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: 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.     

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.     

Fishing destabilizes the biomass flow in the marine size spectrum

Fishing impacts on marine food webs are predicted by simulations of a size spectrum community model. In this model, predation is determined by predator and prey size and abundance, and drives predator growth and prey mortality. Fishing amplifies temporal oscillations in the biomass flow. Oscillations appear at lower fishing intensity and have wider amplitude when fishing is selective (removes a narrow size range) and/or when large fish are targeted, than when fishing is more balanced (catching a larger size range) or when small fish are targeted. A novel index of size diversity is developed, and is shown to be sensitive to both fishing intensity and selectivity. To avoid unstable food web dynamics with potential harmful consequences for fisheries, limiting both fishing intensity and selectivity might be an appropriate exploitation strategy.     

Long-Term Changes in the Diet of Gymnogobius isaza from Lake Biwa,Japan: Effects of Body Size and Environmental Prey Availability

Body size and environmental prey availability are both key factors determining feeding habits of gape-limited fish predators. However, our understanding of their interactive or relative effects is still limited. In this study, we performed quantitative dietary analysis of different body sizes of goby (Gymnogobius isaza) specimens collected from Lake Biwa between 1962 and 2004. First, we report that the diet was composed mainly of zooplankton (cladocerans and copepods) before the 1980s, and thereafter, shifted to zoobenthos (gammarids). This foraging shift coincided with, and thus can be linked to, known historical events in the lake at that time: decrease in zooplankton abundance with the alleviation of eutrophication, increase in fish body size resulting from fish population collapse, and increase in gammarid abundance due to reduced fish predation pressure. Supporting this view, our data analyses revealed how the long-term changes in the diet composition would be co-mediated by changes in fish body size and environmental prey availability. Specifically, while zoobenthos abundance strongly affected the fish diet composition, larger (smaller) fish preferred zoobenthos (zooplankton). Furthermore, the body size effects were stronger than those of prey availability. These results provide the best long-term evidence that fish feeding habits vary over decades with its body size and prey community due to anthropogenic disturbances.     

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.     

Systematic deviations from linear size spectra of lake fish communities are correlated with predator–prey interactions and lake‐use intensity

Size structure of organisms at logarithmic scale (i.e. size spectrum) can often be described by a linear function with a negative slope; however, substantial deviations from linearity have often been found in natural systems. Theoretical studies suggest that greater nonlinearity in community size spectrum is associated with high predator–prey size ratios but low predator–prey abundance ratios; however, empirical evaluation of the effects of predator–prey interactions on nonlinear structures remains scarce. Here, we aim to empirically explore the pattern of the size‐specific residuals (i.e. deviations from the linear regression between the logarithmic fish abundance and the logarithmic mean fish size) by using size spectra of fish communities in 74 German lakes. We found that nonlinearity was strong in lakes with high predator–prey abundance ratios but at low predator–prey size ratios. More specifically, our results suggest that only large predators, even if occurring in low abundances, can control the density of prey fishes in a broad range of size classes in a community and thus promote linearity in the size spectrum. In turn, the lack of large predator fishes may cause high abundances of fish in intermediate size classes, resulting in nonlinear size spectra in these lakes. Moreover, these lakes were characterized by a more intense human use including high fishing pressure and high total phosphorus concentrations, which have negative impacts on the abundance of large, predatory fish. Our findings indicate that nonlinear size spectra may reflect dynamical processes potentially caused by predator–prey interactions. This opens a new perspective in the research on size spectrum, and can be relevant to further quantify the efficiency of energy transfer in aquatic food webs.     

Oscillations in a size-structured prey-predator model

This article introduces a predator–prey model with the prey structured by body size, based on reports in the literature that predation rates are prey-size specific. The model is built on the foundation of the one-species physiologically structured models studied earlier. Three types of equilibria are found: extinction, multiple prey-only equilibria and possibly multiple predator–prey coexistence equilibria. The stabilities of the equilibria are investigated. Comparison is made with the underlying ODE Lotka–Volterra model. It turns out that the ODE model can exhibit sustain oscillations if there is an Allee effect in the net reproduction rate, that is the net reproduction rate grows for some range of the prey’s population size. In contrast, it is shown that the structured PDE model can exhibit sustain oscillations even if the net reproductive rate is strictly declining with prey population size. We find that predation, even size-non-specific linear predation can destabilize a stable prey-only equilibrium, if reproduction is size specific and limited to individuals of large enough size. Furthermore, we show that size-specific predation can also destabilize the predator–prey equilibrium in the PDE model. We surmise that size-specific predation allows for temporary prey escape which is responsible for destabilization in the predator–prey dynamics.     

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.     

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.     

The effects of age,sex, and habitat on body size and shape of the blackstripe topminnow,Fundulus notatus (Cyprinodontiformes: Fundulidae) (Rafinesque 1820)

Lake and stream habitats pose a variety of challenges to fishes due to differences in variables such as water velocity, habitat structure, prey community, and predator community. These differences can cause divergent selection on body size and/or shape. Here, we measured sex, age, length, and eight different morphological traits of the blackstripe topminnow, Fundulus notatus, from 19 lake and stream populations across four river drainages in central Illinois. Our goal was to determine whether size and shape differed consistently between lake and stream habitats across drainages. We also considered the effects of age and sex as they may affect size and morphology. We found large differences in body size of age 1 topminnows where stream fish were generally larger than lake fish. Body shape mainly varied as a function of sex. Adult male topminnows had larger morphological traits (with the exception of body width) than females, in particular longer dorsal and anal base lengths. Subtle effects of habitat were present. Stream fish had a longer dorsal fin base than lake fish. These phenotypic patterns may be the result of genetic and/or environmental variation. As these lakes are human‐made, the observed differences, if genetic, would have had to occur relatively rapidly (within about 100 years). © 2013 The Linnean Society of London     

Predators, resources, and trophic chains in the regulation of plankton population and biomass in oligothrophic lakes

The relative strength of "top-down" versus "bottom-up" control of plankton community structure and biomass in two small oligotrophic lakes (with and without fish), located near the Polar circle (Russia), has been investigated for two years, 1996 and 1997. The comparative analyses of zooplankton biomass and species abundance showed strong negative effect of fish, stickeback (Pungitius pungitius L.), on the zooplankton community species, size structure and biomass of particular prey species but no effect on the biomass of the whole trophic level. An intensive predation in Verkhneye lake has lead to: 1) sixfold decline in biomass of large cladoceran Holopedium gibberum comparing to the lake lacking predator, 2) shift in the size mode in zooplankton community and the replacement of the typical large grazers by small species--Bosmina longirostris and rotifers. Their abundance and biomass even increased, demonstrating the stimulating effect of fish on the "inefficient" and unprofitable prey organisms. The analysis of contributions of different factors into the cladoceran's birth rate changes was applied to demonstrate the relative impact of predators and resources on zooplankton abundance. An occasional introduction of the stickleback to Vodoprovodnoye lake (the reference lake in 1996) in summer 1997 lead to drastic canges in this ecosystem: devastating decrease of zooplankton biomass and complete elimination of five previously dominant grazer species. The abundance of edible phytoplankton was slightly higher in the lake with fish in 1996 and considerably higher in the lake where fish has appeared in 1997 showing the prevailing "top-down" control of phytoplankton in oligotrophic ecosystem. The reasons of trophic cascade appearance in oligotrophic lakes are also discussed.     

Long-term responses of zooplankton to invasion by a planktivorous fish in a subarctic watercourse

1. Introduced or invading predators may have strong impacts on prey populations of the recipient community mediated by direct and indirect interactions. The long-term progression of predation effects, covering the invasion and establishment phase of alien predators, however, has rarely been documented.
2. This paper documents the impact of an invasive, specialized planktivorous fish on its prey in a subarctic watercourse. Potential predation effects on the crustacean plankton, at the community, population and individual levels, were explored in a long-term study following the invasion by vendace ( Coregonus albula ).
3. Over the 12-year period, the density and species richness of zooplankton decreased, smaller species became more abundant and Daphnia longispina , one of the largest cladocerans, was eliminated from the zooplankton community.
4. Within the dominant cladocerans, including Daphnia spp., Bosmina longispina and Bosmina longirostris , the body size of ovigerous females and the size at first reproduction decreased after the arrival of the new predator. The clutch sizes of Daphnia spp. and B. longirostris also increased.
5. Increased predation pressure following the vendace invasion induced many effects on the crustacean zooplankton, and we document comprehensive and strong direct and indirect long-term impacts of an introduced non-native predator on the native prey community.     

Prey vulnerability to a gape-size limited predator: behavioural and morphological impacts on northern pike piscivory

The northern pike ( Esox lucius ) is a selective and important predator in lake ecosystems. Prey size in pike is limited by pike gape size, which is a linear function of pike body length. Here we show that the absolute gape-size limit in pike is greater than previously considered, and that maximum ingestible prey size is limited by prey body depth. Further, we experimentally show that pike prefer shallow-bodied roach before deeper-bodied common bream, and small prey sizes within each prey species. Handling time in pike increases with prey body depth, and since common bream are deeper-bodied than roach, handling time is longer for bream than for roach of the same length, but equal considering body depth. Prey handling time is suggested to be a major cost to the pike, since it increases the risk of losing the prey, as well as exposure to predation, kleptoparasitism and cannibalism. Consequently, prey vulnerability is determined by risk of predation and intraspecific interactions, and behavioural preferences in the pike, and not by pike gape-size limits. The consequences for natural populations is evaluated by analysing size structures of predator and prey fish populations in a eutrophic lake.     

When phenology matters: age–size truncation alters population response to trophic mismatch

Climate-induced shifts in the timing of life-history events are a worldwide phenomenon, and these shifts can de-synchronize species interactions such as predator–prey relationships. In order to understand the ecological implications of altered seasonality, we need to consider how shifts in phenology interact with other agents of environmental change such as exploitation and disease spread, which commonly act to erode the demographic structure of wild populations. Using long-term observational data on the phenology and dynamics of a model predator–prey system (fish and zooplankton in Windermere, UK), we show that age–size truncation of the predator population alters the consequences of phenological mismatch for offspring survival and population abundance. Specifically, age–size truncation reduces intraspecific density regulation due to competition and cannibalism, and thereby amplifies the population sensitivity to climate-induced predator–prey asynchrony, which increases variability in predator abundance. High population variability poses major ecological and economic challenges as it can diminish sustainable harvest rates and increase the risk of population collapse. Our results stress the importance of maintaining within-population age–size diversity in order to buffer populations against phenological asynchrony, and highlight the need to consider interactive effects of environmental impacts if we are to understand and project complex ecological outcomes.     

Dynamics of a stochastic predator-prey model with habitat complexity and prey aggregation

Interplay between predator and prey is a complex process in ecosystems due to its nature. The population dynamics can be affected by many extrinsic and intrinsic factors. In this paper, we make an attempt to uncover the effects from environmental disturbances when populations are subject to habitat complexity and aggregation effect. We firstly propose a stochastic predator-prey model with habitat complexity and aggregation efficiency for prey. We then mathematically analyze the model, to demonstrate the existence, uniqueness and the stochastically ultimately boundedness of the global positive solution, and to establish sufficient conditions for the existence of ergodic stationary distribution of the solution. We also establish sufficient conditions under which either only predator population dies out or the entire predator-prey model becomes extinct. Our theoretical and numerical results indicate that: (1) the environmental noises are disadvantage for the survival of biological populations; (2) when the density of prey is greater than one, prey aggregation can heighten the capability of predator species to capture prey and reduce the effect of environmental fluctuations, while when the density of prey is less than one, the results are opposite; (3) habitat complexity is propitious to the survival of prey population and may seriously threaten the persistence of the predator population.     

A New Stochastic Individual-Based Model for Pattern Formation and its Application to Predator–Prey Systems

Reaction–diffusion theory has played a very important role in the study of pattern formation in biology. However, a group of individuals is described by a single state variable representing population density in reaction–diffusion models, and interaction between individuals can be included only phenomenologically. In this paper, we propose a new scheme that seamlessly combines individual-based models with elements of reaction–diffusion theory and apply it to predator–prey systems as a test of our scheme. In the model, starvation periods and the time to reproductive maturity are modeled for individual predators. Similarly, the life cycle and time to reproductive maturity of an individual prey are modeled. Furthermore, both predators and prey migrate through a two-dimensional space. To include animal migration in the model, we use a relationship between the diffusion and the random numbers generated according to a two-dimensional bivariate normal distribution. Despite the simplicity of this model, our scheme successfully produces logistic patterns and oscillations in the population size of both predator and prey. The peak for the predator population oscillation lags slightly behind the prey peak. The simplicity of this scheme will aid additional study of spatially distributed negative-feedback systems.     

Scale dependent effects of predatory fish on stream benthos

In open predation experiments the effects of predators on prey densities can be influenced by predator consumption and by prey movements in to and out of experimental arenas. A published model predicts that the predator effects observed in such experiments are scale dependent over the scale range where there is a transition from movement control (of prey densities) to consumption control. The scale dependence follows from the assumption that per capita rate of emigration out of an experimental arena decreases with increasing arena size.
To test this model the effects of a small benthic fish ( Cottus gobio ) on densities of stream invertebrates was investigated in instream channels of different length (0.5, 2 and 8 m). The effect of fish predation was scale dependent for four prey taxa. For three of these taxa predator effects increased with experimental scale, which is in agreement with model predictions. However, this proved to be a case of "making the right prediction for the wrong reason" as the basic assumption of scale dependent emigration rate was not upheld. By analyzing the behaviour of the model, parameterized with emigration and consumption rates observed in the experimental channels, it was found that observed scale effects occurred because prey emigration in response to the predator treatment was modified by the experimental scale. Further analysis of the parameterized model suggested that the densities of most prey taxa were controlled by prey movements and not by consumption by the sculpins.     

Effect of disease-selective predation on prey infected by contact and external sources

We propose and analyze a simple mathematical model for susceptible prey (S)–infected prey (I)–predator (P) interaction, where the susceptible prey population (S) is infected directly from external sources as well as through contact with infected class (I) and the predator completely avoids consuming the infected prey. The model is analyzed to obtain different thresholds of the key parameters under which the system exhibits stability around the biologically feasible equilibria. Through numerical simulations we display the effects of external infection and the infection through contact on the system dynamics in the absence as well as in the presence of the predator. We compare the system dynamics when infection occurs only through contact, with that when it occurs through contact and external sources. Our analysis demonstrates that under a disease-selective predation, stability and oscillations of the system is determined by two key parameters: the external infection rate and the force of infection through contact. Due to the introduction of external infection, the predator and the prey population show limit-cycle oscillations over a range parametric values. We suggest that while predicting the dynamics of such an eco-epidemiological system, the modes of infection and the infection rates might be carefully investigated.     

Forecasting the effects of global change scenarios on bioaccumulation patterns in great lakes species

Climate change will have substantial impacts on biodiversity, particularly for aquatic species. Warming temperatures and changing weather patterns will also remobilize and modify chemical partitioning. Holding millions of cubic yards of sediments contaminated with persistent legacy chemicals such as polychlorinated biphenyls (PCBs) and dioxins, the Laurentian Great Lakes are a laboratory for observing interactions between biological and chemical responses to climate change. They provide a wide range of habitat to a variety of species, from littoral forage fish to deep‐water predators. In this paper, we couple bioenergetic and bioaccumulation models to investigate the biological and chemical effects of climate change in the Great Lakes. We consider three species: round goby, a warm‐water invasive forage fish; mottled sculpin, a cool‐water native forage fish; and lake trout, a cold‐water native predator. Using our coupled models, we calculate the accumulation of a representative persistent chemical, PCB‐77, under four climate scenarios for Lake Erie and Lake Superior. Predator–prey (lake trout–round goby) interactions and food availability (high–low) are incorporated into our simulations. For cool‐ to cold‐water species (sculpin, lake trout) we find that warm temperatures limit growth. For warm‐water species (round goby) cold temperatures limit growth. The impact of climate warming on growth depends on the winter lows as well as the summer highs of the scenario, in combination with the species' critical upper and lower thermal limits. We find conditions for high growth and consumption rates generally lead to high bioaccumulation. However, this can be confounded by predator–prey dynamics, as mismatches in the temperature preferences of predator and prey can lead to mismatches in relative growth and uptake rates. As predator–prey dynamics are expected to undergo substantial shifts with changing climate, these relative thermal sensitivities will be key in determining the implications of climate change for bioaccumulation, particularly in top predator species.