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

Summary

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:

• 1) The probability thats individuals are found on a plant at timet ₀:Q(s);

• 2) The probability thati individuals leave the plant and remain on the ground from timet ₀ tot ₁: _s C_ip ⁱq^s−i andp+q=1, wherep andq are the proportions of individuals which do not leave a plant and which leave it once or more, respectively;

• 3) The probability thatj individuals climb a plant between timet ₀ tot ₁ and stay there at timet ₁:e^−λλ^j/λ^!, where λ is the mean of the individuals.

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.