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

28 plant-pollinator dynamics: stability reconsidered
A
0.001 γ ik = 0.99
B
0.001 γ ik = 0.7
0.000
0.000
−0.001
−0.001
−0.002
−0.002
Community Stability
−0.003
−0.003
0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0
C
D
0.001 γ ik = 0.5
0.001 γ ik = 0.2
0.000
0.000
−0.001
−0.002
−0.003
−0.001
−0.002
−0.003
Pollen carryover:
B = 1
B = 2
B = 4
B = 8
B = 16
B = 100
0.0 0.2 0.4 0.6 0.8 1.0
Pollinator Specialization
0.0 0.2 0.4 0.6 0.8 1.0
Figure 2.3: Relationship between pollinator specialisation and stability of
plant-pollinator systems at four different levels of plant niche
overlap. Community stability was defined as C = 1 − |ˆλ|, where
ˆλ is the leading eigenvalue of the Jacobian matrix for the equilibrium
at which all four species coexist. Results are shown for
six different values of pollen carryover (parameter B), the maximum
number of flower visits between pollen removal and deposition,
and for decreasing values of plant niche overlap with
respect to abiotic resources (γ ik ). The dashed horizontal line indicates
the stability of a plant community without pollinators.
Other parameter values used for this figure: β P = 3.75 · 10 −6 ,
β A = 6.33 · 10 −7 , d P = 3 · 10 −8 , d A = 3 · 10 −7 , b veg = 3.5 · 10 −8 ,
N = 1.1, H P = 10000.
In comparison to the stability of a plant community without
pollinators (dashed horizontal lines in Fig. 2.3 and 2.4), plantpollinator
systems exhibited higher or lower community stability
depending on the combined effects of all parameters mentioned
above. Since completely generalised plant-pollinator systems
(S = 0) always had stability values of exactly zero or lower,
an increase in stability compared to a plant community with
only vegetative reproduction required a certain degree of pollinator
specialisation. The same factors that resulted in increased
community stability of plant-pollinator systems in general (see