 The light, we got lost in the park. I got lost in the park on the way up here. So thanks very much to my organizers, co-organizers, and also want to acknowledge the various funding sources for this. What I'm going to try to do today is to raise some challenges rather than providing answers for the most part. And following up to some extent on Daniel's lecture, I want to specifically explore the role that mathematics and physics might play, because that's what this institute was set up for, but also especially suggest the potential benefits of an ecological and an evolutionary perspective. And in turn, the fact that ecologists and evolutionary biologists are learning the power of studying microbial systems as the way to get at some of the general questions of interest. So across a wide range of systems, so I'm not following one with one. I thought I had it all shut off here. So on the upper left, you see starlings over Rome. Plus, if you look carefully, one hawk. But the examination of systems, whether they're physical systems like magnetization or whether they're biofilms or whether they are systems of vertebrates, in all of these systems, there's interest in understanding how macroscopic patterns might emerge from microscopic details, largely independent of some of those details. And so in the scaling problem, one has to try to determine what are the details that are important at the microscopic level. So like these examples, microbial communities are complex adaptive systems. It's a term you're going to hear a lot of. Karina said that's what she works on, which is true. This means systems that are made up of individual agents who interact with each other and based on those interactions, they're emergent patterns. So they're problems that go on multiple scales. They're conflicts that go on on multiple scales. There's complementary function, as you heard right at the end of Daniel's talk. And we won't understand how those macroscopic patterns are emergent from the microscopic interactions and indeed not just the microbial communities but the broader ecosystems of which they are part. Now in physics, whether we're dealing with pressure or changing temperature or the like, statistical mechanics develop that thermodynamics is a way to understand how we can describe the broader macroscopic properties in terms of large numbers of individuals smashing into each other. And it's much easier in physics than it is for biological systems where there are highly nonlinear interactions. So that means we have to find ways to scale to relate phenomena across scales from cells to organisms, from organisms to groups of organisms, all the way up to ecosystems and the biosphere. And if I were talking to a different audience, I would include the social and economic systems in which the biological systems are embedded. And to ask questions like, and you'll hear a lot about this this week, how robust are the properties of the ecosystem? How is the robustness of those macroscopic properties relate to things that are going on much finer scales, the ecological and evolutionary dynamics? And to ask if we can develop nonlinear statistical mechanics of microbial systems and of the ecosystems of which they are part. My former post-doctor, Andrew Hyde, my current post-doctor, Chadstrom, Rone Stocker, an ETH of many of you know, and his group, have a fairly recent grant from the Silence Foundation, which asks, how do we derive macroscopic equations for all these things like the interaction rates from individual-based models of ecological interactions? One of the most successful efforts, in my opinion, to do that is from Mick Follows in his group at MIT, who worked in particular with Penny Chisholm, in which his group has derived a group of equations Daniels suggested to us for a nutrients phytoplankton and zooplankton in the ocean to try to describe the macroscopic dynamics of the ocean using standard uptake functions and things of that sort. And then putting lots of types into competition, doing rather crude evolutionary competition, just to sort it out and see what's left at the end. These models have been remarkably successful in predicting not where individual species will be, but where what they call ecotypes, groups of species across the planet. These models work very well. And we and others have been working in a large number of collaborations in order to try to put these into an evolutionary framework to understand the dynamics. This is a paper that George Hatch, German Eye, just published in Ecosystems. And I want to focus on these, or do I need that? On these features, which is understanding marine ecosystems as complex adaptive systems. And the three things after the colon are the things I want to focus on. Emergent patterns, critical transitions, and public goods problems, which you heard from Daniel at the end of his lecture. Now there's been a large increase in agent-based models. The increase in computational power is very seductive. We can build models in which you can look at individuals and give them all the rules you want. That's the great advantage of these models. It's also the great disadvantage because the models are too complex. You don't really know what's going on. You don't know how robust the outcomes are. They've been used for bird flocks, for fish schools, for those reindeer that you see at the bottom in which individuals are simply following other individuals and wonderful emergent patterns come out. And they can be used in microbial communities. But one has to be very careful because ultimately, especially in this building, one ought to be trying to use those as ways to get at reduced dimensional descriptions, either using well-trodden methods like hydrodynamic limits or moment closure techniques as we're often used in statistical mechanics, or the newer data-driven equation-free methods that my colleague Giannis Kevrickides and others have been developing or other approaches to aggregation. But ultimately, we ought to be taking those into agent-based models and collapsing them into much smaller dimensional sets of equations that help us understand what's going on. So there are a number of theoretical questions I want to raise, especially having to do with the microbiome. And this is where I think the great challenge... My group has been starting to interact with Marty Blazer's group at NYU and Jalex Xavier's group at Sloan Kettering to look at questions of this sort. Can we understand the macroecology, which is a term from ecology, of the microbiome that is how are things distributed within the body and across regions? How do you measure the diversity of the microbiome community? What's the importance of neutral theory? Which got its start in population genetics, but it has become popular since Steve Hubbell's book in ecological theory as well. Or has everything got a purpose there? An important ecological notion is of competitive release. That is, you eliminate one competitor and something else spreads. Can we help to understand the microbiome and medical treatment of it using ecological theory? For example, heavy uses of antibiotics often attacks many organisms, but not see difficile, which often goes into outbreak in individuals that have had treatments with antibiotics. What about the ecosystem dimensions of the human body and the microbiome? Nutrient cycles, you just heard this in the last few slides from Daniel. H. Pallori, I'll come back and talk about in just a moment, but this was especially of Marty Blazer, H. Pallori is declining in the human population, which he thinks is a bad thing. As you may know, H. Pallori has been associated with ulcers and with stomach cancer, but Blazer's hypothesis is it's actually protective against esophageal cancer. So what's going on in terms of our microbiomes? By the way, I recommend his book to those who haven't seen it called Missing Microbes in which he argues that heavy use of antibiotics and caesarean sections has reduced the diversity of our microbiomes and caused outbreaks or rises in things like asthma, esophageal, reflux, obesity, et cetera. What about the theory of biological evasions very well developed and the role of probiotics? I take a probiotic every morning, I don't know what I'm doing. There's no theory associated with it. How many organisms is one introducing and what is the theory associated with the dynamics of the community in relationship to the things that you introduce through probiotics or of course what's received more attention to antibiotics? And can we understand these communities in terms of their ecosystem properties and how those evolve? So these are the four topics I want to focus on. First of all, temporal patterning. In an ecological community, or I should say a traditional ecological community, like a forest community, one understands that disturbances occur all the time, that when those disturbances occur, a certain species that you see on the left there begin to come in to occupy space. They get replaced by those who are not as vagile in getting there but are better competitors which in turn are replaced by others that are more down the spectrum until you get to the competitive dominance at the end that take their time getting there. This is a standard secondary successional pattern. Do those successional patterns exist in the microbiome for sure they do? But what do we know about patterns of colonization and succession in the microbiome? So that's why at the beginning I wanted to raise questions and in microbial communities more generally. What about daily cycles and other cycles? What about like seasonality? What can we say about those? Now, there are two different ways to think about, whoa, you okay Bruce? Make this one a little tension. What was I talking about, everybody remember? There are two different ways to think about what's going on in terms of ecosystem structure and function. One is the issue that I'll come back to at the end that Daniel touched on, the notion that there's co-evolution at multiple levels to the mutual benefit of the host and the biome and of the multiple species who are in centrophic relationships. But in addition to co-evolution there's another process going on which is just self-organization. That is things come together in their emergent patterns and maybe there's a filtering so that the ensembles we see are more robust than other ensembles, but it's not an evolutionary process in the same sense that we typically think about where selection's going on for particular types. To some extent the co-evolution and self-organization can be destructive to the host and to some extent it can be beneficial. But the fact that this can be destructive also of course applies to our own cells. Cancer is an example that I mentioned Martin Blazer's work already about the role of H. Pallori and its relationship both to stomach cancer and GERD. Tumors are a good example of a breakdown of the public goods, of a breakdown of the commons and that tumor cells begin to proliferate and to do so ultimately to the harm of the host. So that's a self-organization process. Selection hasn't operated sufficiently to restrain them. Obviously it has to some extent or else we'd be having cancer at much higher rates. Together with Corina who we'll talk later but probably not about this. And George Pacheco you see in the center of physicists and game peers and David Dingley a terrific oncologist. We've hoped to explore another aspect of the public goods dimensions of tumors in that tumor cells have to produce things like cytokines that are crucial to the growth of the tumor. So it was David's hypothesis that he could engineer tumor like cells that don't produce these and he's done that. And now the question is, which is a game theoretic problem, can you get them to spread? This might be a novel way to treat cancer by getting the proliferation of cheater cells that don't produce what's necessary for the tumor to grow. So I talked about temporal pattern. I wanna talk about alternative stable states now. This has become a topic of great current interest. Not the first time this has become a topic of current interest but Martin Steffer's book called critical transitions in nature and society which talked about the multiple stable states that could exist under certain conditions as shown by the diagram on the left. And the early warning indicators that might be associated with the potential for a system to flip from one state to another. Martin has led a number of publications on this topic on early warning signals and Jeff Gore and his group have been applying this and I imagine we'll hear from Jeff, will we hear from you about it in coffee breaks and things but he's not gonna talk about it. And I think this is a very exciting idea that before the transition there might be early warning indicators of those changes but I wanna exercise some caution here as well. I started in this field before almost any of you here maybe before any of you here. In the late 1960s when Renee Tom popularized the notion of catastrophe theory we spent a lot of time reading those papers, the ways in which systems could transition from one state to another. They became very popular and then because of overreach that is just because A implies B doesn't mean when you see B it's because of A but people started to say well it must be this phenomenon going on all over the place. The whole subject lost its currency and I worry that the overreach on early warning indicators which are characteristic of a certain class of transition would have the same effect. But there are a number of theoretical questions for microbial communities that this raises. Are there alternative stable states in our microbiomes or microbiomes of the microbial systems more generally? For example, could the early application of antibiotics have a permanent or a nearly permanent effect on community dynamics or given enough time would we eventually recover from that? Bruce Levin could answer that question and probably will a little later. Even if the early effects are transient could there be long lasting ecosystem effect? Remember that antibiotics are given in agriculture in order to make animals fatter, it works. That's why Marty Blazer has argued that there's an obesity epidemic that to some extent is associated with the use of antibiotics. We don't know the answer to that. And in the last part I wanna talk about the spatial patterns and coupling in space and time. This is the second goal of the assignments grant that we got. How do you understand the importance of heterogeneity in ecological systems and the spatial distribution of resources and consumers and organisms ability to exploit this. So here's an area that potentially can build on foraging theory from ecology, but it's complicated by problems of detection and uncertainty. For example, one of the most successful sets of equations drawn from mathematics and physics to apply to microbial communities was the work of Evelyn Keller and Lee Siegel long ago. They were interested ultimately in slime molds but that led them to the study of chemotaxis and the development of equations which to this day are still widely used to describe these systems and I think work very well. But how do you derive these equations? They're not usually, there are multiple ways as most of you will know to derive diffusion equations and diffusion like equations. One of them is to just look at fluxes across boundaries and write down those equations. But if you wanna take into account the fact that you're dealing with individuals and derive equations for the movements of individuals, this was what I was implying earlier on and find the correct way to derive the continuum limits, then there are complications. And in the Simon's grant, because of the great capacity of Roman Stocker's group to make measurements in the field, we wanna understand where cells can do chemotaxis in terms of what they can detect and how important noise is. Many of you will know Herbie Levine's work and the beautiful work that he and the late Eshel Ben Jacob did in studying the fantastic emerging spatial patterns in these communities. Well in ecology, there's a lot of work traditionally on spatial patterns. What you just saw were largely in Eshel Ben Jacob and Herb Levine's work, emergent patterns and dogenous patterns in constant environments. But the first thing an ecologist would do would be to map out something like this where this comes originally from the Holdridge diagrams but this is my late colleague, Robert H. Whitaker in which you look at different regions in terms of their temperature and their humidity and say what kind of vegetation you would expect to appear there, not which species but what kinds of vegetation, where would you get tropical rainforest, where would you get tundra, where would you get grassland, et cetera. And to a first approximation these work very well then often within these regions there's some multiple stable states that are possible. There's some overlap, the boundaries are not as sharp as you see in this picture. But we ought to do this at multiple levels for the microbiome. For example, at a previous meeting on this topic that I went to at the Wellcome Trust, another Segre who hoped to be here, Julia Segre, talked about the microbiome of different parts of the skin. Well that's very different than of course than what's in your gut. Most of us when we think about the microbiome the first thing we think about is the gut but there are many other different regions in the body with their own microbial communities. And of course when you get a cold or something of that sort it will affect different regions because different microbes are living in different regions of your body. Can we map this out to understand what the community looks like in different parts of the body and what about globally? Well work has begun on understanding differences in the human microbiome. In response for example to what people eat in different areas as well as other environmental conditions. So we need a Holdridge diagram for the human body and we need a Holdridge diagram to understand the distribution of the microbial communities across the globe. The idea of endogenous patterns as in any kind of community has always interested theoreticians. And the most famous piece of work is that by Alan Turing who was interested in developmental biology and how an organism can develop a homogeneous cell with really no blueprint and just rules for local interactions and no external forces except gravity could develop over time and he proposed an interaction between two species you here and activator species and V and inhibitor which have their own dynamics of interaction given by F and G and then diffuse and diffuse at different rates, you and V. And his idea was that an initially homogeneous distribution of activator and inhibitor could become destabilized when there's a random perturbation of say activator which stimulates production, causes the activator to rise up, causes the inhibitor to rise up but then the inhibitor which ought to be dampening it down if it's got a higher diffuser rate diffuses the way the activator keeps going. There's inhibitor over here which suppresses activator production and that breaks symmetry and patterns can emerge from that. So there's been a lot of work not so clear how well this works for the systems that Turing originally proposed but people have looked at this in ecological systems. On the left the tiger brush patterns that Echudmyron and others, Chris Klausmeyer have studied and this work on the right that Karina led with a number of people here as collaborators in trying to understand the degree to which these patterns might be observed or things like these patterns or these patterns modified by other factors like termite mounts in ecological systems. Early on Lee Siegel and I and Akira Okubo separately proposed that this might work to understand the patterns of plankton distribution in the oceans and we thought about phytoplankton as the activators, zooplankton as the inhibitors. The trouble is that really didn't work very well because the zooplankton don't move randomly so the diffusion model didn't work and in fact, instead of there being more spread out as the inhibitors should be, they're the ones that are more patchily distributed so that led to an attention to collective motion more generally and mathematical approaches to describing those. Going from the individual based model to the ensemble, my student Danny Cohen, I'm sorry, Danny Grubow led this research and later we did work with Glenn Flarell and Don Olson but what Danny did in this thesis was to start with Newton's laws, force equals mass times acceleration but the forces were not just the forces inherited from the fluid dynamics and from chemotaptic motion but from individuals moving towards each other so this is an individual based model. He did this for every individual, developed the statistical mechanics on the ensemble and then using some local rules about Poisson arrivals derived Eulerian descriptions so that there are standard ways to do this and very few, little of it has been done for microbial communities. The last thing I wanna mention was the last thing that Daniel talked about which is the last bullet in this paper namely public goods and their role in these systems. Whatever we have, as I said at the beginning, phenomena going on a multiple scales in an evolutionary process, there's potential conflict between what's good for the individuals and what's good for the group and how do we get to the emergent property? So as I said, this is the last part of Daniel's talk. I almost put down the penultimate part because he went from talking about public goods to talking about the emergence of ecosystems but I would argue and I think he would too that that's still a public goods problem. How do we get the emergent properties of the community that sustain everything? So in ecology, there are lots of examples of public goods and common pool resources. I don't wanna get into the economic distinction between them, think of them as the same for now. The most obvious one is information. When you have collective search going on, some individuals are foragers and some are simply scavengers on that. How much of the available nutrient pool do you use up? If things are well mixed, you better use it up now or else your competitors are gonna use it up. But if there's a structured environment, you might actually leave things to use later. In particular, if you have scenario force that Kielearn or something else that holds it available to you, that might be a good thing to do. But once it's out there, a neighbor can still steal it so there is the same sort of conflict that Daniel talked about. Nitrogen fixation poses exactly the same problem. Individuals fix nitrogen. Let's say a plant does it, it's in their leaves, the leaves drop to the ground, neighboring trees can utilize it. Antibiotics are classic public goods problems in two ways. One is in nature, bacteria, for example, produce antibiotics and I'll talk about this a little bit more in just a second, other individuals can take advantage of that by being resistant to it but still benefiting from the competitive effect on natures. And we all know about the problem of antibiotics in our societies and the overuse of those antibiotics. And bacteria produce extracellular polymers that allow them to form biofilms. Many of you said you're working on quorum sensing and these also produce an extracellular matrix for growth. In the paper with George Hagstrom, we talk in particular about syntrophy and the point that which others have documented that often one finds a strong correlation with the genes for production of different extracellular enzymes. So there seems to be some sort of high level cooperation going on. It's been called the black queen high thought hypothesis that different lineages either specialize in public goods production or in cheating. This is very analogous to the producer's grounder literature in ecology, behavioral ecology. Bacteria also produce toxins to which they're immune but as Bruce and Lynn Shal showed when they tried to evolve this in a well-mixed medium, it was very difficult to do because cheaters arose. However, and this is work with them, I actually used to give Bruce credit for it but he told me I shouldn't do that. Rick Durett and I built a spatial model that showed that if you had the cheaters together with the wild types and the toxin producers in the same culture in a spatially structured environment you could get coexistence of all three types. The problem is that the colicin is the toxin. Producer allows the individuals to produce it to out-compete the colon sensitive types but the type that's resistant can out-compete the producer because it doesn't pay all the price of production and still gets the benefits but it loses in direct competition with the colicin-sensitive type so you get a non-hierarchical competition. In a spatial environment, the three types chase each other around and you get coexistence. And this was followed up by Ben Kerr and his collaborators who did experimental work building on our model and demonstrated that this can really go on in nature. And finally, as many of you know much better than I, bacteria also cooperate. They produce these public goods. I already mentioned the extracellular polymers that are important for quorum sensing. And so with Kerry Nadell, who was a joint student between me and Bonnie Bassler and Jalex Xavier and Kevin Foster, we examined this problem some years ago taking into account that some bacterial types turn on the production of this extracellular polymer at high density, some do it at low densities, some potentially do it constitutively, some don't do it at all. So we put these types into competition, allowed nutrients to flow and watched under what conditions one could get to production of these extracellular polymers in relationship to mixing, et cetera. So there's a lot of potential for modeling to understand these problems. I stuck these slides in after listening to Daniel's talk because the sorts of questions that come up came up several centuries ago in economics where Adam Smith, whom you see pictured on the left, said against Charles Darwin here, talked about the invisible hand. He said that the baker, by pursuing his own interest frequently promotes the interest of society more effectively than when he really intends to promote it. This is an idea that at least produces many notions of an economic organization that society's more organized themselves. This is sort of a very conservative philosophy, let the free market operate in that area. Of course, we learned in 2008 that we hadn't heard before that the invisible hand that Adam Smith talked about doesn't protect society, that one needs some balance. So I think it's an open question, the degree to which these sort of considerations apply to microbial systems. So let me just summarize. Collective phenomena and emergence characterize all complex adaptive systems from microbial communities to the biosphere. There's a potential for critical transitions. Fundamental challenge for those with mathematical and physical inclinations is to learn on a scale from the macroscopic to the macroscopic and understand in particular consensus formation and how collective phenomena emerge, but also characteristic of these systems is conflict between individuals and collectives at the public goods problems that they raise. And so finally, I just want to go back to where I was at the beginning and to say that I think methods from not only mathematics and physics, but ecology and evolution have a lot of potential that Bruce has been arguing this for decades ever since I was in high school. To inform the study of these systems, but I also want to argue that all four of these disciplines can be inspired by these new applications and lots of examples in mathematics in particular where applications, for example, for biology have inspired new ideas in mathematics. So it's a great time to be in there.