Discrete vs Continuous Growth
• populations w/ distinct breeding season
demonstrate discrete growth
• Populations that reproduce year round demonstrate
continuous growth
Continuous Growth
Density
Discrete Growth
Time
l: Discrete Growth Rate
• N0 = pop size at time 0
• N1 = pop size at time 1
• Discrete growth rate = l = N1/N0
• N1 = N0l or Nt = N0lt
Continuous Growth
• l like an annual interest rate
• Growth rate over a discrete period of time
• r = per capita growth rate at any particular instant
• Simple relationship between l and r
• l = er , r = ln(l)
Thus ….
• if l is the discrete growth rate
• And Nt = N0lt
• And r is the instantaneous growth rate
• And l = er
• then substituting er for l gets you
• Nt = N0ert
R0 vs r
• R0 = generational growth
• l = discreet growth rate
• r = per capita or instantaneous growth rate
• l = (R0/g) where g = generation time
• r = ln(R0/g)