There are three phases of population growth curves: 1) slow growth due to a limited number of species, 2) rapid exponential growth as reproduction increases, doubling in size each interval, and 3) leveling off as resources become limited. Populations undergo intraspecific competition for resources and interspecific competitive exclusion where one species uses resources more effectively, eliminating others. Predator-prey relationships involve predators reducing prey population, then competing with fewer prey, causing fluctuations that create evolutionary pressures.