 Mateo, do you want to say anything today? Or should I just start? OK, great. OK, so this is the third lecture of this viral ecology series for the week. You got it. OK, I'll put that down. Fine. OK, welcome back. Again, I'm Joshua Weitz, lecture number three. And I had a plan early in the week. But as you can see, we've been improvising a little bit and made some changes. So today, I will continue building up this notion, which we started on Monday of trying to understand dynamical feedbacks between viruses and microbial hosts. On Monday, I focused predominantly on foundations and principles, really thinking about ways in which ecology leads to endogenous oscillations. And then on Tuesday, I extended that both to evolution and co-evolution. And today, I'll begin to think more broadly about complex networks of phage and bacteria. OK, and so in doing so, I just want to re-emphasize some of these concepts that I explained already, that there are a lot of viruses in natural systems. This was the illustration from 1989 by Berg, showing that there were 250 million viruses per milliliter. Typically, it's something more like 10 million per milliliter. So there are a lot of them. It's not as if just because we can find resistance in the laboratory means that somehow these viruses can't make it in natural environments. And likewise, we went back. This was some early work in 1989. We wanted to go see how general this was. So my group, along with a number of other groups, went back and revisited virus and host samples taken from marine systems at the surface and blew deeper in the ocean below 100 meters or in green. And we went back and tried to ask the question again, well, just how many viruses or virus-like particles are there? And the answer is, there are a lot. And there often, you may have heard this before, there are 10 viruses for every microbe in marine systems. Has anyone heard that idea? Maybe you haven't, or approximately. That's approximately true. But in fact, there's typically quite a lot of variation. There tends to be more viruses than there are bacteria, something or more virus than there are microbes, something like at least one, if not up to 100 to one. So you get a lot of variations between this. And you can look at the y and x-axis to see that we're talking about averages on the order of 10 to the 6 for microbes and 10 to the 7 for viruses. But there's substantial variation. And obviously, there's going to be more, I don't know why I have the colors wrong, but there are more abundant types at the surface than there are at depth. So we have a lot of bacteria, a lot of viruses, and they're also quite diverse. So I'm trying to build up and make an argument as to why we can't just look at single-virus host pairs or groups of, let's say, a single host and two viruses or two hosts and one virus. So we can't just keep doing this sort of progressive process. It would take us a long time. People have tried to examine just how diverse systems are. This is, in some sense, like a collector curve, a little bit different, where the x-axis is the number of viral genotypes, and the y-axis is the percent of the most abundant type. And you also have something here where you have more of a rank-abendance curve. So you can sometimes see these in ecological systems where physicists have played a role or Yacopa works on these kind of systems, where you rank the order of the type. So number one is the most abundant. Number two is second most abundant. And you just plot its relative abundance. And they can sometimes have different shapes. This is a bit unusual. But the point is, there's a very long tail of relatively rare types. So we have a lot of diversity in these systems, and it's actually very hard to estimate the tail. So in this paper from over 15 years ago, they estimated that there were between 10,000 and 1 million viral genotypes. So that should tell you there's a lot of diversity. It should also tell you that estimating the size of this tail is very difficult and it's not really a stable estimate for all sorts of reasons. And the principal reason is that you don't see the tail. So you take a sample and you see typically the abundant things and you're trying to infer the shape of the tail from the bulk of the distribution. But there's really no information in the bulk that tells you about the tail. So if you actually try to count exactly how deep that tail is, you tend to fail unless you get close to the system size itself. Out of viral genotypes. No, I haven't talked about it yet. Okay, are you going to talk about this? Probably not so much today, but these are always operational terms. So for bacteria, if you want to count them, when you think about species counting in a typical sense when you can actually have the animal or plant in mind, then there's usually a notion of some separation of reproduction. So reproductive isolation. But for bacteria, you look at ribosomal DNA, right? Right, so you look at the gene responsible of the ribosomal RNA and then it's either the 16S or the 23S different sizes and you can use these essentially marker genes. So there's something that you can look at in the genome that is found across all bacteria. And so I'll explain it in a moment, virus is a little harder. So that is found across all bacteria that share this little segment. And then you compare and you say if they are within such and such similarity, we can organize that as an operational taxonomic unit or an OTU. But if they're farther apart and usually there's like a 97% similarity cutoff, then you say no, those are different things. Viruses do not possess a universal gene, right? So these are often other kinds of ways to cluster them operationally. But I'm not going, that's not really what I'm going to go into today for all sorts of reasons. But you're right that this problem of how do we even talk about, I didn't say species, these are genotypes. So somehow they're clustered together. It's a harder problem. Good, so how do we actually characterize who infects whom? And in fact, everything I'm going to talk about in the next section will predominantly rely not on this operational approach but actually on trying to learn about who infects whom from systems in which we can bring into the laboratory because that's a bit more tractable. So how do you figure out who infects whom? There's a lot of diversity out there. There's a lot of bacteria and a lot of viruses. Clearly not all the viruses are infecting all the hosts, right? They have specificity. I have E. coli phage and cholera phage and phage that infect prochlorococcus or cynicococcus. And I know I'm using a lot of words and this is a physics spring college, that's okay. So you can think of these as different types of bacteria and they're infected by different types of viruses. But it turns out that neither does one virus infect only one host, nor is it true that one virus infects all the hosts, right? They have some specificity but it's not so narrow that it's also only one type. So how do we actually figure this out? What people do in practice is they collect bacteria and phage for all sorts of reasons. Maybe they get them from the environment and are able to isolate them in the laboratory. So they actually have them in culture, in a test tube, in a flask vial, in the freezer which they can bring out and they can use for experiments. And then they use these spot assays to see whom infects whom. And by a spot assay, it's precisely the thing that I already talked to you about which are essentially looking for these little clearances or what I call plaques. And you remember we did talk about that already. That if we have an agar plate and we were to put some media that has some amount of bacteria in it, we get these colonies and if we count them, we usually count them in CFUs, colony forming units and whatever density we wanna do. For phage, they have to replicate on a bacteria. So if we know their bacteria that they can grow on, we grow up this lawn of bacteria and now I, oh, there it is. Good. And if it's wet, that's ideal. Yes, it's a little wet. So we grow up this lawn, we put the viruses and they make these little holes which are called plaques. And if we count those, we get PFUs, plaque forming units. That is what you're seeing there. And what you should see with the notation is that they've tried on a particular bacterial lawn which is written in the center to place a particular kind of virus which is written kind of at the top. And you can see in some cases, you get clearance and it's not necessarily a perfect hole. In fact, there's lots you can learn from the fact that those aren't perfect but in some cases, you see nothing. It's not as if they didn't try, right? The right side, right plate, left side, there's no clearance which denotes the fact that that phage was not able to infect that bacteria. Okay? So if you do that kind of study, any questions about this? Okay. If you do that kind of study many times over, you can get both a quantitative and a qualitative assay. A plus minus can it infect and you can even get a degree to which it can infect. Because you may have to dilute this to a certain level or you may actually find that there's a sort of rate or size of the plaque so you sometimes it's scored quantitatively but I'll just worry about the qualitative side. And to point out that eventually you can get these things that fundamentally are a network in which you have hosts as the rows, the phage as the columns and these squares denote the fact that that particular phage can infect that particular host. And I'll call that either a virus host network or a phage-bacteria interaction network or infection network, okay? So these things where we have the host and the phage, I might call these a phage-bacteria infection network, okay? Good. So you can see that this is an example of what happens each one of those squares is itself an experiment in which people have tried to let these phage grow on these bacteria. And so if we wanna start to use the techniques of Monday and Tuesday, these dynamical system techniques to ask questions, what happens in larger systems? We have to have some sense of understanding, well, what is even the structure of these networks? We could try to use those first principles and posit what the structure should be and sometimes in some work we've done that, but another way to think about this is actually to look at natural systems and look at these examples and try to see if there are any common patterns and then try to understand how those common patterns might arise. So that's what we did. A long time ago, collecting 38 different studies representing greater than 12,000 infections with a whole bunch of diversity and now each one of these little, almost thumbnails, these little portraits, you understand what those mean. That's a phage-bacteria interaction network in which each square represents this kind of experiment. And if the clearance happened and now somehow it's going away, the chalk is growing back in to the spot, if those holes are there, that denotes the fact that that phage can infect that bacteria. We had hoped when we had originated the study that it would be very apparent as to what the pattern was because then we could use these sort of same structures of quantitative interactions and feedbacks to say, well, what kind of dynamics do we expect in those communities? But I think you can look at it and say, it's not so apparent that there's any pattern at all. Just because you're looking at them, hold on, Mateo, you're not in this class. I'm gonna ask them some questions. Hold on, wait, just give me a second. I was doing fine without you the Monday and Tuesday and now you're asking all the questions. Let me ask them a question. So I wanted to ask people other than Mateo whether or not you see any patterns and then I'll take your question, but I wanna ask them first. Do you recognize any patterns here? Anything that you think seems interesting or not just looking like a random mess. Feel free to shout it out and or use the mic and I can repeat it if Mateo doesn't reach you. If you keep the mic away from Mateo, then more questions for you. In the center network there is like a straight line. This one? Yeah, this one's interesting and this is gonna be a helpful guide. A straight line. What is interesting about that? Let's elaborate. So yes, there's a straight line, but what would that say biologically you think? Remembering that the phage are the columns back here of the rows. Yeah, maybe it means that they evolved such that they increased the number of us they can infect. So here's a phage that can infect almost none of these bacteria. Here's one that can infect many. Yeah. You're suggesting somehow that maybe evolution acted this way for the phage. Increased its host range. Of course, could have acted that way and decreased it, but we talked before about these expansions. And likewise, the bacteria I'm just gonna now elaborate on it. You see some of them seem to be very well defended. They can't be infected by almost this top one by none and here only by a few where some seem to be very susceptible. Yes, in the back. How they arrange. How they are there. I'm about to answer that in the next slide. Yeah. So originally these were not done when people present these studies they're usually just trying to characterize or type things or often in the order of collection. So there's not necessarily a rhyme or reason and I'll show you in a moment that there's a better way to look at these. Okay. Good. And I'm about to elaborate on that. Yes. I was seeing that like none of the phages can like maybe just a little bit can infect like all the bacteria they were tested on. So that also goes back to a point I was making before. We rarely see in this particular case. And again, these are often focused in and I'll talk about that too. You're hitting a lot of the topics I'm about to go through in the next five or 10 minutes which is we don't see necessarily a phage that can infect all these particular bacteria. And I'll elaborate on that's not necessarily universally true. I could have, we could have chosen examples with that would happen, but you tend to see that there's some resistance. So we see a spectrum, right? Of things that look more specialized a little bit more generalized. We see some spectrum of the bacteria that seem to be a little bit more resistant or more susceptible. Okay. This data are about genotypes as before or about species of bacteria phages. You should think of these as isolates. So they could, I'll say in a moment these are certainly not different at what a virologist would call species level. Except for maybe if there's one or two that may be at the equivalent of viruses infecting different hosts in different genera. But beyond that, no. And I'll talk about that in a moment. So we're looking at a micro diversity infection in the sense of the diversity by both the host and the phage are relatively small. Okay. Okay. So the problem here goes back to your question of the ordering. They looked at these one way. We were expecting some pattern that we could then build in. Because remember the other day we had these little models like n dot is some growth minus phi and v minus omega n and v dot might be theta phi and v minus phi and v minus omega v. And we talked about all the consequences but what happens if I were to put i and j there? And we have many types. Then I have to figure out that this is not just a scalar but it's a matrix, right? Or a tensor, right? It's this relationship. And I have no idea what to put in there when I get to larger communities. The problem with just looking at this and looking for a pattern based on how they presented is then they weren't necessarily looking at the same question the same reason as I was. So how many different ways are there in fact to present the same data? How many ways are there to visualize the same matrix? Right? If we have p number of phage and capital H number of hosts. How many ways could you represent the data? Just in terms of different row column configurations. I'm hearing the word, someone said factorial. Is that true? He said factorial. So I have a choice of which phage I want to put in the first column. And once I do that I have p minus one to choose for the next and p minus two and so on. So I have a factorial, p factorial, I have H factorial. That's a very large number. So there's no reason necessarily that this particular configuration might have been the best one to reveal a pattern. And so what we did was reexamine it using in fact the one that you notice as our guide, this one that seemed to have a straight line which we term as a indicative of a nested pattern. So not only, I'll use that word nested which is written on the top or nestedness. You will notice that there is a relationship between this generalist phage and the next most generalist phage and the next which is that the host range as we move from the generalist to the specialist is nested within the subsequent one. So if I have this as being my host range for the most generalist type, the next one infects things that the generalist does but not as many and the next one infects fewer but they're always nested within the larger group. Which means that the specialist ends up infecting the host that is most easiest to access. Likewise, the phage range let's say of the host are also nested, right? So this relationship of which phage can affect which host or vice versa are themselves have this structure. This one is obvious. These other ones were not so obvious and I'll give you some zoomed in examples. And of course we have to be careful given the size of the networks we don't know if these are statistically significant or not. The lines that you see that are a little bit hard to know where all the relationships should be if these were perfectly nested and obviously they're not perfectly nested but they tend to be. I'll show you in a moment more about how we did that. So let me just show you one way to do this on your own. This is the simplest one. It's actually not the most robust for various reasons but it's the most intuitive. You take your matrix and you reorder things by how susceptible they are from the most to the least and you resort the columns based on their infectivity from the most to the least. This is left to right and top to bottom. And what we've done in these two moves is take this matrix and now make it look like this. It's the same data but just resorted. Is everyone okay with that? It's the same data, the same relationship, every phage vector relationship is the same. I've just resorted them. And then we draw this little line, this isocline and all the technical details will be on the slides. You don't have to memorize this. I'm just trying to explain the method by which people do this and it's just one of many. And you'll notice that if it were perfectly nested, all of the relationship should be above this isocline because that would denote the fact that we have this sort of embedding. And then you find the exceptions, places in which we expected there to be a relationship where we don't, places where we find a relationship where we don't expect it. And then this particular algorithm tries to calculate and wait how off we were from perfect nestedness and the farther we're away, we're gonna count that a little bit higher. Okay, it is just one way. Just to point out that there is a methodology. The problem with this methodology of course is it depends a little bit on this embedding. Whereas there's other ways in which you're actually formally calculating the extent to which these relationships are really subsets of each other. It's just not as visually evident. So I'm showing you this one. Okay, so let me now show you an example in which I don't think it was apparent initially. Here is what we saw in the initial presentation and this is what it looks like after you do the procedure I just described. I would call this significantly nested as does the algorithm. But it wasn't apparent to us when we looked at the first time that there was any pattern there. You can see there's a spectrum from specialist to generalist and statistically speaking, the specialists are specializing on the most susceptible hosts as are the generalist phage. In this example, there are some bacteria for which there were no phage that can infect it. Those bottom few rows. This is the procedure by which we applied for each one. And this is somewhat helpful because it points out that despite the fact that we're looking at very different kind of systems, maybe there are some patterns that transcend the particular details, which is a very physics-y thing to hope for. Almost a belief system. We can talk about that some other day. Nonetheless, I know we're not supposed to believe things as scientists, but there is some motivating belief among physicists that somehow stuff like this can happen and happens a lot. Okay, now I'll go back to your question in the corner. Was this in some sense unexpected? Here we've calculated the nestiness using that temperature calculator that I just showed you because if I don't orient things in the right way, it won't appear to be nested. If I haven't done the pre-sorting, this is the nestiness value originally after our sorting. And you can see in almost every case, it wasn't necessarily realized in advance that there was this extent to which these networks were nested. So this is not only some evidence that there is a pattern, but also that the pattern wasn't necessarily known before we began to look at things in a different way. Okay? Questions at this stage? Okay, in one of the previous slides when you presented all the graphs, initially they were originally presented and then after you resorted them and looked for nestedness, they were divided into categories, if I remember correctly. Most of them were presented nestedness while others didn't, right? Correct, so I'm gonna get into what those other patterns are. Okay, and the fact that they didn't present nestedness means that the value of nestedness was under a certain threshold. It meant that if we were to take those interactions, so what did I mean by the fact that I classified some as nested and some as not? And just because they're not nested doesn't mean they have a random pattern, just we didn't find them to be nested. What it means is that if we were to take the same number of interactions, and you can constrain things in different ways, but essentially throw those interactions down at random and then resort them. You would still get some nestedness value that may be above that which is random in your ensemble, because sometimes you'll generate by chance a somewhat nested relationship. If we generate enough of those, we'll get a distribution and our question is our observed value higher than that expected by chance? And if it's not, we don't classify it. If it is, we do and it doesn't mean it's perfect. So that's what I mean by that classification. So it's in some sense comparing to an ensemble with a particular constraint. I think that answers your question. Could you repeat the concept of nestedness because I'm not sure I understood well? Sure. Let's, where's my thing? Let's imagine that this, and actually, can I write on this again? That this circle denotes the hosts that phase one can infect. And I will do that by making a bunch of circles. Now I knew it was that dangerous because here they're colonies. So actually maybe I'll put letters on these. So A and B and C and D and F, H and, you know, Phi one and Z, these are all different kinds of bacteria. Okay, I'm gonna put enough of these down. Now, let me put some more on the outside. This is how all of the things in that circle denote the hosts that, these are the hosts that phase one can infect. Now I'm gonna denote this is going to be all the hosts that phase two can infect. And you see they're nested within the set that phase one can infect. And if I were to draw another diagram, this is the host that phase three can infect. They are contained within two, which is the selfs contained within one. And finally, I could do that and this would be four. This is what I mean by nested. If you know the matryoshka dolls in which they are the resting dolls that you take one out and there's one inside, this is that concept. So it's like a measure of interaction between neighbors, phages which are neighbors. It is a property of the network as a whole. Okay. And it's a property to which the extent to which that the infection ranges can be organized as subsets of one another. Okay, it's good, thank you. But why are we expecting nest and nest to appear? Wouldn't it be evolutionary more efficient to divide the population so that different viruses would infect on different hosts? Okay, that's a great question in so many ways. There are two ways in which it's a great question. First of all, who would it be more efficient for? So that's a great thing because, and I love the way you asked it because I think it allows us to talk about purpose and evolution. It's not necessarily for us or for the virus or the bacteria, these are emergent properties. So although it would be maybe more efficient if we were a drug developer and we're trying to knock out things but that doesn't necessarily mean it's more efficient for any of these things involved. So just let's keep that in mind. On the other hand, you are absolutely right that if I were to look more broadly at phage-bacteria interactions, then I should not expect this kind of pattern to be universal if I get to a big enough scale and in a few slides I will show you a different kind of pattern, precisely the kind that you just described. And it arises not necessarily because that's just a more efficient way and the universe has evolved to divide up which phage get which bacteria. It's not a monopoly on these bacteria that they've colluded to decide which ones get which is because at some point they're becoming compatible, right? And so if a bacteria starts to evolve in a certain way and a virus co-evolves to infect it, it may lose the ability to infect something else, right? So these sorts of separations may be byproducts of the evolutionary process. But let me get to it in a second and I think what you're talking about is modularity and I'll show you examples in a moment, okay? Great, great question. Okay, so this is a tentative conclusion. In fact, because of this question, I don't want to write definitive conclusion, it's a tentative one that they are typically nested. So I'm using a lot of caveat words but here I want to just elaborate what I mean by nested now in terms of a network. Here we have a spectrum in which we have these generalist phage and you can see they're all going outwards and notably the specialist phage doesn't infect the bacteria that is hardest to infect, it infects the bacteria that is easiest to infect and that's a consequence of this nested property, okay? So we have a spectrum from hard to infect to susceptible, generalist to specialist and also that extends a little bit of the idea that I was trying to say the other day in terms of these evolution of resistance and then host range expansion but now it's taking it out into a network, okay? This broadening of host range, in other words, we could have thought that what's going to happen is the virus infects this new type but loses the ability to infect the one behind and we wouldn't have had a nest in this, we would just have a bunch of specialists but we actually see that there is an ability to have a spectrum from generalism to specialist and it appears common in both ecological and evolutionary studies. This is a tentative conclusion. I do want to now go into a little bit of this which is now that we found a pattern, we might ask the question, how can they coexist? How is it possible for these virus and bacteria strains to coexist given that they have nested networks? And I think that's a reasonable question to ask because we have this bacteria which seems to be the most resistant type. It is infected by virus five. So is everyone else. It's not infected by any other types. Why doesn't it out-compete everything else if it were in that environment? And likewise, why isn't a specialist virus out-competed by everything else? It infects the bacteria that's easiest to infect but so does everyone. The other viruses have the ability to infect other types of bacteria, okay? So how can we try to reconcile this? Any speculations before I elaborate? It doesn't have to be. It's okay. So what I'm going to do is to anticipate something like this and now I will do it a little bit more formally and I'll try to rewrite it here which is we can take this simplified dynamical system view which is I have my host I, right? And my virus J and I can think of this now as being embedded in some sort of network which eventually I'll call M, these phage bacteria interaction networks. And so for each type, I might have a standard logistic like growth and I've gotten rid of that little chemist that turn anyway. It's just a discounted growth rate. And obviously I now need to think about the fact that they can be laced by any one of these different viruses and I have to add up the contributions of this infection laces from all the kinds. And likewise here, if I ignore, there would be some infected state but if I ignore that and I just think, well, I'm going to have a particular kind of virus in mind, then I have to look across the ways in which this virus can infect all these different hosts and the sum is over I not over J. And of course then there can be some decay as well and I probably should make it possible for those to be different. Just walking through what I just have on the board but allowed me to slow down a little bit and explain it. So we have logistic like growth, infection, in which we have some network, right? And I've just showed you that this would be an interesting thing to study, networks with this property, which we just spent some effort identifying. It turns out that this kind of idea has been around for quite a long time in the virus host literature. I gave you an example of single one-one relationships from the late 70s by Bruce Levin which goes back down on Campbell which we already talked about on Monday. I gave you an examples of two by one and two by two that I showed had very different kinds of dynamics but it tended to be the case that when one looked at large systems there was an assumption that these were all exclusive, that there was a virus and one host. In which case then you have a bunch of parallel systems although they're coupled to some extent here. And if this coupling breaks down because maybe they're in different ecological niches then you really just have one-one systems and you're just replicating and it's somewhat trivial to understand. The difference is that now we wanna ask this question in which there is in fact cross infection. There is overlapping ranges in which we see that it's not as if each virus has just one host but they share hosts. Yes. Why is the Phi ij- No, I used them. Ah, no, Phi j, sorry. I was getting too excited about my double notation just in the end. It's true that it actually could be because we could actually have adsorption rates that are differing but then I would conflict with what I wrote there. So I'm gonna assume that that's a virus property and just whether or not it infects is the property with that host. Thank you for noticing that. Yep. Is the fact that beta depends only on the kind of virus and not the kind of host an experimental result? This is a simplification. It certainly is the case that this can be different. There tends to be some viral takeover so you can have tendencies but it could also depend on i. So more generally I probably should write Phi ij and even the latent period can depend on both but that gets a bit harder to do. So we're focusing now on just the impact of which infects but keeping life history traits separate for the host and viruses. Okay, good. So I'm gonna give an example here in which I take this kind of system and apply it to a simple two by two network in which we have viruses and hosts. We have a specialist, generalist, susceptible, resistant type. So it's two by two system. Both of the examples you see there have this same network structure. They have the same M structure but you see in one community, one virus and one host coexist and the other one they both coexist. So the question is at least in the simulation what did I do differently? What was different about these two? They have the same network. In one case we see the collapse of diversity and the other one that we see the maintenance of diversity. Any thoughts on what could be the difference between these two? What did I do differently in these two systems? Starting values. I could have changed somehow the starting values. Maybe we have alternative stable states and I just ended up in one versus the other. Could be, and that certainly could be the case in certain systems. What's another possibility? Yes? I'll repeat it so just yell it out. Go ahead. Right, so in the left case both of them I've using the same network but yet in one example we have one of the virus and one of the host disappearing locally going extinct and the other virus and host remaining and we know already that a virus host can persist even though the virus kills the host it doesn't mean it kills the population but on the right hand side both we have two virus populations and two host populations coexist. So let me just try to unpack this and say that you were asking me before about traits so I've done something different with the traits. Not necessarily the initial conditions. And what I've done essentially is change these traits so that there may or may not be any consequence to having a different range. And I'll try to elaborate on that next. So if we were to unpack these models you can begin to see that this generalist host if we look at the specialist dynamic this specialist virus if we were to look at its dynamic it only has a single term and because it has only a single term it is setting the density of the most susceptible type. Once that is fixed we could go to the next virus that other density is set here and so then we get a new steady state determined by the next specialist virus and you can see why this is precisely the kind of form. Remember I had m over beta-phis in our solutions and let me try to remind you of that. When I have just a single kind remember if I just have v dot I'm a specialist and I have something like this this implies that the host that I'm specialing on will be driven to a density of m over beta-phi. And this obviously needs to be less than k for that virus to coexist because I need to have less need to drive it downwards if I needed more than was the carrying capacity that virus can't exist on that host. That's why all of these host steady states start with these kind of m over beta-phis and then it becomes about the differences between the life history traits and you can begin to see that we have an ordering if the most specialist virus drives down the host to a very low value it can allow us to pack in species or pack in types. Whereas if the specialist virus requires quite a lot so this number is very high then I can't make these differences positive. So you can begin to see the roots of a trade-off. If it is the case that specialist viruses are very efficient in infecting their hosts it is possible progressively for all those hosts to coexist. And likewise let's go back and see what the consequences are. If I look at the H-dot equation and I'm limited just by one thing keep in mind that I will get something like r over phi, when H-dot is zero this implies that r over phi one minus m over beta-phi k equals v. The growth rate of that most susceptible host and the traits of that most specialist virus go into setting its density. So if I go to the next kind you can see that that next virus is also going to be determined now whereas here we're determined by the relative host traits here by the relative viral traits by the relative host traits. So if there is a difference between the growth rates such that that which is most vulnerable grows the fastest then we can have again this kind of trade-off that can lead progressively to packing both of hosts and of viruses. And if we do that I see fear of scrambling all the slides will be available but the concept should be already here that we are limiting by these specialist kinds and that allows us to set up a sequence if we have this kind of relationship where the most vulnerable type has the highest growth rate and the least vulnerable type has the lowest growth rate and likewise the specialist exploits in other words drives down the host to the lowest level relative to the others whereas the generalist does not. If we have this kind of spectrum then we can get arbitrary large coexistence in these kind of nested networks. I've taken you through an arc of trying to get to the point where we can ask questions about coexistence but because the space of networks is so large I wanted to anchor myself with an empirically observed network which is why we went and looked for it in the first place. You're also getting a taste of like what is it that scientists actually do? We have a hunch that we'd like to see some pattern we look for it, we found one and then we try to understand some of the consequences. But obviously then we need to ask the question is there evidence for such trade-offs? Well I would say that there is partial evidence and this I will unpack in a moment too. There are multiple examples and I'm gonna give you two here. Here's growth rate of a wild type and here are a bunch of partially resistant strains in this particular example you can see that there's a tendency but on a universal tendency for resistance to be associated with some sort of cost in growth in the absence of viruses. And likewise people have done studies looking for what are called pleiotropic costs of niche expansion that's a lot of words. All that really means is that if you take a mutation that somehow expands the host range of a virus and then you look and say how fast does that now grow on the original host, what is its fitness? You can see that for the most part the fitness has gone down. So broadening the host range tends to come not, we went back to the no free lunch, it's not necessarily a free lunch that there's some cost on growing on the original type. But again it's not perfect which is also gonna lead to a next set of questions. Okay, so I think I've explained that. So what I wanted then to do is ask the question does nestiness itself beget or somehow favor some notion of biodiversity in the sense of having more types that kind of coexist together? This is sort of a claim that maybe that these systems that are diverse are there because they have significant nestiness. And it turns out that when you take these systems and you have this kind of trade off then even imperfectly nested networks can have an increase in diversity. So when you have this trade off in mind then it's true that actually partial nestiness it doesn't have to be perfect can lead to tendencies to have more types. Because remember these conditions that I explained required perfect nestiness but we've already seen that it's not perfect. Okay, okay. It turns out that this is true in a more general sense even when we make all sorts of different and it's not that important here what the differences are but we can make sort of differences in terms of what our initial life history traits were how far we are from this idealized state but we examine this in some depth in part because we notice that these weren't perfect nested networks. So we look for a pattern, this archetype we see that there's some reason or rationale with trade offs, we could get it and that if we have more or less nestedness that could lead to more, as we have more nestedness we have more types in the system. Joshua just to be clear so this is the result of numerical simulation of this. Correct, yeah, that's right, that's right. So I've, the empirical side was all looking actually at the pattern itself but connecting obviously this to dynamics is a much harder problem. I wanted to stop there with nestedness because I feel like I've been talking about it for about 25 minutes and now switch over to other features of phage bacteria infection networks. Okay, is it the only feature? Well the answer of course is no, it's not the only feature, in fact it was some of those other features were apparent even in the prior study but let me try to unpack. Some folks asked earlier on what is the nature of these particular studies? Well how does it work in practice? You're a microbiologist, you're focusing not on every bacteria, you're focusing on E. coli or Vibrio or maybe some Pseudomonas strain or some lactic acid bacteria or maybe Streptococcus or some other pathogen. You A, don't expect that viruses that infect some other hosts will affect your host and also it's very difficult to embed and have all these conditions for them to grow so in these studies you can now see that these are the species that were examined for the host so all those different isolates were different variants of the green named species. And the viruses, these little loops are those showing the fact that we have a virus that infects that particular kind. Only in a few studies and really these are all closely related, E. coli, Salmonella, Proditions, Shigella are super closely related in which we're actually examining between these different species and in one case across genera these very important marine bacteria, Prochlorococcus and Cinecococcus, okay? So for the most part, all of this stuff that I've just showed you was about a narrower sense of diversity. So whatever this pattern was then they say operate when we go to large scales. So we then posited what would happen if one of these groups were to have talked with another group and actually looked at the cross infection between the species of one, the virus of one bacteria species and the virus of another. So imagine we have these networks that look perfectly nested alone. What do you think they would look like if we were to combine them? Meaning, let me try to now do it here. Here I have the sten home, I wanna put S and here we have the mire, I wanna put M. And sten home was very busy at all and my friend of mine, Justin Meyer, was very busy looking at their systems and you can see that if we were to look at the dynamics between they've established that these are highly nested networks. They're very different kinds of bacteria. So now neither one of them has done these experiments taking the phage which are turned out E. coli and I'm pretty sure that's a flavobacterm. I think it's a phish pathogen that has phage that infects this phish pathogen. I can't remember now but I'm almost certain it's flavobacterm. So if we were to mix very different kinds of bacteria and say the phage of one kind of bacteria now tries to infect out of the other, what do you think we would find in those off diagonal corners? Does everyone understand my question? So I'm asking you if I did this experiment but I have a lawn, let me make it a lawn of S and I have phages of M. Would I expect to see plaques or not? What is your intuition? I'm seeing some people like this which I don't know means like no or like oh my goodness. So it could be one of those two things. So if one of you went like this can you tell me what you're thinking oh my goodness or no? You weren't the only one who did that move so if you're one of those people who did it you can share. I'd be happy to have a volunteer. Well I have no idea if this is right of course. That's okay I don't think anyone has an idea at this point. Well I would say that there will be no pattern in the other experiment because they have not developed some kind of resistance or... So you think in fact, go ahead, this is great. You think it should be like this? Yes. Okay, that's interesting. Those bacteria haven't been hanging out with those viruses and because they haven't experienced that selective pressure maybe they're very vulnerable to that virus. Yes. Okay, great. We have hypothesis one, complete infection and I understand why you would think that because let's think about unfortunately SARS-CoV-2. We're all immunologically naive something then jumps and then we all get infected. So it's maybe you think because there's no it's selection pressure no prior experience that actually promotes more vulnerability. Great. What is an alternative hypothesis? Yes. We could say that those viruses are less used to infect the other bacteria and so are less able to infect them and so we could say the opposite thing. You could say the opposite thing. This is the great fun about biology. It could be the total opposite and it's not even that they're less used because let's go back to sort of... We're not the ones who are using them, right? They're in these natural systems but they tend not to infect this other kind and so maybe there's no infection. Yes, there's gonna be a third. This reminds me of an old story in theory where some biological theorists came up and said it could be A or B and had to be reminded there was another possibility it could be C. So yes, tell me C. That there is the same type of nested nest. Same type of nested nest, okay fine. H3, I can't take any more, we'll take three. More nestedness. It's like turtles all the way down, nestedness all the way down. So maybe these are also nested, great. So it turns out that in environmental systems if a bacteria, a virus has specialized in a particular bacteria, it tends to be the case that they cannot jump across major species barriers and infect other things for all sorts of reasons. Let's go back to the life cycle. This is also why, although SARS-CoV-2 has been awful, things aren't popping out all the time from zoonoses and spreading across the entire world. There are many more viruses that never make that jump. And keep in mind that we have a particular paradigm of viruses when we think about mammals which are relatively closely related, bacteria compared to two mammals that can be so vastly different that there's almost no way that there could be a real relationship, although they all look small and maybe even look boring and they're not that charismatic, metabolically and genetically they are widely and far more divergent than we are than these other mammals. To me that favors no infection. And that's what we thought, but we don't have a way to test it because we can't convince Meyer and Stenholm were very busy to actually look for such things. So we decided had anyone else ever gone back and actually tried to do such a crazy thing. Look at such a large scale that perhaps they had found some of these different kind of patterns. So we expected something like this, that there would be modules and nest in this within the module. That's what we expected. So I'm not saying we're right or wrong, but this is what our hypothesis was because we didn't think there was much evidence that viruses of one species could infect even at the level of general and certainly not the level of better families and filaments on. So we have wildly divergent differences. Back around 40 years ago, about 30 years before we started the study, it's been about 10 years since we started doing all these crazy things, Mobus and Nat Kemper went out to the Atlantic Ocean collected water from 48 different samples, brought the water aboard, isolated bacteria, then used those bacteria to isolate the viruses. In other words, they did this kind of thing, brought them down to a single colony, picked that colony, grew it up and now they have a bacterial type. They don't even know what it is. This is pre our ability to rapidly sequence or type things. But it's gonna get exciting in a moment. And this actually lecture is more exciting than it would have been even a month ago for various reasons, which I'll explain soon. So they get all these bacteria, these little flasks and then they use them whether in a flask context or on these various plates and take the seawater and look for lysis which is a signal of clearance says that there are actually viruses infecting that bacteria. They take those viruses and then bring them down to the level that we get these individual plaques, pick the plaques. When I say pick the plaques is literally you're picking out a little bit of material from the plaque which you think comes from a single virus and then grow that up in a flask full of hosts and now you have a viral isolate. Does everyone more or less catch what I just described? You want me to describe that again? Does anyone want me to tell you how do you do that again? Seeing some knots, okay. I have a water sample. This is the, we're going between non-linear dynamics of basic microbiology prep in the same lecture. I have this water sample. It's messy. It's full of different kinds of bacteria which I've labeled with these different letters, full of different kinds. Inside they're also, and remember I make these bad houses but they're supposed to be viruses not drawn to scale. They're all different kinds of viruses inside and they're all mixed together and I've shown you before that there's something like 10 to the 7th per milliliter of those and something like 10 to the 6th per milliliter of those and there are many kinds. I like to just get one of these out and one of these out and get a lot of them out. So what I can do is take my growth media and do some physical separation to eliminate the very small things. I might put a filter here of 0.2 microns and hope that the viruses go through that and what's left on the filter are my bacteria and then put them onto a growth media and dilute it, one out of 10 and then one out of 100 and one out of 1,000 and if I dilute it low enough eventually when I look on this particular lawn I'll see colonies and then I'll take a sterile loop and literally pick out the material in this colony and I'm gonna make it like that to make it clear that it's full of bacteria, presumably all from one of these kinds. This is all the Z kind and this one is alpha two and this one is X, it doesn't matter, I'm making up silly names. Now that I've picked it, I put this in a flask and I grow it up and it's full of Z. Modulosa mutations that are popping up because I can't avoid it. This is one of my bacteria that now I put in the fridge or the freezer and that's one of my types, okay? That process just described in theory, in theory how you do this, okay? Now that I have Z, I could make a flask full of Z and add this stuff that went through the .2 micron filter that I think is viruses and look to see if this clears, oh look it's clear. Maybe that'll take 12 hours but here in the amazing magic of lecturing I've made it happen in about a millisecond. So here we have clearance. This now is full of all different kinds of viruses that can infect this. So what I can now do is again dilute and using the wet cloth, I find plaques. These plaques are each formed presumably by a single virus, right? And I can again use my little sterile loop and grow it back in an environment and when it clears, now I have a phage isolate. Here I have a host isolate, here I have a phage isolate. Now when I've done that, I can cross infect because I can mix them together and look for lysis for any one of these bacteria and any one of these phage. And that's what Mobus and Nat Kepper did again and again and again collecting hundreds of hosts and hundreds of phage and then doing all the cross infection. I mean it's a crazy kind of experiment. The output, and this paper had been known in literature, the output is this. Do you see the little dots there? Each one of those dots out of about 60,000 trials were a little bit over a thousand which were positive. One out of 60 times more or less, it didn't infect. So something like 1.5%, 1.6% of the time you had an infection and that makes a dot. And it turns out, for experimental work, for theorists, this piece of paper was like a big piece of paper that folded, you remember when you go to the library, you may all be too young to go to the library. There's things called libraries, you go there, they have books, inside some of these books are fold-out pieces of paper and this one, all this data was presented in this giant piece of fold-out paper. So we wanted to understand what the structure was but there was no digital version of this so we put it on a big scanner, we scanned it in a slight rotation so we used image analysis techniques, very exciting experimental work for theorists and then we digitized this network. 286 bacteria, 215 phages, more than 1300 interactions, quite a lot, out of 60,000 possible. I mean, the amount of work that went in here is insane. And I'll show you again in a little bit why it's very exciting to talk to you about this because this is probably the first lecture I could give on this topic that actually has a new piece of data 40 years forward inspired by some of this work. So it took a lot and I think this is, when you think about science and why we do it and when things can be interesting to others, it turns out that if you have to put some work into something, it may be that other people haven't put that time in. So usually when you work for a little while on something, you've already done something, maybe that'll be useful to others and this was the original structure. Does anyone notice, as I asked before, any properties of this network? There's one apparent property. Does anyone notice a property? Yes, just blurt it out and I'll repeat. There's a diagonal trend. Now keep in mind, I have to have a host isolate a virus. So the first time that I find this that automatically gives me one, right? And those hosts are in my system, I have a virus. So I'm immediately getting some of this diagonal trace. That's right. So there's something that looks like this diagonal trace. Anything else anyone sees? It's maybe one other pattern that should be apparent. A recurrence plot. What is the person referring to? Do you know what they're referring to? We can ask in the chat. Maybe ask in the chat. Does anyone notice any other feature here? Someone I haven't heard from, yes? Maybe some symmetry. You might be seeing something in the middle here that's giving you the impression of symmetry. Maybe there's some symmetry. I'm not sure, it's hard because remember, symmetry would imply that I'm in one place and as I have a flip and it's very hard in such a sparse network to know. So I don't actually know. But visually there seems to be something going on the middle but maybe that's what your eyes are interpreting as symmetry. Does it look nested to you? Yes, no? Let's see. We thought, well, let's look for nestedness. Not really. We did our best. Yes, you can always condemn some things there but if we were to plot, put these number of interactions in a very sparse network, some of the times we might be able to embed that many in the upper left. Was there anything about what recurrence was? No, not about recurrence. Someone else said there are some blocks on the diagonal. Blocks. OK, the blocks are important. Yes, so whoever said that, if they can hear me, thank you. There are some blocky looking things but they seem to be very sparse those blocks. So let's keep that in mind. So blocks, that's going to help us. It doesn't seem to be significantly nested. Instead, we looked at the blocks. We looked at a method to find blocks and we found, in fact, that it was almost perfectly blocky or modular. This is the same network reorganized into modules. I think this actually should be surprising to you that this data that I'm showing here is the same data I showed you a couple of slides before. Meaning that every row and column interaction has been preserved. I've just changed the orders of rows and columns and now highlighted the modules in those gray blocks. No data has been changed. What this suggests, going back to a question that was asked, I don't know how many iterations ago, was maybe they separate out. And in fact, they do. Yes, there are some exceptions, but almost all of the points here are embedded in these modules, which is why you saw the thing on the diagonal, which is why probably you thought you saw symmetry, and certainly why you saw some blocks. A module is a group, because this is, we often think of modularity in terms of networks, all of the same kind. This is a bipartite network. This is bipartite. It has two parts. It has the phage and the bacteria, which means it doesn't necessarily need to be a square. If it was a unipartite network, it would be a square, because we have as many kinds we're looking at interactions. Bipartite networks can be rectangular, because we can have a different degree in terms of the number of hosts and the number of phage. This says that these modules, we found them by trying to organize and identify a group of phage and bacteria in which the interactions preferentially happen within the module and not outside the module. And this is not a modularity algorithm class, but that gives you the spirit of what these algorithms are trying to do. Let me now compare. This is the same data. By looking at a much larger scale, this is an ocean basin level scale, which is picking up many different kinds of bacteria, although they weren't even identified at the time, we ended up getting something that we thought we would see if some experimentals have been willing to do such a crazy thing, which is some sort of pattern, and we'll get to it in a second, an absence of interactions across these different groups. That's one finding. If we look at large scale, we actually see a new pattern, not nested in this, but modularity, which raises the question, what are these modules, what do they contain? They are comprised of hosts and viruses that tend to cross-infect. So the virus in that module preferentially infects the host in that module, and the hosts in that module are preferentially infected by viruses in that module. But they need not have been isolated from the same station. Here, the black or bacteria, the white or the phage, the arrows denote the ability of that phage to infect the bacteria, and the numbers denote the station in the ocean. And those numbers aren't supposed to mean anything to you, but it suggests that we should maybe look at them and see if there's any relationship whatsoever to where they were sampled from. When we went to look, we started to see patterns like these. I think it should be apparent to you that these modules are not from anywhere. They tend to be from somewhere. In other words, there's less geographic diversity in a module than might be expected by chance. So the modules tend to be from nearby stations, which also there's a time and space element because you've gotta go across the ocean to reach these stations. So there's both a time and a location, but they're not perfect. You can have a phage from the past isolated thousands of kilometers away infecting a host from the future, but the specialization is at least correlated with geographic location. Geographic location is often associated with different kinds of environmental drivers. So it also implies that there may be some differences, even in species or types that are driving these relationships, but there was no way to know that back in 1981. So that's finding two. We have modules. The modules are not just by chance. They seem to have some geographic structure. And then the other cool part is that they have structure within the modules. Now it's not perfectly nested. It tends to be nested, but it suggests that even these modules can have structure. So it means that in some sense, we might expect that if we were to able to one day do this experience, we expect a multi-scale structure where we have some level, which we have specialization and other levels at which we might have some nestiness or other order. Okay. So let me wrap up this part, but there are two bonus parts to it. And I think that's what I'm gonna do today. Let me sum up some of the concepts I introduced. I tried to show you that if we take a complex network, then we first of all find a pattern of nestedness and that to the extent that we have nestedness, then trade-offs can often facilitate coexistence. That was true even in our two-better one-virus case where we had this trade-off, this resistant type came out of some growth disadvantage, which is why we ended up getting these cryptic cycles and not just the loss of viruses entirely. So this notion of trade-offs can be important in understanding coexistence in dynamical systems. The relative abundance of these hosts depends on trade differences. It doesn't mean that the most abundant type needs to be the specialist or the generalist. It really depends on niche separation. How different are you than the most similar type? And that's really what's determining abundance. Nestedness nor trade-offs need to be perfect for coexistence and large-scale networks can have very different structures. Okay. So I have two bonus sections here, depending on how far I got in today's lecture. And if you remember yesterday, I thought I went to 10.30. But now I have two bonuses, so I can go to 10.45 today. Or I can stop a few minutes early, because I know I've been going nonstop. So I want to revisit this incredible work by Mobus and Nat Kemper, and that's why I was saying that, you know, if I had given this lecture maybe a month or two before, it wouldn't have been nearly as fun because it turns out that this group, led by Katherine Kaufman, who's based in Buffalo, La Buchekello, New York, Martin Poles, who moved from MIT over to Austria recently, have been looking at Vibrios, these very fast-growing but often low-abundant bacteria that you can easily isolate. I have isolated them. I have isolated the phage of bacteria. I'm a very bad experimentalist. I've done four PCRs in my life. All four worked. I retired after four. You can basically go to any natural water sample with either this filtration technique here, you can grow them, and then you can do these cross-infections. And this is what Katherine, La Buchekello, Martin and team did, and these are all these different kinds of Vibrios. There's one or two exceptions, some Shuanella and Enteros, but largely Vibrios. And the suspicion had been that Mobus and Nat Kemper basically were working with Vibrios and Vibrio phage all that time. There's a whole backstory of some of their original cultures were lost because of a freezer failure. Nonetheless, they went back and started to look at this. And it uses now modern techniques. They can sequence stuff. They're looking at a focal study system. They can do phylogenies because they can actually look at core genes. And they can even measure the concentration of age, not whether or not just they're there or not, any two other sort of stuff. And I'm not affiliated all with this study. I just think it's awesome. Okay. So what did they find? They went back and looked at 248th age and 259th bacteria and found this structure. 40 years into the future after Mobus and Nat Kemper. I mean, it's uncanny. Has anyone seen such a thing before? Not before today, but just minutes ago. Totally different data. 40 years into the future. I mean, this is sort of radical for biology that stuff works like this actually. And I don't think you all appreciate it. And I should have made some jokes about the multi-log transform, but maybe I'll do that at the end about precision and biology. But you can see already that this phage bacteria interaction network is almost entirely modular. We can organize it along diagonals. There are some big kinds. There may be even some notions. You notice that they've organized in a way that there even seems to be some structure within. It's not just random. I wanna contrast it now with the Mobus and Nat Kemper data. On the right, Kauffman and all, on the left, the table at the top points out the size. The connectance about 2% of these interactions in both cases were positive. 1300 out of 61,000, 1400 out of 69,000. Almost all of the same properties in terms of the number of mean interactions, about five, both being hosts get affected by about five things and viruses are affecting about five or six things. And the modularity is almost exactly the same, 40 years later. And again, I know you're coming from a different background. I can't explain the extent to which this is sort of insane that this would be the case. So now I wanna make my multi-log transform joke. Everyone knows what a log is, right? I can take a log of something. And it makes the number smaller with more digits. But you can do that three or four times. So there's been some proposals that it's not fair that physicists get to measure things like the fine structure constant to 12 digits. And we're doing things like we measured 50 plus or minus 20 zebra. It's not fair. So from now on, there's been some proposals. I recommend this, that you should use the multi-log transform, which is you keep taking whatever number it is in biology and this is Jonathan Dushoff has proposed this, that you take your number like 50, you take enough logs and all of a sudden you're measuring 0.1237521 plus or minus a very small number of zebra. And you feel better about yourself. Obviously that's not true. Don't do that, but it's a very funny piece by Jonathan Dushoff. On the multi-log transform, you can look it up some other time. This is a rare case when you actually seem to be getting not only a recapitulation of a prior result, but really almost this precision in terms of the structure. So it's quite interesting. Now, there's more that they can do here. They weren't looking at the geographic diversity per se, but they could actually figure out the species. Here are the different species of bacteria here, broadly speaking, different groups of phage. It's a little bit harder to define those groups. But what you can see is that the members of the modules, these big modules, tend to be closely related phage. They have different kinds of morphotypes. And embedded from a subset of the bacteria. And likewise, this purple one right here is all one species of bacteria. So you can begin to see that depending on our species, we have all these phage that can, in fact, and these others can. We're beginning to get at this concept. So these species level differences are significant driver of why modularity is arising in the first place. Are you all following what's going on? With that. Recap, yes. Has anyone seen, you've seen the Princess Bride, the way you asked for recap reminded me. Let me sum up. No, there's too much to sum up. Like, do you know that? Anyway, it doesn't matter. Watch the Princess Bride. There's some effort to recap, but there's too much to recap. So let me sum up. So you can see here the colors. These colors of the largest types are how they color these particular relationships. But now rather than presenting it for modularity, they're organizing the rows and columns by genotypic similarity. And what you can see is that if I look at this blue module, it's not comprised of just any old bacteria or respective species. It's comprised of from four different groups essentially. And from the phage is basically all of this tailless phage. Looks like a proto-virus. Maybe that's a proto-virus, but a non-tailed virus, okay? So what you see here is that there's a relationship between the genetic similarity. Seems like this group can affect many different kinds. So there's some sort of generalists. Whereas other phage, these tailed phage in this purple group are all basically closely related. So this group is full of closely related phage. And for the most part, you can see that these things are not distributed horizontally. That if you are similar in type, that is somehow determining in some sense which species that you're infecting. Which we could not see in the Mobis Nat Kemper. We just saw the geographic signal. That's all we had. What is in what is based the differences in species? So for the most part, these are different types from these are all Vibrio species, but different types of Vibrio. So there's even diversity within the Vibrios. So these are, if you can look at the bottom, almost everything here is a Vibrio. It's a couple exceptions, Shou and Nella and Entero Vibrio. So there are micro-scale differences even within broadly speaking the Vibrios. And there are many different kinds of Vibrios out there. So there's different types of Vibrio bacteria and those are the way that they've organized. I don't know what else to say. I don't work on Vibrio all the time. So I can't tell you all the life history about each one of these Vibrio and what makes them different. Okay. So what they found is a nested modular network, highly similar structure to Novus and Nat Kemper. Vast majority of interaction within modules, that should be apparent. But there's species level drivers, right? That somehow this relationship is not just irrespective, but there's somehow a notion of specialization and generalization is tied to the genotype. The other thing that they then find and they try to make sense of is what does this mean for evolution? It turns out they rarely found examples in which they had the same bacteria or at least they don't think, being infected at the same time by these two different kinds of viruses. And they suspect that those bacteria that are infected by many things, the viruses that get in move so quickly that they will tend to produce these single types. If they were to be co-infected, they could make what is called a recombinant, recombining the genomes together. Once these viral genomes are inside the same host, they can then recombine and make a chimera between the two. It turns out that in some cases, the viruses can get in, but the host is better defended. And now going back to this notion of immunity, if there's intercellular resistance, a virus gets in and injects a genetic material, but doesn't actually lice, which means you have viral genome just parts inside the cell. And if a cell that, a virus comes in that can infect and exploit that particular host gets out, it can pick up some of those new viral types. And it turns out there's all these examples in their data set of recombination which they suspect is being generated in part between a mixture of overlapping niches and the fact that some of this resistance is happening inside cells. So there's a neat story here, which goes well beyond what I can do today in the lecture if you're interested to learn more about how these overlapping ranges and different levels of infectivity can drive evolution. Okay? Let me pause there. There's been a lot of material. Any questions? Yes. You cannot be sure that when you take one of these plagues, it's just one kind of viruses here. So if you were to, this goes back to early work in the field that says that a single virus particle is sufficient to make a plaque. Now, if you, let's go back as a colony example. Where are my colonies? Here. You could ask the same thing. It could be the case that these bacteria are somehow living in close proximity and they're sharing, they're maybe cross feeding, in which case you're right. It could be a bacteria and a partner that are growing there and then they're growing out together. So going back to whether or not, when you do this sort of thing, how do you know that the bacteria that were in that particular sample didn't already have a virus in them that's gonna pop out? All right, so I don't know if that's what you were asking, but certainly if you were to go and try to grow up bacteria alone, you do this filtration, it's not perfect, there's some viruses left, you could accidentally get clearance, you don't have your bacteria to grow. Maybe you think that's because the culture failed or was contaminated, maybe there was a virus in it. A dilution series, which are often used to isolate, says that you, and there are other more modern ways, but you're taking without using microfluidics, you take a bacteria at high levels density, you dilute it, so you take one-tenth of the sample with sterile media and you do that progressively, and soon instead of having 10 to the sixth per mil, you're down to 10 to the two per mil. Depending on how much volume you take and put down on your plate, you expect a countable number. So if you have images of these, they get to the point where you have, for the most part, non-overlapping bacterial colonies. Each one of those, it takes time, they don't pop up immediately, so you can think of what's really happening if you were to do a time lapse, is that you have points and then over time, they start to replicate and make these colonies. If I take the same analogy here for viruses and I have a single virus that infects by chance and manages to get into a host cell, replicates, now I have 100 nearby. Viral diffusion is very slow. In a agar plate, they are moving by killing. They then replicate onto the next, in fact the next adjacent bacteria and keep going. It does raise a question, why did these plaques stop? Right? I don't know. I know you weren't asking that. I'm taking your question all sorts of ways. Why don't these plaques stop? There are bacteria around. It's a question. Why don't plaques stop? Everyone understand what a plaque is, right? I mean, the bacteria could become resistant to the virus. They could be, but remember these bacteria are all supposed to be susceptible. Now, the first thing I started with on day one was the Luria-Delbrick experiment. It is certainly possible that somewhere in this plate are some resistant bacteria, but almost certainly a small number. Even if that small number is 100, right? Because we just basically did, we're always doing Luria-Delbrick experiments. That's the lesson you learn in life. You're always doing the Luria-Delbrick experiment. Somewhere in there there might be some resistant, but it's unlikely to be here. Maybe that's the reason why you would actually see regrowth in because that bacteria would start to regrow, but we don't see that. Often we just see the plaque stop. So why did the plaque stop? Anyone have any thought? Why would a plaque stop? You have a virus, you have bacteria. I reach a kind of a equilibrium bomb between the off-quick system. So it's some equilibrium, but remember the viruses need bacteria. There are a lot of bacteria there. We're not resupplying new resources, which may be a clue. Anyone else want to help? Yes? Because otherwise they will consume all the bacteria. But that's fine. Does that bother you or the bacteria or the viruses? They could. Yes, but then if there are no more bacteria, the viruses will die. It's okay, it's in my experiment. I'm not worried about that. You're worried about the viruses in their future, which is nice. But for this experiment it's okay. I think you're also saying that maybe in a general evolutionary sense, maybe you're saying that evolution, because if you have too virulent a type, it would have led to local extinction. That would be bad for the viruses. So somehow less virulent viruses have evolved, which is the reason why they're stopping here, right? I think that's what you're saying. So I don't know. I'm trying to make a joke for everyone to be involved. I'm not making fun of you. I'm just trying to raise the point and see paradoxes. The problem is this isn't necessarily how they're evolving. So you could have situations of evolution which have different constraints, but in the laboratory there's no constraint. If they die here, that virus is still gonna define the nature. We could have local extinction of the bacteria and local extinction of the virus. I would argue that keep in mind, you have a virus that's infecting a cell. The cell, if it runs out of food and stops being metabolically active, it makes it very hard for a virus to take over and turn on the cell metabolic machinery that has nothing to go on. So it is possible that when we write these models, and maybe this will be my final point, I had some other material but I think I'm gonna wrap up here. And this is a nice point, not the multi log transform, that was just dumb. You can imagine if we were to write something else, I'm gonna go back to the very first model I wrote, the simplified version without the chemist that term. The reason why I wrote this is implicitly I'm saying that when the H gets high, we're probably running out of resources which is why we're reaching some carrying capacity. So it's possible that this infection happens, but I might need to hit both of these terms with something like a limitation term, that when the host reach their carrying capacity because they've run out of resources, then the virus can't just replicate. Maybe it can't even infect. If you add a term like this, all of a sudden it's possible for the virus to spread if I add it early enough and the hosts are still growing, but when the hosts around it have reached some sort of their own equilibrium, viruses might get in but no longer be able to replicate because locally the resources are depleted. And strains differ. Some viral plaques can get grow and grow and grow and some stop because viruses differ on the extent to which they're essentially turning the host cells resource stores into more viruses and others which must actively pull in new resource stores. And if that's the case, then they can't keep going when the cell has nothing else to pull in, okay? And this stuff about how Cro-infection can lead to evolution and either in questions like these, maybe models to come in. There's like a whole nother bonus, but that I'm not gonna do. Okay. Does that say something about the way viruses infect his host? Yes, and to actually unpack it, there's a paper from 2014 that we looked at that tried to ask what limits the birth size of viruses? Is it space in the cell? Is it the carbon? Is it the nitrogen? Is it the phosphorus? There seems to be a lot of space to have more virus than our typical birth size and a lot of carbon, even a lot of nitrogen, probably not enough phosphorus. And if you look at the phosphorus content, people have actually done things where they've used radioactively labeled phosphorus and then asked the question, where did the phosphorus come from in the new virus particles? Was it from the outsider? Or was it from the cells that were already there, the phosphorus embedded in the cells? And that can actually differ, but it does show that they're pulling in new phosphorus from outside. There's some label phosphorus experience from a Zoms group many, many, many years ago. But it points to the ways in which viruses are not just coming into a space and just chopping it up into little pieces because eventually you need the integrity of the cells in order to replicate, they're actually pulling in resources from outside. Mike, yeah, my question is more like, the idea is that it comes the virus and it goes inside a cell, I don't know exactly how. But if the cell is looking for food, for nutrients or something, and the virus has this shape that is similar, so the cell should absorb the virus because it's looking for it. But if it doesn't absorb the virus because there is no food, then it's like the virus needs the food to come flat and go inside the cell to do something. It's like, why the cell doesn't absorb the virus if there is no food? Okay, so it could be, let me try to, I'm getting near the end of time, so let me try to unpack that question. There are certainly receptors like the maltose uptake receptor, lambi within phage lambda that pulls in maltose and also is the site for phage lambda to do infecticola. In that case, in which there's no more maltose around, maybe the cell would eventually react and down-regulate the presence of that receptor. There also can be resistance in which it shuts it down entirely. But to the extent to which the receptor is there and the phage gets in, what I'm trying to say is that even if it's able to inject the genetic material into the host, if the cell for other reasons unrelated to the port of entry is no longer metabolically active, it may be very hard if not impossible for the virus to redirect host cell machinery, which requires ribosomes and active replication to make more of itself. Taking over a dormant host or host that's not metabolically active is not very easy. Sometimes impossible, that's what I'm saying. Talking about it more at the break, perhaps. Okay, so let me wrap up, because I think I'm at time. What I tried to do today, remember starting on day one, I had individual interactions, really ecology. The second day I did evolution. Today I went out to a broader range and showed you there really is abundance and diversity, that the structure is not random. We can see different kinds of structures, including nested structures with specialists in generalists, as well as modules in which we do have specialization. I've shown you that get again, that if we embed these in our dynamical systems framework, it points to the relevance of trade-offs and measuring them to figure out why things coexist. And in fact, this approach to trying to make forward predictions, and I didn't get there today. Mateo, and I'm not sure I will, which is you can even do the inverse, which is given time series, could you even try to work backwards and figure out who infects whom rather than just relying on these culture-based techniques? And I think that's it. There's a lot here that I went over today. Tomorrow I plan to switch gears a little bit and stop talking only about killing, but talk about integration in ways that a virus infection doesn't have to end with the killing of a host. So I'm going to introduce concepts relative to latency tomorrow. And right now I still plan on Friday to do an interactive laboratory, Mateo, I have to talk to you since you're in charge here, rather than giving a fifth lecture, just to give you all the chance to actually put some of these ideas into practice. So thank you very much and see you tomorrow morning at nine.