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Modelling multigenic resistance to potato cyst nematodes
Author(s) -
JONES F. G. W.
Publication year - 1985
Publication title -
eppo bulletin
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.327
H-Index - 36
eISSN - 1365-2338
pISSN - 0250-8052
DOI - 10.1111/j.1365-2338.1985.tb00216.x
Subject(s) - gene , biology , resistance (ecology) , population , genetics , r gene , plant disease resistance , ecology , demography , sociology
After making simplifying assumptions, the ability of female potato cyst nematodes to develop and reproduce is modelled by expressions of the type i x · x and i x ·(1 ‐ x ), where x is the frequency within a population of females able to circumvent the effects of a real resistance gene. Such females are potentially able to develop to maturity and reproduce to maximum capacity. For this class of females i x = 1, i.e. they are unaffected by the resistance gene. The frequency of other classes of females is given by (1 ‐ x ) and for them i x ranges in value from just less than 1 to 0 according to the effectiveness of the gene. When i x approaches 0, females in these classes are eliminated and the gene responsible is said to be a ‘major’ resistance gene. For values of i x greater than 0, the genes responsible are called ‘minor’ genes. If full reproductive power is 1, then the total reproductive power in the presence of the resistance gene is [ x + i x (1 ‐ x )] or when several genes are present by [ x + i x (1 ‐ x)]·[ y + i y (1 ‐ y )]·[ z + i z (1 ‐ z )] etc. That is, the effects of these genes depend on the frequencies of females able to reproduce in their presence and on the effectiveness of the different genes as measured by i. Furthermore, ‘major’ and ‘minor’ genes are part of a continuum described by i. The model is used to illustrate the effects of combining ‘major’ and ‘minor’ genes and the effects of some arbitrary combinations are calculated. Data with which to test the model are sparse but what little there is tends to support it. Interactions between resistance genes, the fitness of females, the selection of males and the effects of resistant cultivars on populations are discussed. Selection by resistant potato hybrids in pots is surprisingly rapid and sometimes becomes evident after only five generations. Ways in which resistant cultivars might be used to prolong the useful life of resistant cultivars are briefly discussed.