In the demographic part of the model plant ontogeny is described in terms discrete age states. We also consider a conception of polivariance ontogeny, according to which there are some variants of ontogeny for each element. We deal with one of five types of polivariance, i.e dynamic polivariance. It implies different development rate of populaton elements and original transition from one age state to another.
We used transition matrices obtained from experiments described in detail in paper by Zukova, Komarov (1991). As result we obtained matrices determining a set of transition probabilities or limination for various densities of spacing.
Another question was to evaluate the interaction between plants of various age states.
Evidently, the influence zone of a young plant is much less then that of a mature plant.
We used data of expert stimation.
The variant of the model deals with a simple genetic system that consists of one loci and two alleles. election and mutations are not taken into account.
Plantago major is a partially self-pollinated plant, as it is known that the frequence of self-pollination is 85% (Van Dijk, 1991). The value was taken in our model. The frequency is determined by the species biology and local environs. We separate obligate (determining by species biology, and it is one of the model parameters) and competitive pollination. Competitive pollination consists of cross-pollination and competitive self-pollination. Their ratio defines local environs. The general frequency is a sum of obligate nd competitive self-pollinations.
Actually, during reproduction a pollen cloud from generative plants is formed all over the simulated area. At different points its composition and density are different and depend on local environs strongly.
Assuming that the distribution of pollen is normal and knowing the distances between
plants we can calculate the amount of pollen that attains mother plant and determines
its genetic composition.
Next we determine how many descendants originate from self-pollination. Their number is different in plants of different age states (we introduce a coefficient of differential productivity). Descendant that falls into occupied place or outside the area perishes. Thus we can consider potential and real productivity.
The structure of model is not constant. We intend that further development of the model will be gradually complicated. We plan to elaborate some versions of the model, each can be a task of separate investigation."
Tsiplianovsky, A.M., Glotov, N.V., Zhukova,. A., Komarov, A. S. 1997. Simulation modelling of plant populations on the example of plantain (Plantago major L.). II Open Scientific Conference of Young Scientists of Pushchino. Pushchino 1997. pp 207-208.