Permanence induced by life-cycle resonances: the periodical cicada problem

Periodical cicadas are known for their unusually long life cycle for insects and their prime periodicity of either 13 or 17 years. One of the explanations for the prime periodicity is that the prime periods are selected to prevent cicadas from resonating with predators with submultiple periods. This paper considers this hypothesis by investigating a population model for periodical predator and prey. The study shows that if the periods of the two periodical species are not coprime, then the predator cannot resist the invasion of the prey. On the other hand, if the periods are coprime, then the predator can resist the invasion of the prey. It is also shown that if the periods are not coprime, then the life-cycle resonance can induce a permanent system, in which no cohorts are missing in both populations. On the other hand, if the periods are coprime, then the system cannot be permanent.     

Red-winged blackbird predation on periodical cicadas (Cicadidae: Magicicada spp.): bird behavior and cicada responses

Summary Predation by red-winged blackbirds Agelaius phoeniceus L. on 13-year periodical cicadas (Magicicada spp.) and reactions by periodical cicadas to predators were studied during emergence of Brood XIX during summer of 1985 in northwestern Arkansas (USA). Emergences of periodical cicadas are classic examples of predator satiation due to high local densities of cicadas and birds are the major predators of adult periodical cicadas. Reactions of periodical cicadas to predators were assessed by recording behaviors exhibited by cicadas when approached in trees by a human hand during the 3-week period of peak adult densitics. Most male cicadas made a noise in association with escape behaviors when approached, and 50% of the females, which are silent, attempted escape behaviors. Observations of predation attempts on cicadas by red-winged blackbirds were made during the period of peak predation pressure. Red-winged blackbirds spent less time searching for cicadas over that 2-week period of increasing predation pressure, and became increasingly efficient at capturing cicadas. Handling time of cicadas by red-winged blackbirds increased by about 20 seconds over that period, as blackbirds spent more time consuming female cicadas. The flysquawk response, used only by male cicadas, was effective in deterring red-winged blackbirds; only 5% of the attacks by blackbirds were successful when that behavior was exhibited. All cicadas that remained motionless and silent when approached by blackbirds were captured and consumed. Because females remained inactive when approached more often than did males, blackbirds may have consumed more female cicadas. Changes that appeared in reactions of preiodical cicadas to the model predator and to the attacks of blackbirds reflect both changes in the sex ratio of the cicada populations and changes in behaviors of cicadas associated with mating and egg laying. The loud noise made by male periodical cicadas at mating centers did not appear to deter predation by blackbirds. Changes in the behavior of blackbirds that appeared to be in association with greater predation on female periodical cicadas relates directly to aspects of foraging theory, particularly predictions concerning more selective foraging during periods of abundant food resources.     

Generalist and specialist predators that mediate permanence in ecological communities

 General dynamic models of systems with two prey and one or two predators are considered. After rescaling the equations so that both prey have the same intrinsic rate of growth, it is shown that there exists a generalist predator that can mediate permanence if and only if there is a population density of a prey at which its per-capita growth rate is positive yet less than its competitor’s invasion rate. In particular, this result implies that if the outcome of competition between the prey is independent of initial conditions, then there exists a generalist predator that mediates permanence. On the other hand, if the outcome of competition is contingent upon initial conditions (i.e., the prey are bistable), then there may not exist a suitable generalist predator. For example, bistable prey modeled by the Ayala–Gilpin (θ-Logistic) equations can be stabilized if and only if θ<1 for one of the prey. It is also shown that two specialist predators always can mediate permanence between bistable prey by creating a repelling heteroclinic cycle consisting of fixed points and limit cycles. Received 10 August 1996; received in revised form 21 March 1997     

6-year periodicity and variable synchronicity in a mass-flowering plant

Periodical organisms, such as bamboos and periodical cicadas, are very famous for their synchronous reproduction. In bamboos and other periodical plants, the synchronicity of mass-flowering and withering has been often reported indicating these species are monocarpic (semelparous) species. Therefore, synchronicity and periodicity are often suspected to be fairly tightly coupled traits in these periodical plants. We investigate the periodicity and synchronicity of Strobilanthes flexicaulis, and a closely related species S. tashiroi on Okinawa Island, Japan. The genus Strobilanthes is known for several periodical species. Based on 32-year observational data, we confirmed that S. flexicaulis is 6-year periodical mass-flowering monocarpic plant. All the flowering plants had died after flowering. In contrast, we found that S. tashiroi is a polycarpic perennial with no mass-flowering from three-year individual tracking. We also surveyed six local populations of S. flexicaulis and found variation in the synchronicity from four highly synchronized populations (>98% of plants flowering in the mass year) to two less synchronized one with 11-47% of plants flowering before and after the mass year. This result might imply that synchrony may be selected for when periodicity is established in monocarpic species. We found the selective advantages for mass-flowering in pollinator activities and predator satiation. The current results suggest that the periodical S. flexicaulis might have evolved periodicity from a non-periodical close relative. The current report should become a key finding for understanding the evolution of periodical plants.     

Modelling Disease Introduction as Biological Control of Invasive Predators to Preserve Endangered Prey

Invasive species are a significant cause of bio-diversity loss particularly in island ecosystems. It has been suggested to release pathogenic parasites as an efficient control measure of these mostly immune-naïve populations. In order to explore the potential impacts of such bio-control approach, we construct and investigate mathematical models describing disease dynamics in a host population that acts as a predator embedded in a simple food chain. The consequences of Feline Immunodeficiency Virus (FIV) introduction into a closed ecosystem are addressed using a bi-trophic system, comprising an indigenous prey (birds) and an introduced predator (cats). Our results show that FIV is unlikely to fully eradicate cats on sub-Antarctic islands, but it can be efficient in depressing their population size, allowing for the recovery of the endangered prey. Depending on the ecological setting and disease transmission mode (we consider proportionate mixing as well as mass action), successful pathogen invasion can induce population oscillations that are not possible in the disease-free predator–prey system. These fluctuations can be seen as a mixed blessing from a management point of view. On the one hand, they may increase the extinction risk of the birds. On the other hand, they provide an opportunity to eradicate cats more easily in combination with other methods such as trapping or culling.     

Secondary predation: quantification of food chain errors in an aphid-spider-carabid system using monoclonal antibodies

"Secondary predation" occurs when one predator feeds on a second predator, which has in turn eaten a target prey. Detection of prey remains within predators using monoclonal antibodies cannot distinguish between primary and secondary predation, potentially leading to quantitative and qualitative food chain errors. We report the first fully replicated experiments to measure secondary predation effects, using an aphid-spider-carabid system. Aphids, Sitobion avenae, were fed to spiders, Lepthyphantes tenuis, which were allowed to digest their prey for a range of time intervals. The spiders were then fed to carabids, Poecilus (=Pterostichus) cupreus, which were again allowed to digest their prey for set periods. The anti-aphid monoclonal antibody used to identify S. avenae remains in P. cupreus was one that detected an epitope that increased in availability over the first few hours of digestion, amplifying the signal, extending detection periods and thus increasing the chances of detecting secondary predation. Despite this, and the fact that spiders are known to digest their prey more slowly than many other predators, detection of secondary predation was only possible if the carabids were killed immediately after consuming at least two spiders which were, in turn, eaten immediately after consuming aphids. As this scenario is unlikely to occur frequently in the field it was concluded that secondary predation is unlikely to be a serious source of error during field studies.     

A functional response model of a predator population foraging in a patchy habitat

1. Functional response models (e.g. Holling's disc equation) that do not take the spatial distributions of prey and predators into account are likely to produce biased estimates of predation rates. 2. To investigate the consequences of ignoring prey distribution and predator aggregation, a general analytical model of a predator population occupying a patchy environment with a single species of prey is developed. 3. The model includes the density and the spatial distribution of the prey population, the aggregative response of the predators and their mutual interference. 4. The model provides explicit solutions to a number of scenarios that can be independently combined: the prey has an even, random or clumped distribution, and the predators show a convex, sigmoid, linear or no aggregative response. 5. The model is parameterized with data from an acarine predator-prey system consisting of Phytoseiulus persimis and Tetranychus urticae inhabiting greenhouse cucumbers. 6. The model fits empirical data quite well and much better than if prey and predators were assumed to be evenly distributed among patches, or if the predators were distributed independently of the prey. 7. The analyses show that if the predators do not show an aggregative response it will always be an advantage to the prey to adopt a patchy distribution. On the other hand, if the predators are capable of responding to the distribution of prey, then it will be an advantage to the prey to be evenly distributed when its density is low and switch to a more patchy distribution when its density increases. The effect of mutual interference is negligible unless predator density is very high. 8. The model shows that prey patchiness and predator aggregation in combination can change the functional response at the population level from type II to type III, indicating that these factors may contribute to stabilization of predator-prey dynamics.     

Destabilizing effect of cannibalism on a structured predator-prey system

The dynamics of a predator-prey system, where the predator has two stages, a juvenile stage and a mature stage, are modelled by a system of three ordinary differential equations. The mature predators prey on the juvenile predators in addition to the prey. If the mortality rate of juveniles is low and/or the recruitment rate to the mature population is high, then there is a stable equilibrium with all three population sizes positive. On the other hand, if the mortality rate of juveniles is high and/or the recruitment rate to the mature population is low, then the equilibrium will be stable for low levels of cannibalism, but a loss of stability by a Hopf bifurcation will take place as the level of cannibalism increases. Numerical studies indicate that a stable limit cycle appears. Cannibalism can therefore be a destabilizing force in a predator-prey system.     

Do native predators benefit from non‐native prey?

Despite knowledge on invasive species’ predatory effects, we know little of their influence as prey. Non‐native prey should have a neutral to positive effect on native predators by supplementing the prey base. However, if non‐native prey displace native prey, then an invader's net influence should depend on both its abundance and value relative to native prey. We conducted a meta‐analysis to quantify the effect of non‐native prey on native predator populations. Relative to native prey, non‐native prey similarly or negatively affect native predators, but only when studies employed a substitutive design that examined the effects of each prey species in isolation from other prey. When native predators had access to non‐native and native prey simultaneously, predator abundance increased significantly relative to pre‐invasion abundance. Although non‐native prey may have a lower per capita value than native prey, they seem to benefit native predators by serving as a supplemental prey resource.     

Analysis of a competitive prey–predator system with a prey refuge

Gauss's competitive exclusive principle states that two competing species having analogous environment cannot usually occupy the same space at a time but in order to exploit their common environment in a different manner, they can co-exist only when they are active in different times. On the other hand, several studies on predators in various natural and laboratory situations have shown that competitive coexistence can result from predation in a way by resisting any one prey species from becoming sufficiently abundant to outcompete other species such that the predator makes the coexistence possible. It has also been shown that the use of refuges by a fraction of the prey population exerts a stabilizing effect in the interacting population dynamics. Further, the field surveys in the Sundarban mangrove ecosystem reveal that two detritivorous fishes, viz. Liza parsia and Liza tade (prey population) coexist in nature with the presence of the predator fish population, viz. Lates calcarifer by using refuges.     

Persistence of predator-prey systems in an uncertain environment

Summary The time derivatives of prey and predator populations are assumed to satisfy a set of inequalities, instead of a precise differential equation, reflecting an uncertain environmental and/or lack of knowledge by the modeler. A system of differential equations is found whose solution gives the boundary of a persistent set, which is positive flow invariant for any system satisfying the inequalities. Conditions are given for the persistent set to be bounded away from both axes, which show that resonance effects cannot drive either predator or prey to extinction if that does not happen for an autonomous system satisfying the inequalities. In general predator-prey systems are more persistent when there is strong asymptotic stability, when there is correlation between prey and predator dynamics, when the effect of perturbations is density dependent, and are more persistent under perturbations of the prey than of the predator.     

Existence and bifurcation of stable equilibrium in two-prey,one-predator communities

In this paper, stability of two-prey, one-predator communities is investigated by Lyapunov's direct method and Hopf's bifurcation theory. Three patterns of three-species coexistence are possible. A globally stable non-negative equilibrium exists for the system even if two competing prey species without a predator cannot coexist. The stable equilibrium bifurcates to a periodic motion with a small amplitude when the predation rate increases. It is also shown that a chaotic motion emerges from the periodic motion when one of two prey has greater competitive abilities than the other. This predator-mediated coexistence can be realized by the intimate relationship between preferences of a predator and competitive abilities of two prey.     

一类分段光滑的捕食-食饵模型的动力学分析

考虑到某些动物有冬眠的习性,本文提出了食饵有冬眠习性的分段光滑的捕食-食饵模型,得到了平凡周期解全局稳定的条件.数值模拟表明,在一定的条件下,捕食者食饵将持续共存.     

Advanced autumn migration of sparrowhawk has increased the predation risk of long-distance migrants in Finland

Predation affects life history traits of nearly all organisms and the population consequences of predator avoidance are often larger than predation itself. Climate change has been shown to cause phenological changes. These changes are not necessarily similar between species and may cause mismatches between prey and predator. Eurasian sparrowhawk Accipiter nisus, the main predator of passerines, has advanced its autumn phenology by about ten days in 30 years due to climate change. However, we do not know if sparrowhawk migrate earlier in response to earlier migration by its prey or if earlier sparrowhawk migration results in changes to predation risk on its prey. By using the median departure date of 41 passerine species I was able to show that early migrating passerines tend to advance, and late migrating species delay their departure, but none of the species have advanced their departure times as much as the sparrowhawk. This has lead to a situation of increased predation risk on early migrating long-distance migrants (LDM) and decreased the overlap of migration season with later departing short-distance migrants (SDM). Findings highlight the growing list of problems of declining LDM populations caused by climate change. On the other hand it seems that the autumn migration may become safer for SDM whose populations are growing. Results demonstrate that passerines show very conservative response in autumn phenology to climate change, and thus phenological mismatches caused by global warming are not necessarily increasing towards the higher trophic levels.     

Population dynamics of a generalist rodent in relation to variability in pulsed food resources in a fragmented landscape

1. Pulsed food resources are often considered equivalent in their potential impact on the reproduction and population dynamics of consumers, but differences in the attributes of food pulses and their distribution in the landscape may cause differences in their effects. 2. We tested whether a perishable pulsed resource (periodical cicadas, Magicicada spp.) had similar effects on the population dynamics of a generalist forest rodent, Peromyscus leucopus, as have been reported for a cacheable pulsed resource (acorn mast). 3. Because the availability of periodical cicadas may vary between edge and interior habitat, we also tested whether habitat type (edge vs. interior) and fragment size affected the abundance of cicadas and P. leucopus. 4. Nearly 90% of the variation in the relative population densities of P. leucopus was explained by the variation in the relative densities of periodical cicadas, and fragments with more cicadas tended to have more reproductive female mice and litters. 5. We found more cicadas and more P. leucopus in edge than interior habitat, but no differences in the relative densities of either in relation to fragment size. 6. Data from a non-emergence year revealed no differences other than the presence of periodical cicadas that could explain the 50% higher relative densities of P. leucopus in the emergence year. 7. At the beginning of the emergence of periodical cicadas, the three fragments with the highest numbers of emergence holes had three times more mice than the fragments with the lowest numbers of emergence holes, suggesting that P. leucopus is able to anticipate the emergence of periodical cicadas and increase reproduction prior to the pulse. 8. Hence, despite differences in perishability, seasonal timing and nutritional quality of pulsed food resources in a fragmented landscape, they appear to have similar positive effects on the population dynamics of the generalist rodent, P. leucopus and, in fact, P. leucopus may be able to anticipate resource pulses.     

Evolutionary branching and evolutionarily stable coexistence of predator species: Critical function analysis

On the ecological timescale, two predator species with linear functional responses can stably coexist on two competing prey species. In this paper, with the methods of adaptive dynamics and critical function analysis, we investigate under what conditions such a coexistence is also evolutionarily stable, and whether the two predator species may evolve from a single ancestor via evolutionary branching. We assume that predator strategies differ in capture rates and a predator with a high capture rate for one prey has a low capture rate for the other and vice versa. First, by using the method of critical function analysis, we identify the general properties of trade-off functions that allow for evolutionary branching in the predator strategy. It is found that if the trade-off curve is weakly convex in the vicinity of the singular strategy and the interspecific prey competition is not strong, then this singular strategy is an evolutionary branching point, near which the resident and mutant predator populations can coexist and diverge in their strategies. Second, we find that after branching has occurred in the predator phenotype, if the trade-off curve is globally convex, the predator population will eventually branch into two extreme specialists, each completely specializing on a particular prey species. However, in the case of smoothed step function-like trade-off, an interior dimorphic singular coalition becomes possible, the predator population will eventually evolve into two generalist species, each feeding on both of the two prey species. The algebraical analysis reveals that an evolutionarily stable dimorphism will always be attractive and that no further branching is possible under this model.     

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.     

The influence of vigilance on intraguild predation

Theoretical work on intraguild predation suggests that if a top predator and an intermediate predator share prey, the system will be stable only if the intermediate predator is better at exploiting the prey, and the top predator gains significantly from consuming the intermediate predator. In mammalian carnivore systems, however, there are examples of top predator species that attack intermediate predator species, but rarely or never consume the intermediate predator. We suggest that top predators attacking intermediate predators without consuming them may not only reduce competition with the intermediate predators, but may also increase the vigilance of the intermediate predators or alter the vigilance of their shared prey, and that this behavioral response may help to maintain the stability of the system. We examine two models of intraguild predation, one that incorporates prey vigilance, and a second that incorporates intermediate predator vigilance. We find that stable coexistence can occur when the top predator has a very low consumption rate on the intermediate predator, as long as the attack rate on the intermediate predator is relatively large. However, the system is stable when the top predator never consumes the intermediate predator only if the two predators share more than one prey species. If the predators do share two prey species, and those prey are vigilant, increasing top predator attack rates on the intermediate predator reduces competition with the intermediate predator and reduces vigilance by the prey, thereby leading to higher top predator densities. These results suggest that predator and prey behavior may play an important dynamical role in systems with intraguild predation.     

What Happens When Predators Do Not Completely Consume Their Prey?

A mathematical model is presented for the dynamics of predator-prey interactions when predators do not consume prey (or clumps of prey) in their entirety. Using a combination of analytical and numerical methods, I demonstrate that predator-mediated changes in the distribution of intact and partially consumed prey can affect the outcome of competition between predators in unexpected ways. In some cases, two predators can coexist on a single prey species owing to tradeoffs between the ability to consume prey completely and other competitive abilities. In other cases, predators exhibit frequency-dependent dynamics in which the first predator to occupy the habitat can prevent the other from invading. Conditions for stable coexistence usually expand if the larger predator scatters uneaten prey parts, if prey renewal includes both small and large items, or if the predator with the smaller retrieval capacity is poor at catching intact prey relative to the other predator.     

Did Gause Have a Yeast Infection?

We planned to develop predator–prey models using Paramecium and yeast, but they have not been empirically examined since work by Gause in the 1930s. Therefore, we evaluated if Paramecium aurelia ingests and grows on eight yeasts. Recognising that it ingested yeasts but could not grow, we assessed if it might grow on other yeasts, by empirically parameterising a predator–prey model that relies on ingestion, not growth. Simulations were compared to P. aurelia‐yeast time‐series data, from Gause. We hypothesised that if the model simulated predator–prey dynamics that mimicked the original data, then possibly P. aurelia could grow on yeast; simulations did not mimic the original data. Reviewing works by Gause exposed two issues: experiments were undoubtedly contaminated with bacteria, allowing growth on bacteria, not yeast; and the population cycle data cannot be considered a self‐sustaining time series, as they were manipulated by adding yeast and ciliates. We conclude that past and future work should not rely on this system, for either empirical or theoretical evaluations. Finally, although we show that P. aurelia, P. caudatum, Euplotes patella, and Blepharisma sp. cannot grow on yeast, Tetrahymena pyriformis and Colpidium striatum can; these may provide models to explore predator–prey dynamics.