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Keywords = antipredator model

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7 pages, 518 KB  
Communication
Avian Escape and Prevailing Light Levels
by Michael A. Weston and Kaori Yokochi
Birds 2025, 6(3), 47; https://doi.org/10.3390/birds6030047 - 4 Sep 2025
Viewed by 556
Abstract
Anti-predator behaviour in birds is required by day and night but has barely been studied at night. For prey which detect predators visually, low light levels may diminish detection or monitoring of approaching threats. We conducted standardised approaches to Silver Gulls (Chroicocephalus [...] Read more.
Anti-predator behaviour in birds is required by day and night but has barely been studied at night. For prey which detect predators visually, low light levels may diminish detection or monitoring of approaching threats. We conducted standardised approaches to Silver Gulls (Chroicocephalus novaehollandiae) by day and night along an urban foreshore in Melbourne, Australia, measuring light levels (Lux) experienced by the gull, Flight-initiation Distance (FID; the distance at which escape is initiated), and Starting Distance (the initial distance between the observer and the bird). We fitted models reflecting different conceptual possibilities for the relationship between Lux and FID. Support existed for a model with a stepwise effect of light on FID. Longer FIDs (i.e., earlier escape) in darker conditions suggest that gulls can detect an approaching threat in darkness at least as well as by day, but the tolerance of closer approaches may be diminished in dull and dark conditions, perhaps due to difficulty in monitoring an approaching threat and/or because nighttime represents a time of greater predator risk. Starting Distance was positively related to FID, a result commonly reported for many taxa by day. Full article
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14 pages, 1447 KB  
Article
Mixed-Species Flock Diversity and Habitat Density Are Associated with Antipredator Behavior in Songbirds
by Eric K. Frazier, Zaharia A. Selman, Charles A. Price, Monica Papeş and Todd M. Freeberg
Diversity 2025, 17(5), 363; https://doi.org/10.3390/d17050363 - 20 May 2025
Viewed by 698
Abstract
Human-caused changes to habitats like forestry practices and traffic noise can negatively influence antipredator and foraging behavior in animals. These behavior patterns are also frequently positively influenced by individuals being part of mixed-species groups. However, we know little about how such human-induced changes [...] Read more.
Human-caused changes to habitats like forestry practices and traffic noise can negatively influence antipredator and foraging behavior in animals. These behavior patterns are also frequently positively influenced by individuals being part of mixed-species groups. However, we know little about how such human-induced changes impact these behaviors in individuals of mixed-species groups. To address this gap, we examined the effects of mixed-species group composition, traffic noise, and vegetation density on antipredator and foraging behavior. We used feeders to attract mixed-species flocks of Carolina chickadees (Poecile carolinensis), tufted titmice (Baeolophus bicolor), and white-breasted nuthatches (Sitta carolinensis). Once we detected a flock at a feeder, we presented a Cooper’s hawk model and recorded flocks’ seed-taking and calling behaviors. Titmice avoided feeders more when hawk models were presented at sites with greater vegetation density. Nuthatches called more quickly with more conspecifics in their flocks, and they tended to take seed more quickly with greater diversity of species in their flocks. We did not detect the effects of physical or social environmental variables on chickadee behavior. Our results reveal individual sensitivity to environmental variation in contexts involving visual predator stimuli. More work is needed to investigate how various predator stimulus modalities affect antipredator behaviors of mixed-species flock members. Full article
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23 pages, 442 KB  
Article
Dynamics of a Predator-Prey System with Asymmetric Dispersal and Fear Effect
by Xinyu Meng, Lijuan Chen and Fengde Chen
Symmetry 2025, 17(3), 329; https://doi.org/10.3390/sym17030329 - 22 Feb 2025
Cited by 1 | Viewed by 994
Abstract
Predator-prey interactions are among the most common and crucial ecological phenomena in nature. Over the course of long-term evolution, prey populations have developed various anti-predation strategies to cope with the threat of predators, with population dispersal being one of the most common strategies. [...] Read more.
Predator-prey interactions are among the most common and crucial ecological phenomena in nature. Over the course of long-term evolution, prey populations have developed various anti-predation strategies to cope with the threat of predators, with population dispersal being one of the most common strategies. In traditional ecological models, the prey population is typically constrained by direct predation. However, an increasing body of empirical evidence suggests that the fear effect from the predator significantly alters the physiological behavior of prey, leading to a decrease in reproduction rate and an increase in mortality rate. In this paper, we investigate a predator-prey system incorporating asymmetric dispersal and the fear effect, which influences the birth and death rates of the prey species. We rigorously establish the existence and local stability of equilibrium points, derive sufficient conditions for global stability, and prove the occurrence of a transcritical bifurcation at the boundary equilibrium. Our analysis reveals an optimal dispersal rate that maximizes prey population density; beyond this threshold, increased dispersal drives both populations to extinction. Furthermore, the fear effect and its maximum cost exhibit significant negative impacts on predator abundance, though they do not alter the equilibrium stability or existence. These findings provide critical insights for designing habitat corridors in endangered species conservation and underscore the pivotal role of prey dispersal in shaping population dynamics. Full article
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18 pages, 2987 KB  
Article
Grouping Behaviour and Anti-Predator Responses in the Helmeted Guineafowl Numida meleagris
by Johann H. van Niekerk, Giovanni Forcina and Rodrigo Megía-Palma
Birds 2024, 5(4), 685-702; https://doi.org/10.3390/birds5040047 - 18 Oct 2024
Cited by 1 | Viewed by 1752
Abstract
Little is known about landbird group dynamics in response to predation. Here, we describe the interactions between the Helmeted Guineafowl (Numida meleagris) and its predators regarding the survival advantages grouping behaviour may provide. Livestream webcam observations were conducted in Madikwe Game [...] Read more.
Little is known about landbird group dynamics in response to predation. Here, we describe the interactions between the Helmeted Guineafowl (Numida meleagris) and its predators regarding the survival advantages grouping behaviour may provide. Livestream webcam observations were conducted in Madikwe Game Reserve (South Africa) from August 2020 to August 2021. Emphasis was placed on predator–prey interaction and its effect on group size and structure in a spatial framework. We hypothesise that while grouping is crucial for a number of daily activities in this highly social species, it might turn into a higher predatory pressure. We found, indeed, that the probability of attacks by black-backed jackals (Lupulella mesomelas) significantly increased with guineafowl group size, unlike what happened with raptors. Moreover, when attacked by jackals, the birds responded by standing close to each other. These results suggest, in line with the proposed hypothesis, that a trade-off occurs between the defensive function of grouping in this galliform and the probability of jackal attack that increases as a function of prey group size. Nevertheless, we argue that Helmeted Guineafowl cooperative social groups also play a role as a defensive strategy against predators, with the many-eyes and dilution effects likely compensating for the higher predatory pressure. Full article
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25 pages, 929 KB  
Article
Impulsive Effects and Complexity Dynamics in the Anti-Predator Model with IPM Strategies
by Wenjie Qin, Zhengjun Dong and Lidong Huang
Mathematics 2024, 12(7), 1043; https://doi.org/10.3390/math12071043 - 30 Mar 2024
Cited by 3 | Viewed by 1218
Abstract
When confronted with the imminent threat of predation, the prey instinctively employ strategies to avoid being consumed. These anti-predator tactics involve individuals acting collectively to intimidate predators and reduce potential harm during an attack. In the present work, we propose a state-dependent feedback [...] Read more.
When confronted with the imminent threat of predation, the prey instinctively employ strategies to avoid being consumed. These anti-predator tactics involve individuals acting collectively to intimidate predators and reduce potential harm during an attack. In the present work, we propose a state-dependent feedback control predator-prey model that incorporates a nonmonotonic functional response, taking into account the anti-predator behavior observed in pest-natural enemy ecosystems within the agricultural context. The qualitative analysis of this model is presented utilizing the principles of impulsive semi-dynamical systems. Firstly, the stability conditions of the equilibria are derived by employing pertinent properties of planar systems. The precise domain of the impulsive set and phase set is determined by considering the phase portrait of the system. Secondly, a Poincaré map is constructed by utilizing the sequence of impulsive points within the phase set. The stability of the order-1 periodic solution at the boundary is subsequently analyzed by an analog of the Poincaré criterion. Additionally, this article presents various threshold conditions that determine both the existence and stability of an order-1 periodic solution. Furthermore, it investigates the existence of order-k (k2) periodic solutions. Finally, the article explores the complex dynamics of the model, encompassing multiple bifurcation phenomena and chaos, through computational simulations. Full article
(This article belongs to the Special Issue Advances in Mathematical Biology and Applications)
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20 pages, 4994 KB  
Article
Temperature Compensation of Laser Methane Sensor Based on a Large-Scale Dataset and the ISSA-BP Neural Network
by Songfeng Yin, Xiang Zou, Yue Cheng and Yunlong Liu
Sensors 2024, 24(2), 493; https://doi.org/10.3390/s24020493 - 12 Jan 2024
Cited by 10 | Viewed by 1831
Abstract
We aimed to improve the detection accuracy of laser methane sensors in expansive temperature application environments. In this paper, a large-scale dataset of the measured concentration of the sensor at different temperatures is established, and a temperature compensation model based on the ISSA-BP [...] Read more.
We aimed to improve the detection accuracy of laser methane sensors in expansive temperature application environments. In this paper, a large-scale dataset of the measured concentration of the sensor at different temperatures is established, and a temperature compensation model based on the ISSA-BP neural network is proposed. On the data side, a large-scale dataset of 15,810 sets of laser methane sensors with different temperatures and concentrations was established, and an Improved Isolation Forest algorithm was used to clean the large-scale data and remove the outliers in the dataset. On the modeling framework, a temperature compensation model based on the ISSA-BP neural network is proposed. The quasi-reflective learning, chameleon swarm algorithm, Lévy flight, and artificial rabbits optimization are utilized to improve the initialization of the sparrow population, explorer position, anti-predator position, and position of individual sparrows in each generation, respectively, to improve the global optimization seeking ability of the standard sparrow search algorithm. The ISSA-BP temperature compensation model far outperforms the four models, SVM, RF, BP, and PSO-BP, in model evaluation metrics such as MAE, MAPE, RMSE, and R-square for both the training and test sets. The results show that the algorithm in this paper can significantly improve the detection accuracy of the laser methane sensor under the wide temperature application environment. Full article
(This article belongs to the Section Optical Sensors)
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33 pages, 7785 KB  
Article
Modeling and Dynamical Analysis of a Fractional-Order Predator–Prey System with Anti-Predator Behavior and a Holling Type IV Functional Response
by Baiming Wang and Xianyi Li
Fractal Fract. 2023, 7(10), 722; https://doi.org/10.3390/fractalfract7100722 - 30 Sep 2023
Cited by 7 | Viewed by 1778
Abstract
We here investigate the dynamic behavior of continuous and discrete versions of a fractional-order predator–prey system with anti-predator behavior and a Holling type IV functional response. First, we establish the non-negativity, existence, uniqueness and boundedness of solutions to the system from a mathematical [...] Read more.
We here investigate the dynamic behavior of continuous and discrete versions of a fractional-order predator–prey system with anti-predator behavior and a Holling type IV functional response. First, we establish the non-negativity, existence, uniqueness and boundedness of solutions to the system from a mathematical analysis perspective. Then, we analyze the stability of its equilibrium points and the possibility of bifurcations using stability analysis methods and bifurcation theory, demonstrating that, under specific parameter conditions, the continuous system exhibits a Hopf bifurcation, while the discrete version exhibits a Neimark–Sacker bifurcation and a period-doubling bifurcation. After providing numerical simulations to illustrate the theoretically derived conclusions and by summarizing the various analytical results obtained, we finally present four interesting conclusions that can contribute to better management and preservation of ecological systems. Full article
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42 pages, 799 KB  
Review
The Herbicide Glyphosate and Its Formulations Impact Animal Behavior across Taxa
by Becky Talyn, Kelly Muller, Cindy Mercado, Bryan Gonzalez and Katherine Bartels
Agrochemicals 2023, 2(3), 367-408; https://doi.org/10.3390/agrochemicals2030022 - 10 Jul 2023
Cited by 10 | Viewed by 7273
Abstract
Use of glyphosate and glyphosate-based herbicides is ubiquitous in US agriculture and widespread around the world. Despite marketing efforts to the contrary, numerous studies demonstrate glyphosate toxicity to non-target organisms including animals, primarily focusing on mortality, carcinogenicity, renal toxicity, reproductive, and neurological toxicity, [...] Read more.
Use of glyphosate and glyphosate-based herbicides is ubiquitous in US agriculture and widespread around the world. Despite marketing efforts to the contrary, numerous studies demonstrate glyphosate toxicity to non-target organisms including animals, primarily focusing on mortality, carcinogenicity, renal toxicity, reproductive, and neurological toxicity, and the biochemical mechanisms underlying these physiological outcomes. Glyphosate toxicity also impacts animal behavior, both in model systems and in agricultural and environmentally relevant contexts. In this review, we examine the effects of glyphosate and glyphosate-based herbicides on animal behaviors, particularly activity, foraging and feeding, anti-predator behavior, reproductive behaviors, learning and memory, and social behaviors. Glyphosate can be detected both in food and in the environment, and avoided through activity and feeding strategies. However, exposure also reduces activity, depresses foraging and feeding, increases susceptibility to predation, interferes with courtship, mating, fertility and maternal behaviors, decreases learning and memory capabilities, and disrupts social behaviors. Changes in animal behavior as a result of glyphosate toxicity are important because of their sometimes severe effects on individual fitness, as well as ecosystem health. Implications for human behavior are also considered. Full article
(This article belongs to the Special Issue Feature Papers to Celebrate the Inaugural Issue of Agrochemicals)
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12 pages, 1162 KB  
Article
Hopf Bifurcation in a Predator–Prey Model with Memory Effect in Predator and Anti-Predator Behaviour in Prey
by Wenqi Zhang, Dan Jin and Ruizhi Yang
Mathematics 2023, 11(3), 556; https://doi.org/10.3390/math11030556 - 20 Jan 2023
Cited by 9 | Viewed by 2281
Abstract
In this paper, a diffusive predator–prey model with a memory effect in predator and anti-predator behaviour in prey is studied. The stability of the coexisting equilibrium and the existence of Hopf bifurcation are analysed by analysing the distribution of characteristic roots. The property [...] Read more.
In this paper, a diffusive predator–prey model with a memory effect in predator and anti-predator behaviour in prey is studied. The stability of the coexisting equilibrium and the existence of Hopf bifurcation are analysed by analysing the distribution of characteristic roots. The property of Hopf bifurcation is investigated by the theory of the centre manifold and normal form method. Through the numerical simulations, it is observed that the anti-predator behaviour parameter η, the memory-based diffusion coefficient parameter d, and memory delay τ can affect the stability of the coexisting equilibrium under some parameters and cause the spatially inhomogeneous oscillation of prey and predator’s densities. Full article
(This article belongs to the Special Issue Recent Advances in Theory and Application of Dynamical Systems)
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8 pages, 525 KB  
Article
Avian Alarm Calls Do Not Induce Anti-Predator Response in Three Anuran Species
by Longhui Zhao, Yuanyu Qin, Jichao Wang and Wei Liang
Animals 2022, 12(24), 3537; https://doi.org/10.3390/ani12243537 - 14 Dec 2022
Cited by 2 | Viewed by 2210
Abstract
Many species produce alarm calls in response to predators, and the anti-predator signals are often used by other species. Eavesdropping on heterospecific alarm calls has been widely found in bird and mammal species. Other taxa, such as reptiles and amphibians, however, receive limited [...] Read more.
Many species produce alarm calls in response to predators, and the anti-predator signals are often used by other species. Eavesdropping on heterospecific alarm calls has been widely found in bird and mammal species. Other taxa, such as reptiles and amphibians, however, receive limited attention at present. Here, we selected three types of alarm calls of Japanese Tits (Parus minor) that were evoked by the Siberian Chipmunk (Eutamias sibiricus), Eurasian Sparrow Hawk (Accipiter nisus), and model snake (Elaphe spp.), respectively, and then carried out playback experiments to test whether three frog species changed their behaviors in response to the three treatments of Japanese Tit calls while the tit’s territory song was used as a control. The results showed that Little Torrent Frogs (Amolops torrentis), Ornamented Pygmy Frogs (Microhyla fissipes) and Spot-legged Treefrogs (Polypedates megacephalus) did not jump off their positions in response to the same four acoustic signals. They also did not change their calling behaviors in response to the alarm calls of Japanese Tits. This study found no evidence that these anuran species can eavesdrop on heterospecific tits’ alarm signals. Full article
(This article belongs to the Section Birds)
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26 pages, 7955 KB  
Article
Research on Carbon Emissions Prediction Model of Thermal Power Plant Based on SSA-LSTM Algorithm with Boiler Feed Water Influencing Factors
by Xindong Wang, Chun Yan, Wei Liu and Xinhong Liu
Sustainability 2022, 14(23), 15988; https://doi.org/10.3390/su142315988 - 30 Nov 2022
Cited by 19 | Viewed by 2841
Abstract
China’s power industry is a major energy consumer, with the carbon dioxide (CO2) generated by coal consumption making the power industry one of the key emission sectors. Therefore, it is crucial to explore energy conservation and emissions reduction strategies suitable for [...] Read more.
China’s power industry is a major energy consumer, with the carbon dioxide (CO2) generated by coal consumption making the power industry one of the key emission sectors. Therefore, it is crucial to explore energy conservation and emissions reduction strategies suitable for China’s current situation. Taking a typical cogeneration enterprise in North China as an example, this paper aims to establish a generalized regression prediction model for carbon emissions of coal-fired power plants, which will provide a reference for China to seek strategies for carbon peaking and carbon neutralization in the future. Firstly, in terms of the selection of influencing factors, this paper uses objective index screening methods, simulation means, and the eXtreme Gradient Boosting algorithm (XG-Boost) to analyze the feature importance of various influencing factors. It is concluded that the relevant influencing factors of the boiler feed water system have a strong correlation and characteristic importance with the carbon emissions results of coal-fired power plants. Therefore, this paper proposes to introduce these factors into the regression prediction model as auxiliary variables to more scientifically reflect the carbon emissions results of coal-fired power plants. Secondly, in the aspect of regression prediction model establishment, inspired by the sparrow’s foraging behavior and anti-predation behavior, this paper selects the sparrow search algorithm (SSA) with strong optimization ability and fast convergence speed to optimize the super parameters of the long short-term memory network algorithm (LSTM). It is proposed to use the SSA-LSTM algorithm to establish the carbon emissions regression prediction model of coal-fired power plants. The advantage of the SSA-LSTM algorithm is that it can effectively simplify the super parameter selection process of the LSTM algorithm, effectively solve the global optimization problem, prevent the model from falling into overfitting and local optimization, and make the carbon emissions regression prediction model of coal-fired power plants achieve a better fitting effect. By comparing the performance indicators of the model before and after the improvement, it is found that the regression prediction effect of the SSA-LSTM coal-fired power plant carbon emissions regression prediction model, which introduces boiler feed water influencing factors, has been effectively improved. Therefore, the model proposed in this paper can be used to conduct a comprehensive impact factor analysis and regression prediction analysis on the carbon emissions intensity of China’s coal-fired power plants, formulate targeted carbon emissions reduction countermeasures, and provide a theoretical basis for energy conservation and emissions reduction of China’s coal-fired power plants. Full article
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38 pages, 7515 KB  
Article
Complex Dynamics of a Predator–Prey Interaction with Fear Effect in Deterministic and Fluctuating Environments
by Nirapada Santra, Sudeshna Mondal and Guruprasad Samanta
Mathematics 2022, 10(20), 3795; https://doi.org/10.3390/math10203795 - 14 Oct 2022
Cited by 12 | Viewed by 3423
Abstract
Many ecological models have received much attention in the past few years. In particular, predator–prey interactions have been examined from many angles to capture and explain various environmental phenomena meaningfully. Although the consumption of prey directly by the predator is a well-known ecological [...] Read more.
Many ecological models have received much attention in the past few years. In particular, predator–prey interactions have been examined from many angles to capture and explain various environmental phenomena meaningfully. Although the consumption of prey directly by the predator is a well-known ecological phenomenon, theoretical biologists suggest that the impact of anti-predator behavior due to the fear of predators (felt by prey) can be even more crucial in shaping prey demography. In this article, we develop a predator–prey model that considers the effects of fear on prey reproduction and on environmental carrying capacity of prey species. We also include two delays: prey species birth delay influenced by fear of the predator and predator gestation delay. The global stability of each equilibrium point and its basic dynamical features have been investigated. Furthermore, the “paradox of enrichment” is shown to exist in our system. By analysing our system of nonlinear delay differential equations, we gain some insights into how fear and delays affect on population dynamics. To demonstrate our findings, we also perform some numerical computations and simulations. Finally, to evaluate the influence of a fluctuating environment, we compare our proposed system to a stochastic model with Gaussian white noise terms. Full article
(This article belongs to the Special Issue Advances in the Mathematics of Ecological Modelling)
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20 pages, 921 KB  
Article
Analysis of a Delayed Reaction-Diffusion Predator–Prey System with Fear Effect and Anti-Predator Behaviour
by Zhenglong Chen, Shunjie Li and Xuebing Zhang
Mathematics 2022, 10(18), 3270; https://doi.org/10.3390/math10183270 - 8 Sep 2022
Cited by 5 | Viewed by 1839
Abstract
This paper is devoted to studying the dynamics of a delayed reaction-diffusion predator–prey system incorporating the effects of fear and anti-predator behaviour. First, based on its mathematical model, the global attractor is analyzed and the local stability of its positive equilibria is derived. [...] Read more.
This paper is devoted to studying the dynamics of a delayed reaction-diffusion predator–prey system incorporating the effects of fear and anti-predator behaviour. First, based on its mathematical model, the global attractor is analyzed and the local stability of its positive equilibria is derived. Moreover, the Hopf bifurcation induced by the time delay variable is also investigated. Furthermore, the existence and non-existence of non-constant positive solutions are analyzed. Finally, numerical simulations are presented to validate the theoretical analysis. Full article
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19 pages, 1969 KB  
Article
Adaptive Vertical Positioning as Anti-Predator Behavior: The Case of a Prey Fish Cohabiting with Multiple Predatory Fish within Temperate Marine Algal Forests
by Pierre D. Thiriet, Antonio Di Franco, Adrien Cheminée, Luisa Mangialajo, Paolo Guidetti, Samuel Branthomme and Patrice Francour
Animals 2022, 12(7), 826; https://doi.org/10.3390/ani12070826 - 24 Mar 2022
Cited by 5 | Viewed by 3456
Abstract
Prey fish cohabit with specialized predator fish within structurally complex habitats. How the vertical stratification of the habitat affects lethal and behavioral predator–prey interactions and contributes to explaining these patterns has never been investigated within a forest-like marine habitat, i.e., a habitat containing [...] Read more.
Prey fish cohabit with specialized predator fish within structurally complex habitats. How the vertical stratification of the habitat affects lethal and behavioral predator–prey interactions and contributes to explaining these patterns has never been investigated within a forest-like marine habitat, i.e., a habitat containing three vertical strata (understory, canopy, open-water above). We studied this in tank experiments, with a model prey (the wrasse Symphodus ocellatus) and two model predators (the stalk-and-attack comber Serranus cabrilla and the sit-and-wait scorpionfish Scorpaena porcus), which are among the most abundant prey and predators cohabiting in Mediterranean Cystoseira forests. Wrasse anti-predator behavior was predator-specific. When exposed to the scorpionfish, the wrasse increased its vertical distance from the predator, regardless of the habitat structure. Conversely, when exposed to the comber, the wrasse sought refuge within forest structures: (1) the canopy provides more hiding opportunities due to its high complexity, and (2) the understory provides more escape/avoidance opportunities due to (a) its low complexity that allows for fast prey movements, and (b) the presence of the canopy above that limits the comber’s access to the understory. Our results suggest that habitat vertical stratification mediates predator–prey interactions and potentially promotes the co-existence of prey and multiple predators within marine forests. Full article
(This article belongs to the Special Issue Species Interactions in Marine Benthic Communities)
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18 pages, 2441 KB  
Article
Dynamical Analysis of a Delayed Diffusive Predator–Prey Model with Additional Food Provided and Anti-Predator Behavior
by Ruizhi Yang, Xiao Zhao and Yong An
Mathematics 2022, 10(3), 469; https://doi.org/10.3390/math10030469 - 31 Jan 2022
Cited by 29 | Viewed by 4773
Abstract
We studied a delayed predator–prey model with diffusion and anti-predator behavior. Assume that additional food is provided for predator population. Then the stability of the positive equilibrium is considered. The existence of Hopf bifurcation is also discussed based on the Hopf bifurcation theory. [...] Read more.
We studied a delayed predator–prey model with diffusion and anti-predator behavior. Assume that additional food is provided for predator population. Then the stability of the positive equilibrium is considered. The existence of Hopf bifurcation is also discussed based on the Hopf bifurcation theory. The property of Hopf bifurcation is derived through the theory of center manifold and normal form method. Finally, we analyze the effect of time delay on the model through numerical simulations. Full article
(This article belongs to the Special Issue Recent Advances in Theory and Application of Dynamical Systems)
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