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.     

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.     

Predator density and the functional responses of coral reef fish

Predation is a key process driving coral reef fish population dynamics, with higher per capita prey mortality rates on reefs with more predators. Reef predators often forage together, and at high densities, they may either cooperate or antagonize one another, thereby causing prey mortality rates to be substantially higher or lower than one would expect if predators did not interact. However, we have a limited mechanistic understanding of how prey mortality rates change with predator densities. We re-analyzed a previously published observational dataset to investigate how the foraging response of the coney grouper (Cephalopholis fulva) feeding on the bluehead wrasse (Thalassoma bifasciatum) changed with shifts in predator and prey densities. Using a model-selection approach, we found that per-predator feeding rates were most consistent with a functional response that declines as predator density increases, suggesting either antagonistic interactions among predators or a shared antipredator behavioral response by the prey. Our findings suggest that variation in predator density (natural or anthropogenic) may have substantial consequences for coral reef fish population dynamics.     

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.     

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.     

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.     

An experimental study of the effects of predatory fish on macroinvertebrates in a Hong Kong stream

SUMMARY. 1. Predation upon macroinvertebrates by the loach Oreonectes platycephalus Günther (Cobitidae) was studied using predator inclusion/exclusion cages in a series of pools along a Hong Kong stream. Treatments employed were predator exclusion, medium (approximately natural) predator densities (1 fish cage⁻¹) and high predator densities (2 fish cage⁻¹). Macroinvertebrate abundance in cages was monitored after 2 and 4-weeks exposure to predators.
2. The presence of fish was associated with significant declines in the total numbers of macroinvertebrates colonizing cages. However, taxa were influenced differently, with mayflies decreasing by a factor of two while the more mobile shrimps (Atyidae) were unaffected. Chironomid abundance (largely Chironominae) was unaffected by predator density and increased in week 4. Detritus acted as a confounding variable at this time because chironomid abundance was significantly correlated with the weight of accumulated detritus in cages.
3. While invertebrates were more abundant in cages lacking fish, there were no fewer invertebrates in cages with 2 fish than with 1 fish. This may indicate the presence of secure refuges among substrates in the cages, preventing the additional fish from depleting prey further, or a lack of precision of methods due to natural variations in prey densities and spatial patchiness.
4. No significant effects of predators on relative prey abundance or species richness were detected.
5. The impact of predation on prey abundance weakened on week 4, perhaps due to extra refuges among the accumulated detritus. However, drying of the stream increased fish densities in pools so that cages may have become zones of relative safety that were colonized readily by macroinvertebrates. This result highlights the need for year-round investigations to quantify predation effects in Hong Kong's seasonal tropical climate.     

Harvesting and predation of a sex- and age-structured population

We study a discrete-time system of equations for a structured ungulate population exploited by human harvesting or a dynamic predator. The population is divided into juveniles, and female and male adults. Harvesting is concentrated on adults (trophy hunting of males or population control measures on females), whereas predation occurs in juveniles. Though the model consists of four nonlinear equations, we find explicit expressions for the steady states. We use these explicit expressions to investigate harvesting rates that allow population persistence, rates that ensure population control, and optimal harvesting efforts. Several reductions of complexity allow for a detailed analysis of the dynamics of the model. Most notably, we find that even compensatory density dependence can lead to a period doubling bifurcation, that the model does not support consumer–resource cycles, and that an Allee effect can emerge from the interplay of stage-specific predation and density-dependent prey reproduction.     

Effect of predator density dependent dispersal of prey on stability of a predator-prey system

This work presents a predator-prey Lotka-Volterra model in a two patch environment. The model is a set of four ordinary differential equations that govern the prey and predator population densities on each patch. Predators disperse with constant migration rates, while prey dispersal is predator density-dependent. When the predator density is large, the dispersal of prey is more likely to occur. We assume that prey and predator dispersal is faster than the local predator-prey interaction on each patch. Thus, we take advantage of two time scales in order to reduce the complete model to a system of two equations governing the total prey and predator densities. The stability analysis of the aggregated model shows that a unique strictly positive equilibrium exists. This equilibrium may be stable or unstable. A Hopf bifurcation may occur, leading the equilibrium to be a centre. If the two patches are similar, the predator density dependent dispersal of prey has a stabilizing effect on the predator-prey system.     

Predator density and competition modify the benefits of group formation in a shoaling reef fish

Synthesis Predation risk experienced by individuals living in groups depends on the balance between predator dilution, competition for refuges, and predator interference or synergy. These interactions operate between prey species as well: the benefits of group living decline in the presence of an alternative prey species. We apply a novel model‐fitting approach to data from field experiments to distinguish among competing hypotheses about shifts in predator foraging behavior across a range of predator and prey densities. Our study provides novel analytical tools for analyzing predator foraging behavior and offers insight into the processes driving the dynamics of coral reef fish. Studies of predator foraging behavior typically focus on single prey species and fixed predator densities, ignoring the potential importance of complexities such as predator dilution; predator‐mediated effects of alternative prey; heterospecific competition; or predator–predator interactions. Neglecting the effects of prey density is particularly problematic for prey species that live in mixed species groups, where the beneficial effects of predator dilution may swamp the negative effects of heterospecific competition. Here we use field experiments to investigate how the mortality rates of a shoaling coral reef fish (a wrasse: Thalassoma amblycephalum), change as a result of variation in: 1) conspecific density, 2) density of a predator (a hawkfish: Paracirrhites arcatus), and 3) presence of an alternative prey species that competes for space (a damselfish: Pomacentrus pavo). We quantify changes in prey mortality rates from the predator's perspective, examining the effects of added predators or a second prey species on the predator's functional response. Our analysis highlights a model‐fitting approach that discriminates amongst multiple hypotheses about predator foraging in a community context. Wrasse mortality decreased with increasing conspecific density (i.e. mortality was inversely density‐dependent). The addition of a second predator doubled prey mortality rates, without significantly changing attack rate or handling time – i.e. there was no evidence for predator interference. The presence of a second prey species increased wrasse mortality by 95%; we attribute this increase either to short‐term apparent competition (predator aggregation) or to a decrease in handling time of the predator (e.g. through decreased wrasse vigilance). In this system, 1) prey benefit from intraspecific group living though a reduced predation risk, and 2) the benefit of group living is reduced in the presence of an alternative prey species.     

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.     

Mixed encounters, limited perception and optimal foraging

This article demonstrates how perceptual constraints of predators and the possibility that predators encounter prey both sequentially (one prey type at a time) and simultaneously (two or more prey types at a time) may influence the predator attack decisions, diet composition and functional response of a behavioural predator-prey system. Individuals of a predator species are assumed to forage optimally on two prey types and to have exact knowledge of prey population numbers (or densities) only in a neighbourhood of their actual spatial location. The system characteristics are inspected by means of a discrete-time, discrete-space, individual-based model of the one-predator-two-prey interaction. Model predictions are compared with ones that have been obtained by assuming only sequential encounters of predators with prey and/or omniscient predators aware of prey population densities in the whole environment. It is shown that the zero-one prey choice rule, optimal for sequential encounters and omniscient predators, shifts to abruptly changing partial preferences for both prey types in the case of omniscient predators faced with both types of prey encounters. The latter, in turn, become gradually changing partial preferences when predator omniscience is considered only local.     

Altered predator/prey behavior in polluted environments: implications for fish conservation

Predator/prey behavior has important consequences for individual survival and recruitment into fish populations, both of which can be affected by stressors such as environmental contaminants. The degree to which prey capture or predator avoidance abilities of a predator or prey species are affected will determine the direction in which the balance will be shifted. In a contaminated estuary we have studied, prey capure and predator avoidance of resident mummichogs, Fundulus heteroclitus, are impaired, which may account for individuals in that estuary having reduced growth and longevity compared with those from uncontaminated sites. Exposure to sediments, water, and grass shrimp from the contaminated site can impair the predatory abilities of mummichogs from a clean site. An important prey species, the grass shrimp, Palaemonetes pugio, has a greater population density and a greater proportion of large individuals at the polluted site, apparently because of reduced predation pressure. Mummichog larvae at the polluted site are initially more active and better at prey capture and predator avoidance than larvae from clean sites, but later they become poorer at both. Differences in predator vulnerability among larvae appear to be due to population differences in behavior, which may be due in part to both genetic and environmentally-caused factors. Conservation of fish populations should consider fish behavior and its interaction with contaminants.     

Dynamics and responses to mortality rates of competing predators undergoing predator-prey cycles

Two or more competing predators can coexist using a single homogeneous prey species if the system containing all three undergoes internally generated fluctuations in density. However, the dynamics of species that coexist via this mechanism have not been extensively explored. Here, we examine both the nature of the dynamics and the responses of the mean densities of each predator to mortality imposed upon it or its competitor. The analysis of dynamics uncovers several previously undescribed behaviors for this model, including chaotic fluctuations, and long-term transients that differ significantly from the ultimate patterns of fluctuations. The limiting dynamics of the system can be loosely classified as synchronous cycles, asynchronous cycles, and chaotic dynamics. Synchronous cycles are simple limit cycles with highly positively correlated densities of the two predator species. Asynchronous cycles are limit cycles, frequently of complex form, including a significant period during which prey density is nearly constant while one predator gradually, monotonically replaces the other. Chaotic dynamics are aperiodic and generally have intermediate correlations between predator densities. Continuous changes in density-independent mortality rates often lead to abrupt transitions in mean population sizes, and increases in the mortality rate of one predator may decrease the population size of the competing predator. Similarly, increases in the immigration rate of one predator may decrease its own density and increase the density of the other predator. Proportional changes in one predator's birth and death rate functions can have significant effects on the dynamics and mean densities of both predator species. All of these responses to environmental change differ from those observed when competitors coexist stably as the result of resource (prey) partitioning. The patterns described here occur in many other competition models in which there are cycles and differences in the linearity of the responses of consumers to their resources.     

Density-dependent prey behaviours and mutable predator foraging modes induce Allee effects and over-prediction of prey mortality rates

1. Predator–prey models are often used to represent consumptive interactions between species but, typically, are derived using simple experimental systems with little plasticity in prey or predator behaviours. However, many prey and predators exhibit a broad suite of behaviours. Here, we experimentally tested the effect of density-dependent prey and predator behaviours on per capita relative mortality rates using Florida bass (Micropterus floridanus) consuming juvenile Bluegill (Lepomis macrochirus).
2. Experimental ponds were stocked with a factorial design of low, medium, and high prey and predator densities. Prey mortality, prey–predator behaviours, and predator stomach contents were recorded over or after 7 days. We assumed the mortality dynamics followed foraging arena theory. This pathologically flexible predator–prey model separates prey into invulnerable and vulnerable pools where predators can consume prey in the latter. As this approach can represent classic Lotka–Volterra and ratio-dependent dynamics, we fit a foraging arena predator–prey model to the number of surviving prey.
3. We found that prey exhibited density-dependent prey behaviours, hiding at low densities, shoaling at medium densities, and using a provided refuge at high densities. Predators exhibited ratio-dependent behaviours, using an ambush foraging mode when one predator was present, hiding in the shadows at low prey–high predator densities, and shoaling at medium and high prey–high predator densities. The foraging arena model predicted the mortality rates well until the high prey–high predator treatment where group vigilance prey behaviours occurred and predators probably interfered with one another resulting in the model predicting higher mortality than observed.
4. This is concerning given the ubiquity of predator–prey models in ecology and natural resource management. Furthermore, as Allee effects engender instability in population regulation, it could lead to inaccurate predictions of conservation status, population rebuilding or harvest rates.

     

Oscillations in large mammal populations: are they related to predation or rainfall?

Cyclic population dynamics is relatively common among populations of small mammals in high latitudes but is not yet established among African savanna ungulates. However, oscillations may be expected in large mammal populations subject to quasi‐periodic oscillations in regional rainfall. We evaluated evidence for environmentally entrained oscillations in a large‐mammal predator–prey system in Kruger National Park (KNP), South Africa, where rainfall exhibits quasi‐periodic oscillations. The evaluation is based on analysis of comparative changes in the abundance of twelve ungulate species throughout South Africa's KNP using population counts over the period 1965–1996. We present evidence suggesting that (i) twelve ungulate populations display cyclic variability with half‐periods ranging between 10 and 18 years, (ii) this variability was associated with lagged rainfall between 3 and 10 years back in the past for different ungulate species, and (iii) the ungulate species respond in contrasting ways to rainfall, with some reaching highest abundance during periods of low rainfall and others under conditions of high rainfall. These findings are not consistent with the response pattern we would expect if the population oscillations were driven directly by the rainfall influence on food availability. Instead they seem to be an outcome of predator–prey interactions, which are entrained by the effect of rainfall on habitat conditions affecting the relative susceptibility of the different ungulate species to predation.     

The complex dynamics of a diffusive prey–predator model with an Allee effect in prey

This paper investigates complex dynamics of a predator–prey interaction model that incorporates: (a) an Allee effect in prey; (b) the Michaelis–Menten type functional response between prey and predator; and (c) diffusion in both prey and predator. We provide rigorous mathematical results of the proposed model including: (1) the stability of non-negative constant steady states; (2) sufficient conditions that lead to Hopf/Turing bifurcations; (3) a prior estimates of positive steady states; (4) the non-existence and existence of non-constant positive steady states when the model is under zero-flux boundary condition. We also perform completed analysis of the corresponding ODE model to obtain a better understanding on effects of diffusion on the stability. Our analytical results show that the small values of the ratio of the prey's diffusion rate to the predator's diffusion rate are more likely to destabilize the system, thus generate Hopf-bifurcation and Turing instability that can lead to different spatial patterns. Through numerical simulations, we observe that our model, with or without Allee effect, can exhibit extremely rich pattern formations that include but not limit to strips, spotted patterns, symmetric patterns. In addition, the strength of Allee effects also plays an important role in generating distinct spatial patterns.     

Dampening prey cycle overrides the impact of climate change on predator population dynamics: a long‐term demographic study on tawny owls

Predicting the dynamics of animal populations with different life histories requires careful understanding of demographic responses to multifaceted aspects of global changes, such as climate and trophic interactions. Continent‐scale dampening of vole population cycles, keystone herbivores in many ecosystems, has been recently documented across Europe. However, its impact on guilds of vole‐eating predators remains unknown. To quantify this impact, we used a 27‐year study of an avian predator (tawny owl) and its main prey (field vole) collected in Kielder Forest (UK) where vole dynamics shifted from a high‐ to a low‐amplitude fluctuation regime in the mid‐1990s. We measured the functional responses of four demographic rates to changes in prey dynamics and winter climate, characterized by wintertime North Atlantic Oscillation (wNAO). First‐year and adult survival were positively affected by vole density in autumn but relatively insensitive to wNAO. The probability of breeding and number of fledglings were higher in years with high spring vole densities and negative wNAO (i.e. colder and drier winters). These functional responses were incorporated into a stochastic population model. The size of the predator population was projected under scenarios combining prey dynamics and winter climate to test whether climate buffers or alternatively magnifies the impact of changes in prey dynamics. We found the observed dampening vole cycles, characterized by low spring densities, drastically reduced the breeding probability of predators. Our results illustrate that (i) change in trophic interactions can override direct climate change effect; and (ii) the demographic resilience entailed by longevity and the occurrence of a floater stage may be insufficient to buffer hypothesized environmental changes. Ultimately, dampened prey cycles would drive our owl local population towards extinction, with winter climate regimes only altering persistence time. These results suggest that other vole‐eating predators are likely to be threatened by dampening vole cycles throughout Europe.     

Long-period endogenous oscillations in fish population size: Mathematical modeling

We present a mathematical model of an aquatic community, where the size-and-age structure of hydrobiont populations is taken into account and the corresponding trophic interactions between zooplankton, peaceful fish, and predatory fish are described. We show that interactions between separate components of the aquatic community can give rise to long-period oscillations in fish population size. The period of these oscillations is on the order of decades. With this model we also show that an increase in the zooplankton growth rate may entail a sequence of bifurcations in the fish population dynamics: steady states → regular oscillations → quasicycles → dynamic chaos.     

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.