The chosen method for selecting items using the limma package: "quadratic" for 
a quadratic trend test on dose ranks, "linear" for a linear trend test on dose 
ranks and "ANOVA" for an ANOVA-type test.

The ANOVA_based test ("ANOVA") is classically used for selection of omics data 
in the general case but it requires many replicates per dose to be efficient, 
and is thus not really suited for a dose-response design.

The linear trend test ("linear") aims at detecting monotonic trends from
dose-response designs, whatever the number of replicates per dose. 
As proposed by Tukey (1985), it tests the global significance of a linear 
model describing the response as a function of the dose in rank-scale.

The quadratic trend test ("quadratic") tests the global significance of a 
quadratic model describing the response as a function of the dose in rank-scale. 
It is a variant of the linear trend method that aims at detecting monotonic and 
non monotonic trends from a dose-response designs, whatever the number of 
replicates per dose (default chosen method).

We recommend the use of the latter for selecting both monotonic
and biphasic trends form a dose-response design (see Larras et al., 2018).

For details, see 

Tukey JW, Ciminera JL and Heyse JF (1985).
Testing the statistical certainty of a response to increasing doses of a drug. 
Biometrics, 295-301.

Larras F, Billoir E, Baillard V, Siberchicot A, Scholz S, Wubet T, Tarkka M,
Schmitt-Jansen M and Delignette-Muller ML (2018). DRomics: a turnkey tool to 
support the use of the dose-response framework for omics data in ecological 
risk assessment. Environmental science & technology.