Transcript Folie 1

Small Mammal Dispersion
from: Frank Stegemann
Tobias Schwatinski
Kai Dischereit
1 Introduction
Environmental and agricultural benefits:
-
habitat for a large number of wildlife species
improved water quality
improved productivity of adjacent land for
livestock grazing
fertile soils for agricultural production when
drained
BUT
- Damage wood
-> Cause costs
Need to limitate beaver
populations to a certain
number of beavers
1 Mathematical Formulation of the Social Fence Hypothesis
…rate of change of beavers/square-inch in controlled area A
…rate of change of beavers/square-inch in uncontrolled area B
…functions for isolated populations
…function of relationship between beavers of both areas
-> social fence
1 Mathematical Formulation of the Social Fence Hypothesis
Population of beavers in both areas without influence of human and themselves
Area 1 -> logistic model
Area 2 -> exponential model
1 Mathematical Formulation of the Social Fence Hypothesis
within-group
aggression of Y
between-group
aggression
between X and Y
…carrying capacity
Migration from Y to X
…constant rate of
beavers/square mile/year
2 The Social Fence Formulation without Trapping
2 The Social Fence Formulation without Trapping
3 The Social Fence Formulation with Trapping
p>0
3 The Social Fence Formulation with Trapping
Trapping P = 25%
equilibrium point x = 55%