BIO 3360 Lecture Notes - Lecture 14: Cyclic Model, Logistic Function, Exponential Growth
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Let n(t) to denote the population size at time t, then the rate of change in a simple model can be described by: dn(t)/dt = births - deaths + migration. Now making birth proportional to population size dn(t)/dt = bn(t) - dn(t) is birth rate. But exponential isn"t realistic, instead use logistic growth. Many pops slow when close to carrying capacity. K is carrying capacity, r is growth rate. As n(t) approaches k, growth rate goes to zero. If initial population is larger than k, the growth rate will be negative. Predation of one species by another to explain oscillatory levels of certain fish. P(t) = predator a,b,c,d are all positive constants. In the prey model, instead of a death rate, have a population number of predator (p(t)) In the predator model, growth rate depends on food, n(t) Prey in absence of predator grows exponentially (malthusian)
