Page 129 - Breeding and regulatory opportunities, Renaud

Broccoli crop improvement

4.2.7 Statistical Analysis

Various linear mixed models were used for the analysis of trait variation. Our

approach was comparable to that of Lorenzana and Bernardo (2008). All linear

mixed models were itted in GenStat 15 (VSNi, 2012). The models can be

formulated informally as:

Response = environment + replicate within environment + genotype + genotype

by environment interaction + error

More formally we can write the general form of our mixed models as

y = E + R(E) + G + G × E + e,

with the individual terms in the formal model corresponding to those in the

informal model just above it. Depending on the analysis, the terms included in

E (the environments) varied. For the most general analysis, E contained all main

efects and interactions of Season (S), Location (L) and Management (M). Thus,

in that case

E = S + L + S ×L + M + S ×M + L ×M + S ×L ×M and G ×E = G ×S + G ×L + G ×S

×L + G ×M + G ×S ×M + G ×L ×M + G ×S ×L ×M,

where the combination of S, L and M deined individual trials. The term S

(Season) contained a combination of year (2006, 2007, 2008) and season

within year (spring, fall). Efectively, there were only four year by season within

year combinations included: fall 2006, spring 2007, fall 2007, spring 2008). For

convenience, in our general model, we itted one factor ‘Season’ to cover the four

trialing periods. However, other model formulations are possible. For example,

we can deine a factor ‘Year’ with two levels (level 1 = fall 2006 + spring 2007;

level 2 = fall 2007 + spring 2008) and factor ‘Season’ with two levels (spring,

fall). The main efects of these factors ‘Year’ and ‘Season’ plus their interaction

covers the same variation as the original factor‘Season’with four levels. We used

this second formulation in analysis per location to obtain a more ine grained

interpretation of the variation.

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