Predator Populations Research Articles

Study of dynamical behaviors of harvested stage-structured predator–prey fishery model with fear effect on prey under interval uncertainty

The lack of clarity in many parameters used in ecological models is due to the constant changes in nature. The fundamental predator–prey model discussed in this article takes into account several ecological parameters as parametric-functional interval numbers. It discusses the dynamic characteristics of the model within the context of an uncertain environment. To account for this uncertainty, the model incorporates the concepts of bionomic equilibria and maximum sustainable yield (MSY). The article explores the optimal harvesting policy by applying Pontryagin’s maximum principle in an imprecise and uncertain environment. The proposed imprecise model formulation includes two additional variables: the influence of fear on prey population growth rate and the harvesting of prey and juvenile predator populations. The system of interval differential equations governs the interactions between these imprecise species, allowing for mathematical analysis of the proposed system. The aim of this study is to evaluate the robustness of an imprecise prey–predator model within an unpredictable environment. The article concludes by presenting rigorous numerical simulations that support all the analytical findings.

Bistability in modified Holling II response model with harvesting and Allee effect: Exploring transitions in a noisy environment

Here, we explore the complex dynamics of a predator–prey system with a modified Holling type II functional response and the Allee effect that accounts for a reduced hunting efficiency due to intra-predator interactions. Besides the growth due to focal prey, the predator population follows a Beverton–Holt-like reproduction due to the alternative food sources. The model also considers the impact of harvesting on the predator population, reflecting economic interests in biological resource exploitation. We systematically investigate key aspects, including solution’s positivity, system’s equilibria, stability analysis, and various type of bifurcation. The model is extended to its stochastic version; conditions for the extinction as well as persistence of species are derived. All the theoretical findings are validated with numerical examples. In the deterministic scenario, the Allee effect, harvesting intensity, and the growth in predators due to external food sources exhibit intricate dynamics, such as Hopf, saddle–node (LP) and transcritical bifurcations; we also observe bistable behavior of the system. Notably, less growth in predators due to the other food sources results in extinction, while low intensity of Allee effect leads to bistability, where initial population size matters. A higher Allee effect reduces the region of stability generated by the harvesting effort and the predators’ growth due to additional foods. The stochastic system uncovers diverse transitions in scenarios with high noise intensity, affecting bistability occurred for lower noise intensity. Overall, this study provides valuable insights into predator–prey dynamics, with practical implications for the ecological conservation and resource management.

ANALISIS KESTABILAN MODEL PREDATOR PREY DENGAN TINGKATAN USIA PADA DUA PREY DAN DUA PREDATOR DENGAN FUNGSI RESPON MONOD HALDANE DAN KANIBALISME

This paper discusses a predator-prey stage structure model for two predators and two preys with Monod Haldane and cannibalism response functions that describe the interactions between populations of young prey, adult prey, young predator, and adult predator. In this model it is assumed that only adult predators are capable of attacking to consume young predators, only adult prey are capable of reproduction, there is a Monod-Haldane effect describing the phenomenon of group defense where predation is reduced, or even prevented altogether, because the ability increases from prey for further defense or camouflage when their numbers are large enough. Dynamic analysis is carried out by determining the equilibrium point and its existence conditions and analyzing the local stability of the equilibrium point. The predator-prey model has three equilibrium points, namely the trivial equilibrium point, the prey free equilibrium point and an interior point that exists under certain conditions. The equilibrium points is locally asymptotically stable under certain conditions. The results of the numerical simulations show suitability with the results of dynamic analysis.

Modelling Predator–Prey Interactions: A Trade-Off between Seasonality and Wind Speed

Predator–prey interactions do not solely depend on biotic factors: rather, they depend on many other abiotic factors also. One such abiotic factor is wind speed, which can crucially change the predation efficiency of the predator population. In this article, the impact of wind speed along with seasonality on various parameters has been investigated. Here, we present two continuous-time models with specialist and generalist type predators incorporating the effect of wind and the seasonality on the model parameters. It has been observed that wind speed plays a significant role in controlling the system dynamics for both systems. It makes the systems stable for both of the seasonally unperturbed systems. However, it controls the chaotic dynamics that occur in case of no wind for the seasonally perturbed system with the predator as a specialist. On the other hand, for the seasonally perturbed system with a generalist predator, it controls period-four oscillations (which occur considering no wind speed) to simple limit-cycle oscillations. Furthermore, the wind parameter has a huge impact on the survival of predator species. The survival of predator species may be achieved by ensuring a suitable range of wind speeds in the ecosystem. Therefore, we observe that seasonality introduces chaos, but wind reduces it. These results may be very useful for adopting necessary management for the conservation of endangered species that are massively affected by wind speed in an ecosystem.

Role of Alternative Food in Controlling Chaotic Dynamics in an Eco-Epidemiological Model with Strong Allee Effects in Prey Populations

This paper explores a predator–prey system with disease in the predator population, focusing on the impact of alternative food sources. Investigating the eco-epidemiological systems with strong Allee effects in prey populations, the study analyzes local stability, introduces ecological and disease basic reproduction numbers, and observes the community structure. Extensive numerical simulations reveal varied global behaviors, including stable focus, limit cycles, period-doubling, and chaos in response to changes in the infection levels. The research emphasizes the role of alternative food in mitigating chaotic dynamics, noting that increased availability promotes stability, while decreased availability leads to a shift from chaos to a stable focus. Overall, the study underscores the significance of incorporating alternative food sources in conservation efforts for ecosystems with predator populations experiencing strong Allee effects, offering insights into the complex dynamics of eco-epidemiological systems and their implications for biodiversity conservation and disease management.

Turning a Pest into a Natural Enemy: Removing Earwigs from Stone Fruit and Releasing Them in Pome Fruit Enhances Pest Control.

The European earwig Forficula auricularia (L.) (Dermaptera: Forficulidae) is an omnivorous insect that is considered a minor pest of stone fruit and a key predator of pests in pome fruit orchards. In many pome fruit orchards, earwigs are absent or in low abundance due to broad-spectrum spray programs and the slow recolonization rate of earwigs. Orchards in transition to organic or "selective" conventional programs often struggle to achieve effective levels of biological control, and thus, may benefit from inoculating earwigs to expedite their re-establishment. In a two-year study, we evaluated the potential for mass trapping earwigs from stone fruit using rolled cardboard traps to reduce fruit damage and provide earwigs for augmentation in pome fruit. We also tested whether a single mass release or five releases (on alternating weeks) of the same total number of earwigs in apples and pears reduced pests relative to plots where no releases occurred. Mass trapping did not decrease earwig abundance or substantially reduce fruit damage in stone fruit orchards. However, trapping was an efficient method for providing earwigs for augmentation. Earwig abundances were only increased in orchards where earwigs were previously low or absent; however, multiple orchards with varying prior levels of earwigs exhibited reductions in key pests (woolly apple aphid and pear psylla). For some other pests evaluated, plots with mass releases of earwigs had a slight trend in overall lower pest density when compared with control plots. A strategy for moving earwigs out of stone fruit orchards and into pome fruit orchards could be an effective method for augmenting orchard predator populations.

Interests, beliefs, experience and perceptions shape tolerance towards impacts of recovering predators

Abstract The modification of landscapes is increasing the interface between humans and wildlife, while conflicts concerning predator impacts on human activities persist. Some previously persecuted but now protected predator species are experiencing recovery and range expansion. Tolerance is considered essential for achieving coexistence between humans and wildlife; however, its conceptualisation remains unresolved. Little is known about tolerance in the context of recovering predators, particularly which drivers are relevant to all or specific species and human interests. Using an online questionnaire survey shared with members of organisations with interests in rural land‐based activities, we collected data on interests and beliefs, and attitudes, perceptions, experience and management preferences for six recovering vertebrate predators in the United Kingdom (n = 819). We created a species tolerance score representing the management choices of the respondents in different conflict scenarios, which differed in the degree of impact on the predator population. Our species tolerance score was characterised by a complex combination of the interests and beliefs of the respondents about wildlife management, perceptions and experience of that species (perceived benefits, population trend, positive and negative experience, indirect negative experience) and negative experience of other recovering predators. We found a tolerance gradient between interest groups with notable overlap between groups with primary interests in wildlife conservation, shooting, farming and fishing. Although higher perceived benefits consistently corresponded to higher tolerance, having a negative experience of the species dampened the effect of perceived benefits on tolerance. When both negative personal and indirect experiences were reported, tolerance was dramatically reduced. The classification of species from least to most tolerated was consistent between interest groups. The application of our species tolerance score as the normative dimension (i.e. acceptability) in Brenner and Metcalf's (2020) Social Tolerance of Wildlife Framework highlights that tolerance (negative attitude—high acceptability) is potentially rare and more positive attitudes must be achieved before acceptance of the impacts of species can increase. Our findings highlight that considering only primary interests may hinder debates concerning recovering predators. Strategies to reduce negative experiences or change how they are perceived could significantly increase tolerance in combination with increasing positive experiences. Read the free Plain Language Summary for this article on the Journal blog.

Diet Specialization in an Insular Population of Coastal Peregrine Falcons

Individual diet specialization is known to occur in populations of generalist predators, where specific individuals develop specialist feeding strategies. Diet specialization has been reported in many raptor species and it may be an important driver of intraspecific population structure. Here, we quantify the diet of Peregrine Falcons Falco peregrinus from five breeding territories on an island determined from prey remains collected over four breeding seasons. Three prey species accounted for 69.8% of total prey frequency, with Manx Shearwater Puffinus puffinus being the primary prey accounting for 47.3% by frequency and 40.8% by biomass. European Herring Gull Larus argentatus was the second most important prey species by frequency (13.8%) and biomass (29.8%) followed by Feral Pigeon Columba livia (frequency: 8.7%, biomass: 7.0%). Prey frequency on specific prey groups varied substantially between breeding pairs and months. Two pairs specialized on Manx Shearwater, one pair specialized on Herring Gull and Manx Shearwater, with the remaining two pairs having a relatively generalist diet of Manx Shearwaters, Feral Pigeon and small passerines. Prey frequency on Manx Shearwaters increased throughout the breeding season with a peak in total diet frequency of 63.8% in July, with a concurrent decrease in Herring Gull prey frequency. Higher percentage of Manx Shearwater in the diet explained 87% of the variation in a narrower dietary breadth for the Peregrine pairs. Our results suggest individual diet specialization may be one of multiple factors important for understanding population density in insular raptor populations.

DYNAMIC STUDY OF A RATIO-DEPENDENT PREDATOR–PREY MODEL WITH STRONG ALLEE EFFECT AND NONLINEAR HARVESTING

The harvesting of species occurs in terrestrial and aquatic habitats across the world. It not only causes alteration in the population structure of the species subjected to harvesting but also of the species in interaction with the harvested species. The present work investigates the effect of nonlinear prey harvesting on the dynamics of a ratio-dependent predator–prey system with a strong Allee effect in prey population. It is found that the system exhibits a rich spectrum of dynamics including saddle-node bifurcation, Hopf bifurcation and homoclinic bifurcation with respect to the parameters that shape the nonlinear harvesting rate, namely, the maximum harvesting rate and a half-saturation constant that represents the prey density at which half of the maximum harvesting rate is reached. It is found that the basin of attraction of the stable coexistence state shrinks as the harvesting rate increases and if the harvesting rate is above a threshold value at which saddle-node bifurcation occurs, the stable coexistence of predator and prey populations is not possible for any initial start. It is also found that the harvesting policies in which the harvesting rate increases less rapidly at low prey population size are more favorable for the stable coexistence of species. The presence of Allee effect in the prey population is found to increase the chances of extinction of both species by reducing the threshold value of the harvesting rate at which the unconditional extinction occurs. Numerical simulations are carried out to support the analytical findings.

Large‐scale one‐off sea urchin removal promotes rapid kelp recovery in urchin barrens

Sea urchin overgrazing is a leading cause of kelp forest loss and in such cases their removal is increasingly advocated for kelp forest restoration. However, refining removal approaches is needed to improve the efficiency and success of restoration, as most previous removal studies have been small scale and require ongoing removals to maintain low densities and allow kelp recovery. We investigated the effectiveness of one‐off urchin removal from large, semi‐discrete areas of urchin barrens as a tool to promote kelp recovery. We removed sea urchins (Evechinus chloroticus) from four areas (1.6–2 ha) of urchin barrens in northeastern New Zealand. Exposed urchins were reduced to approximately 7% of initial densities and remained low, yet cryptic urchin densities increased after 2 years. Kelp (Ecklonia radiata) and fucoid (Sargassum sinclairii, Carpophyllum spp.) densities increased rapidly in removal areas, but remained constant or declined in adjacent control urchin barren areas. Macroalgal canopy recovery varied among and within removal areas, but increased on average from approximately 5 to 43% in 2 years. Densities of large sea urchin predators did not increase with kelp recovery, likely due to ongoing fishing within removal areas. Our results demonstrate that a single urchin removal from large, semi‐discrete areas of urchin barrens can effectively and efficiently promote rapid multi‐species macroalgal recovery without additional actions (e.g. repeated urchin removals or macroalgae enhancement) for at least 2 years. However, this approach does not restore whole ecosystems and consequently restoration benefits through kelp recovery will be temporary without longer‐term urchin management and/or rebuilding of predator populations.

Intercropping Okra and Castor Bean Reduces Recruitment of Oriental Fruit Moth, Grapholita molesta (Lepidoptera: Tortricidae) in a Pear Orchard.

Intercrops can lower pest densities by increasing plant diversity, altering chemical communication in the arthropod community, and integrating well with other IPM tactics. We used two years of field observations and Y-tube olfactometer assays to explore the effects of intercropping a pear orchard with okra and castor bean on the cosmopolitan fruit-boring pest Grapholita molesta (Lepidoptera: Tortricidae). Intercropping okra reduced G. molesta trap catches in the pear orchard in both years, and intercropping with castor bean reduced them in the second year. Hydrocarbons, phenols, and ketones predominated in the GC-MS assay of okra volatiles, whereas castor bean volatiles were rich in aldehydes, ketones, and esters. Five of the commercially available volatiles released by these plants exhibited repellency to G. molesta in olfactometer trials, especially cinnamaldehyde, dibutyl phthalate, and thymol; the former compound also exhibited attraction to the egg parasitoid Trichogamma dendrolimi (Hymenoptera: Trichogrammatidae). In addition to their repellent properties, okra and castor bean may enhance integrated control of G. molesta in orchards by hosting prey that support populations of generalist predators that either provide biological pest control services within the orchard ecosystem or generate non-consumptive effects that contribute to pest deterence. Among the plant volatiles evaluated, cinnamaldehyde has the best potential for deployment in orchards to repel G. molesta without disrupting augmentative releases of T. dendrolimi.

Effects of large carnivores, hunter harvest, and weather on the mortality of moose calves in a partially migratory population

Survival of juvenile ungulates represents an important demographic parameter that influences population dynamics within ecosystems. In many ecological systems, the mortality of juvenile ungulates is influenced by various factors, including predation by large carnivores, human hunting activities and weather. While wolves Canis lupus are known to prey on moose Alces alces throughout all seasons, brown bears Ursus arctos primarily engage in predation during early summer, while human harvest primarily occurs in autumn and early winter. Hence, understanding the impacts of predation, harvest, and weather on the survival of juvenile moose is crucial for adaptive population management and the determination of sustainable harvest rates. To investigate the summer and autumn–winter survival of moose calves in relation to carnivore occurrence (wolf presence and bear density), summer habitat productivity, winter severity, human harvest, and migratory behaviour (migratory versus resident), we analysed data collected from 39 GPS‐collared female moose in south‐central Scandinavia. Our findings revealed significant interannual variation in summer survival rates, with areas with relatively higher bear densities exhibiting calf mortality rates twice as high as those in regions with low bear density. During the autumn–winter period, calf survival was lowest in the presence of wolves and deep snow, and it exhibited a negative correlation with the proportion of clearcuts and young forests within the mother's home range. Additionally, calf survival was negatively correlated with the risk of human hunting, and calves of stationary females displayed ten times higher survival rates compared to migratory individuals. Our study provides valuable insights into the survival of moose calves coexisting with two large carnivores and humans. Improving our understanding of the mechanisms causing calf survival to fluctuate has become increasingly important as many local moose populations in Scandinavia are declining and exposed to expanding predator populations, intense hunting pressure, and other threats associated with climate change.

Invasive mammal control selects for trap-recalcitrant behaviour and personality

Kill-trapping is an important management tool for suppressing invasive mammalian predator populations in New Zealand, including the common brushtail possum (Trichosurus vulpecula). We conducted a combined field and pen experiment to test the hypothesis that intensive kill-trapping selects for survivors that differ behaviourally from the general population present before trapping begins. We installed 109 kill traps in a 120 ha forest reserve and over 20 weeks removed > 95% of the reserve’s possum population. Effort required rose from 12 trap nights per possum removed at the start of the operation to 560 trap nights per possum removed after 20 weeks of control. As the operation progressed, the estimated probability of possums being kill-trapped in the reserve declined from 0.30 to 0.15 per possum per week. Similarly, camera monitoring revealed that the average probability of a possum being killed when it encountered a kill-trap fell by 59% during the operation, indicating that the surviving population was becoming increasingly trap-recalcitrant. Behavioural testing of possums live-captured from the reserve at three time points revealed that survivors live-trapped 20 weeks into the operation were significantly shyer than those live-trapped before the operation began. In captivity, personality associated with boldness and activity/exploration was a significant predictor of whether a possum would trigger pest control devices it had not previously encountered. Heterogeneity of trappability affects the effort and cost required to eradicate invasive mammalian predators. Understanding the influence of personality on trappability is an important first step towards developing more effective methods to target trap-recalcitrant individuals.

Who eats the yellowmargined leaf beetle? Field observations and genetic surveillance to identify local predators of a novel invasive pest

The yellowmargined leaf beetle, Microtheca ochroloma Stahl (Coleoptera: Chrysomelidae), invaded the Southeastern United States and rapidly emerged as a leading pest of crucifer crops, yet little is known about which native predators might effectively provide biological control. The objective of this research is to identify potential predators of this understudied invader through field observation and genetic surveillance. Over two years, arthropods were surveyed on a variety of susceptible Brassica cultivars and a shortlist of commonly associated predators was developed. In a survey of turnip plants in year 1, lady beetles were positively predicted by densities of M. ochroloma, suggesting a numerical response to densities of the invasive pest. Surveys at a different site in year 2 revealed that big-eyed bugs were also positively predicted by M. ochroloma, while pink-spotted lady beetles negatively associated, suggesting a pattern of suppression. Ants (primarily the red imported fire ant) and spiders were commonly observed predators on plants in both years, but neither associated with densities of M. ochroloma. No predators were observed consuming M. ochroloma eggs. Molecular gut-content analysis using specially generated M. ochroloma primers confirmed the observed predatory links and suggested a density-dependent tracking response from pink-spotted lady beetles and ground beetles also have density-dependent tracking re Table 3. Our results may enable farmers to bolster these predator populations with fine-tuned habitat management tools and better suppress the spreading pest.

Size-dependent functional response of the round goby Neogobius melanostomus; implications for more accurate impact potential calculation

Abundance and per-capita foraging efficiency are essential factors for predicting and quantifying an invasive predator impact on prey, i.e., the impact potential (IP). However, population structure is not included in the calculation, and IP accuracy might be improved by incorporating predator body size. The population structure of the round goby Neogobius melanostomus, a highly invasive predator, was surveyed in the Elbe River. We determined the functional response (FR, per capita foraging) of the three most abundant size classes of N. melanostomus on the water louse Asellus aquaticus. We then calculated the IP for each size class and for the entire population with (the actual impact potential – IPA) and without (the impact potential for limit size rage – IPLSR) population body size structure (based on FR of the medium size class). All three size classes of the predator showed type II FR with respect to A. aquaticus. The estimated FR parameters, attack rate and handling time, as well as the maximum feeding rate, were size dependent. Despite the lowest per capita foraging efficiency, small individuals displayed the highest IP among the tested size classes because of their high abundance. Conversely, medium and large individuals, although showing highest per capita foraging efficiency, displayed lower IP. Hence, IPA showed more precise IP calculations compared to IPLSR. Overestimation of the potential impact as a consequence of omitting predator population size structure was negligible at the investigated locality. The IP of the N. melanostomus population five years post-invasion can be accurately calculated based on the FR of medium-sized fish.

An eco-epidemiological model with predator switching behavior

AbstractSwitching mechanism is adopted by predator populations when they are provided with two types of prey: susceptible and infected. In this study, we propose a modification of an eco-epidemiological model with the predator switching mechanism. In the presence of switching behavior, the existence of steady states and their stability have been discussed. The qualitative changes in the proposed model have been observed by the existence of transcritical and Hopf bifurcation. Numerical simulations are performed to support our numerical findings. In the context of species’ survival when disease is present in the system, it gives some theoretical views for eco-managers to understand the dynamics.

Veni, vidi, vici? Future spread and ecological impacts of a rapidly expanding invasive predator population.

Economic and ecological consequences of invasive species make biological invasions an influential driver of global change. Monitoring the spread and impacts of non-native species is essential, but often difficult, especially during the initial stages of invasion. The Jorō spider, Trichonephila clavata (L. Koch, 1878, Araneae: Nephilidae), is a large-bodied orb weaver native to Asia, likely introduced to northern Georgia, U.S. around 2010. We investigated the nascent invasion of T. clavata by constructing species distribution models (SDMs) from crowd-sourced data to compare the climate T. clavata experiences in its native range to its introduced range. We found evidence that the climate of T. clavata's native range differs significantly from its introduced range. Species distribution models trained with observations from its native range predict that the most suitable habitats in North America occur north of its current introduced range. Consistent with SDM predictions, T. clavata appears to be spreading faster to the north than to the south. Lastly, we conducted surveys to investigate potential ecological impacts of T. clavata on the diversity of native orb weaving spiders. Importantly, Trichonephila clavata was the most common and abundant species observed in the survey, and was numerically dominant at half of the sites it was present in. Our models also suggest that there is lower native orb weaver species richness and diversity closer to where T. clavata was initially found and where it has been established the longest, though human population density complicates this finding. This early study is the first to forecast how widely this spider may spread in its introduced range and explore its potential ecological impacts. Our results add evidence that T. clavata is an invasive species and deserves much more ecological scrutiny.

Bifurcation analysis of impulsive fractional-order Beddington–DeAngelis prey–predator model

In this paper, a fractional density-dependent prey–predator model has been considered. Certain reading of local and global stabilities of an equilibrium point of a system was extracted and conducted by applying fractional systems’ stability theorems along with Lyapunov functions. Meanwhile, the persistence of the aforementioned system has been discussed and claimed to imply a local asymptotic stability for the given positive equilibrium point. Moreover, the presented model was extended to a periodic impulsive model for the prey population. Such an expansion was implemented through the periodic catching of the prey species and the periodic releasing of the predator population. By studying the effect of changing some of the system’s parameters and drawing their bifurcation diagram, it was observed that different periodic solutions appear in the system. However, the effect of an impulse on the system subjects the system to various dynamic changes and makes it experience behaviors including cycles, period-doubling bifurcation, chaos and coexistence as well. Finally, by comparing the fractional system with the classic one, it has been concluded that the fractional system is more stable than its classical one.

Rapid assessments of the rice brown planthopper (Nilaparvata lugens Stal) outbreak in Semarang District, Central Java: Effects of farmers’ low KAP

Rapid assessments on the outbreak of rice brown planthoppers (BPH) (Nilaparvata lugens Stal) were conducted to investigate the status of BPH populations and the causative factors behind the outbreak. These assessments served as the basis for developing a proper action program. The assessments took place in Banyubiru Sub-District, Semarang District covering four villages (Kebondowo, Rowoboni, Tegaron, Kebumen) in December 2013. We analyzed BPH data, along with information about farmers’ practices in managing pests collected through interviews conducted in January 2018 in Indramayu. Additionally, we examined data on the number of BPH-infested areas in Java from 2010 to 2020 and the stock of insecticides in Java in 2021. Simple statistical analyses were carried out. The BPH population had spread throughout Banyubiru and was present in all sampled plots. The average number of BPH eggs ranged from 115.25 to 379.65 per rice hill, while the BPH nymphs and imagoes ranged from 3.42 to 11.87 per rice hill. The relatively low nymphs to imagoes ratio might be influenced by the high BPH predator populations, which ranged from three to six individuals per rice hill. Suspected causes of BPH resistance and resurgence included the application of banned and improper insecticides, as well as the repeated use of the same insecticide active ingredients for an extended period. It is recommended to discontinue the mass spraying of insecticides to prevent further plant damage. In 2022, the Pest Control Movement has suggested replacing chemical insecticides with biological or natural pesticides. Intensive extension programs are strongly needed.

Stochastic Modeling of Three-Species Prey–Predator Model Driven by Lévy Jump with Mixed Holling-II and Beddington–DeAngelis Functional Responses

This study examines the dynamics of a stochastic prey–predator model using a functional response function driven by Lévy noise and a mixed Holling-II and Beddington–DeAngelis functional response. The proposed model presents a computational analysis between two prey and one predator population dynamics. First, we show that the suggested model admits a unique positive solution. Second, we prove the extinction of all the studied populations, the extinction of only the predator, and the persistence of all the considered populations under several sufficient conditions. Finally, a special Runge–Kutta method for the stochastic model is illustrated and implemented in order to show the behavior of the two prey and one predator subpopulations.