• optimizing program size

• run multiple cohorts

• recycling parents earlier

• use selection index for multi-trait selection

• evaluation strategy and optimal integration of GS/GP efforts (product development vs population improvement)

For \(k\) traits, a linear index takes the form:

\[ I = w_1 \times t_1 + w_2 \times t_2 + \ldots + w_k \times t_k \]

where:

• \(w_i\) is the weight for trait \(i\)

• \(t_i\) is the phenotypic value for trait \(i\).

\[ I = \mathbf{w}^{T}\mathbf{t} \]

• base index: \(\mathbf{w}=\mathbf{a}\), where \(\mathbf{a}\) is the \(k\)-dimensional vector of economic weights

• retrospective index: \(\mathbf{w}=\mathbf{P}^{-1}\mathbf{s}\), where \(\mathbf{P}\) is the phenotypic variance-covariance matrix and \(\mathbf{s}\) the observed selection differential

• Smith-Hazel index: \(\mathbf{w}=\mathbf{P}^{-1}\mathbf{G}\,\mathbf{a}\), where \(\mathbf{G}\) is the genotypic variance-covariance matrix

Weights for three scenarios depending on different sets of traits used for retrospective index:

• S1: Breeder priority traits
• S2: Breeder priority traits with non-adjusted values
• S3: All traits

sw2 <- read.csv("./data/weights_in_sunits.csv")
sw <- cbind(sw[, 2:4], sw2[, 3:5])
colnames(sw) <- c("w S1", "w S2", "w S3", "w S1 (su)", "w S2 (su)", "w S3 (su)")
rownames(sw) <- c("AUDPC", "MTYA", "TTYA", "MTYNA", "TTYNA", "DM",
             "Tuber Uniformity", "Tuber Appareance", "Tuber Size")
sw %>%
  kbl() %>%
  kable_paper("hover", full_width = F)

su: In standardized units

Common selected genotypes (out of 500):

temp <- data.frame(Scenario = c("S1: Breeder priority",
                                "S2: Breeder priority non-adjusted",
                                "S3: All traits"),
                   csg.num = csg.num)
colnames(temp)[2] <- "Common genotypes"
temp %>%
  kbl() %>%
  kable_paper("hover", full_width = F)

Observed means for total population (2748) and for selected fraction (500 best) under different scenarios

temp <- sdm[, c(1, 2, 4, 6, 8)]
colnames(temp) <- c("Means total", "Means BS", "Means S1", "Means S2", "Means S3")
temp %>%
  kbl() %>%
  kable_paper("hover", full_width = F)

temp <- sdm[, c(1, 3, 5, 7, 9)]
colnames(temp) <- c("Means total", "Sel. Dif. BS", "Sel. Dif. S1", "Sel. Dif. S2", "Sel. Dif. S3")
temp %>%
  kbl() %>%
  kable_paper("hover", full_width = F)

temp <- d[, c("index.bp", "Selected")]
temp$Group <- "Population"
colnames(temp)[1] <- "Index"

temp1 <- temp[temp$Selected == "S" & !is.na(temp$Selected), ]
temp1$Group <- "Selected"
temp <- rbind(temp, temp1)

ggplot(temp, aes(x = Group, y = Index)) +
  geom_dotplot(binaxis = "y", binwidth = .03, stackdir = "center")

df <- data.frame(Trait = rep(rownames(sdm), 2),
                 Selection = c(rep("Breeder selection", 9),
                               rep("Breeder priority index", 9)),
                 value = c(sdm$dif.bs, sdm$dif.bp)
)

ggplot(df, aes(fill = Selection, y = value, x = Trait)) +
  geom_bar(position = "dodge", stat = "identity") +
  ylab("Selection differential %")

• Determine strategy on how and where to apply index selection

• Perform simulations to choose optimal index
  \(\rightarrow\) fine tune index weights (input breeders needed)

• Implement other quick wins in this pipeline?

• Repeat analysis with other pipelines