Species dynamics alter community diversity–biomass stability relationships

The relationship between community diversity and biomass variability remains a crucial ecological topic, with positive, negative and neutral diversity–stability relationships reported from empirical studies. Theory highlights the relative importance of Species–Species or Species–Environment interactions in driving diversity–stability patterns. Much previous work is based on an assumption of identical (stable) species‐level dynamics. We studied ecosystem models incorporating stable, cyclic and more complex species‐level dynamics, with either linear or non‐linear density dependence, within a locally stable community framework. Species composition varies with increasing diversity, interacting with the correlation of species' environmental responses to drive either positive or negative diversity–stability patterns, which theory based on communities with only stable species‐level dynamics fails to predict. Including different dynamics points to new mechanisms that drive the full range of diversity–biomass stability relationships in empirical systems where a wider range of dynamical behaviours are important.     

Persistence conditions of symmetric social hybridogenesis in haplo-diploid hymenoptera

In eusocial Hymenoptera species, females variably develop into either alate females (queens) or workers, and in most cases, caste differentiation is determined environmentally. Recently, however, female castes in two harvester ant species, Pogonomyrmex rugosus and P. barbatus, were found to be determined genetically in hybrid zones of these two species. In the hybrid populations, homozygous females (e.g. AA or BB) and heterozygous females (AB) develop into alate females and workers, respectively. This genetic caste determination system is called symmetric social hybridogenesis (SSH). It is clear that populations with SSH can persist only if all four genotypes (AA and BB females, and A and B males) coexist simultaneously. However, it is not obvious that these populations are always persistent when the four genotypes simultaneously exist. Here, we examined the stability and persistence of an SSH population using a simple mathematical model. According to the analysis of the model, the SSH population persists only when some conditions are satisfied: (1) each female mates with more than two males, and (2) male production increases less steeply than linearly with increasing numbers of workers in a colony, and alate female production increases more steeply than linearly with increasing numbers of workers, or (2') male production increases more steeply than linearly with increasing numbers of workers in a colony, and alate female production increases much more steeply than male production. Therefore, it is not obvious that SSH populations are maintained and are stable for long periods. We discuss whether these conditions are satisfied in real SSH populations.     

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.     

Linking biodiversity to ecosystem function: implications for conservation ecology

We evaluate the empirical and theoretical support for the hypothesis that a large proportion of native species richness is required to maximize ecosystem stability and sustain function. This assessment is important for conservation strategies because sustenance of ecosystem functions has been used as an argument for the conservation of species. If ecosystem functions are sustained at relatively low species richness, then arguing for the conservation of ecosystem function, no matter how important in its own right, does not strongly argue for the conservation of species. Additionally, for this to be a strong conservation argument the link between species diversity and ecosystem functions of value to the human community must be clear. We review the empirical literature to quantify the support for two hypotheses: (1) species richness is positively correlated with ecosystem function, and (2) ecosystem functions do not saturate at low species richness relative to the observed or experimental diversity. Few empirical studies demonstrate improved function at high levels of species richness. Second, we analyze recent theoretical models in order to estimate the level of species richness required to maintain ecosystem function. Again we find that, within a single trophic level, most mathematical models predict saturation of ecosystem function at a low proportion of local species richness. We also analyze a theoretical model linking species number to ecosystem stability. This model predicts that species richness beyond the first few species does not typically increase ecosystem stability. One reason that high species richness may not contribute significantly to function or stability is that most communities are characterized by strong dominance such that a few species provide the vast majority of the community biomass. Rapid turnover of species may rescue the concept that diversity leads to maximum function and stability. The role of turnover in ecosystem function and stability has not been investigated. Despite the recent rush to embrace the linkage between biodiversity and ecosystem function, we find little support for the hypothesis that there is a strong dependence of ecosystem function on the full complement of diversity within sites. Given this observation, the conservation community should take a cautious view of endorsing this linkage as a model to promote conservation goals. Received: 2 September 1999 / Accepted: 26 October 1999     

Evolutionary regime shifts in simulated ecosystems

Catastrophic regime shifts in ecosystems occur when the system is tipped into a new attractor state under some external forcing. Here we consider whether evolutionary adaptations within ecosystems can trigger similar transitions. We use an individual‐based, evolutionary model of interconnected ecosystems to analyze nonlinear changes in global state resulting from local adaptations. Transitions between periods of stability occur when new traits arise that allow exploitation of under‐utilized resources. Subsequent rapid growth of the population carrying the new trait causes abrupt environmental change that drives incumbent species extinct. We call these transitions ‘evolutionary regime shifts’. These internally generated perturbations can result in ecosystem collapse, followed by recovery to an alternate stable state, or occasionally system‐wide extinction. While these disruptions may have a negative impact on ecosystem productivity in individual simulation runs, mean results over many simulations show a trend for increasing ecosystem productivity and stability over time. Feedback between life and the abiotic environment in the model creates a ‘long‐tailed’ distribution of extinction sizes without any external trigger for large extinction events.     

Effective competition determines the global stability of model ecosystems

We investigate the stability of Lotka-Volterra (LV) models constituted by two groups of species such as plants and animals in terms of the intragroup effective competition matrix, which allows separating the equilibrium equations of the two groups. In matrix analysis, the effective competition matrix represents the Schur complement of the species interaction matrix. It has been previously shown that the main eigenvalue of this effective competition matrix strongly influences the structural stability of the model ecosystem. Here, we show that the spectral properties of the effective competition matrix also strongly influence the dynamical stability of the model ecosystem. In particular, a necessary condition for diagonal stability of the full system, which guarantees global stability, is that the effective competition matrix is diagonally stable, which means that intergroup interactions must be weaker than intra-group competition in appropriate units. For mutualistic or competitive interactions, diagonal stability of the effective competition is a sufficient condition for global stability if the inter-group interactions are suitably correlated, in the sense that the biomass that each species provides to (removes from) the other group must be proportional to the biomass that it receives from (is removed by) it. For a non-LV mutualistic system with saturating interactions, we show that the diagonal stability of the corresponding LV system close to the fixed point is a sufficient condition for global stability.     

Climate change alters stability and species potential interactions in a large marine ecosystem

We have little empirical evidence of how large‐scale overlaps between large numbers of marine species may have altered in response to human impacts. Here, we synthesized all available distribution data (>1 million records) since 1992 for 61 species of the East Australian marine ecosystem, a global hot spot of ocean warming and continuing fisheries exploitation. Using a novel approach, we constructed networks of the annual changes in geographical overlaps between species. Using indices of changes in species overlap, we quantified changes in the ecosystem stability, species robustness, species sensitivity and structural keystone species. We then compared the species overlap indices with environmental and fisheries data to identify potential factors leading to the changes in distributional overlaps between species. We found that the structure of the ecosystem has changed with a decrease in asymmetrical geographical overlaps between species. This suggests that the ecosystem has become less stable and potentially more susceptible to environmental perturbations. Most species have shown a decrease in overlaps with other species. The greatest decrease in species overlap robustness and sensitivity to the loss of other species has occurred in the pelagic community. Some demersal species have become more robust and less sensitive. Pelagic structural keystone species, predominately the tunas and billfish, have been replaced by demersal fish species. The changes in species overlap were strongly correlated with regional oceanographic changes, in particular increasing ocean warming and the southward transport of warmer and saltier water with the East Australian Current, but less correlated with fisheries catch. Our study illustrates how large‐scale multispecies distribution changes can help identify structural changes in marine ecosystems associated with climate change.     

Bottom-up effects of species diversity on the functioning and stability of food webs

1. The importance of species diversity for the stability of populations, communities and ecosystem functions is a central question in ecology. 2. Biodiversity experiments have shown that diversity can impact both the average and variability of stocks and rates at these levels of ecological organization in single trophic-level ecosystems. Whether these impacts hold in food webs and across trophic levels is still unclear. 3. We asked whether resource species diversity, community composition and consumer feeding selectivity in planktonic food webs impact the stability of resource or consumer populations, community biomass and ecosystem functions. We also tested the relative importance of resource diversity and community composition. 4. We found that resource diversity negatively affected resource population stability, but had no effect on consumer population stability, regardless of the consumer's feeding selectivity. Resource diversity had positive effects on most ecosystem functions and their stability, including primary production, resource biomass and particulate carbon, nitrogen and phosphorus concentrations. 5. Community composition, however, generally explained more variance in population, community and ecosystem properties than species diversity per se. This result points to the importance of the outcomes of particular species interactions and individual species' effect traits in determining food web properties and stability. 6. Among the stabilizing mechanisms tested, an increase in the average resource community biomass with increasing resource diversity had the greatest positive impact on stability. 7. Our results indicate that resource diversity and composition are generally important for the functioning and stability of whole food webs, but do not have straightforward impacts on consumer populations.     

Turing instability in pioneer/climax species interactions

Systems of pioneer and climax species are used to model interactions of species whose reproductive capacity is sensitive to population density in their shared ecosystem. Intraspecies interaction coefficients can be adjusted so that spatially homogeneous solutions are stable to small perturbations. In a reaction-diffusion pioneer/climax model we will determine the critical value of the diffusion rate of the climax species, below which the equilibrium solution is unstable to non-homogeneous perturbations. For diffusion rates smaller than this critical value, an equilibrium solution remains stable to spatially homogeneous perturbations but is unstable to non-homogeneous perturbations. A Turing (diffusional) bifurcation leads to the formation of spatial patterns in species' densities. Forcing, interpreted as stocking or harvesting of the species, can reverse the bifurcation and establish equilibrium solutions which are stable to small perturbations. The implicit function theorem is used to determine whether stocking or harvesting of one of the species in the model is the appropriate remedy for diffusional instability. The use of stocking or harvesting by a natural resource manager thus influences the long-term dynamics and spatial distribution of species in a pioneer/climax ecosystem.     

Evolutionary stability in Lotka-Volterra systems

The Lotka-Volterra model of population ecology, which assumes all individuals in each species behave identically, is combined with the behavioral evolution model of evolutionary game theory. In the resultant monomorphic situation, conditions for the stability of the resident Lotka-Volterra system, when perturbed by a mutant phenotype in each species, are analysed. We develop an evolutionary ecology stability concept, called a monomorphic evolutionarily stable ecological equilibrium, which contains as a special case the original definition by Maynard Smith of an evolutionarily stable strategy for a single species. Heuristically, the concept asserts that the resident ecological system must be stable as well as the phenotypic evolution on the "stationary density surface". The conditions are also shown to be central to analyse stability issues in the polymorphic model that allows arbitrarily many phenotypes in each species, especially when the number of species is small. The mathematical techniques are from the theory of dynamical systems, including linearization, centre manifolds and Molchanov's Theorem.     

On the generality of stability-complexity relationships in Lotka-Volterra ecosystems

Understanding how complexity persists in nature is a long-standing goal of ecologists. In theoretical ecology, local stability is a widely used measure of ecosystem persistence and has made a major contribution to the ecosystem stability-complexity debate over the last few decades. However, permanence is coming to be regarded as a more satisfactory definition of ecosystem persistence and has relatively recently become available as a tool for assessing the global stability of Lotka-Volterra communities. Here we document positive relationships between permanence and Lotka-Volterra food web complexity and report a positive correlation between the probability of local stability and permanence. We investigate further the frequency of discrepancy (attributed to fragile systems that are locally stable but not permanent or locally unstable systems that are permanent and have cyclic or chaotic dynamics), associate non-permanence with the local stability or instability of equilibria on the boundary of the state-space, and investigate how these vary with aspects of ecosystem complexity. We find that locally stable interior equilibria tend to have all locally unstable boundary equilibria. Since a locally stable boundary is inconsistent with permanent dynamics, this can explain the observed positive correlation between local interior stability and permanence. Our key finding is that, at least in Lotka-Volterra model ecosystems, local stability may be a better measure of persistence than previously thought.     

Phenotypic diversity and stability of ecosystem processes.

The resistance of an ecosystem to perturbations and the speed at which it recovers after the perturbations, which is called resilience, are two important components of ecosystem stability. It has been suggested that biodiversity increases the resilience and resistance of aggregated ecosystem processes. We test this hypothesis using a theoretical model of a nutrient-limited ecosystem in a heterogeneous environment. We investigate the stability properties of the model for its simplest possible configuration, i.e. , a system consisting of two plant species and their associated detritus and local resource depletion zones. Phenotypic diversity within the plant community is described by differences in the nutrient uptake and mortality rates of the two species. The usual measure of resilience characterizes the system as a whole and thus also applies to aggregated ecosystem processes. As a rule this decreases with increased diversity, though under certain conditions it is maximum for an intermediate value of diversity. Resistance is a property that characterizes each system component and process separately. The resistance of the inorganic nutrient pools, hence of nutrient retention in the ecosystem, decreases with increased diversity. The resistance of both total plant biomass and productivity either monotonically decreases or increases over part of the parameter range with increased diversity. Furthermore, it is very sensitive to parameter values. These results support the view that there is no simple relationship between diversity and stability in equilibrium deterministic systems, whether at the level of populations or aggregated ecosystem processes. We discuss these results in relation to recent experiments.     

Competitive coexistence of two predators utilizing the same prey under constant environmental conditions

A model for an ecosystem consisting of two predator species and a single prey species was developed. Computer calculations showed that there is a range of parameters that results in permanent coexistence of all three species. This is in apparent contradiction to the competitive exclusion principle and to a theorem of Volterra that no odd membered ecosystem can persist. This remains an exception to the usual formulations of the former principle, but not to the latter statement which excludes even dynamic stability to three membered ecosystems. The model chosen here made allowance for self-competition of the prey species, whereas self-competition is frequently neglected.     

Temporal stability in forest productivity increases with tree diversity due to asynchrony in species dynamics

Theory predicts a positive relationship between biodiversity and stability in ecosystem properties, while diversity is expected to have a negative impact on stability at the species level. We used virtual experiments based on a dynamic simulation model to test for the diversity–stability relationship and its underlying mechanisms in Central European forests. First our results show that variability in productivity between stands differing in species composition decreases as species richness and functional diversity increase. Second we show temporal stability increases with increasing diversity due to compensatory dynamics across species, supporting the biodiversity insurance hypothesis. We demonstrate that this pattern is mainly driven by the asynchrony of species responses to small disturbances rather than to environmental fluctuations, and is only weakly affected by the net biodiversity effect on productivity. Furthermore, our results suggest that compensatory dynamics between species may enhance ecosystem stability through an optimisation of canopy occupancy by coexisting species.     

Conservation implications of the link between biodiversity and ecosystem functioning

The relationship between biodiversity and individual ecosystem processes is often asymptotic, saturating at relatively low levels, with some species contributing more strongly than others. This has cast doubt on arguments for conservation based on maintenance of the functioning of ecosystems. However, we argue that the link between biodiversity and ecosystem functioning is an important additional argument for conservation for several reasons. (1) Although species differ in importance to ecosystem processes, we do not believe that this argues for preservation of just a few species for two reasons: first, it is nearly impossible to identify all species important to the numerous systems and processes on which humans depend; second, the important species themselves may depend on an unknown number of other species in their communities. (2) Arguments for conservation based on ecosystem functioning are complementary to other utilitarian, ethical and aesthetic justifications. No single reason will convince all people or protect all species, however the combination produces a strong case for conservation of biodiversity. (3) Even if the relationship between biodiversity and ecosystem functioning is asymptotic at local spatial scales and in the short term, effects of biodiversity loss are likely to be important at larger temporal and spatial scales. (4) Initial arguments for the importance of biodiversity for ecosystem functioning were largely based on a precautionary approach (points 1-3). However, we are now moving to a scientific position based on accumulating experimental evidence. The future challenge is the integration of this scientific research with policy.     

The Lotka-Volterra predator-prey model with foraging-predation risk trade-offs

This article studies the effects of adaptive changes in predator and/or prey activities on the Lotka-Volterra predator-prey population dynamics. The model assumes the classical foraging-predation risk trade-offs: increased activity increases population growth rate, but it also increases mortality rate. The model considers three scenarios: prey only are adaptive, predators only are adaptive, and both species are adaptive. Under all these scenarios, the neutral stability of the classical Lotka-Volterra model is partially lost because the amplitude of maximum oscillation in species numbers is bounded, and the bound is independent of the initial population numbers. Moreover, if both prey and predators behave adaptively, the neutral stability can be completely lost, and a globally stable equilibrium would appear. This is because prey and/or predator switching leads to a piecewise constant prey (predator) isocline with a vertical (horizontal) part that limits the amplitude of oscillations in prey and predator numbers, exactly as suggested by Rosenzweig and MacArthur in their seminal work on graphical stability analysis of predator-prey systems. Prey and predator activities in a long-term run are calculated explicitly. This article shows that predictions based on short-term behavioral experiments may not correspond to long-term predictions when population dynamics are considered.     

Biodiversity dynamics of freshwater wetland ecosystems affected by secondary salinisation and seasonal hydrology variation: a model-based study

Freshwater wetlands worldwide are under threat from secondary salinisation and climate change. Given that many freshwater wetlands naturally have highly variable hydrology, it is important to understand the combined effects of salinity and water regime on wetland biodiversity. Here a mathematical model has been developed to explore the biodiversity dynamics of freshwater wetland ecosystems affected by secondary salinisation and seasonal hydrology variation. The model shows that seasonal hydrological change can drive the wetland ecosystem into a stable oscillatory state of biodiversity, with the same period as the wetting and drying cycle. The initial condition of a wetland mediates the ecological response of the wetland ecosystem to salinity and seasonal variability. There are two manifestations of stability that occur in relation to wetland biodiversity: monostability and bistability. In model simulations, some wetland ecosystems may respond to the effects of seasonal change quickly, while others may do so more slowly. In ‘slow response’ wetlands, seasonal variability has a weak impact on the ecosystem properties of stability, resilience, sensitivity and the species richness–mean salinity relationship. In contrast, ‘fast response’ wetlands are seasonally controlled heavily. Seasonal variability can play a critical role in determining ecosystem properties. Changes in the strength of seasonality can induce the transition between monostability and bistability. Seasonal variability may also reduce wetland resilience, exacerbating the risk of secondary salinisation. On the other hand, seasonal variability may provide opportunities for the restoration of salinised wetlands by increasing their sensitivity to management actions and facilitating recovery processes. Model simulations show that the response of the stable biodiversity oscillation to changing mean salinity is dependent on seasonality strength (primarily for fast response wetlands) and other wetland conditions. Generally, there are two types of wetland responses to changes in mean salinity: type 1 wetlands exhibit a graded response of species richness (a surrogate for biodiversity), whereas a hysteretic response occurs in type 2 wetlands. Species diversity displays critical behaviour: regime shifts in diversity occur at the thresholds of mean salinity, strength of seasonality or initial species diversity. The predictions are consistent with previously-published field observations in salinised freshwater wetlands. Handling editor: D. Hamilton     

Coupling of green and brown food webs and ecosystem stability

Ecosystems comprise living organisms and organic matter or detritus. In earlier community ecology theories, ecosystem dynamics were normally understood in terms of aboveground, green‐world trophic interaction networks, or food webs. Recently, there has been growing interest in the role played in ecosystem dynamics by detritus in underground, brown‐world interactions. However, the role of decomposers in the consumption of detritus to produce nutrients in ecosystem dynamics remains unclear. Here, an ecosystem model of trophic food chains, detritus, decomposers, and decomposer predators demonstrated that decomposers play a totally different role than that previously predicted, with regard to their relationship between nutrient cycling and ecosystem stability. The high flux of nutrients due to efficient decomposition by decomposers increases ecosystem stability. However, moderate levels of ecosystem openness (with movement of materials) can either greatly increase or decrease ecosystem stability. Furthermore, the stability of an ecosystem peaks at intermediate openness because open systems are less stable than closed systems. These findings suggest that decomposers and the food‐web dynamics of brown‐world interactions are crucial for ecosystem stability, and that the properties of decomposition rate and openness are important in predicting changes in ecosystem stability in response to changes in decomposition efficiency driven by climate change.     

Grazing-induced losses of biodiversity affect the transpiration of an arid ecosystem

Degradation processes often lead to species loss. Such losses would impact on ecosystem functioning depending on the extinction order and the functional and structural aspects of species. For the Patagonian arid steppe, we used a simulation model to study the effects of species loss on the rate and variability (i.e. stability) of transpiration as a key attribute of ecosystem functioning. We addressed (1) the differences between the overgrazing extinction order and other potential orders, and (2) the role of biomass abundance, biomass distribution, and functional diversity on the effect of species loss due to overgrazing. We considered a community composed of ten species which were assigned an order of extinction due to overgrazing based on their preference by livestock. We performed four model simulations to test for overgrazing effects through different combinations of species loss, and reductions of biomass and functional diversity. In general, transpiration rate and variability were positively associated to species richness and remained fairly constant until half the species were lost by overgrazing. The extinction order by overgrazing was the most conservative of all possible orders. The amount of biomass was more important than functional diversity in accounting for the impacts of species richness on transpiration. Our results suggest that, to prevent Patagonian steppes from shifting to stable, low-production systems (by overgrazing), maintaining community biomass is more important than preserving species richness or species functional diversity.     

Theoretical analysis of mixed Plasmodium malariae and Plasmodium falciparum infections with partial cross-immunity

A deterministic model for assessing the dynamics of mixed species malaria infections in a human population is presented to investigate the effects of dual infection with Plasmodium malariae and Plasmodium falciparum. Qualitative analysis of the model including positivity and boundedness is performed. In addition to the disease free equilibrium, we show that there exists a boundary equilibrium corresponding to each species. The isolation reproductive number of each species is computed as well as the reproductive number of the full model. Conditions for global stability of the disease free equilibrium as well as local stability of the boundary equilibria are derived. The model has an interior equilibrium which exists if at least one of the isolation reproductive numbers is greater than unity. Among the interesting dynamical behaviours of the model, the phenomenon of backward bifurcation where a stable boundary equilibrium coexists with a stable interior equilibrium, for a certain range of the associated invasion reproductive number less than unity is observed. Results from analysis of the model show that, when cross-immunity between the two species is weak, there is a high probability of coexistence of the two species and when cross-immunity is strong, competitive exclusion is high. Further, an increase in the reproductive number of species i increases the stability of its boundary equilibrium and its ability to invade an equilibrium of species j. Numerical simulations support our analytical conclusions and illustrate possible behaviour scenarios of the model.