To live on Earth is to live as part of a network:
a giant web where almost every creature
depends on others for survival.
These networks are so complex that it's difficult to predict how resilient
they might be to changing conditions.
Let's take an ecosystem in Australia, where certain plants
have a symbiotic relationship with various ants.
The ants act as bodyguards protecting the plants
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;
that would be much too easy.
In fact, each ant can visit a variety of plants
and each plant benefits from the protection
of a number of different kinds of ant.
You can see how quickly a network becomes very complicated.
Let's take all the plants in the ecosystem and draw lines
between any two species that share the same ants.
This ecosystem can be represented by a network.
The plants are the nodes and the connecting lines are the ants.
Two plants are linked if they share at least one ant species.
If they share more than one, the link is even stronger.
By helping the ants, these plants are also indirectly helping each other.
The success of one plant might lead to more ants
which could benefit another plant.
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.
If one of these ants disappears the network can compensate.
It's resilient...
...up to a point.
As we remove ant species at random, one by one,
the connections in the network grow weaker and start to disappear.
As we go along, as well as losing whole plant species
the abundance of remaining species gradually decreases as well.
There comes a key point for every network
where the population of the remaining species suddenly crashes.
The network can no longer compensate for further changes.
Where this point comes represents the network's resilience.
This resilience is usually thought to be completely unpredictable
as it varies so much between different networks
but researchers have developed a new tool to try and simplify things.
They started with complex, multi-dimensional networks,
all with different properties.
The clever part is then using various mathematical techniques
to transform all these networks into a standard model
in which the crash is always in the same place.
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.
Climate change, for example, can affect all species in a network
and their relationships,
weakening the strength of all the connections.
This can make the resilience of a network so low
that it might only take the removal of a handful of species
to bring about complete collapse.
This is particularly worrying for already fragile ecosystems
in which a tiny change could cause the extinction
of a whole host of plants and animals.
That's why it's important to have tools to predict and prevent
these catastrophic network failures,
like the disappearance of honey bees
or unexpected collapses in commercial fisheries.
And these models don't just apply to ecological systems.
The same tools can be used to examine networks of people
from social networks to the spread of epidemics,
banking networks in a financial crisis
and even networks of air traffic in which a single problem
could cause huge delays.
Models of all these things are often available already,
based on specific real-world data,
but these new mathematical tools can be
applied generally to a whole range of different systems.
They should allow us to predict how any network will respond to change
and could even suggest specific strategies
for preventing catastrophic damage.
Whether its plants, planes or people
we may be a little closer to understanding
the giant, complex networks of our planet.