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. 

The European Ecology Federation Congress, day 3

*sorry for the delay in getting the last day up, I've been catching up. The first talk of the morning was by Georgina Mace -great talk, and I will have an extended post on it later. Here are the other talks. This meeting was great!

Elisa Thebault. This was a great talk. She talked about the structure and stability of mutualistc and antagonistic networks. Nested interactions means that several generalists and specialists, but specialists use the same resource as generalists and do list overlap with other specialists. She addressed two main questions. First are there differences between mutualistic and antagonistic networks? Second, do these differences have consequences for coexistence and stability? First question, herbivores seem to have less nestedness and interact with closely related plants, while pollinators are more nested but less phylogenetically structured. For the second question, with is examined using modeling, using coupled predator prey equations (with a positive effect in the mutualism model) and simulated communities. She looked at two types of stability, persistence of species and resilience. She showed some very interesting results, for mutualistic networks, connectence and diversity increase stability, while for antagonistic, the opposite. Because of diversity change in the simulation, the mutualistic networks become more nested and more connected, again the opposite for antagonistic network, which becaome less connected and nested. What happens when you put these interactions together with both mutualistc and antagonist models? The same patterns emerge with muralists being more nested and connected.

Pedro Jordano. He talked about the functional role of complex networks including different types of seed dispersers and pollinators. Can phylogenetic relationships explain patterns of interactions between the seed dispersers and plants. In degraded habitats, through hunting, only a restribected subset of species are interacting with plants. What is the minimum complexity required to maintain ecosystem function.

Jason Tylianakis. He talked about global change and ecosystem function. In an example dataset, soil resource availability and grazing intensity affected trait compositiona dn diverisyt and changed plant productivity. When resources are heterogeneous then diversity affects function, but not when resources were homogeneous. Across a gradient of land use intensitfication, networks become simpler with functional links being dominated by few species. He looked at 133 host-parasitoid interaction webs. These webs deviate from null expectation and some habitats were significantly less complex than predicted.

Daniel Stouffer. He talk about understanding species roles and importance in food webs. Different types of interactions (sub webs) have differential probabilities of being present. Certain motifs appear to differentially contribute to stability. This approach can inform species conservation if a particular species appears in different motifs that contribute to network function or stability. Certain species may be common in motifs that reduce stability. Using New Zealand river food webs, he asked three questions: is the benefit of species phylogenetically conserved -yes, certain clades add benefit. Are these benefits community specific? No, beneficial species are so in all communities (bit similar communities). How general are these results? He compared the results to webs elsewhere in the world. Similar species are similarly beneficial elsewhere.

-Here I lost my notes from Jane Memmott’s plenary talk (sorry Jane!). It was a great overview of her research in restoration. At the heart of her talk was about making restoration scientifically rigorous.

Henrique Pereira. His talk was on modeling the response of biodiversity to global change. Biodiversity indicators for global change are biassed towards North America and Europe and certain taxa. Major uncertainty in extinction rates and what are the sources of uncertainty? A big source is the differences in scenarios for land change and human population growth. Also lack of ecological knowledge. Finally there are differences between models. He proposes a countryside species area relationship (cSAR) instead of regular SAR, which assumes an uninhabited matrix. Multiplies area by the affinity of species to live in that area, and so as long as a species has an affinity greater than zero for marginal habitat, it can persist in those areas –changing our predictions about habitat loss on species persistence. The cSAR predicts much lower extinction rates compared to classical SARs. Need data to classify affinities, such as uses surveys to cluster species by where they are found. The cSAR fits real data better than SAR.

Christophe Randin. His presentation was on whether elevational limits of deciduous trees match their thermal latitudinal limits. Species often not at equilibrium with their predicted fundamental niche, may reflect dispersal limitation. Species should reach their equilibrium since climate change so much quicker. Based olots of data, he presented where the distributional limitation should be and examined the distance from that edge. Surprisingly, the latitudinal limit was less likely to be reached by. Species, thus they are lagging on mountains.

Rita Bastos. She used a Dynamic model for understanding the recovery of the Azorean bullfinch in a changing environment, a lot a land use change and invasive species. Specifically, the model is a stochastic, spatially explicit model that incorates environmental variables and projected habitat change. She was able to test different management scenarios. Certain management actions on habitats can significantly increase population sizes but not spread.

Diogo Alagador. He spoke on adjusting protected areas to account for climate range adjustments. Species will move with climate change, but reserves do not move. Planning must involve multiple potential reserves and likely assisted migration. It is difficult to extrapolate for multiple species. Persistence then is the product of suitablility and dispersal ability for a species for each time period in future projections. This can be summed across species. This was tested for seveal species across all major taxa. There is variability in persistence across species and are very sensitive to disperal pathways.

Emergent linkages in seemingly unconnected food chains

Food webs are notoriously complex, and a difficult aspect of ecology is to offer a priori model-derived predictions of food web processes. There are some ecologists, such Neo Martinez and Jordi Bascompte, who have advanced our understanding of the general mechanisms of food web properties and dynamics through tools such as network theory. Such advanced approaches rely on direct interactions among species, or at least indirect interactions that are mediated through changes in abundance of different network players. However, what is missing from our general understanding of food web interactions is the role that behavioral responses can affect patterns of consumption and network connectivity.

Washington State University ecologists, Renée Prasad and William Snyder convincingly show how behavioral responses to predation can fundamentally alter food web interactions and link previously independent predator-prey interactions. They used two spatially independent insect predator-prey links in a novel, factorially-designed experiment. The two food chains consisted of a ground-based one, where ground beetles consume fly eggs and a plant-based one, where green peach aphids feed on the plants and are consumed by lady beetles. Under the ground-based chain only, the ground-based chain plus aphids, or ground-based chain plus lady beetles, the ground beetles consume a high proportion of the fly eggs. However, when both aphids and lady beetles are present, aphids respond to lady beetles by dropping off the plants and the ground beetles switch from consuming fly eggs to aphids. Under this last treatment, very few fly eggs are consumed, fundamentally altering the strength of the linkages in the two food chains and connecting them together.

This research highlights the inherent complexity in trying to understand multispecies systems, where the actors potentially have behavioral responses to other species, changing the nature of interactions. These types of responses may also generally increase the connectedness of such networks, which may result in more stable food webs, but this would need to be empirically tested. Regardless, this type of experiment offers food-for-thought to scientists trying to work general processes into a broad understanding of food web dynamics.

Prasad, R., & Snyder, W. (2009). A non-trophic interaction chain links predators in different spatial niches Oecologia DOI: 10.1007/s00442-009-1486-7

Exotic plants integrate into plant-pollinator networks

At almost any spot on the globe, there are species present that are not native to that locale, having been transported by human activities. Whether and how exotic species impact communities is a multifaceted problem that requires understanding the multitude of direct and indirect species interactions that occur. In a paper published in the Proceedings of the Royal Society, B, Montserrat Vila and colleagues asked if exotic plants where integrated into plant-pollinator networks, and whether this integration had any observable impacts on these networks. This is an important question, as most ecological theory predicts that plant-pollinator networks are actually quite resilient to perturbations since most associations tend to be between generalists as opposed to the more susceptible specialists.

They studied invaded plant communities across Europe, observing pollinator visits to flowers in multiple 50 x 50 m plots. They calculated connectance as the number of interactions standardized by network size. They showed that exotics fully integrated into plant-pollinator networks. Exotic species accounted for 42% of all pollinator visits and 24% of all network connections -a testament to the overall abundance of exotics in many communities. However, these exotics did not affect overall changes in network connectedness, revealing that these networks are quite robust to invasions.

That said, researchers must now ask if this is true in networks that do contain high numbers of specialists (e.g., orchids) or if the relative few specialists in generalist-dominated systems are more susceptible to changes from exotics.

Vila, M., Bartomeus, I., Dietzsch, A., Petanidou, T., Steffan-Dewenter, I., Stout, J., & Tscheulin, T. (2009). Invasive plant integration into native plant-pollinator networks across Europe Proceedings of the Royal Society B: Biological Sciences, 276 (1674), 3887-3893 DOI: 10.1098/rspb.2009.1076

Mutualistic networks for beginners

Research on the role of positive interactions in ecology has been increasing rapidly in the last 15 years or so. An example of this is the study of mutualistic networks, which are among the most exciting and fast-moving areas of ecology. In the last few years a number of really amazing papers have shown that studying these networks can really increase our understanding of natural systems. In a recent review papers in Frontiers in Ecology and the Environment Jordi Bascompte describes briefly but thoroughly the history and current state of this field of research. Starting with observations by Charles Darwin, he describes the importance of positive interaction and how during many decades research had been focused on single plants or pollinator, or highly coevolved interactions which has produced fundamental information. However, now with this network approach a lot can be learn about their stability and effects of species extinctions, among many other aspects. A very interesting comparison that is made is with the Internet. Apparently, a lot has been learn from this human made network, where studies have shown that networks are more stable and resistant to random attacks if they are heterogeneous (some part of the network being much more connected than most) that if they are homogeneous (all nodes being equally important / connected). The internet is actually a heterogeneous network, and so are the mutualistic networks. Bascompte also mentions the role of non-reductionist approach to science in the study of this highly complex networks since studying the parts of the network doesn’t allow researches to fully understand its behavior (e.g. you can know a lot about pairs of interactive species, but it has been proven that it will not tell you about the stability of the network to say, the extinction of same of its members). Also, he highlights the role of multidisciplinary approaches to complex problems, since the study of mutualistic networks has relayed heavily on research from other areas of science.

Jordi Bascompte (2009). Mutualistic networks Frontiers in Ecology and the Environment DOI: 10.1890/080026