So, Jeneer, do you want me to go ahead and you want me to go ahead and start? Should we introduce ourselves first or how do you? My name is Jeneer. I'm I'm a faculty member at the University of Georgia in mathematics and engineering And I have authored Econet and that's what I'm going to be talking about today and Stuart is going to start Okay, and I'm Stuart Whipple and I'm an adjunct Professor in ecology and I've worked a lot with Jeneer on on Developing the ecology side of this and we're kind of a kind of going to try to tag team this because his Jeneer has developed Econet and he's He's he's very good at that and I'm going to sort of try to give you the background of What where the analogy the theory in the background of where the analysis has come from so I'm going to give you a power point And hopefully it's going to last I'm going to try to keep it to half an hour Hopefully less and then we're going to jump into Econet and Start doing some actual analysis and you and get more interactive with with you guys So if you could leave yourselves muted for right now Unless you have a really pressing question and if you do just say something like if you're not if something's not working You know or something like that So I'm going to go ahead and share my screen now and and start the presentation and then once I finish that I'll hand it off to Jeneer and he'll share his and then And then we can proceed from there. I think in a slightly more interactive route. Okay. All right, so here we go All right, Jeneer. Do you see that on the screen now a presentation? Okay? I'm going to move move some of this stuff around over here to make it smaller So I can see better What's going on? Oops And I will go ahead and start the presentation. Okay, so what we're going to be doing here Really through Econet eventually is is we're going to be talking about network environment analysis And I'm going to give you some of the history and background And I'm going to do a few examples of some research questions and things Analysis that you can look at and I'll talk about the way that that links into Econet and another package Which we won't specifically talk about a lot although we can answer some questions about it I've used it For one project is ENAR, which is an R package that was not developed by Jeneer was developed by Stewart Bort, Matt Lowe and colleagues So network environment analysis. What is it? Well? It's it's basically an environmental systems theory was developed by Bernard Patton and Colleagues largely at University, Georgia that seeks to answer the question What is the essential nature of the organism environment relationship? i.e. what is environment and The methodology that it uses of NEA is a set of numerical analysis that are based originally on Input output analysis Matrix-based technique that was developed for economics by Leontief back in the 60s And it's used to gain insight into the structure and function of weighted steady-state networks network models And it's NEA is grounded in state space system theory and a differential equation Representation and you use open steady-state networks as you'll see with a conservative currency of matter or energy So what are environments? Well the basic idea as it was developed is is it's the measurable Intra-system that is within the system boundary Environment of all the system components So if we have a component here any kind of a component in our case my case It would be some kind of component of the ecosystem, but it could be anything in a model And it has an input from outside the system and that generates what we call an output environment for that particular Compartment and then if you look if you take something out look at coming out of the out of the system with why Labeled here. There's an input environment that is created that includes the intra-system Inputs as well as the inputs from outside the system so we need to have some terminology and then I'm going to give you an exam overview of how the how the how the method works and then a couple of examples of how it how to look at it so that we can do some interpretation when we get to actually doing some of the Analysis in real life on on eco net so the system boundary is important As I just mentioned everything that we're going to talk about happens within the boundary So we have a set of state variables or compartments as I'll often call them. They're three here refer to in compartments We have an input vector. I have an output vector we have Intra intercompartmental flows and the matrices a matrix and adjacency matrix which is labeled a here Can tell you where those flows occur in the model in the model that shown what you're shown with the digraph arrows and for example The the flow here from let me get my point of going from two to three is represented in the second column and the third bow by one Now the rest of the flows that are there are represented by ones. Everything else is zeros So we had we can wait those flows Okay, and we'll call those f and those are those are in the same place as they were before and then we can we can Quantify a through flow, which is the total flow at a particular compartment as an example We use compartment to here. So if an input from outside the system We have an inflow from another compartment here representing the in the through flow in then the through flow out a Flow out from two to three and a flow out of the system Okay, that's through flow to so and these models which I mentioned before at steady state That means that DXDT change of the compartment Mounting a compartment is zero. We can say that to free flow in equals through flow out That's an important assumption for the model for the set of models that we've got here So then we can have a through flow vector Which is just the total flow at each of the compartments that we have we can define a total system through through flow TST as the sum of all three of those it gives you the total activity in that particular model so Here's the setup that's going to really be the basis for pretty much everything we talk about from now on I call this the big picture Theoretical development. So here's the same model We're going to focus on compartment to again again We've got the rest of the compartments there the x vector the z vector and the y vector state Variables or compartments inputs and outputs respectively at the flow matrix And we've got through flow in through flow out I'm repeating this again because this is an important concept that we're going to be using here in the analysis and again We're at steady state. So DXDT equals zero through flow any was through through flow out And we're going to look at that what we call the output environment and the forward analysis remember in that diagram I just showed you there's the z coming in Produces the output environment. Hey, that's the analysis. I'm going to get that's the one I'm going to actually show you the analogous one I'm not going to actually show the example of it. We're going to put it but we can we can get the analysis for it later So in this particular case, we're going to be going forward So we're pushing inputs into the system and looking at how that what the results are there in terms of the In terms of the structure of the model so to do that we need a through flow specific coefficient g Okay, in this case, we're going to we're going to use the example of g3 to Okay, and Which is over here, which is that f3 to divided by the through flow at to the donating compartment Okay, we can array those into a matrix g Okay, and oops, sorry Into a matrix and then we can use that to map inputs the z here into through flows to do the analysis And to get that to get that mapping matrix We have to take i minus g that's the identity matrix minus g inverse and that gives us in Okay, which is the which is one of the important matrix result in matrices from environment analysis And that's going to give us the through flow environment compartment wise and system wise measures Okay, and we can also do this what we call storage where we take into account not just the flows in the model But also the storage vector and we can develop we can do that again. We're going forward from inputs into storage We need stock specific Stock specific coefficients. Sorry, and in this case the example is compartment two we can get seat three two Okay by dividing f three two by the storage Okay, again same way instead of mapping inputs in the through flow in this case we're mapping inputs in the storage We take that c matrix after we do all of the C's and we do minus c inverse to give us a matrix s Which will give us the compartment wide environment measures and the system wide measures for the storage analysis so their analogous Matrices for the input environment case where you're looking backward against the flow of the of the of the arrows And I'm not going to show those in the interest of time But I do want to talk about what something that's important for the interpretation analysis, which is the extended path structure That is that is underneath that that sort of is part of the theoretical background of this of this This analysis we're going to start out looking at the adjacency matrix So we're just going to look at the at the flow at the actual digraph and the flows. So again The adjacency matrix just has zeros and ones ones where there is a non zero flow between the compartments and zero Otherwise given the example of flow three two again the flow from two to three which is in column three Excuse me column two row three here so We can do a power series of the a matrix which represents the number of pathways in the ink from compartment J To I over whatever the wherever the power is in So for example, if we square this adjacency matrix We get an additional two entries here that I'm going to show you how they get there For this entry here We have a path length of one going back to itself So it's a cycle going from one to three and back to one over a path length of two In the next one here a flow from two to one we can get there over this path of two to three to one That's why that entries there Again, you see as we go up in the number in the path length All of the compartments are reachable once you get to higher path lengths and you see those go up quickly And the important idea here is that these direct paths within the system are represented by adjacency matrix But the indirect paths are represented by the higher powers Okay, and I referred to that the extended path structure. You hear me mention that again now when we go to weighted paths That's where the actual environment analysis part comes in. So again reminding us We've got the through flow normalized flow intensities the G's and we can get that mapping matrix again the N So through flow equals N times Z when we do I minus G inverse And then another another interpretation of this is that we can take the same idea of the extended path structure and do a power series of the G matrix Okay, which actually which actually ends up Converging to I minus G if you have an open system, although that's not necessary to really get into now Or what's important here is the analogy between the direct and indirect part of the extended path structure So we can also do this for the storage I'm not going to go into it but the important thing is is that this is extended past structure is the Microscopic interpretation behind the idea that an environment analysis traces the input From the first apartment where it's kind where it comes in from outside the system through this extended past structure The indirect past structure until it's exhausted as output Another piece of this is that the extended past structure is also the mechanism Behind the dominance of indirect effects that any any a results show for most cyclic networks Okay, and you'll be seeing that in the in the eco net Portion of our bit now the last part we're going to talk about is Utility analysis, okay utility analysis is Another version of this analysis where you where you create a D matrix or difference matrix which represents the net flow between Between X and between two different compartments, okay, and it's computed by The flow forward minus the flow back towards the other compartment normalized by or divided by the through flow and This measure you can get an ultimate measure you matrix by taking I minus the inverse and that we call that intensive utility And it's unitless and again the direct and indirect Extended past structure also applies in this particular in this kind of an analysis So here I'm going to give you an overview of the kind of analysis and then I'm going to give you a couple of examples That I'm going to go through fairly fairly quickly I'm only going to I'm only going to sort of highlight that give you some highlights of the analysis because this analysis produces a Lot of output and you have to sort of focus on a few things actually to actually make sure you get an idea What's going on? So we already talked about the matrix power series pathway numbers flex decomposition is something that That that janeer has developed with an econnet that we'll talk about that also uses the unweighted adjacency matrix now the weighted flow Adjacency matrix we have the transactions and we have the through flow matrix the in matrix here We talked about and I mentioned compartment wise and system-wide measures Well, I'm going to talk about I'm going to give you a little bit of detail because I'm going to be giving an example of this Compartment wise the in matrix you can derive the intercompartmental flow partition and boundary flows that go with that particular environment and also get the number of compartment visits That correspond for that particular environment Input and for system-wide measures you can get a measure of cycling And a measure of indirect effects for the storage you need the flow matrix and the and the X and the the and the compartment Vector as well and with that in addition to the environment environment flows You can get the storages and you can also get resonance time and also you can get system-wide measures from that as well Now with utility analysis, we had the net flow That's through flow normalized We get the ultimate utilities with the u matrix and from that we can get weighted utility math values and a qualitative Interaction type and from system-wide we can get measures that are mutualism and Synergism which are measures whole system measures of using using the u matrix Quantities So the question is what kind of what kind of things can we actually do with this in environment analysis? And one that's really that I'm going to give you an example of is what I've actually turned here an analytic tracer So that you can input Take an input into the system or an output and see what what what that what that actually does I actually probe the system to see what what how that works can also get storage or resonance times You can do cycle analysis You can get a measure of the actual activity generated For that particular environment using the total environment through flow that's analogous to the total system through flow that I talked about before So here's three examples then I'm going to give you actually a numerical example But here's like here's the general concept of what I'm going to be talking about in that in that in those two and there's two Examples so you've got three models down there And we've got three different three different inputs or outputs and each one generates a unique set of flows Inter-compartmental flows biology flows and storages in this way We're able to evaluate the system-wide consequences of that input or output So for example, we can say well What is the environment flow between compartment two or three? We have an input to compartment one That would be the through flow environment one in the end out of the end matrix Now if we take an output from compartment two We can say what would the input have to be to compartment one to generate that output? Now if we're doing storage analysis, we can say if we have an input to compartment two Excuse me to compartment three What is the storage that's generated in compartment one and that would be in the S matrix and would be the storage and Output environment for number three And also the residence time can also be derived from that because storage and residence time are related So here's an example of a system We're going to be doing a water budget model of the Okefenokee watershed that was developed by Ed Reichel for his dissertation working with Perney Pad and I'm going to show you the initial conceptual model very briefly So we've got upland storage in the Okefenokee watershed Which is highlighted on the right here and swamp storage, which is on the right The reason I'm showing you that is the model that we're going to show you as a four-compartment version of this conceptual model So here's that model, okay? We got four four four four compartments to make it simple the upland surface is compartment one up in ground water is compartment two Swamp surface is compartment three Swamp sub-surface is compartment more. We're going to have precipitation on the uplands precipitation on the swamp and we have outputs Briefly they can be included in evapotranspiration stream flow and groundwater Not going to do anything much with the transfers and of course their units here It's volume of water and it's volume of water per year and the watershed is the area So here's an actual environment output Environment what you can get from environment analysis. So what we want to know is what is the fate of the water that's input to the system? We've got two possibilities Okay, the first one is oops. Sorry. I lost my cursor. The first one is is that if we input To compartment three and the surface of the swamp if it rains there What where how does that? Where is that? Where can that water go? What can environment analysis tell us about that? Well, immediately you see that water can't go uphill to the uplands So that entire sector of the model doesn't have anything on it. It's all zeros so with it if you look at the consequences of this From the in matrix and derived from the in matrix you'll see that most of the output is going to evapotranspiration and Streamflow directly from that swamp surface compartment a tiny bit goes into the subsurface that very very little and The total amount of activity generated is just a tiny bit more than what was originally input So if we look at if something if we have precipitation on that on the upland surface Okay, what are the consequences of that? So that's and put into compartment one So we see that the whole model is activated because all you see that all of the all the all the arrows there in The whole model has some had non-zero inputs.  Most of it moves down to the upland groundwater and leaves from there as output a small amount of it actually moves over to the swamp surface and Leaves as two outputs from that compartment evapotranspiration and sleep stream flow And a tiny bit ends up moving in to the swamp subsurface So if we compare this overall picture, we can see that what environment analysis has been able to tell us is that there are big Consequences depending on where this input comes into the system in terms of how this How this how this how this this unit of input moves around the extended past structure of this of this system Until it's dissipated. Okay, you notice that when it comes in to the swamp to the swamp surface Okay, as opposed to the uplands much less activity is generated a third of the adolescent a third of the activity is generated And you see that the whole model is actually activated here Okay, whoops. I got a lost my corner again. Sorry. So here's a system level measure It's really the only the only one I'm going to show you the total environment through flow There's technically one that was basically for the other model But I'm going to show you another model here very briefly and this is a nitrogen model of Lake Okeechobee That was developed at the South Water Water Management District by Tom James and his colleagues and there's six compartments here and It's not important. They're why it's basically different forms of nitrogen and phytoplankton in the water column versus the sediment Which is an important thing for this particular system But what's important to note here is that this is an actual in matrix that we've got here Okay for this particular model and you'll know. Oops. Sorry lost my potter again You'll notice that these principal diagonal elements Which quantify that number of compartment visits that I mentioned before is one of the things comes out of the in matrix You see a lot of variation here when you look through the different compartments anywhere from 11 visits down to a little over one Okay, and what you can do with that with those diagonal entries is that with using the fin cycling index that was developed and if you wait those Diagonal entries by the through flow you can develop a cycling index for each compartment and for the whole system. So for example For the two organic nitrogen compartments here that are visited about 11 times In other words, that means that the comp that have you input to those can compartments It's the what the nitrogen cycles around on average about 11 times to through that compartment again You get about 91% cycle very high if you go to the water column in organic nitrogen in the phytoplankton It's about 2.6 times and using the cycling index that corresponds to about 61% The last two much lower 37 and 24 the overall cycling index is about 86% So it's a highly cyclic model, but that's not unusual when you're talking about a biogeochemical system We found that that's generally true if you're talking about other kinds of systems Retentiveness of the amount of cycling of the substance how much it stays in the system and hits the compartments before it leaves Could be a whole lot lower So the last part I'm going to talk about is give one very simple example utility analysis There's a lot to this and This it's very hard to kind of come up with a real simple example what I've tried so so far We've talked about Transactions and environments, but can we use these transaction networks that derive relations between compartments? Okay, and we can use utility analysis to do that and what I mean by relations one example of that a simple way I think of that is just the ecosystem interaction types the plus minus Minus plus minus minus competition and mutualism that we can get and then there are whole system measures that I mentioned before I'll give one example of that in the inner and the example that I'm going to give you so quickly. It's a very simple toy model But in this particular model, we're going to start out saying that if we've got two compartments here in this case A bear and a wolf feeding on caribou. They're competing to eat that to eat the caribou but if we introduce a way where by the bear actually eats the wolf and The caribou and the wolf only eats the caribou then we've got cross level or what ecologists often call intra-gill filled feeding and Then it becomes indeterminate in Terms of what the interaction types would be based on that and it turns out that when you do the if you look at the analysis That this sort of structure the flow weights and for that particular model actually determine What that is what what what the interaction types will be and and one of the first papers that was done on that path Patton and Whipple said called this parametric determination So if we show this as an example, we've got two cases. So here's a here's a here's a quantified example of that same exact model Okay, the question is is what is the relationship between the bear and the caribou in this case? so we do the utility analysis and we take the sign of the you matrix we find that Actually, the relationship is a plus minus which you might expect because the bear is a predator on the caribou However, if you change the weightings of the intercompartmental flow slightly and say well What is the relationship here? Is it the same in this particular case surprisingly enough for a predator? From an ecologist point of view the relationship actually turns to mutualism Despite the fact that individual caribou obviously are still being consumed on a system level The relationship turns out to be plus plus. That's kind of a really interesting result I think so we find that when we change the weights of the intercompartmental flows by a certain amount Which basically would mean just changing the amount that the bear chooses to feed on one or the other It changed the sign of the interaction matrix from predation or nihilism It's another way to say that to mutualism and then for a system-wide measure if we add up Do a ratio of the number of positive Interaction positive number Positive values in each of these we see that in the case one we have six over three Six pluses the three minuses which gives us a mutualism for the system of two Whereas in case two on the right there are actually seven so seven over two gives us a mutualism of three point five So it's a pretty big difference for just changing the the actual the distribution of flows Otherwise the model the models are are identical So I'm going to give a really brief discussion because Janir may mention it because it's output from eco net It's a little bit a little bit a little bit off the track But it's related in terms of trying to understand the structure of these models So if we have a model here, that's real that's talked about as F The flux decomposition is a way of parsing that into an arbitrary network of two types The first type is a simple path With one input and one output and no related and no repeated flows. So the first of those Comes in at compartment one goes to two and outputs there The second second one of those for this model would input at one go to tube three and then output That's flux number two the last one is a simple cycle including all the compartments In this particular case one two and three and no inputs or outputs and the decomposition The actual result of this is that you can represent it as a linear combination of these fluxes So in this for this particular model, you can take one point three times this flux Quantitatively two times this flux and one point two times this flux Which is the cycle and that will actually reconstitute the original flow the original the original model So very very briefly because I've already taken up pretty close to my a lot of time and we have we have limited time here today Equinette basically will allow us to do the analyses and more that I that I showed here and Ena are that was developed by Stuart Warren and Matt Lau and that's the reference for it You've already got that in the PDF that I emailed you guys one of those emails bounce by the way We'll have to handle that at the end Or at some point to get to get to get that person's correct here Anyway, this is an R package that does a lot of the same kinds of things and more actually Then what you'll see that Joneer is going to demonstrate with Econet But for the purpose is a time and because Joneer is so familiar with the Econet since he developed it And he knows everything and the ins and outs of how it works We're going to stick with that but all of these kinds of analysis. I was just talking about the structural analysis The through flow and storage analysis of the environs utility and the environs themselves can be gotten from Ena are so if we have some folks That are familiar with our this is a really powerful package And it's it's actually pretty easy to do and I actually have a website that I can that I can point you to that Actually will step you through an analysis that Stuart has shown. It's basically a sort of an online workshop. I would say So now Now that I've finished giving you this very quick introduction there I know there may be some questions later on when we talk about internet Econet But I think in the context the analysis with Joneer that it will things things that I talked about from a more of a theoretical point Of view and just an example When you're able to see how this works and actually see the and see him change the models and things that will come a lot clearer So here's Joneer Oops. Oh, I've unmuted Joneer. Okay. Hang on. Can you hear me now? Yes, sorry about that. I didn't know I had done that. I Think I did that but that's okay. Okay. So okay Let me repeat myself So I'm going to be talking about Econet With a presentation right now and then go go ahead and demonstrate it and at which point You can also run your own little simulations and ask any questions that you have and I think we agreed that people would raise hands and we would basically answer questions based on that and So this is the presentation. So what is Econet is basically a web-based simulation software and What it does is basically it takes the model that you put in and it creates a network diagram of it and it will take the Input and we'll turn it into a mathematical equations This would be a differential equation a stochastic process depending on the options chosen And then it will numerically solve them and then it would basically give you a plot the time course and based on the last State of the system it will do network analysis and also include that results and throughout the presentation some of the Items will be in this color. Those are the features that are not present in the current version of the Econet But the test version which I'm also going to show you towards the end But if something is in this color it means that it's a feature being implemented So this is basically what it looks like It's quite simply test three parts. The first part is a big text box where you enter your model Using the keyboard and the second part is a numerical method chosen for simulation and the third part are parameters depending on the Simulation method chosen. So for example, if you were to choose, let's say you list these stochastic algorithm Well, that does not have a step size in so this will disappear and only a time would appear So these options are depending on the method chosen here and then you hit run model and wait So the regular version of the Econet is limited to two-minute runs So if your simulation takes more than two minutes, it will stop and show the current state It really happens because it's really fast, but if you have something really big It might take a long time, but often you can choose these options to make it run faster And the default method chosen is pretty fast as it is And the test version that we have is unlimited right now, so And that's why it's the test version But we'll see So how does the model structure look like? So how would one describe its model into Econet? So it basically is again form of four parts. The first is the relations the interactions between those compartments and There you you put a dash and the large larger than sign that would constitute the flows and The names of the compartments you just write them as they are and you represent the environment using a star So this would mean that the detritus and environmental input and then these are the flows between compartments and This would basically these two compartments would have an output to the environment and And then of course how fast do these occur right and that speed is probably going to change over time So both of those are represented using this single term So C is actually is Related to not just the speed, but also the type of flow that I'm going to go over Momentarily, this is the speed. So how fast is likely this to happen? But then again, so here there's a flow from detritus to microbiota This flow can depend on the amount of detritus or can depend on the amount of microbiota or both So this choice is is governed by this letter C here And of course not just the type but also there's a rate, right? All of them might be of the same type but might just have the tendency to occur faster than the others so The rate at which the plants consume Let's say the rates at which The insects consume biomass is going to be different than the rate at which a large cat is going to consume biomass So that speed difference would be represented by the constant and then well You have to have an initial condition to start where things are going to evolve from there And those are represented by the name of the compartment and equal to sign and then some value Now it's important that you have a space around the equal to sign here, but no space is needed Actually most pace should be around the flow that that's how you connect distinguishes flow types from initial conditions And the rest is just comments. You can put comments around it using starting with this square sign And that's it. So these are the four four parts that would constitute an equinate model comments flow types and coefficients flows and initial conditions now It has a really flexible structure. So it need not be exactly in this configuration this is the exact same model as you've seen before and What we see here is there's a flow there's a type and then the initial condition and other flow and other rate and Here we have some initial conditions and some other flows and you can see some other rates So this model is going to be interpreted correctly and run exactly as the same as this previous one. So this Flexibility is what's going to make it really easy to make changes and run it as we'll see When we start working on it So what are the properties of this network diagram that it draws? So it's hierarchical. So it's based on trophic levels pretty much But not exactly. So if you have something if it's here, this is the oyster reef ecosystem model Not that pretty much every other compartment is basically Getting its energy from the filter feeders to oysters. That's why it's at the top and the top predator would be At the bottom. So this is the predator. That's basically feeding on everything else So it's at the bottom and everything else is going to be laid out in between again, according according to its hierarchical level and It's optimized for usually for mission What that means is that the compartments that are well connected are going to be centralized and There will be very few flow of intersections and you can see that there are none here because it was possible But if you have a really large model that has this really complex then it's impossible to avoid but it will try to minimize those and Another one is short low-pervature flow. So there are no sharp intersections and it's going to be smooth And again, those are going to be as low-pervature as possible. So you won't have a low that just circles around with an intersection It's really well optimized and Also, it's publication quality. So the pictures that you see on the equinec website are going to be Gifts for PNG files But once you click on the figure, it'll ask you to save it in EPS format, which is the vector base so a figure in EPS format can be converted to a Gift a PNG or a G JPEG of any size So you can include it in a paper a poster if you can magnify it and it will always look smooth and Indicates flow values usually numerically. So this is again a future that will be implemented in the new version It's ready, but it's not up in the website yet. So this is what that looks like and We're still, you know, working out some of the details like this large arrow is a little bit protruding here But what this does is the previous version it just shows you the flows the existence the interactions But this will actually show you it will quantify the interactions So at steady state when everything is finished and the simulation is done These are the flow rates between the compartments So here we see a miracle Flow rates so you can see that this is really large. This is the next large and this is the third largest then So here this one is really slow for example This is the feeding of the predators and you can see that reflected by the thickness of the arrows here So the thicker the arrow The higher the flow rate. So this contains more information Than the previous one and we will we'll try to find a way to do this especially this one you can see that You know, this is nice. It gives you more information, but not the record information This does but at the cost of having a little bit more convoluted. So as you include more information It gets more difficult to interpret it You know, so what I mean what I meant by the flow types and flow rates is the following so assume that you have a flow from compartment A to compartment B and Assume this is a downward control flow in that If you change the amount of B, the flow rate does not change. So this would be like the deer Giving biomass to the plants. So the true pickle matter There will be a transfer of material from the deer compartment of the plants And but the plants do not have the capability to demand from the deer The more the deer you have the more difficult matter the more of the input to the to the plants So that is going to be a total control flow then it's just going to be depending on the amount of A So for that type of flow, you would say C equals the C is the letter use and then the differential equation or the Stochastic process used to implement this flow is going to be computed as three times the storage amount of A Now, but if you have a feeding relationship, let's say between a Predator of deer like a wolf pack and deer then while that Speed of flow is going to be depending on both the amount of the deer we have and the amount of wolf we have so and For that type of flow the donor recipient control flow you would use R And that would mean that so the interpreter would compute the flow rate as three times the amount of A times the amount of B and So this is again a feature that is not yet up on the regular version of the connect so this is Mikaelos Menten and this this has two coefficients in it and This is how the equation is computed It's also called monod type of flow interaction or hill type flow interaction he'll type one so what this means is that often Not that there is no recipient control flow so we do not have an option where it's only equal to a constant times the amount of E and that's Intentional because if you do that then the equations are going to demand what they may not exist and That is going to give you a negative storage values in certain cases So avoid that but to have the capability of recipient flow This is invented So what this is not econ it's of course, this is well-documented. So what this does is if you have an abundance of the source material a At the limit if you take the limit of this expression as the storage amount of a goes to infinity These two are going to be cancelled because this five is going to be negligible Compared to the storage amount of a so we can ignore five and then the storage of a will be cancelled But this one it will be like three times sort of your feet. So it will be almost like a recipient control so think about Fishing when the fishing season just started everywhere is full of fish. So you're basically limited by the amount of fish you can catch But but this requires two Components so that's in the so wherever trying to make it work at the moment So how does a model get turns into an ODE so this is just an example So you have an environmental input into plants. So that would now since this is an environmental input The environment does not have a storage value. So it's just taken to be unity. So it's just going to be one So the P by dt P represents the plants be the detritus. I'm sorry D the deer so here it's going to be like 25 and Then the plants in the deer have this predator relationship and it's R is used so it's going to be one point one times P times D and This is taken out from the plants and added to the deer so it's a negative here in the positive here and The deer is when feeding the plants with some right and now this is donor control So I use the C and here is going to be again Added to the plant but subtracted from the deer and then they are do migrate or die So it's a death rate and it again only depends on the deer So it's just that and if you change this one or it would not matter Because again the storage amount of the environment is taken to be one and Then these are taken as to the initial conditions So this is what the if your chosen method was the adaptive rangakata or regular rangakata Those are ordinary differential equation solution methods the equinec would basically simulate this equation and pull up the solution and So those are the two methods So the adapter one so normally differential equation solutions contain something called a step size and this if it often has to be small to be accurate accuracy increases with Being small, but when you make it small it takes longer. So a method was developed that is adaptive meaning that it would change its steps To the differential equation. That's the default method in equinec now if it's running too long If there is some issue as as a debugging method this regular step or order fixed step size method can be chosen But this works almost great in any chance. This is also the recommended one to be used in MATLAB and octave It also contains two stochastic methods One is based on Gillespie's algorithm. The other one is continuous. So this is the screen This is a continuous method. These are a little bit more complicated, but but they're accurate and they work well But you'd have to read about them to be able to you well, you can just use them without doing anything unique on it, but It's difficult to explain what these are But but basically here each time you run them they will look different But if you take an average of say a thousand runs these will match the open differential equation So that they are well designed According to so there's a paper on this from 1977 and this was published I believe in 2006 or something On Econet if you click on the link, you'll see these explained in detail So network particle tracking not not up yet But this is going to be a future of the new one what this does is that instead of looking instead of tracking the total Total storage amount. It would actually track the Individuals particles. So if it's a flow of nitrogen, it will basically Track little packets of nitrogen which would represent the fifth amount of nitrogen It's like nitrogen atoms, but of course a Simulation in the atomic resolution will not be possible But think about small amounts of nitrogen packets that flow through the network And it will basically check each and every one of them and give you an output of those paths So this is what that basically looks like for the Econet model. So what we see here is the Ulster read ecosystem model and it has six compartments one two three four five six and the Number here correspond to those compartments. So and this is a path so one two four two is a path and that corresponds to the Here a path is particle coming into this network spending some time on it and then exiting the system So this one would represent a particle came into compartment one and then left so it would basically correspond to this path Now this one one two three means that a particle came into compartment one past to two past to three and then exited the system And one six would be a particle came in here went to compartment six and exited the system This is basically a frequency of those paths. So among all the material that entered into the system over 60 percent of them this About slightly higher than 10 percent of them done does this and About again about slightly about the same percentage does this and etc So this will basically give you a picture of this. It can also give you when each of those happen Because each of these are a lot of little events But that's what we're trying what what it does. So it's it's a little bit more Computationally heavy. So I think it will have not a two-minute limit But stay a little bit more, but we're trying to make sure that it will work for everybody Simultaneously, so this you can it has been up since 2007 It's numerical components is fast But it's limited with your internet connection also like things might be downloading slower But often the numerical portion is done at an instant The remaining stuff is other components. So it's critical components is written in C++. That's why it's fast And it's a server-side application meaning that it does not run on your computer You can run it from your cell phone It will run at almost at the same speed because it does not use your cell phones computational resources and It's results that are available. Also, you can export the results to MATLAB in a spreadsheet format and also ENIR Again, this is in the works and That's on our package that the Stuart mentioned earlier and it's flexible to work with you can modify your models easily And also you can email a model everything is in text format. So it's extremely important Price I'd like to mention this. So, you know, you answer a model what happens to it so to be able to work with it equinec is going to have to sort it in a text file and That's in a directory in the server and on Monday every week at about like 5 a.m All of them get deleted So that's what happens to a model and who has access to the server. It's just me and the IT IT people at the engineering at the University of Georgia and This is the there's no direct link to the beta version that has some of these new new features That is implemented in this is this one. So you have to type this literally in there is no link pointing towards it And that's because it does not have any safeguards in it. So again, the regular econnet It'll do it'll run for two minutes and it's going to self-terminate. There's something wrong This does not and when you act when anybody runs this one I get an email not to my regular account, but an email to a separate thing but saying that it's being used from this IP address And etc. So just so you know, you can certainly use this one, but The same privacy is not and I'm doing this just because to see what issues there are So so if something does not work, I'd like to know what in the model causes that and I'll try to fix things as we observe Okay so this is a Turkish small bus driver and originally from Turkey and there has been a study about seven eight years ago about how the Structure of the brain of London taxi drivers are different from almost everybody else They have a larger hippocampia part of the brain that manages spatial Navigation so so this fancy creature is a Turkish bus driver We probably do not have that fancy a brain as a London taxi driver, but these have amazing Capabilities for multitasking so you see this person is driving the bus smoking drinking tea giving money back to a customer and driving at the same time And probably hunting for new passengers because these you hold up your hand and it will stop like they don't have regular bus stops at all So what we hit run modeling equine it will spawn these medical simulations and while it's doing that It will use graph this to put the network diagram the placement of the nodes and the arrows is a difficult optimization problem And I did not write that an open source software for graph this handles that and it will use the no plot to do the time course plot Time course figure which is like madlabs graphing libraries, but open source and the Python will do the network flux decomposition on the beta version and everything is tied together using when it's shell script and the CGI is handling the web interface and Okay, so this is it. We're going to demonstrate it. This is a nice quote not the actor to melon, but the complexity Scientists the science is not about the truth. It's about which lies we can afford to tell. I guess this is Pretty much every model contains this has to represent what happens in real life as best as possible But of course contain not simplifications to be able to do so so what I'm going to do right now is going to I'm going to stop the presentation and Spawn a web browser and I'm going to e-connect and at this point. I'm going to ask Stuart to join me as well So I'll share the web browser So here is the web browser that we need to have smaller perhaps So you can adjust the size of this window and But so I just I did not answer anything into you connect by the way, so this is the address And I think if you just search for you connect Software, that's what you'll you'll see. All right, so That's that I sent in the in the PDF that I email folks before the Right, so if you search for you connect software that is what should come up on Google So and this is the model that you already have In it as as a text version and if you just hit run model, it should run so Not much a learning curve at the beginning So here is the and again, this is a PNG figure and if you click on it It'll it'll spawn a new window which you probably you might not be seeing at this point It basically tells me we don't see that janeer, but that's asking if you Networkraft out EPS so that EPS is stands for encapsulated post script But that's vector-based and it can be converted into SVG and again the regular bitmap versions of any resolution really so and that also holds for this figure and See, but if you'd like to create another figure, you can just click on this it will give you the data Again, it asked me what to do with this text file is that just the text file of that contains all of this data that you can use any other software to Form that graph So these are the initial storage values of each compartment, so right So how is this organized? There are compartmental properties system-wide properties and matrix properties So it's dependent on the size of the output engineer hang on just sec I was gonna make a comment Are you gonna comment on what what why you chose this particular model because it looks familiar Should it look it should look familiar to folks that are watching does anybody reckon you guys recognize why why this model is familiar? Based on my previous presentation Anyway, I know we can't all respond but but anyway, so you get you can give them the answer to me. I'll be quiet now Go ahead Um, did you ask me story? I just wanted you to say that this this I wanted to say that this model I was asking you see if anybody could if you wanted to comment It's basically the the the inter-gill predation model. It's just a different set of it's just a set different set of the just the Compartments are just labeled differently So we can we can court you can make that correspondence back to the previous you know back to the presentation That's all I was trying to do right. So it's basically the fish is feeding directly on the phytoplankton or through an intermediary compartment called soil plankton, right? So a couple people on chat figured it out before before before we figured out our little a little setup here. Good job I'll ask you to like actually build the link as we modify it And so the compartmental properties are the initial storage the final storage and then the environmental inputs and outputs from each compartment And again the name of the compartments on the left. So the through flow is the amount of Total flow passing through our compartment and you know amount of total input amount of total output Comparing these two you can see if the system that's the state or not And also if you take a look at the speaker everything is a straight line meaning that there are no changes anymore So the input into any compartment should be equal to the output rate from any compartment And that and how so this is a straight line, but how straight it is. Well, this difference will tell you and Residence time is again how much the material Spend at each compartment on average and the traffic level is the traffic level And you have some system-wide properties here Off-node are I guess the cycling and again, there is no cycling here. Take a look at the network diagram Nothing cycles and hence that's equal to zero But you know you can add some cycling to see what percentage of cycling there is in the system And again here at this point you have a little indices here like synergism in direct effects if you'd like to learn about any of these you can hit learn more and Here all of them are explained if it's simple We will directly give you and a definition of it But if it's more complicated, we'll give you links to papers if you'd like to learn about the thin cycling in this To click on here That basically give you the link of the paper that you could learn about that at the separate window So you can see that there's a lot more. There's a lot more There's a lot more for example system-wide properties represented here than I gave. I just wanted to give some a couple of examples Right So so basically what you're near is telling you is that there's There's a whole set here and that you can actually see where they come from By clicking on that on that link just wanted to point that out right And this is the adjacency matrix. So is there's a link between any compartments. It's a one otherwise is equal to zero Stochometric matrix is something similar So it basically tells us How the compartmental values change when a flow happens And again at any office if you hit learn more You'll see what that is. You'll see references to it And why you should be concerned about that And flow matrix is pretty much the same as the adjacency matrix, but it's weighted And this is the end matrix that Stuart was referring to And we wanted to point out something notice when we when when I showed the example of the nitrogen model Do you guys remember back to that one? You remember that all of those values were greater than one for all of the compartments at six compartments It was a bigger model, but you notice If you have a model any time and you notice that those values are exactly one You know that you've got it You've got a tree model. You have no cycling things just come in And flow through and come out and that's it So you see that the that when we start changing the model and add cycling and notice that that changes And of course once that changes You'll see also that the reflected in the fencycline index being something other than zero right And then this is the utility analysis These are the how the compartments are affected from each other so so this basically tells us that the The zooplankton is affecting the phytoplankton negatively because the speeding on it and likewise phytoplankton is affecting zooplankton positively Of course zooplankton speeding on it And that relation can be a little bit difficult to decipher in larger networks, but it's computed in printed here and here you see the analysis data in matlab active format So if you'd like to export all of this data Into matlab, you can do so So again, if you click on this it will give you a text file again, but in matlab format And and and it also contains the model and all the matrices the vectors and the scalar outputs of this system And also it contains a model Variable called NEA And if you take that and input it into the NEA dot m Matlab file that was written by cat and boric in 2004. I think right so you will see The email that stood people sent you all earlier. It does contain a link to that paper So it's a matlab file matlab code for doing more than this it it also does environs But it does everything in here as well besides the numerical simulation part. It's a static analysis So this will basically When the system stopped evolving right at the very end it will package all the Flow rates inputs and outputs and the storages and that you can directly feed into matlab And and So actually you can see that if you take a look at the code log. I think here These are the right. So I I implemented it 2010 and this is basically The name of the file that you'll be downloading is called Econet results And then you can directly run this in matlab if you so this capital a is the name of the code that Button boric wrote in 2004 which is available in matlab file exchange And this is the variable that is included in the Econet results and you can directly get the output You know without adding anything modifying anything this immediately And I think there is also a link here, right? So this I think is going to directly point to the paper Oh, no the okay Right. So so this is where you can download the NEA dot amp file I I included the I included the web link and the paper in in the in there. They have a reference for it And this is the common separated File any if you click on it it will ask you to save it. So it'll put everything in a spreadsheet format and Simulation for time course. This is the same as the data that is present right here And it also has show extended results So here it has a little bit more information Excuse me, uh, but uh, yeah, I In the new version we'll get rid of this because I guess it contains a lot of A lot of output as is So, uh one one change. So I will uh ask input from Stewart at this point as well. So I think we decided to do the Include cycling first, right? So what if we have a What if we want cycling in the system and actually there should be fish is going to have some Experiments that are going to be a nitrogen source for the pilot line So what if we put that back in and that would constitute a cycle? So you can do that easily by say you have a You want a flow from fish Back to pilot length And it has to occur at some rate Right. So here's that rate and now hit run model again And now we should have some cycling in the system And right there it is and that changed the values a little bit But if you take a look at the cycling index, you should have a positive cycling index right now And if you go through the n matrix Now we have some values that are larger than one on the main diagonal again referring to what Stewart showed you earlier about cycling So you can see that that that that that what what what this what this analysis is is Sort of trying to point out to you is is that you immediately are able to understand The relationship between when you make a change in the model and you say, okay I get a change in the in the output in terms of the state variables, but then what does that actually mean For the for the extended pass structure the internal structure of what's actually going on inside the model And so that that this this as you can see From the perspective of environment analysis A big step has been taken here in terms of the fact that that this has changed a lot quite a few of the of the Of the properties of the model if generic if you could go back up to the top Where you have the system-wide measures for a second I wanted to show another one. Okay. Look whoops So if you look at the the indirect effects Okay, you'll see That it's actually if we compare it I don't know if we can compare it to the previous run, but it's it's going to I'm sure almost positive It's probably going to be a lot going to be higher Okay, and that's generally what you find In most of the models is that when you include cycling indirect effects are going to go up Okay in general. Yeah, okay So this is this is a really simple model. So some of these things are the changes may not be may not be easily You know may not be easily seen initially, but but but but but the fundamental change in the model is is nevertheless you know reflected in some of them and In many of the measures Take some digging sometimes to actually see this because of course, you know intuitively you might think well if I make this change I expect this well We find out that when we when we start talking about, you know, things like indirect effects and cycling and models Particularly if you've got a model, it's more complicated than what we've got here Things can get a little more difficult to sort of intuit your way around Which is what I'm going to do is like include say a predator fish make the model larger So what I'm going to do is add a flow from fish to let's say sharks At some rate and I'm going to make it on the recipient control With this rate So now we have a new compartment and now if I try to run this There's going to complain so it basically tells me that Uh here no issue condition exists for sharks. So that and that's true, right? It has to have an initial amount of sharks in it for it to be able to simulate so So you will get often open the meaningful Messages from equivalent like that So again, this is some population density and I'm not going to make it Too much Right. So let's let's see what happens now Okay, now it did run right and I have a sharks compartment right now and Now one thing here looks nice But there's no output from sharks meaning that things are going to accumulate at sharks And it might just get out of hand over time. And as you see in the time course figure These two appear to be at steady state, but sharks kind of keep increasing, right? And now this simulation was run for 100 time units and again the units are Can be days weeks months. It depends on your model model specific So let's run this for let's say 200 or 300 time units to see what will be different So I'm going to run it. Let's say for 200 time units And you'll see that it won't matter much because it's adaptive And it gets worse. It's exponential and maybe things are going to go really out of hand if I do it 300 here And sure it does, right? It does just it explodes and this is no way a model should run And that's because sharks should either die or migrate So they should have some death term in them. Otherwise, this is never going to stabilize So I can do that by adding sharks go to the environment with again some rate Okay, let's run that now Okay Perhaps I was attacked too aggressive. It's really close It's really close to zero It just died out really fast But but we can balance that But now it's it's it's a working system And again, everything is computed at each time you hit this and I do not want to spend too much time on this but would like to answer more questions So here are the methods that you choose and if you choose, let's say Stochastic so adapt those steps size. So if you choose this one, so this is the adapter one It's total time and sensitivity is basically how accurate you want your solutions to be And it is a proportion of the actual values. So if you run your model You'll see that your values are in the order of tens So the values are at most 10. So an accuracy value of 0.001 is pretty good But if your values are in the orders of hundreds of thousands Then it might run slow with this sensitivity and you might just to increase it Let me see if we can actually trigger that to happen So I guess that would happen if we increase the rates that had like meet the output small, I guess meet the initial conditions large too Let's see what happens. Let's see what happens. So I'm going to go back to this sensitivity value and let's see If it works or not, okay. Well, it did not increase much. It's on the in the order of hundreds right now And what happened was things got Stabilized probably we need to restrict the outputs further So that things can accumulate more A lot of charts this problem is a good idea Um, what are there any other outputs? No, and let's increase the input further All right, let's see what happens. So I'm just trying to get high values So now you see that it is running at paths lower than before Because this thing probably has a lot of high values and my sensitivity my accuracy desired accuracy is really low so I'm going to At this point you can You can you could not want to wait you can just hit back and you can Increase the sensitivity and then run again And okay, so here it says amount of users going to access infinite low Low means that everybody gets a computing core node But if any node is shared it'll show It'll show Medium and if everybody is sharing the node it will show high So you can see how heavy you can it is being utilized. Okay, so that's the reason we get the values, right? And and it's still not have stabilized yet. We'll probably need to run it longer But that's how the sensitivity parameter helps us to make this work And is this the sharks Yeah, the sharks are not dying. That's enough and I don't What's that? Yeah, I think I think you I think the I think the sharks sort of sort of sort of like just kept going because I had a very small output Right, right. So I think I'll just go ahead and do this and maybe run this attached shorter Let's see that I'd like to show the Okay, so that's that's what that looks like it's being stabilized right now But I wanted to show the stochastic one just in case So this is Had tricky honestly, but let's see if it works It works, but You have to okay. So you see it's the same as the ODE, but there are these fluctuations and if you average them you'll get the ODE and this is kind of Mathematically and weirdly really difficult to to do right And and this works and if I hit reload it will run it again and the results are going to look a little bit different this time Okay, so uh, believe it or not, both of them are actually correct Okay, uh, oh so the default value was 10. I think it's doing that So it's different than what I had earlier because uh It's a different model. So, uh, it doesn't match the very first one that I did But so this one and now it seems like intersecting with each other if I run this again It will look different But both of them are okay And if you average them it should match the ODE perfectly But that's what I'm going to say Say, uh, here is there anything that you'd like to add this to it? um, well, I mean We're doing a lot of dynamic stuff right now One thing I like to to try to show is that when we when we had the original model without the sharks Um, we don't even necessarily have to have we go to the original one even without the cycling And I wanted to I wanted to talk about this this bit that I showed that the two cases um, where I changed the amount that the um That that the fish are feeding on the um on the phytoplanked and I reduced that and that actually changed the the the the um That changed the utility matrix The signs of the utility matrix So if we can run the original one that we did that you had set up originally And then if we could change that so that we had a smaller Smaller flow from the fish to phytoplank than the fish then to compare those so that we could actually see that The the same kind of result. I just want to want to make an analogy to the to the model that we did So right now the relationship between the fish is that the fish affects the phytoplankton negatively Okay, whereas the phytoplankton affects the fish positively Corresponds to the to case one that I had in the right So so here, uh, basically fish is feeding on the phytoplankton. So it's affected negatively But if this flow occurs a lot less than these two I guess That would be the opposite scenario. So let's check that So let's have the rate from phytoplankton to fish. Let's say 10 times smaller Okay, so right now the fish affects the phytoplankton positively and the reason for that is This is not as strong as the as these two now And the more of the fish the less the zooplankton the more of the phytoplankton right Yeah, so so basically the The idea is is that if you is that is it is it what the utility analysis in this case is able to show you Is that is that for this given model structure? Okay, where you've got it. We've got a predator here that's feeding on the intermediate predator the prey the zooplankton and also Excuse me the the fish. Sorry the fish is feeding on the zooplankton I'm looking at the opposite way fish is feeding on the zooplankton and the phytoplankton The zooplankton only feeding on the fish, but the zooplankton has the fish also as a predator That structure let me how the relationship between these compartments Utility analysis has we've done some models on this Uh different models and it's shown that this in this particular case That that the weight of the flows is going to actually determine that in certain really simple cases Okay, for example, we have one two predators and one prey Okay, just just if you had phytoplank if you had zooplankton and and fish feeding on the phytoplankton But not on each other it would just be a competitive relationship. No matter what the flows are so what this what this tells you is is that when when you're doing this this analysis is is that is that is that it you've got an interplay between How you're structuring the model for example when you introduce the cycling we change the structure Introduce the whole new flow in this particular case all we did was change We changed the the uh, we changed essentially the the final weight of the flow The engineer did it in the simulation by changing the the coefficient But the resulting the result of that was was that the was that the was that the study state values at the end of the simulation that it came to actually changed and so you One thing I think that's really useful about eco net and that will and that interplays with the environment analysis is that Is that when you you can change your model and then use simulation and you say okay I understand that the The situation in terms of the how the how the values change over time but then When you look inside the model in terms of things like the indirect effects or cycling index Or the utility analysis you can actually sort of sort of peek under the hood of the model so to speak Using the systems analysis to actually tell you so what does it really mean? When I change that and so that to me that's a powerful feature of eco net because the fact that you can It has such a nice flexible situation where you can you can change the change the the different parameters and Even change the structure of the model fairly easily But then you can compare that so the idea is is if you use this In your work and you have a set a model and you say well, I'd really like to know You know, is it does it really matter? You know if I have this interaction? You know be zero or non-zero or does it really matter? If this interaction or this one or various ones in the model really are strong or weak now if you get a really complicated model You know this can of course get more difficult. We're we're dealing with fairly small models and so You know the interpretation is often a lot more straightforward, but the but the same principles apply So I don't you have any more to add to that janeer. Go please do so. So, uh, I think we'll be open to questions now So do you want people to say question janeer? Do you want them to chat them? And then we call on folks or how do we how do we really want to do that? Do you I believe we did so like have people raise hands and then in in zoo So let me stop share. So I think in the participants list. There is the option to raise a hand And if you do so, uh, you will basically call your name and Or you can use chat whichever whichever people feel more comfortable, I guess So you can either raise your hand and ask your question verbally or or you know comments Or you can just write it on the chat and we can You can And it can be on any part of it. It can be on on on it can be on what we talked about I talked about in the presentation or On the things we talked about in epa net either one is either one is fair game as far as far as I'm concerned If you'd like to speak up or not that everybody's pretty much muted You can yeah, you you're allowed to unmute yourself folks by the way if you want to ask a question And you know with auditory I don't have the hand raised function So I hope that is not the same for everybody but If you're a host, you don't have the raise hand if it's a participant they can raise hands Okay And that's on the bottom of the participant list bottom of the part. Yeah Yeah, if you open your participant window if you and everyone can unmute themselves if needed Right. Thank you So so king's question is what are the units of the pool in the model? Okay, you talking about the models that Joneer is running Are you talking about the the models that that that I was that I was doing in the dimension in the in the presentation Hi, this is kim. I think I'll just unmute me I'm talking about eco net so the pools of the So the sharks to the fight of plankton. So what what values would you use perhaps from the fields to populate those Values or what units are they? right. So so so the units are Entirely user defined and that is because Of the rates. So let's say the if let's say the Unit is kilogram nitrogen now the rate of flow if the unit is kilogram nitrogen would be a thousand times less If the unit were one gram of nitrogen So basically the units are inherently or implicitly included or defined by the flow rates The c or the r values That that also is defining the time unit Day versus week versus month, let's say Does that make sense? I think so. So if you were to go in the fields, it would at least be a math. So for your I would say you're so plankton on your fish. You couldn't use something like abundance. I imagine right so you do have to Think about math and then use the same units and that would be That would be the way to do it. Yes. It would not The entire network analysis literature Of the analysis method methodology is based on conservation So the units have to be the flow currency has to be a conserved quantity. What that means is then let's say if you have An insect eater that is going to consume a 100 An ant eater, you know consuming 100 ants, but gaining a little bit biomass at the end So 100 individuals will be lost, but like Point one ant eater will be gained. So that would be the loss of conservation That's why it has to be in terms of biomass So if it's comparing phytoplankton fish would compare the total biomass of the phytoplankton with the total biomass of the fish Right and then you can just decide your own time units. So perhaps an average of a year or an average of a day Okay, exactly. So i'll make a general comment to you kim Basically what only thing that's required and it works. It's it'll work this way new connect or In using the other analysis Uh packages I I didn't really talk a lot about units in the in the in my in my talk I maybe I should have but basically the the whole idea is is that all the compartments The only requirement is is that all the compartments have the same units So you can't you can't have different units for different compartments If you use grams of carbon or you use grams of dry biomass you use killer calories To represent energy or you use Grams of water or milliliters of water. It doesn't really matter what your units are. They have to be the same They're consistent. So all the flows that you see In the things I presented as well as what you see in eco net those those those flows represent the same units and the biomass the The biomass of the x the compartments x 1 x 2 Or the fish, whichever they are those all represent the same units They represent different categories of the units Okay, but they represent the same unit. That's really that that's really the only requirement Essentially for consistency Great. Thanks sure And brian path asks does the new version of eco net include calculations for the information theory indices that professor ulano covered this morning Unfortunately, I was not at that Talk So I will ask brian to comment on what those are. Is it the ratio of the Ratio of the overhead to the Yeah, it's the average mutual information over the total system capacity So it's basically those three terms overhead AMI and total system, right? Yes, yes, it will It's the currently the only ones that we have I believe are the ascendancy and the overhead. Let's check It has ascendancy and development capacity Now we just well It has been understood I guess that those by themselves are highly correlated with through flow So it makes a lot more sense to take a look at their ratios So those ratios Well, the the the measures themselves will be included and I believe that when you go up to the ratios AMI over So I think both of them are I think these do like ascendancy. I believe is just the through flow scale version of average mutual information So, uh, I think the ratios turn out to be the same. Is that is that correct? Yeah, yeah, that's Thank you. Yes. Thanks Sure. Um, I just saw somebody asked something about about the About eco net as a package and are and I guess I mean, I I let janeer talk a little bit about eco net after but what I would respond to that would be that Yeah, eco net and are do there's a lot of overlap between the three packages that that were mentioned The the the earliest one that's actually brian fath who just asked a question Uh, was the primary developer of is a matlab? A set of things to do the the the network analysis Work do the through flow and storage? And I'm not sure whether or not it it does utility on it. It very well may. I'm not sure but but and the are package does Um, does pretty much everything that eco net does except it's not a simulator It it works on simply the the steady state Values and it has a lot of other Um, measures that the the steward board and matlab have put into it. And so I think if you have a set of a model or set of models you're developing You could actually freely use any of these Um eco net was designed to be able to use on the web And janeer can can make a comment as to whether or not that has you know, he can it can be used offline or whatever I'm not sure. Um advantage of that would be or how that as much as anything It's certainly so the question is is there a chance of the eco net as a package? In are so to work offline um It's certainly possible. It would be very difficult on my part in that interpreter the part that takes in the model and uh extract sets as a differential equation Is is a a shell script, which is uh very different than a an r The second complication which would be a little Less probably would be the speed right now the coin it uses a c c plus plus as its miracle engine and it's going to be Significantly slower not significantly, but it wouldn't scale as well when run with uh r It would still work. Um But large models would like any connect you can actually put I think As much as you can put 200 compartment models and in either one it actually is really fast on that front Uh, one thing that you Directly it is doable. We'll look to procure in the next two three years. I don't think so But if there's a demand you can basically accommodate it and have you know hire somebody to work We say that one way you can interact them would be that if you wanted to do some some experimentation But doing some of the simulations and eco net And you wanted to take advantage of some of the there are some additional analyses that are included in enar I wasn't able to go over them because we just don't have enough time here But if you look at the reference and also if you go to the to the online the online Demonstration that steward board and matt have put together and some other folks You'll get a sense of what's available. But once you have the steady state model Really, I mean enar and the matlab function Are going to do the network analysis and they have some of them have certain things. I think they're not all exactly the same I think what munica refers to is like you don't have to be only for to use if you have to be online right and that's the limitation and I I tried to So the way that I try to extend this is you know being online is basically being common But it's still an issue if you're in the field But the way the way that I like to so equities free I like I want equinate to be as easily used and best integrated with other software as possible So, um, I try to include, you know, it Output in matlab format. It will up with this spreadsheet. It'll output in enar our format So that it can be integrated in a lot of things It might also be possible to have to call Econet in our through an API and interface That that that might be a possibility But but that will also require internet connection yet again. Yeah If you have any suggestions or you know, uh, please do that's how it connects is going to be shaped in the future anyways Thank you very much for the answer. I was just I was just curious because I'm using our and I've been doing path analysis and the other Modeling so That was just a thought but thanks for concerned. It's just it's not like I would be pushing or something to say Maybe there will be more people showing the future of the time You know As that's how we're that's how we can kind of know that what people need so that we can you know That's for everybody to use that's why it's free But we would like it to be as useful as possible. So, you know, uh, whether it's possible or not But you know, if there's a demand we will try to make it happen Well, the easiest way is right now having this Online in in the web. So I don't have to you know, write any codes and scripting and bother just put the model put information and And it does the whole work and I just wait for results. That's a perfect when you know, sometimes you want to take your data and That was just just a thought Thank you for the concern Appreciate great presentation. Thank you very much. Thank you So we've got about 20 minutes left. Um Should we see get some feedback from folks as to what what what they might want us to to do in terms of whether we want to do more More gaming experiment with things with eco net or if they want to talk about You know other other other issues of network analysis or other things that that we've got. I mean We we've sort of presented the basic idea. I mean, there's a whole lot more obviously of different different kinds of things that could be done it's a lot to It's a lot to absorb in terms of you know in terms of trying to understand the The background of of NEA and the interpretation, but So either that or do you have any ideas janeer for some for for for something else that you want to try or Or do you want to do you want to see if we get any? feedback either you can either say it through chat or you can just or you can just unmute yourself and and make a you know make a comment to us about something you want to see or If you have a question about about something we talked about that you want us to try to clarify Anything to add janeer That there is one more question. Are there capabilities of including effects of environmental factors? to the groups in the model Can I ask to clarify Like perhaps by an example from kim sure so maybe uh effects of temperature or or salinity or or anything like that Yes, yes, there are uh, that's basically the flow rates would be dependent on time or certain parameters, right? Is that what you mean? Well, I'm just wondering if is this just predator prey or are there other factors that can affect the size of the pools of these groups over time um The size of the pools are purely managed by the flow of inputs and outputs to each compartment, however Like uh, so let's say the phytoplankton bloom through irradiance levels, right? So they're basically the capability of nitrogen uptake of the phytoplankton will be dependent on the irradiance levels So so if there's a lot of light it'll so it will basically be a function of time in in in a way like as as it's As the daylight Duration increases it will be able to feed more So and that would be a function of time and but and that means that the input into phytoplankton would change by time So maybe that's an interesting example of how to change irradiance on phytoplankton or something like that Well before well before we go too much further It's a great example, janeer, but what I would point out is that is that is that is that what what you're asking is that Is kind of a it's it's a modeling. It's a modeling question obviously and it's relevant to what we're doing, but The beauty of econet is that is that basically all of the all of the things that going to affect the flow whether it's an input from outside the system or an output from a compartment or Are the interactions between the or the the flows between the between the compartments all of that is essentially Put into those into those into those into those one into that one coefficient So I think what you would what you would have to do if you wanted to use this If you had a conceptual model that had a whole had one or more types of controls of things that whether it's temperature whether it's irradiance whether it's moisture or whether it's all sorts of things You would have to build you have to have a conceptual model And then you would have to decide how those things end up changing That that parameter would at whichever it is the the lumped parameter as I would call it An econet and then you would have to then you would have to go ahead and run the model again Thing is is an econet isn't really designed to create these these I mean you I suppose If there are there are ways you could do it if you could design a way to have a function So that c was not just not just a constant But but but it would take it would take some it would take some creative doing generic What I said, so We thought about this like instead of having a c equals r equals v equals We could have like an f equals where somebody can input a function That includes as well as other compartments sometimes a compartment would affect a flow between two other Apartments differently like a predator its appearance is going to decrease the pd rate so both could be theoretically done and we thought about how to do that the one issue that I come up with So it's not so easy is the flexibility would probably be Would have to be compromised in another one just right now. It's equal. It is so easy You just do c equals r equals v equals and it just runs But if you want like free function entry The input would probably be not as simple as before It's doable and it's it's So the thing is if you have such a system you can it becomes useless because it doesn't intimidate that So I think for those type systems One way to go ahead in my mind, which is not realized yet though is to have a different interface with small structure Where the flows are written line by the line and the function is written next to it, right? That wouldn't be hard to turn into a differential equation and stimulate right Well, if you if you're interested I'll comment if you're interested in doing the network analysis part Okay, then then then really you need you whatever simulator you use whether you whether you have your own Whether you have your own program you write in whatever language our python Or even some other language c plus plus or something Or you or you do it in Stella once you get that then you can do the network analysis The beauty of of eco net really and I guess that it's the beauty and the weakness as janeer said It was designed to be this way is that is that you can gen up a model Okay, and then and modify it fairly easily It's it's fairly it's fairly transparent that way and then you can get a simulation of it using the various methods that janeer talked about And then you can do the network analysis But if you're talking about getting really into doing a lot of this Bit where you've got these complex functions Then I think you're either going to have to go one of two routes either you're going to have to use a program like stella And there are others i'm sure i'm that's what i'm most familiar with where you can do You know you can actually set up, you know function control functions for these various inputs outputs or intercompartmental flows Or or if you write your own of course then you can write at any kind of arbitrary function as janeer pointed out So I guess I guess You know there's ways you could do it Yeah, I think there are ways that that it could address it but Once you get I think too far away from from from this from the simple sort of simple setup Not that it's simple in terms of the background, but in terms of the way it the way you build the model That part gets very tricky Right at that point, but janeer can make an additional comment if he if he has one Great got it. Thank you. Okay Any other questions comments suggestions? And i'll throw out a general thing is a Right now we've got I guess about 15 a little less than 15 minutes If any of them if anybody that's here that's seen what we've done and I know like I said it's it's very hard to absorb all this because you're absorbing You know a theoretical Background and and a set of analyses that are that are not that Not always that easy to understand if you've never sat dealt with them before and An analysis program that is also a simulator by the way and has a lot of Things that you have to learn about it. It's a lot to absorb but if anybody has anything that they want us to either Talk about more expand more on or Use the time to go into eco net and you know and try something and see if it happens That could be something that might be useful or if somebody has some other idea You know about how they think would be useful to use the time. I mean basically we're here To try to help you to understand, you know what we've done You know so that so that at the end of this you will at least be able to go away and say well At least I have some idea of what you know of how I might how I might actually do this You know with with some sort of with something with some Some scenario either some some setup that you have that from your You know from your own work that you either have an existing model or a model that you have an idea you want to build Is that sound reasonable janeer? You could expand or if you had run eco net yourself meanwhile and Got an error or any questions about what you did you feel free to share your screen And comment on it and I don't think they can actually do that janeer I I think that and I guess you could allow them to write Yeah, they they can send us comments and they can they can talk to us, but i'm not so sure they can share our screen, but they can they could they could Send a model by chat and we you could run it or something like if they want to I mean i'm not Or they or they could just send you send something to you say can you try this? And then you could just implement an eco net. That's one way to do it And depending on what people want. I mean I we don't have any strict Rules here about what to what to try or do really. I mean it's really At this point. I think a lot of it is up to what you guys are thinking. I know it's a lot to absorb so at this point you might have some questions about You know about about what what some of the things we're doing mean or how How how what we're doing interfaces with with your the things that you're interested in either your set of models or or the kinds of things that that you do in in your You know in your in your work And I'm monitoring the current right now. So if anybody has run something or has issues I can comment on the model directly without even sending anything Well, if there are no questions comments we can perhaps end the meeting or What do we do? I it's up to it's up to these guys in I'm just I just don't I don't want to shortchange folks, but if folks are if folks are if everybody's okay with You know with what we've done I I just you know I we have been only heard from a few and full of folks but So I hesitate to end but I I'd like to see if if anybody has any You know anything they want us to try to clarify We don't have a ton of time. So we don't have a lot of time to go into a lot of You know into a lot more, you know detail on on some of the things A lot of the things were sort of brushed over very quickly because You know we had we were trying to cover a lot of a lot of ground here Obviously and it's it is a lot to absorb. So it could be that people are Maybe a little bit overwhelmed by the You know by all of the different pieces and don't have anything specific to So shall we ask our host to See what should we do? Oh Came up. I think it's Kim again. Is there a way to remove masks from a group? Export migration fishing That that would be done by again Adding a flow to the environment. So if you'd like to remove a mass Over time though, I guess, right? Is it over time? Yes Right. So so so you can certainly have so if there is If the deer migrate over time You could basically have deer and arrow and then star and the migration rate Why don't you share your screen jenaire and then we can maybe you could Tell us how to do an example camp maybe See if you could try that That might that might help for her to understand or me to understand what she means and her to understand what So, uh, right. So I actually this term right here Would be seen as death or migration And uh, we can increase that so let's run that for now and we will see an output Oh, it's still doing this. Yeah, you're doing that. You're doing the stochastic. It's a little hard to to deal with that Listen the regular one So right so the fish so it stabilized around like two units and if me changed this to let's say Two it would it would basically it would be a migration basically or death and That's leaving the boundary. So it does not matter if you know leaves the boundary to afterlife or So I have a question related to what you say when you say removing from a group Do you mean from a set of compartments more than one? Or do you just mean from any particular compartment that happens to be in the model? That's what i'm trying to right. I mean any particular compartment So for example from the fish group you could have a fishery Maybe you could represent that with the model by some type of removal term I see. So do you mean can you have multiple outputs jr. Nir would have to answer that? I don't think that you can't um so if the output is It does not if the output is like out Uh, but it's not really if you do not really care where It is all length into one Some so this so for example to represent a fishery here If you wanted to know that is a real if you want to have another output You could actually create fishery or humans here And then have a flow to it and then just leave the output from fish being just general mortality Yeah, or or or or immigration from the from the from the bit So otherwise if you want to you can't have multiple outputs in terms of to the environment But if you but if you if you wanted to know about something That had another output, and then you wanted just a general out of the environment. That's certainly feasible Does that make sense cam? What I just said. Yeah. Yeah, and that's indeed more what I mean because it's not just an output to the Uh system is actually taking away from the system somehow Right. So so I just put in like, you know fish catch and and again You really do not are not you're not including details of humans in our model So I just put zero for the initial condition and you'll see this is basically the catch is accumulating over time And that's correct because it will be accumulating over time, right? Right Right, so it gets those kinds of issues become difficult modeling issues here because for example You know the people are obviously not the fish aren't just accumulating, you know on the dock or on the boat They're getting they're getting brought and you know and sold and sent to markets And so so in order to really do that realistically You know if you had it as a compartment you would kind of have to have You know an output as well But you could you could play with that in terms of the fact that you know No matter how you no matter how you set this up The eco net is going to try to do it and it for example here when you don't include an output From the from the humans that tells you okay, wait a minute Maybe my conceptual model is a little you know, maybe that's not really exactly what's happening because of course You know, you're not just taking fish out of the system and just they're not just piling up and accumulating forever You know, they're they're going to go somewhere So that gives you an idea of how that That gives you an idea of how with eco net you get this fast feedback In terms of things that once you you create it, you know, you run it and boom You know, you're gonna you're gonna see the result and then you then you can scratch your head and say well Is that really what I meant or if this is what you meant then You know, what are the implications of that for what I you know for how I'm trying to conceptualize my system? So if that makes sense, so if you have any other comments, junior go ahead Great, thank you. Does that make sense camp? Yeah, it does So I did indeed wanted so it doesn't return to detritus or the or the environment So did you do indeed have the ability to remove something? So, yeah, I could see that We have about like two three minutes any last night questions Yeah, last minute. We basically at this point we're at last minute questions of anything you want to ask us before Of course, you know You can email us and those kinds of things because you know, I assume everybody got people's emails I'm not sure about that, but I'm assuming that you did right So if you if you keep feedback here and if you just write something That will send me an email or you can really send me an email Again, it's my first name at uga.edu right And I think my I think people people I think people got my email through the through the through the Through the registration site. I'm not positive of that, but if you don't You know, I can I could I could send the number email to all the participants except the one person that was Fay V however, he said exactly has says his name And send that I did I did not yeah, well you have my email because I sent it that's correct So you can you could respond to that I forgot Sorry, my brain is a little off right now. I I've been scrambling here trying to process everything, but So did we get any did we get any other questions? Or does anybody have any last minute things? Before we say have any we had last thanks for the presentation. Do you have any lesson? Plans related to e-connect if not and if I develop one would you want me to send you absolutely And if you'd like to discuss this If there's any way that I could help please get in touch with me I I'd be happy to share the presentation that I have and I I've been given these over over time At the various conferences. I'd be happy to work with you or help you Yeah, I mean I would to to the extent I'm not an expert on e-connect, but as far as you know developing models and doing analysis and things like that I I've done a lot of that if you were interested in You know and any input from from me as well I'm not any the expert on e-connect is right here engineer because he's the one who and I'd be happy to you know Receive anything that should develop as well Yeah, great. Thank you very much. I appreciate it. Okay. Thanks Cassandra. Thank you I guess we'll defer to our post Okay, I guess if we don't hear anything else I guess yeah people are people are signing or are signing off. So I think folks must be done I'm gonna I can tell unless somebody Things So thank you guys for participating. Thanks for the for the questions and comments and things. We appreciate it I hope you got something out of it. Those of you who are still there listening and Thank you. All right