The corresponding STELLA model is shown in Fig. 30.2. In the model the
feedback from soil community to the plants is quantified by the interaction coefficient I s , which in turn is defined as
I s ¼ α A þ β B À α B À β A
ð30:1Þ
The direction of interaction coefficient, I s , captures co-existence of two plant
species. Additionally, in natural systems, the succession of plant communities may
be affected by the delayed feedback effect from the soil communities [2].
With the assumption that both plant and microbe communities start with an even
relative abundance of 0.5, we change the feedback coefficient to arrive at alternate
co-existence patterns of plant A and plant B. Data used in this model is from the
paper published by Bever [1], van Wesenbeeck et al. [3] and Yamazaki et al. [4].
Figures 30.3 and 30.4 show the plant community dynamics without the soil community feedback (I s ¼ 0). As shown in Fig. 30.1, plant A goes extinct in the given field
within 50 years. This is because of the fact that we assumed, for this model run, plant B
to be a stronger competitor (C A ¼ 0.885, K A ¼ 100; C B ¼ 0.98, K B ¼ 120).
What are the effects of strong negative feedbacks on the coexistence of plant A
and plant B? To answer this question we first adde a strong negative soil community
feedback (I s ¼ À0.43) to the system (Figs. 30.5 and 30.6). Instead of extinction of
one species, plant A and plant B take turns to dominant the system. The dynamics of
the relatively dominant soil microbial communities changes over time, Fig. 30.5).
When we increase the strength of feedback from strongly negative (I s ¼ À0.43)
to strongly positive (I s ¼ 0.43), we observe that the plant community dynamics
quickly changes from one where plant A and B take turns to dominant to one where
plant A becomes distinct (Fig. 30.7). As the feedback strength becomes more
positive, plant A goes to extinction more quickly.
So far, the model does not allow for any randomness in the system. How may the
randomness of the growth coefficients RA and RB, the carrying capacities KA and
KB, and the delayed effect change the coexistence of plants A and B? To answer
this question we introduced randomness to the growth coefficients RA and RB
(Fig. 30.8), and to the carrying capacities KA and KB (Fig. 30.9) separately.
N A
S A
N B
S B
C A
C B
a A
1
b A
a B
b B
n
Fig. 30.1
250
30 Plant–Microbe Interaction
feedback from soil community to the plants is quantified by the interaction coefficient I s , which in turn is defined as
I s ¼ α A þ β B À α B À β A
ð30:1Þ
The direction of interaction coefficient, I s , captures co-existence of two plant
species. Additionally, in natural systems, the succession of plant communities may
be affected by the delayed feedback effect from the soil communities [2].
With the assumption that both plant and microbe communities start with an even
relative abundance of 0.5, we change the feedback coefficient to arrive at alternate
co-existence patterns of plant A and plant B. Data used in this model is from the
paper published by Bever [1], van Wesenbeeck et al. [3] and Yamazaki et al. [4].
Figures 30.3 and 30.4 show the plant community dynamics without the soil community feedback (I s ¼ 0). As shown in Fig. 30.1, plant A goes extinct in the given field
within 50 years. This is because of the fact that we assumed, for this model run, plant B
to be a stronger competitor (C A ¼ 0.885, K A ¼ 100; C B ¼ 0.98, K B ¼ 120).
What are the effects of strong negative feedbacks on the coexistence of plant A
and plant B? To answer this question we first adde a strong negative soil community
feedback (I s ¼ À0.43) to the system (Figs. 30.5 and 30.6). Instead of extinction of
one species, plant A and plant B take turns to dominant the system. The dynamics of
the relatively dominant soil microbial communities changes over time, Fig. 30.5).
When we increase the strength of feedback from strongly negative (I s ¼ À0.43)
to strongly positive (I s ¼ 0.43), we observe that the plant community dynamics
quickly changes from one where plant A and B take turns to dominant to one where
plant A becomes distinct (Fig. 30.7). As the feedback strength becomes more
positive, plant A goes to extinction more quickly.
So far, the model does not allow for any randomness in the system. How may the
randomness of the growth coefficients RA and RB, the carrying capacities KA and
KB, and the delayed effect change the coexistence of plants A and B? To answer
this question we introduced randomness to the growth coefficients RA and RB
(Fig. 30.8), and to the carrying capacities KA and KB (Fig. 30.9) separately.
N A
S A
N B
S B
C A
C B
a A
1
b A
a B
b B
n
Fig. 30.1
250
30 Plant–Microbe Interaction