Predator-Prey and Plant Herbivore Interactions
Do predators influence prey populations?
1.Predators may limit prey populations:
Cyclamen mites damage strawberry crops. Predatory mites (Typhlodromus) rapidly reduce cyclamen mites. Where parathion is used, the predatory mites are reduced and cyclamen mite populations explode.
2.Predator and prey populations may exhibit coupled oscillations:
The Lotka-Volterra model is a simple model of predator-prey interactions. The differential equations were developed independently by Lotka (1925) and by Volterra (1926):
dN/dt=aN-bNP
dP/dt=cNP-dP
Where:
N=#prey
P=#predators
a=per capita rate change for prey in absence of predators
d=per capita rate change of predators in absence of the prey
b and c are the rates of change for prey and predator resulting from the interaction
Lotka /Volterra predator-prey models are not very realistic. They do not consider other interaction types. The simple models allow prey population to grow exponentially without any carrying capacity.
Predators do not reach saturation. The rate of prey consumption is linearly proportional to prey density. There are no interactions among predators. Thus, it is not surprising that the model shows no asymptotic stability. However many modifications that make the model more realistic exist.
A Lotka-Volterra predator-prey model
Nicholson and Bailey developed an alternative that has discrete generations and uses difference equations. The Nicholson Bailey Model is a simple model of host-parasitoid and consumer herbivore interactions. Trichogramma wasps and corn borers provide an excellent
example of host-parasitoid interactions.The Nicholson Bailey Model makes the following assumptions:
1) The host population increases exponentially in the absence of a parasitoid.
2) Parasitoids search independently and encounter hosts at random.
The Nicholson -Bailey model is:
Ht+1 = R Ht exp( - a Pt )
Pt+1 = c Ht [ 1 - exp( -a Pt ) ]
Where: R is the intrinsic net reproductive rate of the host,
and c is the mean number of parasitoids produced per parasitized host.
The Nicholson-Bailey model has a single equilibrium point: