68 Using a Generalized Linear Model to Reveal Spatial Pattern in Plant Reproduction

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We are interested in assessing ~300 maize genes, selected based on genomic data, for mutations that affect the biological fitness of maize pollen. For each gene, a 1:1 mix of mutant and wild-type pollen is crossed onto a non-mutant ear. In an offspring maize ear, any deviation from a 1:1 proportion between wild-type and mutant kernels would suggest that the associated mutation changes the fitness of the pollen. To detect genes that affect fitness, a generalized linear model (GLM) is used to test if mutations significantly deviated from the 1:1 proportion. The model assumes a quasi-binomial distribution to account for variation across maize ears. For the 30 mutations found to reduce fitness, we also investigate the idea that altered pollen fitness will result in a non-uniform spatial distribution of mutant/wild-type kernels on an ear. A spatial analysis using GLM is therefore conducted on each fitness-altering allele to test for non-random spatial patterns of mutant versus wild-type kernels on a maize ear, such as a gradient effect. Consistent with our motivating idea, results identify several alleles that produce a non-random spatial pattern.

Generalized Linear Models

Genotype-phenotype

Quasi-binomial regression

Biological fitness

Spatial Pattern 

Section on Statistics in Genomics and Genetics