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Keywords = prey switching

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17 pages, 1710 KB  
Article
Dynamical Regimes in a Delayed Predator–Prey Model with Predator Hunting Cooperation: Bifurcations, Stability, and Complex Dynamics
by Chao Peng and Jiao Jiang
Modelling 2025, 6(3), 84; https://doi.org/10.3390/modelling6030084 - 18 Aug 2025
Cited by 1 | Viewed by 831
Abstract
In this paper, a predator–prey model with hunting cooperation and maturation delay is studied. Through theoretical analysis, we investigate the existence of multiple stability switches of the positive equilibrium. By applying Hopf bifurcation theory, the conditions for Hopf bifurcation are derived, indicating the [...] Read more.
In this paper, a predator–prey model with hunting cooperation and maturation delay is studied. Through theoretical analysis, we investigate the existence of multiple stability switches of the positive equilibrium. By applying Hopf bifurcation theory, the conditions for Hopf bifurcation are derived, indicating the emergence of periodic solutions as the maturation delay passes through critical values. Utilizing center manifold theory and normal form analysis, we determine the stability and direction of the bifurcating orbits. Numerical simulations are performed to validate the theoretical results. Furthermore, the simulations vividly demonstrate the appearance of period-doubling bifurcations, which is the onset of chaotic behavior. Bifurcation diagrams and phase portraits are employed to precisely characterize the transition processes from a stable equilibrium to periodic, period-doubling solutions and chaotic states under different maturation delay values. The study reveals the significant influence of maturation delay on the stability and complex dynamics of predator–prey systems with hunting cooperation. Full article
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16 pages, 2417 KB  
Communication
Owl Habitat Use and Diets After Fire and Salvage Logging
by Angelina J. Kelly, Frank I. Doyle and Karen E. Hodges
Fire 2025, 8(7), 281; https://doi.org/10.3390/fire8070281 - 16 Jul 2025
Viewed by 1305
Abstract
Megafires are transforming western boreal forests, and many burned forests are salvage logged, removing more structure from landscapes and delaying forest regeneration. We studied forest-dwelling owls in a post-fire and salvage-logged landscape in central British Columbia, Canada, in 2018–2019 after the 2010 Meldrum [...] Read more.
Megafires are transforming western boreal forests, and many burned forests are salvage logged, removing more structure from landscapes and delaying forest regeneration. We studied forest-dwelling owls in a post-fire and salvage-logged landscape in central British Columbia, Canada, in 2018–2019 after the 2010 Meldrum Creek Fire and the 2017 Hanceville Fire. We examined owl habitat selection via call surveys compared to the habitats available in this landscape. Owl pellets were dissected to determine owl diets. We detected six owl species, of which Northern Saw-whet Owls (Aegolius acadicus) were the most common. Owls had weak and variable habitat selection within an 800 m radius of detections; all species used some burned area. Great Gray Owls (Strix nebulosa) and Great Horned Owls (Bubo virginanus) obtained more prey from mature forests (e.g., red-backed voles, Myodes gapperi, snowshoe hares, Lepus americanus) than other owls did, whereas other owls primarily consumed small mammals that were common in burned or salvaged areas. These results indicate a diverse community of owls can use landscapes within a decade after wildfire, potentially with some prey switching to take advantage of prey that use disturbed habitats. Despite that, owl numbers were low and some owls consumed prey that were not available in salvage-logged areas, suggesting that impacts on owls were more severe from the combination of fire and salvage logging than from fire alone. Full article
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40 pages, 2146 KB  
Article
Global Dynamics of a Predator–Prey System with Variation Multiple Pulse Intervention Effects
by Gang Wang, Ming Yi and Zaiyun Zhang
Mathematics 2025, 13(10), 1597; https://doi.org/10.3390/math13101597 - 13 May 2025
Viewed by 531
Abstract
A continuous point of a trajectory for an ordinary differential equation can be viewed as a special impulsive point; i.e., the pulsed proportional change rate and the instantaneous increment for the prey and predator populations can be taken as 0. By considering the [...] Read more.
A continuous point of a trajectory for an ordinary differential equation can be viewed as a special impulsive point; i.e., the pulsed proportional change rate and the instantaneous increment for the prey and predator populations can be taken as 0. By considering the variation multiple pulse intervention effects (i.e., several indefinite continuous points are regarded as impulsive points), an impulsive predator–prey model for characterizing chemical and biological control processes at different fixed times is first proposed. Our modeling approach can describe all possible realistic situations, and all of the traditional models are some special cases of our model. Due to the complexity of our modeling approach, it is essential to examine the dynamical properties of the periodic solutions using new methods. For example, we investigate the permanence of the system by constructing two uniform lower impulsive comparison systems, indicating the mathematical (or biological) essence of the permanence of our system; furthermore, the existence and global attractiveness of the pest-present periodic solution is analyzed by constructing an impulsive comparison system for a norm V(t), which has not been addressed to date. Based on the implicit function theorem, the bifurcation of the pest-present periodic solution of the system is investigated under certain conditions, which is more rigorous than the corresponding traditional proving method. In addition, by employing the variational method, the eigenvalues of the Jacobian matrix at the fixed point corresponding to the pest-free periodic solution are determined, resulting in a sufficient condition for its local stability, and the threshold condition for the global attractiveness of the pest-free periodic solution is provided in terms of an indicator Ra. Finally, the sensitivity of indicator Ra and bifurcations with respect to several key parameters are determined through numerical simulations, and then the switch-like transitions among two coexisting attractors show that varying dosages of insecticide applications and the numbers of natural enemies released are crucial. Full article
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20 pages, 3246 KB  
Article
Changes in the Diet of an Invasive Predatory Crab, Chionoecetes opilio, in the Degrading Benthic Community of an Arctic Fjord
by Alexander D. Kiselev and Anna K. Zalota
Biology 2024, 13(10), 781; https://doi.org/10.3390/biology13100781 - 29 Sep 2024
Cited by 2 | Viewed by 1838
Abstract
The introduction of a new species can lead to substantial changes in a new ecosystem. Local and introduced species’ survival depends on their ability to adapt to the new environment. Studying such adaptations is often hindered by multiple factors affecting the ecosystem. The [...] Read more.
The introduction of a new species can lead to substantial changes in a new ecosystem. Local and introduced species’ survival depends on their ability to adapt to the new environment. Studying such adaptations is often hindered by multiple factors affecting the ecosystem. The introduction of a large predatory snow crab, Chionoecetes opilio, into the Kara Sea, is a unique invasive species affecting an otherwise undisturbed ecosystem. The crab has caused drastic changes in the macro- and megabenthic taxonomic structure, abundance, and biomass of the most common species in an Arctic fjord, Blagopoluchiya Bay. Stomach content and stable isotope analysis were applied to study crabs’ feeding habits. As the abundance of the most common prey items diminished, the crabs switched to other less accessible food. Prior to substantial changes in benthic communities, the diet of the snow crabs was similar to that of other invaded and native areas, where animal food predominates. However, with the degradation of the ecosystem, detritus contribution has substantially increased. The changes in prey items did not change the crab’s trophic status, and they continued to feed within the same trophic niche. In the depleted benthic communities of Blagopoluchiya Bay, the snow crab is forced to use all available food sources. Full article
(This article belongs to the Section Ecology)
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14 pages, 1905 KB  
Article
Prey Switching and Natural Pest Control Potential of Carabid Communities over the Winter Wheat Cropping Season
by Ambre Sacco--Martret de Préville, Karin Staudacher, Michael Traugott, David A. Bohan, Manuel Plantegenest and Elsa Canard
Insects 2024, 15(8), 610; https://doi.org/10.3390/insects15080610 - 13 Aug 2024
Cited by 3 | Viewed by 2050
Abstract
To date, evaluating the diets of natural enemies like carabids has largely been limited to spatially explicit and short-term sampling. This leaves a knowledge gap for the intra-annual dynamics of carabid diets, and the provision and timing of delivery of natural pest control [...] Read more.
To date, evaluating the diets of natural enemies like carabids has largely been limited to spatially explicit and short-term sampling. This leaves a knowledge gap for the intra-annual dynamics of carabid diets, and the provision and timing of delivery of natural pest control services. Season-long pitfall trapping of adult carabids was conducted in conventional winter wheat fields, from November 2018 to June 2019, in five French departments. Diagnostic Multiplex PCR of carabid gut contents was used to determine the dynamics of carabid diets. The overall detection rate of target prey DNA was high across carabid individuals (80%) but varied with the prey group. The rate of detection was low for pests, at 8.1% for slugs and 9.6% for aphids. Detection of intraguild predation and predation on decomposers was higher, at 23.8% for spiders, 37.9% for earthworms and 64.6% for springtails. Prey switching was high at the carabid community level, with pest consumption and intraguild predation increasing through the cropping season as the availability of these prey increased in the environment, while the detection of decomposer DNA decreased. Variation in diet through the cropping season was characterized by: (i) complementary predation on slug and aphid pests; and (ii) temporal complementarity in the predominant carabid taxa feeding on each pest. We hypothesize that natural pest control services delivered by carabids are determined by complementary contributions to predation by the different carabid taxa over the season. Full article
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17 pages, 962 KB  
Article
Stability and Hopf Bifurcation of a Delayed Predator–Prey Model with a Stage Structure for Generalist Predators and a Holling Type-II Functional Response
by Zi-Wei Liang and Xin-You Meng
Symmetry 2024, 16(5), 597; https://doi.org/10.3390/sym16050597 - 11 May 2024
Cited by 2 | Viewed by 1692
Abstract
In this paper, we carry out some research on a predator–prey system with maturation delay, a stage structure for generalist predators and a Holling type-II functional response, which has already been proposed. First, for the delayed model, we obtain the conditions for the [...] Read more.
In this paper, we carry out some research on a predator–prey system with maturation delay, a stage structure for generalist predators and a Holling type-II functional response, which has already been proposed. First, for the delayed model, we obtain the conditions for the occurrence of stability switches of the positive equilibrium and possible Hopf bifurcation values owing to the growth of the value of the delay by applying the geometric criterion. It should be pointed out that when we suppose that the characteristic equation has a pair of imaginary roots λ=±iω(ω>0), we just need to consider iω(ω>0) due to the symmetry, which alleviates the computation requirements. Next, we investigate the nature of Hopf bifurcation. Finally, we conduct numerical simulations to verify the correctness of our findings. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry of Differential Equations in Biomathematics)
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13 pages, 2373 KB  
Article
Effects of Prey Switching at Different Stages on Life Parameters of Neoseiulus bicaudus
by Zixin Nie, Li Zuo, Siqiong Tang, Chen Fang, Ying Ma, Xiang Li, Jianping Zhang and Jie Su
Agriculture 2024, 14(5), 728; https://doi.org/10.3390/agriculture14050728 - 8 May 2024
Cited by 1 | Viewed by 1738
Abstract
The phenomenon of prey switching is prevalent in the natural world and represents a strategic adaptation of predators to their environment. Neoseiulus bicaudus, a native predatory mite found in Xinjiang, serves as a natural enemy to numerous small pests. The utilization of [...] Read more.
The phenomenon of prey switching is prevalent in the natural world and represents a strategic adaptation of predators to their environment. Neoseiulus bicaudus, a native predatory mite found in Xinjiang, serves as a natural enemy to numerous small pests. The utilization of Tyrophagus putrescentiae as an alternative prey for the mass breeding of N. bicaudus is employed to fulfill the demands of enhanced breeding efficiency and cost-effectiveness. Following the introduction of mass breed N. bicaudus into the agricultural ecosystem, there was a switching in the prey of N. bicaudus from Ty. putrescentiae to Tetranychus turkestani. The objective of this study was to investigate the impact of prey switching at various stages on N. bicaudus. This study employed the age-stage, two-sex life table to assess the life parameters of N. bicaudus undergoing prey switching at different stages. The results showed that the survival rate of N. bicaudus was significantly decreased, the developmental period was significantly prolonged, the fecundity was improved during prey switching, and the intrinsic rate of increase of N. bicaudus was significantly decreased. The negative effects of prey switching in larva and deutonymph stages were greater than those in protonymph and adult stages. The stage and age of N. bicaudus undergoing prey switching were positively correlated with the male ratio, and negatively correlated with the total preoviposition period and the mean generation time. The comprehension of prey switching effects on N. bicaudus can enhance our understanding of the predator adaptation to environmental changes and contribute to the artificial rearing and application of natural enemy. Full article
(This article belongs to the Section Crop Protection, Diseases, Pests and Weeds)
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20 pages, 6712 KB  
Article
Taking the Deer by the Antlers: Deer in Material Culture in the Balkan Neolithic
by Selena Vitezović
Arts 2024, 13(2), 64; https://doi.org/10.3390/arts13020064 - 30 Mar 2024
Cited by 1 | Viewed by 4629
Abstract
Prehistoric communities had strong ties with the animal world that surrounded them—animals were prey, sources of food, and raw materials, but also threats and mysteries, and certain animals often had an important place in the symbolic realm. With the process of domestication and [...] Read more.
Prehistoric communities had strong ties with the animal world that surrounded them—animals were prey, sources of food, and raw materials, but also threats and mysteries, and certain animals often had an important place in the symbolic realm. With the process of domestication and the switch to animal husbandry as the main source of animal food, these relations changed considerably, and a certain dichotomy between “the domestic” and “the wild” may be noted in numerous past communities. When it comes to the Neolithic period in the Balkans, domestic animals had an important place in subsistence and economy, and it seems that cattle had a particularly prominent symbolic role. Wild species preserved some of their significance in both subsistence and symbolic realms, especially cervids (red deer, roe deer, and fallow deer). In this paper, the place of deer in the material culture of the Neolithic communities in the Balkans will be analysed: skeletal elements of deer were used for the production of diverse items, including non-utilitarian ones, or were part of ritual depositions, and deer representations are encountered in other materials, such as clay figurines. The symbolic meaning of deer cannot be reconstructed with certainty; however, it is probable that deer were tied with territoriality and the landscape. Full article
(This article belongs to the Special Issue Animals in Ancient Material Cultures (vol. 3))
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15 pages, 9673 KB  
Article
Pattern Formation in a Predator–Prey Model with Allee Effect and Hyperbolic Mortality on Multiplex Networks
by Lei Shi, Jiaying Zhou and Yong Ye
Mathematics 2023, 11(15), 3339; https://doi.org/10.3390/math11153339 - 30 Jul 2023
Cited by 9 | Viewed by 2266
Abstract
With the rapid development of network science, Turing patterns on complex networks have attracted extensive attention from researchers. In this paper, we focus on spatial patterns in multiplex ER (Erdös-Rényi) random networks, taking the predator–prey model with Allee effect and hyperbolic mortality as [...] Read more.
With the rapid development of network science, Turing patterns on complex networks have attracted extensive attention from researchers. In this paper, we focus on spatial patterns in multiplex ER (Erdös-Rényi) random networks, taking the predator–prey model with Allee effect and hyperbolic mortality as an example. In theory, the threshold condition for generating Turing patterns is given using the Turing instability theory of multiplex networks. Numerically, we design relevant experiments to explore the impact of network topology on Turing patterns. The factors considered include model parameters, diffusion rate, average degree of the network, and differences in the average degree of different layers. The results indicate that the importance of diffusion rate and network average degree for Turing patterns is affirmed on the single-layer network. For multiplex networks, the differentiation of average degrees in different layers controls the generation of Turing patterns, which are not affected by the diffusion rates of the two populations. More interestingly, we observe the switching of Turing patterns and spatiotemporal patterns. We believe that these findings contribute to a better understanding of self-organization on complex networks. Full article
(This article belongs to the Special Issue Complex Biological Systems and Mathematical Biology)
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17 pages, 1253 KB  
Article
Study on Dynamic Behavior of a Stochastic Predator–Prey System with Beddington–DeAngelis Functional Response and Regime Switching
by Quan Wang, Li Zu, Daqing Jiang and Donal O’Regan
Mathematics 2023, 11(12), 2735; https://doi.org/10.3390/math11122735 - 16 Jun 2023
Cited by 8 | Viewed by 1885
Abstract
In this paper, by introducing environmental white noise and telegraph noise, we proposed a stochastic predator–prey model with the Beddington–DeAngelis type functional response and investigated its dynamical behavior. Persistence and extinction are two core contents of population model research, so we analyzed these [...] Read more.
In this paper, by introducing environmental white noise and telegraph noise, we proposed a stochastic predator–prey model with the Beddington–DeAngelis type functional response and investigated its dynamical behavior. Persistence and extinction are two core contents of population model research, so we analyzed these two properties. The sufficient conditions of the strong persistence in the mean and extinction were established and the threshold between them was obtained. Moreover, we took stability into account and, by means of structuring a suitable Lyapunov function with regime switching, we proved that the stochastic system has a unique stationary distribution. Finally, numerical simulations were used to illustrate our theoretical results. Full article
(This article belongs to the Section E3: Mathematical Biology)
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14 pages, 1643 KB  
Article
Stability Switching in Lotka-Volterra and Ricker-Type Predator-Prey Systems with Arbitrary Step Size
by Shamika Kekulthotuwage Don, Kevin Burrage, Kate J. Helmstedt and Pamela M. Burrage
Axioms 2023, 12(4), 390; https://doi.org/10.3390/axioms12040390 - 17 Apr 2023
Cited by 3 | Viewed by 2741
Abstract
Dynamical properties of numerically approximated discrete systems may become inconsistent with those of the corresponding continuous-time system. We present a qualitative analysis of the dynamical properties of two-species Lotka-Volterra and Ricker-type predator-prey systems under discrete and continuous settings. By creating an arbitrary time [...] Read more.
Dynamical properties of numerically approximated discrete systems may become inconsistent with those of the corresponding continuous-time system. We present a qualitative analysis of the dynamical properties of two-species Lotka-Volterra and Ricker-type predator-prey systems under discrete and continuous settings. By creating an arbitrary time discretisation, we obtain stability conditions that preserve the characteristics of continuous-time models and their numerically approximated systems. Here, we show that even small changes to some of the model parameters may alter the system dynamics unless an appropriate time discretisation is chosen to return similar dynamical behaviour to what is observed in the corresponding continuous-time system. We also found similar dynamical properties of the Ricker-type predator-prey systems under certain conditions. Our results demonstrate the need for preliminary analysis to identify which dynamical properties of approximated discretised systems agree or disagree with the corresponding continuous-time systems. Full article
(This article belongs to the Special Issue Mathematical Modeling with Differential Equations)
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9 pages, 1478 KB  
Communication
Photuris lugubris Female Fireflies Hunt Males of the Synchronous Firefly Photinus palaciosi (Coleoptera: Lampyridae)
by Yara Maquitico, Aldair Vergara, Ilana Villanueva, Jaime Camacho and Carlos Cordero
Insects 2022, 13(10), 915; https://doi.org/10.3390/insects13100915 - 8 Oct 2022
Cited by 6 | Viewed by 4518
Abstract
Femmes fatales (Ff) are female fireflies that hunt and feed on the males of other firefly species that they attract by responding with glows or flashes to their bioluminescent signals. Here, we present field observations demonstrating that Photuris lugubris females are [...] Read more.
Femmes fatales (Ff) are female fireflies that hunt and feed on the males of other firefly species that they attract by responding with glows or flashes to their bioluminescent signals. Here, we present field observations demonstrating that Photuris lugubris females are Ff of male Photinus palaciosi, a synchronous firefly exploited as a tourist attraction in the mountains of central Mexico. We show that the hunting success of the Ff is low, as observed in previous studies, suggesting that the impact of predation on the prey population is low. We present experimental data showing sex-specific hunting behaviour, since only female P. lugubris fed on P. palaciosi. We also present experimental data showing that at least some female P. lugubris mate multiple times; we discuss the implications of this discovery for the switch between the mating and hunting modes of Ff. We discuss open questions, as well as the possible impact of Ff on tourism focused on synchronous fireflies. Full article
(This article belongs to the Section Insect Behavior and Pathology)
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20 pages, 8206 KB  
Article
Efficiently Detecting Non-Stationary Opponents: A Bayesian Policy Reuse Approach under Partial Observability
by Yu Wang, Ke Fu, Hao Chen, Quan Liu, Jian Huang and Zhongjie Zhang
Appl. Sci. 2022, 12(14), 6953; https://doi.org/10.3390/app12146953 - 8 Jul 2022
Cited by 2 | Viewed by 2453
Abstract
In multi-agent domains, dealing with non-stationary opponents that change behaviors (policies) consistently over time is still a challenging problem, where an agent usually requires the ability to detect the opponent’s policy accurately and adopt the optimal response policy accordingly. Previous works commonly assume [...] Read more.
In multi-agent domains, dealing with non-stationary opponents that change behaviors (policies) consistently over time is still a challenging problem, where an agent usually requires the ability to detect the opponent’s policy accurately and adopt the optimal response policy accordingly. Previous works commonly assume that the opponent’s observations and actions during online interactions are known, which can significantly limit their applications, especially in partially observable environments. This paper focuses on efficient policy detecting and reusing techniques against non-stationary opponents without their local information. We propose an algorithm called Bayesian policy reuse with LocAl oBservations (Bayes-Lab) by incorporating variational autoencoders (VAE) into the Bayesian policy reuse (BPR) framework. Following the centralized training with decentralized execution (CTDE) paradigm, we train VAE as an opponent model during the offline phase to extract the latent relationship between the agent’s local observations and the opponent’s local observations. During online execution, the trained opponent models are used to reconstruct the opponent’s local observations, which can be combined with episodic rewards to update the belief about the opponent’s policy. Finally, the agent reuses the best response policy based on the updated belief to improve online performance. We demonstrate that Bayes-Lab outperforms existing state-of-the-art methods in terms of detection accuracy, accumulative rewards, and episodic rewards in a predator–prey scenario. In this experimental environment, Bayes-Lab can achieve about 80% detection accuracy and the highest accumulative rewards, and its performance is less affected by the opponent policy switching interval. When the switching interval is less than 10, its detection accuracy is at least 10% higher than other algorithms. Full article
(This article belongs to the Section Computing and Artificial Intelligence)
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14 pages, 11756 KB  
Article
Turnover Rates and Diet–Tissue Discrimination Factors of Nitrogen and Carbon Stable Isotopes in Seahorse Hippocampus reidi Juveniles Following a Laboratory Diet Shift
by Jorge Hernández-Urcera, Mario Davi Dias Carneiro and Miquel Planas
Animals 2022, 12(10), 1232; https://doi.org/10.3390/ani12101232 - 10 May 2022
Cited by 4 | Viewed by 3020
Abstract
The initial development of seahorse juveniles is characterized by low digestion capabilities. Stable isotope analysis is an effective tool in studies of trophic food webs and animal feeding patterns. The present study provides new insights for the understanding of growth and food assimilation [...] Read more.
The initial development of seahorse juveniles is characterized by low digestion capabilities. Stable isotope analysis is an effective tool in studies of trophic food webs and animal feeding patterns. The present study provides new insights for the understanding of growth and food assimilation in early developing seahorses following a laboratory diet switch. The study was performed in the early life stages of the seahorse Hippocampus reidi by assessing the influence of diet shift on changes and turnovers in carbon (δ13C) and nitrogen (δ15N) stable isotope in juveniles. Newborn seahorses were fed for 60 days following two feeding schedules (A6 and A11) based initially on copepods Acartia tonsa and subsequently on Artemia nauplii (since days 6 and 11, respectively). After the prey shift, we determined δ13C and δ15N turnover rates as functions of change in either body mass (fitting model G) and days of development (fitting model D), contributions of metabolism and growth to those turnover rates, and diet–tissue discrimination factors. Survival, final dry weight, and final standard length for diet A11 were higher compared to diet A6. The shift from copepods to Artemia led to fast initial enrichments in δ13C and δ15N. Afterwards, the enrichment was gradually reduced until the isotopic equilibrium with the diet was reached. In most cases, both fitting models performed similarly. The isotopic analysis revealed that 100% of tissue turnover was attributed to growth in diet A11, whereas 19–25% was linked to metabolism in diet A6. Diet–tissue discrimination factors were estimated for the first time in seahorse juveniles, resulting in higher estimates for diet A11 (2.9 ± 0.7‰ for δ13C; 2.5 ± 0.2‰ for δ15N) than in diet A6 (1.8 ± 0.1‰ for δ13C; 1.9 ± 0.1‰ for δ15N). This study highlights the relevance of feeding on copepods and their effect on isotopic patterns and discrimination factors in seahorse juveniles after a dietary shift. Regarding the application of the results achieved in relation to the feeding schedules in the rearing of H. reidi, a long period of feeding on copepods during the first days of development is highly recommended. Full article
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19 pages, 4032 KB  
Article
Stability Switching Curves and Hopf Bifurcation of a Fractional Predator–Prey System with Two Nonidentical Delays
by Shuangfei Li, Yingxian Zhu, Yunxian Dai and Yiping Lin
Symmetry 2022, 14(4), 643; https://doi.org/10.3390/sym14040643 - 22 Mar 2022
Cited by 9 | Viewed by 2437
Abstract
In this paper, we propose and analyze a three-dimensional fractional predator–prey system with two nonidentical delays. By choosing two delays as the bifurcation parameter, we first calculate the stability switching curves in the delay plane. By judging the direction of the characteristic root [...] Read more.
In this paper, we propose and analyze a three-dimensional fractional predator–prey system with two nonidentical delays. By choosing two delays as the bifurcation parameter, we first calculate the stability switching curves in the delay plane. By judging the direction of the characteristic root across the imaginary axis in stability switching curves, we obtain that the stability of the system changes when two delays cross the stability switching curves, and then, the system appears to have bifurcating periodic solutions near the positive equilibrium, which implies that the trajectory of the system is the axial symmetry. Secondly, we obtain the conditions for the existence of Hopf bifurcation. Finally, we give one example to verify the correctness of the theoretical analysis. In particular, the geometric stability switch criteria are applied to the stability analysis of the fractional differential predator–prey system with two delays for the first time. Full article
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