It is known that the competitive exclusion principle holds for a large kind of models involving several species competing for a single resource in an homogeneous environment. Various works indicate that the coexistence is possible in an heterogeneous environment. We propose a spatially heterogeneous system modeling the competition of several species for a single resource. If spatial movements a...

In this paper we present and analyse a simple two populations model with migrations among two different environments. The populations interact by competing for resources. Equilibria are investigated. A proof for the boundedness of the populations is provided. A kind of competitive exclusion principle for metapopulation systems is obtained. At the same time we show that the competitive exclusion...

We study a chemostat model that describes competition between n microbial species for a single-limited resource based on storage. The model incorporates internal resource storage variables that serve the direct connection between species growth and external resource availability. Mathematical analysis for the global dynamics of the model is carried out by using the fluctuating method. It is sho...

We consider a discrete time model of semelparous biennial population dynamics. Interactions between individuals are modelled with the aid of an "environmental" variable I. The impact on and the sensitivity to the environmental condition is age specific. The main result is that competitive exclusion between the year classes is possible as is their coexistence. For moderate values of the basic re...

We study a chemostat model that describes competition between n microbial species for a single-limited resource based on storage. The model incorporates internal resource storage variables that serve the direct connection between species growth and external resource availability. Mathematical analysis for the global dynamics of the model is carried out by using the fluctuating method. It is sho...

Toxic or allelopathic compounds liberated by toxin-producing phytoplankton (TPP) acts as a strong mediator in plankton dynamics. On an analysis of a set of phytoplankton biomass-data that have been collected by our group in the North-West part of the Bay of Bengal, and by analysis of a three-component mathematical model under a constant as well as a stochastic environment, we explore the role o...

Adaptation does not necessarily lead to traits which are optimal for the population. This is because selection is often the strongest at the individual or gene level. The evolution of selfishness can lead to a 'tragedy of the commons', where traits such as aggression or social cheating reduce population size and may lead to extinction. This suggests that species-level selection will result when...

Sympatric speciation requires coexistence of the newly formed species. If divergence proceeds by small mutational steps, the new species utilize almost the same resources initially, and full speciation may be impeded by competitive exclusion in stochastic environments. We investigate this primarily ecological problem of sympatric speciation by studying the population dynamics of a diverging ase...

In this paper, we study the global dynamics of a chemostat model with a single nutrient and several competing species. Growth rates are not required to be proportional to food uptakes. Our approach is based on the construction of Lyapunov functions. The Lyapunov functions extend those used by Hsu [SIAM J. Appl. Math. (1978) 34:760-763] and by Wolkowicz and Lu [SIAM J. Appl. Math. (1992) 57:1019...

Universal grammar(UG) is a list of innate constraints that specify the set of grammars that can be learned by the child during primary language acquisition. UG of the human brain has been shaped by evolution. Evolution requires variation. Hence, we have to postulate and study variation of UG. We investigate evolutionary dynamics and language acquisition in the context of multiple universal gram...