Exploring nonlinear functional responses of zooplankton grazers in dilution experiments via optimization techniques

We study the permanence of periodic predator-prey system with general nonlinear functional responses and stage structure for both predator and prey and obtain that the predator and the prey species are permanent.

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Stabilizing effect of intra-specific competition on prey-predator dynamics with intraguild predation

Mathematical Modelling of Natural Phenomena ◽

10.1051/mmnp/2018033 ◽

2018 ◽

Vol 13 (3) ◽

pp. 29 ◽

Cited By ~ 3

Author(s):

Toshiyuki Namba ◽

Yasuhiro Takeuchi ◽

Malay Banerjee

Keyword(s):

Intraguild Predation ◽

Complex Dynamics ◽

Self Regulation ◽

Functional Responses ◽

Predator Species ◽

Nonlinear Functional ◽

High Productivity ◽

Stable Coexistence ◽

Stability And Bifurcation

Multi-species population models with various types of interactions are important to understand the stable coexistence of prey and predator species and the role of various factors leading to complex dynamics and extinction of one or more species. Models of two predators sharing one prey population are analyzed by some researchers and the role of nonlinear functional responses and interaction strengths are reported to be responsible for the stable coexistence of three species. However, one-prey-two-predator models with intraguild predation have received relatively less attention from researchers. Recent literature on this topic mainly focused on the study of local and global stability properties of possible equilibria and appearance of various types of bifurcations. Intra-specific competition among predator species is an important factor for coexistence of more than one predator species competing for one shared prey. Hence it is quite essential to understand the role of intra-specific competition on the stability and bifurcation behavior. In this work we wish to demonstrate the stabilizing role of intra-specific competition among intermediate and top predators when the growth rate of prey species is adequate to support both the predator species. With the help of stability and bifurcation analysis we show the stabilizing role of intra-specific competition among predators. Moreover, strong self-regulation in intraguild predator prevents extinction of intraguild prey at high productivity and resolve the contradiction between empirical and previous theoretical results on the fate of intraguild prey at high productivity. To establish our claim we present, apart from analytical results, extensive numerical simulation results and couple of bifurcation diagrams.

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The Effects of Enrichment of Three-Species Food Chains with Nonlinear Functional Responses

Ecology ◽

10.2307/1939435 ◽

1994 ◽

Vol 75 (4) ◽

pp. 1118-1130 ◽

Cited By ~ 102

Author(s):

Peter A. Abrams ◽

James D. Roth

Keyword(s):

Food Chains ◽

Functional Responses ◽

Nonlinear Functional

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Sparse Radiographic Tomography and System Identification Imaging from Single View, Multiple Time Sample Density Plots

Computational Methods in Applied Mathematics ◽

10.2478/cmam-2006-0022 ◽

2006 ◽

Vol 6 (4) ◽

pp. 354-366

Author(s):

T.J. Asaki ◽

E.M. Bollt ◽

K.R. Vixie

Keyword(s):

Inverse Problem ◽

System Identification ◽

Simple Technique ◽

Search Algorithm ◽

Optimization Techniques ◽

Multiple Time ◽

Nonlinear Functional ◽

Numerical Examples ◽

Single View ◽

Sample Density

Abstract Tomography is a classic inverse problem in which multiple density projections of an object are processed to infer some approximation of the original. We consider the highly sparse inverse problem of single angle projection, but seek to reduce the ambiguity through multiple time observations in a dynamic system of known or partially known dynamics. In this work we solve the planar problem by optimization techniques based on a gradient-free multi-directional search algorithm to minimize our nonlinear functional. We demonstrate convincingly successful numerical examples to support our relatively simple technique.

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Nonlinear functional models for functional responses in reproducing kernel hilbert spaces

Canadian Journal of Statistics ◽

10.1002/cjs.5550350410 ◽

2007 ◽

Vol 35 (4) ◽

pp. 597-606 ◽

Cited By ~ 28

Author(s):

Heng Lian

Keyword(s):

Hilbert Spaces ◽

Reproducing Kernel ◽

Reproducing Kernel Hilbert Spaces ◽

Functional Responses ◽

Nonlinear Functional ◽

Functional Models ◽

Kernel Hilbert Spaces

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Analysis and simulation on dynamics of a partial differential system with nonlinear functional responses

Nonlinear Analysis Modelling and Control ◽

10.15388/namc.2021.26.22356 ◽

2021 ◽

Vol 26 (2) ◽

pp. 293-314

Author(s):

Yunfeng Jia

Keyword(s):

Positive Solutions ◽

Computational Analysis ◽

Large Time ◽

Food Resource ◽

Reaction Diffusion ◽

Large Time Behavior ◽

Time Behavior ◽

Functional Responses ◽

Nonlinear Functional ◽

Partial Differential System

We introduce a reaction–diffusion system with modified nonlinear functional responses. We first discuss the large-time behavior of positive solutions for the system. And then, for the corresponding steady-state system, we are concerned with the priori estimate, the existence of the nonconstant positive solutions as well as the bifurcations emitting from the positive constant equilibrium solution. Finally, we present some numerical examples to test the theoretical and computational analysis results. Meanwhile, we depict the trajectory graphs and spatiotemporal patterns to simulate the dynamics for the system. The numerical computations and simulated graphs imply that the available food resource for consumer is very likely not single.

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Existence and construction of large stable food webs

10.1101/097907 ◽

2017 ◽

Author(s):

Jan O. Haerter ◽

Namiko Mitarai ◽

Kim Sneppen

Keyword(s):

Food Webs ◽

Weak Interactions ◽

Apparent Competition ◽

Species Interaction ◽

Volterra Equations ◽

Interaction Patterns ◽

Functional Responses ◽

Nonlinear Functional ◽

Starting Point ◽

Simple Product

AbstractEcological diversity is ubiquitous despite the restrictions imposed by competitive exclusion and apparent competition. To explain the observed richness of species in a given habitat, food web theory has explored nonlinear functional responses, self-interaction or spatial structure and dispersal — model ingredients that have proven to promote stability and diversity. We here instead return to classical Lotka-Volterra equations, where species-species interaction is characterized by a simple product and spatial restrictions are ignored. We quantify how this idealization imposes constraints on coexistence and diversity for many species. To this end, we introduce the concept of free and controlled species and use this to demonstrate how stable food webs can be constructed by sequential addition of species. When we augment the resulting network by additional weak interactions we are able to show that it is possible to construct large food webs of arbitrary connectivity. Our model thus serves as a formal starting point for the study of sustainable interaction patterns between species.

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Nonlinear functional responses and ecological pleiotropy alter the strength of disruptive selection in consumers

10.1101/283911 ◽

2018 ◽

Author(s):

Kyle E. Coblentz

Keyword(s):

Functional Response ◽

Intraspecific Competition ◽

Ecological Effects ◽

Disruptive Selection ◽

Feeding Rates ◽

Functional Responses ◽

Resource Model ◽

Ecological Opportunity ◽

Nonlinear Functional ◽

Consumer Dependence

AbstractMuch of the theory on disruptive selection has focused on selection in generalist consumers caused by ecological opportunity through the availability of alternative resources and intraspecific competition for those resources. This theory, however, makes several ecologically unrealistic assumptions. First, this theory assumes that consumers have a linear, resource-dependent functional response, ignoring well-documented effects of resource handling times and consumer dependence. Second, this theory assumes that the trait under selection only influences the percapita attack rates of the consumer, ignoring other effects of the trait that may influence feeding rates and hence fitness. Here, I develop a one consumer-two resource model to investigate how nonlinear functional responses and ecological pleiotropy (traits that have multiple simultaneous ecological effects) influence the strength of disruptive selection. I find that handling times and interference among consumers are capable of altering disruptive selection by changing feeding rates differentially across consumer phenotypes. In particular, handling times cause a decrease in the strength of disruptive selection while the effects of interference depend on the mechanism through which interference occurs. The effects of handling times and interference, however, are dependent on whether and how ecological pleiotropy causes correlations between handling times or interference rates and attack rates. Overall, my results suggest that features defining the functional responses of consumers and the relationships among those features determine the likelihood and strength of disruptive selection. In particular, disruptive selection should be strongest in generalist populations composed of individual diet specialists who experience lower handling times and interference rates on the resources for which their attack rates are highest.

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