Predator-prey Population Dynamics Research Articles

Analysis of Predator–Prey Model With Inclusion of Temperature Variability in Prey Refugees

One of the central concerns in ecology is assessing the impact of environmental changes, such as global temperature shifts, on the dynamic interactions between predators and prey across diverse ecosystems. This study explores the relationship between prey and predator populations in the context of climate‐induced temperature changes. Utilizing linearization and the Lyapunov approach, we analyze the local and global stability of the system’s equilibrium points. Applying Sotomayor’s theorem, we further investigate the local bifurcation of the fixed points. Additionally, the persistence of the model system is studied. The ecological models developed in this research aim to explore the stability of these predator–prey systems and provide insights to prevent the decline of endangered species. Numerical simulations are conducted to study the impact of environmental changes on the proposed models. The simulation results indicate that the temperature dependence of the predator–prey population dynamics is directly proportional to the size of the reserved habitat area for the prey when the temperature is high. These findings suggest that the preservation of sufficient habitat reserves plays a crucial role in promoting the long‐term survival of species and stabilizing their ecological interactions.

A stochastic model of predator-prey population dynamics

We present results of an analysis for a randomized three-dimensional predator-prey model representing the dynamics of wolf-deer interactions.

A predator–prey population dynamics simulation for biological control of Frankliniella occidentalis (Western Flower Thrips) by Orius laevigatus in strawberry plants

The use of predatory insect species to control agricultural pests is a key aspect of Integrated Pest Management (IPM) that can help to reduce the use of chemical pesticides. A simulation model that captures the population dynamics and interactions of this predator–prey system can serve as a valuable IPM decision-support tool. However, such a simulation is challenging to construct due to the interactions between life stages of insect predators, prey and the crop plants. Frankliniella occidentalis (Western Flower Thrips, WFT) is an economically devastating global pest that damages diverse crops. Orius laevigatus is an effective and commercially available predator that controls WFT. We, therefore, developed a population dynamics simulation that models their interactions to better understand these insects’ predator–prey dynamics in a strawberry crop. The model considers critical multi-stage predator–prey interaction, prey consumption reduction due to intraspecific competition, and the relationship between predation and oviposition rates of Orius. The simulation was structured using the boxcar train method, a stage-structured approach allowing insect populations to flow from one stage to the next over time. It was parameterised using data from existing literature. The results indicate the potential of the model to forecast the predator and prey species’ population dynamics for different initial populations. A global sensitivity analysis identified that the daily oviposition rate of WFT and egg survival rate of Orius were the most significant parameters. The prey handling time of Orius on WFT did not significantly impact population variation. This model provides a useful tool for scenario exploration and assessment of the effects of Orius on WFT that can aid decision-making in IPM prior to implementation.

Influence of multiple delays mechanisms on predator–prey model with Allee effect

Although there are many factors that influence population fluctuations, the impact of delay on population dynamics is one of the most significant ones. In this paper, we explore how the Allee effect in combination with a double delay (competition and cooperation) affects predator–prey population dynamics. One can determine the requirements for the equilibrium’s asymptotic stability and the presence of Hopf bifurcations by investigating the roots of a characteristic equation. The rigorous mathematical proofs of the stability and direction of the Hopf bifurcating periodic solutions are derived with the help of the normal form theory and the center manifold theorem. Numerical simulation shows that different delay mechanisms can generate different behaviors, such as the competitive delay that produces regular and irregular oscillations, as well as the chaotic, while the cooperative delay results in the stability switch. These theoretical and numerical results are illustrated that depending on the chosen delayed mechanism, delay may not necessarily lead to instability, and also can help for understanding the biological implications corresponding to the interaction dynamics of predator and prey.

Predator discrimination of prey promotes the predator-mediated coexistence of prey species.

The predator discrimination of prey can affect predation intensity and the prey density dependence of predators, which has the potential to alter the coexistence of prey species. We used a predator-prey population dynamics model accounting for the predator's adaptive diet choice and predator discrimination of prey to investigate how the latter influences prey coexistence. The model revealed that (i) prey species that are perceived as belonging to the same species by a predator are attacked in the same manner, and it is more difficult for them to coexist than those that are recognized as different prey species, and (ii) prey species that are not discriminated by a predator-and therefore cannot coexist-may coexist in the presence of an alternative predator that does discriminate between them. These results suggest that prey diversity, which favours the predator discrimination of prey, and the different capabilities of predators to identify prey species both enhance prey coexistence.

Effects of Predator-Driven Prey Dispersal on Sustainable Harvesting Yield

Dispersal of organisms between patches is a common phenomenon in ecology and plays an important role in predator–prey population dynamics. We propose a nonsmooth Filippov predator–prey model in a two-patch environment characterized by a generalist predator-driven intermittent refuge protection of an apprehensive prey along with a balanced dispersal of the prey between refuge and nonrefuge areas. By employing qualitative techniques of nonsmooth dynamical systems, we see that the switching surface is a repeller whenever the interior equilibria are virtual, causing long-term population fluctuations. We find that the level of prey vigilance and the rate of prey dispersal play pivotal roles in the total harvesting yield. We observe that a sustainable high harvesting yield is possible when the prey is less vigilant and obtain the harvesting efforts for maximum sustainable total yield (MSTY). We further modify the model by considering a continuous threshold predator-driven prey dispersal and show that the model exhibits a Hopf bifurcation when the level of prey vigilance exceeds some critical threshold value. By comparing the dynamics of the two models we see that for a sustainable high harvesting yield of the system with continuous threshold dispersal, the prey needs to be highly vigilant compared to that of the system with intermittent dispersal of the prey. Further, we find numerically that the estimated MSTY from both models remains the same.

Prey–predator dynamics with adaptive protection mutualism

Prey can ease the burden of exploitation by attracting a third party that interferes with their predators. Such is the case for plant-ant or aphid-ant mutualisms, where the victim supplies food to the ants, while the ants attack or drive away the offenders. Since ants are adaptive foragers, defense services can be altered by alternative food sources (e.g., other plants, or human-supplied resource). This article explores the prey-predator-ant system, using a model that combines predator-prey population dynamics with ant optimal foraging, where ants consume prey-supplied resources or alternative resources. Feedbacks between prey-predator dynamics and adaptive ant foraging leads to complex dynamics. For a given ant colony size and supply rate of alternative resources, prey can coexist with predators at alternative stable states, or along alternative limit cycles. Limit cycles extend the scope of defensive mutualism beyond the point where ants would abandon prey in favor of alternative resources under equilibrium conditions. These results highlight the importance of trait-mediated indirect interactions for natural mutualistic–antagonistic systems, and potential outcomes of manipulating ant defense services using baits in the case of agriculture.

Predator–prey population dynamics may induce the evolutionary dynamics of behavioral unpredictability

Behavioral unpredictability (within-individual behavioral variability that cannot be explained by extrinsic and intrinsic factors) has been observed in a wide variety of species, but its adaptive significance is not well understood. This study examines the possibility that behavioral unpredictability is maintained through predator–prey population dynamics. An individual-based model was constructed to track the status of individual predators. The handling time of a predator is characterized by its expected value and unpredictability, which are heritable, and each predator features a unique combination of these characteristics. A discrete generation model in which one prey species and one predator species interact was constructed. The model showed that the evolutionarily stable strategy (ESS) of handling time is associated with no behavioral unpredictability and that the ESS handling time depends on the densities of the prey and predators. When populations exhibit cyclic dynamics, the ESS also changes along with the population dynamics, thereby creating mismatches between the traits of predators and the ESS because the dynamics of the ESS and population are faster than the evolution of the handling time traits. This mismatch can generate conditions in which individuals with behavioral unpredictability are at least transiently selected because of the topology of the fitness landscape. However, the model also showed that the selection strength of behavioral unpredictability is weak and can be overruled by inherent stochastic processes.

Derivation of Predator Functional Responses Using a Mechanistic Approach in a Natural System

The functional response is at the core of any predator-prey interactions as it establishes the link between trophic levels. The use of inaccurate functional response can profoundly affect the outcomes of population and community models. Yet most functional responses are evaluated using phenomenological models which often fail to discriminate among functional response shapes and cannot identify the proximate mechanisms regulating predator acquisition rates. Using a combination of behavioral, demographic, and experimental data collected over 20 years, we develop a mechanistic model based on species traits and behavior to assess the functional response of a generalist mammalian predator, the arctic fox (Vulpes lagopus), to various tundra prey species (lemmings and the nests of geese, passerines, and sandpipers). Predator acquisition rates derived from the mechanistic model were consistent with field observations. Although acquisition rates slightly decrease at high goose nest and lemming densities, none of our simulations resulted in a saturating response in all prey species. Our results highlight the importance of predator searching components in predator-prey interactions, especially predator speed, while predator acquisition rates were not limited by handling processes. By combining theory with field observations, our study provides support that the predator acquisition rate is not systematically limited at the highest prey densities observed in a natural system. Our study also illustrates how mechanistic models based on empirical estimates of the main components of predation can generate functional response shapes specific to the range of prey densities observed in the wild. Such models are needed to fully untangle proximate drivers of predator-prey population dynamics and to improve our understanding of predator-mediated interactions in natural communities.

Impacts of predator-induced behavioural plasticity on the temperature dependence of predator-prey activity and population dynamics.

Predation is a key ecological interaction affecting populations and communities. Climate warming can modify this interaction both directly by the kinetic effects of temperature on biological rates and indirectly through integrated behavioural and physiological responses of the predators and prey. Temperature dependence of predation rates can further be altered by predator-induced plasticity of prey locomotor activity, but empirical data about this effect are lacking. We propose a general framework to understand the influence of predator-induced developmental plasticity on behavioural thermal reaction norms in prey and their consequences for predator-prey dynamics. Using a mesocosm experiment with dragonfly larvae (predator) and newt larvae (prey), we tested if the predator-induced plasticity alters the elevation or the slope of the thermal reaction norms for locomotor activity metrics in prey. We also estimated the joint predator-prey thermal response in mean locomotor speed, which determines prey encounter rate, and modelled the effect of both phenomena on predator-prey population dynamics. Thermal reaction norms for locomotor activity in prey were affected by predation risk cues but with minor influence on the joint predator-prey behavioural response. We found that predation risk cues significantly decreased the intercept of thermal reaction norm for total activity rate (i.e. all body movements) but not the other locomotor activity metrics in the prey, and that prey locomotor activity rate and locomotor speed increased with prey density. Temperature had opposite effects on the mean relative speed of predator and prey as individual speed increased with temperature in predators but decreased in prey. This led to a negligible effect of body temperature on predicted prey encounter rates and predator-prey dynamics. The behavioural component of predator-prey interaction varied much more between individuals than with temperature and the presence of predation risk cues in our system. We conclude that within-population variation in locomotor activity can buffer the influence of body temperature and predation risk cues on predator-prey interactions, and further research should focus on the magnitude and sources of behavioural variation in interacting species to predict the impact of climate change on predator-prey interactions and food web dynamics.

Hair cortisol as a reliable indicator of stress physiology in the snowshoe hare: Influence of body region, sex, season, and predator–prey population dynamics

Hair cortisol concentration is increasingly used as a convenient, non-invasive, and integrative measure of physiology and health in natural populations of mammals. However, the use of this index is potentially confounded by individual variation in body region-specific differences in cortisol deposition rates. Here we examine correlations in cortisol concentrations in hair collected from the ear, shoulder, and thigh of wild snowshoe hares, Lepus americanus, as well as the influence of sex on cortisol measurements. We further evaluated this technique’s ability to capture seasonal and cyclical patterns of snowshoe hare glucocorticoid secretion from 2013 to 2015 in the southwestern Yukon (Canada). We found positive correlations (R2 = 0.20–0.32) in all pairwise comparisons among body regions, and differences among individuals accounted for the greatest proportion of variance (47.3%) in measurements. From 2013 to 2015 the hares’ primary predator – Canada lynx – approximately doubled in population abundance. We found a significant increase in hare hair cortisol concentrations across this time period. Cortisol indices were higher in summer than winter pelage, reflecting predicted physiological responses to seasonal variation in food availability and individual risk. Variation in hair cortisol concentrations was more similar to long-term (weeks-months) integrative indices of adrenal capacity than point samples of fecal glucocorticoid metabolite concentrations. Overall, we find that hair cortisol analysis is a simple and useful tool for estimations of population-level stress physiology in wild mammals, and sampling of core body regions with consistent moulting patterns produced the most robust results in this species.

The Impact of Microplastic Particles on Population Dynamics of Predator and Prey: Implication of the Lotka-Volterra Model

Microplastic particles are widely distributed in a variety of ecosystems and can be transferred to predators along a food chain after being ingested by prey. However, how microplastic particles affect prey and predator populations is not fully understood. In this study, using the Lotka-Volterra model, we theoretically investigated predator-prey population dynamics in terms of toxicological response intensity (strength to population growth rate) to microplastic particles, and examined the negative effects on prey feeding ability and predator performance due to microplastic particles. Results of numerical simulations indicate the critical properties of the predator-prey system in response to microplastic particles: (i) predators are more vulnerable than prey under exposure to microplastic particles; (ii) the effect of microplastic particles on prey and predator population growths can be negligible when toxicological response intensities of prey and predator are small; (iii) this system is prey dependent for predator functional response, whose stability highly relies on the density of prey; (iv) the reduced feeding capacity of prey and predator induced by microplastic particles does not significantly affect the population dynamics of the predator-prey system. Moreover, our analysis suggests that dynamic Lotka-Volterra models can play a vital role in predicting ecological impacts of microplastic particles on predator-prey population dynamics.

Characterizing the Phase Transitions between Stable Equilibrium and Periodic Oscillations in Predator-prey Population Dynamics: A Theoretical Appraisal from an Extended Nicholson & Bailey Model

Multi-phase patterns with more or less sharp phase transitions, first highlighted in thermodynamics, have progressively revealed having wider relevance, being encountered in various other contexts, for example fluid mechanics, and can even occur in the interactive dynamics in biological populations involving two or more species that share opposite interests, such as predator-prey or parasite-host pairs of species. In the latter, the pattern of abundances of both interacting species usually reaches an equilibrium level which can be either stable or cyclic (with large periodic oscillations in the latter case). Both alternative modes are separated by well-define boundaries and, accordingly, can relevantly be described in terms of phases and phase transitions. While this has recently been approached from very general perspectives, a more focused analysis is still lacking, regarding the nature of the phase transitions between stable and oscillatory equilibria and – still more importantly – how the nature of these phase transitions may possibly depend (or not) on the biological and contextual factors driving the parasite-host interactive dynamics. These issues are addressed hereafter, on a theoretical basis, yet intimately related to the real field context, by taking advantage of a newly derived extension of the classical Nicholson & Bailey model of parasite-host interactions. Highlighted in particular are the possibility of either first-order, second-order or continuous phase-transitions, depending on (i) the respective own dynamics of both host and parasite, (ii) the density of feeding resource for the host, (iii) the level of migration exchange in a meta-population context.

Warming can destabilize predator-prey interactions by shifting the functional response from Type III to Type II.

The potential for climate change and temperature shifts to affect community stability remains relatively unknown. One mechanism by which temperature may affect stability is by altering trophic interactions. The functional response quantifies the per capita resource consumption by the consumer as a function of resource abundance and is a suitable framework for the description of nonlinear trophic interactions. We studied the effect of temperature on a ciliate predator-prey pair (Spathidium sp. and Dexiostoma campylum) by estimating warming effects on the functional response and on the associated conversion efficiency of the predator. We recorded prey and predator dynamics over 24hr and at three temperature levels (15, 20 and 25°C). To these data, we fitted a population dynamic model including the predator functional response, such that the functional response parameters (space clearance rate, handling time and density dependence of space clearance rate) were estimated for each temperature separately. To evaluate the ecological significance of temperature effects on the functional response parameters, we simulated predator-prey population dynamics. We considered the predator-prey system to be destabilized, if the prey was driven extinct by the predator. Effects of increased temperature included a transition of the functional response from a Type III to a Type II and an increase of the conversion efficiency of the predator. The simulated population dynamics showed a destabilization of the system with warming, with greater risk of prey extinction at higher temperatures likely caused by the transition from a Type III to a Type II functional response. Warming-induced shifts from a Type III to II are not commonly considered in modelling studies that investigate how population dynamics respond to warming. Future studies should investigate the mechanism and generality of the effect we observed and simulate temperature effects in complex food webs including shifts in the type of the functional response as well as consider the possibility of a temperature-dependent conversion efficiency.

Small-Sized Microplastics Negatively Affect Rotifers: Changes in the Key Life-History Traits and Rotifer-Phaeocystis Population Dynamics.

Most coastal waters are at risk from microplastics, which vary in concentration and size. Rotifers, as important primary consumers linking primary producers and higher trophic consumers, usually coexist with the harmful alga Phaeocystis and microplastics in coastal waters; this coexistence may interfere with rotifer life-history traits and ingestion of Phaeocystis. To evaluate the effects of microplastics on rotifers, we designed a series of experiments concerning rotifer Brachionus plicatilis life-history traits and rotifer-Phaeocystis (predator-prey) population dynamics under different concentrations and sizes of microplastics. The results showed that small-sized microplastics (0.07 μm) at high levels (≥5 μg mL-1) decreased rotifer survival and reproduction, prolonged the time to maturation, and reduced the body size at maturation, whereas large-sized microplastics (0.7 and 7 μm) had no effect on rotifer life-history traits. For rotifer-Phaeocystis population levels, small-sized microplastics (0.07 μm) significantly delayed the elimination of Phaeocystis by rotifers; this is the first study to test the effects of microplastics on predator-prey dynamics. The results of rotifer-Phaeocystis population dynamics are consistent with the changes in the life-history traits of rotifers and further confirm the negative effects of small-sized microplastics (0.07 μm) on rotifers. These findings help to reveal the effect of pollutants on predator-prey population dynamics.

Turing instability in two-patch predator-prey population dynamics

Turing instability in two-patch predator-prey population dynamics

Exploring the dynamics of a Holling–Tanner model with cannibalism in both predator and prey population

Cannibalism is an intriguing life history trait, that has been considered primarily in the predator, in predator–prey population models. Recent experimental evidence shows that prey cannibalism can have a significant impact on predator–prey population dynamics in natural communities. Motivated by these experimental results, we investigate a ratio-dependent Holling–Tanner model, where cannibalism occurs simultaneously in both the predator and prey species. We show that depending on parameters, whilst prey or predator cannibalism acting alone leads to instability, their joint effect can actually stabilize the unstable interior equilibrium. Furthermore, in the spatially explicit model, we find that depending on parameters, prey and predator cannibalism acting jointly can cause spatial patterns to form, while not so acting individually. We discuss ecological consequences of these findings in light of food chain dynamics, invasive species control and climate change.

Chilean loco snail at risk in future climate scenarios

The ecological consequences of a predator going on the blink can be catastrophic. Single species can rampage out of control with their natural checks and balances removed, even if the predator is just a snail. Paolo Domenici, from CNR-IAMC, Italy, and Patricio Manríquez, from CEAZA, Chile, explain that the large marine snail Concholepas concholepas, a Chilean delicacy known as ‘loco’, resides along the length of the rocky Pacific coast of Chile and Peru where it dines on several species of mussel, including Semymitilus algosus, ensuring that the mussel does not exclude other species. In addition to maintaining biodiversity along the shoreline, the snail is prized by small-scale fisheries, making it vital that we understand the potential impact of rising sea temperatures and CO2 levels on this species as we continue pumping greenhouse gases into the atmosphere. Because elevated CO2 levels in water can affect the behaviour of predator and prey alike, Domenici, Manríquez and their colleague Rodrigo Torres decided to find out more about the impact of future climate scenarios on this key Chilean species.As the lateralization (handedness) of some animals – the direction that they prefer when turning – can alter as CO2 levels rise, Domenici and Manríquez measured the turning preferences of 40 juvenile locos that had experienced modern-day CO2 levels and temperatures by tempting them through a T-shaped maze with a delicious morsel of S. algosus placed behind a Plexiglas wall. At the end of the channel, the snails were forced to turn either left or right before circumnavigating the obstruction to receive their reward. After filming the snail's painstakingly slow progress eight times, Manríquez then measured whether the snail turned left exclusively, was right handed, had a slight preference for one or the other direction, or was ‘ambidextrous’. Then, Manríquez and Torres began the arduous task of maintaining each of the snails in their own individual mini biodomes for 6 months, setting the temperature at either 15°C or 19°C and the CO2 level at either 500 μatm (current levels) or 1400 μatm (future levels), before retesting their handedness.While the snails that had been residing in modern (500 μatm CO2) mild and warm climate scenarios had retained their handedness, preferring to turn to the side that they had favoured 6 months earlier, the snails that had experienced the future (1400 μatm CO2) mild and warm climate scenarios had lost their earlier preference and now had a completely different turning behaviour. And when Domenici analysed the snails’ overall performances, it was clear that the snails that had been reared in warm future climate conditions were slower when they negotiated the maze, and both groups of future CO2 snails took longer to decide which direction to turn. The higher CO2 climate also seemed to impair the ability of the snails to follow their noses and avoid the barrier, often colliding with the obstruction as they attempted to manoeuvre around it, while the snails that had been kept in a lower CO2 environment negotiated the barrier without impediment.Increases in CO2 levels similar to those that are predicted to occur by the end of the century had clearly changed the behaviour of this key predator on the rocky Chilean coast and affected the ability of the animals to repeat behaviours that were previously hard-wired. And Domenici is concerned about the effect that future change may have on this delicate ecosystem, saying, ‘The negative effects of ocean acidification on locomotion traits associated with prey-finding may cause cascading effects beyond those described at the individual level, such as predator–prey population dynamics and community structure’.

Growth, Grazing, and Starvation Survival in Three Heterotrophic Dinoflagellate Species.

To assess the effects of fluctuating prey availability on predator population dynamics and grazing impact on phytoplankton, we measured growth and grazing rates of three heterotrophic dinoflagellate species-Oxyrrhis marina, Gyrodinium dominans and Gyrodinium spirale-before and after depriving them of phytoplankton prey. All three dinoflagellate species survived long periods (>10d) without algal prey, coincident with decreases in predator abundance and cell size. After 1-3wks, starvation led to a 17-57% decrease in predator cell volume and some cells became deformed and transparent. When re-exposed to phytoplankton prey, heterotrophs ingested prey within minutes and increased cell volumes by 4-17%. At an equivalent prey concentration, continuously fed predators had ~2-fold higher specific growth rates (0.18 to 0.55d-1 ) than after starvation (-0.16 to 0.25d-1 ). Maximum specific predator growth rates would be achievable only after a time lag of at least 3d. A delay in predator growth poststarvation delays predator-induced phytoplankton mortality when prey re-emerges at the onset of a bloom event or in patchy prey distributions. These altered predator-prey population dynamics have implications for the formation of phytoplankton blooms, trophic transfer rates, and potential export of carbon.

Predator refuges for conservation biological control in an intermediately disturbed system: the rise and fall of a simple solution

Summary Managed systems harvested at intermediate time‐scales have advantages over annual short‐cycled systems in maintaining top‐down control of insect herbivores, and the flexible harvest regimes in these systems provide opportunities for habitat management that can stabilize predator–prey population dynamics across harvests – resulting in reduced risk of pest outbreaks. In a large‐scale field experiment, we explored whether retaining refuges, that is preserving parts of the stand to reduce predator mortality, could reduce the risk of pest insect outbreaks in willow short‐rotation coppice. Population densities of three omnivorous predator species and three outbreaking herbivorous leaf beetle species were monitored over four years after coppice (stem harvest) in eight stands with refuges (treatment) and eight stands without refuges (control). Predation pressure was estimated in years three and four. Contrary to our predictions, leaf beetle densities were higher in stands with refuges and predator densities were higher in stands without refuges. Leaf beetle egg mortality increased with total predator density, but did not differ between stands with and without refuges. These unexpected results can be attributed to interactions between dispersal and patch age. The altered phenology of coppiced stems may have triggered leaf beetle aggregation in refuges and migration from stands without refuges. A behavioural response to resource concentration in retained old patches likely transformed the predator refuge from a ‘source’ to a ‘sink’. Synthesis and applications. This study shows that retaining refuges in willow short‐rotation coppice to facilitate predator population recovery after harvest can come at the cost of more attractive herbivore habitats – and thus increased pest problems. We conclude that crop refuges in systems with intermediate disturbance regimes pose new challenges for conservation biological control, in particular the need to consider how patch age affects dispersal and recolonization of both pest and predators.