ECOSYSTEM MODELING AND SIMULATION: APPLICATION OF SONCHES TO AN AGROECOSYSTEM
2 STAGES OF AGROECOSYSTEM MODELING
2.4 Fundamental Intracompartment Processes
In modeling the free-body input-output behavior of any given compartment the following three processes are considered (their interconnections are illustrated in a block diagram in Figure 2).
(i) The uptake of distributable environmental quantities:
The fraction w of the environmental quantity x taken up is not only a function o f x but also a function of state variables. This fact is taken into account in the demand d , which is calculated depending on N and V. (This is the food-uptake feedback for a donor-induced recipient-controlled process.) If the input quantities x,, x,,
. . .
, x n do not vary indepen- dently of one another then the correlations between them have to be considered (input coupling).(ii) The calculation of the physiological state:
The modifying influence of undistributed quantities u l , u,,
. .
. , uk (temperature, pH, etc.) on V as function of distributable quantities is separately considered in the internal"feed-forward". The internal feedback
is used for modeling time-lagged first-order adaptation to environmental variations.
(iii) Growth/multiplication:
The growth rate at is calculated at the individual level:
Growth at the compartment level is biomass induced (self-induction),
N; = atN:, K = induction parameter (6)
and density regulated (density feedback),
N t = N;h(Nt-,) h(Nt-,) = density function (7)
Modeling agroecosystems: the SONCHES model 173
(cf. Getz, 1978). These mutually interdependent processes form the framework for the modeling procedure. Each functional response has t o be identified for all compartments (see Section 3).
2.5 Interactions
Without going into details we list here the kinds of interactions which have to be considered, outlining the problems of the second modeling stage: (i) competition for energy, water, nutrients, and habitat within plant compartments; (ii) competence within plant compartments reflecting interferences caused by different degrees of adaptednesses (Steinmiiller, 1980); (iii) competition within fungal and animal pest compartments for metabolic products and biomass; (iv) trophic interactions between plant and fungal pest compartments; (v) trophic interactions between plant and animal pest compartments.
The interactions are schematically displayed in Figure 3; different ontogenetic compart- ments of the species are not distinguished.
3 GROWTH MODEL FOR THE VEGETATIVE COMPARTMENT OF Stellaria media The vegetative compartment is the most important one with respect to the pest problem. Up to now n o weed model has been available for modeling complex pest prob- lems. Later on the model can be tested against experimental results and can be used for explaining observed irregularities in the normally rapidly-increasing plant mortality during the summer. As regards environmental quantities, the water available for plants measured as water capacity W (percentage water content) and the air temperature T ("C) have been considered explicitly. The remaining quantities have been assumed to be optimal and are not considered in the first-cut model.
3.1 Dynamics
The change of the state variable N (surface covering) is modeled (cf. eqns. 4-7) by
where the time step is one week, and the other variables have the following meanings:
N is the extent of surface covering (%),
1s the maximum growth rate per week (0.9
+
0.1% week-'), a(V, T ) is the normalized growth rate (see below),h(N) is the density feedback (h(N) = 1 - ( ~ / 1 0 0 ) ~ , and
0
= 0.7+
0.1),pmax is the estimated maximum mortality rate (0.5% week-'), and H(T, W, V ) is the step function:
174 K . Bellmonn et al.
( 1 otherwise
where Tmin and T,,, are, respectively, the lower and upper values of the existence interval with respect to T (Tmin = 5 "C, Top, = 15 "c, T,, = 35 "C), and W,,, and
W ,
,
are, respectively, the lower and upper values of the existence interval with respect to W (Wmin = lo%, Wopt = 7W, Wmax = 130% (fictive value)).We have restricted the maximum change of V per time step (internal feedback) to map a time-lagged and damped response to environmental changes.
v;Y-:
v(W1)> v7+
-y+ = 0.5v
v(w')<
v Y - -y- = 1.6 V(W1) otherwiseW' is the water uptake W modified by the influence of temperature
where K and v are free parameters which have to be adjusted for modeling the linear and nonlinear influence of T on water stress (K = 1, v = 1). The function V(W) is assumed to be equal to the normalized growth rate a(W) measured in laboratory conditions where the water capacity of the soil has been kept fwed in each measurement and thus the physiological state has been adapted to the environment.
The growth rate a(W) and a(T) can be fitted by the same expression
with
K = exP (- ~[(Xmax -Xopt)/(Xmu - Xmin)Iz) for X Xopt
where X,,, and Xmi, are, respectively, upper and lower values of the existence interval and Xop, is the value for optimal growth. The growth rate 4 T ) is asymmetric with respect to the optimal value described by p ( T < Top,) = $p(T
>
Top,). Different combinations of a ( T ) and V have been used for a(T, V) where a(T, V) = [Va(T)]1'2 fits best to map a time-delayed and damped response to environmental changes. The developments of water and temperature conditions were simulated byand
W, = - p 1 cos 2 t
+
q, cos t+
q3+
0 2Modeling agroecosystems: the SONCHES model
176 K. Bellmann er al.
"42 52 10 2 0
Week number
FIGURE 4 The annual development of Srellaria media for different climatic types: ----, maritime, p , = 5 " c , p 2 = i s 0 c , q , = 11.25%,q2 = 17.5%,q3 = 7 8 . 7 5 % ; - - - , temperate,^, = 1 3 " c ,
. . .
p2 = 1 3 0 C , q l = 2 5 % . q 2 = 30%,q3 = 6 5 % . continental. p l = 1 7 . 5 " C , p 2 = 1 2 . 5 " ~ , ~ , = 17.5%,q2 = 15%, q , = 32.5%.
where p , and p, are temperature parameters ( p , = 13 "c, p, = 13 "c), q , , q , , and q 3 are water parameters (water contents) ( q , = 25%, q 2 = 30%, q3 = 65%), and 0 , and 0 , are evenly distributed random numbers within the given intervals (- 3 OC, 3 OC) and (- 20%,20%), respectively, for stochastic simulations.
3.2 Discussion
All the parameters except p , , p , , q , , q , , and q , change the course of surface cover- ing qualitatively but produce no breakdown which is dependent only on the environ- mental parameters. Different climatic types are generated by different parameter sets.
The corresponding growth is shown in Figure 4. Here intuitive experience is confirmed;
the best growth condition is the maritime climate. Using stochastic variants of the moderate climate, simulation results are compared with experimental data on the surface covering ofstellaria media in the years 1974-1977 (Figure 5). Periods of two or three
Modeling agroecosysfems: the SONCHES model
19741 1975
/
temperateldry 8040
8 -
0 0
2
80E
.$
9 2
(4 40
0
C m
.- 5
0' J o
a 80
'5
Im
1 9761 1977I
coldlwet40
0
Oct
NO^^^^ an
F e b ~ a r A ~ r May Jun Jul MonthFIGURE 5 The development o f the normalized surface covering of the weed Stellaria media for the years 1974-1977 (0) compared with simulation results (-) for three different weather situations during the period. (The data were obtained from experiments of the Institute of Plant Protection Research o f the GDR Academy of Agricultural Science.)
months during the three years were classified as wet, moist, dry, cold, temperate, or warm according t o the total precipitation and the mean temperatures within the periods. Those stochastic scenarios of the simulation results were chosen which correspond to the pre- viously classified weather patterns. The calculated results coincide well with the experi- mental data.
Although the estimation of soil water by classification of precipitation was very inaccurate the calculated results coincide well with the experimental data without further model adaptation. The observation that the normal summer mortality of the weed was absent in 1977 could be reproduced by the model and explained by the maritime-like climate experienced during the summer of that year.
K. Bellmann et al.
4 CONCLUDING
REMARKS
In this paper only a few problems of modeling agroecosystems could be described.
It has been shown that our modeling procedure is guided by a total ecosystem concept which will be further developed by considering ecological control mechanisms on higher decision levels of self-adaptation and self-organization. In most cases there is no real chance of a global adaptation of the model behavior because the responses of the modeled subject to definite input vectors take too much time or cannot be modeled for other reasons. Thus the decomposition of complex ecosystems into subsystems (performed by hand for the modeled agroecosubsystem with stepwise increases in complexity) and the separate validation and adaptation of the corresponding sections seem t o remain the only technique. A model for the smallest possible subsystem (the free-bodycase/one- compartment model) was qualitatively compared with field data; this showed a useful application of the ecosystem concept in explaining observed irregularities in the annual development of the weed Stellaria media.
REFERENCES
Caswell, H., Koenig, H.E., Resh, J.A., and Ross, Q.E. (1972). An introduction to systems science for ecologists. In B.C. Patten (Editor), Systems Analysis and Simulation in Ecology, Vol. 2.
Academic Press, New York, pp. 3-78.
van Dyne, G.M. (1974). A systems approach to grasslands. In D. Daetz and R.H. Pantell (Editors), Environmental Modeling: Analysis and Management. Benchmark Papers in Electrical
Engineering and Computer Science 6. Dowden Huchison and Ross, Stroudsburg, Pennsylvania, pp. 89-101.
Getz, W.M. (1978). On modeling temporal patterns in stressed ecosystems - recreation in a coniferous forest. Ecological Modeling, 5 : 237-257.
Hampicke, U. (1977). Landwirtschaft und Umwelt (Agriculture and Environment). Dissertation, D 83, Nr. 24. Technische Universitat Berlin.
Holling, C.S., Jones, D.D., and Clark, W.C. (1976). Ecological Policy Design: Lessons from a Study of Forest/Pest Management. University of British Columbia, Vancouver.
Innis, G.S. (1975). Role of total systems models in thegrassland biome study. In B.C. Patten (Editor), Systems Analysis and Simulation in Ecology, Vol. 3. Academic Ress, New York, p. 17.
Knijnenburg, A., Matthaus, E., and Stocker, G. (1980). Zur Begriffsbestimmung des okologischen Compartments - eine Grundkonzeption zur ~kosystemanalyse (On the Definition of the Notion
"Ecological Compartment" - a Fundamental Concept for Ecosystem Analysis). Flora, 170:
484-497.
Knijnenburg, A., Matthaus, E., Lattke, H., Eggert, H., and Kalmus, A. (1981). Diskrete Simulation von okologischen Regelmechanismen und ihre Anwendung am Beispiel eines Grobmodells der vegetativen Entwicklung von Stellaria media (Discrete simulation of ecological control mechanisms and their application to a model of the vegetative development of Stellaria media).
In K. Unger and G. Stocker (Editors), Biophysikalische 0kologie und tikosystemforschung.
Akademie-Verlag, Berlin, pp. 275-308.
Matthaus, E. (1978). Investigations of ecosystems by means of simulation. In Proceedings of the Conference on Mathematical Modeling of the Biogeocenotic Process, Puscino, USSR. (In Russian.)
Patten, B.C. (Editor) (1971, 1973, 1975, 1976). Systems Analysis and Simulation in Ecology, Vols.
1-4. Academic Press, New York.
~teinmiiller, K.-H. (1980). Model considerations on niche overlap and interaction. Biometrical Journal, 22: 211-228.