And thank you, I want to thank the organizer for inviting me here in this beautiful air

language that has a weather as good as south of Italy, as you know in Germany we have such

a good weather.

So today I will talk about replicator dynamic that is actually the model that Professor

Orlando just talked about but on a network.

And this research is a part of a project, of a national project trying to study, I mean,

the biodiversity into the Mediterranean Sea.

The point is that, as I think all of you know, in the Mediterranean Sea and honestly in all

the seas around the globe, you have that there are a lot of species that are non-indigenous,

right?

Meaning that there are a lot of species that somehow were brought into that zone.

And the point is try to, the point of this project is, you know, try to first explain

how and why indigenous species are, we have so many indigenous species in those seas

and how to protect those species.

So with our workgroup we are starting to, you know, take some maps in order to understand

where are the zones that need to be protected in a sense.

And as you can see in this map, you have a lot of reserves that are zones in which you

have the majority of biodiversity indeed within the Mediterranean Sea.

I mean, Barry is in the hill.

No, no, I mean, everyone knows, everyone knows where Barry is.

Barry Caputmundi, you know.

Barry is in the hill of Italy, right?

I mean, my arm is too short, I cannot, goes there, but Barry is over there.

Okay.

And I mean, those zones are the biological reserves you ideally want to protect.

The interesting thing is that you can completely overlap this map with the ship routes and

with the most used routes and ports.

Okay.

This is not, you know, just a casualty.

As you know, for example, the blue crab, okay, it was brought from abroad into the Mediterranean

Sea through a ship.

It's indigenous, it's an alien into the Mediterranean Sea and now the Mediterranean Sea is its preferred

habitat.

But it was put into the Mediterranean Sea from a ship.

So this is quite usual, I mean, in terms of biological exchange.

Now the idea is to build a network in which every node of the network is a biological

reserve and is regulated by the replicator dynamics by Professor Orlando with a transport

term that is an extra reserve function that will let the species move back and forth from

a node to another.

Indeed, you have to consider that for all the properties of the replicator model that

Gianluca just told us, this function cannot be any function.

It needs to move the species from the simplex to the simplex.

It's a map between, I mean, from the standard simplex in R to the N to the standard simplex

in R to the N.

In this way, we build a model of N species consisting of N-V nodes connected by N-E edges

or roots.

That is the same, I mean.

For the transport term, we kept two functions.

The first one that is quite simple, I mean, is just a linear function exchanging species

from a node to another proportionally to the difference between the K-species in this node