Population Cycles in Mathematical and Laboratory Models

Population Cycles in Mathematical and Laboratory Models
Lotka-Volterra predation model assumes host population grows exponentially,
and population size is limited by parasites, pathogens, and predators:
dNh/dt = rhNh – pNhNp
rhNh = exponential growth by host population.
Balanced by the number of hosts killed by exploiter:
– p = rate of parasitism / predation.
– Nh = Number of hosts.
– Np = Number of exploiters
Population Cycles in Mathematical and Laboratory Models
• The model assumes growth rate of exploiter is determined by rate of
conversion of food into offspring minus mortality rate of exploiter population:
dNp/dt = cpNhNp-dpNp
• cpNh = predation rate times a conversion factor (expresses how quickly prey
are converted to offspring, think r ) times host population size
• Np = Population size of exploiter.
• dpNp = exploiter death rate
Model Behavior
• Host exponential growth often opposed by exploitation.
– Host reproduction immediately translated into destruction by predator.
– Increased predation = more predators.
– More predators = higher exploitation rate.
– Larger predator population eventually reduces host population, in turn
reducing predator population.
Model Behavior
Reciprocal effects produce oscillations in two populations.
– As prey population declines, the number of prey converted to predators
– Growth rate (think r ) of predators declines
– Prey populations increase
Graphical Analysis (Fig. 14.17)
Gause and Refuges (Fig. 14.19)
Refuges (fig14.20)
Huffaker studied six-spotted mite Eotetranychus sexmaculatus and predatory
mite Typhlodromus occidentalis.
– Separated oranges and rubber balls with partial barriers to mite dispersal.
– Typhlodromus crawls while Eotetranychus balloons.
– Provision of small wooden posts to serve as launching pads maintained
population oscillations spanning 6 months.
Size as Refuge (Fig. 14.26, 14.27)