Predator-prey models: an application for the plankton dynamics of lake Geneva

In this paper we present a hierarchical Bayesian analysis for a predator-prey model applied to ecology considering the use of Markov Chain Monte Carlo methods. We consider the introduction of a random effect in the model and the presence of a covariate vector. An application to ecology is considered using a data set related to the plankton dynamics of lake Geneva for the year 1990. We also discuss some aspects of discrimination of the proposed models.

Limit cycles of a predator-prey model with intratrophic predation

Hill, Joe M., Lloyd, Noel G., Pearson, Jane M., 'Limit cycles of a predator-prey model with intratrophic predation', Journal of Mathematical Analysis and Applications Volume 349, Issue 2, 15 January 2009, Pages 544-555

The role of predator overlap in the robustness and extinction of a four species predator-prey network

Predators and preys often form species networks with asymmetric patterns of interaction. We study the dynamics of a four species network consisting of two weakly connected predator-prey pairs. We focus our analysis on the effects of the cross interaction between the predator of the first pair and the prey of the second pair. This is an example where the predator overlap, which is the proportion of predators that a given prey shares with other preys, is not uniform across the network due to asymmetries in patterns of interaction. We explore the behavior of the system under different interaction strengths and study the dynamics of survival and extinction. In particular, we consider situations in which the four species have initial populations lower than their long-term equilibrium, simulating catastrophic situations in which their abundances are reduced due to human action or environmental change. We show that, under these reduced initial conditions, and depending on the strength of the cross interaction, the populations tend to oscillate before re-equilibrating, disturbing the community equilibrium and sometimes reaching values that are only a small fraction of the equilibrium population, potentially leading to their extinction. We predict that, contrary to one`s intuition, the most likely scenario is the extinction of the less predated preys. (C) 2010 Elsevier B.V. All rights reserved.

On certain new exact solutions of a diffusive predator-prey system

We construct exact solutions for a system of two coupled nonlinear partial differential equations describing the spatio-temporal dynamics of a predator-prey system where the prey per capita growth rate is subject to the Allee effect. Using the G'/G expansion method, we derive exact solutions to this model for two different wave speeds. For each wave velocity we report three different forms of solutions. We also discuss the biological relevance of the solutions obtained. © 2012 Elsevier B.V.

Solving Ratio-Dependent Predator-Prey System with Constant Effort Harvesting using Variational Iteration Method

Due to wide range of interest in use of bio-economic models to gain insight into the scientific management of renewable resources like fisheries and forestry,variational iteration method (VIM) is employed to approximate the solution of the ratio-dependent predator-prey system with constant effort prey harvesting.The results are compared with the results obtained by Adomian decomposition method and reveal that VIM is very effective and convenient for solving nonlinear differential equations.

The role of productivity in the ecological and evolutionary dynamics of predator-prey interaction

Productivity is predicted to drive the ecological and evolutionary dynamics of predator-prey interaction through changes in resource allocation between different traits. However, resources are seldom constantly available and thus temporal variation in productivity could have considerable effect on the species' potential to evolve. To study this, three long-term microbial laboratory experiments were established where Serratia marcescens prey bacteria was exposed to predation of protist Tetrahymena thermophila in different prey resource environments. The consequences of prey resource availability for the ecological properties of the predator-prey system, such as trophic dynamics, stability, and virulence, were determined. The evolutionary changes in species traits and prey genetic diversity were measured. The prey defence evolved stronger in high productivity environment. Increased allocation to defence incurred cost in terms of reduced prey resource use ability, which probably constrained prey evolution by increasing the effect of resource competition. However, the magnitude of this trade-off diminished when measured in high resource concentrations. Predation selected for white, non-pigmented, highly defensive prey clones that produced predation resistant biofilm. The biofilm defence was also potentially accompanied with cytotoxicity for predators and could have been traded off with high motility. Evidence for the evolution of predators was also found in one experiment suggesting that co-evolutionary dynamics could affect the evolution and ecology of predator-prey interaction. Temporal variation in resource availability increased variation in predator densities leading to temporally fluctuating selection for prey defences and resource use ability. Temporal variation in resource availability was also able to constrain prey evolution when the allocation to defence incurred high cost. However, when the magnitude of prey trade-off was small and the resource turnover was periodically high, temporal variation facilitated the formation of predator resistant biofilm. The evolution of prey defence constrained the transfer of energy from basal to higher trophic levels, decreasing the strength of top-down regulation on prey community. Predation and temporal variation in productivity decreased the stability of populations and prey traits in general. However, predation-induced destabilization was less pronounced in the high productivity environment where the evolution of prey defence was stronger. In addition, evolution of prey defence weakened the environmental variation induced destabilization of predator population dynamics. Moreover, protozoan predation decreased the S. marcescens virulence in the insect host moth (Parasemia plantaginis) suggesting that species interactions outside the context of host-pathogen relationship could be important indirect drivers for the evolution of pathogenesis. This thesis demonstrates that rapid evolution can affect various ecological properties of predator-prey interaction. The effect of evolution on the ecological dynamics depended on the productivity of the environment, being most evident in the constant environments with high productivity.

Integrability and singularity structure of predator‐prey system

The ‘‘extended’’ ARS (Ablowitz, Ramani, and Segur) algorithm is introduced to characterize a dynamical system as Painlevé or otherwise; to that end, it is required that the formal series—the Laurent series, logarithmic, algebraic psi series about a movable singularity—are shown to converge in the deleted neighborhood of the singularity. The determinations thus obtained are compared with those following from the α method of Painlevé. An attempt is made to relate the structure of solutions about a movable singularity with that of first integrals (when they exist). All these ideas are illustrated by a comprehensive analysis of the general two‐dimensional predator‐prey system.

Anti-grazing properties of the toxic dinoflagellate Karlodinium veneficum during predator-prey interactions with the copepod Acartia tonsa

Karlodinium veneficum (syn. Karlodinium micrum, Bergholtz et al. 2006; J Phycol 42:170–193) is a small athecate dinoflagellate commonly present in low levels in temperate, coastal waters. Occasionally, K. veneficum forms ichthyotoxic blooms due to the presence of cytotoxic, hemolytic compounds, putatively named karlotoxins. To evaluate the anti-grazing properties of these karlotoxins, we conducted food removal experiments using the cosmopolitan copepod grazer Acartia tonsa. Wild-caught, adult female A. tonsa were exposed to 6 monoalgal or mixed algal diets made using bloom concentrations of toxic (CCMP 2064) and non-toxic (CSIC1) strains of K. veneficum. Ingestion and clearance rates were calculated using the equations of Frost (1972). Exposure to the toxic strain of K. veneficum did not contribute to an increased mortality of the copepods and no significant differences in copepod mortality were found among the experimental diets. However, A. tonsa had significantly greater clearance and ingestion rates when exposed to a monoalgal diet of the non-toxic strain CSIC1 than when exposed to the monoalgal diet of toxic strain CCMP 2064 and mixed diets dominated by this toxic strain. These results support the hypothesis that karlotoxins in certain strains of K. veneficum deter grazing by potential predators and contribute to the formation and continuation of blooms.

Predator-prey interactions between brown trout Salmo trutta and native and introduced amphipods; their implications for fish diets

An attempt to improve the food base for brown trout Salmo trutta in Northern Ireland was made in 1958.59 by deliberately introducing English Gammarus pulex into several Irish rivers. In addition. another amphipod Crangonyx pseudogracilis, was later accidently introduced into II ish waters. Our study represents the first attempt to examine the trophic interactions between a native fish predator (S. trutta) and an array of these native (Gammarus duebeni celticus) and introduced (G. pulex and C. pseudogracilis) amphipods. Feeding experiments, involving young brown trout predators and ampiphod prey, revealed that the fish actively selected C. pseudogracilis relative to two alternative Gammarus prey species. Although the trout encountered the Gammarus species more than C. pseudogracilis, they were eaten less than Crangonyx. Difficulties in handling and ingestion of Gammarus by trout may be a. key component of the preference fbr the smaller, more easily handled Crangonyx. The microdistribution of the species was altered by the fish, due to predation being greater in particular microhabitats, Our study showed that the introduction of the herbivorous C. pseudogracilis into Irish freshwaters may represent a useful addition to fish diets. particularly for small and/or juvenile fish. The reprecussions of the deliberate introduction of G. pulex are less clear. It may improve feeding for fish. but only if it can coexist with indigenous macroinvertebrates and thus ultimately improve the range and quantity of possible food items in predator diets. Alternatively, being highly predatory towards other macroinvertebrates including G. d. celticus and C. pseudogracilis. G. pulex may be deleterious to the diversity of the resident benthic community and hence reduce the diversity of prey available to fish predators.

Temporal Variability in Predator-Prey Relationships of a Forest Floor Food Web

Connectance webs represent the standard data description in food web ecology, but their usefulness is often limited in understanding the patterns and processes within ecosystems. Increasingly, efforts have been made to incorporate additional, biologically meaningful, data into food web descriptions, including the construction of food webs using data describing the body size and abundance of each species. Here, data from a terrestrial forest floor food web, sampled seasonally over a 1-year period, were analysed to investigate (i) how stable the body size abundance and predator prey relationships of an ecosystem are through time and (ii) whether there are system-specific differences in body size abundance and predator prey relationships between ecosystem types.

Temperature, predator-prey interaction strength and population stability

Warming could strongly stabilize or destabilize populations and food webs by changing the interaction strengths between predators and their prey. Predicting the consequences of warming requires understanding how temperature affects ingestion (energy gain) and metabolism (energy loss). Here, we studied the temperature dependence of metabolism and ingestion in laboratory experiments with terrestrial arthropods (beetles and spiders). From this data, we calculated ingestion efficiencies (ingestion/metabolism) and per capita interaction strengths in the short and long term. Additionally, we investigated if and how body mass changes these temperature dependencies. For both predator groups, warming increased metabolic rates substantially, whereas temperature effects on ingestion rates were weak. Accordingly, the ingestion efficiency (the ratio of ingestion to metabolism) decreased in all treatments. This result has two possible consequences: on the one hand, it suggests that warming of natural ecosystems could increase intrinsic population stability, meaning less fluctuations in population density; on the other hand, decreasing ingestion efficiencies may also lead to higher extinction risks because of starvation. Additionally, predicted long-term per capita interaction strengths decreased with warming, which suggests an increase in perturbation stability of populations, i.e., a higher probability of returning to the same equilibrium density after a small perturbation. Together, these results suggest that warming has complex and potentially profound effects on predator-prey interactions and food-web stability.