The paradox of the clumps mathematically explained

The lumpy distribution of species along a continuous one-dimensional niche axis recently found by Scheffer and van Nes (Scheffer and van Ness 2006) is explained mathematically. We show that it emerges simply from the eigenvalue and eigenvectors of the community matrix. Both the transient patterns—lumps and gaps between them—as well as the asymptotic equilibrium are explained. If the species are evenly distributed along the niche axis, the emergence of these patterns can be demonstrated analytically. The more general case, of randomly distributed species, shows only slight deviations and is illustrated by numerical simulation. This is a robust result whenever the finiteness of the niche is taken into account: it can be extended to different analytic dependence of the interaction coefficients with the distance on the niche axis (i.e., different kernel interactions), different boundary conditions, etc. We also found that there is a critical value both for the width of the species distribution s and the number of species n below which the clusterization disappear

Use of open-top chambers to study the effect of climate change in aquatic ecosystems

The aim of this research was to explore the possibility to use inexpensive open-top chambers (OTCs) as passive artificial warming devices in experimental aquatic studies. Our results show that OTCs give a significant temperature increase compared with the control. The measured increase (up to an average of 2.3°C) corresponds with predicted climatic warming. Due to their open top, the light quantity and quality is only minimally reduced. We found that OTCs are especially suited for studying the effect of climate change in small waters as the vertical temperature gradients remain unchanged. They can also easily be transported to remote environments. We discuss other advantages and disadvantages of these devices for aquatic studies and compare them with other warming devices

slow recovery from perturbations as a generic indicator of a nearby catastrophic shift

The size of the basin of attraction in ecosystems with alternative stable states is often referred to as "ecological resilience." Ecosystems with a low ecological resilience may easily be tipped into an alternative basin of attraction by a stochastic event. Unfortunately, it is very difficult to measure ecological resilience in practice. Here we show that the rate of recovery from small perturbations (sometimes called "engineering resilience") is a remarkably good indicator of ecological resilience. Such recovery rates decrease as a catastrophic regime shift is approached, a phenomenon known in physics as "critical slowing down." We demonstrate the robust occurrence of critical slowing down in six ecological models and outline a possible experimental approach to quantify differences in recovery rates. In all the models we analyzed, critical slowing down becomes apparent quite far from a threshold point, suggesting that it may indeed be of practical use as an early warning signal. Despite the fact that critical slowing down could also indicate other critical transitions, such as a stable system becoming oscillatory, the robustness of the phenomenon makes it a promising indicator of loss of resilience and the risk of upcoming regime shifts in a system

Omnivory by planktivores stabilizes plankton dynamics, but may either promote or reduce algal biomass

Classical models of phytoplankton–zooplankton interaction show that with nutrient enrichment such systems may abruptly shift from limit cycles to stable phytoplankton domination due to zooplankton predation by planktivorous fish. Such models assume that planktivorous fish eat only zooplankton, but there are various species of filter-feeding fish that may also feed on phytoplankton. Here, we extend these classical models to systematically explore the effects of omnivory by planktivorous fish. Our analysis indicates that if fish forage on phytoplankton in addition to zooplankton, the alternative attractors predicted by the classical models disappear for all realistic parameter settings, even if omnivorous fish have a strong preference for zooplankton. Our model also shows that the level of fish biomass above which zooplankton collapse should be higher when fish are omnivorous than when fish are zooplanktivorous. We also used the model to explore the potential effects of the now increasingly common practice of stocking lakes with filter-feeding fish to control cyanobacteria. Because omnivorous filter-feeding fish forage on phytoplankton as well as on the main grazers of phytoplankton, the net effect of such fish on the phytoplankton biomass is not obvious. Our model suggests that there may be a unimodal relationship between the biomass of omnivorous filter-feeding fish and the biomass of phytoplankton. This implies that to manage for reductions in phytoplankton biomass, heavy stocking or strong reduction of such fish is bes

Spatial correlation as leading indicator of catastrophic shifts

Generic early-warning signals such as increased autocorrelation and variance have been demonstrated in time-series of systems with alternative stable states approaching a critical transition. However, lag times for the detection of such leading indicators are typically long. Here, we show that increased spatial correlation may serve as a more powerful early-warning signal in systems consisting of many coupled units. We first show why from the universal phenomenon of critical slowing down, spatial correlation should be expected to increase in the vicinity of bifurcations. Subsequently, we explore the applicability of this idea in spatially explicit ecosystem models that can have alternative attractors. The analysis reveals that as a control parameter slowly pushes the system towards the threshold, spatial correlation between neighboring cells tends to increase well before the transition. We show that such increase in spatial correlation represents a better early-warning signal than indicators derived from time-series provided that there is sufficient spatial heterogeneity and connectivity in the syste

Effects of submerged vegetation on water clarity across climates

A positive feedback between submerged vegetation and water clarity forms the backbone of the alternative state theory in shallow lakes. The water clearing effect of aquatic vegetation may be caused by different physical, chemical, and biological mechanisms and has been studied mainly in temperate lakes. Recent work suggests differences in biotic interactions between (sub)tropical and cooler lakes might result in a less pronounced clearing effect in the (sub)tropics. To assess whether the effect of submerged vegetation changes with climate, we sampled 83 lakes over a gradient ranging from the tundra to the tropics in South America. Judged from a comparison of water clarity inside and outside vegetation beds, the vegetation appeared to have a similar positive effect on the water clarity across all climatic regions studied. However, the local clearing effect of vegetation decreased steeply with the contribution of humic substances to the underwater light attenuation. Looking at turbidity on a whole-lake scale, results were more difficult to interpret. Although lakes with abundant vegetation (>30%) were generally clear, sparsely vegetated lakes differed widely in clarity. Overall, the effect of vegetation on water clarity in our lakes appears to be smaller than that found in various Northern hemisphere studies. This might be explained by differences in fish communities and their relation to vegetation. For instance, unlike in Northern hemisphere studies, we find no clear relation between vegetation coverage and fish abundance or their diet preference. High densities of omnivorous fish and coinciding low grazing pressures on phytoplankton in the (sub)tropics may, furthermore, weaken the effect of vegetation on water clarity

Large species shifts triggered by small forces

Changes in species composition of communities seem to proceed gradually at first sight, but remarkably rapid shifts are known to occur. Although disrupting disturbances seem an obvious explanation for such shifts, evidence for large disturbances is not always apparent. Here we show that complex communities tend to move through occasional catastrophic shifts in response to gradual environmental change or evolution. This tendency is caused by multiple attractors that may exist in such systems. We show that alternative attractors arise robustly in randomly generated multispecies models, especially if competition is symmetrical and if interspecific competition is allowed to exceed intraspecific competition. Inclusion of predators as a second trophic level did not alter the results greatly, although it reduced the probability of alternative attractors somewhat. These results suggest that alternative attractors may commonly arise from interactions between large numbers of species. Consequently, the response of complex communities to environmental change is expected to be characterized by hysteresis and sudden shifts. Some unexplained regime shifts observed in ecosystems could be related to alternative attractors arising from complex species interactions. Additionally, our results support the idea that ancient mass extinctions may partly be due to an intrinsic loss of stability of species configurations

Shallow lakes theory revisited: various alternative regimes driven by climate, nutrients, depth and lake size

Shallow lakes have become the archetypical example of ecosystems with alternative stable states. However, since the early conception of that theory, the image of ecosystem stability has been elaborated for shallow lakes far beyond the simple original model. After discussing how spatial heterogeneity and fluctuation of environmental conditions may affect the stability of lakes, we review work demonstrating that the critical nutrient level for lakes to become turbid is higher for smaller lakes, and seems likely to be affected by climatic change too. We then show how the image of just two contrasting states has been elaborated. Different groups of primary producers may dominate shallow lakes, and such states dominated by a particular group may often represent alternative stable states. In tropical lakes, or small stagnant temperate waters, free-floating plants may represent an alternative stable state. Temperate shallow lakes may be dominated alternatively by charophytes, submerged angiosperms, green algae or cyanobacteria. The change of the lake communities along a gradient of eutrophication may therefore be seen as a continuum in which gradual species replacements are interrupted at critical points by more dramatic shifts to a contrasting alternative regime dominated by different species. The originally identified shift between a clear and a turbid state remains one of the more dramatic examples, but is surely not the only discontinuity that can be observed in the response of these ecosystems to environmental change

Climate-dependent CO2 emissions from lakes

Inland waters, just as the world's oceans, play an important role in the global carbon cycle. While lakes and reservoirs typically emit CO2, they also bury carbon in their sediment. The net CO2 emission is largely the result of the decomposition or preservation of terrestrially supplied carbon. What regulates the balance between CO2 emission and carbon burial is not known, but climate change and temperature have been hypothesized to influence both processes. We analyzed patterns in carbon dioxide partial pressure (pCO2) in 83 shallow lakes over a large climatic gradient in South America and found a strong, positive correlation with temperature. The higher pCO2 in warmer lakes may be caused by a higher, temperature-dependent mineralization of organic carbon. This pattern suggests that cool lakes may start to emit more CO2 when they warm up because of climate ch