Successful invasion of a food web in a chemostat

A food web in a chemostat is considered in which an arbitrary number of competitor populations compete for a single, essential, nonreproducing, growth-limiting substrate, and an arbitrary number of predator populations prey on some or all of the competitor populations. Although any number of predator populations may prey on the same competitor population, each predator population preys on only one competitor population. The dynamics of substrate uptake is modeled by Lotka-Volterra or Michaelis-Menten (Holling type I or II), but the dynamics of competitor uptake is restricted to Lotka-Volterra. Based on certain parameters, the model predicts the asymptotic survival or extinction of each of the different populations and suggests how competitor and/or predator populations could successfully invade the chemostat with or without causing a diverse ecosystem to crash. Similarly, it suggests how the elimination of certain populations could result in a more diverse or less diverse system.     

Effects of sterile insect releases on a population under predation or parasitism

A continuous-time differential equation model was constructed which describes the population dynamics of a predator prey system in which sterile prey are released in a program designed to eradicate or reduce the prey population. It was found that the dynamics of the system behave quite differently when predators are present. Two conditions were found which have differing implications for the control program. If the predators still exist when the wild prey population declines to extinction, then the SIRM is assisted by the predators, sometimes to a considereble extent. If the predators decline to extinction before the wild prey population goes extinct, then the predators may or may not assist the SIRM depending on the parameters of the system. If the predators do assist the SIRM, then a potentially dangerous situation exists in which an explosion of the prey population could occur after the predators go extinct. Predator polyphagy would probably minimize this danger of an explosion since it would stabilize the predator population.     

Diseased Social Predators

Social predators benefit from cooperation in the form of increased hunting success, but may be at higher risk of disease infection due to living in groups. Here, we use mathematical modeling to investigate the impact of disease transmission on the population dynamics benefits provided by group hunting. We consider a predator–prey model with foraging facilitation that can induce strong Allee effects in the predators. We extend this model by an infectious disease spreading horizontally and vertically in the predator population. The model is a system of three nonlinear differential equations. We analyze the equilibrium points and their stability as well as one- and two-parameter bifurcations. Our results show that weakly cooperating predators go unconditionally extinct for highly transmissible diseases. By contrast, if cooperation is strong enough, the social behavior mediates conditional predator persistence. The system is bistable, such that small predator populations are driven extinct by the disease or a lack of prey, and large predator populations survive because of their cooperation even though they would be doomed to extinction in the absence of group hunting. We identify a critical cooperation level that is needed to avoid the possibility of unconditional predator extinction. We also investigate how transmissibility and cooperation affect the stability of predator–prey dynamics. The introduction of parasites may be fatal for small populations of social predators that decline for other reasons. For invasive predators that cooperate strongly, biocontrol by releasing parasites alone may not be sufficient.     

Scaling up population dynamic processes in a ladybird–aphid system

Here, we study how scaling up to the metapopulation level affects predictions of a population dynamics model motivated by an aphidophagous predator–aphid system. The model incorporates optimization of egg distribution in predatory females, cannibalism among their offspring, and self-regulation of the prey population. These factors determine the within-year dynamics of the system and translate the numbers of prey and predator individuals at the beginning of the season into their numbers at the end of the season at the level of one patch—one suitable host plant or a group of these. At the end of each season, all populations of prey and all populations of predators are mixed (this simulates aphid host-alternation and ladybird migration to hibernation sites), and then redistributed at the beginning of the next season. Prey individuals are distributed at random among the patches as a “prey rain”, while adult predators that survived from the previous season optimize the distribution of their offspring, in that they prefer patches with sufficient amount of prey and absence of other predators. This redistribution followed by within-season dynamics is then iterated over many seasons. We look at whether small-scale trends in population dynamics predicted by this model are consistent with large-scale outcomes. Specifically, we show that even on the metapopulation scale, the impact of predators on prey metapopulation is relatively low. We further show how the dates of predator arrival to and departure from the system affect the qualitative behaviour of the model predictions.     

Syrphid flies suppress lettuce aphids

Syrphid flies are abundant in lettuce fields, where their larvae are key predators of aphids. However, the presence of predators in the field does not always result in economically significant levels of prey suppression. Even when predators are numerous, their effects on prey population dynamics may be variable. Over a two year period we surveyed lettuce fields in coastal California, USA to test whether syrphid flies are capable of colonizing fields with aphids and suppressing aphid population growth. The survey showed that female syrphids oviposited more eggs at locations with more aphids, and that greater numbers of syrphid larvae resulted in lower rates of increase in the aphid populations. We also directly manipulated syrphid densities by adding syrphid eggs to uncaged lettuce plants, and these syrphid additions resulted in lower aphid population growth. This research shows that syrphid flies have the ability to suppress aphid populations in lettuce fields.     

Predator-prey interactions in a nonequilibrium context: the metapopulation approach to modeling "hide-and-seek" dynamics in a spatially explicit tri-trophic system

Predators and prey are usually heterogeneously distributed in space so that the ability of the predators to respond to the distribution of their prey may have a profound influence on the stability and persistence of a predator‐prey system. A special type of dynamics is “hide‐and‐seek” characterized by a high turnover rate of local populations of prey and predators, because once the predators have found a patch of prey they quickly overexploit it, whereupon the starving predators either should move to better places or die. Continued persistence of prey and predators thus hinges on a long‐term balance between local extinctions and founding of new subpopulations. The colonization rate depends on the rate of emigration from occupied patches and the likelihood of successfully arriving at a suitable new patch, while extinction rate depends on the local population dynamics. Since extinctions and colonizations are both discrete probabilistic events, these phenomena are most adequately modeled by means of a stochastic model. In order to demonstrate the qualitative differences between a deterministic and stochastic approach to population dynamics, a spatially explicit tritrophic predator‐prey model is developed in a deterministic and a stochastic version. The model is parameterized using data for the two‐spotted spider mite (Tetranychus urticae) and the phytoseiid mite predator Phytoseiulus persimilis inhabiting greenhouse cucumbers.
Simulations show that the deterministic and stochastic approaches yield different results. The deterministic version predicts that the populations will exhibit violent fluctuations, implying that the system is fundamentally unstable. In contrast, the stochastic version predicts that the two species will be able to coexist in spite of frequent local extinctions of both species, provided the system consists of a sufficiently large number of local populations. This finding is in agreement with experimental results. It is therefore concluded that demographic stochasticity in combination with dispersal is capable of producing and maintaining sufficient asynchrony between local populations to ensure long‐term regional (metapopulation) persistence.     

Bi-trophic food chain dynamics with multiple component populations

Food web models describe the patterns of material and energy flow in communities. In classical food web models the state of each population is described by a single variable which represents, for instance, the biomass or the number of individuals that make up the population. However, in a number of models proposed recently in the literature the individual organisms consist of two components. In addition to the structural component there is an internal pool of nutrients, lipids or reserves. Consequently the population model for each trophic level is described by two state variables instead of one. As a result the classical predator-prey interaction formalisms have to be revised. In our model time budgets with actions as searching and handling provide the formulation of the functional response for both components. In the model, assimilation of the ingested two prey components is done in parallel and the extracted energy is added to a predators reserve pool. The reserves are used for vital processes; growth, reproduction and maintenance. We will explore the top-down modelling approach where the perspective is from the community. We will demonstrate that this approach facilitates a check on the balance equations for mass and energy at this level of organization. Here it will be shown that, if the individual is allowed to shrink when the energy reserves are in short to pay the maintenance costs, the growth process has to be 100% effective. This is unrealistic and some alternative model formulations are discussed. The long-term dynamics of a microbial food chain in the chemostat are studied using bifurcation analysis. The dilution rate and the concentration of nutrients in the reservoir are the bifurcation parameters. The studied microbial bi-trophic food chain with two-component populations shows chaotic behaviour.     

Induced changes in island fox (Urocyon littoralis) activity do not mitigate the extinction threat posed by a novel predator

Prey response to novel predators influences the impacts on prey populations of introduced predators, bio-control efforts, and predator range expansion. Predicting the impacts of novel predators on native prey requires an understanding of both predator avoidance strategies and their potential to reduce predation risk. We examine the response of island foxes (Urocyon littoralis) to invasion by golden eagles (Aquila chrysaetos). Foxes reduced daytime activity and increased night time activity relative to eagle-na?ve foxes. Individual foxes reverted toward diurnal tendencies following eagle removal efforts. We quantified the potential population impact of reduced diurnality by modeling island fox population dynamics. Our model predicted an annual population decline similar to what was observed following golden eagle invasion and predicted that the observed 11% reduction in daytime activity would not reduce predation risk sufficiently to reduce extinction risk. The limited effect of this behaviorally plastic predator avoidance strategy highlights the importance of linking behavioral change to population dynamics for predicting the impact of novel predators on resident prey populations.     

Chaotic dynamics of a food web in a chemostat

We analyze a mathematical model of a simple food web consisting of one predator and two prey populations in a chemostat. Monod's model is employed for the dependence of the specific growth rates of the two prey populations on the concentration of the rate-limiting substrate and a generalization of Monod's model for the dependence of the specific growth rate of the predator on the concentrations of the prey populations. We use numerical bifurcation techniques to determine the effect of the operating conditions of the chemostat on the dynamics of the system and construct its operating diagram. Chaotic behavior resulting from successive period doublings is observed. Multistability phenomena of coexistence of steady and periodic states at the same operating conditions are also found.     

Host-parasitoid spatial ecology: a plea for a landscape-level synthesis

A growing body of literature points to a large-scale research approach as essential for understanding population and community ecology. Many of our advances regarding the spatial ecology of predators and prey can be attributed to research with insect parasitoids and their hosts. In this review, we focus on the progress that has been made in the study of the movement and population dynamics of hosts and their parasitoids in heterogeneous landscapes, and how this research approach may be beneficial to pest management programs. To date, few studies have quantified prey and predator rates and ranges of dispersal and population dynamics at the patch level--the minimum of information needed to characterize population structure. From host-parasitoid studies with sufficient data, it is clear that the spatial scale of dispersal can differ significantly between a prey and its predators, local prey extinctions can be attributed to predators and predator extinction risk at the patch level often exceeds that of the prey. It is also evident that populations can be organized as a single, highly connected (patchy) population or as semi-independent extinction-prone local populations that collectively form a persistent metapopulation. A prey and its predators can also differ in population structure. At the landscape level, agricultural studies indicate that predator effects on its prey often spill over between the crop and surrounding area (matrix) and can depend strongly on landscape structure (e.g. the proportion of suitable habitat) at scales extending well beyond the crop margins. In light of existing empirical data, predator-prey models are typically spatially unrealistic, lacking important details on boundary responses and movement behaviour within and among patches. The tools exist for conducting empirical and theoretical research at the landscape level and we hope that this review calls attention to fertile areas for future exploration.     

Safety in numbers for secondary prey populations: an experimental test using egg predation by small mammals in New Zealand

New Zealand's native avifauna is threatened by introduced mammalian predators. Native species are often not the primary prey of these predators, which depend on introduced mice and rabbits as their primary food source. Theoretical models predict that predation risk for a subsidiary, or "secondary" prey species is inversely proportional to its population size. This prediction was tested by a quasi-natural experiment in which four different sized prey "colonies" were constructed at four existing sooty shearwater breeding sites. Domestic hens' eggs were placed in shearwater burrows immediately following the shearwater breeding season and egg predation rates monitored at five, ten and fifteen days. Treatments were switched between sites and the experiment run for a second time after a two-week stand-down period. The net effect of increasing colony size was to lower individual risk of predation. The larger number of individuals present served to effectively "buffer," or dilute, per-capita predation risk from predators whose numbers are fixed by extraneous factors: chiefly the abundance of their primary prey. Although eggs were removed more slowly from smaller colonies than from larger ones, each loss had a greater per-capita effect on individual mortality risk. The inverse density dependent relationship found between colony size and predation risk implies that predator population dynamics are largely independent of secondary prey numbers. Abundant introduced predators can therefore easily drive a small secondary prey population to extinction. Control of primary prey populations may be an important management tool in these circumstances.     

A model of the predatory impact of larval marine fish on the population dynamics of their zooplankton prey

A simulation model of the population dynamics of two speciesof calanoid copepods (Calanus.r pacificus and Pseudocalanussp.) was forced with predation pressure from a genetic, hypotheticalpopulation of larval marine fish. Results of the model are sensitiveto changes in parameters describing the dynamics of both predatorand prey populations, including initial numbers, fecundity,growth, mortality, size of prey organisms and feeding selectivityof the predators; the relative importance of these parametersis tested by way of a brute-force sensitivity analysis. Usingresults from recent ichthyoplankton surveys in Dabob Bay, WA,USA, the model was also forced with predation from populationsof larval Pacific herring (Clupea harengus pallasi) and Pacificwhiting (Merluccius productus). Results of the various simulationruns lead to the conclusion that marine fish larvae can significantlyimpact the population dynamics of their calanoid copepod prey,but that the magnitude of this impact is highly dependent onspecies-specific values of various population parameters.     

Eco-physiological Characterization of Soil Bacterial Populations in Different States of Growth

The method based on characterization of microbial populations in terms of their growth rate in agar plates has been used for testing the prediction of the theory of r- and K-selection in a microbial community from a tropical soil. Conditions which could lead bacterial populations to grow exponentially or to enter into a stationary phase were obtained by growing soil microbial populations in a chemostat and in a chemostat with recycle, respectively. Significant differences in population distribution patterns were observed by comparing results from the two growth systems. When soil community was grown in a chemostat and subjected specifically to well-defined r- and K-conditions, stable associations of organisms with r- and K-type characteristics developed as a consequence of environmental pressure. In contrast, when cultivated in chemostat with recycle under the same r- and K-conditions imposed on chemostat cultures, distribution patterns of r- and K-selected populations appeared very little affected by changes in substrate availability.     

Bifurcation analysis of a predator-prey model with predators using hawk and dove tactics

Most classical prey-predator models do not take into account the behavioural structure of the population. Usually, the predator and the prey populations are assumed to be homogeneous, i.e. all individuals behave in the same way. In this work, we shall take into account different tactics that predators can use for exploiting a common self-reproducing resource, the prey population. Predators fight together in order to keep or to have access to captured prey individuals. Individual predators can use two behavioural tactics when they encounter to dispute a prey, the classical hawk and dove tactics. We assume two different time scales. The fast time scale corresponds to the inter-specific searching and handling for the prey by the predators and the intra-specific fighting between the predators. The slow time scale corresponds to the (logistic) growth of the prey population and mortality of the predator. We take advantage of the two time scales to reduce the dimension of the model and to obtain an aggregated model that describes the dynamics of the total predator and prey densities at the slow time scale. We present the bifurcation analysis of the model and the effects of the different predator tactics on persistence and stability of the prey-predator community are discussed.     

Effects of spatial heterogeneity on the dynamics of a microbial feeding interaction

A mathematical model for an ideal chemostat in which one microbial population feeds on another and where Monod's model is used for the specific growth rates of both populations predicts a less stable behavior for the system than the one observed experimentally. Various factors have been proposed as being the reason for the increased stability of such systems. In this work, the effect of spatial heterogeneity on the dynamics of the microbial feeding interaction is studied. It is concluded that spatial heterogeneity has a stabilizing effect on the system. This effect combined with other factors could be the reason for the increased stability observed in systems where a microbial feeding interaction occurs.     

Inbreeding depression effects on extinction time in a predator—prey system

Summary Traditional methods of assessing population viability ignore both genetic—demographic interactions as well as community level dynamics. We address these deficiencies by presenting a model that investigates the effects of predation on a prey population experiencing inbreeding depression. Beginning with a simple Lotka—Volterra predator—prey system, we rewrite prey per capita mortality as a function of inbreeding. Inbreeding varies as a function of population size. Using computer simulation, we find that prey extinction times are inversely related to the level of inbreeding depression with and without predation. For all but very low levels of inbreeding depression, predation appreciably reduces persistence time. At moderate levels of inbreeding, predators go extinct before prey. When migration is introduced at low and moderate rates, persistence times only improve for those populations with low inbreeding depression measures. At a higher migration rate, persistence times are lengthened for low and moderately depressed prey populations. Increasing birth rates produce a visible, though noisy, trend towards increased times to extinction for low to moderate levels of inbreeding.     

Immigration can destabilize tri-trophic interactions: implications for conservation of top predators

Top predators often have large home ranges and thus are especially vulnerable to habitat loss and fragmentation. Increasing connectance among habitat patches is therefore a common conservation strategy, based in part on models showing that increased migration between subpopulations can reduce vulnerability arising from population isolation. Although three-dimensional models are appropriate for exploring consequences to top predators, the effects of immigration on tri-trophic interactions have rarely been considered. To explore the effects of immigration on the equilibrium abundances of top predators, we studied the effects of immigration in the three-dimensional Rosenzweig-MacArthur model. To investigate the stability of the top predator equilibrium, we used MATCONT to perform a bifurcation analysis. For some combinations of model parameters with low rates of top predator immigration, population trajectories spiral towards a stable focus. Holding other parameters constant, as immigration rate is increased, a supercritical Hopf bifurcation results in a stable limit cycle and thus top predator populations that cycle between high and low abundances. Furthermore, bistability arises as immigration of the intermediate predator is increased. In this case, top predators may exist at relatively low abundances while prey become extinct, or for other initial conditions, the relatively higher top predator abundance controls intermediate predators allowing for non-zero prey population abundance and increased diversity. Thus, our results reveal one of two outcomes when immigration is added to the model. First, over some range of top predator immigration rates, population abundance cycles between high and low values, making extinction from the trough of such cycles more likely than otherwise. Second, for relatively higher intermediate predator migration rates, top predators may exist at low values in a truncated system with impoverished diversity, again with extinction more likely.     

A reinforcement learning-based predator-prey model

Classic population models can often predict the dynamics of biological populations in nature. However, the adaptation process and learning mechanism of species are rarely considered in the study of population dynamics, due to the complex interaction of species, seasonal variation, spatial distribution or other factors. We use reinforcement learning algorithms to improve the existing individual-based ecosystem simulation algorithms, which allows species to spontaneously adjust their strategies according to a short period of experience and then feed back to improve their abilities to make action decisions. Our results show that the reinforcement learning of predators is beneficial to the stability of the ecosystem, and predators can learn to spontaneously form hunting patterns that surround their prey. The learning of prey makes the ecosystem oscillate and meanwhile leads to a higher risk of extinction for predators. When individuals are more likely to die, these herbivores rely on reproductive behavior to maintain their populations; when individuals live longer, herbivores spend more time eating to maintain their own survival. The co-reinforcement learning of predators and prey helps predators to find a more suitable way to survive with their prey, that is, the number of predators is more stable and larger than when only predator or only prey learns.     

Complex dynamics of a predator–prey–parasite system: An interplay among infection rate,predator's reproductive gain and preference

Parasites are considered as an important factor in regulating their host populations through trait-mediated effects. On the other hand, predation becomes particularly interesting in host–parasite systems because predation can significantly alter the abundance of parasites and their host population. The combined effects of parasites and predator on host population and community structure therefore may have larger effect. Different field experiments confirm that predators consume disproportionately large number of infected prey in comparison to their susceptible counterpart. There are also substantial evidences that predator has the ability to distinguish prey that have been infected by a parasite and avoid such prey to reduce fitness cost. In this paper we study the predator–prey dynamics, where the prey species is infected by some parasites and predators consume both the susceptible and infected prey with some preference. We demonstrate that complexity in such systems largely depends on the predator's selectivity, force of infection and predator's reproductive gain. If the force of infection and predator's reproductive gain are low, parasites and predators both go to extinction whatever be the predator's preference. The story may be totally different in the opposite case. Survival of species in stable, oscillatory or chaotic states, and their extinction largely depend on the predator's preference. The system may also show two coexistence equilibrium points for some parameter values. The equilibrium with lower susceptible prey density is always stable and the equilibrium with higher susceptible prey density is always unstable. These results suggest that understanding the consequences of predator's selectivity or preference may be crucial for community structure involving parasites.     

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.