Download Lattice model of invasive dynamics of short- and long

Lattice model of invasive dynamics of short- and long- rhizomes grasses
N.V. Mikhailova , N.E. Bogdanova
Institute of Mathematical Problems of Biology, Moscow region, Pushchino, Institutskaja st., 4,
Russia, [email protected]
Key words: plant population, lattice model, invasion, seed and vegetative dispersal
Introduction
The evaluation of the rate and mechanism of plants invasion on bare territory is one of the basic
problems of vegetation restoration. The fixedness of plants, their spatially explicit positions and
interaction with the nearest neighbors are the main characteristics of a plant population life. A
plant population represents a spatially distributed set of separate individuals differing by size and
age. These individuals are able to disseminate their offsprings by many ways and with diverse
spatial pattern. These circumstances make plant populations to be describing by complex spatial
dynamics (Komarov et al., 2003).
We used computer modeling for analyzing the plants spatial pattern arising from the seed and
vegetative propagation.
Three species of grasses with various types of territory occupation were chosen: Aegopodium
podagraria L., which is a competitor, Stellaria holostea L., which is a reactive species and a
stress-tolerant Asarum europaeum L. The model is based on the field experimental data collected
in the “Bryanskii Les” State reserve in the centre of European Russia.
Our model is a dynamic finite automata model being discrete in time and space. For simplicity
we considered the plant population development from the ontogenetic point of view. Individual
plant development may be treated as a number of successive stages (Uranov, 1975). The stages
are marked out on the basis of morphological indicators reflecting functional importance of
plants at different stages. Thus population may be described as a set of individuals belonging to
certain age stages with their corresponding distribution - age stages spectrum.
The main rules of the model are:
 a plant population consists of population elements (sprouts) which originate either from
seeds or from vegetative dissemination;
 plants are assigned to the bounded cells of a two-dimensional integer lattice, with no
more then one sprout per cell;
 cell size is different for each species and depends on the distance of dauther sprouts
spreading
 time step is equal to one year.
 plants change their age states, in the certain age plants spread its daughter sprouts on
neighbor cells;
 on reaching the generative age state the sprout is flowering and it dies next year doing
the corresponding cell vacate;
 seed rain is defined as the probability of random appearance of a seedling plant in an
empty cell being in dependence on the distance from blooming plant (some special
assumptions about other mechanisms of seeds transportation such as zoochoric transfer
is also included into the model);
The chosen species differ in the geometrical properties of propagation of sprouts, rate of
expanding and intensity of appearance of sprouts from mother plant. The Aegopodium
podagraria population development is affected by light condition. The dynamic pattern of
sprouts and their relative abilities were simulated in correspondence with experimental data
(Table).
Table. Measured experimental data used in the models
Species, Conditions
Aegopodium
podagraria in
shadowed conditions
Aegopodium
podagraria in light
conditions
Asarum europaeum
Stellaria holostea
Sprout life
longevity,
years
The seed
Vegetative
Vegetative
Sprout
germination
dissemination dissemination
blossom age number per
age
radius, m/year
sprout/year
13
6
0,3
8
0
13
2
0,3
2
175
10
3
2
2
0,03
0,42
6
2
5
5
Results and discussion
We investigated different scenarios: 1) the invasion of different species separately on bare soil
with or without shadowing for Aegopodium podagraria species; 2) the plant propagation
dependence on presence or absence of zoochoric transfer 3) the role of plant community
resistance at invasion; we define it as the heterogeneity of a territory for plants’ occupation
treated as presence of busy cells, which prevent sprout propagation and seed germination. Last
experiments are carried out with different probabilities of busy cells with random distribution
using Monte-Carlo techniques.
In first scenario we found that Aegopodium podagraria has the fastest growth of the population
at invasion on bare soil. At shadowing Aegopodium podagraria species do not produce seeds and
the rate of invasion slows down. whereas invasion rate of Stellaria holostea does not depend on
seed germination.
All species have dependence on presence or absence of zoochoric transfer mostly Asarum
europaeum, its rate ov invasion increases ten times in comparison with two-three times for
others. The Asarum europaeum population without seeds does not spread.
All species have their specific dynamics at third scenario. If the probability of busy cells
presence is more then some critical probability being specifically for the species from number of
all cells, the invasion stops. Without seeds the species have different critical probability number:
0.5 for Aegopodium podagraria, 0.1 for Asarum europaeum and 0.8 for Stellaria holostea.
Again, with seed generation Aegopodium podagraria and Asarum europaeum have the same
critical probability number but Stellaria holostea has not critical probability number at all.
Conclusions
Populations of Aegopodium podagraria have the fastest growth in presence the seed production,
Stellaria holostea is the most adaptive species because of its vegetative overgrowth mechanism.
The survival of Asarum Europaeum populations need the zoochoric transfer.
Acknowledgements
This work was supported by the grant 02-04-48965 of Russian Foundation of Basic Researches.
References
Komarov A.S., Palenova M.M., Smirnova O.V. The concept of discrete description of plant
ontogenesis and cellular automata models of plant population. Ecological Modelling, 170, p.
427-439, 2003.
Uranov A.A. Age spectrum of the phytocoenopopulations as a function of time and energetic
wave processes. Biological Sciences, Moskow, 2, p. 7-34, 1975.