03_interacao.qmd

---
title: "03: Adaptabilidade e estabilidade de genótipos experimentais de linhaça cultivados em ambientes contrastantes de Santa Catarina"
---

```{r global_options, include = FALSE}
knitr::opts_chunk$set(cache = FALSE,
                      comment = "##",
                      collapse = TRUE,
                      warning = FALSE,
                      message = FALSE)

```



# Pacotes

```{r warning=FALSE, message=FALSE}
library(rio)
library(tidyverse)
library(metan)
library(ggridges)
library(ggthemes)
library(patchwork)

df <- import_list("data/progresso.xlsx")
g2022 <- df$`2022` |> select(GEN, RGPLA) |> rename(A2022 = RGPLA)
g2023 <- df$`2023` |> select(GEN, RGPLA) |> rename(A2023 = RGPLA)
g2024 <- df$`2024` |> select(GEN, RGPLA) |> rename(A2024 = RGPLA)


dfge <- 
  reduce(list(g2024, g2023, g2022), left_join) |> 
  remove_rows_na()

df_ggplot <- 
  dfge |> 
  pivot_longer(-GEN, names_to = "AMB", values_to = "RGPLA")
```


# Exploração
```{r}
p0 <- ge_plot(df_ggplot, AMB, GEN, RGPLA)
```


# Interação genótipo ambiente

$$
y_{ij} = m + g_i + a_j + (ga)_{ij}
$$

$$
\hat{g_i} = \bar{g_i} - m  \\
\hat{a_j} = \bar{a_j} - m  
$$
$$
\hat{(ga)_{ij}} = y_{ij} - m - \hat{g_i} - \hat{a_j} \\
\hat{(ga)_{ij}} = y_{ij} - \bar{g_i} - \bar{a_j} + m
$$


```{r}
gemat <- 
  dfge |> 
  column_to_rownames("GEN") |> 
  as.matrix()


m <- mean(gemat)
geef <- matrix(NA, nrow = nrow(gemat), ncol = ncol(gemat))
rownames(geef) <- rownames(gemat)
colnames(geef) <- colnames(gemat)

for(j in 1:ncol(geef)){
  for(i in 1:nrow(geef)){
    mg1 <- mean(gemat[i, ])
    ma1 <- mean(gemat[, j])
    # Calcular efeitos
    efg1 <- mg1 - m
    efa1 <- ma1 - m
    geef[i, j] <- gemat[i, j] - m - efg1 - efa1
  }
}


heatmap(geef)
geef |> 
  as.data.frame() |> 
  rownames_to_column("GEN") |> 
  pivot_longer(-GEN) |> 
  ge_plot(name, GEN, value)


```


# Análise AMMI

$$
y_{ij} = m + g_i + a_j + \sum_{i=1}^{k}{\lambda_k\tau_{ik}\omega_{jk}}
$$


```{r}

# Decomposição por valor singular
s <- svd(geef)
d <- s$d[1:2]
u <- s$u[, 1:2]
v <- s$v[, 1:2]

# retorna a matriz dos efeitos da interação
u %*% diag(d) %*% t(v)

# escores dos genótipos
escoregen <- 
  u %*% sqrt(diag(d)) |> 
  as.data.frame() |> 
  mutate(code = rownames(geef),
         tipo = "gen") |> 
  rename(IPCA1 = V1, IPCA2 = V2)

# escores dos ambientes
escoreamb <- v %*% sqrt(diag(d)) |> 
  as.data.frame() |> 
  mutate(code = colnames(geef),
         tipo = "amb") |> 
  rename(IPCA1 = V1, IPCA2 = V2)

dfplot <- bind_rows(escoregen, escoreamb)

library(ggrepel)
p1 <- 
  ggplot(dfplot, aes(IPCA1, IPCA2, color = tipo)) + 
  geom_vline(xintercept = 0) +
  geom_hline(yintercept = 0) +
  geom_text_repel(aes(label = code)) +
  geom_point() +
  theme_minimal() +
  geom_segment(aes(x = 0, y = 0,
                   xend = IPCA1,
                   yend = IPCA2),
               data = dfplot |> filter(tipo == "amb"),
               arrow = arrow(length = unit(0.1, "inches")))


p0 + p1
```



# Adaptabilidade
## Método WAAS
OLIVOTO, T. et al. Mean Performance and Stability in Multi‐Environment Trials I: Combining Features of AMMI and BLUP Techniques. Agronomy Journal, v. 111, n. 6, p. 2949–2960, 2019. 


```{r}
explicacao <- d^2 / sum(d^2)
dfplot
## WAAS G1
(0.296928317 * 0.7554673) + (0.12003188 * 0.2445327)

# computar as médias dos genótipos e ambientes

mg <- 
  df_ggplot |> 
  group_by(GEN) |> 
  summarise(RGPLA = mean(RGPLA)) |> 
  rename(code = GEN)
ma <- 
  df_ggplot |> 
  group_by(AMB) |> 
  summarise(RGPLA = mean(RGPLA)) |> 
  rename(code = AMB)

waas <- 
  dfplot |> 
  rowwise() |> 
  mutate(WAAS = weighted.mean(abs(c_across(IPCA1:IPCA2)), w = explicacao)) |> 
  left_join(bind_rows(mg, ma))

# média versus estabilidade
ggplot(waas, aes(RGPLA, WAAS, color = tipo)) +
  geom_point() +
  geom_hline(aes(yintercept = mean(WAAS))) +
  geom_vline(aes(xintercept = mean(RGPLA))) +
    geom_text_repel(aes(label = code))
```





# Estabilidade
## Método Wricke

WRICKE, G. Zur Berechnung der Ökovalenz bei Sommerweizen und Hafer. Zeitschrift für Pflanzenzüchtung, v.52, p.127-138, 1965.

```{r}

```




# Section info
```{r}
sessionInfo()
```