The “Crossing-within-Spike-Progeny (CSP) method” is a method to efficiently screen for mutants in allogamous (cross-fertilizing) plants. This paper presents a theoretical analysis of how to minimize the total number of plants in the screening generation (
T) and the total cost (
Tc) required to detect one or more mutants with a given probability when using the CSP method.
Tc depends on the number of plants per line in the screening generation (
n), the number of plants per hill plot in the M
2 generation (
h), the ratio of the cost needed in non-screening generations to that in the screening generation (
W), and the mutation rate per cell (
p1).
T was lowest when
n = 1 (
T = 47.93 ×
p1−1), irrespectively of
h. On the other hand, the value of
n which gave minimum
Tc (designated
n*) was not constant, but varied with
h.
n* was 6 when
h = 2, increased as
h increased, and was 15 when
h = 48, when
W = 10. Unlike in the case of autogamous species, the presence of chimeras in the M
1 inflorescences greatly increased both
T and
Tc. A method for estimating the mutation rate per cell is also presented.
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