known location on a chromosome.

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So here you can see a map
of 156 genetic markers,

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so at each location we get
a genotype for that marker.

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And the aim of the game is to correlate
the genetic outcomes of the genetic markers

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with the coat colour expressions
in terms of mathematics.

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All the chromosomes are now stacked up one
after each other we've added them together

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so we're basically scanning the
genome for what's called linkage

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between the coat colour trait
here and the genetic marker loci.

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On the Y axis is our statistical
measure here called the LOD score.

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A LOD score of about three is considered
statistically significant and you can see

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that we've identified two coat colour loci so
we were easily able to map the agouti locus

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to chromosome 2 where we know it
resides, and similarly the albino locus

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to chromosome 7 where we also know it resides.

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So maths and stats are incredibly
vital in genetics.

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In my particular area we're
assessing relationships between traits.

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We're interested in identifying diseases
running in families, and the methodology

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that I've displayed here with
regards to identifying the loci

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for the coat colours that's exactly
the same methods that we use.

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The mathematical machinery is the same,
so we use this technique all the time

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and it's a very powerful technique.