In priviere/PPBstats: An R package to perform analysis found within PPB programmes

Study reponse to selection {#response-to-selection}

For a given trait, selection differential corresponds to the difference between mean of the selected spikes and mean of the bulk (i.e. spikes that have not been selected). Response to selection correponds to the difference between mean of spikes coming from the selected spikes and the spikes coming from the bulk (Figure \@ref(fig:SR)). Selection differential ($S$) and response to selection ($R$) are linked with the realized heritability ($h^2_r$): $R = h^2_r \times S$.

knitr::include_graphics("figures/SandR_EN-7.png")

Workflow and function relations in PPBstats regarding response to selection analysis

Figure \@ref(fig:main-workflow-family-4-SR) displays the functions and their relationships. Table \@ref(tab:function-descriptions-workflow-family-4-SR) describes each of the main functions.

You can have more information for each function by typing ?function_name in your R session.

knitr::include_graphics("figures/main-functions-agro-family-4-SR.png")

| function name | description | | --- | --- | | design_experiment | Provides experimental design for the different situations corresponding to the choosen family of analysis | | format_data_PPBstats | Check and format the data to be used in PPBstats functions | | plot | Build ggplot objects to visualize output | Table: (#tab:function-descriptions-workflow-family-4-SR) Function description.

Steps with PPBstats

To study response to selection, you can follow three steps (Figure \@ref(fig:main-workflow-family-4-SR)):

Format the data with format_data_PPBstats()
Describe the data with plot()
Get mean comparison from family 1's model as explained in section \@ref(family-1) by
running the model
get mean comparisons
use plot()

Format data

In this section, the data set used is coming from data_model_GxE (section \@ref(ammi)) with three dedicated columns:

group which represents differential selection (S) or reponse to selection (R)
version which represents bouquet or vrac.
expe_id: an id with
- S couple and R couple (i.e. four rows) OR
- S couple (i.e. two rows) OR
- R couple (i.e. two rows)

expe_id is useful for example if there are several selection in one germplasm or if there are several origin for a given germplasm.

Describe and get mean comparison from family 1's model

For all model, stars on a pair of entries corresponds to the pvalue:

| pvalue | stars | | --- | --- | | $< 0.001$ | * | | $[0.001 , 0.05]$ | | | $[0.05 , 0.01]$ | * | | $> 0.01$ | . |

Classic anova model

To Do !!!

#data(data_agro_SR_1)
#data_agro_SR_1 = format_data_PPBstats(data_agro_SR_1, type = "data_agro_SR")

Spatial analysis model

To Do !!!

#data(data_agro_SR_2)
#data_agro_SR_2 = format_data_PPBstats(data_agro_SR_2, type = "data_agro_SR")

Mixed model for incomplete block design

To Do !!!

#data(data_agro_SR_3)
#data_agro_SR_3 = format_data_PPBstats(data_agro_SR_3, type = "data_agro_SR")

Hierarchical Bayesian intra-location model

data(data_agro_SR_4)
data_agro_SR_4 = format_data_PPBstats(data_agro_SR_4, type = "data_agro_SR")
head(data_agro_SR_4)

First, describe the data.

p = plot(data_agro_SR_4, vec_variables = "tkw", plot_type = "barplot")

The plot has two lists: - one for each id where each element of the list is an expe_id. - one on post hoc analysis with all couple S (election differential) and R (response to selection) where each element of the list refer to germplasm, location or year

p$tkw$analysis_for_each_id$id_1

p$tkw$post_hoc_analysis$germplasm

In addition, the realized heritability ($h^2_r$: $R = h^2_r \times S$) can be displayed.

p = plot(data_agro_SR_4, vec_variables = "tkw", plot_type = "barplot", heritability = TRUE)

p$tkw$analysis_for_each_id$id_1

p$tkw$post_hoc_analysis$germplasm

In order to add significance differences from the Hierarchical Bayesian intra-location model presented in section \@ref(model-1), the argument mean_comparisons must be filled with the output of mean_comparisons of the model.

The pvalue is computed as describe in Section \@ref(mean-comp-bayes) if the parameters have been estimated with the model.

load("./data_PPBstats/out_mean_comparisons_model_bh_intra_location_mu.RData") # To save time
p = plot(data_agro_SR_4,
         mean_comparison = out_mean_comparisons_model_bh_intra_location_mu, 
         vec_variables = "tkw",
         plot_type = "barplot")
p$tkw$analysis_for_each_id$id_1

For environments where MCMC did not converge or without environments, it is a \@ref(t.test) which is perform when there are more than 1 obervation for a given seed lot.