Biomedical subjects

A Sikder

Publications and source records attributed to A Sikder.

7 recordsLinked to original sources

PubMed2000

Uniform persistence for sigmoidal diet selection with keystone prey species.

In this paper we discuss uniform persistence (UP) criteria of two prey- one predator systems, where we consider that the predator's diet selection is a sigmoidal function of the most profitable prey type in place of a step function of conventional diet choice theory. We also derive UP results of the system with direct interspecific competition between the prey. The role of the most profitable prey item as a keystone species, the magnitude of its carrying capacity, the ability to withstand predation of both prey species, and the ratios of their profitability values (to predators) are important to whether or not adaptive foraging may promote UP. In general, foraging decision rules play no role in UP if the alternative prey item is the keystone species. The result is also not affected by the effect of direct competitive coexistence or dominance relationship of the prey. In some cases, dominance of one of the prey species provides the most advantageous situation for ensuring UP.

Animal Feed↗

PubMed1999

Optimal foraging and predator-prey dynamics, II.

In this paper we consider one-predator-two-prey population dynamics described by a control system. We study and compare conditions for permanence of the system for three types of predator feeding behaviors: (i) specialized feeding on the more profitable prey type, (ii) generalized feeding on both prey types, and (iii) optimal foraging behavior. We show that the region of parameter space leading to permanence for optimal foraging behavior is smaller than that for specialized behavior, but larger than that for generalized behavior. This suggests that optimal foraging behavior of predators may promote coexistence in predator-prey systems. We also study the effects of the above three feeding behaviors on apparent competition between the two prey types.

Animals↗

PubMed1998

Attracting theorems for cyclic sets and impermanence.

We derive attraction theorems for a cycle connecting nonempty compact (isolated) invariant sets using an average Lyapunov function. An application is given to a concrete system having such a cycle with the object to obtain the impermanence of the system.

Animals↗

PubMed1994

Multiple cyclic sets connecting saddle points and limit cycles of a four-species system and its uniform persistence.

Considering a model of a generalized Gause-type four-species system of two predator-prey pairs linked by competition, the authors derive sufficient conditions for the existence of three different invariant cyclic sets connecting saddle points and limit cycle(s) on the boundary of its state space. Also discussed is the uniform persistence of the model in the presence of such cycle sets.

Animals↗

PubMed1994

Persistence of a generalized gause-type two prey-two predator pair linked by competition.

We consider a generalized Gause-type model of a two predator-two prey system in which the predators are prey-specific and the prey are in competition with each other. Uniform persistence, weak persistence, and the existence of different types of heteroclinic cycles with multiple boundary equilibria are discussed.

Animals↗

PubMed1994

A co-evolutionary model of mutualism from a commensal association on Lotka-Volterra dynamics.

This paper considers a Lotka-Volterra type of model of competition between a commensal pair of species and a mutualistic pair, presumed to have descended from a single ancestral pair of species. The species are behaviourally isolated but compete for resources. We have studied in detail the effects of the benefits of mutualism over commensalism. Specifically, it is shown that co-evolution of the mutalistic pair from the commensal association is not possible if (i) some of the interacting parameters coincide for the two pairs, or (ii) mutualists suffer more from competition, or (iii) mutualists produce a smaller competitive effect. If the costs of mutualism are density-independent, co-evolution of the mutualism is possible provided (i) the specific growth rate(s) of one or both of the mutualistic species is positive at the steady state of the commensal pair and (ii) the specific growth rate(s) of one or both of the commensal species is positive at the steady state of the mutualistic pair. Lastly, whenever the mutualists co-exist with the commensalists and the feasible interior equilibrium of the model is unstable, we have shown that the co-evolutionary model of mutualism collapses to the stable two-species mutualistic relationship, causing the ultimate extinction of both the species of the original commensal association.

Animals↗

PubMed1993

Persistence of a four species food chain with full omnivory.

We consider here a food chain composed of four species with full omnivory with Lotka-Volterra dynamics. Conditions for uniform persistence and weak persistence of the food chain are derived. It is also shown that the system exhibits a heteroclinic cycle.

Animals↗