Scramble and contest competition, unequal resource allocation, and resource monopolization as determinants of population dynamics

Questions: How do unequal resource allocation, asymmetry, and resource monopolization each affect a population's stability and persistence? How do they differ in their importance to stability and persistence? How may one define precisely the terms 'scramble competition' and contest competition'. Might individual-based modelling help us to develop general population theory? Or is it useful only as a method of computer simulation in applied ecology? Methods: Address the questions with the simplest pre-existing analytical models. Use generation-to-generation difference equations. Define scramble and contest competition according to them. Use models of pure scramble and contest competition and develop and analyse a model of competition in which individuals have abilities to monopolize resources that vary along a continuum. Relate the results to empirical data from field and laboratory studies. Results: Equal resource allocation among population members prevents Population stability and population persistence. If some population members monopolize the resources, both stability and persistence are guaranteed. The generation-to-generation difference equations permit one to define precisely a theoretical gradient of monopolization ranging from complete equality to full monopolization. In some cases, this gradient also permits both stability and persistence.