Interspecific Interactions I: Predation and Parasitism

2020 ◽  
pp. 47-66
Author(s):  
Michael J. Fogarty ◽  
Jeremy S. Collie
Keyword(s):  
Aquatic Ecosystems ◽  
Multiple Equilibria ◽  
Interspecific Interactions ◽  
Disease Outbreaks ◽  
Predator Population ◽  
Predator Prey ◽  
Predation Effects ◽  
Human Predation ◽  
Predator Prey Models ◽  
Aquaculture Facilities

Predation and parasitism are dominant forms of interspecific interactions in aquatic ecosystems. Predation effects have been more commonly quantified in aquatic ecosystems than disease. Diet studies documenting predation are substantially more common that routine monitoring for disease in aquaculture systems. The simplest predator–prey models predict lagged cycles of prey and their predators. Density-dependent regulation of the prey or predator population is required for stable coexistence of predator and prey populations. Predator–prey models are extended with the incorporation of non-linear functional responses, which can result in multiple equilibria. The behavior and dynamics of natural predators hold important insights in our consideration of human predation on aquatic resource species. Disease outbreaks have wrought tremendous impacts on a very broad spectrum of aquatic species. For economically important species, these impacts include significant economic costs to fishing communities and aquaculture facilities.

scholarly journals Applying predator-prey theory to modelling immune-mediated, within-host interspecific parasite interactions

Parasitology ◽  
2010 ◽  
Vol 137 (6) ◽  
pp. 1027-1038 ◽  
Author(s):  
ANDY FENTON ◽  
SARAH E. PERKINS
Keyword(s):  
Functional Response ◽  
Interspecific Interactions ◽  
Parasite Load ◽  
Multiple Infections ◽  
Functional Responses ◽  
Predator Prey ◽  
Immune Activity ◽  
Parasite Communities ◽  
Immune Mediated ◽  
Predator Prey Models

SUMMARYPredator-prey models are often applied to the interactions between host immunity and parasite growth. A key component of these models is the immune system's functional response, the relationship between immune activity and parasite load. Typically, models assume a simple, linear functional response. However, based on the mechanistic interactions between parasites and immunity we argue that alternative forms are more likely, resulting in very different predictions, ranging from parasite exclusion to chronic infection. By extending this framework to consider multiple infections we show that combinations of parasites eliciting different functional responses greatly affect community stability. Indeed, some parasites may stabilize other species that would be unstable if infecting alone. Therefore hosts' immune systems may have adapted to tolerate certain parasites, rather than clear them and risk erratic parasite dynamics. We urge for more detailed empirical information relating immune activity to parasite load to enable better predictions of the dynamic consequences of immune-mediated interspecific interactions within parasite communities.

scholarly journals Controller design techniques for the Lotka-Volterra nonlinear system

2005 ◽  
Vol 16 (2) ◽  
pp. 124-135 ◽  
Author(s):  
Magno Enrique Mendoza Meza ◽  
Amit Bhaya ◽  
Eugenius Kaszkurewicz
Keyword(s):  
Controller Design ◽  
Nonlinear Dynamical System ◽  
Volterra Model ◽  
Predator Population ◽  
Ecological Context ◽  
Mathematical Ecology ◽  
Nonlinear Dynamical ◽  
Predator Prey ◽  
Predator Prey Models ◽  
Design Techniques

A large class of predator-prey models can be written as a nonlinear dynamical system in one or two variables (species). In many contexts, it is necessary to introduce a control into these dynamics. In this paper we focus on models of two species, and assume, as is common in mathematical ecology, that the control corresponds to a proportional removal of the predator population. Six controller design techniques are applied to the Lotka-Volterra model, which is thus used as a benchmark to evaluate and compare these techniques in an ecological context.

scholarly journals Qualitative Analysis of a Resource Management Model and Its Application to the Past and Future of Endangered Whale Populations

2021 ◽  
Vol 14 (1) ◽  
pp. 1-18
Author(s):  
Ledder Ledder
Keyword(s):  
Rapid Decline ◽  
Predator Population ◽  
Population Declines ◽  
Phase Line ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Intermediate Consumption ◽  
Stable Equilibria ◽  
Predator Prey Models ◽  
Type 3

Observed whale dynamics show drastic historical population declines, some of which have not been reversed in spite of restrictions on harvesting. This phenomenon is not explained by traditional predator prey models, but we can do better by using models that incorporate more sophisticated assumptions about consumer-resource interaction. To that end, we derive the Holling type 3 consumption rate model and use it in a one-variable differential equation obtained by treating the predator population in a predator-prey model as a parameter rather than a dynamic variable. The resulting model produces dynamics in which low and high consumption levels lead to single high and low-level stable resource equilibria, respectively, while intermediate consumption levels result in both high and low stable equilibria. The phase line analysis is made more transparent by applying a particular structure to the function that gives the derivative in terms of the state. By positing a consumption level that starts low, gradually increases through technological change and human population growth, and decreases as a result of public policy, we are able to tell a story that explains the unexpectedly rapid decline of some resources, such as whales, followed by limited recovery in response to conservation. The analysis also offers guidelines for how to establish sustainable harvesting for restored populations. We include a bifurcation analysis and suggestions for how to teach the material with three different levels of focus on the modeling aspect of the study.

scholarly journals Bifurcation analysis of the predator–prey model with the Allee effect in the predator

2021 ◽  
Vol 84 (1-2) ◽  
Author(s):  
Deeptajyoti Sen ◽  
Saktipada Ghorai ◽  
Malay Banerjee ◽  
Andrew Morozov
Keyword(s):  
Allee Effect ◽  
Mathematical Formulation ◽  
Global Bifurcation ◽  
Predator Population ◽  
Stable Limit ◽  
Bifurcation Structure ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Predator Prey Models

AbstractThe use of predator–prey models in theoretical ecology has a long history, and the model equations have largely evolved since the original Lotka–Volterra system towards more realistic descriptions of the processes of predation, reproduction and mortality. One important aspect is the recognition of the fact that the growth of a population can be subject to an Allee effect, where the per capita growth rate increases with the population density. Including an Allee effect has been shown to fundamentally change predator–prey dynamics and strongly impact species persistence, but previous studies mostly focused on scenarios of an Allee effect in the prey population. Here we explore a predator–prey model with an ecologically important case of the Allee effect in the predator population where it occurs in the numerical response of predator without affecting its functional response. Biologically, this can result from various scenarios such as a lack of mating partners, sperm limitation and cooperative breeding mechanisms, among others. Unlike previous studies, we consider here a generic mathematical formulation of the Allee effect without specifying a concrete parameterisation of the functional form, and analyse the possible local bifurcations in the system. Further, we explore the global bifurcation structure of the model and its possible dynamical regimes for three different concrete parameterisations of the Allee effect. The model possesses a complex bifurcation structure: there can be multiple coexistence states including two stable limit cycles. Inclusion of the Allee effect in the predator generally has a destabilising effect on the coexistence equilibrium. We also show that regardless of the parametrisation of the Allee effect, enrichment of the environment will eventually result in extinction of the predator population.

scholarly journals Predator-Prey in Tumor-Immune Interactions: A Wrong Model or Just an Incomplete One?

2021 ◽  
Vol 12 ◽  
Author(s):  
Irina Kareva ◽  
Kimberly A. Luddy ◽  
Cliona O’Farrelly ◽  
Robert A. Gatenby ◽  
Joel S. Brown
Keyword(s):  
Immune System ◽  
Immune Cell ◽  
Interference Competition ◽  
Prey Type ◽  
Cell Types ◽  
Cell Populations ◽  
Natural Food ◽  
Predator Population ◽  
Predator Prey ◽  
Predator Prey Models

Tumor-immune interactions are often framed as predator-prey. This imperfect analogy describes how immune cells (the predators) hunt and kill immunogenic tumor cells (the prey). It allows for evaluation of tumor cell populations that change over time during immunoediting and it also considers how the immune system changes in response to these alterations. However, two aspects of predator-prey type models are not typically observed in immuno-oncology. The first concerns the conversion of prey killed into predator biomass. In standard predator-prey models, the predator relies on the prey for nutrients, while in the tumor microenvironment the predator and prey compete for resources (e.g. glucose). The second concerns oscillatory dynamics. Standard predator-prey models can show a perpetual cycling in both prey and predator population sizes, while in oncology we see increases in tumor volume and decreases in infiltrating immune cell populations. Here we discuss the applicability of predator-prey models in the context of cancer immunology and evaluate possible causes for discrepancies. Key processes include “safety in numbers”, resource availability, time delays, interference competition, and immunoediting. Finally, we propose a way forward to reconcile differences between model predictions and empirical observations. The immune system is not just predator-prey. Like natural food webs, the immune-tumor community of cell types forms an immune-web of different and identifiable interactions.

scholarly journals PENYELESAIAN MODIFIKASI MODEL PREDATOR PREY LESLIE-GOWER DENGAN SEBAGIAN PREY TERINFEKSI MENGGUNAKAN ADAMS BASHFORTH MOULTON ORDE EMPAT

2019 ◽  
Vol 19 (2) ◽  
pp. 53
Author(s):  
Liatri Arianti ◽  
Rusli Hidayat ◽  
Kosala Dwija Purnomo
Keyword(s):  
Fourth Order ◽  
Local Stability ◽  
Predator Population ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Spreading Model ◽  
Disease Spreading ◽  
Predator Prey Models ◽  
Infected Prey ◽  
Model Predator

Eco-epidemiology is a science that studies the spread of infectious diseases in a population in an ecosystem where two or more species interact like a predator prey. In this paper discusses about how to solve modification Leslie Gower of predator prey models (with Holling II response function) with some prey infected using fourth order Adams Bashforth Moulton method. This paper used a simple disease-spreading model that is Susceptible-Infected (SI). The model is divided into three populations: the sound prey (which is susceptible), the infected prey and predator population. Keywords: Adams Basforth Moulton, Eco-epidemiology Holling Tipe II, Local stability, Leslie-Gower, Predator-Prey model

The global dynamics of stochastic Holling type II predator-prey models with non constant mortality rate

Filomat ◽  
2017 ◽  
Vol 31 (18) ◽  
pp. 5811-5825
Author(s):  
Xinhong Zhang
Keyword(s):  
Mortality Rate ◽  
Stochastic Model ◽  
Sufficient Conditions ◽  
Positive Periodic Solution ◽  
Global Dynamics ◽  
Type Ii ◽  
Predator Prey ◽  
Persistence In The Mean ◽  
The Mean ◽  
Predator Prey Models

In this paper we study the global dynamics of stochastic predator-prey models with non constant mortality rate and Holling type II response. Concretely, we establish sufficient conditions for the extinction and persistence in the mean of autonomous stochastic model and obtain a critical value between them. Then by constructing appropriate Lyapunov functions, we prove that there is a nontrivial positive periodic solution to the non-autonomous stochastic model. Finally, numerical examples are introduced to illustrate the results developed.

Plugging Space into Predator-Prey Models: An Empirical Approach

2006 ◽  
Vol 167 (2) ◽  
pp. 246
Author(s):  
Bergström ◽  
Englund ◽  
Leonardsson
Keyword(s):  
Empirical Approach ◽  
Predator Prey ◽  
Predator Prey Models

scholarly journals Functional genomics study of Pseudomonas putida to determine traits associated with avoidance of a myxobacterial predator

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Shukria Akbar ◽  
D. Cole Stevens
Keyword(s):  
Pseudomonas Putida ◽  
Bacterial Communities ◽  
Predator Avoidance ◽  
Phenotypic Diversity ◽  
Myxococcus Xanthus ◽  
Predator Prey ◽  
Mucoid Conversion ◽  
Small Colony ◽  
Predator Prey Models ◽  
Insight Into

AbstractPredation contributes to the structure and diversity of microbial communities. Predatory myxobacteria are ubiquitous to a variety of microbial habitats and capably consume a broad diversity of microbial prey. Predator–prey experiments utilizing myxobacteria have provided details into predatory mechanisms and features that facilitate consumption of prey. However, prey resistance to myxobacterial predation remains underexplored, and prey resistances have been observed exclusively from predator–prey experiments that included the model myxobacterium Myxococcus xanthus. Utilizing a predator–prey pairing that instead included the myxobacterium, Cystobacter ferrugineus, with Pseudomonas putida as prey, we observed surviving phenotypes capable of eluding predation. Comparative transcriptomics between P. putida unexposed to C. ferrugineus and the survivor phenotype suggested that increased expression of efflux pumps, genes associated with mucoid conversion, and various membrane features contribute to predator avoidance. Unique features observed from the survivor phenotype when compared to the parent P. putida include small colony variation, efflux-mediated antibiotic resistance, phenazine-1-carboxylic acid production, and increased mucoid conversion. These results demonstrate the utility of myxobacterial predator–prey models and provide insight into prey resistances in response to predatory stress that might contribute to the phenotypic diversity and structure of bacterial communities.

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