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

2.6 appendix 35
Here, S and T denote the maximum number of seeds or pollinator
offspring, respectively, that a single individual can produce
within one time step. h P and h A are half-saturation constants.
All other parameters are as defined in the main text.
Community Stability
0.001
0.000
−0.001
−0.002
γ ik = 0.99
B=1, Holl I
B=16, Holl I
B=1, Holl II
B=16, Holl II
Community Stability
1e−03
5e−04
0e+00
γ ik = 0.5
−0.003
−5e−04
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
Pollinator Specialization
Figure 2.5: Effect of a Holling type II functional response on community stability.
In both graphs, community stability of a system with two
plant and two pollinator species is plotted against the degree of
specialisation of plant-pollinator interactions for Holling type I
(black lines) and Holling type II functional responses (grey lines)
of both plant and animal birth rates. Results are shown for two
degrees of plant niche overlap (γ ik , left and right panel) and
two different values of pollen carryover (B). Community stability
was measured as C = 1 − |ˆλ|, where ˆλ is the largest eigenvalue
of the Jacobian matrix at the coexistence equilibrium. The following
parameter values were used for this figure: S = 1 · 10 −5 and
h P = 2.6666 or β P = 3.75 · 10 −6 , respectively, T = 1 · 10 −5 and
h A = 15.5797 or β A = 6.33 · 10 −7 , respectively, d P = 3 · 10 −8 ,
d A = 3 · 10 −7 , b veg = 3.5 · 10 −8 , H P = 10000, N = 1.1.
The introduction of a saturating functional response for plant
and pollinator reproduction did not induce a fundamental
change in the relationship between pollinator specialisation and
community stability (Fig. 2.5). However, a decrease in plant
niche overlap from γ ik = 0.99 to γ ik = 0.5 had a stronger effect
on a system with Holling type I functional responses. Otherwise,
effects of pollinator specialisation and pollen carryover
were identical.
2.6.2 Relationship between specialisation and community stability without
a trade-off between generalist and specialist feeding behaviour
The measure of specialisation of plant-pollinator networks S
used in the main article implies that a trade-off between specialist
and generalist interactions exists. In order to investigate