ecosystem
YANGYANG
Competitioninlife.pptx2 April 2018
ECS 111
Donald Olson
Organisms as Competition
How to organisms interact?
How to two species interact in terms of resources and growth?
dPi/dt = ri Pi (1 – Pi/K - bij Pj/Ki) where I,j =1,2
These equations are sometimes called the Lotka-Volterra Eqs.
What occurs when the bij >0. Competition for Ki.
When bij< 0; species gain from each others presence Mutualism or Symbiosis.
The case where bij changes signs in the equations, one species gains from the other. Parasitism or predator/prey
Before exploring these… the crop problem
Here we only have one population equation:
So…. Calculate the equilibrium for the pest
What does insecticide use do?
P
^
δ
Increasing insecticide use leads to lower populations. Up to a critical point there are two equilibria. The upper is stable.
The lower is unstable up to a point in P where it becomes stable.
The population beyond the critical point is unstable and decays.
Then what happens if we spray……
P
r
^
Two equilibria due to quadratic. For small growth rates P is constant and unstable, insects become extinct.
Higher r, produces two states. Higher one says insects win if r is high enough.
What about the lower equilibrium?
∂RHS/∂P =r/1+r
P
r
Agri-business Solutions
Japanese beetles as vector for fungus infections and rot in corn and soybeans.
Pesticides:
