Invasion sequence affects predator-prey dynamics in a multi-species interaction

Global Dynamics of a Predator–Prey Model with Fear Effect and Impulsive State Feedback Control

In this paper, a predator–prey model with fear effect and impulsive state control is proposed and analyzed. By constructing an appropriate Poincaré map, the dynamic properties of the system, including the existence, nonexistence, and stability of periodic solutions are studied. More specifically, based on the biological meaning, the pulse and the phase set are firstly defined in different regions as well as the corresponding Poincaré map. Subsequently, the properties of the Poincaré map are analyzed, and the existence of a periodic solution for the system is investigated according to the properties of the Poincaré map. We found that the existence of the periodic solution for the system completely depends on the property of the Poincaré map. Finally, several examples containing numerical simulations verify the obtained theoretical result.

Manipulating the strength of organism-environment feedback increases nonlinearity and apparent hysteresis of ecosystem response to environmental change

Theory predicts that organism-environment feedbacks play a central role in how ecological communities respond to environmental change. Strong feedback causes greater nonlinearity between environmental change and ecosystem state, increases the likelihood of hysteresis in response to environmental change, and augments the possibility of alternative stable regimes. To illustrate these predictions and their dependence on a temporal scale, we simulated a minimal ecosystem model. To test the predictions, we manipulated the feedback strength between the metabolism and the dissolved oxygen concentration in an aquatic heterotrophic tri-trophic community in microecosystems. The manipulation consisted of five levels, ranging from low to high feedback strength by altering the oxygen diffusivity: free gas exchange between the microcosm atmosphere and the external air (metabolism not strongly affecting environmental oxygen), with the regular addition of 200, 100, or 50 ml of air and no gas exchange. To test for nonlinearity and hysteresis in response to environmental change, all microecosystems experienced a gradual temperature increase from 15 to 25°C and then back to 15°C. We regularly measured the dissolved oxygen concentration, total biomass, and species abundance. Nonlinearity and hysteresis were higher in treatments with stronger organism-environment feedbacks. There was no evidence that stronger feedback increased the number of observed ecosystem states. These empirical results are in broad agreement with the theory that stronger feedback increases nonlinearity and hysteresis. They therefore represent one of the first direct empirical tests of the importance of feedback strength. However, we discuss several limitations of the study, which weaken confidence in this interpretation. Research demonstrating the causal effects of feedback strength on ecosystem responses to environmental change should be placed at the core of efforts to plan for sustainable ecosystems.

Environmental degradation amplifies species' responses to temperature variation in a trophic interaction

Land‐use and climate change are two of the primary drivers of the current biodiversity crisis. However, we lack understanding of how single‐species and multispecies associations are affected by interactions between multiple environmental stressors.

We address this gap by examining how environmental degradation interacts with daily stochastic temperature variation to affect individual life history and population dynamics in a host–parasitoid trophic interaction, using the Indian meal moth, Plodia interpunctella, and its parasitoid wasp Venturia canescens.

We carried out a single‐generation individual life‐history experiment and a multigeneration microcosm experiment during which individuals and microcosms were maintained at a mean temperature of 26°C that was either kept constant or varied stochastically, at four levels of host resource degradation, in the presence or absence of parasitoids.

At the individual level, resource degradation increased juvenile development time and decreased adult body size in both species. Parasitoids were more sensitive to temperature variation than their hosts, with a shorter juvenile stage duration than in constant temperatures and a longer adult life span in moderately degraded environments. Resource degradation also altered the host's response to temperature variation, leading to a longer juvenile development time at high resource degradation. At the population level, moderate resource degradation amplified the effects of temperature variation on host and parasitoid populations compared with no or high resource degradation and parasitoid overall abundance was lower in fluctuating temperatures. Top‐down regulation by the parasitoid and bottom‐up regulation driven by resource degradation contributed to more than 50% of host and parasitoid population responses to temperature variation.

Our results demonstrate that environmental degradation can strongly affect how species in a trophic interaction respond to short‐term temperature fluctuations through direct and indirect trait‐mediated effects. These effects are driven by species differences in sensitivity to environmental conditions and modulate top‐down (parasitism) and bottom‐up (resource) regulation. This study highlights the need to account for differences in the sensitivity of species’ traits to environmental stressors to understand how interacting species will respond to simultaneous anthropogenic changes.

Warming at the population level: Effects on age structure, density, and generation cycles

The impact of climate change on strongly age-structured populations is poorly understood, despite the central role of temperature in determining developmental rates in ectotherms. Here we examine the effect of warming and its interactions with resource availability on the population dynamics of the pyralid moth Plodia interpunctella, populations of which normally show generation cycles, a consequence of strong and asymmetric age-related competition. Warming by 3°C above the standard culture temperature led to substantial changes in population density, age structure, and population dynamics. Adult populations were some 50% larger in warmed populations, probably because the reduced fecundity associated with warming leads to reduced larval competition, allowing more larvae to develop to adulthood. Warming also interacted with resource availability to alter population dynamics, with the generation cycles typical of this species breaking down in the 30° populations when standard laboratory diet was provided but not when a reduced nutrient poor diet was used. Warming by 6° led to either rapid extinction or the persistence of populations at low densities for the duration of the experiment. We conclude that even moderate warming can have considerable effects on population structure and dynamics, potentially leading to complete changes in dynamics in some cases. These results are particularly relevant given the large number of economically important species that exhibit generation cycling, in many cases arising from similar mechanisms to those operating in P. interpunctella.

Temporal autocorrelation in host density increases establishment success of parasitoids in an experimental system

Environmental variation is classically expected to affect negatively population growth and to increase extinction risk, and it has been identified as a major determinant of establishment failures in the field. Yet, recent theoretical investigations have shown that the structure of environmental variation and more precisely the presence of positive temporal autocorrelation might alter this prediction. This is particularly likely to affect the establishment dynamics of biological control agents in the field, as host–parasitoid interactions are expected to induce temporal autocorrelation in host abundance. In the case where parasitoid populations display overcompensatory dynamics, the presence of such positive temporal autocorrelation should increase their establishment success in a variable environment. We tested this prediction in laboratory microcosms by introducing parasitoids to hosts whose abundances were manipulated to simulate uncorrelated or positively autocorrelated variations in carrying capacity. We found that environmental variability decreased population size and increased parasitoid population variance, which is classically expected to extinction risk. However, although exposed to significant environmental variation, we found that parasitoid populations experiencing positive temporal autocorrelation in host abundance were more likely to persist than populations exposed to uncorrelated variation. These results confirm that environmental variation is a key determinant of extinction dynamics that can have counterintuitive effects depending on its autocorrelation structure.

ROLE OF HARVESTING IN CONTROLLING CHAOTIC DYNAMICS IN THE PREDATOR–PREY MODEL WITH DISEASE IN THE PREDATOR

Predator–prey model with harvesting is well studied. The role of disease in such system has a great importance and cannot be ignored. In this study we have considered a predator–prey model with disease circulating in the predator population only and we have also considered harvesting in the prey and in the susceptible predator. We have studied the local stability, Hopf bifurcation of the model system around the equilibria. We have derived the ecological and the disease basic reproduction numbers and we have observed its importance in the community structure of the model system and in controlling disease propagation in the predator population. We have paid attention to chaotic dynamics for increasing the force of infection in the predator. Chaotic population dynamics can exhibit irregular fluctuations and violent oscillations with extremely small or large population abundances. In this study main objective is to show the role of harvesting in controlling chaotic dynamics. It is observed that reasonable harvesting on the prey and the susceptible predator prevents chaotic dynamics.

Contingency and statistical laws in replicate microbial closed ecosystems

Contingency, the persistent influence of past random events, pervades biology. To what extent, then, is each course of ecological or evolutionary dynamics unique, and to what extent are these dynamics subject to a common statistical structure? Addressing this question requires replicate measurements to search for emergent statistical laws. We establish a readily replicated microbial closed ecosystem (CES), sustaining its three species for years. We precisely measure the local population density of each species in many CES replicates, started from the same initial conditions and kept under constant light and temperature. The covariation among replicates of the three species densities acquires a stable structure, which could be decomposed into discrete eigenvectors, or "ecomodes." The largest ecomode dominates population density fluctuations around the replicate-average dynamics. These fluctuations follow simple power laws consistent with a geometric random walk. Thus, variability in ecological dynamics can be studied with CES replicates and described by simple statistical laws.

The biology of small, introduced populations, with special reference to biological control

Populations are introduced into novel environments in different contexts, one being the biological control of pests. Despite intense efforts, less than half introduced biological control agents establish. Among the possible approaches to improve biological control, one is to better understand the processes that underpin introductions and contribute to ecological and evolutionary success. In this perspective, we first review the demographic and genetic processes at play in small populations, be they stochastic or deterministic. We discuss the theoretical outcomes of these different processes with respect to individual fitness, population growth rate, and establishment probability. Predicted outcomes differ subtly in some cases, but enough so that the evaluating results of introductions have the potential to reveal which processes play important roles in introduced populations. Second, we attempt to link the theory we have discussed with empirical data from biological control introductions. A main result is that there are few available data, but we nonetheless report on an increasing number of well-designed, theory-driven, experimental approaches. Combining demography and genetics from both theoretical and empirical perspectives highlights novel and exciting avenues for research on the biology of small, introduced populations, and great potential for improving both our understanding and practice of biological control.

Alternative community compositional and dynamical states: the dual consequences of assembly history

1. Much work on ecological consequences of community assembly history has focused on the formation of history-induced alternative stable equilibria. We hypothesize that assembly history may affect not only community composition but also population dynamics, with assembled communities differing in species composition potentially residing in different dynamical states. 2. We provided an empirical test of the aforementioned hypothesis using a laboratory microcosm experiment that manipulated both the colonization order of three bacterivorous protist species in the presence of a protist predator and environmental productivity. 3. Both priority effects and random divergence emerged, resulting in two different community compositional states: one characterized by the dominance of one prey species and the other by the extinction of the same prey. While communities in the former state exhibited noncyclic dynamics, the majority of communities in the latter state exhibited cyclic dynamics driven by the interaction between another prey and the predator. 4. Temporal variability of total prey community biovolume consequently differed among communities with different histories. 5. Changing productivity altered priority effects on the structure and dynamics of communities experiencing only certain histories. 6. Our results support the dual (compositional and dynamical) consequences of assembly history and emphasize the importance of incorporating the dynamical view into the field of community assembly.

Effects of abundance on infection in natural populations: field voles and cowpox virus

Detailed results on the dynamics of cowpox virus infection in four natural populations of the field vole, Microtus agrestis, are presented. Populations were sampled every 4 weeks (8 weeks in mid-winter) for 6 years. The purpose was to examine the relationships between overall or susceptible host abundance (N, S) and both the number of infected hosts (I) and the prevalence of infection (I/N). Overall, both I and I/N increased with N. However, evidence for a threshold abundance, below which infection was not found, was at best equivocal in spite of the wide range of abundances sampled. Cross-correlation analyses reflected annual and multi-annual cycles in N, I, S and I/N, but whereas N was most strongly correlated with contemporary values of I and I/N, in the case of S, the strongest correlations were with values 1 to 2 months preceding the values of I and I/N. There was no evidence for a 'juvenile dilution effect' (prevalence decreasing with abundance as new susceptibles flush into the population) and only weak evidence of a time-delayed effect of abundance on the number infected. We argue that these effects may occur only in systems with characteristics that are not found here. Transfer function analyses, which have been neglected in epidemiology, were applied. These models, with ln(S) as the input parameter, in spite of their simplicity, could be linked closely to conventional formulations of the transmission process and were highly effective in predicting the number infected. By contrast, transfer function models with ln(N) as the input parameter were less successful in predicting the number infected and/or were more complex and more difficult to interpret. Nonetheless, overall, we contend that while monitoring numbers susceptible has most to offer, monitoring overall abundance may provide valuable insights into the dynamics of infection.

The interplay between determinism and stochasticity in childhood diseases

An important issue in the history of ecology has been the study of the relative importance of deterministic forces and processes noise in shaping the dynamics of ecological populations. We address this question by exploring the temporal dynamics of two childhood infections, measles and whooping cough, in England and Wales. We demonstrate that epidemics of whooping cough are strongly influenced by stochasticity; fully deterministic approaches cannot achieve even a qualitative fit to the observed data. In contrast, measles dynamics are extremely well explained by a deterministic model. These differences are shown to be caused by their contrasting responses to dynamical noise due to different infectious periods.

Complex interactions between a plant pathogen and insect parasitoid via the shared vector-host: consequences for host plant infection

Plant viruses modify the development of their aphid vectors by inducing physiological changes in the shared host plant. The performance of hymenopterous parasitoids exploiting these aphids can also be modified by the presence of the plant pathogen. We used laboratory and glasshouse microcosms containing beans (Vicia faba) as the host plant to examine the interactions between a plant virus (pea enation mosaic virus; PEMV) and a hymenopterous parasitoid (Aphidius ervi) that share the aphid vector/host Acyrthosiphon pisum. Neither PEMV-infection of V. faba, nor the carriage of PEMV virions by A. pisum, affected the growth or morphology of the aphid, or the oviposition behaviour and development of A. ervi. The presence of developing Aphidius ervi larvae within Acyrthosiphon pisum did not affect the ability of the aphids to transmit PEMV. However, by reducing their longevity, parasitism ultimately decreased the time viruliferous aphids were able to inoculate plants. In terms of virus dispersal, parasitized aphids exhibited more movement around experimental arenas than unparasitized controls, causing a slight increase in the proportion of beans infected with PEMV. Exposure to adult Aphidius ervi caused Acyrthosiphon pisum to rapidly drop off bean plants and disperse to new hosts, resulting in considerably higher plant infection rates (70%) than that seen in control arenas (25%). The results of this investigation demonstrate that when parasitoids are added to a plant-pathogen-vector system, benefits to the host plant due to reduced herbivore infestation must be balanced against the consequences of parasitoid-induced aphid dispersal and a subsequent increase in the level of plant infection.

Microcosm experiments can inform global ecological problems

Global-scale environmental problems are rarely regarded as amenable to traditional scientific experiment. We argue here that small-scale experiments using 'model organisms' in microcosms or mesocosms can be a useful approach for apparently intractable global problems, such as ecosystem responses to climate change or managing biodiversity through the design of nature reserves. An experimental, small-scale research programme can easily be coupled with the development of theory and act as a stimulus to further research, thereby hastening both understanding of the issues and development of practical solutions. This process--from microcosm experiment to the development of practical application--has previously been influential but also has a long time lag. We suggest short-cuts in an attempt to stimulate the use of small-scale experiments to address globally urgent issues with meaningful policy implications.

Application of the lumped age-class technique to studying the dynamics of malaria-mosquito-human interactions

A series of models of malaria-mosquito-human interactions using the Lumped Age-Class technique of Gurney & Nisbet are developed. The models explicitly include sub-adult mosquito dynamics and assume that population regulation occurs at the larval stage. A challenge for modelling mosquito dynamics in continuous time is that the insect has discrete life-history stages (egg, larva, pupa & adult), the sub-adult stages of relatively fixed duration, which are subject to very different demographic rates. The Lumped Age-Class technique provides a natural way to treat this type of population structure. The resulting model, phrased as a system of delay-differential equations, is only slightly harder to analyse than traditional ordinary differential equations and much easier than the alternative partial differential equation approach. The Lumped Age-Class technique also allows the natural treatment of the relatively fixed time delay between the mosquito ingesting Plasmodium and it becoming infective. Three models are developed to illustrate the application of this approach: one including just the mosquito dynamics, the second including Plasmodium but no human dynamics, and the third including the interaction of the malaria pathogen and the human population (though only in a simple classical Ross-Macdonald manner). A range of epidemiological quantities used in studying malaria such as the vectorial capacity, the entomological inoculation rate and the basic reproductive number (R0) are derived, and examples given of the analysis and simulation of model dynamics. Assumptions and extensions are discussed. It is suggested that this modelling framework may be a natural and useful tool for exploring a variety of issues in malaria-vector epidemiology, especially in circumstances where a dynamic representation of mosquito recruitment is required.

Disease induced dynamics in host-parasitoid systems: chaos and coexistence

All animals and plants are, to some extent, susceptible to disease caused by varying combinations of parasites, viruses and bacteria. In this paper, we present a mathematical model of interactions between a host, two parasitoids and a pathogen which shows that the presence of an infection can preserve and promote diversity in such multi-species systems. Initially, we use a system of ordinary differential equations to investigate interactions between two species of parasitoids, a host and a host infection. We show that the presence of all four species is necessary for the system as a whole to persist, and that in particular, the presence of the pathogen is necessary for the coexistence of the two parasitoid species. The inclusion of infection induces a wide range of dynamics, including chaos, and these dynamics are robust for a wide range of parameter values. We then extend the model to include spatial effects by introducing random motility (diffusion) of all three species and examine the subsequent spatio-temporal dynamics, including travelling waves and other more complicated heterogeneous behaviour. The computational simulation results of the model suggest that infection in the hosts can blunt the effects of competition between parasitoids, allowing the weaker competitor to survive. Regardless of the nature of the stability of the coexistent steady state of the system, there is an initial period of transient dynamics, the length of which can be extended by an appropriate choice of initial conditions. The existence of these transient dynamics suggests that systems subject to regular restoration to a starting state, such as agro-ecosystems, may be kept in a continual state of dynamic transience, and this has implications for the use of natural enemies to control insect pests, the preservation of biodiversity in farmland habitats and the more general dynamics of disease processes.

Intraspecific competition: the role of lags between attack and death in host-parasitoid interactions

Many natural enemies do not immediately kill their host, and the lag this creates between attack and host death results in mixed populations of uninfected and infected hosts. Both competition and parasitism are known to be major structuring forces in ecological communities; however, surprisingly little is known about how the competitive nature of infected hosts could affect the survival and dynamics of remaining uninfected host populations. Using a laboratory system comprising the Indian meal moth, Plodia interpunctella, and a solitary koinobiont parasitoid, Venturia canescens, we address this question by conducting replicated competition experiments between the unparasitized and parasitized classes of host larvae. For varying proportions of parasitized host larvae and competitor densities, we consider the effects of competition within (intraclass) and between (interclass) unparasitized and parasitized larvae on the survival, development time, and size of adult moths and parasitoid wasps. The greatest effects were on survival: increased competitor densities reduced survival of both parasitized and unparasitized larvae. However, unparasitized larvae survival, but not parasitized larvae survival, was reduced by increasing interclass competition. To our knowledge, this is the first experimental demonstration of the competitive superiority of parasitized over unparasitized hosts for limiting resources. We discuss possible mechanisms for this phenomenon, why it may have evolved, and its possible influence on the stability of host-parasite dynamics.

The dynamical consequences of developmental variability and demographic stochasticity for host-parasitoid interactions

Few age-structured models of species dynamics incorporate variability and uncertainty in population processes. Motivated by laboratory data for an insect and its parasitoid, we investigate whether such assumptions are appropriate when considering the population dynamics of a single species and its interaction with a natural enemy. Specifically, we examine the effects of developmental variability and demographic stochasticity on different types of cyclic dynamics predicted by traditional models. We show that predictions based on the deterministic fixed-development approach are differentially sensitive to variability and noise in key life stages. In particular, we find that the demonstration of half-generation cycles in the single-species model and the multigeneration cycles in the host-parasitoid model are sensitive to the introduction of developmental variability and noise, whereas generation cycles are robust to the intrinsic variability and uncertainty that may be found in nature.

Population dynamics of Cosmoclopius nigroannulatus Stal (Hemiptera, Reduviidae) in tobacco culture

The role of predators influencing populations of insects considered as pests is extremely important for agroecosystems. The population ecology of Cosmoclopius nigroannulatus, a predatory reduvid associated with the tobacco culture was investigated aiming to study the population dynamics of adults, along the culture cycle. In an experimental plot of approximately 300 m2, in Porto Alegre (30 degrees 0'S; 51 degrees 13'W), RS, Brazil, 270 tobacco plants were grown; each plant identified by alphanumeric coordinates. Using the mark-release-recapture method, daily samplings were done from August to December 1999, and three times a week from this date until April 2000. The adults were captured by hand, marked, sexed and released on the same plant they were captured. The individual number and plant coordinate were registered. Population estimates were analyzed by the Fisher-Ford method. In 107 sampling occasions, 604 individuals were marked, 273 males and 331 females. Three generations of C. nigroannulatus were registered during the culture cycle. The colonizing generation was represented by 14 males and 15 females (a sex ratio of 0.48), the first by 109 males and 137 females (0.44) and the second by 150 males and 179 females (0.46). The estimated daily survival rate varied between generations decreasing from 98% in the colonizing generation to 87% in the second. The observed longevity or permanence time in the experimental area varied significantly among generations, being at about 40 days in the colonizing generation, 13 days in the first and 5 days in the second. It was observed that as the population increases, the survival and/or permanence time in the area decreases, suggesting a relation between this and a decline in the available resources probably with an associated increase in intra-specific competition.

Population growth rates: issues and an application

Current issues in population dynamics are discussed in the context of The Royal Society Discussion Meeting 'Population growth rate: determining factors and role in population regulation'. In particular, different views on the centrality of population growth rates to the study of population dynamics and the role of experiments and theory are explored. Major themes emerging include the role of modern statistical techniques in bringing together experimental and theoretical studies, the importance of long-term experimentation and the need for ecology to have model systems, and the value of population growth rate as a means of understanding and predicting population change. The last point is illustrated by the application of a recently introduced technique, integral projection modelling, to study the population growth rate of a monocarpic perennial plant, its elasticities to different life-history components and the evolution of an evolutionarily stable strategy size at flowering.

On the determinants of population structure in antigenically diverse pathogens

Many pathogens exhibit antigenic diversity and elicit strain-specific immune responses. This potential for cross-immunity structure in the host resource motivates the development of mathematical models, stressing competition for susceptible hosts in driving pathogen population dynamics and genetics. Here we establish that certain model formulations exhibit characteristics of prototype pattern-forming systems, with pathogen population structure emerging as three possible patterns: (i) incidence is steady and homogeneous; (ii) incidence is steady but heterogeneous; and (iii) incidence shows oscillatory dynamics, with travelling waves in strain-space. Results are robust to strain number, but sensitive to the mechanism of cumulative immunity.

Blowout bifurcation with non-normal parameters in population dynamics

Interesting dynamic behaviors have been associated with the transverse stability of an invariant subspace (e.g., riddled basins or on-off intermittency). Recently, these complex behaviors have been generalized to cases of models with non-normal parameters showing that these behaviors might be widespread. In this Brief Report I demonstrate this type of complex dynamics in models of interacting populations for which the invariant subspace is defined by species extinction. In the context of the current biodiversity crisis, implications of these behaviors for population biology are discussed.