A conceptual model of the dynamics of the Syamozero Lake community

We present a conceptual mathematical model of the dynamics of a spatially heterogeneous population system whose prototype is the fish community of Lake Syamozero. Analysis of the solutions of this model is used to demonstrate that interactions between the predator and prey populations in two neighboring biotopes (the pelagic and coastal zones) may result in either undamped oscillations or steady states of the population sizes. The model population densities are of the same order of magnitude as the values obtained in long-term observations of the Syamozero biota. It is also demonstrated that the transition to steady states may be accompanied by long-term (dozens or hundreds of years) damped oscillations of the prey and predator population densities. Under natural conditions, long transitional periods may prevent fish communities from reaching stationary modes.     

Invasion of an intermediate predator: the dynamics of fish populations in the mathematical model of a trophic chain (as applied to the Syamozero lake)

We present a mathematical model of the dynamics of a spatially heterogeneous predator-prey population system. A prototype of the model system is the Syamozero lake fish community. We study the impact of the invader, an intermediate predator, on the dynamics of the fish community. We show that the invasion can lead to the appearance of chaotic oscillations in the population density. We show also that different dynamical regimes resulting from the invasion, i.e., stationary, non-chaotic oscillatory and chaotic ones, can coexist. The "choice" of a specific regime therewith depends on the initial invader density. Our analysis of solutions of the mathematical models shows that the successful invasion of the alien species takes place solely in the absence of the competition between the invaders and the native species.     

Interdependence of plankton spatial distribution and plancton biomass temporal oscillations: mathematical simulation

The dynamics of aquatic biological communities in a patchy environment is of great interest in respect to interrelations between phenomena at various spatial and time scales. To study the complex plankton dynamics in relation to variations of such a biologically essential parameter as the fish predation rate, we use a simple reaction-diffusion model of trophic interactions between phytoplankton, zooplankton, and fish. We suggest that plankton is distributed between two habitats one of which is fish-free due to hydrological inhomogeneity, while the other is fish-populated. We show that temporal variations in the fish predation rate do not violate the strong correspondence between the character of spatial distribution of plankton and changes of plankton biomass in time: regular temporal oscillations of plankton biomass correspond to large-scale plankton patches, while chaotic oscillations correspond to small-scale plankton patterns. As in the case of the constant fish predation rate, the chaotic plankton dynamics is characterized by coexistence of the chaotic attractor and limit cycle.     

Invasion of an intermediate predator: Fish population dynamics in a mathematical model of a trophic chain (As applied to Syamozero lake)

A mathematical model is presented for the dynamics of a spatially heterogeneous predator-prey population system; a prototype is the Syamozero lake fish community. We show that the invasion of an intermediate predator can evoke chaotic oscillations in the population densities. We also show that different dynamic regimes (stationary, nonchaotic oscillatory, and chaotic) can coexist. The “choice” of a particular regime depends on the initial invader density. Analysis of the model solutions shows that invasion of an alien species is successful only in the absence of competition between the juvenile invaders and the native species.     

A conceptual model of the dynamics of the Syamozero lake community

We have developed a conceptual mathematical model of the dynamics of a spatially heterogeneous population system, the prototype of which is the Syamozero lake fish community. Based on the analysis of solutions of the model, we show that interrelations between prey and predator populations in two neighboring habitats (pelagic and offshore zones) can lead to both undamped oscillations and stationary values of the population size. The population density was found to be close to the values oblained in the course of long-term observations of the biota of the Syamozero lake. Besides, we showed that the transition to the stationary states can be accompanied by long-term (dozens and hundreds of years) damped oscillations of the prey and predator population size. In natural waters, long-term transition periods can prevent the attainment of stationary regimes of fish community functioning.     

A conceptual mathematical model of the aquatic communities of lakes Naroch and Myastro (Belarus)

A conceptual mathematical model of the dynamics of fish and zooplankton (rotifer) populations of connected lakes Naroch and Myastro (Belarus) is built and examined with parameters based on field data. It is shown that community coupling and trophic interactions give rise to both regular and irregular oscillations in population numbers.     

Seasonal migration determined by a trade-off between predator avoidance and growth

Migration is a common phenomenon in many organisms, terrestrial as well as aquatic, and considerable effort has been spent to understand the evolution of migratory behaviour and its consequences for population and community dynamics. In aquatic systems, studies on migration have mainly been focused on commercially important fish species, such as salmon and trout. However, seasonal mass-migrations may occur also among other freshwater fish, e.g. in cyprinids that leave lakes and migrate into streams and wetlands in the fall and return back to the lake in spring. In a conceptual model, we hypothesized that this is an adaptive behaviour in response to seasonal changes in predation (P) and growth (G) and that migrating fish change habitat so as to minimise the ratio between predation mortality and growth rate (P/G). Estimates from bioenergetic modelling showed that seasonal changes in the ratio between predator consumption rate and prey growth rate followed the predictions from the conceptual model and also gave more precise predictions for the timing of the habitat change. By quantifying the migration of more than 1800 individually marked fish, we showed that actual migration patterns followed predictions with a remarkable accuracy, suggesting that migration patterns have evolved in response to seasonally fluctuating trade-offs between predator avoidance and foraging gains. Thus, the conceptual model provides a mechanistic understanding to mass-migration in prey fish. Further, we also show that the dominant prey fish is actually absent from the lake during a major part of the year, which should have strong implications for the dynamics of the lake ecosystem through direct and indirect food-web interactions.     

Can size distributions of European lake fish communities be predicted by trophic positions of their fish species?

An organism''s body size plays an important role in ecological interactions such as predator–prey relationships. As predators are typically larger than their prey, this often leads to a strong positive relationship between body size and trophic position in aquatic ecosystems. The distribution of body sizes in a community can thus be an indicator of the strengths of predator–prey interactions. The aim of this study was to gain more insight into the relationship between fish body size distribution and trophic position in a wide range of European lakes. We used quantile regression to examine the relationship between fish species'' trophic position and their log‐transformed maximum body mass for 48 fish species found in 235 European lakes. Subsequently, we examined whether the slopes of the continuous community size distributions, estimated by maximum likelihood, were predicted by trophic position, predator–prey mass ratio (PPMR), or abundance (number per unit effort) of fish communities in these lakes. We found a positive linear relationship between species'' maximum body mass and average trophic position in fishes only for the 75% quantile, contrasting our expectation that species'' trophic position systematically increases with maximum body mass for fish species in European lakes. Consequently, the size spectrum slope was not related to the average community trophic position, but there were negative effects of community PPMR and total fish abundance on the size spectrum slope. We conclude that predator–prey interactions likely do not contribute strongly to shaping community size distributions in these lakes.     

Effect of the rate of phytoplankton growth on the spaced-time dynamics of plankton communities in an homogeneous environment

We use a conceptual mathematical reaction-diffusion model to investigate the mechanisms of spatial structure formation and complex temporal dynamics of plankton in a heterogeneous environment. We take into account basic trophic interactions, namely, "prey-predator" interactions between phytoplankton, zooplankton, and fish in upper layers of natural waters. We consider plankton as a passive contaminant in turbulent waters. We show that plankton structure formation can result from the difference in phytoplankton growth rate in neighboring habitats. Phytoplankton and zooplankton biomass is shown to undergo both regular and chaotic oscillations. The fish predation rate substantially affects the spatial and temporal dynamics of plankton in a heterogeneous environment.     

The role of refugia for fishes during drought: a review and synthesis

• 1 Drought is a natural disturbance of aquatic ecosystems and can be a major factor in structuring aquatic communities. For individuals, populations and communities to persist in disturbed environments, they must have refuge from disturbance or disturbance must be minimal. Refugia convey spatial and temporal resistance or resilience in the face of disturbance, but the role of refugia in aquatic systems remains poorly understood. 2. We review available literature on aquatic refugia for fishes in order to synthesise current knowledge and provide suggestions for needed research. Our objectives were to clarify definitions of disturbance and refugia in the context of drought in aquatic systems, review how refuge habitats influence fish community structure, and consider the potential impact of refugia on fish population and community dynamics during drought. 3. Droughts cause a decrease in surface area/volume and an increase in extremes of physical and chemical water quality parameters. These conditions are linked with biotic interactions that structure the community of fishes residing in low‐flow or dry season refugia by increasing mortality rates, decreasing birth rates and/or increasing migration rates. Many aquatic organisms seek refuge from disturbance and/or have adaptations (e.g. physiological tolerance) that provide refuge. 4. Drought in aquatic systems leads to shifts in refugia spacing and connectance at multiple spatial and temporal scales. Refuge size, disturbance intensity, and mobility of organisms is predicted to play a large role in population persistence. We expect that refuge habitats will experience net immigration during drying and net emigration after rewetting, with the opposite occurring in surrounding habitat patches. Population dynamics of fishes using refugia during drought are best modelled by modified source‐sink dynamics, but dynamics are likely to change with spatial scale.

     

Notonecta exhibit threat-sensitive,predator-induced dispersal

Dispersal is a central process determining community structure in heterogeneous landscapes, and species interactions within habitats may be a major determinant of dispersal. Although the effects of species interactions on dispersal within habitats have been well studied, how species interactions affect the movement of individuals between habitats in a landscape has received less attention. We conducted two experiments to assess the extent to which predation risk affects dispersal from an aquatic habitat by a flight-capable semi-aquatic insect (Notonecta undulata). Exposure to non-lethal (caged) fish fed conspecifics increased dispersal rates in N. undulata. Moreover, dispersal rate was positively correlated with the level of risk imposed by the fish; the greater the number of notonectids consumed by the caged fish, the greater the dispersal rate from the habitat. These results suggest that risk within a habitat can affect dispersal among habitats in a landscape and thus affect community structure on a much greater scale than the direct effect of predation itself.     

Developing fish community based ecohydrological indicators for water resources management in Taiwan

With concerns about the maintenance of both aquatic communities and flow conditions, a number of hydrologic indicators have been developed. These indicators are generally based on the development of hydrologic statistics for flows that are important to the maintenance of aquatic ecosystems. Although the hydrologic basis for indicators is well defined by common techniques in stochastic hydrology, the basis for ecological integration is still being developed. A critical evaluation of hydrologic indicators intended to protect aquatic ecosystems finds that proposed indicators are based more on standard hydrologic statistics and measures of hydrologic alteration than the habitat needs and ecological requirements of local or desired aquatic communities. We argue that hydrologic indicators are not ecohydrological indicators unless direct connections between flow events and aquatic community habitat and ecological needs are the basis of the indicator development and selection. In this article, we identify ecohydrological indicators that are based on habitat and ecological needs of fish communities. The indicator identification process is initiated with the analysis of community needs using an autecology matrix. Hydrologic statistics are then selected that are appropriate to the target fish community. The resulting ecohydrological indicators provide a direct connection to fish community flow requirements and the physical habitat conditions and associated ecology and life history needs of fish species. Handling editor: J. A. Cambray     

Corals and starfish devastation of the great barrier reef: Aggregation methods

Aggregation methods allow one to replace a large scale dynamical system (micro-system) by a reduced dynamical system (macro-system) governing a small number of global variables. This aggregation of variables can be performed when two time scales exist, a fast time scale and a slow time scale. Perturbation theory allows to obtain an approximated aggregated dynamical system which describes the behaviour of a few number of slow time varying variables which are constants of motion of the fast part of the micro-system. Aggregation methods are applied to the case of the devastation of the great barrier reef by the starfishes. We recall the Antonelli/Kazarinoff model which implies a stable limit cycle for the corals and starfish populations. This prey-predator model describes the interactions between two species of corals and the starfish. Then, we generalize the Antonelli/Kazarinoff model to the case of two spatial patches with a fast part describing the starfish migration on the patches and the human manipulation of the communities by divers and, a slow part describing the growth and the interactions between the populations. We obtain an aggregated model governing the total coral densities on the patches and the total starfish population. This model can exhibit stable limit cycle oscillations and a Hopf bifurcation. The critical value of the bifurcation parameter is expressed in terms of the proportions of coral species and starfish on the two patches. This implies for example that rather than random killing of starfish by the Australian military, it may be better to send teams of divers to outbreaking reefs when they first occur who will then manipulate the community structure to increase protection.     

Size distribution of aquatic invertebrates in two prairie wetlands, with and without fish, with implications for community production

1. We compared the size distribution of aquatic invertebrates in two prairie wetlands, one supporting a population of fathead minnows and the other fishless. Both wetlands were sampled in three depth zones on three dates, allowing assessment of temporal and spatial variation.
2. We determined biomass of aquatic invertebrates in 17 log₂ size classes, and used these data to develop normalized size spectra. We also coupled size distributions with an allometric model to estimate relative production at the community level.
3. The composition of the invertebrate communities differed greatly between sites, and invertebrate biomass was higher in nearly all size classes in the fishless wetland. Intercepts of normalized size spectra were significantly different between wetlands, but slopes generally were not, indicating differences in standing-stock biomass but similar size structures between the two invertebrate communities. Higher standing-stock biomass in the fishless wetland resulted in higher relative production per unit area, but similar size distributions resulted in similar mass-specific production (P/B) between wetlands.
4. Our results indicate that invertebrate communities in prairie wetlands may have relatively consistent size structures in spite of large differences in community composition and standing-stock biomass. We hypothesize that the observed differences are because of predation by the minnow population and/or differences in the macrophyte communities between the two sites. However, the relative importance of macrophytes and fish predation in structuring invertebrate communities in prairie wetlands is poorly known.     

Colonization under threat of predation: avoidance of fish by an aquatic beetle, Tropisternus lateralis (Coleoptera: Hydrophilidae)

Documenting the role of past interactions in the assembly of present communities has proven problematic. Colonization is a key process in community assembly that is both potentially driven by past interactions and amenable to experimental approaches. Colonization and oviposition by an aquatic beetle (Tropisternus lateralis) was assayed in the presence and absence of both 'harmless' and tactilely/visually isolated predatory fish (Lepomis gibbosus and L. macrochirus). Beetles avoided each treatment with fish when compared to fish-free experimental pools. Activity levels after colonization also differed significantly between adults in fish and fish-free tanks. Predator effects on species composition are typically ascribed to contemporary predation events; the presence of a strong avoidance response demonstrates that past species interactions affect present distributions and may play an important role in the ongoing assembly of contemporary communities. Documentation of such avoidance behavior in a growing number of species fundamentally alters our view of the processes affecting species distributions and the process of community assembly.     

Asexual reproduction changes predator population dynamics in a life predator–prey system

Many organisms display oscillations in population size. Theory predicts that these fluctuations can be generated by predator–prey interactions, and empirical studies using life model systems, such as a rotifer-algae community consisting of Brachionus calyciflorus as predator and Chlorella vulgaris as prey, have been successfully used for studying such dynamics. B. calyciflorus is a cyclical parthenogen (CP) and clones often differ in their sexual propensity, that is, the degree to which they engage into sexual or asexual (clonal) reproduction. Since sexual propensities can affect growth rates and population sizes, we hypothesized that this might also affect population oscillations. Here, we studied the dynamical behaviour of B. calyciflorus clones representing either CPs (regularly inducing sex) or obligate parthenogens (OPs). We found that the amplitudes of population cycles to be increased in OPs at low nutrient levels. Several other population dynamic parameters seemed unaffected. This suggests that reproductive mode might be an important additional variable to be considered in future studies of population oscillations.     

A community-based framework for aquatic ecosystem models

Here, we communicate a point of departure in the development of aquatic ecosystem models, namely a new community-based framework, which supports an enhanced and transparent union between the collective expertise that exists in the communities of traditional ecologists and model developers. Through a literature survey, we document the growing importance of numerical aquatic ecosystem models while also noting the difficulties, up until now, of the aquatic scientific community to make significant advances in these models during the past two decades. Through a common forum for aquatic ecosystem modellers we aim to (i) advance collaboration within the aquatic ecosystem modelling community, (ii) enable increased use of models for research, policy and ecosystem-based management, (iii) facilitate a collective framework using common (standardised) code to ensure that model development is incremental, (iv) increase the transparency of model structure, assumptions and techniques, (v) achieve a greater understanding of aquatic ecosystem functioning, (vi) increase the reliability of predictions by aquatic ecosystem models, (vii) stimulate model inter-comparisons including differing model approaches, and (viii) avoid ??re-inventing the wheel??, thus accelerating improvements to aquatic ecosystem models. We intend to achieve this as a community that fosters interactions amongst ecologists and model developers. Further, we outline scientific topics recently articulated by the scientific community, which lend themselves well to being addressed by integrative modelling approaches and serve to motivate the progress and implementation of an open source model framework.     

The effect of top‐predator presence and phenotype on aquatic microbial communities

The presence of predators can impact a variety of organisms within the ecosystem, including microorganisms. Because the effects of fish predators and their phenotypic differences on microbial communities have not received much attention, we tested how the presence/absence, genotype, and plasticity of the predatory three‐spine stickleback (Gasterosteus aculeatus) influence aquatic microbes in outdoor mesocosms. We reared lake and stream stickleback genotypes on contrasting food resources to adulthood, and then added them to aquatic mesocosm ecosystems to assess their impact on the planktonic bacterial community. We also investigated whether the effects of fish persisted following the removal of adults, and the subsequent addition of a homogenous juvenile fish population. The presence of adult stickleback increased the number of bacterial OTUs and altered the size structure of the microbial community, whereas their phenotype affected bacterial community composition. Some of these effects were detectable after adult fish were removed from the mesocosms, and after juvenile fish were placed in the tanks, most of these effects disappeared. Our results suggest that fish can have strong short‐term effects on microbial communities that are partially mediated by phenotypic variation of fish.     

The impact of environmental variability and species composition on the stability of experimental microbial populations and communities

Understanding how environmental fluctuations affect the stability of populations and communities is complex, for example, because direct effects of environmental variability on populations may be modified and propagated across communities by species interactions. One way to explore and further understand these complexities is via a factorial manipulation of community composition and environmental conditions. Using laboratory based aquatic microcosms we manipulated environmental fluctuation by creating two environments; one with variable light and one with constant light. Within these environments, community composition was manipulated by constructing communities from all possible combinations of three species that vary in their reliance on light for growth (an autotroph: a diatom completely reliant on light, a heterotroph: a Paramecium species not reliant on light, and a mixotroph: a Paramecium species somewhat reliant on light). Community composition was predicted to affect populations and communities by introducing and altering competitive interactions between species and affecting the degree of niche differentiation between species. We found that population stability was predominantly influenced by an interaction between community composition and environmental variability, whereby the effect of environmental variability synergistically combined with effects of community composition to reduce population stability. Covariance of populations was determined by an interaction between community composition and environmental variability, though this did not result from the effect of niche differentiation between species. Species interactions drove correlations between population biomass and the environment which otherwise did not exist. Our results demonstrate the complex and interrelated effects of abiotic and biotic factors on population and community stability, and suggest the need to consider aspects of community composition when predicting the impact of environmental fluctuations.     

Community Structure and Multi-Modal Oscillations in Complex Networks

In many types of network, the relationship between structure and function is of great significance. We are particularly interested in community structures, which arise in a wide variety of domains. We apply a simple oscillator model to networks with community structures and show that waves of regular oscillation are caused by synchronised clusters of nodes. Moreover, we show that such global oscillations may arise as a direct result of network topology. We also observe that additional modes of oscillation (as detected through frequency analysis) occur in networks with additional levels of topological hierarchy and that such modes may be directly related to network structure. We apply the method in two specific domains (metabolic networks and metropolitan transport) demonstrating the robustness of our results when applied to real world systems. We conclude that (where the distribution of oscillator frequencies and the interactions between them are known to be unimodal) our observations may be applicable to the detection of underlying community structure in networks, shedding further light on the general relationship between structure and function in complex systems.