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Modelling the branching structure of strawberry inflorescences

This work, which was completed several years ago, was joint with Diana Cole and Byron Morgan at Kent and stemmed from a collaboration with David Taylor, formerly of East Malling Research.

The flowers of the cultivated strawberry occur on branched structures called inflorescences. A single plant may produce several inflorescences during a growing season.

Botanically, the branching structure is a dichasium. The main axis of the inflorescence terminates with a single primary (or rank 1) flower. Two lateral branches emanate from the main axis, each terminating in a rank 2 flower. Similarly, from each of these branches, two further lateral branches arise, each terminating in a rank 3 flower, and so on. Ideally then there is a single rank 1 flower, two rank 2 flowers, four rank 3 flowers and so on.

In practice, not all branches are present and there is considerable variability in the branching structure of different inflorescences. It is unusual to have flowers of rank greater than 5. Inflorescence structure is important agronomically, because the size and weight of the strawberry generally decreases with rank.

Ridout, Morgan and Taylor [3] proposed a model for inflorescence structure in which branching is determined by two parameters, λ and ρ. Let L and R be indicator variables for the presence of the left and right branches from a given parent branch, i.e. L=1 if the left branch is present and L=0 if it is absent; R is defined similarly. Then
λ = Pr(L=1) = Pr(R=1).
and the parameter ρ is the correlation between the binary variables L and R.

In general, the parameters λ and ρ vary with rank and may also depend on the total number of flowers present at the previous rank. There is also evidence that parameter values for the first inflorescence produced by a plant differ from those of subsequent inflorescences [3].

As part of her EPSRC-funded PhD, Diana Cole extended the original model firstly to incorporate covariate effects (e.g. to allow comparisons of varieties) and secondly to incorporate random effects, to model variability in overall vigour between inflorescences. See also Diana's page about this work.

References

Ridout, M.S., Morgan, B.J.T & Taylor, D.R. (1999) Modelling variability in the branching structure of strawberry inflorescences. Applied Statistics, 48, 185-196. [journal link]

Cole, D.J., Morgan, B.J.T. & Ridout, M.S. (2003) Generalized linear mixed models for strawberry data. Statistical Modelling, 3, 273-290. [journal link]

Cole, D.J., Morgan, B.J.T. & Ridout, M.S. (2005) Models for strawberry inflorescence data. Journal of Agricultural, Biological and Environmental Statistics, 10, 411-423. [journal link]