 So first off, I'd just like to thank all the organizers, Dr. Mercedes, for putting together such a great group of talks. We already saw some really, a really diversity of talks about diversity and I'm really honored and excited to be here and chat a little bit about my research today. So I'm gonna switch things up a little bit in when we talk about the controls on diversity and I'm gonna do this two ways. So the first is I'm gonna talk about diversity with respect to functional diversity. So moving beyond species and talking about how can we look at the controls on other types of diversity in these systems? And also I'm gonna move beyond looking at just a community and take a much broader scale lens of diversity to try to understand how diversity shifts as we move across scales. So let's think about this idea of community assembly so we can take this island and really what we're asking about is given a snapshot of who's there, can we try to make some inference about the mechanisms that gave rise to that or given just a bare pot of ground, can we try to make some prediction about what types of processes will give rise to diversity in these systems? And when we think of something like this, you know, you have seeds that disperse onto the island, they sprout the seedlings or if we're thinking through plants or trees and some die off because maybe it's too dry or hot and the rest are left there to compete and there's these various biotic processes that prune that system. Now, when we think of this lens of community assembly, I'm sure all of you are somewhat familiar with this type of toy diagram but we often think of it through the idea of these two different filters. So there's an abiotic filter and this biotic filter and we heard a little bit about that yesterday talking about this environmental or habitat filtering. And generally what we're interested in is given this final community, can we try to infer something like the relative importance of these two filters? So there's a regional species pool, species that can survive and give a location sort of pass through the filter. We have the local species pool that would be all the things that could get there and could survive if they're growing in isolation in monoculture. They then interact with each other in this biotic filter and some more species get excluded and we're left with the final abundance of species and some network of their interactions, how they relate to each other. And I'm gonna talk about today this biotic filter primarily through the lens of competition in part because we're thinking of forests, they're really unique organisms, they're very long lived and they're a really nice study system for looking at competition. It's not to say they don't have tons of other processes like herbivory and parasitism. But again, on first approximation competition is a really dominant structuring force in communities. So suppose we just go and we just take snapshots of all these communities, how can we sort of look back in time and try to infer what's going on historically in these systems? And the first idea for this was proposed about 25 years ago, Bayer and Kettie coined this term under dispersion or dispersion and they're talking about it primarily through the lens of functional dispersion. Though now there's a lot of work also with phylogenetic dispersion and this is my definition not theirs, but it's the extent to which the functional diversity of a community differs from that of the species pool. So essentially it's not about whether something is high or low diversity per se, it's about how the diversity of a local community compares to what could be there. And Bayer and Kettie put forth this really simple null hypothesis that when you have really high environmental adversity, so essentially suboptimal conditions, you should see this clustering, this homogenization of functional traits. Things should not only have low diversity, but that should be even lower than you would expect at random. We can sort of think of this if we think of something like the boreal forest, right? There's a lot of frost risk, wind risk. And if you're a tree that sticks out above the canopy, you're actually gonna increase your risk of mortality. So even at the just the sort of maybe idiosyncratic assembly processes will select for species that essentially don't stick out in any way. There's the selection for similarity. It could also just be due to the overarching importance of matching specific traits to specific microsite variables. If it's stressful to begin with, you maybe can't survive unless you have exactly the right carbon or nitrogen ratio. So we're gonna see this homogenization, presumably in the systems. At the other end, where we have an absence of environmental adversity, so essentially optimal conditions, this is where we would expect to see competition and other biotic processes really playing a strong role. Things like the principle of limiting similarity, minimization of niche overlap will presumably drive these communities to be more diverse than you would otherwise get if you assembled them at random. So if we think of this through this no model, this little toy diagram, what we're really talking about here are the how permissive and how restrictive these filters are. So in the first case, you have a very restrictive abiotic filter. So it's a really harsh environmental conditions. The only things that pass through are going to be very similar in terms of traits or again, if we're thinking phylogeny in terms of phylogeny. And maybe there's some additional pruning due to competition, but in the end, the resulting community is going to be very, very similar. And so this would be called under dispersion, the diversity of this community relative to the diversity of the regional species pool. And it's often seen as a proxy for the importance of abiotic conditions. Conversely, when you have a very permissive abiotic filter, everything passes through. And then this very restrictive biotic filter in part just due to the intensity of competition weeds out many more species. And what we're left with are species that are functionally very, very different, very unique compared to if you sampled at random. So part of what I'm gonna talk about today is sort of through this idea of trying to disentangle biotic and abiotic processes. But for reasons I'll talk about a bit later, this can also be a little dubious. There are multiple reasons why, for example, competition can cause things to look similar. But one thing we can take away from this just by looking at dispersion is the relative importance of the sort of core principle governing survival. Do species survive by being similar or dissimilar from each other? And I shouldn't this is sort of a powerful way of viewing the idea of coexistence and survival because it's right on the cusp of applied and theoretical in part because this is something you could sort of manage for or something you could measure. It's really hard to go and, you know, manage for something like, I don't like destability or something in these communities. But you certainly on first approximation could try to infer how if species or subsets of species coexist, if you understood the role of similarity and dissimilarity in really governing individual survival. Now, again, I'm sure a lot of you're familiar with this idea, however, at the same time, there's been relatively few really robust tests of the hypotheses before and by her and Katie. The important because the hypothesis is quite complex. They say in order to really understand dispersion, you have to look at four things simultaneously. You can't just look at overall functional diversity. You really have to look at individual traits and try to understand what patterns they show, how these patterns vary across space, maybe within a habitat. How does the size of the species pool? Most importantly, the range of species that you consider, how does this affect this type of pattern? At the most local scale, you're looking at sort of maybe true competition as you zoom out, you're increasingly looking at evolutionary processes, biogeographical sorting, that's governing how different species and different habitats relate to each other. And then lastly, other patterns consistent or do they vary among habitats or across ecosystems or ecoregions? So a lot of people, me included, have done previous work with dispersion, but we tend to take a sort of fix the context. We say this study system in this location across these few pots, and then we say, do we see over under dispersion? Or really to address these hypotheses, we need to look at multiple things simultaneously. We need different spatial scales, multiple habitats and multiple traits. And this really precludes, or is part of the reason why this approach is used a little bit less in community ecology and coexistence theory because this is not something we tend to get. Most experimental oncologists are working on relatively few species or in a single site or maybe across a grading or something like that. So we set out to ask, how could we actually test these questions? And we settled on looking at the global forest system. And this is for sort of two reasons. First off, we have really good compositional data of global forests due to things like a long history of national forest inventories. We also have really good estimates of tree traits compared to a lot of other species. Really basic things like canopy measurements, seed characteristics, these can be much more readily measured on trees, making it a really nice study system for looking at functional dispersion across different spatial scales. And then lastly, we already have really sort of clear expectations for what sort of environments should be optimal, like tropical subtropical rainforest down to dry Mediterranean forest or boreal forest as well. So using sort of the global forest system, we wanted to ask this question, where and how do species survive by being similar or dissimilar? So where does community assembly essentially limit or promote diversity among coexisting individuals? And again, secondarily, maybe we can look at where the abiotic and biotic processes dominate, but I think that's a little riskier. However, in some cases, as I'll talk about with respect to certain traits, we can make pretty clear assumptions about what is going on. So to do this, we're combining two global data sets. So the first is the GFBI data set. This is the Global Forest Biodiversity Initiative. It's over 1.2 million forest plots all across the globe, over 30 million tree-level measurements. And what's really powerful about it, again, is it's true absolute abundance data. We have tree diameter, tree height. We have really robust measurements to give us a really sort of unprecedented snapshot of community composition at the scale. Now, the second thing we need are traits and we obviously don't have measurements for every trait in every location. So we can impute these using the tri-plant trait database, which is, again, tens of millions of plant measurements, not just trees, but herbaceous plants as well. For the full analysis, we focus on 30 different functional traits. Today, I'm just gonna talk about nine of them. And we can actually estimate traits with fairly high accuracy. So using machine learning models, a combination of phylogeny and environmental variables, we have about a 70% accuracy in predicting traits, which for our purposes is fine because we have, with over a million plots, we have such high statistical power that we can sort of overcome any of the noise due to trait mismatch. So the general approach, we combine JPI, we combine tri, and then we're gonna calculate functional dispersion for each plot at varying sampling scales. So these sampling scales define a different size of the regional species pool. And not just ask, what is the functional dispersion of the plot, but ask how this functional dispersion changes as we move across these scales. So I don't wanna make this a talk about no models, but I'll just give you a quick idea of how we actually go about doing this. So we pick a focal plot from GFBI. So here we have seven, seven different plots. This red one is our focal plot. Maybe it has five different tree species in it. Again, we're not just doing presence absence, we're actually looking at the abundances of species too. From this, we have the imputed traits for every species in that location. So a mixture of leaf, wood, root, seed, crown traits. Whatever we think is being selected on both either by biotic or abiotic processes. And then you can use your favorite functional diversity metric. Throughout this analysis, we use Rauss quadratic entropy, in part just because it's been shown to really high statistical power to disentangle biotic from abiotic filtering. Now we need some sort of no model randomization here. So again, this depends on the regional or the size of the species pool. So we can start off at the hyper local scale. We draw a 10 meter radius around the plots. We pick up one new plot and that plot has two new species in it. So now we have a total species pool of seven species. We do a standard randomization where we hold the number of species fixed. And we also hold the relative abundance distribution fixed. In part because we wanna tease apart the precise role of functional trait diversity from other things like just overall diversity. And even though Rauss quadratic entropy is relatively insensitive to richness, a lot of these functional trait metrics really can vary heavily depending both on richness and abundance distributions. So to a thousand randomly sampled communities, for each one of these, we're just shuffling the trait matrix, essentially we're just shuffling traits at random. And we can calculate this no functional diversity distribution across these 1000 randomly sampled communities. Then to estimate dispersion, it's just an estimate of the empirical P value. So we compare our no model to our actual observed functional diversity at this plot. And we see that for example, here it's greater than 96% of the simulations. And therefore our functional dispersion is going to be 0.96. And we can actually do this for increasing sampling radius. So here we have 10 meters, then maybe we've got to 100 meters. We have a new no model randomization. We get a new functional dispersion value. We zoom out to one kilometer and so on and so on. And what I'm gonna talk about today is that to 250 kilometers, right around 300,000 square kilometers. Now we can do this not just for each individual plot, but every single plot, we can do this no model randomization. And that's being over 25 trillion no model randomizations for this dataset. So it's computationally a fun thing to work on as well as sort of theoretically. Actually, but before I go on, does anyone have any questions about sort of this general approach at this point? I don't see any question in the chat. Okay. Yeah, just shoot something in the chat if you are unclear about this. And this sort of no model approach is generally standard. The only difference is again, how you choose the no model. You know, if you're doing something like neutrality, you might use a different type of no model, but the general principle, I'm certain all of you are somewhat familiar with me. So let's look at some other results from this. So what we'll get here are just the marginal curves of dispersion split out across six of the dominant forest biomes. So across the x-axis, we have sampling radius going up to 250 kilometers. The y-axis is dispersion. Here it's just scaled from one to minus one. So zero is no dispersion, essentially extinguishable from the null distribution. A value of one is perfectly over dispersed. So maybe more biotic processes, but things are essentially very, very different than you would get at random. Minus one is things are very clustered, much more clustered than you would get if you sampled at random. And the first thing that jumps out when we look at this is that there's really consistent trends within some biomes and there's some very different trends when we look across these different biomes. So let's start here on the left-hand side looking at boreal forest. Now, boreal forest, I've sort of been using them as my null hypothesis for suboptimal conditions. And in fact, that's exactly what we see playing out, that in these systems, we see a clear consistent signal of under dispersion. At the most local scale, within the sort of meter scale, there's essentially no signal in part just because we're underpowered. But as we zoom out to about a kilometer, we see the strong signal of clustering emerge, suggesting that things are more homogenous, lower functional diversity than you would otherwise expect if you sampled at random. And this under dispersion just grows as you zoom out further and further. When we zoom over to something like the tropical forest, we see the opposite. At local scales, we see a clear signal of over dispersion and this is strongest, somewhat paradoxically in the dry, broadly forest, which I'll talk about a bit more in a minute. And this actually persists for relatively large sampling scales. So it's not until we go out to about 20 kilometer sampling radius in the tropical dry broadly forest that we see the system flip over to sort of habitat filtering emerging as the dominant structuring force. In tropical moist, it's maybe a little bit less, it's about one kilometer. And then when we look at these temperate systems, they tend to fall somewhere in between. Temperate broadly, if we still see over dispersion, but a much flatter curve and the tropical forest just have much higher variation overall in part because both temperate coniferous and tropical coniferous really encompasses a lot of different plant strategies and also has relatively low species richness. The other thing to notice, which I'm sure all of you picked up on that the rate at which this drops from over to under is much stronger in these tropical forests than in the boreal. And part of that is just the diversity of these systems. As we move out to and pick up new plots in tropical systems, we're picking up new species much more rapidly. Whereas in the boreal forest, it's much more homogenous and it's enormous. And so zooming out 250 kilometers, you're still in a boreal forest and it looks very similar to your plot. So we could scale this x-axis perhaps unlike the proportion of new species and maybe make this a little more uniform, but this really shows how quickly you have this turnover in community as you sample out. Now to get back to the key idea of this workshop, what does this tell us about the mechanisms sort of in quotes that provoked survival and I'd say sort of coexistence, but coexistence in a meta-community framework. Well, the boreal forest again is the easiest thing to think about. Species survive by being similar no matter what. So sort of similarity is the overarching principle that governs survival in these systems. Whereas when we look up to some of these ecoregions that have this transition point, it varies. If you're looking at small scales, then species survive by being dissimilar. At a certain point, there's this inflection point where actually the mechanism governing survival flips and we move from dissimilarity to similarity. This is what I think is sort of to me the most compelling and sort of profound part of this type of work. Thinking back to what we talked about yesterday when there was some debate over the role of triads and these intransitive loops and the difficulty saying is a transitivity really governing coexistence or is it just there independent? And I actually think the problem is a bit deeper than that. It's that there is no such thing as one thing ensuring species survive. That this to some extent is always going to be scale dependent. If you zoom out to 50 kilometers, for example, what this is saying is that survival, whether or not species can coexist, you can predict at least the first order approximation just based on how similar they are dissimilar they are. It has nothing to do with dynamics. Eventually that takes over but that's not what we need to know if we're dealing with these larger areas. And as you zoom across this sampling radius, the so-called mechanism is actually shifting based on the focal scale at which you're operating. Now to go back to Viher and Kedi's first series of questions, they say functional diversity is great but you really need to look at traits. And in fact, look at traits gives us a much more interesting and nuanced view. So here we have the boreal forest and the tropical moist and this is the individual trait dispersion for nine of these traits. So the boreal forest was consistently under dispersed which we see for a lot of traits with the exception of crown height and root depth. For crown height, we just see really, really strong under dispersion. Essentially no matter what scale you look at things have to be as similar with respect to crowns as possible. And again, this makes sense from a biological perspective that if you have different crowns, if you stick out too far, you're increasing risk of frost and wind damage. But if you don't have a big enough crown, you are also, you sort of have less photosynthetic capacity than you otherwise need to be competitive in those systems. However, when we look at something like root depth even though overall functional diversity was under dispersed we see a really strong signal of over dispersion and presumably competition with respect to these below ground processes. And again, this makes sense in the boreal forest below ground conditions are much less variable. They're relatively optimal compared to above ground. And so although above ground is saying everything is as similar as possible we actually see below ground things are as different as possible. So we actually can see how this process governing survival splits based on above versus below ground mechanisms simply by looking at these different traits. And again, if you knew nothing about coexistence theory and I gave you a handful of species in the boreal forest and said, could these survive together? Just based on this you could start to make some basic assumption about whether or not species could coexist relative to another handful of species simply by looking at their functional trait diversity and above versus below ground traits. When we look at the tropical moist broadly forest we see although it was over dispersed we now see why perhaps it was sort of attenuated. Some traits are strongly over dispersed some traits are actually strongly under dispersed. So things like leaf phosphorus root depth specifically vary a lot of these things with like the leaf economic spectrum that we would expect to be indicative of competition we see strong nutrients above and below ground diversification in these systems. But this also shows that the challenge of saying when we see over dispersion or under dispersion we see the importance of biotic versus abiotic. Presumably what we're actually seeing here with leaf area is not the role of abiotic conditions being too stressful with respect to leaf area but almost certainly this is a signal of hierarchical competition. So leaf area is basically directly correlated with your photosynthetic capacity your ability to grow tall to out compete other species and so it's linear or at least correlated strongly with competitive ability. And so things are under dispersed because in order to survive in the tropics you have to have large leaves with the exception of some specific micro sites where maybe there are some trade-offs necessary. When we look at something like stem conduit diameter we're seeing the same basic idea and this reflects this trade-off between moisture stress and moisture uptake. If you have really thin conduits to prevent sort of cavitation under drought conditions this really affects your ability to keep stomata open to be photosynthetically active. And so you're essentially penalized in these tropical conditions if you have really small stem conduit diameters because you limit your photosynthetic capacity. So when we break it up by individual traits we actually really start to get an idea for how species are competing and the mechanisms they're using to interact with each other. Does anyone have any questions at this point? There are a couple of questions in the chat which are about around the same thing. So the question is in summary if you could explain again how the new model was built and in particular I think that the question is about what is the pool of species. So you take this local area and compare the traits with some randomization. So which traits, functional traits and which species go into this randomization? Yes, okay, so the first thing to answer is so the metric we use we use this Rouse quadratic entropy which is essentially mean pairwise distance. So we look at the mean pairwise distance we normalize all the traits so they're sort of all scaled to have the same units and we just get the mean pairwise distance in this nine dimensional trait space. And then we compare that mean pairwise distance to the average mean pairwise distance when we randomize across all different traits. And we use a p-value, this empirical p-value but you could use these scores there's a bunch of different ways and it really doesn't matter much how you do it. The second question of how do we actually pick new species? And this is conditional on, let me go back to a figure real quick. So this is actually conditional on the plots located near that plot. So let's go to smaller. So here we have some focal plot we specify 100 meter radius and then we include in our null model all of the species that occur within plots within that 100 meter radius. So if in some cases if there's a plot that has nothing around it we only use that plot for one point in those plots. So we don't just sort of keep duplicating that value unless we pick up a new species at a different scale. And this sort of touches upon one of the big challenges is that this is conditional on the data and almost certainly we are under sampling rare species in these systems and presumably we're under sampling them most strongly in places like the tropics and potentially this could also be why we're seeing this sort of attenuation. We would have expected to see massive over dispersion in the tropics but in fact we're seeing sort of less than we would have thought and in part that could just be because we're not really adequately capturing the true diversity the true set of species in that regional species pool that were excluded in part because if you're excluded often as seedlings you could be quite rare in these systems and these forest inventories often have like a five or 10 centimeter diameter cutoff. So if you're just a seedling or a small tree you're going to be excluded from that system. Hopefully that at least gives a rough idea but feel free to answer any follow up questions. Actually I saw one just come in how are the randomizations done? Yeah so the randomizations where we keep the what they call the community matrix not to be confused with the sort of stability community matrix but they keep this matrix of abundance richness constant and we shuffle the trait values across species. So we're conditioning on species abundances when we do these randomizations. And the idea there is to make sure we're disentangling differences in richness from differences in functional diversity. But I guess the question is when you take these community matrix and you have these list of species and you say you randomize the functional trait associated with species. So you randomize within what pool of species. So you take all the species at the global scale or you take all the species in boreal forests and you randomize their traits within the boreal forest or you trade all the species within a certain region and you randomize the traits among the species within the region. Yeah exactly. So what we're doing is we're saying like for this point let's say like the first point here in the tropical moist broadly force. This is the randomization involving all, for each plot, this is sort of actually an aggregate curve taken across tens of thousands of plots. For each plot we do a separate randomization for that plot including only the species within 10 meters of that plot. And so every single plot has its own no model distribution that starts off with all the species located within 10 meters and we do a randomization then for that same plot we zoom out a little bit larger and we do all the species contained within one kilometer of that plot. So by the time we get, if we zoom this out to a sampling radius of 1,000 kilometers that would be doing a randomization across all traits at the global scale. But here we're only randomizing across species that are nearby to that plot and in growing increasingly far away from that plot. I hope that answers it. I'm not sure if I... So just to be sure then we can move on so basically this would be equivalent to shuffle the abundances of the species that are present within that plot keeping the function, the trait constant. Yeah, that's another thing. We keep our trait matrix constant and we are just... So we have this big trait matrix of all species that occurs within a region and then we just randomly shuffle that abundance distribution for that plot across this trait matrix. Okay. And there are different ways. Some people destroy the correlations among traits but that generally doesn't change much. Here we're assuming, we're keeping each species and instead of traits constant we never break those up. So we're sort of keeping implicit trade-offs and correlations among traits connected within this no model approach. Okay, I think we can move on. Okay. So let's see. Yeah, so I think this sort of goes in a little bit at least with respect to sort of some of the other processes that might be operating here. So when we look at these sort of patterns there's these weird little artifacts that emerge. So in many of these we see this initial low spot and the sort of peak that happens at one or five kilometers outward. In other cases they just sort of hover right around zero. And this is a bit related to what I talked about here. There's the sort of suppression of functional diversity even though tropical moist is generally the most optimal for tree species we see that the dispersion essentially sort of tamp down towards zero. And this is because sort of as a hint at that I'm sure a lot of you are thinking about there's actually another process going on here or presumed process which is that of neutrality in these systems. And when we zoom in really, really far when we essentially look just within a plot or we maybe move a few meters over we pick up a plot right next door we're really only adding one species we're getting we have really no statistical power to really see what's going on in that species pool. And so we're maybe essentially seeing a signal neutrality just as an artifact. And this is sort of Jonathan Chase really put this nicely in this little diagram showing that as you move in zoom in suit closer and closer and closer you move away from niche processes until you've sort of removed all niche sorting and you're just looking at the signal of neutrality. And also in these tropical forests that's where we would expect neutrality to be strongest or at least that's where the idea of neutrality emerged specifically looking through the idea of functional redundancy. So our hypothesis for why the tropical moist is sort of tamped or sort of biased towards zero compared to tropical dry is that tropical dry are often typified by these really strong wet and dry seasons there's really strong niche partitioning temporal niche partitioning and there's much less opportunity for things to be truly neutral, right? You sort of have to be optimized to one scenario or another whereas in these tropical moist there's essentially everything is always good and so potentially this is just a greater signal of neutrality playing out here. And so when we look at these curves that sort of rise in peak at some point that peak gives us sort of the maximal scale the optimal scale at which we can distinguish competition and as we zoom in closer we're moving just like Jonathan Chase showed away from niche processes more towards these stochastic or neutral processes. And this isn't quite along the lines of this workshop but just to show you I've been looking at marginal trends in part because they really illustrate these ideas really clearly but we can do some more true statistics and modeling beneath the scenes so we can sort of control for environmental variables we can control for human activity for soil conditions and try to understand how dispersion varies across these different environmental gradients. When we do this sampling area comes out as the strongest predictor just as we saw as you zoom out things always tend to go down and we know at the global scale a boreal forest is very different than a tropical forest and so sampling area must be the biggest predictor but we also see some things like solar radiation precipitation seasonality, temperature seasonality precipitation of the driest month as well as some soil conditions which we know matter for tree growth like soil again at carbon, cation exchange capacity. So this starts to inform what are the gradients that really define optimal versus suboptimal in these environments. And not to go into it too much detail but just to give you an idea of what we can get out of this so we can actually fit the model the marginal model predicted curves. So here we have high solar radiation, low solar radiation. When we see there's this dual interaction between radiation and solar organic carbon. So if you're in high solar radiation essentially near the equator we see the significant interaction with solar organic carbon that governs over versus under dispersion. But when you move to more solar radiation areas again more towards the poles we now see that there's much less of an effect of solar organic carbon. So in other words we can say that solar radiation is sort of the primary limiting factor and once this primary limiting factor is alleviated, solar organic carbon emergence as a secondary factor. So this is just a hint of some of the other things that we can get out of this as well. Sort of just in the sake of time I'll skip that last slide and move on to some of the things more applied questions that we can do this. Again not really for what we're talking about today but we can actually do some really cool and interesting things. So we can fit a curve for each plot not just the marginal curve that fit a curve to each plot each plot sort of dispersion curve across sampling area. And we can make a map for example of the slope the x-intercept sort of that transition point the y-intercept what the maximum dispersion might be or the minimum dispersion. And just to give you an example so this is global functional dispersion at one kilometer level. And I mean it looks a lot like functional diversity apart from some of these more interesting things you know it's not the Amazon basin that necessarily has the highest functional dispersion even though it might have the highest functional diversity but it's some of these areas like Southeast Asia and Indonesia where we have again these really typified by wet and dry seasons monsoon seasons where we see really strong niche partitioning that is driving higher functional dispersion. And the lowest functional dispersion actually ends up being in these drier regions you know like parts of Australia and then moving up into the boreal forest as well. So this is just an example of the types of sort of applied questions we can do. So just to wrap up what I think is really useful about this first off we can look at these overarching principles governing survival similarity versus dissimilarity which we don't really think of through coexistence but I think I would argue it's maybe one of the the sort of key overarching principles at the global scale when we think of these communities so I'd be eager to chat a bit more about that. Maybe we can get an assembly processes but I think that again is a bit more dubious unless you really look at individual traits. And then for some of these more applied questions we can look at the environmental drivers governing this as well as which traits are most sensitive to these drivers. And then as I alluded to before I think the most interesting thing about this and what I'd be interested to chat more about is how this illustrates that these mechanisms for coexistence are very context dependent. On the one hand we know this if we think of like a patch occupancy model we know the criteria for stability is not the same as stability within a community. But I think that also really questions what we mean when we talk about coexistence. And if we zoom in so close that we're looking at coexistence within a single closed community is that really indicative of these true processes that are what governs at least survival long-term persistence of species at the global scale. And with that I'd like to thank my funding sources again thank the organizers for today thank all of you for listening and just a shameless plug I'm hiring a postdoc so if any of you are interested or know a colleague who's looking for a postdoc position and really anything theoretical it's quite broad feel free to get in touch. And with that thanks again and I'm happy to answer some official questions. Thanks Ben so thanks a lot. There are a couple of questions so Mercedes the question so if you want to ask it and... Yes, thank you Daniel very interesting talk. One question that I think is of relevance is these data sets largely have traits that relate to demography. And there was a very interesting paper on data from the sites in Panama from the famous forest sites in Panama where they showed that if you are looking for traits that influence the frequency dependent negative frequency dependent interactions that underlie some of the hypotheses for coexistence in the rainforest because they are the ones that may underlie both niche formation and some form of balancing selection then and co-evolution then the traits that seem to matter the most were traits that had to do for example with the chemistry of the leaves and not with the demography. So they were completely orthogonal traits to the traits related and this somehow may it's the question I had is a lot of the traits in this data as I said they have to do with demography competition along an access where you want to be more similar or more neutral to coexist. Whether you need some form of negative frequency dependent selection which this kind of effect of distance is very reminiscent of the Johnson-Connell hypothesis operating nearby for which many of the chemical traits may be important. Yeah, I think this is I think raise a really sort of good point. I mean, I'm sort of saying like these are different processes but when we're talking about something like limiting similarity we're really talking about niche differentiation and in effect we're talking about the role of intraspecific self-regulation these negative feedbacks that are driving this here. And so in a way when we see this really strong sort of pushing apart in trade space of species this is some to some extent suggesting that there is some sort of negative density dependence operating these systems. But I think that the demographic traits is a really interesting idea. And I think when we going back to the slide actually pull it up or we talk about hierarchical competition in a sense what we're talking about are traits that are sort of demographic can be related to demographics in some way. And we see different selection operating on something like leaf phosphorus which is true niche it's sort of nutrient differentiation. Presumably root depth is also similar thing they're accessing very different nutrients. We do look at things we also I didn't include them here but we can look at above ground biomass maximum tree growth rate. And those things are generally under dispersed as you would expect like if you're in the tropics you have to be able to grow big in order to survive. And so some of these demographic traits map exactly what we would expect to see. And I think what I sort of like about this and part of this is when we're dealing at these scales there's this I really enjoy working with patterns more and more because we know these patterns are driven by some underlying dynamical process that's operating. But obviously we can't go to every place and measure apart from these really rigorous studies like in Panama you can't necessarily measure long-term growth. And so the patterns they're suggestive but again they give us some nice insight that I think really maps on to what you've mentioned that we see this split by demographic versus nutrient competition in these systems. There was a question from Miguel Rodriguez. Hello, thank you that's really cool work. I have two very minor questions towards the end you had some potential predictors of that dispersion from the different environments but I noted you measuring their strength with R square but then the solar radiation was clearly non-linear the effect of solar radiation. Well, I shouldn't say the effect but the correlation between solar radiation and the dispersion was clearly non-linear. Could that be hiding some important predictors that maybe they are tightly correlated with the dispersion but in not in a linear way for the others that have low values? Yeah, that's a great question. So half the reason we use random force is just because these things are incredibly non-linear and random force it's prone to overfitting a bit but I would rather it's unbiased with respect to the shape of the functional form that you assume, you know, we can fit a linear model and maybe we can extrapolate a bit better but we're going to be wrong everywhere a little bit but your question about R squared so I should have been a bit more clear. So this is actually like you might call it the coefficient of determination it's essentially the normalized mean squared error. So we just plot observed versus predicted and it's just the square of the standard deviation divided by the overall standard deviation. So it's not fitting a line. We're not doing a regression. Yeah, we're just comparing observed to predicted. Okay, that makes a little more sense, thank you. Yeah, and like, you know, it's still relatively high and I do think like, of course there has to be huge variation in part because, you know, people like even though human footprint isn't a great predictor part of that is because somewhere like in Europe where we have these force inventory data everything has a human footprint of essentially one, you know, it's a hundred percent human footprint and so when we go back long enough this idea that humans are disturbing this or just creating noise is going to significantly drop these a little bit. But yeah, it's a good question. Thanks. If I can ask just an unrelated quick one is there a way to control in these kind of models have you addressed the problem of relatedness between the species? You have evaluated the traits but some of these effects might just be the by-product of having very closely related species or very distant related species in the same plots and that way to control for that. Yeah, that's a good question. I would certain how to control for it. We do an analogous randomization where we look at phylogenetic diversity so we use mean phylogenetic distance. I didn't show it because it's a little more complex because when you start to zoom out even closely if we think of something like the tropics there's been a long history of more rapid evolution compared to more pole work systems where the glaciers sort of scraped them and now they're slowly starting to recolonize. So the trends are a lot more complex in part because when we zoom out even to 100 kilometers or something reasonable we're really seeing these evolutionary processes start to govern these patterns much more quickly than we see true competition among things. But to your same extent it could be that what we're seeing is trait differences might just be this neutral trait that has no selective pressure and is again just a by-product of some sort of adaptive radiation somewhere along the lines in history. I mean, it's actually a really interesting point. We haven't thrown this into a predictor like we could certainly throw it into these models and look at something like evolutionary diversification or minimize paralyzed distance or something like that and try to see controlling for environmental conditions and controlling for evolutionary history do we still see traits come out? It would be a cool way to get at the relative importance of traits in phylogen. So that's a nice idea.