 Sorry to break the coffee break, I know a lot of interesting discussions going on at the coffee break and let me once more thank the organizers of the conference to give me the opportunity to come once more actually in this beautiful place and That this very inspiring conference And to also give me the opportunity to talk about my work here today As an oceanographer, well, we have been mentioned before that this conference is very interdisciplinary and As an oceanographer for me this implies that actually the type of questions that we'll ask and the type of methods that I will show here They have a little bit of more applied kind of feeling so I will show methods and things that can contribute for example to fishery management or mitigation of climate change or a conservation of particular species, so we don't really wish to go Well, at least we don't have the aim to go towards a sort of universal law that can explain anything But more trying to produce simple models that can help us in understanding something. That's the general idea So I was carried away about the discussion. We had the other day about the physics boring biology complex It's actually quite interesting discussion there So I could go with two offerings here one is that all model are wrongs, but we don't want to say that so the other one that actually is interesting Is this paper that you probably might know That's a I mean in a kind of difficult English. I've entered another and perhaps equally reckless generalization Nothing makes sense in biology except in light of evolution Stop species evolution and a good friend of mine a physicist Simone P. Golotti some of you might know him. It says that a very good approximation of this sentence is this one Nothing makes sense in biology Which I kind of agree with him, but yeah, so we try to make some sense out of it and My main motivation in this one is actually about long-distance migrations in in in the ocean This is something it's a well very interesting topic, of course Has been evolving of the airs because we didn't really have much data before In tracking fish. So for example understanding of tuna migration was based on the hooks found on the tuna in Spain But they were coming from hooks that have were produced in Brazil for example Stuff like that. So deduction between populations moving from one place to another today We have a little bit more advanced a way of understanding these tracks or these trajectories or these migrations With these satellites pop up archival of tags They are not as precise as the one that are I suppose commonly used Interracial ecosystems because we don't really have the GPS signal going underwater and fish most of the time to spend the time underwater or in a dish, but They basically rely on additional informations like a light level and Temperature depth and based on that you can reconstruct quite accurately the location that they have been migrating to and from So and the the reason one that I shown top from sequela and the colleagues in 2018 they actually they claim that they have enough data now to start thinking about these migrations in a more quantitative way So in describing maybe patterns for different class of animals of migrations One of the things that actually strikes me. Well, what they found is that okay They they don't move much randomly, but they have a kind of ballistic motion makes sense And you'll do kind of long-distance migrations. That also makes sense, but yeah One thing that actually is interesting is that the correlation between these Maximum distance that they travel and the sides of the body There is a very interesting paper by Hein and colleagues in 2011 where they actually derive this from a mechanistic approach So they understand the term all well the metabolic cost of migrations or movement and the type of Either if you want to walk fly or swim and they can actually predict this correlation these allometric function quite accurately and Exactly for a swimming organism. I try to put one point for copper pods so zooplankton species They are about one milligram and they can still migrate vertically for about a kilometer and still it fits with that slope So quite interesting stuff Something that sticks out of this is a tartles and tartles is actually one special animal in many ways First of all is also because we can actually in that case a touch some sort of GPS tracker to them So we have actually quite good Trajectories for them and the other thing is that they stick out of this curve So they are for their sides they migrate much more than the other fish apparently So I just want to talk about tartles basically that was the excuse to talk about it So a colleague of mine frame highs working at the moment in Australia docking University Contacted me saying well have these tracks. They're nice very high precision, but they change over the years quite often So for example they had for 2010 and 2011 Migrations they have a breeding ground in the Greece Zaxintos, I think it's called the island and they migrate for the feeding ground in In the african coast. I might even have a pointer. Yeah here But for this year, they are quite straight They go I mean from the origin to the final destination in a quite a straight line while in other years It's more convoluted path So if they were like humans walking in a square One hypothesis could have been that they were all drunk for example, but since our fish. Well, not even fish reptiles Swimming in the ocean First hypothesis was that it could be something related to the ocean currents So that the currents In this specific year that was 2010 should be stronger than the one in 2011 From a visual inspection actually you couldn't do much Doesn't look like that at least very striking pattern on that if you actually Extract the velocity along the trajectory. It seems that actually on average these velocity are stronger But we kind of use this data to motivate ourselves to look a little bit about The concept of migration for long distances in a shear flow So this problem was actually presented at the beginning of the last century from Ernst Zermelo quite a famous mathematician in in many sectors including control systems and Yes, basically, okay The question is what is the minimum travel time from zero to one in a shear flow like this So you have a weak current here and a kind of stronger current here We expanded a little bit upon this concept saying, okay Let's say that the turtles are using different behavioral rules to navigate in this field So for example, they use like okay, they fix the direction and they start swimming So what you will get depending on the velocity of the current that you will get a deviation of these trajectories away from the target If they adjust They're heating while navigating then it depends on the relative velocity between the velocity of which the swimming They are swimming and the velocity of the current you might have different type of course including this type of banded curves Still getting to the final destination But if you want to cross this in a minimum time You will do something quite different So you will swim against the current where the current is weak and then you you will use the current actually to Go faster towards the target So we tested these hypothesis with the different tracks and well for some of them these behavioral models They seem to kind of agree Qualitatively we have some metrics to do it in a quantitative way For some of them. They really didn't agree much like for example in this case In other cases some of them agree, but the optimal one seems to stick out most of the time as the one that actually doesn't really Take it so these are an example of the type of simulations We have been doing and the analysis actually is based on some sort of Markov process to define this optimality curve And here is another example where basically yeah, we didn't really get the at all The black one is the is the observed track and this one are the different models As you can see here is like okay It's a different totally different type of behavior in the sense They get somewhere then they realize for some environmental conditions that is is not the place where they want to go And then they make a correction about it moving along the coast So when you introduce this in the model you kind of mimic a little bit what they do So they are definitely not optimal in what they do and That's yeah showing some medic in terms of crossing time for the different behavioral models But the main message is that they are really not optimal What we didn't write in the papers that if you actually then play a little bit with this velocity field Changing it randomly either the departure time or the different years in a way giving a kind of Climatic envelope because this current can change quite a lot So they are not optimal yet, but they are not too far from the optimality So they are not optimal, but not even totally Stupid in that sense. So we want to expand a little bit on this concept and we are working with well Jerome that is now a PhD student in my institute Antonio who is here and co-organizer of the conference and Ufa Tickston to expand on the concept and using maybe control theory to understand What type of behavior they are actually using so the mathematical model that we are thinking of is that the trajectory is actually a composite The observed trajectory is actually a composition of the velocity field plus some swimming and this women could be sort of Considered as a control velocity And there is some noise. This noise is either because they do errors during the navigations, but also because The currents are kind of mesoscale structures in the ocean that can affect them and Then we make explicit in the cost function for this migration two terms one is the metabolic cost of swimming with some function of gamma and another one is actually the The crossing time so the fact that they have to get there at a given time Otherwise them is maybe mating opportunities or feeding opportunity or they don't want they don't get enough food or whatever Plus we also include a term modulating what type of Personalities if you want they use in this migration. So are they taking risks going maybe into areas of a strong Velocity of the current that goes against the direction they want to go But men could be better after that or they don't take risk there needs a risk neutral or risk adverse So we are working at the moment on this is very much Work in progress. We have been using different tracks than to do statistical influence of this using this model And we have tracks for whales and turtles Something that seems to come up from this Work is basically that they cluster So these behavioral traits if you want these terms of gamma beta and alpha They could be considered different type of behavioral traits. They seem to cluster for different type of organisms But as you might notice I mean Turtles they don't really traveling groups. So these are very little to do with the group formation and decision-making that I'm supposed to talk about but fish they do they move in schools and One thing to consider about fish is also that when they move in school to reach different feeding grounds, for example They really compete with each other. I mean the worst competitor for a tuna is another tuna most likely so since I will go to talk about tuna, I'll just introduce it a little bit and Bluefin tuna, which is the Atlantic Bluefin tuna that I will be talking about is among the largest Marine animals that we have It can be long up to five meter 700 kilos It can basically leave everywhere in the Atlantic Ocean from tropical areas to polar areas Has a very it's warm-blooded so has a cardiovascular system that is actually quite similar to the human one We have been fishing it for ages So and at the moment is a very high valuable commodity fish commodity It moves in schools and opportunistic feeder So one thing that is actually interesting is that they can leave basically everywhere But to reproduce the only going to places the Gulf of Mexico and the Mediterranean Sea and That's even in the Mediterranean Sea very specific locations there apparently That's interesting and also they do this in a very narrow window of time about 15 days in between weeks So after that they move out most likely and they migrate in different places As I mentioned before we have tags for these species thanks to the group Foundation called tag a giant actually they did fantastic work in tagging these animals And showing us more or less their distributions So I don't want to spend too much time But basically this shows that they are distributed all over the North Atlantic with also presence in the in the Mediterranean Quite a lot of time spent in the western part of the Atlantic Oceans The thing that is interesting is that different seasons they seems to have they are widespread But actually they have a kind of hotspots of aggregations And they seem to migrate between these hotspots So this week actually we can use it for to model the behavior of migrations across the different hotspots And we use kind of network theory approach Where we have different nodes of the network With different habitats this is habitats might change over time because of changes in Well habitat quality temperature food or whatever And then what we want to understand is basically the Changes in time or the population in the different Habitats different highs so that's basically depends on how many are coming in minus how many are going out But the decision about going in or out depends on some sort of reward function that has Utility based on the fact that they will get some food in the habitat, but also some cost of migration To make it short. This is basically a framework for a game theory model applied on a network and It's I mean now some complications in solving it But of course as a value that you can have different strategies emerging from this setup So different fish moving in different places And we can sort of validate this dynamics based on the time series that we have in some of these places So what we get from the model? Is basically that the phenology of these migrations are reproduced quite correctly here different colors are different classes So we had like a the full demography of the bluefin tuna from the young of the year to the adults more than eight years ability Some regions they only have presence of the adults for example other regions They have a more mixed population structures that seems quite in agreement with what we observe in different areas The other thing we can do is to reproduce or having emerging Migration roots out of this one because not all the roots are used This one is basically showing the distribution of biomass in different locations and the full line is basically an active Root of migrations where a dashed one is a migration that is not used a root of migration that is not used for some reason and You can see changing some of the parameters of the model Basically what you get is that some of the more extreme nodes in the network are kind of excluded from this migration game so take a message from this is basically that there are different strategies con can coexist in the population the phenology seems to be okay and When conditions in the habitats are good all habitats should be full But this doesn't quite fit with what we observe. Oh You cannot see a map here. Can you see a map? but there was a map of the Atlantic and What he shows is the presence basically of the bluefin tuna from the Gulf of Mexico in the Mediterranean Sea north Atlantic But there is something missing Which is there are no more tunas in the North Sea on the Nordic areas and they were used to be there So these are landing time series of tunas from 1900 to 2010 What you see is that there is a peak here of landings. So these are the amount of tuna that have been catched In in North Sea in Nordic seas and then there is a kind of sharp decrease and then zero tuna So the zero tuna before is basically because they didn't know what it was They had the tuna present in their fishing operations And they were annoyed because they were fishing herring and this tuna was eating the herring And then they didn't want to have this tuna, but they didn't know that was a tuna So at some point they realized that actually the the single tuna that they were trying to Kill was more valuable than the old herring that they have catched during the year So they started fishing it and was very valuable fishery For a few years and then it collapsed completely So why is that? Yeah, this is just to show that actually they were tunas before in the area quite abundant actually before they started fishing and These are an image of the tuna stored in in Denmark during 1946 I think something like that. So one of the good year in these times years So why is that why we don't have tuna maybe because the stock is too low so they don't get there Well, no not quite. So this is again the time series of landings now in this case I think is biomass converted with some fishing effort and This is one is the spawning stock biomass. So it's the total population of the bluefin tuna Didn't I mean there is some change but not quite substantial as this one. So there should be tuna in the North Sea What about the prey the prey had a reduction in that period But now it's fully recovered. It's actually very abundant So why they're not feeding on this very abundant stock here other things like temperature salinity. No, it doesn't matter Just to show you. Yeah, maybe I have a little bit of time Just to show you how the fishing is actually done for bluefin tuna There are big vessels around in the Mediterranean sea for example There are big nets here In these operations, they have to locate the school and what they do for locating the school is Should be visible in a few seconds Yeah, they use airplanes so they go on airplanes and experience fishermen goes on that and They start looking around for a school of tuna that most of the time is actually on the surface And then when the school is identified they release a small vessel they start extending these net around the school Quite quickly moving more or less at ten nodes Okay, still moving At some point they close the net and they take it up, but actually they don't kill them Now they are closing the net from the bottom Some of them of course are killed by the operation which is quite It's stressing quite a lot of them But not that many it's a very minor fraction that is actually Killed in this one. Those are the one that didn't make it. But now what they do they call basically another vessel Coming with a big big cage 100 meters diameter and what they do they attach this cage to the net and then they transfer the entire school into the cage for fattening so the tuna is better when it's fat and Each gram actually is money a single tuna of that can be like worth two million dollars on the Japanese market Well, it's one single because it's an auction and they really want to pay for it because then the restaurant becomes very famous Nonetheless hundred thousands of dollars here easily for a single tuna So then we send a diver in the cage to see the operation This is the cage they attach it there. Yeah, but it's a bit longer than few minutes This is the diver and some point you should see how they actually enter the cage Yeah here So this basically is transferring there and they stay for months in these cages Fed with the anchovies our deans and other things not very efficient, but definitely Economically viable. Yeah, and to close down with a nice cool formation that you will see in a second We didn't really analyze this Actually, I'm not even allowed to show it but now it's few years that we have collected So I feel free to to show it here So maybe you will not get much out of my presentation in terms of the models But one thing you will remember next time that you order your sushi is the airplane. That's That's the way to catch it So but going back to the migrations Again, sorry for the quality of the map here. That's the Mediterranean sea and this one is the Well, North Sea here and Norwegian sea up here So what is showing is that I mean in the past we had this migration route used by many of them So all kind of classes from the young of the year to the old tunas After a few years, we had especially after the 70s when they entered with the big vessels in the Mediterranean sea Only the big one were traveling there But now it's really zero. There are no tunas in the North Sea So why is that? Did a kilo of them or the actual question here is how where is this information how? Where is it lost? I mean, where is the information about migration path? So we have some ideas about it To answer basically, where is the information about the migration path stored? and the idea is that there was some sort of a collecting memory that was Destroyed somehow by the fishing activity. So we have a paper called which a very nice nice title Maybe the paper is not that good, but the title is great fishing out collecting memory of migratory schools and the concept is that Well, I'll show you in a second You can build a model to explain how the information can be stored in a large group and how this can be perturbed by humans so the general idea is that each individual is able to interact socially with others in the group and only a fraction has the information about where to go the right direction to go and Social interactions Might be used by the each individual basically to enhance the knowledge about the direction to go and reach a sort of consensus Well, yes So how do we build the model the model is basically based on it is an agent based an individual based model and each agent basically has his own Information but also the ability to interact with the other agents with some rules probabilistic rules And we could use like a spatially explicit type of model like the district model or some other with alignment and avoidance of velocities and Well here again, there is some missing stuff But we didn't use that because I mean space information in this case is not really critical for us So we went for another type of approach that actually has been showed yesterday as well Using graph theory. So we have nodes In this network and these nodes interact with some probabilistic rules among each other But what you have is two types of dynamics here One is the dynamic on the networks. So the links creation and destruction And the other one is the change of preference of the fish. So the internal dynamic of each node This work has been done in collaboration with a former PhD student here to see that John cattle the luca and Yeah, it goes a little bit in details I don't know how much we have to go into details But we have a given number of individuals in the group and each one has a internal preference about where to go The state of the system is basically defined by this the neighbor Network and the preference of each of them as I mentioned before we have two type of dynamics one is the internal dynamics of the network and the other one is the internal dynamics in the nodes and the Dynamic on the network In a not very simple way. We can basically solve this master equation But let me focus on the probabilistic value only for the quality of the plots here There are some extra colors that is missing But the point is that you can go from this configuration on the network where basically i and j they don't have a connection But if they share a preference about where to go then they can make a connection with some probability Ada in this case So we have obviously a given function for the probability to make connections between two individuals in the in the network and equally we also have a probability And yeah, well I'll say it later You also have a probability to destroy this network or destroy the link the specific link with another probability So it's really stochastic Each agent can change its internal state And the internal state depends on the preference that they have for a given destination So we have a number of destination q destinations And for each of them there is a preference So when they are not linked they will update Their internal state If they have a strong preference, they will be more there will be a higher probability for them to select The destination where they want to go, but they can still change destination and also going maybe in destinations where they don't want to go especially when they Select a destination where they don't want to go and then they link to other agents So in that case basically they are forced to go somewhere else The main message here is that there are no real leaders here. I mean the information is there But it's not clear if this information under which condition this information can emerge So when they are linked to each other, we have a voting mode voting model So sticking basically with the majority which seems to fit with the At least mimicking more or less the the spatial explicit type of model of this back this check And yeah, we have some rate of frequency also in updating these The links that they have internally So the h value here measure basically the strength Of the preference that each agent has for some specific destination That's what we have to keep in mind I'll skip the detail balance And I'll go to this invariant distribution that we can derive One thing to notice in this well first of all Yeah, it's quite complex, but One thing is actually interesting is that this ratio appears So it's basically the ratio of probabilities to make a link over the probability to destroy the link And this actually can be merged in a single parameter that we call Sociality, so how social they are in making links how frequent they can make links Then we can also notice that we have an h dependency here And also the dependency on the number of people a number of individuals that have information five minutes so Let me show you the results we analyze them In terms of what is called the network theory the giant component So we try to understand in which conditions the system actually behaves like a group or there are groups formed And where these groups are going are they going to their preference directions or they are going somewhere else Let's start looking at the results when there is no information. So in this case, we have a bunch of individuals And they don't really have a preference. They can go any of the queue destinations that we have If this is a society is very low We are on this branch here, then there is no group formation They are all like a small groups here and there, but there is not this giant component emerging from the system But you can see that There is also a solution where we actually have a very polarized network a very Coherent network or all the individuals linked together or most of the individuals linked together and this frequency The number of individuals there is not changing over time. So it's stable And there is a region where basically you can have two solutions and this is also kind of Yeah missing color, but some hysteric cycle basically that we reproduce without information We can also solve the system analytically basically in some conditions. So for not A given number of individuals, but for an infinite number of individuals And the solution basically fits with the numerical predictions When we introduce the information in the system, there are two effects Which you cannot see but trust me So the first one is that actually the We have queue destinations one has a preference for the group What you get is that the one with a preference is the one that is stable or the one that is most frequently selected But you also have Q minus one destinations that they can still be selected by the group Plus you still have this possible transition from no schooling to some schooling So you have three solutions here. No schooling at all schooling it to the wrong place or schooling to the preference Praise and this depends on the number of Individuals that are informed and the preference that they have for the given place Well, this one was a key figure which is basically invisible But this line is the critical line that I showed you before of the transition And here there is a shade Of blue that basically tells you how this critical zone shrinks Increasing the number of informed individuals Basically to make the group moving You need like 15 percent of the individuals with some information about where to go In that case the most likely configuration of the model is that you have a school and it goes to the right place If you change the preference So in this case you increase the preference what you get now it's a little bit more visible But you get that this fraction is reduced. So here you needed like a 17 percent of the individual with information Here you need less than 10 and the group is formed and the direction is taken up So how does it fit with our tunas? I showed you before these landings and the dynamic of the prey Maybe some of you can already notice that this kind of cycle here It's a sort of a hysteric cycle in the system So if you start putting this data on a face plot like this with the herring biomass here and bluefin tuna biomass here Over the years there is a decrease in the biomass of both predator and prey and then at some point No tuna anymore, but the prey are increasing Hysteric cycle that we also find in the model So this one is a plot of fraction of informed individuals Polarization of the network so scooting efficiency and the preference for the habitat If you start reducing the number of individual with information And also killing the prey which basically means over time you are reducing the preference for that specific habitat You quickly go towards a rapid transition here where there is no more group formed And now even if you increase the preference because the prey are back You don't form the school anymore So an hysteric cycle that seems to be in the data and is definitely present in the in the model as well I don't know how I'm about with time Two minutes. Well, this one is basically the last slide I think but now a good news Because I mean in the model we predicted one thing so collapse Based on the fact that you are phishing out the information But possibility of recovery because when you are here if you allow the group to Regain that information you can basically jump this transition here and you're back To a very good kind of dynamic in terms of migrations So we predicted that in 2010 And tunar back Well, we we have been cited by the danish national authority is saying oh they say that And so tunar back now in the north sea Very recently a couple of years First observations of few vagrants individuals in the area and now over the years It seems that this information is regained in the group So now they know The place again and it seems that they are going back We started basically a tagging program on it Not very easily done because these tags. They are not very reliable. They they touch easily So but we started making some investigation about Well, now that they are here This is danmark Copening in this down here And those are the one that actually we have been tagging Some of them they went back to spain So it seems that the route that historically was lost is now Back in business I think I stop here and thanks all the people that have been contributing to this Thanks