Small Mammal Dispersion
from: Frank StegemannTobias SchwatinskiKai 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
…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
Migration from Y to X
1 Mathematical Formulation of the Social Fence Hypothesis
within-group
aggression of Y
between-group
aggression
between X and Y
…carrying capacity
…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%