Type Functional Response Research Articles

Complex dynamical properties and chaos control for a discrete modified Leslie-Gower prey-predator system with Holling II functional response

In this study, the semi-discretization technique is employed to establish a discrete representation of a modified Leslie-Gower prey-predator system that includes a Holling II type functional response. The dynamics of this model are then analyzed through the application of center manifold theory and bifurcation theory. We present comprehensive results for the local stability of the fixed points across the entire parameter space. Additionally, we provide sufficient conditions for the occurrence of flip bifurcation and Neimark-Sacker bifurcation. Besides, the system has experienced a flip bifurcation to chaos controlled using the method of chaos control, viz., state feedback method, pole placement technique, and hybrid control strategy. Furthermore, we provide specific conditions to ensure that bifurcation and chaos can be stabilized. Finally, numerical simulations are conducted to validate theoretical analysis and illustrate several new complex dynamical behaviors between two species.

Biomarker development from functional precision medicine datasets via explainable machine learning.

10061 Background: Genomics precision medicine, deployed via tumor panel sequencing, now assists in deploying targeted therapies to cancer patients. Numerous clinical trials have investigated the utility and benefit of genomics precision medicine in multiple cancer indications. Current large-scale studies report actionability rates from ~35% to ~60%, although clinical benefit rates have been shown to be closer to 10%. While this has positively impacted patients in need, the gap between actionability and benefit remains a clinical challenge attributed to multiple factors including the complex, multi-factorial relationship between molecular status and response to therapy. These differences go beyond simple disease states and may be reflective of multiple clinically relevant features including age, sex, and race/ethnicity. Methods: We implemented a functional precision medicine (FPM) program where patients with advanced pediatric cancers were prospectively profiled via high-throughput drug sensitivity testing (DST) of FDA-approved agents on patient-derived tumor cells as well as genomics testing. The objective was to investigate the clinical utility and benefit of FPM guidance in the treatment of pediatric cancer and elucidate the relationship between molecular status of patients’ diseases and treatment responses. We generated DST data (n = 21 patients) and genomic profiling data (n = 20 patients) on pediatric cancer patients in Miami, FL, as well as post-hoc whole exome and transcriptome sequencing data (n = 13 patients) and investigated three specific relationships. Results: We analyzed the relationship between racial/ethnic background and functional response to anti-cancer agents, determining potential differences in response to therapeutic classes. Next, we examined relationships between functional response and cancer type, identifying an unanticipated lack of clustering between disease indications in patients with advanced pediatric cancers. Finally, we applied an explainable machine learning (xML) framework to the functional genomic dataset to develop multi-omics biomarker hypotheses for the chemotherapy agent idarubicin, pinpointing a potential multi-cancer relationship between response to idarubicin and known disease mechanisms in acute myeloid leukemia (AML), the sole indication where idarubicin is approved. We further present additional proof-of-concept studies generating biomarker hypotheses via xML, demonstrating a framework for development of multi-omics biomarkers. Conclusions: We are now expanding our pan-pediatric cancer functional genomics dataset through an NIMHD-funded expansion cohort (NCT05857969, n = 65 patients) to further investigate multi-omics relationships between functional and molecular characteristics and understand the role of race/ethnicity in the complex relationship.

Impact of Spatial Variability in Zooplankton Grazing Rates on Carbon Export Flux

AbstractThe biological carbon pump is a key controller of how much carbon is stored within the global ocean. This pathway is influenced by food web interactions between zooplankton and their prey. In global biogeochemical models, Holling Type functional responses are frequently used to represent grazing interactions. How these responses are parameterized greatly influences biomass and subsequent carbon export estimates. The half‐saturation constant, or k value, is central to the Holling functional response. Empirical studies show k can vary over three orders of magnitude, however, this variation is poorly represented in global models. This study derives zooplankton grazing dynamics from remote sensing products of phytoplankton biomass, resulting in global distribution maps of the grazing parameter k. The impact of these spatially varying k values on model skill and carbon export flux estimates is then considered. This study finds large spatial variation in k values across the global ocean, with distinct distributions for micro‐ and mesozooplankton. High half‐saturation constants, which drive slower grazing, are generally associated with areas of high productivity. Grazing rate parameterization is found to be critical in reproducing satellite‐derived distributions of small phytoplankton biomass, highlighting the importance of top‐down drivers for this size class. Spatially varying grazing dynamics decrease mean total carbon export by >17% compared to globally homogeneous dynamics, with increases in fecal pellet export and decreases in export from algal aggregates. This study highlights the importance of grazing dynamics to both community structure and carbon export, with implications for modeling marine carbon sequestration under future climate scenarios.

A Novel Interaction of Nesidiocoris tenuis (Hemiptera: Miridae) as a Biological Control Agent of Bactericera cockerelli (Hemiptera: Triozidae) in Potato.

Nesidiocoris tenuis (Hemiptera: Miridae) is a generalist predator commonly used to control the whitefly Bemisia tabaci in Europe. This mirid has been found and established in South Texas, where it was initially observed feeding on nymphs of the psyllid Bactericera cockerelli (Hemiptera: Triozidae) in open tomato fields. B. cockerelli is the vector of the fastidious bacterium "Candidatus Liberibacter solanacearum" that causes diseases in several solanaceous crops, including zebra chip (ZC) disease in potatoes. There is a need to better understand how this predator impacts the control of important crop pests, such as potato psyllids. We assessed the interactions between N. tenuis and B. cockerelli in three different environmental settings. First, we estimated the numeric response of N. tenuis preying on B. cockerelli under laboratory and greenhouse conditions. Second, we evaluated the predator-prey interaction under controlled field cage conditions. Then, we exposed N. tenuis under controlled field release conditions to the natural occurrence of B. cockerelli. Finally, we assessed the compatibility between the use of N. tenuis as a biological control agent in a field study and its impact on ZC disease incidence, severity in potato tubers, and potato yield. Laboratory and greenhouse experiments resulted in diverse types of functional model responses, including exponential and linear mathematical models. Our findings revealed a significant predation effect exerted by N. tenuis, resulting in a reduction of more than fourfold in the number of B. cockerelli nymphs per cage. Specifically, the nymphal population decreased from 21 ± 3.2 in the absence of N. tenuis to 5 ± 1.6 when N. tenuis was present. Furthermore, the combination of N. tenuis with a reduced insecticide program increased potato yields, but only reduced ZC tuber incidence in one of two potato cultivars evaluated, and in one season. Findings from these studies indicate that N. tenuis could be effective as a biological control agent for B. cockerelli in potato production in South Texas. This is the first report of N. tenuis preying on immature stages of any psyllid species.

Analysis of Prey-Predator Scheme in Conjunction with Help and Gestation Delay

This paper presents a three-dimensional continuous time dynamical system of three species, two of which are competing preys and one is a predator. We also assume that during predation, the members of both teams of preys help each other and the rate of predation of both teams is different. The interaction between prey and predator is assumed to be governed by a Holling type II functional response and discrete type gestation delay of the predator for consumption of the prey. In this work, we establish the local asymptotic stability of various equilibrium points to understand the dynamics of the model system. Different conditions for the coexistence of equilibrium solutions are discussed. Persistence, permanence of the system, and global stability of the positive interior equilibrium solution are discussed by constructing suitable Lyapunov functions when the gestation delay is zero, and there is no periodic orbit within the interior of the first quadrant of state space around the interior equilibrium. As we introduced time delay due to the gestation of the predator, we also discuss the stability of the delayed model. It is observed that the existence of stability switching occurs around the interior equilibrium point as the gestation delay increases through a certain critical threshold. Here, a phenomenon of Hopf bifurcation occurs, and a stable limit cycle corresponding to the periodic solution of the system is also observed. This study reveals that the delay is taken as a bifurcation parameter and also plays a significant role for the stability of the proposed model. Computer simulations of numerical examples are given to explain our proposed model. We have also addressed critically the biological implications of our analytical findings with proper numerical examples.

The link between functional response and longevity of Trichogramma evanescens strains indigenous to Türkiye: A comparative assessment of parameters

AbstractA previous comprehensive survey in the Mediterranean and Southeastern regions of Türkiye investigating the natural egg parasitism of lepidopteran maize pests, Sesamia spp, (Lepidoptera: Noctuidae) Ostrinia nubilalis Hbn. and Chilo partellus (Swinhoe; Lepidoptera: Crambidae) by Trichogramma evanescens Westwood (Hymenoptera: Trichogrammatidae) yielded successful establishment of laboratory cultures of six strains molecularly clustering into two main groups. In this study, the functional response and adult longevity of the strains reared and tested on a factitious host, Ephestia kuehniella Zeller (Lepidoptera: Pyralidae) were investigated to provide insights into their potential as candidate biocontrol agents under constant laboratory conditions. The functional response modelling process consisted of two main sequential steps: model selection using polynomial logistic regression and parameter estimation using an iterative maximum likelihood estimation method. The functional response of two strains showed negative linear parameters (type II): HAP068M and HAP268S. Although their attack rate did not differ, the handling time of HAP268S was longer than that of HAP068M. In contrast, four strains had positive linear and negative quadratic parameters (type III) in their functional response: HAP044S, HAP070S, HAP210S, and HAP258M. The strains exhibiting type III functional response did not differ in their handling time, while HAP044S had a higher attack coefficient than HAP070S, HAP210S, and HAP258M. The longevity of both female and male adults significantly differed between strains. More importantly, the females belonging to strains exhibiting type II functional response presented a shorter longevity, compared to those with type III functional response. Males also showed a similar trend in their longevity. This paper discusses the differences in functional response types and estimated parameters of the strains in relation to their relevance for biological control programs and reveals a link between their functional response and longevity as potential reciprocal predictors.

Spatiotemporal patterns in a diffusive resource–consumer model with distributed memory and maturation delay

In this paper, we propose a diffusive consumer–resource model in which the consumer is involved with spatiotemporal memory and the resource has maturation delay. Firstly, for the case without maturation delay, the influence of the spatiotemporal distributed memory on the stability of the positive steady state is investigated. It has been shown that memory delay can induce Turing bifurcation for the negative memory-based diffusion coefficient and induce Hopf bifurcation for the positive memory-based diffusion coefficient. Then the joint effect of the memory delay and the maturation delay on the stability of the positive steady state is investigated and it has been shown that the joint effect of the memory delay and the maturation delay can induce more complicated spatiotemporal dynamics via Turing–Hopf bifurcation and double Hopf bifurcation. Finally, we apply our theoretical analysis results to a consumer–resource model with Holling-II type functional response to illustrate the existence of the different spatiotemporal patterns.

Functional response of Franklinothrips vespiformis (Thysanoptera: Aeolothripidae) to eggs and nymphs of Bemisia tabaci (Hemiptera: Aleyrodidae).

The Middle East Asia Minor 1 biotype of Bemisia tabaci Gennadius (Hemiptera: Aleyrodidae) is a greenhouse and field crop pest of global significance. The objective of this study was to assess the potential of the generalist predatory thrips, Franklinothrips vespiformis Crawford (Thysanoptera: Aeolothripidae), as a biological control agent for B. tabaci. This was achieved by determining the functional responses of F. vespiformis larvae and adults to the egg and nymphal stages of B. tabaci under laboratory conditions. Analyses consisted of 10 replicates of each predator and prey stage combination on bean leaf discs for a 24-h period. Following logistic regression analyses to determine the functional response type exhibited, response parameters were estimated with nonlinear least squares regression using Roger's equation. Results showed that F. vespiformis larvae and adults exhibited a Type II functional response when feeding on immature B. tabaci. The handling times (Th) of F. vespiformis larvae and adults were magnitudes higher for B. tabaci nymphs than they were for eggs, which were in part driven by the higher attack rates (a) observed on eggs. The maximum attack rate (T/Th) for B. tabaci eggs and nymphs exhibited by first-stage larvae, second-stage larvae, and adult F. vespiformis increased with increasing predator age. Results from this study suggest that F. vespiformis larvae and particularly adults are promising biological control agents for B. tabaci and are efficient predators at both low and high prey densities.

Functional and numerical response and mutual interference of Goniozus legneri (Hymenoptera: Bethylidae) on Cydia pomonella (Lepidoptera: Tortricidae): Its implications for biological control

AbstractThe functional and numerical response and the potential for mutual interference are key components in the selection of parasitoids for biological control. In this study, functional and numerical responses of Goniozus legneri to different densities of fifth instar Cydia pomonella larvae and mutual interference of this parasitoid were studied under laboratory conditions. Logistic regression was used to find the type of functional response and the result was type II. The attack rate, handling time, the parasitoid searching efficiency and the maximum host mortality rate were estimated by fitting the Holling model to the data. The numerical response of the parasitoid did not vary based on the availability of codling moth larvae. The negative value of the interference coefficient (−0.228) in the mutual interference analysis showed an inverse relationship between parasitoid density and per capita searching efficiency. This suggests that when the density of G. legneri and C. pomonella larvae is equivalent, the parasitoid proves to be more effective in pest control. The findings of this study contribute to increasing the knowledge of G. legneri and its potential as a biocontrol agent.

Modelling effects and control of soil contaminants on the dynamics of plant–herbivore species system

In this paper, we have proposed and analysed a mathematical model to study the effects of impulsive input of contaminants in soil on the dynamics of interacting species system consisting of contaminants, soil-nutrients, plant biomass and herbivore population in order to investigate the criteria for the survival or extinction of plant biomass and herbivore population. The uptake function for herbivore population considered in the model of the paper shows saturation effect and this type of uptake function behave linearly with respect to plant biomass for low density. Also, the saturation for large plant biomass is a reflection of the limited herbivore capability or perseverance when the plant biomass is abundant. Therefore, the uptake function considered in this paper is more natural to lotka volterra and holling type functional responses. We have shown that the plant–herbivore extinction periodic solution exists and also the plant–herbivore extinction periodic solution is locally and globally stable if the impulsive depletion rate of nutrients due to contaminants is more than some critical value. Further, it is concluded that if the impulsive input period for contaminants is increased and impulsive depletion rate of nutrients due to contaminants is decreased then both the plant and herbivore population will survive otherwise they will tend to extinction.

Predatory preferences of a non-indigenous crab do not depend on prey invasion scenarios

AbstractPredatory non-indigenous species (NIS) have profound impacts on global ecosystems, potentially leading to native prey extinction and reshaping community dynamics. Among mechanisms potentially mediating predator impacts and prey invasion success are predator preferences between native vs. non-indigenous prey, a topic still underexplored. Using functional response and prey preference experiments, this study focused on the predation by the non-indigenous Japanese brush-clawed shore crab, Hemigrapsus takanoi, between the native gammarid Gammarus duebeni and the analogous non-indigenous Gammarus tigrinus. Although H. takanoi showed subtle differences in its functional response type between the two prey species, its preferences across their environmental frequencies were not strongly influenced by the prey invasion scenario. The findings highlight the need for a comprehensive understanding of interactions in ecosystems with multiple NIS, offering fresh insights into complex feeding interactions within marine environments.

Microplastics influence the functional responses of a tropical estuarine calanoid Pseudodiaptomus annandalei

Being chemically inert and morphologically similar (<5 mm in size) to the natural prey of copepods, microplastics (MPs) affect them through entanglement, ingestion, and interference with their natural prey selection. The effects of external factors, such as MP, can be observed in the form of alterations in the functional and numerical responses of copepods. Functional response is explained as the relationship between the intake rate of a consumer and the amount of food available in a particular ecotope. Considered three types of functional response: (i) with increasing food density, when intake rate increases linearly until asymptote, called Type-I functional response; (ii) when the proportion of prey ingested by the consumer decreases monotonically with prey density, considered as a Type-II functional response; and (iii) when ingestion rate and food density show a sigmoid relationship, is considered as Type-III functional response. In the present study, we attempted to elucidate the effects of MP on the functional responses of brackish water, demersal, calanoid copepod, Pseudodiaptomus annandalei, feeding on the rotifer Brachionus rotundiformis, and the ciliate Frontonia microstoma. The ability of P. annandalei to survive environmental fluctuations and its nutritional value make it an ecologically important organism in estuarine ecosystems. The experiment for estimation of functional response included four setups with adult and copepodite stages of P. annandalei, each with six replicates at six different prey densities, in the presence and absence of MP particles. Without MPs, P. annandalei showed a typical Type-II functional response, where the proportion of prey consumed significantly declined with increasing prey density. In the MP-applied medium, the proportion of prey consumed did not exhibit a significant relationship with the initial prey density. The number of ciliates and rotifers ingested by copepodites and adults was significantly lower in MP-contaminated medium than in prey either monospecific or in combination with microalgae. Because of the comparable size of MP to the prey species and unspecialized feeding of P. annandalei in natural waters, we hypothesized reduced predation rates as a result of pseudo-satiation resulting from MP ingestion leading to malnutrition and MP storage in copepod biomass.

Bifurcation analysis of predator–prey model with Cosner type functional response and combined harvesting

In this paper, we consider a predator–prey model with Cosner type functional response and combined harvesting. First, we explore the existence and stability of the equilibria. Then using the center manifold theorem and normal form theory, we investigate codimension one and codimension two bifurcations of the model. The analysis shows that the system has a variety of bifurcation phenomena including transcritical bifurcation, saddle‐node bifurcation, Hopf bifurcation, Bogdanov–Takens bifurcation and homoclinic bifurcation. Our findings indicate that the dynamics with harvesting are significantly richer than the system without harvesting. Finally, numerical simulations are provided to support the analytical results.

Dynamics of a generalist predator–prey system with harvesting and hunting cooperation in deterministic/stochastic environment

In this investigation, we explore a predator–prey system characterized by generalist predators exhibiting cooperative behavior during hunting, subject to nonlinear harvesting rate. Employing a Beverton–Holt type functional response to capture the impact of additional food sources on predator growth, our numerical findings affirm the destabilizing influence of hunting cooperation, excessive predation, and supplementary food sources. Conversely, the system demonstrates stabilization in response to increased prey species growth. We unveil the occurrence of both forward and backward bifurcations in the system due to the predator growth attributed to additional food sources, contingent on the degree of hunting cooperation. To broaden the scope, we extend our proposed model to its stochastic counterpart, introducing environmental white noises. Our numerical results anticipate that higher intensities of white noises lead to fluctuations of greater amplitude, while smaller intensities exhibit a more modest impact. Additionally, we elucidate the dynamics of prey and predator populations through histogram plots. The theoretical and numerical insights derived from this study provide a deeper understanding of the intricate dynamics within predator–prey systems of ecological communities, emphasizing the significance of additional food sources for cooperative predators subject to harvesting in both constant and fluctuating environments.

Traveling waves of modified Leslie–Gower predator–prey systems

This paper focuses on the spreading phenomena within modified Leslie–Gower reaction–diffusion predator–prey systems. Our main objective is to investigate the existence of two distinct types of traveling waves. Specifically, with the aid of the upper and lower solution methods, we establish the existence of traveling waves connecting the prey-present state and the coexistence state or the prey-present state and the prey-free state by constructing different and appropriate Lyapunov functions. Moreover, for traveling wave connecting the prey-present state and the prey-free state, more information about the monotonicity of the wave profile can be obtained by analyzing its asymptotic behavior at negative infinity. Finally, our results are applied to modified Leslie–Gower system with Holling-II type functional response or Lotka–Volterra type functional response, and a novel Lyapunov function is constructed for the latter, which further enhances our results. Meanwhile, some numerical simulations are carried out to support our results.

Статическая работоспособность и особенности функционального реагирования на мышечную нагрузку юношей разных соматотипов

The aim of the research is to study the strength characteristics and type of functional response to muscle load of young men of different somatotypes, depending on physical fitness. The study involved 128 practically healthy young men aged 18 to 23 years. The group of subjects included qualified athletes, swimmers, as well as healthy young men engaged in physical culture within the framework of the university program. Somatotype was assessed in all subjects using Hit-Carter method, arm strength and static endurance – according to Rosenblat method, and the type of functional response with Kaznacheev method. It was found that young men of the endomorphic somatotype were characterized by a strong physique, a larger amount of skin-fat folds, low values of the muscle index, less endurance of the hands and did not demonstrate a distinct preference for the type of functional response. The young men of the ectomorphic somatotype had a less robust physique, a smaller thickness of the skin-fat folds, greater endurance of the hands and gravitated to the stayer type of functional response of the neuromuscular apparatus. The young men of the mesomorphic type significantly differed from representatives of other somatotypes by greater arm strength, sprinting type of functional response and, according to other morphofunctional indicators, occupied an intermediate position between endo- and ectomorphs. The analysis revealed functional connections between the components of meso- and ectomorphy, maximum static muscular endurance and types of functional response. The revealed significant differences and interrelations between the morphofunctional parameters under consideration and the types of functional response indicated the phenotypic features of individual development characteristic for each somatotype group. The obtained data should be taken into account when choosing the specifics of physical culture and sports activities.

Статическая работоспособность и особенности функционального реагирования на мышечную нагрузку юношей разных соматотипов

The aim of the research is to study the strength characteristics and type of functional response to muscle load of young men of different somatotypes, depending on physical fitness. The study involved 128 practically healthy young men aged 18 to 23 years. The group of subjects included qualified athletes, swimmers, as well as healthy young men engaged in physical culture within the framework of the university program. Somatotype was assessed in all subjects using Hit-Carter method, arm strength and static endurance – according to Rosenblat method, and the type of functional response with Kaznacheev method. It was found that young men of the endomorphic somatotype were characterized by a strong physique, a larger amount of skin-fat folds, low values of the muscle index, less endurance of the hands and did not demonstrate a distinct preference for the type of functional response. The young men of the ectomorphic somatotype had a less robust physique, a smaller thickness of the skin-fat folds, greater endurance of the hands and gravitated to the stayer type of functional response of the neuromuscular apparatus. The young men of the mesomorphic type significantly differed from representatives of other somatotypes by greater arm strength, sprinting type of functional response and, according to other morphofunctional indicators, occupied an intermediate position between endo- and ectomorphs. The analysis revealed functional connections between the components of meso- and ectomorphy, maximum static muscular endurance and types of functional response. The revealed significant differences and interrelations between the morphofunctional parameters under consideration and the types of functional response indicated the phenotypic features of individual development characteristic for each somatotype group. The obtained data should be taken into account when choosing the specifics of physical culture and sports activities.

Stability and bifurcation in a predator-prey system with effect of fear and additional food

<abstract><p>In the present study, we propose and analyze a three-dimensional prey-predator model. The prey grows logistically in the absence of the predator and their relationship follows the Crowley-Martin type functional response. In this paper, we examine the impact of supply of the additional food to the predators and the influence of fear in the prey population. Since the predator depends partially on the provided other resources, we incorporate a novel parameter, the degree of dependence, which basically demonstrates how dependent the predator is on the prey population. We investigate the steady-state solutions, and their local and global behavior, which contributes to understanding the long-term dynamics of the interaction. We have shown that the degree of dependence and the cost of fear both can cause periodic orbits to appear in the system via a Hopf-bifurcation. Our findings show that with the newly introduced parameter, we can control the oscillations from the system, which helps to balance the ecosystem. The direction and stability have also been investigated using the center manifold theorem and normal form theory. Last, we perform an extensive numerical simulation to validate our theoretical findings. Our main goal of this work is to maintain the ecological balance in the presence of fear effect and additional food for predators.</p></abstract>

The dynamics of a delayed predator-prey model with square root functional response and stage structure

<abstract> <p>In recent years, one of the most prevalent matters in population ecology has been the study of predator-prey relationships. In this context, this paper investigated the dynamic behavior of a delayed predator-prey model considering square root type functional response and stage structure for predators. First, we obtained positivity and boundedness of the solutions and existence of equilibrium points. Second, by applying the stability theory of delay differential equations and the Hopf bifurcation theorem, we discussed the system's local stability and the existence of a Hopf bifurcation at the positive equilibrium point. Moreover, the properties of the Hopf bifurcation were deduced by using the central manifold theorem and normal form method. Analytical results showed that when the time delay was less than the critical value, the two populations will coexist, otherwise the ecological balance will be disrupted. Finally, some numerical simulations were also included to verify the theoretical results.</p> </abstract>

Qualitative analysis and traveling wave solutions of a predator-prey model with time delay and stage structure

<abstract><p>In this paper, we considered a delayed predator-prey model with stage structure and Beddington-DeAngelis type functional response. First, we analyzed the stability of the constant equilibrium points of the model by the linear stability method. Furthermore, we considered the existence of traveling wave solutions connecting the zero equilibrium point and the unique positive equilibrium point. Second, we transformed the existence of traveling wave solutions into the existence of fixed points of an operator by constructing suitable upper and lower solutions, and combined with the Schauder fixed point theorem, we gave the existence of fixed points and obtained the existence of traveling wave solutions of the model.</p></abstract>