782 
trend of area change could be described as a descending curve with the area decrease speeded up (for example 
hydromorphic and mesohydromorphic ecosystems). The trend of area changes for other ecosystems is 
described by an ascending curve with the decreasing rate of increase of area with time. The trend of the area 
increase of saline-meadow ecosystem, for example, is described by function of the following form: 
0.50 0.24 
Y = 6.56(X[i] - 1961) - 2.22(X[i] - 1961) - 0.03. 
Extrapolation of this trend on one-third of training time interval could be predict area of this ecosystem classe 
on 10 years forward. 
Mathematical modelling of the dynamics of the ecosystem combinations is more complicated but forecasting 
on the basis of complex analysis is more correct. Formerly for ecological forecasting we used simple 
Markovian chains. These simple Markovian chains were compiled from comparison of two sets of aerospace 
surveys only. According to this procedure the simple transition matrix for all ecosystem classes during the 
training time interval (M[l-2]) was multiplied by transposed vector of final state (V[2]) of each ecosystem classe 
within the study area. As the result we received a prognosed vector of forecasted state on one time interval 
forward (V[f]): 
M[l-2] x V[2] = V[q. 
In our study area of the Lower Amudarya delta the transition matrix M[1980-1985] is a training sequence of 
the ecosystem areadynmamics for ecological forecasting on 5 years forward. Then, M[1980-1985] is multiplied 
by vector of final state V[1985] and we receive the prognosed vector on 1990, i.e. V[1990]. After this, received 
M[1985-1990] could be multiplied by V[1990] for receiving V[1995] (i.e. forecast for 1995), then likewise for 
2000, etc. [Vinogradov, Popov, 1988]. 
At the present time taking into account the nonlinearity of the dynamic trends we prefer to use an 
heterogeneous transition matrices. These heterogeneous transition matrices request more then two survey sets 
for the same study area. For compilation of these heterogeneous transition matrices we used 
photo-interpretation maps of three survey times 1975,1980, and 1985 which had been received from spacecraft 
"Salyut-4, 6, and 7". 
A normative forecast of the ecosystem dynamics to 2010 reveals the following area changes of all ecosystem 
classes (Fig.l). The most rapid growth is predicted for desert (Xero) and saline (Halo) ecosystems. Only 
these two extraarid ecosystems could occupy to 2010 near 70% of the whole area of the Amudarya delta and 
will be increased by 2.3-3.5 times in comparison with 1985. In contrary, area of mesomorphic ecosystem 
classes could drop to 5% of the delta and will be decreased by 3-9 (!) times. Some ecosystem classes will be 
disappeared at near future (for example, hydromesomorpic meadow-swamps at 2000, mesoxeromorphic 
meadows and forests at 2005). But two ecosystem classes will not change their area sufficiently. Area of 
irrigated fields will be supported on level of near 13-14% by man's efforts. Then, predicted trend of area of 
intermediate haloxeromorphic ecosystem classe will have a fluctuated form on the subclimax level. 
Control of the Forecast 
An experimental control of forecast is underway the procedure "epignosis". According to this procedure the 
previous studied time interval was used as a training sequence of the ecosystem dynamics for forecast of the 
ecosystem state on the recent time, which could be tested during the field control studies. In our area study 
the transition matrix M[1975-1980] was used as training sequence for prediction of area changes on 1985 
(tabl.2). Then, predicted areas of all ecosysytem classes V[1985] were tested during the ground thruth in 1985. 
The comparison of predicted and tested areas in 1985 reveals mean error of forecast for 5 predicted years. 
Mean error of forecast is 10.65% of the whole changed area for 5 predicted years. For more remote prediction 
on future such errors will be larger. We estimated mean error on 10 predicted years near 16%, for 15 near