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

56 can plant-pollinator interactions promote plant diversity?
species i given that it visits any flower during the time step in
question. This conditional probability is
P i
∑ mh=1
P h
α ij
m∑
k=1
(3.6)
P k
∑ mh=1 α kj
P h
Accordingly, the probability that the animal has visited a flower
of species i at least once in the previous B flower visits is
1 − (1 −
P i
∑ mh=1
P h
α ij
m∑
k=1
) B (3.7)
P k
∑ mh=1 α kj
P h
Since the two sums of all plant densities in the numerator and
denominator cancel each other out, this expression can be reduced
to
1 − (1 −
P i
α m∑ ij ) B (3.8)
P k α kj
k=1
Note that with this expression we assume that the densities of
all plant species in the previous B flower visits were identical
to the present densities. Strictly speaking, this assumption only
holds for a system at equilibrium. Under non-equilibrium conditions,
the probability of pollination should reflect the changes
in plant densities during the last B flower visits. Implementing
this feature in the model would introduce a time-delayed effect
of past population densities which might result in greater
instability, possibly leading to population cycles or chaotic dynamics.
However, one may argue that the time scale of pollen
transfer (minutes and hours) is sufficiently different from that
of considerable changes in plant population densities (days and
months) that the changes in plant densities between pollen removal
and pollen deposition are negligible. Therefore, and for
the sake of simplicity, we chose to treat plant densities as constant
within the time span of pollen transfer.
3.6.1.2 Per-capita amount of nectar
The derivation of the expected amount of nectar collected by a
pollinator in one time step is based on the assumption of a Poisson
distribution of flower visitors on flowers. While we could
have simply divided the amount of nectar per flower N by the