A general expectation for the paradox of coexistence

There are several popular approaches to the goal of finding generalities in ecology. One is essentially top down, searching for generalities across ecological patterns in multiple places and at multiple scales and then attempting to understand the underlying mechanisms (e.g. metabolic scaling theory and allometric approaches). Alternatively, the approach can be bottom up. It may consider multiple models or multiple individual mechanisms and find generalities in the patterns or relationships they predict. 

A great example of generalities from multiple models is in a recent paper published in PNAS (from Sakavara et al. 2018). It relies on, links together, and adds to, our understanding of community assembly and the effects of competition on the distribution of niches in communities. In particular, it adds additional support to the assertion that both combinations of either highly similar or highly divergent species can coexist, across a wide variety of models.

Work published in 2006 by Scheffer and van Nes played an important early role towards a reconciliation of neutral theory and niche-based approaches. They used a Lotka-Volterra model to highlight that communities could assemble with clusters of coexisting, similar species evenly spaced along a niche axis (Figure 1). Neutrality, or at least near-neutrality, could result even when dynamics were determined by niche differences. [Scheffer, van Nes, and Remi Vergnon also provide a nice commentary on the Sakavara et al. paper found here].

Fig. 1: From Scheffer and van Nes, emergent 'lumpiness' in communities.

One possibility is that Scheffer and van Nes's results might be due to the specifics of the L-V model rather than representing a general and biologically realistic expectation. Sakavara et al. address this issue using a mechanistic consumer-resource model in "Lumpy species coexistence arises robustly in fluctuating resource environments". Under this model, originally from Tilman's classic work with algae, coexistence is limited by the number of resources that limit a species' growth. For 2 species, for example, 2 resources must be present that limit species growth, and further the species must experience a tradeoff in their competitive abilities for the 2 resources. Coexistence can occur when each species is limited more by the resource on which it is most competitive (Figure 2). Such a model– in which resources limit coexistence—leads to an expectation that communities will assemble to maximize the dissimilarity of species.

Fig 2. From Sakavara et al. (2017).

Such a result occurs when resources are provided constantly, but in reality the rates of resource supply may well be cyclical or unpredictable. Will community assembly be similar (resulting in patterns of limiting similarity) when resources are variable in their supply? Or will clumps of similar species be able to coexist? Sakavara et al. considered this question using consumer-resource models of competition, where there are two fluctuating limiting resources. They simulated the dynamics of 300 competing species, which were assigned different trait values along a trait gradient. Here the traits were the half-saturation coefficients for the 2 limiting resources: these were related via a tradeoff between the half saturation constants for each resource.

What they found is strikingly similar to the results from Scheffer and van Nes and dissimilar to the the results that emerge when resources are constant. Clumps of coexisting species emerged along the trait axis. When resource fluctuations occurred rapidly, only fairly specialized species survived in these clumps (R* values that were high for either resource 1, or resource 2, rather than intermediate). But when fluctuations were less frequent, clusters of species also survived at intermediate points along the trait axis. However, in all cases the community organized into clumps composed of very similar species that were coexisting (see Figure 3). It appears that this occurs because the fluctuating resources result in the system having non-stationary conditions. That is, similar sets of species can coexist because the system varies between those species' requirements for persistence and growth. 

Fig. 3. "Lumpy species coexistence". The y-axis shows the trait value (here, the R*) of species present under 360 day periodicity of resource supply.  

Using many of the dominant models of competition in ecology, it is clearly possible to explain the coexistence of both similar or dissimilar species. This is true across approaches from the Lotka-Volterra results of Scheffer and van Nes, to Tilman's R* resource competition, to Chessonian coexistence (2000). It provides a unifying expectation upon which further research can build. Perhaps the paradox of the planktons is not really a paradox anymore?

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Reference:
Athanasia Sakavara, George Tsirtsis, Daniel L. Roelke, Rebecca Mancy, and Sofie Spatharis. Lumpy species coexistence arises robustly in fluctuating resource environments. PNAS 2017; published ahead of print December 20, 2017, doi:10.1073/pnas.1705944115

What do we mean when we talk about the niche?

The niche concept is a good example of an idea in ecology that is continually changing. It is probably the most important idea in ecology that no one has yet nailed down. As most histories of the niche mention, the niche has developed from its first mention by Grinnell (in 1917) to Hutchinson’s multi-dimensional niche space, to mechanistic descriptions of resource usage and R*s (from MacArthur’s warblers to Tilman’s algae). Its most recent incarnation can be found in what has been called modern coexistence theory, as first proposed by Peter Chesson in his seminal 2000 paper.

Chesson’s mathematical framework has come to dominate a lot of discussion amongst community ecologists, with good reason. It provides a clear way to understand stable coexistence amongst local populations in terms of their ability to recover from low densities, and further by noting that those low density growth rates are the outcome of two types of processes: those driven by fitness differences and those driven by stabilizing effects that reduce interspecific competition relative to intraspecific competition. Many of the different specific mechanisms of coexistence can be classified in terms of this framework of equalizing and stabilizing effects. “Niche” differences between species in this framework can be defined as those differences that increase negative intraspecific density dependence compared to interspecific effects. If, as a simplistic example, two plant species have different rooting depths and so access different depths of the water table, then this increases competition for water between similar root-depth conspecifics relative to interspecific competition. Thus, this is a niche difference. Extensions on modern niche theory have offered insights into everything from invasion success, restoration, and eco-phylogenetic analyses.

But it seems as though the rise of 'modern coexistence theory' is changing the language that ecologists use to discuss the niche concept. When Thomas Kuhn talks about paradigm shifts, he notes that it is not only theory that changes but also the worldview organized around a given idea. At least amongst community ecologists, it seems as though this had focused the discussion of the niche to an increasingly local scale, particularly in terms of stabilizing and equalizing terms measured as fixed quantities made under homogenous, local conditions. A recognition of the role of spatial and temporal conditions in altering these variables seems less common, compared to the direction of earlier, Hutchinsonian-type discussions of the niche.

Note that this was not Chesson's original definition, since he is explicit that: “The theoretical literature supports the concept that stable coexistence necessarily requires important ecological differences between species that we may think of as distinguishing their niches and that often involve tradeoffs, as discussed above. For the purpose of this review, niche space is conceived as having four axes: resources, predators (and other natural enemies), time, and space.”

On a recent manuscript, an editor commented that the term 'niche processes' shouldn't be used to refer to environmental filtering since (paraphrased) “when ecologists refer to niche processes, they are usually thinking of processes that constrain species’ abundances locally, confer an advantage on rare species...” But is it fair to say that this is the only thing we mean (or should mean) when we discuss niches? I’ve had discussions with other people who’ve had this kind of response – e.g., reviewers asking for simulations to be reframed from niches defined in terms of environmental tolerances to things that fit more clearly into equalizing and stabilizing terms. That is a good description of a stabilizing process, which is termed a 'niche difference' in the modern coexistence literature. But there is still a lot of grey space we have yet to address in terms of how to integrate (e.g.) the effects of the environment (including over larger scales) into local 'niche processes' or stabilizing effects. It's a subtle argument - that we can use the framework established by Chesson, but we should try to do so without dismissing too-quickly the concepts that don't fit easily within it. In addition, elsewhere the niche is still conceptualized in varying ways from comparative evolutionary biologists who talk about niche conservatism and mean the maintenance of ancestral trait values or environmental tolerances; to functional ecologists who may refer to multidimensional differences in trait space; to species distribution modellers who thinks of large-scale environmental correlates or physiological determinants of species’ distributions. 

The niche is probably the most fundamental, yet vaguely–defined and poorly understood idea in ecology. So, formalizing the definition and constraining it is a necessary idea. And modern coexistence theory has provided great deal of insight into local coexistence and thus has allowed for a better understanding of the niche concept. But there is also a need to be careful in how quickly and how much we restrict our discussion of the niche. It's possible to gain both the strengths of modern coexistence theory as well as appreciate its current limitations. Modern coexistence theory isn’t yet complete or sufficient. It’s currently easier to estimate stabilizing and equalizing terms from experimental data in which conditions are controlled and homogenous, and this can inadvertently focus future research and discussion on those types of conditions. Models which consider larger scale processes and the impacts of changing abiotic conditions through space in time exist, but across different literatures, and these need continued synthesis. There is still a need to understand how to most realistically incorporating and understand the complex interactions between multiple species (e.g. Levine et al. 2017). The application of modern coexistence theory to observational data in particular is still limited, and such data is essential when species are slow lived or experimentally unwieldy. Further, when quantities of interest (particularly traits or phylogenetic differences) contribute to both equalizing and stabilizing effects, its still not clear how to partition their contributions meaningfully.

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Can coexistence theories coexist?

These days, the term ‘niche’ manages to cover both incredibly vague and incredibly specific ideas. All the many ways of thinking about an organism’s niche fill the literature, with various degrees of inter-connection and non-independence. The two dominant descriptions in modern ecology (last 30 years or so) are from ‘contemporary niche theory’ and ‘modern coexistence theory’. Contemporary niche theory is developed from consumer-resource theory, where organisms' interactions occur via usage of shared resources. (Though it has expanded to incorporate predators, mutualists, etc), Analytical tools such as ZNGIs and R* values can be used to predict the likelihood of coexistence (e.g. Tilman 1981, Chase & Leibold 2003). Modern coexistence theory is rooted in Peter Chesson’s 2000 ARES review (and earlier work), and describes coexistence in terms of fitness and niche components that allow positive population growth.

On the surface these two theories share many conceptual similarities, particularly the focus on measuring niche overlap for coexistence. [Chesson’s original work explicitly connects the R* values from Tilman’s work to species’ fitnesses in his framework as well]. But as a new article in Ecological Monographs points out, the two theories are separated in the literature and in practice. The divergence started with their theoretical foundations: niche theory relied on consumer-resource models and explicit, mechanistic understanding of organisms’ resource usage, while coexistence theory was presented in terms of Lotka-Volterra competition models and so phenomenological (e.g. the mechanisms determining competition coefficients values are not directly measured). The authors note, “This trade-off between mechanistic precision (e.g. which resources are regulating coexistence?) and phenomenological accuracy (e.g. can they coexist?) has been inherited by the two frameworks….”

There are strengths and weaknesses to both approaches, and both have been used in important ecological studies. So it's surprising that they are rarely mentioned in the same breathe. Letten et al. answer an important question: when directly compared, can we translate the concepts and terms from contemporary niche theory into modern coexistence theory and vice versa?

Background - when is coexistence expected? 
Contemporary niche theory (CNT) (for the simplest case of two limiting resources): for each species, you must know the consumption or impact they have on each resource; the ratio at which the two resources are supplied, and the ZNGIs (zero net growth isoclines, which delimit the resource conditions a species can grow in). Coexistence occurs when the species are better competitors for different resources, when each species has a greater impact on their more limiting resource, and when the supply ratio of the two resources doesn’t favour one species over the other. (simple!)

For modern coexistence theory (MCT), stable coexistence occurs when the combination of fitness differences and niche differences between species allow both species to maintain positive per capita growth rates. As niche overlap decreases, increasingly small fitness differences are necessary for coexistence.

Fig 1, from Letten et al. The criteria for coexistence under modern coexistence theory (a) and contemporary niche theory (b).  In (a), f1 and f2 reflect species' fitnesses. In (b) "coexistence of two species competing for two substitutable resources depends on three criteria: intersecting ZNGIs (solid red and blue lines connecting the x- and y-axes); each species having a greater impact on the resource from which it most benefits (impact vectors denoted by the red and blue arrows); and a resource supply ratio that is intermediate to the inverse of the impact vectors (dashed red and blue lines)."

So how do these two descriptions of coexistence relate to each other? Letten et al. demonstrate that:
1) Changing the supply rates of resources (for CNT) impacts the fitness ratio (equalizing term in MCT). This is a nice illustration of how the environment affects the fitness ratios of species in MCT.

2) Increasing overlap of the impact niche between two species under CNT is consistent with increasing overlap of modern coexistence theory's niche too. When two species have similar impacts on their resources, there should be very high niche overlap (weak stabilizing term) under MCT too.

3) When two species' ZNGI area converge (i.e. the conditions necessary for positive growth rates), it affects both the stabilizing and equalizing terms in MCT. However, this has little meaningful effect on coexistence (since niche overlap increases, but fitness differences decrease as well).

This is a helpful advance because Letten et al. make these two frameworks speak the same (mathematical) language. Further, this connects a phenomological framework with a (more) mechanistic one. The stabilizing-equalizing concept framework (MCT) has been incredibly useful as a way of understanding why we see coexistence, but it is not meant to predict coexistence in new environments/with new combinations of species. On the other hand, contemporary niche theory can be predictive, but is unwieldy and information intensive. One way forward may be this: reconciling the similarities in how both frameworks think about coexistence.

Letten, Andrew D., Ke, Po-Ju, Fukami, Tadashi. 2016. Linking modern coexistence theory and contemporary niche theory. Ecological Monographs: 557-7015. http://dx.doi.org/10.1002/ecm.1242
(This is a monograph for a reason, so I am just covering the major points Letten et al provide in the paper. It's definitely worth a careful read as well!).

What are important directions for ecology?

I was recently asked “what is the most important problem in ecology?”. I was dissatisfied with whatever I ended up answering, so it has been on my mind. I think there is an analogy with medicine here – it’s a little like asking a medical scientist “what is the most important disease to cure?” Similarly, there are multiple possible answers, and the one you give will depend on your area of interest/what type of doctor you are. (I also assume this is a question about basic research, and the answer is not as simple as saying, stop extinctions or prevent habitat loss).

Levels of biological organisation.

The medical analogy breaks down a little because ecology is *far* more complicated than medical science. Medicine has a foundation in anatomy and physiology, which in turn rely on basic sciences like cell biology and genetics. This creates a reasonably constrained framework within which further learning/investigation can be organized. Medicine typically stops at the level of the individual, but ecology inherently involves many additional levels of organization (from individuals, to populations, to species and communities, to ecosystems, and beyond). Within any one of these higher levels of organization (population, community, ecosystem), there can be such an immense amount of variation in outcomes and dynamics that ecologists can lose sight of connections with lower and higher levels. For example, community ecology encompasses so much complexity on its own, that also considering the impacts of population level processes and on ecosystem level processes is a tall order. But, we should also appreciate, given these barriers to understanding, just how far ecology has actually advanced in the last 100 years. The combination of reductionist experiments and descriptive work at all scales has been immensely successful (e.g. see this blog post for a partial list). Many general tools have been developed that we can then use to answer specific ecological questions (the integration with statistics with ecology has been highly successful; the use of specific mathematical models). Still, the ability to reconcile multiple levels of organization and scales still limits ecology.

This is a problem that cell biology has also experienced, and is now approaching via systems biology: "The reductionist approach has successfully identified most of the components and many of the interactions but, unfortunately, offers no convincing concepts or methods to understand how system properties emerge...the pluralism of causes and effects in biological networks is better addressed by observing, through quantitative measures, multiple components simultaneously and by rigorous data integration with mathematical models"(1): to me, this quote rings so true for ecology as well. Systems biology uses mechanistic, mathematical and computational models to attempt to represent multi-scale complexity.

Of course, the optimism about systems biology might be premature in that it hasn’t produced many useful models yet, such that it may be “more of an agenda than a body of results.”. Some of the best “systems ecology” (e.g. meta-ecosystem models) are very system specific and data-heavy (e.g. 2). Can they inform us about generality in ecology?

All of which is to say, I think the most important problems in ecology relate to this need to make the connections between studies and systems and levels of organization. But, doing so may be difficult.

More specific problems

1. The scaling of ecological processes. Many ecologists include a line about being ‘interested in questions of scale’ on their website blurbs. Despite this, our understanding of the aggregate outcome of multiple processes that are occurring at different spatial or temporal scales remains limited, and poorly predictive. There have been a few useful starts (particularly in Peter Chesson’s scale transition papers (3, 4)), but recent theoretical interest seems to be low. We have data at the community scale, and data at the macro-scale. How do we connect these (and can we)? Models describing how processes occurring at smaller scales produce larger scale dynamics can be complex: they may include non-linearities, autocorrelation between regions, the combination of discrete and continuous events, and multiple attractors.

2. Mechanisms maintaining multi-species coexistence in the real world. Hutchinson’s paradox of the plankton remains unsolved*. Community ecologists have invested a lot of time and energy into understanding species interactions as seen in natural communities. To explore the mechanisms behind coexistence, usually (but not always) ecologists have focused on two-species interactions (or maybe 3): understanding coexistence in larger groups tends to be mostly restricted to theory. But fitting the individual pieces into the larger puzzle is exponentially more difficult: in observed large groups of interacting species, what is the relative contribution of the many coexistence mechanisms identified? Which mechanisms are most important, and how do they change through space and time?

*Perhaps not surprisingly, given it is a paradox...

3. Moving farther away from species. In so many ways, focusing on ‘species’ as the unit of measurement is limiting, because ‘species’ is a discrete term and ecology is interested in quantitative measures. Important advances have been made by redefining ecology as the outcome of species traits and species interactions (5). But I think our ability to connect these ideas more closely to species’ multidimensional niches can still improve. In particular, understanding that traits and interactions can change in context-dependent ways (plasticity, ontogeny, environment) will be important (6, 7).

4. Reproducibility of ecological research. This is more of a philosophical question - how do we achieve reproducibility in a science where context-dependence, alternative stable states, chaos and stochasticity all affect results? How do we differentiate between reproducibility (same results under identical conditions) and generality (same results under similar conditions) in results?

References:
1) Sauer, Uwe; Heinemann, Matthias; Zamboni, Nicola. Genetics: Getting Closer to the Whole Picture. Science 316 (5824): 550–551. doi:10.1126/science.1142502. PMID 17463274.

2) Dominique Gravel, Frédéric Guichard, Michel Loreau and Nicolas Mouquet. Source and sink dynamics in meta-ecosystems. Ecology 91(7): 2172-2184.

3) Chesson, Peter. Scale transition theory with special reference to species coexistence in a variable environment. Journal of biological dynamics 3.2-3 (2009): 149-163.

4) Melbourne, Brett A., and Peter Chesson. The scale transition: scaling up population dynamics with field data. Ecology 87.6 (2006): 1478-1488.

5) McGill, Brian J., et al. Rebuilding community ecology from functional traits. Trends in ecology & evolution 21.4 (2006): 178-185.

6) Poisot, T., Canard, E., Mouillot, D., Mouquet, N., Gravel, D. & Jordan, F. (2012) The dissimilarity of species interaction networks. Ecology letters, 15, 1353–61.

7) Siefert, A., Violle, C., Chalmandrier, L., Albert, C.H., Taudiere, A., Fajardo, A., Aarssen, L.W., Baraloto, C., Carlucci, M.B., Cianciaruso, M.V. and L Dantas, V. A global meta‐analysis of the relative extent of intraspecific trait variation in plant communities. Ecology letters 18.12 (2015): 1406-1419.

What explains persistent species' rarity in communities?

Someone asked me what is the most important or lingering issue in community ecology recently. (There’s probably a whole post to answer that question (to come...)). One answer is the mystery of species coexistence: for more than 50 years (from Hutchinson’s paradox of the plankton through today) we have tried to explain the immense and variable diversity on earth by understanding what allows two or more species to coexist. There are many ways to explain coexistence, and yet the details and the specifics for any given system are also still usually incompletely understood.

A good and fascinating example is that of persistent rarity. Why are so many species in communities rare? What allows species to remain rare for long periods of time, given that small populations should be at greater risk for stochastic extinction? A new preprint from Yenni et al. (1) considers the empirical evidence for one potential explanation for persistent rarity: asymmetric negative frequency dependence (see also Yenni et al. 2012 (2)).

Coexistence theory (Chesson 2000) considers stabilizing mechanisms to be those that allow intraspecific competition to be greater than interspecific competition (often defined as ‘niche’ mechanisms). The strength of such stabilizing mechanisms can be estimated by looking at how a species’ population growth rate is limited by the frequency of conspecifics compared to the frequency of heterospecifics in the community. Negative frequency dependence is expected when stabilizing mechanisms are strong. This allows species to increase when rare, since limitation by conspecifics is low, followed by a decline in growth rates as conspecific frequency increases.

Asymmetric negative frequency dependence may explain persistent rarity, since it suggests especially strong conspecific limitation. As a species’ frequency increases, their growth rate greatly declines and intraspecific interactions, rather than interspecific competition, determine abundances. Species are rare, but also less likely to experience extinctions through competition with other species. The authors suggest that as a result of this, we should expect rare species to have stronger negative frequency dependence, in comparison to more common species. They look for evidence for asymmetric frequency dependence using data from 148 communities collected across multiple taxonomic groups (birds, fish, herpetofauna, invertebrates, mammals, and plants), 5 continents, and 3 trophic levels. The data represented time series of species abundances, which the authors used to estimate negative frequency dependence as the relationship between a species’ frequency in the community and their annual per capita population growth rate.

Several aspects of the results are particularly interesting. First, the authors had to omit rare species that are not persistent, since other processes likely explain the presence of such ephemeral members of communities. The frequency of ephemeral species (not stably coexisting at a local scale), for example, was quite high, particularly in plant communities (average of 82 species per community, of which only 22.6 species were on average identified as ‘persistent’). This may suggest the importance of spatial mechanisms for coexistence or co-occurrence. Their overall prediction of stronger negative frequency dependence in rare species appeared to holds in 46% of the communities they examined, consistently for all of the taxonomic groups but one (herps!). Additionally, the opposite pattern (common species having stronger negative frequency dependence) was never observed.

Rarity in nature is common :-) but not well predicted using most coexistence theory. Many interesting and important questions arise from it, and from results like those shown in Yanni et al. For example, do rare species have rare traits or rare niches? Is the frequency dependent growth rate context dependent (i.e. can a species be strongly limited by conspecifics in one environment but not another)?

*Note I haven’t reproduced any figures here, since this is a preprint. However, it is openly available, so do have a look (link 1 below). I’m not certain if there is a rule of thumb on blogging about preprints, but I imagine it is much like blogging about conference talks. The work may not have been peer reviewed/published yet, but the broad results and ideas remain interesting to discuss.

References:

1. Glenda Yenni, Peter Adler, Morgan Ernest. Do persistent rare species experience stronger negative frequency dependence than common species? doi: http://dx.doi.org/10.1101/040360. Preprint.

2. Yenni, Glenda, Peter B. Adler, and S. K. Ernest. "Strong self‐limitation promotes the persistence of rare species." Ecology 93.3 (2012): 456-461.

#ESA100 Declining mysticism: predicting restoration outcomes.

Habitat restoration literature is full of cases where the outcomes of restoration activities are unpredictable, or where multiple sites diverge from one another despite identical initial restoration activities. This apparent unpredictability in restoration outcomes is often attributed to undetected variation in site conditions or history, and thus have a mystical quality where the true factors affecting restoration are just beyond our intellect. These types of idiosyncrasies have led some to question whether restoration ecology can be a predictable science.

Photo credit: S. Yasui

The oral session “Toward prediction in the restoration of biodiversity”, organized by Lars Brudvig, showed how restoration ecologists are changing our understanding of restoration, and shedding light on the mystical qualities of success. What is clear from the assembly of great researchers and fascinating talks in this session is that recent ecological theories and conceptual developments are making their way into restoration. Each of the 8 of 10 talks I saw (I had to miss the last two) added a novel take on how we predict and measure success, and the factors that influence it. From the incorporation of phylogenetic diversity to assess success (Becky Barak) to measuring dispersal and establishment limitation (Nash Turley), and from priority effects (Katie Stuble) to plant-soil feedbacks (Jonathan Bauer), it is clear that predicting success is a multifaceted problem. Further, from Jeffry Matthews talk on trajectories, even idiosyncratic restoration trajectories can be grouped into types of trajectories (e.g., increasing diversity vs plateauing) and then relevant factors can be determined.

What was most impressive about this session was the inclusion of coexistence theory and basic demography into understanding how species perform in restoration. Two talks in particular, one from Loralee Larios on coexistence theory and the other from Dan Laughlin on predicting fitness from traits by environment interactions, shed new light on predicting restoration. Both of these talks showed how species traits and local environmental conditions influence species’ demographic responses and the outcome of competition. These two talks revealed how basic ecological theory can be applied to restoration, but more importantly, and perhaps under-appreciated, these talks show how our basic assumptions about traits and interactions with other species and the environment require ground-truthing to be applicable to important applied problems.

Equalizing and stabilizing traits?

Plant functional traits and the multidimensional nature of species coexistence. 2015. Nathan J. B. Kraft, Oscar Godoy, and Jonathan M. Levine. PNAS.

(This isn’t a brand new paper, but somehow I’m already behind on reading papers in the new year...) 

A recent paper from Kraft et al. in PNAS does a really nice job in filling a gap that has been in literature for a while, which is to extend the influential theoretical work on coexistence from Chesson (and extended more recently by Jonathan Levine et al.) to explicitly incorporate functional traits and trait-based approaches to ecology. Chesson’s work (particularly ARES 2000) lays out a framework for understanding coexistence and competitive interactions, which focuses on the importance of stabilizing effects (niche differences) and equalizing effects (fitness differences) between competing species (e.g.). This theory makes strong predictions of when and how coexistence is expected (for example, when species have strong enough niche differences). However, accurate application of the theory is somewhat difficult, perhaps because identifying and calculating niche and fitness differences requires heavy use of mathematical models and careful experimental design.

In contrast, the value of the focus on functional traits in ecology is that they are readily measured, easily conceptualized, and databases of values already exist. In common with equalizing/stabilizing effects, traits are meant to inform our understanding of species' niches, but in contrast, traits are empirically friendly. One of the more common critiques of the Chesson framework was that empirical measures, particularly traits, couldn't be shoehorned into it. After all, traits likely contribute to both equalizing and stabilizing forces in complicated ways that may well shift during a species' life.

What Nathan Kraft and coauthors have done is show that this is not a limitation - traits can contribute to both equalizing and stabilizing forces, and mathematical models can tease these effects apart. They relate detailed measurements of leaf, root, seed and whole plant traits for 18 California annual plants with the results of mathematical models of competition and coexistence between these species. The authors found strong and exciting relationships between the theoretically motivated measures of competitive processes and species' traits. Average fitness differences had significant correlations with functional traits, particularly maximum height, leaf [N], leaf area, rooting depth, and phenology.

From Kraft et al. 2015: Correlations between species traits and A) Stabilizing niche differences, and B) Average fitness differences.
The key to interpreting these plots is to understand that where the coloured line overlaps with the grey shading, the correlation is not different than the null model. When the line is between the null and the center of the figure, the correlation is significant and negative; where it is between the null and the external edge, the correlation is significant and positive.

No individual traits correlated with niche differences, but models including multiple traits considered together do correlate with niche differences. A rather nice bit of support for the multidimensional view of the niche.

This paper does a nice job of expanding Chesson's framework a little bit farther towards empirical applications. Further, it reinforces the value of trait approaches. There are still some important limitations - the first is that this particular system of annual plants has been studied in great detail. It seems unlikely that the traits identified in this paper can necessarily be generalized as "equalizing" traits. A trait with an equalizing effect in a California grassland may well contribute less to fitness in a desert system, for example. Perennial species are altogether less integrated into experimental applications of Chesson's framework (life time fitness, among other things, being much easier to capture in annual plants). But this paper is a suggestion of a useful way forward, albeit a way that requires much more data and careful experimentation. The authors acknowledge that more study is due, but also the potential: “These complex relationships argue against the simple use of single traits to infer community assembly processes but lay the foundation for a theoretically robust trait-based community ecology.”

Phylogeny, competition and Darwin: a better answer?

*Sorry for the low frequency of posts these days – I seem to be insanely busy this summer ☺

Oscar Godoy, Nathan Kraft, Jonathan Levine. 2014. Phylogenetic relatedness and the determinants of competitive outcomes. Ecology Letters.

Ecology is hard in part because of the things we can’t (at least easily) measure: fitness, interaction strengths, and the niche, all fundamental ecological concepts. Since we are unable to measure these concepts directly, ecologists have come up with proxies and correlates. Take Darwin’s hypothesis that competition should be greater between closely related species. It relies a chain of assumptions about proxy relationships – first that relatedness should correlate with greater similarity of traits, secondly that similar traits should correlate with greater niche overlap. The true concept of interest, the niche, is un-measurable (if it is an n-dimensional hypervolume) so instead shared evolutionary history provides possible insight into species coexistence.

Ecophylogenetic studies have adopted Darwin's hypothesis as an example of how  molecular phylogenies may provide information about evolutionary history which in turn informs current ecological interactions. Phylogenies ideally capture feature diversity, and so (all things being equal) should provide information about similarity between species based on their relationship.  Despite this, studies have been mixed in terms of finding the relationship predicted by Darwin between phylogenetic relatedness and competition. It is not clear whether this mixed result suggests problems with the phylogenetic approaches being used, or non-generality of Darwin’s hypothesis.

Oscar Godoy, Nathan Kraft, and Jonathan Levine attempt to explore this question once again, but through the lens of Chesson’s coexistence framework (2000). Chesson’s framework describes competitive differences between species not as a single quantity, but instead the outcome of both stabilizing niche differences and equalizing fitness differences between species. This framework predicts that competitive differences should be greatest when species have similar niches (low stabilizing niche differences) and/or when they have large differences in fitness. This divisions alters the predictions from Darwin's hypothesis: if closely related species have similar niches, they should compete more strongly, but on the other hand, if closely related species have similar fitnesses, they should compete less strongly. Darwin’s hypothesis as it has been tested may be too simplistic.

The authors used an experiment involving 18 California grassland species to look at first, whether competitive ability is conserved, and more generally to explore whether phylogenetic distance predicts “the niche differences that stabilize coexistence and the fitness differences that drive competitive exclusion?” Further, can this information be used to predict the relationship between phylogeny and competitive outcomes? To determine this, they quantified germination, fecundity, seed survival, and interaction coefficients for the 18 species based on competition with different competitors (both by identity and density), and quantified the strength of stabilizing and equalizing forces (as in previous works). With this information, they calculated for each species the average fitness and ranked species in a competitive hierarchy using a fully parameterized annual plant population model. Species’ competitive rank did in fact show a phylogenetic signal (Figure 1), and the strongest competitors were clustered in the Asteraceae and its sister node.

Fig 1. Relationship between competitive rank among the 18 CA grassland species.

Competitive rank was then decomposed into fitness differences and niche differences. Fitness differences showed the clearest relationship with phylogeny - distantly related competitors had significantly greater asymmetries in fitness, closely related species had similar fitnesses (Figure 2). However stabilizing niche differences showed no phylogenetic signal at all (Figure 3, solid line).

Fig. 2. Relationships between fitness differences and phylogenetic distance.

Fig 3. Solid line - observed niche distances as a function of phylogenetic distance. Dashed line, size of distances actually needed to assure coexistence.

The authors could then calculate, for a given pair of species with a given phylogenetic distance, the expected fitness difference (based on the fitness difference-phylogeny relationship), and given this, the amount of stabilizing niche differences that would be necessary to prevent competitive exclusion between pairs of species. When they did this, they found that the required stabilizing niche differences were much larger than those that actually existed between the plants. This was especially true between distant related species(dashed line, Figure 3). Darwin’s hypothesis, that closely related species should be more likely to coexist, seemed to be reversed for these species.

How should we interpret these results more broadly? Is this reinforcement of the use of phylogenetic information to answer ecological questions, provided the questions are asked correctly? One of the most interesting contributions of this paper is their discussion of the oft-seen, but poorly incorporated, increase in variation in a trait (here fitness differences) as phylogenetic distances increase. This uneven variance often leads to phylogenetic-trait correlations being labelled non-significant, since it violates the assumptions of linear models. In contrast, here the authors suggest that this uneven variance is important. “For example, even if on average, both niche and fitness differences increase with phylogenetic distance, the increasing variance in these relationships means that only distant relatives are likely combine large competitive asymmetries with small niche differences (rapid competitive exclusion), or large niche differences with small competitive asymmetries (highly stable coexistence). Overall, our results suggest that increasing variance in niche or fitness differences with phylogenetic distance may play a central role in determining the phylogenetic relatedness of coexisting species.”

This discussion is important for questions about phylogenetic relatedness and coexistence – variability is part of the answer, not evidence against the existence of such relationships. However, a few caveats seem important: Because fitness differences and niche differences as defined in the Chesson framework may not be easily associated with traits (since a single trait might contribute to both components), it seems that it will be a little difficult to expand these analyses to less rigourous experimental settings. This might also be important to hypothesize how fitness or niche differences per se become associated with phylogenetic differences, since traits/genes are actually under selection. But the paper definitely provides an interesting direction forward.

Chesson, P. 2000. Mechanisms of maintenance of species diversity. Annual Review of Ecology and Systematics 31:343-366.

Community structure - what are we missing?

Some of the most frequently used ecological concepts can be difficult to define. Sometimes this lack of clarity leads to a poor understanding and a weak base for further research. A great example is “community structure”, a concept frequently mentioned and rarely defined that probably changes a lot from use to use. The phrase “we’re interested in how communities are structured” is tossed around a lot, and I suppose an understood definition is that community structure encompasses the species that are present in a community and their abundances. Community structure may refer to  both a very simple concept (the abundances of species present in a community) and a very complicated one, connecting as it does mechanisms and models, observational data, and statistical measures. As a result, the precise way that ecologists delineate community structure and quantify it is both varied and vague.

The connection between models, community
structure and metrics.

In the literature, it seems that there are two ways of approaching “community structure”: bottom-up, in which community structure is a predicted outcome of theoretical models of different mechanisms, and top-down, in which community structure is measured in a relatively statistical or descriptive fashion. Both are valuable approaches: while statistical metrics often are interpreted as providing evidence for particular models or mechanisms, the reverse logic – that a model predicts particular results for a given metric – is rarely explicitly considered. Making connections between the model results and the descriptive metrics might actually be fairly difficult. Model predictions are often complex and multidimensional, predicting changes through time, growth rates, the combinations of species that can or cannot coexist (but only if assumptions hold), or particular relationships between measures like diversity, abundances, and range sizes. Metrics are necessarily confined to a few dimensions (or perhaps are ordination approaches), focus on straightforward observational measures like abundance and presence, and further include observational error (sampling, etc). Because community structure means something different to these two approaches, the connections between metrics and models are poorly explored. A theoretician might find it difficult to relate ordinations of communities with the typical predictions from a mathematical model (which might be something like growth rates in relation to changes in abundance), while someone collecting field data might feel that the data they can collect is difficult to relate to the predictions of models.

Part of the problem is that for a long time, the default focus was on what types of interactions structured communities (environment, competition, predation, mutualisms), and niches were assumed to be necessarily driving community structure. The type of measurements and metrics used reflected this search for niches (e.g. comparing environmental gradients with community structure). Many quantitative metrics may tell you something about how community structure relates to different variables (spatial, environment, biotic) and how much variation is still unexplained. The consideration that niches might not always be important eventually led ecologists to compare patterns in community structure to random, null, or neutral expectations. As a result, in the simplest cases the answers to questions about community structure and niches are binary – different from random (niches matter), or not. Looking for complex patterns predicted by models-for example, the relative contribution of niche based and neutral processes to community structure-is difficult using common metrics of community structure (although there are some papers that do a good job of this).

It is interesting that this problem of disconnection between theoretical models of community structure and community structure metrics received the most attention through criticisms of phylogenetic metrics of diversity. There, patterns of over- and under-dispersion were criticized for not being the necessary outcome from models of competition or environmental filtering (i.e. Mayfield and Levine 2010). While those criticisms were mostly fair, they are equally deserved in most studies of species diversity, where patterns in ordinations or beta-diversity are frequently used to infer mechanisms. In contrast, one of the best approaches thus far to integrating model predictions for community structure with metrics of community structure are null models. Though they differ greatly in ecological realism and complexity, null models suggest expected community structure or metric values if none of the expected processes are structuring a community.

One of the greatest failings of the top-down approach is that recognizing patterns outside of the expected, such as those that include stochasticity or a combination of different processes, or the effects of history, is nearly impossible. Models that can incorporate these complexities provide little suggestion of how the patterns we can easily record in communities might reflect complex structuring processes. Ecological research is limited by the poor connection between both top-down and bottom-up approaches and its vague definition of community structure. Patterns more complicated than those that the top-down approach searches for are likely being missed, while relations between models and metrics (or development of new metrics) aren’t considered often enough. One solution might be to more meaningfully define community structure, perhaps as the association (or lack thereof) between the combination of species present in a community and the combination of abiotic and/or biotic processes present. This association is generally compared to an association between species and processes that might arise from random effects alone. The difference is that structure shouldn’t be considered separately from the processes that produce it, and the connections should be explicitly rather than implicitly made.

Evolution on an ecological scale

Andrew Gonzalez, Ophélie Ronce, Regis Ferriere, and Michael E. Hochberg. 2013. Evolutionary rescue: an emerging focus at the intersection between ecology and evolution. Philos Trans R Soc Lond B Biol Sci. 368 (1610).doi: 10.1098/rstb.2012.0404 (Intro to special issue).

David A. Vasseur, Priyanga Amarasekare, Volker H. W. Rudolf, Jonathan M. Levine. 2011. Eco-Evolutionary Dynamics Enable Coexistence via Neighbor-Dependent Selection. The American Naturalist, Vol. 178, No. 5, pp.E96-E109.

Ecology and evolution are often treated as connected but ultimately discrete areas of study. Ecological processes are usually the main source of explanation for ecological patterns and  ecologists may ignore evolutionary processes under the assumption that these are most important over longer time scales than are of interest (e.g. speciation). However, there is also an increasing recognition that rapid evolutionary dynamics can contribute to ecological observations. In a time where rapid changes to climate and habitat are the greatest threats to most species, the suggestion that rapid evolution might play a role in extinction prevention and diversity maintenance is an important one.

Increasingly researchers are exploring this concept. The concept of evolutionary rescue (ER), has been particularly championed by Andy Gonzalez and Graham Bell of McGill University. ER results when evolution occurs fast enough to arrest population declines and allow populations to avoid extinction in the face of changing conditions. Changing conditions resulting in maladapted populations should result in population declines followed by extinction. However, if selection for resistant types (which are present in the population, or result from mutations) occurs, population declines can be countered. The result is a characteristic u-shape curve, showing the initial geometric decline, followed by a geometric increase – escape from extinction is then a balance between rates of evolution and success of resistant types compared to rates of population decline.

From Bell & Gonzalez 2009.

The question of whether evolution may have relevance to population declines is not precisely new, but it is especially relevant given we are in a period of habitat changes and extinction. A special issue of Proc B is focused only ER, on the question of its importance, prevalence, and predictability. Many of the articles extend theory, exploring assumptions about the type of environmental change, type and extent of the threat, presence of dispersal, spatial gradients, etc. A few articles attempt the more difficult task of testing for ER in natural systems and assessing its likely prevalence and value to conservation activities. It is an interesting journal issue and a great example of the importance of context in determining when an idea takes off. The theoretical background for evolutionary rescue has existed for many years, but it took the context of climate change (and perhaps the collaboration of an ecologist and evolutionary biologist?) for it to gain ground as an area of ecological research.

Another interesting paper, this one linking evolutionary dynamics with community coexistence, is from Vasseur et al. (2011). In this case, the authors suggest an evolutionary mechanism that could augment coexistence when ecological conditions allow for niche partitioning and that could allow coexistence when ecological conditions lead to competitive exclusion. If species exhibit tradeoffs between traits that are optimal for intraspecific interactions and traits that are optimal for interspecific interactions, evo-ecological dynamics can produce coexistence. Such tradeoff means that a species will be a superior interspecific competitor when rare and a poor interspecific competitor when common. Such a tradeoff creates neatly alternately selective pressures depending on whether a species is common (fitness declines) or rare (fitness increases). This is presented as a theoretical model, but it seems like in a tractable system one could easily test for changes in ecological and evolutionary pressures as predicted by the model.

No one would argue with the conclusion that a closer relationship between ecology and evolutionary biology would be beneficial for both. But in practice this seems to be the exception rather than the rule. "Evolutionary ecology" as it exists is fairly restricted, and if complaints about seminar topics is to provide a hint, most ecologists feel disconnected from evolutionary topics and vice versa. If evolutionary dynamics are relevant on an ecological scale, it seems that we should at least attempt to understand their prevalence and importance in natural systems.

Coexistence theory: community assembly's next great hope?

Rethinking Community Assembly through the Lens of Coexistence Theory
J. HilleRisLambers, P.B. Adler, W.S. Harpole, J.M. Levine, and M.M. Mayfield

The big (literally, at 24 pages) paper to read this year is a review by a number of well-known community ecologists that aims to package years of often contradictory and confusing results from community assembly research (Weiher & Keddy 2001) into a manageable package using coexistence theory. Coexistence theory arose particularly out of Peter Chesson’s work (particularly his own annual review paper (Chesson 2000)), and rests in the idea that coexistence between species is the result of a balance of stabilizing forces (i.e. niche differences) and equalizing forces (i.e. fitness similarity) between those species. Coexistence is stable when stabilizing forces dominate, so a species competes more strongly with itself than with other, more dissimilar, species. The most successful adaptations of this framework to “real world” experiments have come from Jonathan Levine’s lab (in collaboration with many of the coauthors on this work). Indeed, there are probably few people more qualified to attempt to re-explain the often complicated findings in community assembly research using coexistence theory.

The classic heuristic model for community assembly involves a regional species pool that is consecutively filtered through environmental and then biotic filters, selecting only for those species adapted to the local environment. While logically appealing, this model may have constrained thinking about assembly: after all, our definition of a niche recognizes that species are impacted by and impact their environments (Chase & Leibold 2003), and unlike a expectations for a biotic "filter", arrival order can alter the outcome of biotic interactions. But does coexistence theory do a better job of capturing these dynamics? 

The important message to take from coexistence theory, the authors suggest, is that stabilizing niche differences facilitate coexistence, whereas relative fitness differences drive competitive exclusion. And although this yields predictions about how similar or different coexisting species should be, coexistence theory diverges in a number of ways from trait-based or phylogenetic approaches to community assembly. “First, competitive exclusion can either preferentially eliminate taxa that are too functionally similar when trait differences function as stabilizing niche differences or preferentially eliminate all taxa that do not possess the near optimal trait when such trait differences translate into fitness differences. Second, both stabilizing niche differences and relative fitness differences are influenced by abiotic and biotic factors. For both reasons, patterns of trait dissimilarity or similarity cannot easily be used to infer the relative importance of environmental versus biotic (competitive) filters, which is an important goal of community assembly studies.”

There are a number of ways in which pre-existing research might provide evidence for the predictions of coexistence theory. You can look at studies which modify fitness differences between species (for example, through nutrient addition experiments), those which modify niche differences (for example, manipulating colonization differences between species), and those which manipulate the types of species competing to establish. You can take advantage of trait or phylogenetic information about communities (and traits are valuable because they provide a mechanistic linkage), although Mayfield and Levine (2010) have already shown there are clear limitations to such approaches. A particularly useful approach may be to look at demographic rates, particularly looking for frequency-dependent growth rates, an indicator of niche differences between species – when niche differences are large, species should have higher growth rates at low density (lower intraspecific competition) than at high density. And indeed, there is some evidence for the effect of fitness differences or niche differences on community composition.

Ultimately reanalyzing old research has its limitations: is it possible that nutrient additions leading to changes in community structure are evidence of fitness differences? Yes. Are there other possible explanations? Yes. Convincing evidence will take new studies, and the authors make some excellent  suggestions to this end: that we need to combine demographic and trait-based approaches so that assembly studies results suggest at mechanisms, not patterns. The focus would be on correlating niche and fitness differences with traits, rather than correlating traits with species’ presence or absence in the community. 

Given the muddle that is community assembly research, a review that offers a new approach is always timely, and this one is very comprehensive and sure to be well cited. Strangely, for me this paper perhaps lacked the moment of insight I felt when I read about coexistence theory being applied to invasive species (MacDougall et al 2009) or phylogenetic analyses of communities (Mayfield and Levine, 2010). There are a few reasons why that might be: one is that there are difficulties that are not well explored, particularly that traits may not realistically be able to be categorized in an either-niche-or-fitness fashion, and that abiotic and biotic factors can interact with traits. The predictions this framework makes for community assembly are less clear: even the tidiness of coexistence theory can't escape the complications of community assembly. But perhaps that is a pessimistic take on community assembly. Regardless, the paper has a lot to offer researchers and will hopefully encourage new work exploring the role of niche and fitness differences in community assembly.