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A model of the plant‐to‐plant movement of aphids I. Description of the model
Author(s) -
Shiyomi Masae
Publication year - 1967
Publication title -
population ecology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.819
H-Index - 59
eISSN - 1438-390X
pISSN - 1438-3896
DOI - 10.1007/bf02521396
Subject(s) - biology , probability distribution , probability model , statistics , mathematics
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: The probability that s individuals are found on a plant at time t 0 : Q(s) ; The probability that i individuals leave the plant and remain on the ground from time t 0 to t 1 : s C ip i q s−i and p+q =1, where p and q are the proportions of individuals which do not leave a plant and which leave it once or more, respectively; The probability that j individuals climb a plant between time t 0 to t 1 and stay there at time t 1 :e −λ λ j /λ ! , where λ is the mean of the individuals. The probability that l individuals are located on a plant at time t 1 is represented by the following equation R l = ∑ i = 0 s∑ s = iQ s· sC i p i q s − i ·e − λλ l − il − i ! .It was shown by simple experiments that the experimental populations were well fitted to the model.