Linking Specialisation and Stability of Plant ... - OPUS Würzburg

4.3 the model 71
Table 4.2: List of parameter definitions and default values
symbol definition default
P i
A j
Population density of plant species i
Population density of animal species j
value
m Number of plant species 2
n Number of animal species 2
α ij
B
N
Degree of trait matching between plant
species i
and animal species j (0 α ij 1)
Maximum number of flower visits from
pollen uptake
to pollen deposition
Amount of reward per plant and unit of
time
H P Habitat capacity for plants 10000
γ ik
β P
β A
Niche overlap of plant species i and k (0
γ ik 1)
Conversion of mutualistic service to plant
offspring
Conversion of mutualistic service to animal
offspring
1.2
1 · 10 −6
2.1 · 10 −7
d P Plant mortality rate 1 · 10 −8
d A Animal mortality rate 1 · 10 −7
G i
F i
R j
Number of visits received by an individual
plant in one time step
Amount of pollen received by an individual
plant in one time step
Amount of reward collected by an individual
animal in one time step
is given by |ˆλ| < 1. Larger values of 1 − |ˆλ| indicate a higher rate
of return to the coexistence equilibrium.
For the purpose of estimating the size of the domain of attraction
around the coexistence equilibrium, numerical simulations
were performed with 2000 combinations of initial population
densities of the two plant and animal species. Initial densities
were drawn from an interval between one and a maximum density.
As maximum initial densities we chose the equilibrium
densities of a single plant species and its perfectly specialised