Theoretical Comparison between Mixture and Rotation Cultivations of Disease-resistant Varieties

Abstract

The mixture and rotation cultivations of resistant varieties were theoretically compared as to which more effective usage is for controlling plant disease. They were compared under the standard conditions where yearly increase of lesions of a fungus strain on a given variety at the initial time of infection in a year is according to dy/dτ=yλ, therefore y=y₀e^λτ. A relation between the longevity of rotation cultivation (T) and that of mixture cultivation (T') of given varieties (v) is given by the equation T/T'=vλ_c'/λ_c, where λ_c and λ_c' are the rate of increase of lesions under both cultivations, under given conditions.
Secondly, a relationship between daily rate (r) and yearly rate (λ) of disease increase was studied. When the daily increase of disease is according to the equation y=y₀e^rt or y=y₀e^r(t-t2/2T), their relationship is given by rt_E+log_eθ=λ or r(T/2)+log_eθ=λ, where t_E or T is the terminal stage of infection in a year respectively and θ is the rate of overwintering.
It was emphasized that the nature of daily increase of disease is necessary to be analyzed especially in relation to the presence or absence of density effect, in order to know the relationship.
The data on cumulative spore numbers at Toyoshina, Nagano Prefecture show that there is no or a little density effect in disease increase at that conditions.