From my 28D3 F4s, (red cherries) none have the gf phenotype. What are the odds that any are gf/+ and thus might have some gf/gf progeny next year? Bayesian analysis to the rescue...
The F1 plant was gf/+. F2 plant 28D was not gf phenotype; therefore it's prior probability of being gf/+ was 2/3. Four F3 plants were grown last year; none had gf phenotype either. 28D3 was one of these. What are the odds that 28D3 still could be a gf/+ carrier?
Hypothesis
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Assume F3 = carrier
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Assume F3 = non-carrier
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Prior
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4/9
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5/9
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Conditional
(prob that all 3 F4s are
non-carriers)
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27/64
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1
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joint
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0.141
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5/9
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posterior
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(0.141)/(0.141)+(5/9)=0.202
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Therefore the posterior probability that the F3 plant, 28D3, was a gf/+ carrier is 0.202.
Given this, the probability that any particular one of the 28D3 F4 plants is also a gf/+ carrier is = 0.202 x 2/3, or ~ 0.135 = 13.5%.
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