M. Yokozawa et T. Hara, Global versus local coupling models and theoretical stability analysis of size-structure dynamics in plant populations, ECOL MODEL, 118(1), 1999, pp. 61-72
A local coupling model for growth dynamics of plant populations is proposed
, in which each individual occupies a square lattice point and follows logi
stic growth with potential maximum relative growth rate c(0) being reduced
by the competitive effects from eight interacting neighbours. The competiti
ve effects are given by the competition function W, which describes the deg
ree of competitive asymmetry between individuals, beta and the distance-dep
endent intensity of competition between individual i and j, alpha(ij), as a
coupling constant. Then a global coupling model corresponding to the local
coupling model is proposed, in which every individual interacts with all t
he other individuals in the field. In the global coupling model, the coupli
ng constant alpha as the same parameter for all the individuals was employe
d instead of alpha(ij)'s in the local coupling model. alpha was given as an
average of alpha(ij)'s of eight interacting neighbours in the local coupli
ng model. Both the coupling constants were normalized by the number of inte
racting individuals to make simulation results comparable between the model
s. Numerical simulations revealed that the local coupling model can be simu
lated by the corresponding global coupling model fairly well if population
growth dynamics are continuous without deaths or new recruits. In both the
models, multi-layered structure of size distribution was more likely to eme
rge under asymmetric and/or intense competition than under symmetric and/or
weak competition. This conforms to the widely known phenomenon of size-str
ucture dynamics in plant populations. Since theoretical analysis is impossi
ble for the local coupling model, linear stability analysis of size-structu
re dynamics was made for the global coupling model. It was theoretically sh
own that if alpha < c(0)/(1 + beta), mono-layered size structure is stable;
if alpha > c(0)/(1 + beta), multi-layered size structure is stable. As alp
ha and/or beta increases (decreases), multi-layered (mono-layered) size str
ucture gets stable. As c(0) (i.e. seedlings' relative growth rate) increase
s, the domain of stable mono-layered (multi-layered) size structure becomes
larger (smaller). Therefore, the above simulation results were supported b
y linear stability analysis of the dynamical systems. Ecological implicatio
ns of these theoretical results are discussed concerning the relationship b
etween the stability of stand size structure and the degree of competitive
asymmetry (multi-layered versus mono-layered). (C) 1999 Elsevier Science B.
V. All rights reserved.