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%