A model of the plant-to-plant movement of aphids I. Description of the model

The plant-to-plant movement of insects in one of the factors determining the distribution of individuals in insect populations. In this report the movement of barley aphids was analyzed by a statistical model. The model is represented as the convolution of three probability functions: The probability thatl individuals are located on a plant at timet 1 is represented by the following equation $$R\left( l \right) = \sum\limits_{i = 0}^s {\sum\limits_{s = i} {Q\left( s \right)} \cdot _s } C_i p^i q^{s - i} \cdot \frac{{e^{ - \lambda } \lambda ^{l - i} }}{{\left( {l - i} \right)!}}.$$ It was shown by simple experiments that the experimental populations were well fitted to the model.