To live on Earth is to live as part of a network:
To live on Earth is to live as part of a network:

a giant web where almost every creature
a giant web where almost every creature

depends on others for survival.
depends on others for survival.

These networks are so complex that it's difficult to predict how resilient
These networks are so complex that it's difficult to predict how resilient

they might be to changing conditions.
they might be to changing conditions.

Let's take an ecosystem in Australia, where certain plants
Let's take an ecosystem in Australia, where certain plants

have a symbiotic relationship with various ants.
have a symbiotic relationship with various ants.

The ants act as bodyguards protecting the plants
The ants act as bodyguards protecting the plants

who in return provide food and shelter for the ants.
who in return provide food and shelter for the ants.

But it's not like every kind of plant has its own species of ant;
But it's not like every kind of plant has its own species of ant;

that would be much too easy.
that would be much too easy.

In fact, each ant can visit a variety of plants
In fact, each ant can visit a variety of plants

and each plant benefits from the protection
and each plant benefits from the protection

of a number of different kinds of ant.
of a number of different kinds of ant.

You can see how quickly a network becomes very complicated.
You can see how quickly a network becomes very complicated.

Let's take all the plants in the ecosystem and draw lines
Let's take all the plants in the ecosystem and draw lines

between any two species that share the same ants.
between any two species that share the same ants.

This ecosystem can be represented by a network.
This ecosystem can be represented by a network.

The plants are the nodes and the connecting lines are the ants.
The plants are the nodes and the connecting lines are the ants.

Two plants are linked if they share at least one ant species.
Two plants are linked if they share at least one ant species.

If they share more than one, the link is even stronger.
If they share more than one, the link is even stronger.

By helping the ants, these plants are also indirectly helping each other.
By helping the ants, these plants are also indirectly helping each other.

The success of one plant might lead to more ants
The success of one plant might lead to more ants

which could benefit another plant.
which could benefit another plant.

Having lots of connections also means the network can adapt to change.
Having lots of connections also means the network can adapt to change.

For example, along the bottom is a list of all the ant species in the system.
For example, along the bottom is a list of all the ant species in the system.

If one of these ants disappears the network can compensate.
If one of these ants disappears the network can compensate.

It's resilient...
It's resilient...

...up to a point.
...up to a point.

As we remove ant species at random, one by one,
As we remove ant species at random, one by one,

the connections in the network grow weaker and start to disappear.
the connections in the network grow weaker and start to disappear.

As we go along, as well as losing whole plant species
As we go along, as well as losing whole plant species

the abundance of remaining species gradually decreases as well.
the abundance of remaining species gradually decreases as well.

There comes a key point for every network
There comes a key point for every network

where the population of the remaining species suddenly crashes.
where the population of the remaining species suddenly crashes.

The network can no longer compensate for further changes.
The network can no longer compensate for further changes.

Where this point comes represents the network's resilience.
Where this point comes represents the network's resilience.

This resilience is usually thought to be completely unpredictable
This resilience is usually thought to be completely unpredictable

as it varies so much between different networks
as it varies so much between different networks

but researchers have developed a new tool to try and simplify things.
but researchers have developed a new tool to try and simplify things.

They started with complex, multi-dimensional networks,
They started with complex, multi-dimensional networks,

all with different properties.
all with different properties.

The clever part is then using various mathematical techniques
The clever part is then using various mathematical techniques

to transform all these networks into a standard model
to transform all these networks into a standard model

in which the crash is always in the same place.
in which the crash is always in the same place.

This means that the resilience of the original networks is now predictable.
This means that the resilience of the original networks is now predictable.

This can be useful in predicting how ecosystems might react to environmental changes.
This can be useful in predicting how ecosystems might react to environmental changes.

Climate change, for example, can affect all species in a network
Climate change, for example, can affect all species in a network

and their relationships,
and their relationships,

weakening the strength of all the connections.
weakening the strength of all the connections.

This can make the resilience of a network so low
This can make the resilience of a network so low

that it might only take the removal of a handful of species
that it might only take the removal of a handful of species

to bring about complete collapse.
to bring about complete collapse.

This is particularly worrying for already fragile ecosystems
This is particularly worrying for already fragile ecosystems

in which a tiny change could cause the extinction
in which a tiny change could cause the extinction

of a whole host of plants and animals.
of a whole host of plants and animals.

That's why it's important to have tools to predict and prevent
That's why it's important to have tools to predict and prevent

these catastrophic network failures,
these catastrophic network failures,

like the disappearance of honey bees
like the disappearance of honey bees

or unexpected collapses in commercial fisheries.
or unexpected collapses in commercial fisheries.

And these models don't just apply to ecological systems.
And these models don't just apply to ecological systems.

The same tools can be used to examine networks of people
The same tools can be used to examine networks of people

from social networks to the spread of epidemics,
from social networks to the spread of epidemics,

banking networks in a financial crisis
banking networks in a financial crisis

and even networks of air traffic in which a single problem
and even networks of air traffic in which a single problem

could cause huge delays.
could cause huge delays.

Models of all these things are often available already,
Models of all these things are often available already,

based on specific real-world data,
based on specific real-world data,

but these new mathematical tools can be
but these new mathematical tools can be

applied generally to a whole range of different systems.
applied generally to a whole range of different systems.

They should allow us to predict how any network will respond to change
They should allow us to predict how any network will respond to change

and could even suggest specific strategies
and could even suggest specific strategies

for preventing catastrophic damage.
for preventing catastrophic damage.

Whether its plants, planes or people
Whether its plants, planes or people

we may be a little closer to understanding
we may be a little closer to understanding

the giant, complex networks of our planet.
the giant, complex networks of our planet.