 lecture three, and let me close this up, in a particular place randomly chosen, you keep going with that, and you replace it with either an non-existing color slash species slash individual with a certain probability of a diversification ratio, whatever you're going to call it, or you replace it with some nearest neighbor or some neighbor which was chosen with respect to a kernel of the domain of influence for which you choose the most numerals, or in a mean field sense whether you choose it from anywhere else based simply on abundance. And that of course entails neutrality in the sense that the preference is simply due to sheer numbers, sheer abundance, and that's the essence of a neutrality assumption. And the patterns that we've seen in there are quite different depending on a sole modification, which is in this case the directional disperser which is embedded in the network structure, the three light structure if you please, or the open to any, I'm sorry nearest direction, sorry I started back, so let's see how we can exploit this is Ignacio Rodriguez-Turbe, emeritus professor at Princeton currently now at Texas A&M, after like a couple of decades in Princeton, in which he said well why don't we assume that each branch of a network structure here becomes like a metapapulation, which is called a directly tributary area, but is a local community within a meta community. One of the points that I made in the first class was that the result that the directional dispersal which is embedded in a network structure for interaction that is that defines your nearest neighbors or a way neighbors in a selective manner is rather insensitive of whether you're talking about an individual-based or a meta-community-based approach, the result still stands and what later on we have done, like field verification of the same result, studies theoretical or empirical on migration fronts for instance that feel the structure of a directional dispersal or laboratory in fact experiments we learned in my lab in which was nothing neutral, there was a living community, the result still stands. So the idea is here is to assume that the large river system, this elementary unit on which you have reactions of physical, biological, chemical nature in this case biological could be a directly tributary area, which is a local community carved within the community like at their each scale and we thought of doing so, we referenced to something which is quite important, we took on the whole archive of local species diversity of fish populations in Mississippi, Missouri river system and LSR means local species richness however defined essentially can count the observed number of species which you have. So in a DTA in one of the notes of the links in which you can partition I'll be showing you now you can extract that objectively and manipulated remotely acquired and objectively manipulate the structure of the Mississippi, Missouri river system on a grand scale. In a DTA a fish unit can be thought of as a subpopulation of fish of the same species and you have a number of ways through which you can do that by expert things by the surveys by the collection that Bill Fagan the fish biologist has compiled for the whole of the United States and the idea of course in this case which you see in fact there is a the color called the local species riches which is different from the various places and what you see here this AARP this rather obscure in fact acronym means annual average runoff production which is essentially runoff I mean the total volume of runoff that passes through any particular cross section that is the hydrology. Now it doesn't take an expert statistician but simply a not a particularly a trained eye to see that there is a correlation between how much runoff you have in a particular place in different directly tributary area that is the hydrology the hydrology control and the local species diversity but to formalize this what you can do we can extract objectively even humongously large networks to detail which is actually in fact one of the reasons why in fact over the debate of critical self-organization that is why in fact certain recurrent characters embedded in a power law distribution of some aggregation structure of a catchment is the same regardless of climate vegetation exposed lithology the scale etc but something truly remarkable already the networks that generated files like or data sets like this one in which you can characterize a structure from the scale of one meter or less to the scale of thousands of kilometers and in terms of area even more so that can be done I hinted at that briefly in the first class and not touching on it but I assume that this is something which when you can trust me we've been working for like 20 years in characterizing those network shapes like these ones so let me see how essentially the model proceed it's it's well I have a few notes here but it's not going to be particularly but the idea is that it's likely experiment you've seen the neutral meta community or meta population experiment that I showed you in the animation I showed before they showed also in lecture one so these the assumptions in this case is every dta that is every unit is essentially saturated at its capacity that is no resource available to fish is assumed to be left unexploited now of course you're talking about some sort of an upper limit to be to a fish diversity but that's also quite remarkable how close I will show you this will be reproduced so the model dynamics proceed as in the other case which you have seen that is at each time step you randomly select a fish unit selected for all the fish units in the in the whole system and you assume it to die and the resources that previously sustained that unit are freed and available out for grabs for a new fish unit so we have certain probability which we term again the diversification ratio the new unit the fish unit will will be a new species it will probably be one minus new in fact it's going to be one of the existing species that colonizes the spot and the cost of diversification ratio a rate in this case could represent external interaction on non-native species we have seen how foreign invasions are so important ecologically for a variety of ecosystems or could be immigration or re-immigration in fact of a new species from outside the region you have seen the case of the example if you may recall from lecture two when we studied the breeding birds of of North America as a or the Kansas prairie uh uh species or Bassius species in fact that um in fact they the concept persistence time local persistence and local extinction has to be seen in the context of the geographical uh area which this is done so um uh with the probability one minus new the new unit can belong in fact to the to the species to be uh to be et cetera and the idea is that in this case you don't uh touch only nearest neighbors but essentially you characterize a probability pji ij i'm sorry that the empty unit in the ith uh dta in the ith node the directly tributary area whatever you're not calling is colonized by a species which is elsewhere in the j uh uh dta's that appear in the system through a kernel a dispersal kernel that you're having to say which uh uh specifies and measures the range of a species colonization now what is important here is a non-neutral effect um which is uh however not dictated by uh by uh a calibration not dictated by uh uh biological dynamics but essentially dictated by hydrological controls because it's geomorphological so you assume that the habitat capacity determining the resource in the place is the fluvial habitat capacity which is established on the scale of the basis of a scaling geomorphic relations we had hinted at that characterized the fact that um you can decide based on certain metric properties which are remarkably obeyed in the runoff producing area of any river worldwide and are dictated by the aggregation structures essentially the habitat capacity in the place is essentially dictated by how much area you had behind your back how many nodes do you collect through the structure of a network again which is a given now what is interesting that the dispersal kernel has certain features of which I shall not discuss but essentially what you have I want to study the particular back to back exponential which has a tradition in ecology one or another in fact we tested several of them um we were asked by the nature reviewers in fact to uh to run a comparative analysis and we apparently convinced them because we got published but the idea is that for instance if you assume the two units two nodes two dta's are uh ij what is the distance that separates them now that's interesting for colonizers because if you assume the colonizer strong fish units right um the path the path that connects you uh i to j could be partly downstream and partly upstream or could be strictly downstream or strictly upstream depending on ij now the question is you may bias the path because if you are a weak juvenile fish for instance a small one you may be way more affected by the velocity that is the drift which is embedded in the stream flow direction that is the oriented nature of the graph then it could be for a strong adult big fish right so either way then you may bias and weigh in fact the downstream direction the upstream direction distances which you have in the system which makes it reasonable and this is a tunable parameter in a sense but in a neutral case we kill it and we assume that all species are equally important to the capital at the at the per capita level so briefly as a result of what you're seeing here is in the frequency distribution of local species richness by letting the model run to stationary state now um it may be uh you may like it you may dislike it a set about for us it was totally remarked on how simply the nature of a connected of a connected system and the habitat size which is produced by scaling relations being embedded in geomorphological laws it's the aggregation structure um can allow us to reproduce wonderfully well um how the alpha diversity the distance to outlet i'm sorry this is i made a mistake i was anticipating what i explained here in fact so this is not a frequency distribution this is the how the alpha diversity unfolds from the outlet to the upstream distances with obvious differences which you have in a certain place for instance um this is blown out because you may have the the data telling you that some freshwater tolerating coastal fish species in fact could or human disturbance in fact or or pollution for that matter um alter what you would have otherwise a distribution that is what the data are showing in the new original new links and the same applies to the same thing at the same time which is also remarkable how the frequency distribution with respect to the distance to be out there the frequency of local species with respect to the thing that is you count essentially the number of species that equally distance from the outlet you got some sort of a range which is reproduced without any tuning by the model signifying once more one of the main tenets of my classes that there is something inherent in the directional dispersal implied by the network structure which is the substrate for ecological interactions which is given the system grant in the system uh reliability and predictability what is interesting also is that if you run the same exercise without changing the habitat capacity per every node embedded as proportional through um predictive geomorphological laws by the structure the aggregation structure which is essentially dictated by the total contributing area at any point deciding how big is your river and then what you see and you screw up completely in fact the uh the exercise and you see the hydrological controls embedded in any neutral model which is the simplest possible zero order approximation there's no description of the of the properties on which fish biology spending lifetimes of scientific work um are mostly explained by the hierarchical size structure of the fluvial network and it's embedded topology which is also reinforcing what we have seen before now things become slightly more complicated if you go into not only starting local species riches by the correlation structure which is a beta diversity that is um what is the probability that the existence of a species in one place is uh matched by the probability of existence of the same species at a certain distance distance being uh measured in so called chemical distance which is along the network structure so this can be done you can generate equi-probability maps which is the ratio between the number of common species that you have and the species in the central DTA to see how the system behaves in fact so this um reinforces the uh the main tenet that I've been hammering on for quite a few times and I am now ready to move on following what Marino Gatto has told you about the evolution of our thinking about spatially explicit epidemiology uh by the original ideas that motivated us to go to jump into COVID-19 studies through the same technological tool in as much as some tales some some small factories that you had in the Milan area we used to make um high-fashion dresses converted the alliance of production into mass productions during the COVID-19 it was a relatively jump um an easy jump for us but I'll spell you how in fact this uh thinking uh this way of thinking and this line of thinking that brought to the book um I talked to you about uh allowed us to move on to jump from fish biodiversity straightforwardly to the study of river networks as ecological corridors for waterborne disease let me see why now um here's a river network and let's assume those dots are human settlements so essentially what we're saying is that um what if we thought notes are human communities where they are in fact with their population of their size etc where disease can spread and um you have a demography of a population of a demography of a disease based on the demographic evolution of susceptible individuals in fact individuals possibly recovered and possibly via the as you've seen in the case of Shisto quite importantly um through the example that um uh that uh Marino has pointed out or which I I'm briefly returning by mentioning his mentor because it's important for one of the tenants of my work that is you may in fact couple these with control variables which pertain again water controlled but uh that pertain the ecology of a disease that is if you have for instance intermediate obligatory um intermediate hosts for the development of a disease so um why this is interesting the example of a Shisto I will just briefly show the main results that Marino showed you the helmings and you see why this is important right and but the motivator I'm giving it um it's more um it's it's a more important that's where we carried out the field work that we carried out with my lab if I think Burkina Faso where we had like a 20 year 20 20 year uh long experience in uh collaboration in in cooperation to develop this so um it what is incredible in this area is that in sub-Saharan Africa you have something like in a debilitating disease which is not killing anyone so it's a neglected tropical disease you have like 15 million uh disability adjusted life years uh that do take into account and what you have in particular regions you have different types of Shisto as Marino has shown I'm just going through briefly because and that's what we had uh in the camp that we have uh in Burkina Faso we deployed and one graduate student in fact carried out his entire PhD thesis on that why this is interesting again it's a complex like cycle and it is interesting for us the existence the need to take into account hydrological controls this is the part which indeed um pertains to how form and function of the river network operates because why because if you have like this marriage this fertilization of the successive stages of the of the uh of the uh disease need to hatch the eggs the best place in which they they are generated within the infected host and they have a worms the fat worms that generate the sarcaria or myra sedia in fact in live in the and they excrete the three thesis they get into a water environment in which I have to um they have to be infecting snails uh in a given time now that depends of course on shear stresses depends on the flow velocity depends on the habitat size it depends on whether the habitat suitability for the intermediate host is given so something in which as you've seen with marino we'll be back into the system so that's what you have and what you have seen and that's the point I'm making um the point I want to make here is that um pricing the planet as a environmental economist pointed out that is um if you don't account for a depreciation of natural capital um that means that um essentially ecosystem services that are carried out that you cannot quantify precisely are worth zero so pricing the planet means that you have to give the monetary value to the services you may lose as an alternative like in this case making way for a commercial center by destroying a mangrove swamp um that means that in the in gross domestic product indicator GDP like indicators are well-being you will see the advantage in the following year of the of the commercial center of the benefits of it but you don't see the loss which is associated with the ecosystem services you lose from flood protection to uh to uh carbon sequestration to uh fish nursery areas and the likes so the idea and that's part of the sculptors main point is that indicators that do not account for the depreciation of natural capital uh put development thinking uh stacked against nature in a sense uh against environmental thinking and the very idea of a misinterpreted kutznet's curve that is that if your GDP goes up uh down goes the inequalities in that place is essentially false as Thomas Piketty in fact has shown quite clearly in his wonderful book the capital of the 21st century what happens is that in reality indicators that omit the depreciation of natural capital are totally unsuitable for describing the wealth of nations and here is my point meta studies um that and i'm i'm reasonably sure that marino hasn't spoken about it and the interviews my discussion in fact showed that there is a clear relationship between the expansion of irrigation canals and some of the 15 000 small dams so we have seen i took this picture near our field site in Burkina Faso in fact uh the uh the construction of irrigation channels that were possible because of a 15 000 world bank funded uh small dams that uh littered Burkina Faso in fact had the consequences so the water resources development scheme of a largely improved GDP of Burkina Faso but in a humongously large expansion of a habitat suitable for the intermediaries host to the disease and thus the prevalence of the disease so the idea is that can we put a price tag on the learning impairing disability brought in by a disease of this kind complicated complicated and our permanent liability our the our inability to predict for instance the number the increased prevalence um in unless you have significant and reasonable models of the expansion of the disease then um you know as a matter of fact i won't be able to put the price tag on and this is the same place and this is a picture that i took in the same place how can you keep uh little guys away uh from uh the water when you have ephemeral ponds generated by the system mind you that in this case as you're very well known because of the wonderful lectures that truly marino has put forth on the subject that um the uh the those largely penetrate the skin uh in matter of second our student that was here only once put his hands in the water dropping the gloves when he dropped scissors just he totally just uh and picked up in a second the scissors that was enough to create to to get the system in a sense why this is important and related to what you have seen um in the uh previous slides for the fish diversity it's a picture you're seeing from marina because the set of equations and i'm not insisting on that is something which you have coupled um coupled uh oddies like in this case is the main word burden that you have uh like in the system here the prevalence of infection in the intermediate host in this case is why and these are the the essentially the densities of a circarie and mirasidia in node i of a of a dta that is of a single node in which you can characterize the system i'm not pretending that you follow the system but you realize that in here you have a number of extensions which are quite important they pertain for instance human mobility that is if you have a guy that migrates to go to a place to cultivate the feeding that uh uh because of the expansion of the irrigation network human mobility does affect in fact carrying away an exposure and the concentration of circarie that generates the burden of disease in an individual that's how the system expands so in a sense you realize that you are moving the study of diseases onto a plane which is completely different and the set of system is a classical system through which used to uh engineering environmental engineering tools and i want build on that in particular know or what you have seen uh with marino about how you characterize the stability of the system and uh possible ideas you have on how to curb again this eigenvector analysis you're seeing with marino is telling you essentially how you can actually generate the patterns of disease and what i really like is the idea is that you cannot make discussions what happens for instance if at random there's an exercise we ran um you remove 10 percent of a small dance thereby reducing the distance the mean distance to the nearest water body which is arguably the most important factor of completely geomorphological origins that generates the exposure so and that's the experiments we had in the place and i'm not building any further uh or uh all the diseases that can be treated in this manner what i'm concentrating here i'm getting back to the first slide in the last 20 minutes of my of my lecture and then i'd be delighted to answer your questions um you remember the little guy here on the banks of a magna river uh where uh we did field work on chronic effect cholera i'll be talking about epidemic cholera in a minute was trying to convince me that it's impossible the mighty waters of a of a magna were the cause of cholera which originated in that region in fact evolutionary um and then from there irradiated worldwide in several waves of pandemics but most significantly 200 meters downstream of the largest derail disease hospital in the world uh in Bangladesh now um the point i'm making and i'll be carrying out to the end is that the inherent predictability that you grant the system by using uh directional dispersal embedded in the known a priori and calculated and treated objectively offline remotely acquired and objectively manipulated offline structure of river network grants unprecedented predictability to disease of this kind and in particular this became absolutely vital when we started we were just working on that we had published the first spatial explicit model of epidemic cholera in with reference to the outbreak that was in KwaZulu Natal in South Africa based on data that were collected much afterwards in hindsight but what happened is that on October uh uh in the week preceding October 10 2010 all of a sudden in a country where cholera free for more than 200 years you've got an outbreak which started propagating downstream the arty bonita either in the heart of in the heart of the Haiti an island the island of Haiti the part of the left not the Dominican Republic you just cut in half good example that Jared Diamond um in fact in his collapse a wonderful book was making an example of how in fact the emperor of sin and the bad management of resources explains the uh a not simply environmental factors uh determine in fact the fate of societies now what was interesting you see the number of cases jumped all of a sudden from day zero to the from 50 to 100 to 200 in places which are small places indeed and right downstream of a un camp of peacekeeping curves what is not only ironic sad and it's it's really affecting me uh very much is the fact that why were peacekeeping troops in Haiti because a few months earlier Haiti the poorest country in the world had been struck by an earthquake that killed 300 000 it destroyed the little infrastructure was there uh uh sewer systems were non-existent and roads were destroyed people died um a civil uh infrastructure was demolished it was a it sits on one of those plate tectonics on which earthquakes can be particularly devastating on top of that we planted the disease because it was shown when it was mapped the genome but it was a Nepalese strain of cholera when it is endemic brought in by asymptomatic uh peacekeeping forces anyways that was a fantastic exercise in a sense because in a completely naive population as that's a term that you use in these cases um they and um but these uh or you can assume safely but because uh no sign of cholera was there for almost 200 years but the entire population was susceptible to the disease and what happens is that then you had thousands of deaths you had a mortality initial mortality we was totally remarkable because there were roadblocks to treat people transported by poor means like on the shoulders of a of a younger in fact to be treated to centers there are roadblocks to make it and say that after a year like eight percent of the population of the million people was uh affected and this picture I took into an hospital in Leogane and you see what was essentially the treatment was even I have to say among the sanctity that I've seen in the Medecin Saint-Francaire hospitals organized in the haste in the place or the Cuban brigade that took up the north of the country to assist but essentially put people on the stretcher you cut a hole in the thing and you collect the stools like six times a day and what is totally remarkable that you survive cholera easily you only have hydration bags to which you should be attached now let me show you the evolution of the daily cases in Haiti for about a year and a half then I think it comes blurred afterwards but that's quite interesting so you have the evolution of the daily cases in the half of the ispaniola island this is a part of Haiti and I didn't put the data which came later on in fact for the two islands they still belong to the same place etc so this is how they disease in terms of simply recall reported number of cases with all the inherent error of the system and that you had in there this is the city of Port-au-Prince here is a large scale of a number of cases if I'm asking you what do you see here well you see the rivers so you even by seeing the most gross indicator number of reported cases what you see in the place is that the avenues of the riverways where the pathogen in fact survives in the environment in the open waters in fact is what generates the system etc so essentially you can't have something in which you essentially can calculate the rate of change of new cases of cholera in every single place that that you have but you have to take into account a spatially explicit system we put settlements where they are connectors where they are and the likes not only that if you take the red curve is what happened in the first wave followed like in covid but for completely different reasons a second wave which is clearly related to factors like the tropical rainfall that you have in the place why well the easiest is not simply an overflow of sewers but simply the wash out of open air defecation sites which you have to take into account and the fact that the freshly shaped bacteria the bacterium in fact like a single infected individuals expels and through the faeces like a hundred times more bacteria that in concentration which are also magnitude larger than any any possible survival in the environment so it is the human human host in fact the main reason of a propagation whether symptomatic or asymptomatic whether it moves or not if you have a susceptible person moving on to the wrong place drinking the wrong water and getting back he brings back the disease it happened to me when I was in the market of our tibonid well I'll tell you when I show you a picture later on so the tools of the trade now is knowing ahead of time where settlements are where patterns of rainfall evolve and how the disease can be predicted under these conditions putting that cities in human settlements where they are connected by the waterways as we can see them directly so the idea that in a system like that you have two different networks a network which you which you have like pathogens connecting nodes if they are downstream of an of a river system or and that's a key place you can have connections among nodes human communities in which we population each population each sub eye this is node i in which the disease can diffuse and grow connected by a multiplex network of a different time of a different kind in this case human mobility as you now very well known from marino gato's lecture on kovid-19 the spreader the mean mechanism whatever its shape it is and but we had seen even in my set of lectures what happens when we consider from a zebra mussel invasion of a mccp Missouri river system you see that you saw that at times unconnected flare-ups of of those development of those clusters of zebra mussels were generated away from a main backbone of a hydrodynamically generated dispersion why because of the ballast water in which belliger survived where we're taken away and and tucked to different place maybe hundreds of kilometers away from the same place the mechanism of generating the system of this kind so the tools of the trade in this case are the tools of the trade of geosciences of digital information systems or geographic information systems if you want that is we can and we could do it remotely when we predicted the evolution of them of the epidemics of cholera in the place which i'll be showing you in a minute because the digital terrain map from which you extract the river network as i hinted at in my introductory class is something we should do with the standard exercise that that master students do where we are you can have pixel-based estimate of population density you can have modeling of human mobility which is something which requires some thought and some care in fact generated maybe simplified at times but i'll tell you what is the capability of attracting places like on the main point like potter plants that you have in this system and the set the tools of the trade i mean they different every time but the that's why i showed you before the ones that marino have shown you for schistow so essentially the state variables are susceptibles at node i at time t infected and node i at time t and the bacterial concentration in the reservoir of the i-th community evolved it because of the different factors which is the mortality the survival of the vibrio in the environment with a certain mortality rate of seeing really how long you get survived or transport in a certain proportion coming from connections that are hydraulic and hydrologic connections that depends on the various sizes of the of the water reservoir the water reservoir which is important because essentially you can assume that one stool a single infected person has a certain probability distribution in terms of absolute number of of bacteria shed which is again six orders of magnitude more than you have for the concentration of bacteria in the free living waters and that is the infection thing that generates the P you see P the infection per unit infected person which is here you have a the force of infection depends on the local infections plus the of infections connected by a mobility matrix this is a mobility factor which you have in the system so of the i persons that live in the community uh i sub i infected person where the symptomatic or asymptomatic stay there and pollute the water or you may have persons that because of mobility and its matrix of fluxes generates the infection shed into the place to which you could possibly add like you have it here the rainfall runoff production of vibrios generated by the system again i cannot pretend to explain the details but you see how this is done for instance um and you have seen in introduction to the disease um ecology that marino put together in this case we assume the timescale of our prediction is one in which recovered persons i mean i put back into the susceptible compartment at a time which is one of the role of the order of two to three years and this is the force of infection depends on a number of factors my scope here is not to it's getting curious about the strength but you see that the structure is exactly the same of the schisto is exactly the same of a Mississippi Missouri biodiversity model and it's exactly the same ones we have seen before so let me show you how the model works if you assume a piano network very important because if you have like in every node you have a population of the same capacity all of them uh uh prone to have the diffusion of the cholera uh that what you will have in the system right and why this interest is a calculated speed of a traveling wave of cholera under a simplifying assumption which depends on the local reproduction number but if you assume as it is meaningful and reasonable the distribution of the in a topologically connected system of this kind you have that no distribution the population distribution is taken drawn from a distribution which is normally i mean almost universally a power log exponent minus two the zipped distribution what you have is that um now what you see in the system that you have flare-ups in a mechanism which is exactly the same and why because that's the effect of factors that can be uh uh remotely measured and objectively uh manipulated in this case the population size and certain effects of the delays that you have in the system especially explicit have nothing to do with the disease and everything to do with the geomorphology and the ecology of the system so i took to haiti a few times uh and uh what these pictures i took they are kind of blurred and i love pictures but the reason being is that um my uh my glasses were shut because people could kill you to steal your camera because there's no police left in the place we have no sewers no streets to stick off and this also shows how large patterns of infection accompanied you consider this safe water bottled water with the guy that handles them uh by the neck in this case quite remarkable or there are places he's taking in the again in the Bangladesh conflict he's taking which the water reservoir which could be a highly abstract uh phenomenal parameter of the system in the case of urban setting possibly proportional to the population or in this case you see it or a very physical system like you had in Bangladesh as i was telling you and this is the market or car food in the outskirts of of Port-au-Prince where i've been sitting in the system and and what i told you and was totally remarkable is this lady which you're seeing here blurred against because of a of a safe glass beyond it uh in a matter of second um uh bought a cabbage at this guy and i couldn't i was speechless when i saw it by showing uh a Nokia 1900 proof of concept uh uh i'm sorry Nokia 1900 telephone is a proof of payment so in a place in which you have no sewer system as you see it water flows through the market in this case you have no roads you have no police but you do have a telephone which is a way less uh biased socially biased system as we have seen and this is hard like human to human transmission this is public transportation high eating fact takes a place and that's the last thing that i want to show you that models and data in fact uh uh they are not perfect modeling things etc i mean you have Bayesian estimation parameters but the very fact that you're using specially distributed quantities uh make sure that in reality the distance within model and data is so small that operational decisions can be taken based on that and i'm skipping this part because it's too late is Marino Gatto and his idea that in especially explicit um uh uh uh models of disease development in fact you can have even an eigenvector can represent the pattern of disease before it happens and quite interestingly you show also that the local reproduction numbers meaning uh the test for the potential for the outbreak to occur is neither necessary nor sufficient the condition for epidemic disease outbreak if you compare to real cases whenever you have a spatial explicit system in which human mobility is a driver not is an embedded driver but it can be calculated and i skip this part i skip also this because i realized i chatted too much about how proliferative kidney infusion can be studied and i jumped from the last two uh uh fish diversity in that case and and the deadly infections in fish are in fact the proper into the channel network was all the network to speak about so my conclusions the whole the general conclusion is that eco-hydrological footprints of river networks as ecological corridors are demonstrated they are pretty strong in fact and from peaks of prevalent in waterborne disease infections to any kind of large scale patterns of species abundance and biodiversity or even the susceptibility to biological evasions that we're seeing it's only the water so in a way it's written is something which could be remotely acquired over over virtually six orders of magnitude and remarkably compelling so in a sense towards a fair distribution of water which is my punch line it is that uh attaching a price tag to certain things which weren't uh material uh materially or observables in economic terms but they are absolutely vital because they don't have a way of predicting what would be the impact for each of the of a an expansion of water resources exploitation patterns in the expansion of a disease for each cost so they open they a quantitatively open to a quantitative evaluation on ecosystem services to rethink in a sense um social equality and I thank you uh with that thank you thank you very much on that we can open the floor for questions quick question yes please um in the in the model towards the beginning when you show the alpha diversity increasing as you go downstream is this is this increase and consequence of accumulation of species going down because they cannot migrate upwards or is it that consequence of just more populations interacting and getting going together uh as we reduce the number of canal downstream that's a good question the kernel for for dispersal species are the same everywhere what makes the difference is the fact that habitat size and thereby the carrying capacity of the population of every species changes uh with respect to the downstream direction because of a natural accumulation so it's an external factor which is dictated by the aggregated structure of a network that gives an inherent predictability even though I mean how could you possibly consider all fish species equally uh equally capable of dispersal for instance or insensitive to drift uh at the per capita level and yet neutral pattern um doesn't require a neutral process that's what I'm saying so a neutral patterns are more general that's what in fact famously pervies and pacala could hold and if I if I made just a quick follow-up was that pattern completely monotonic I noticed it was not it was not a straight line it was there was some no that's you have to see the two patterns uh together so one is the frequency of species distribution uh with respect to the distance to the outlet so essentially you count the number of sites which you had the same distance from the outlet it's a fairly complicated structure so essentially it opens up and closes up and uh and uh and the other one is essentially the simply they you simply measure the average that is the local species that is you have a different distance from the of course if you are interested in the catfish distribution the neutral model won't work right so you have to go into a serious model of the thing I said but if you look at large scale patterns for instance for uh conservation reasons that the the neutral pattern gives you robustness reliability and the capability to make decisions actually especially for conversation for for conservation practice okay if you're not further question I'm starting to be delighted to go because I have another meeting fairly soon