# Summary

The gosset package provides a set of tools and methods to implement a workflow to analyse experimental agriculture data, from data synthesis to model selection and visualisation. The package is named after W.S. Gosset aka ‘Student’, a pioneer of modern statistics in small sample experimental design and analysis.

In this example we show one of the possible workflows to assess trait prioritization and crop performance using decentralized on-farm data generated with the tricot approach [1]. We use the nicabean data. This dataset was generated with decentralized on-farm trials of common bean (Phaseolus vulgaris L.) varieties in Nicaragua over five seasons (between 2015 and 2016). Following the tricot approach [1], farmers were asked to test in their farms three varieties of common bean. The varieties were randomly assigned as incomplete blocks of size three (out of 10 varieties). The farmers assessed which of the three varieties had the best and worst performance in eight traits (vigor, architecture, resistance to pests, resistance to diseases, tolerance to drought, yield, marketability, and taste). The farmers also provided their overall appreciation about the varieties, i.e., which variety had the best and the worst performance based on the overall performance considering all the traits.

Here we use the Plackett-Luce model, jointly proposed by Luce (1959) [2] and Plackett (1975) [3]. This model estimates the probability of one variety outperforming all the others (worth) in the trait based on the Luce’s axiom[2]. The model is implemented in R by Turner et al. (2020) with the package PlackettLuce [4].

The nicabean is a list with two data frames. The first, trial, contains the trial data with farmers’ evaluations, ranked from 1 to 3, with 1 being the higher ranked variety and 3 the lowest ranked variety for the given trait and incomplete block. The rankings in this dataset were previously transformed from tricot rankings (where participants indicate best and worst) to ordinal rankings using the function rank_tricot(). The second data frame, covar, contains the covariates associated to the on-farm trial plots and farmers. This example will require the packages PlackettLuce [4], climatrends [5], chirps [6] and ggplot2 [7].

library("gosset")
library("PlackettLuce")
library("climatrends")
library("chirps")
library("ggplot2")

data("nicabean", package = "gosset")

dat <- nicabean$trial covar <- nicabean$covar

traits <- unique(dat$trait) dat ## id item trait rank ## <int> <chr> <chr> <int> ## 1: 2110 Amadeus 77 Vigor 2 ## 2: 2110 IBC 302-29 Vigor 3 ## 3: 2110 INTA Ferroso Vigor 1 ## 4: 2110 Amadeus 77 Architecture 3 ## 5: 2110 IBC 302-29 Architecture 2 ## --- ## 15035: 3552 INTA Centro Sur Taste 3 ## 15036: 3552 BRT 103-182 Taste 2 ## 15037: 3552 IBC 302-29 OverallAppreciation 2 ## 15038: 3552 INTA Centro Sur OverallAppreciation 3 ## 15039: 3552 BRT 103-182 OverallAppreciation 1 To start the analysis of the data, we transform the ordinal rankings into Plackett-Luce rankings (a sparse matrix) using the function rank_numeric(). We run iteratively over the traits adding the rankings to a list called R. Since the varieties are ranked in an ascending order, with 1 being the higher ranked and 3 the lower ranked, we use the argument asceding = TRUE to indicate which order should be used. R <- vector(mode = "list", length = length(traits)) for (i in seq_along(traits)) { dat_i <- subset(dat, dat$trait == traits[i])

R[[i]] <- rank_numeric(data = dat_i,
items = "item",
input = "rank",
id = "id",
ascending = TRUE)
}

# The multi-layers of farmers’ overall appreciation

Using the function kendallTau() we can compute the Kendall tau ($$\tau$$) coefficient [8] to identify the correlation between farmers’ overall appreciation and the other traits in the trial. This approach can be used, for example, to assess the drivers of farmers choices or to prioritize traits to be tested in a next stage of tricot trials (e.g. a lite version of tricot with no more than 4 traits to assess). We use the overall appreciation as the reference trait, and compare the Kendall tau with the other 8 traits.

baseline <- which(grepl("OverallAppreciation", traits))

kendall <- lapply(R[-baseline], function(X){
kendallTau(x = X, y = R[[baseline]])
})

kendall <- do.call("rbind", kendall)

kendall$trait <- traits[-baseline] The kendall correlation shows that farmers prioritized the traits yield ($$\tau$$ = 0.749), taste ($$\tau$$ = 0.653) and marketability ($$\tau$$ = 0.639) when assessing overall appreciation. ## trait kendallTau ## <chr> <dbl> ## 1: Vigor 0.439 ## 2: Architecture 0.393 ## 3: ResistanceToPests 0.463 ## 4: ResistanceToDiseases 0.449 ## 5: ToleranceToDrought 0.411 ## 6: Yield 0.749 ## 7: Marketability 0.639 ## 8: Taste 0.653 # Performance of varieties across traits For each trait, we fit a Plackett-Luce model using the function PlackettLuce() from the package of the same name. This will allow us to continue the analysis of the trial data using the other functions in the package gosset. mod <- lapply(R, PlackettLuce) The worth_map() function can be used to visually assess and compare item performance based on different characteristics. The values represented in a worth_map are log-worth estimates. From the breeder or product developer perspective the function worth_map() offers a visualization tool to help in identifying item performance based on different characteristics and select crossing materials. worth_map(mod[-baseline], labels = traits[-baseline], ref = "Amadeus 77") + labs(x = "Variety", y = "Trait") # The effect of rainfall on yield To consider the effect of climate factors on yield, we use agro-climatic covariates to fit a Plackett-Luce tree. For simplicity, we use the total rainfall (Rtotal) derived from CHIRPS data [9], obtained in R using the R package chirps [6]. Additional covariates can be used in a Plackett-Luce tree, for example using temperature data from R package ag5Tools [10] or nasapower [11]. We request the CHIRPS data using the package chirps. Data should be returned as a matrix. This process can take some minutes to be implemented. dates <- c(min(covar[, "planting_date"]), max(covar[, "planting_date"]) + 70) chirps <- get_chirps(covar[, c("longitude","latitude")], dates = as.character(dates), as.matrix = TRUE, server = "ClimateSERV") We compute the rainfall indices from planting date to the first 45 days of plant growth using the function rainfall() from package climatrends [5]. newnames <- dimnames(chirps)[[2]] newnames <- gsub("chirps-v2.0.", "", newnames) newnames <- gsub("[.]", "-", newnames) dimnames(chirps)[[2]] <- newnames rain <- rainfall(chirps, day.one = covar$planting_date, span = 45)

To be linked to covariates, the rankings should be coerced to a ‘grouped_rankings’ object. For this we use the function group() from PlackettLuce. We retain the ranking corresponding to yield.

yield <- which(grepl("Yield", traits))

G <- group(R[[yield]], index = 1:length(R[[yield]]))

head(G)
##                      1                      2                      3
## "INTA Ferroso > I ..." "BRT 103-182 > IB ..." "INTA Ferroso > I ..."
##                      4                      5                      6
## "BRT 103-182 > IB ..." "BRT 103-182 > IB ..." "BRT 103-182 > AL ..."

Now we can fit the Plackett-Luce tree with climate covariates.

pldG <- cbind(G, rain)

tree <- pltree(G ~ Rtotal, data = pldG, alpha = 0.1)

print(tree)
## Plackett-Luce tree
##
## Model formula:
## G ~ Rtotal
##
## Fitted party:
## [1] root
## |   [2] Rtotal <= 193.8153: n = 393
## |            ALS 0532-6      Amadeus 77     BRT 103-182      IBC 302-29 INTA Centro Sur
## |             0.0000000       0.6269536       0.7018178       0.6510282       0.5419017
## |          INTA Ferroso  INTA Matagalpa     INTA Precoz      SJC 730-79    SX 14825-7-1
## |             0.3993557       0.3775061       0.3858863       0.4045355       0.6933340
## |   [3] Rtotal > 193.8153: n = 164
## |            ALS 0532-6      Amadeus 77     BRT 103-182      IBC 302-29 INTA Centro Sur
## |             0.0000000      -0.5307674      -0.6414091      -0.9089877      -0.5821163
## |          INTA Ferroso  INTA Matagalpa     INTA Precoz      SJC 730-79    SX 14825-7-1
## |            -1.1910556      -0.6922428      -0.8152149      -0.5724198      -0.2688304
##
## Number of inner nodes:    1
## Number of terminal nodes: 2
## Number of parameters per node: 10
## Objective function (negative log-likelihood): 977.2531

The following is an example of the plot made with the function plot() in the gosset package. The functions node_labels(), node_rules() and top_items() can be used to identify the splitting variables in the tree, the rules used to split the tree and the best items in each node, respectively.

node_labels(tree)
## [1] "Rtotal"
node_rules(tree)
##   node                      rules
## 1    2 Rtotal <= 193.815301895142
## 2    3  Rtotal > 193.815301895142
top_items(tree, top = 3)
##          Node2        Node3
## 1  BRT 103-182   ALS 0532-6
## 2 SX 14825-7-1 SX 14825-7-1
## 3   IBC 302-29   Amadeus 77
plot(tree, ref = "Amadeus 77", ci.level = 0.9)

# Reliability of superior genotypes

We can use the function reliability() to compute the reliability of the evaluated common bean varieties in each of the resulting nodes of the Plackett-Luce tree (Table 3). This helps in identifying the varieties with higher probability to outperform a variety check (Amadeus 77) [12]. For simplicity, we present only the varieties with reliability $$\geq$$ 0.5.

reliability(tree, ref = "Amadeus 77")
##      node         item reliability reliabilitySE worth
##     <int>        <chr>       <dbl>         <dbl> <dbl>
## 2:      2   Amadeus 77       0.500         0.035 0.114
## 3:      2  BRT 103-182       0.519         0.036 0.123
## 4:      2   IBC 302-29       0.506         0.035 0.117
## 10:     2 SX 14825-7-1       0.517         0.033 0.122
## 11:     3   ALS 0532-6       0.630         0.056 0.177
## 12:     3   Amadeus 77       0.500         0.058 0.104
## 20:     3 SX 14825-7-1       0.565         0.053 0.135

The result shows that three varieties can marginally outperform Amadeus 77 under drier growing conditions (Rtotal $$\leq$$ 193.82 mm) whereas two varieties have a superior yield performance when under higher rainfall conditions (Rtotal $$>$$ 193.82 mm) compared to the reference. This approach helps in identifying superior varieties for different target population environments. For example, the variety ALS 0532-6 shows weak performance in the whole yield ranking, however for the sub-group of higher rainfall, the variety outperforms all the others. Combining rankings with socio-economic covariates could also support the identification of superior materials for different market segments.

# Going beyond yield

A better approach to assess the performance of varieties can be using the ’Overall Appreciation”, since we expect this trait to capture the performance of the variety not only for yield, but for all the other traits prioritized by farmers (Table 2). To support this hypotheses, we use the function compare() which applies the approach proposed by Bland and Altman (1986) [13] to assess the agreement between two different measures. We compare overall vs yield. If both measures completely agree, all the varieties should be centered to 0 in the axis Y.

Overall <- PlackettLuce(R[[baseline]])
Yield <- PlackettLuce(R[[yield]])

compare(Overall, Yield) +
labs(x = "Average log(worth)",
y = "Difference (Overall Appreciation - Yield)")