Robert Sokal: Statistical giant in ecologists' boots

Robert Sokal (1960):
from Wikipedia

No student of my generation, trained in ecology and evolutionary biology, will not have heard of Sokal and Rholf’s Biometry textbook. Most would have used it in a class or to inform their analyses. Sadly, Robert Sokal passed away last month at the age of 86. He had a tremendous career, mostly at Stony Brook University in New York, and contributing to statistics and science for over half a century. As a testament to his impact, the third edition of Biometry has been cited over 14000 times! It is the canon for experimental design and analysis in the biological sciences.

He had extraordinary and tumultuous experiences as a youth -fleeing Nazi Germany and being raised in China. Whether, such experiences give rise to greatness, or whether his innate intellectual abilities sealed his destiny is an interesting question. Regardless, his impact and legacy will be deservedly long lasting.

47th Carnival of Evolution: catch the news.

The latest edition of the Carnival of Evolution is up at Evolving Thoughts. Read it, enjoy it, pass it along.

Community ecology is complicated: revisiting Robert May’s weak interactions

Stefano Allesina & Si Tang. 2012. Stability criteria for complex ecosystems. Nature 483, 205–208 (08 March 2012). doi:10.1038/nature10832.

When it comes to explaining species diversity, Stefano Allesina differs from the traditional approach. Community ecology has long focused on the role of two species interactions in determining coexistence (Lotka-Volterra models, etc), particularly in theory. The question then is whether two species interactions are representative of the interactions that are maintaining the millions of species in the world, and Allesina strongly feels that they are not.

In the paper “Stability criteria for complex ecosystems”, Stephano Allesina and Si Tang revisit and expand on an idea proposed by Robert May in 1972. In his paper “Will a large complex system be stable?” Robert May showed analytically that the probability a large system of interacting species is stable – i.e. will return to equilibrium following perturbation – is a function of the number of species and their average interactions strength. Systems with many species are more likely to be stable when the interactions among species are weak.

May’s paper was necessarily limited by the available mathematics of the time. His approach examined a large community matrix, with a large number of interacting species. The sign and strength of the interactions among species were chosen at random. Stability then could be assessed based on the sign of the eigenvalues of the matrix – if the eigenvalues of the matrix are all negative the system is likely to be stable. Solving for the distribution of the eigenvalues of such a large system relied on the semi-circle law for random matrices, and looking at more realistic matrices, such as those representing predator-prey, mutualistic, or competitive interactions, was not possible in 1972. However, more modern theorems for the distribution of eigenvalues from large matrices allowed Allesina and Tang to reevaluate May’s conclusions and expand them to examine how specific types of interactions affect the stability of complex systems.

Allesina and Tang examined matrices where the interactions among species (sign and strength) were randomly selected, similar to those May analyzed. They also looked at more realistic community matrices, for example matrices in which pairs of species have opposite-signed interactions (+ & -) representing predator prey systems (since the effect of a prey species is positive on its predator, but that predator has a negative effect on its prey). A matrix could also contain pairs of species with interactions of the same sign, creating a system with both competition (- & -) and mutualism (+ & +). When these different types of matrices were analyzed for stability, Allesina and Tang found that there was a hierarchy in which mixed competition/mutualism matrices were the least likely to be stable, random matrices (similar to those May used) are intermediate, and predator–prey matrices were the most likely to be stable (figure below).

When the authors looked at more realistic situations where the mean interaction strength for the matrix wasn’t zero (e.g. so a system could have all competitive or all mutualistic interactions), they found such systems were much less likely to be stable. Similarly, realistic structures based on accepted food web models (cascade or niche type) also resulted in less stable systems.

The authors reexamined May’s results that showed that weak interactions made large systems more likely to be stable. In particular they examined how the distribution of interactions strengths, rather than the mean value alone, affected system stability. In contrast to accepted ideas, they found that when there were many weak interactions, predator-prey systems tended to become less stable, suggesting that weak interactions destabilize predator-prey systems. In contrast, weak interactions tended to stabilize competitive and mutualistic systems. The authors concluded, “Our analysis shows that, all other things being equal, weak interactions can be either stabilizing or destabilizing depending on the type of interactions between species.” 

Approaching diversity and coexistence from the idea of large systems and many weak interactions  flies in the face of how much community ecology is practiced today. For that reason, it wouldn't be surprising if this paper has little influence. Allesina suggests that focusing on two species interactions is ultimately misleading, since if species experience a wide range of interactions that vary in strength and direction, sampling only a single interaction will likely misrepresent the overall distribution of interactions. Even when researchers do carry out experiments with multiple species, finding a result of very weak interactions between species is often interpreted as a failure to elucidate the processes maintaining diversity in the system. That said, Allesina’s work (which is worth reading, few people explain complex ideas so clearly) doesn’t necessarily make itself amenable to being tested or applied to concrete questions. Still, there’s unexplored space between traditional, two-species interactions and systems of weak interactions among many species, and exploring this space could be very fruitful. 

Disagreeing about ecology: how debate advances science

• Kraft N.J.B. et al. 2011. “Disentangling the Drivers of β-Diversity Along Latitudinal and Elevational Gradients” Science. Vol. 333:6050 pp.1755-1758
• Qian. H. et al. 2012. Comment on “Disentangling the Drivers of β Diversity Along Latitudinal and Elevational Gradients”. Science 30:1573.
• Tuomisto, H. and Ruokolainen, K. 2012. Comment on“Disentangling the Drivers of β Diversity Along Latitudinal and Elevational Gradients”. Science 30:1573.
• Kraft N.J.B. et al. 2012. Response to Comments on“Disentangling the Drivers of β Diversity Along Latitudinal and Elevational Gradients”. Science 30: 1573.

A good scientific debate makes for excellent spectator sport (although it’s probably less fun for the participants). Many of the best ecological debates are now classics of the literature—Diamond vs. Simerberloff, Lawton vs. Simberloff, Hubbell vs. many—and these historical debates influence present day ecology. Interestingly, debates in ecology seem to revolve around two particular issues: whether the data is appropriate and whether the methods are adequate to draw conclusions about a particular process.

As an example, there’s a typical ecological debate occurring in Science over Kraft et al.’s “Disentangling the drivers of β-diversity along latitudinal and elevational gradients”. In this paper, the authors reevaluate the mechanisms that drive changes in species identity along latitudinal and elevation gradients using a null model. Although β-diversity may vary along biogeographical gradients as a result of processes such as dispersal limitation, range size, and habitat filtering, total (γ) diversity also varies along these gradients (we know that richness is generally higher in the tropics and the lowlands). Since this suggests that γ- and β-diversity aren’t independent, it may be that changes in γ-diversity need to be accounted for as an explanation for changes in β-diversity (Chase 2011). When Kraft et al. controlled for γ-diversity using a null model, they found that the magnitude of β-diversity did not vary along latitudinal or elevational gradients. They stated that this means: “there may be no need to invoke differences in the mechanisms of community assembly in temperate versus tropical systems to explain these global-scale patterns of β-diversity.”

This conclusion is in contrast to multiple papers that have suggested that tropical communities are somehow structured differently from temperate communities. Such work has been far from conclusive, however, finding evidence for everything from stochastic assembly to microhabitat-driven assembly in tropical regions. However, given the strong conclusion from the Kraft et al. paper, it’s not surprising that there were several responses from other researchers of β-diversity (Tuomisto and Ruokolainen and Qian et al.). It’s also not surprising that the points raised in these responses are fairly typical for debates in community ecology, calling into question the suitability of the data, the appropriateness of the spatial scale for capturing the processes of interest, and the question of whether the methods are correct. The debate is as much about the fundamental questions of how we define and measure β-diversity as it is about the particulars of the Kraft et al. article.

For example, both Tuomisto and Ruokolainen and Qian et al. questioned the sampling design of the data, as to whether there was too much within-plot variation (Tuomisto and Ruokolainen) or, alternately, too little between-plot variation (Qian et al.) to correctly capture the amount of β-diversity. Tuomisto and Ruokolainen further suggested that the plots used in the original study undersample local (α) diversity and therefore overestimate the differences between plots. Both sets of authors suggest that inappropriate sampling would make it difficult to generalize Kraft et al.’s results to other studies of β-diversity. Kraft et al.’s response was that although plots are placed to minimize among-plot environmental variation, this does not make them inappropriate to test for finer scale evidence of environmental processes, and that β-diversity still varies markedly between plots. However, given that this debate - about whether there is a “best” spatial scale at which to examine the ecological causes of β-diversity and a “best” way to sample to capture variation among communities – is occurring among experienced β-diversity researchers suggests that these are still fuzzy areas.

Another aspect of this debate relates to the ongoing discussion about the appropriate definition and calculation of β-diversity (Tuomisto 2010). The most traditional methods define β-diversity as a multiplicative or additive function of α- and γ-diversity, and Kraft et al. argue that as a result β-diversity is not independent of those variables. To account for this fact, Kraft et al. use a null model that incorporates γ-diversity, to predict β-diversity under random or stochastic assembly. However, Tuomisto and Ruokolainen argue that the measure of β-diversity used (β_P = 1 – α/γ) is such that γ-diversity can vary without affecting β-diversity, provided alpha-diversity is also free to vary. However, Kraft et al. dispute this, suggesting that perfectly scaled changes in both γ- and α-diversity, such that β-diversity remains unchanged, represent a special case that does not appear in their data set.

Of course, other points were discussed among the authors. Qian et al. disagreed with the use of latitudinal gradients, noting that the ecological “meaning” of a given latitude is rather vague. However, given that the authors admit their site data is likely to capture small-scale variation in β-diversity, it seems that trying to relate their results to large-scale latitudinal or elevational gradients is a greater issue.

Kraft et al. suggested in their response that many of the criticisms were misunderstandings of the methods and findings of the original paper. You might more correctly say that disagreements like this capture important weaknesses or ambiguities in current understanding and theory. It’s true that at their worst, debates create conflict and that since responses are rarely peer-reviewed to the same extent the original publication is, too much weight may be given to meritless counter-arguments. However, good debate should drive progress, force researchers to reevaluate their assumptions, and ultimately hold science accountable. And for that reason it should be encouraged.

**I should note that this post is specifically meant in relation to debate among researchers, not to situations where scientists are in agreement and the debate is occurring in the public sphere.

NCEAS is dead; long live NCEAS. A view towards NCEAS 2.0.

"is this a wake or revival?" Jim Brown

March 21-22, 2012, Santa Barbara, CA. National Center for Ecological Analysis and Synthesis (NCEAS) symposium.

A special invitation- only symposium marking the end of NCEAS as we know it, saw a number of interesting talks and retrospectives about where NCEAS has been and where it is going. 170 people attended, including some former postdocs, working group participants and leaders in ecology. The reason for this introspective meeting is that NCEAS's core NSF funding is about to end, without renewel. Jim Brown's quote from his talk, whether we were here for a wake or a revival really captured the spirit of the meeting.

The goals were twofold. First was to look back and celebrate the accomplishments of NCEAS. University of California at Santa Barbara is globally one the top influential research institutions in the world, and this success has been driven in large part by the success of NCEAS. More than 5000 people have come to NCEAS and their efforts have resulted in thousands of publications, and many citation classics. The early visions of NCEAS were broad and fuzzy and by all accounts NCEAS has exceeded all expectations.

The second motivation for ts meeting was to think about the future. What can NCEAS be under different funding regimes, and how should it move forward? The is no doubt that it will be fundamentally different, but can there be a successful continuation of the NCEAS model, will it die, or will it give birth to a new enerprise, NCEAS 2.0?

The symposium saw great talks, from people like Jim Brown and Jane Lubchenco, and interesting panel discussions on numerous topics (see #treas2012 in twitter for synopsis of the meeting). There were a lot of past tense statements.

However, it was clear that there was much to celebrate. NCEAS clearly impacted ecology. Did its success simply coincide with cultural changes in the field or did it drive changes? The consensus was that it drove changes. It fostered large collaborations. Dave Tilman said that before NCEAS, ecology was largely local and lab-driven, but NCEAS offered a way to get people together to ask bigger questions. The postdoctoral fellows have been extremely successful, with the vast majority ending up in faculty positions in top institutions. It was acknowledged that many sub fields were created or coalesced at NCEAS, including disease ecology and metacommunity dynamics.

Why has it been so successful? NCEAS is a special inclusive place where people want to come, away from their responsibilities. The technical help here and expertise that made anything possible, any data challenges were overcome and analytical difficulties solved. Postdocs were given complete independence and were allowed to pursue collaboration and networking. Jim Brown remarked that NCEAS is the single greatest event in the history of ecology. Subfields now talk, lab projects are now geared towards collaboration and linkages with other work in ways that did not exist before.

So then, what will the future hold for NCEAS? The answer to this was left vague and uncertain. People argued for what NCEAS 2.0 should look like. For example, it was argued that NCEAS 2.0 should resurface something like science 2.0, making the focus data and data sharing, changing methods and philosophy of how science is done. Massive anonymous collaboration requires assumed standards and altruism. Other arguments focused on the need for NCEAS to reach out to new partners and to go global.

Peter Karieva said it well. NCEAS 2.0 should be interacting with major corporations, since they represent the drastic impacts on ecological systems around the world. 1.0 was about data accessability, 2.0 should about applicability and tools to affect change.

Whatever NCEAS 2.0 looks like, it will be different. There seems to be two ways forward. One is that it struggles to maintain its past activities or one that like the Phoenix rises from the ashes and boldly goes forward to again push the ecology in new directions.

On rejection: or, life in academia

I guess it’s not surprising, given that I’ve written about failure in science, that I would write a post about rejection as well. Actually, I’m not so interested in writing about rejection as I am in hearing how people have learned to deal with it.  

Academia is a strange workplace. It’s stocked with bright people who’ve been successful throughout their previous academic endeavours (with some exceptions*). For the most part, they haven’t faced too much criticism of their intellectual abilities. But in academia you will spend your career being questioned and criticized, in large part by your peers. You will constantly be judged (with every submitted manuscript, grant application, or tenure review). And this is the universal truth about academia: you will be rejected. And for some (many?) people, that's a difficult thing to accept.

Rejection may be so painful in part because it can be hard to interpret. After all, it’s an old trope that rejection is a normal part of academia. But how much rejection is normal, when is it just a numbers game and when is it a sign of professional failing? Let alone the fact that rejection depends on a shifting academic landscape where available funding, journal quotas, and research caliber are always changing. So I’m curious: does the ability to deal with rejection factor into academic success? Are some people, based on personality, more likely to weather rejections successfully, and does this translate into academic success? Or is the development of a thick skin just the inevitable outcome of an academic life?

*A couple of the people I know who are generally unfazed by rejections would say that they deal well with rejection because they weren’t particularly great students and so academic failure isn’t new or frightening to them. 

The niche as a changeable entity: phenotypic plasticity in community ecology

Schiffers, K. et al. 2011. Root plasticity buffers competition among plants: theory meets experimental data. Ecology. 92:3.

Ashton et al. 2010. Niche complementarity due to plasticity in resource use: plant partitioning of chemical N forms. Ecology. 91:11.

Nearly all explanations for coexistence in communities focus on differences between species. The scale of these differences may occur over large temporal (e.g. evolutionary history, phylogenetic relationships) or spatial scales (e.g. environmental tolerances), or at the scale of the individual. In plants, interactions at the local scale are given particular attention, including interactions mediated by trait differences between species. At finer scales still, there has been recent focus on differences between individuals of the same species, whether they are driven by genotypic differences (link) or plastic changes in individual phenotypes.

From Ashton et al. 2010

Phenotypic plasticity can be defined as phenotypic differences among individuals of the same genotype that occur in response to an environmental cue. The ability of plant species to alter their usage of resources, for example, has clear relevance to resource partitioning among species, since a given individual could adaptively take advantage of alternate resources in response to their particular competitive environment. In such a case, an individual’s realized niche is a function of phenotypic changes in response to the biotic and abiotic environment and thus physiologically-determined. This is in contrast to the usual approach to species’ niches, where physiological constraints are considered to determine a species’ fundamental niche. Although the plant literature shows clear examples of phenotypic plasticity among plants, including in response to competition (for example, perception of light quality leading to changes in growth form), the topic usually receives only passing mention in the community ecology literature.

The number of papers addressing questions of coexistence and competition through the lens of phenotypic plasticity is slowly rising.

From Schiffer et al. 2011, Lithium uptake is
significantly higher on the non-competitor side

A couple of papers from the last few years provide tantalizing glimpses into the possible contribution of plasticity to coexistence. In Schiffers et al. (2011), the authors use experimental and modeling approaches to test whether root uptake can change in response to the proximity of competitors. In the experimental study, the authors looked at the uptake of lithium (a stable nutrient that will be taken up in the place of potassium) by Bromus hordeaceus. They planted pairs of B. hordeaceus  at varying distances apart and then injected lithium into the soil at different differences from the focal plant. They found that lithium uptake was significantly higher on the non-competitor side of the focal plant than on the competitor side, suggesting that plastic changes in resource uptake occurred in response to competitor proximity. Modelling results from the same study suggest that plasticity may allow individuals minimize competitive pressure by making changes in belowground architecture, thereby using available space more efficiently.

Ashton et al. (2010) take a similar approach, looking at how the uptake of nutrients (in this case three forms of nitrogen (N)) varies among species depending on their competitive environment. They explored the ways in which plasticity could lead to changes in the realized niche. In particular, they explored two hypotheses: that plants would exhibit niche preemption, where the inferior competitor switched to a different form of nitrogen in the presence of the superior competitor; or dominant plasticity, where plasticity actually enhances competitive ability.  The authors looked at 4 species, 3 common and 1 rare(r), in an alpine tundra community, isolating naturally occurring pairs of each combination of species. These ‘competitive arenas’ were isolated, and other species within the arena were removed. After a year, the authors added N¹⁵ tracers to each arena, in three forms (NH4+, NO3-, and glycine): these tracers would allow them to track the N once it was incorporated into the plant tissue. The plants were then harvested and the amount of each type of nitrogen in each was measured. Plant biomass was also recorded, and used to estimate the ‘competitive response’ (basically the ratio of biomass when grown with a competitor compared biomass to when grown solo). Their findings were rather neat: the 3 common plants experienced no negative effect on biomass from growing in competition with the rare plant, but the rare plant had much lower biomass when grown in the presence of any of the common plants. Further, while the common plants showed changes in the form of N they used when growing with the rare plant, the rare plant did not switch its N preference. The rare plant’s lack of plasticity in response to competition may relate to its lower biomass when grown with superior competitors, and ultimately its lower abundance.

Although limited, these studies hint at the role that phenotypic plasticity could play in interspecific interactions. Unfortunately plasticity may be difficult to measure in many contexts, particularly since variation within a species can be attributed to genetic differences or phenotypic plasticity, and these factors must be teased apart. Further, there is an issue of differentiating the effects of resource limitations from ‘adaptive’ plastic changes in growth. While plants are relatively tractable for these types of studies (they’re sessile, they use limited abiotic resources), other organisms are less explored for a reason.

What these studies can’t address is the question of ‘how important is phenotypic plasticity, really’? Reviews of coexistence mechanisms list numerous possible ways by which coexistence is facilitated among species. For plants especially, the limited number of resources required for survival has lead to great consideration of the possible niche axes over which species can differentiate themselves. Phenotypic plasticity's contribution to coexistence may be that it provides another way by which plants can partition resources at very fine scales. And if nothing else, such results provide further evidence that variation within species may be an important component of coexistence.

Thanks to Kelly Carscadden for discussions on the topic.

Island biogeography explains how you feel about giving talks

A good null model is hard to find

de Bello, F. The quest for trait convergence and divergence in community assembly:are null-models the magic wand? Global Ecology and Biogeography, (Global Ecol.Biogeogr.) (2012) 21, 312–317

Ecologists have always found the question of how communities assemble to be of great interest. However, studies of community assembly are often thwarted by the large temporal and spatial scales over which processes occur, making experimental tests of assembly theory difficult. As a result, researchers are often forced to rely on observational data and make inferences about the mechanisms at play from patterns alone. While historical assembly research focused on inferring evidence of competition or environmental filtering from patterns of species co-occurrence, more recent research often looks at patterns of phylogenetic or trait similarity in a community to answer these questions. 

Not surprisingly, when methods rely heavily on observational data they are open to criticism: one of the most important outcomes of early community assembly literature was the recognition that patterns that appeared to support a hypothesis about competition or environmental filtering could in fact result by random chance. This ultimately lead to the widespread incorporation of null models, which are meant to simulate patterns that might be observed by random chance (or other processes not under study), against which the observed data can be compared. Patterns of functional and phylogenetic information in communities can also be compared against null expectations to ensure that patterns of phylogenetic or functional over- or under-dispersion can't arise due to chance alone. However, while null models are an important tool in assembly research, they are sometimes as the foolproof solution to all of its problems.

In a new paper by Francesco de Bello, the author states frankly “whilst reading null-model methods applied in the literature (indeed including my work), one may have the impression of reading a book of magic spells”. While null models are increasingly sophisticated, allowing researchers to determine which processes to control for and which to leave out, de Bello suggests that the decision to include or omit particular factors from a null model can be unclear, making it difficult to interpret results or compare results across studies. Further, results from null models may not mean what researchers expect them to mean.

Using the example of functional diversity (FD; variation in trait values among species in a community), de Bellow illustrates how null models may have different meanings than expected. Ideally, a null model for FD should produce random values of FD, against which the observed values of FD can be compared. Interpreting the difference between the observed and random results can be done using the standardized effect size (SES, the standardized difference between the observed and randomly generated FD values); SES values >0 show that traits are more divergent than expected by chance, suggesting competition structures communities. If SES<0, traits are more convergent than expected by chance, suggesting environmental conditions structure communities. Finally, if SES ~0, then trait values aren’t different from random. However, de Bello shows that the SES is driven by the observed FD values, because the ‘random’ FD values are dependent on the pool of observations sampled. This means that the values the null model produces are ultimately dependent on those observed values, despite the fact you plan to make inferences by comparing the null and observed values as though they are independent. For example, consider the situation where you are building a null model of community structure for plant communities found along two vegetation belts. If the null model is constructed using all the plant communities, regardless of the habitat they are found in, the resulting null FD value will be higher, since species that are dissimilar and found in different vegetation belts are being randomly selected as occurring in a community. If null models are constructed separately for both vegetation belts, the null FD value is lower, since species are more similar. The magnitude of the difference between the null model and the observed values, and further, the biological conclusions one would take from this study, would therefore depend on which null model was constructed.

from de Bello 2012, illustrating how combining species pools (right) can lead to entirely different decisions about whether communities are convergent or divergent in terms of traits than when they are considered separately (left, centre).

De Bello’s findings make important points about the limitations of null models, particularly for functional diversity, but likely for other types of response variable. The type of null model he explores is relatively simplistic (reshuffling of species among sites), and the suggestion that the species pool affects the null model is not unique (Shipley & Weiher, 1995). However, even sophisticated and complex null models need to be biologically relevant and interpretable, and null models are still frequently used incorrectly. Although only mentioned briefly, De Bello also notes another problem with studies of community assembly, which is that popular indices like FD, PD, and others may not always be able to distinguish correctly between different assembly mechanisms (Mouchet et al. 2010, Mayfield & Levine, 2010), something that null model do not control for. 

Should we still be testing neutral theory? If so, how?

Siepielski, A.M. , Hung, K-L., Bein, E.E.B, McPeek, M.A. 2010. Experimental evidence for neutral community dynamics governing an insect assemblage. Ecology. 91. 847-857

For many ecologists, neutral theory was a (good/bad, you choose) idea that dominated ecology for the last decade but failed to provide the burden of empirical proof necessary for its acceptance. Even its creator Stephen Hubbell  recently suggested that the controversial hypothesis is no longer a plausible description of community structure, going as far to say that it is “good starting point”, a “valuable null model”, and a “useful baseline” (in Etienne et al 2011). 

But ideas, when they’re shared, are no longer the sole property of their creators. Other researchers continue to study neutral theory, and despite the apparent consensus that neutral theory is not an important explanation of community structure and dynamics, papers testing neutral theory continue to be published. This leads to an important question: do we still want to test for neutral dynamics? And if we do, how should we approach it, given what we have learned from the past decade of strawman arguments and using pattern-based evidence for processes (e.g. looking at species-area relationships and species abundance distributions)? What empirical evidence would provide strong support for the predictions of neutral theory?

Damselfly larvae
(http://www.uta.edu/biology/robinson/odonate_research.htm)

In “Experimental evidence for neutral community dynamics governing an insect assemblage”, Siepielski et al. (2010) attempt to provide a more rigorous test of neutral theory using two Enallagma (damselfly) larvae. Siepielski et al. focus on changes in demographic rates (growth, mortality) in response to changes in species relative and total abundances. In particular, they predicted that if niche differences drive coexistence, increasing a species’ relative abundance should drive lower growth rates and higher mortality, since that species is above its equilibrium; lowered relative abundances should result in higher growth rates and lowered mortality since the species is below its equilibrium density. As a result, species should return to their equilibrial abundances. Raising the total abundances but leaving the relative abundances untouched should have similar demographic responses across species and have no effect on the relative abundances. In contrast, neutral theory predicts that if all species are equal, their demographic rates depend on the density of the entire group (total abundance) and not on each individual species’ relative abundance. Therefore the response of demographic rates to changes in species relative abundances, while the total abundance is held constant, should provide support to either neutral or niche theory.

For two Enallagma sp. larvae Siepielski et al. used cages in the littoral zone of lakes, with cages receiving different treatments of relative abundance and/or total abundance manipulation. The result of these manipulations were that replicates with increased total abundances and constant relative abundances had lowered per-capita growth rates, while replicates with manipulated relative abundances and constant total abundances showed no change in demographic rates. Both species had similar mortality rates across the experimental treatments, although their growth rates differed slightly. From these results, Siepielski et al. concluded that these species are ecologically equivalent.

One of the reasons work (such as this) from Mark McPeek’s lab is interesting is because he is an outlier: someone whose work is deeply rooted in a natural system, and yet who also argues that ecological equivalency seems plausible, and attempts to support that argument. Regardless of whether the Enallagma species are in fact ecologically equivalent, this paper provides an example of how coexistence theory can be more rigorously tested than simply observing species co-ocurrences and concluding species coexistence. Further, it provides some interesting discussion about whether ecological equivalency is possible within functional groups, with niche differences occurring between functional groups (see Leibold and McPeek 2006, and from MacNaughton and Wolf 1970 for similar suggestions). Future work might focus on questions such as how to capture the effects of small niche differences, which, if balanced against very similar fitnesses could explain stable coexistence. In addition, it might be valuable to look at how resources fluctuate and how much overlap there is in resource requirements among species, when looking at how growth and mortality change with species densities.

With Adam Siepielski, Mark McPeek also published the paper “On the evidence for species coexistence: a critique of the coexistence program” about the apparently lowered standards for tests of niche-based species coexistence compared to those of neutral theory. What is certainly true is that experimental tests of coexistence theory are often less rigorous than necessary to support any coexistence theory, and should strive to take a more rigorous approach. If nothing else, this will allow criticism of particular theories to focus on the ideas themselves, rather than on how those ideas were tested.