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■ Quantifying Phenotypic Plasticity of Crops

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In my previous posts, I explained how to quantify phenotypic plasticity of crops in response to environmental factors, and introduced the concept of responsiveness, calculated using the formula: (Treatment - Control) / Control, as shown in the table below.

Genotype	Control	Treatment	Responsiveness
A	100	90	-10.0% = (90-100)/100
B	120	70	-41.7%
C	115	90	-21.7%
D	95	85	-10.5%
E	110	105	-4.5%

While calculating responsiveness for a single variable is relatively straightforward, it becomes more complex when grouping is involved—for example, calculating nitrogen responsiveness across different genotypes under various fungicide treatments. Performing such analyses by manually sorting and calculating in Excel can be time-consuming and error-prone.

To address this, I recently developed an R package called deltactrl. This package enables users to calculate responsiveness efficiently and consistently across multiple variables and grouping structures.

Here is one dataset.

if(!require(remotes)) install.packages("readr")
library(readr)

github="https://raw.githubusercontent.com/agronomy4future/raw_data_practice/main/fertilizer_treatment.csv"
df= data.frame(read_csv(url(github),show_col_types = FALSE))

head(df,5)
    Genotype Block variable value
1 Genotype_A     I  Control  42.9
2 Genotype_A    II  Control  41.6
3 Genotype_A   III  Control  28.9
4 Genotype_A    IV  Control  30.8
5 Genotype_B     I  Control  53.3
.
.
.

tail(df,5)
     Genotype Block    variable value
60 Genotype_C    IV Fertilizer3  51.8
61 Genotype_D     I Fertilizer3  71.6
62 Genotype_D    II Fertilizer3  69.4
63 Genotype_D   III Fertilizer3  56.6
64 Genotype_D    IV Fertilizer3  47.4

This data has two treatments (Genotype and Fertilizer) with 4 replicates.

xtabs(~variable + Genotype, data=df)

             Genotype
variable      Genotype_A Genotype_B Genotype_C Genotype_D
  Control              4          4          4          4
  Fertilizer1          4          4          4          4
  Fertilizer2          4          4          4          4
  Fertilizer3          4          4          4          4

This graph represents the dataset.

If we calculate responsiveness, we can omit the Control from the graph. The responsiveness metric will indicate how yields at different fertilizer levels deviate from the Control.

■ deltactrl package

First, let’s load the necessary library.

if(!require(remotes)) install.packages("remotes")
if (!requireNamespace("deltactrl", quietly = TRUE)) {
remotes::install_github("agronomy4future/deltactrl", force= TRUE)
}
library(remotes)
library(deltactrl)

After loading the library, you can type ?deltactrl to view the details about the function.

I will calculate responsiveness by grouping the data by genotype, using the ‘Control’ level in the ‘variable’ column as the baseline. The basic code structure will be as follows:

df2= deltactrl(
  data= df,
  group_vars= c("Genotype"),
  treatment_var= variable,
  control_label= Control,
  response_vars= c("value")
)

print(df2, n = Inf)
   Genotype   Block variable    value responsive_value
 1 Genotype_A I     Control      42.9          NA     
 2 Genotype_A II    Control      41.6          NA     
 3 Genotype_A III   Control      28.9          NA     
 4 Genotype_A IV    Control      30.8          NA     
 5 Genotype_B I     Control      53.3          NA     
 6 Genotype_B II    Control      69.6          NA     
 7 Genotype_B III   Control      45.4          NA     
 8 Genotype_B IV    Control      35.1          NA     
 9 Genotype_C I     Control      62.3          NA     
10 Genotype_C II    Control      58.5          NA     
11 Genotype_C III   Control      44.6          NA     
12 Genotype_C IV    Control      50.3          NA     
13 Genotype_D I     Control      75.4          NA     
14 Genotype_D II    Control      65.6          NA     
15 Genotype_D III   Control      54            NA     
16 Genotype_D IV    Control      52.7          NA     
17 Genotype_A I     Fertilizer1  53.8           0.492 
18 Genotype_A II    Fertilizer1  58.5           0.623 
19 Genotype_A III   Fertilizer1  43.9           0.218 
20 Genotype_A IV    Fertilizer1  46.3           0.284 
21 Genotype_B I     Fertilizer1  57.6           0.133 
22 Genotype_B II    Fertilizer1  69.6           0.369 
23 Genotype_B III   Fertilizer1  42.4          -0.166 
24 Genotype_B IV    Fertilizer1  51.9           0.0206
25 Genotype_C I     Fertilizer1  63.4           0.176 
26 Genotype_C II    Fertilizer1  50.4          -0.0654
27 Genotype_C III   Fertilizer1  45            -0.166 
28 Genotype_C IV    Fertilizer1  46.7          -0.134 
29 Genotype_D I     Fertilizer1  70.3           0.135 
30 Genotype_D II    Fertilizer1  67.3           0.0868
31 Genotype_D III   Fertilizer1  57.6          -0.0698
32 Genotype_D IV    Fertilizer1  58.5          -0.0553
33 Genotype_A I     Fertilizer2  49.5           0.373 
34 Genotype_A II    Fertilizer2  53.8           0.492 
35 Genotype_A III   Fertilizer2  40.7           0.129 
36 Genotype_A IV    Fertilizer2  39.4           0.0929
37 Genotype_B I     Fertilizer2  59.8           0.176 
38 Genotype_B II    Fertilizer2  65.8           0.294 
39 Genotype_B III   Fertilizer2  41.4          -0.186 
40 Genotype_B IV    Fertilizer2  45.4          -0.107 
41 Genotype_C I     Fertilizer2  64.5           0.196 
42 Genotype_C II    Fertilizer2  46.1          -0.145 
43 Genotype_C III   Fertilizer2  62.6           0.161 
44 Genotype_C IV    Fertilizer2  50.3          -0.0672
45 Genotype_D I     Fertilizer2  68.8           0.111 
46 Genotype_D II    Fertilizer2  65.3           0.0545
47 Genotype_D III   Fertilizer2  45.6          -0.264 
48 Genotype_D IV    Fertilizer2  51            -0.176 
49 Genotype_A I     Fertilizer3  44.4           0.232 
50 Genotype_A II    Fertilizer3  41.8           0.160 
51 Genotype_A III   Fertilizer3  28.3          -0.215 
52 Genotype_A IV    Fertilizer3  34.7          -0.0374
53 Genotype_B I     Fertilizer3  64.1           0.261 
54 Genotype_B II    Fertilizer3  57.4           0.129 
55 Genotype_B III   Fertilizer3  44.1          -0.133 
56 Genotype_B IV    Fertilizer3  51.6           0.0147
57 Genotype_C I     Fertilizer3  63.6           0.179 
58 Genotype_C II    Fertilizer3  56.1           0.0403
59 Genotype_C III   Fertilizer3  52.7          -0.0227
60 Genotype_C IV    Fertilizer3  51.8          -0.0394
61 Genotype_D I     Fertilizer3  71.6           0.156 
62 Genotype_D II    Fertilizer3  69.4           0.121 
63 Genotype_D III   Fertilizer3  56.6          -0.0860
64 Genotype_D IV    Fertilizer3  47.4          -0.235 

The responsiveness relative to the Control was calculated for each genotype. Now, let’s create a figure to visualize the results. First, the data needs to be summarized to generate a bar graph.

df3= data.frame(subset (df2, variable!="Control") %>%
                    group_by(Genotype, variable) %>%
                    dplyr::summarize(across(c(responsive_value), 
                                            .fns= list(Mean=~mean(., na.rm= TRUE), 
                                                       SD= ~sd(., na.rm= TRUE), 
                                                       n=~length(.),
                                                       se=~sd(.,na.rm= TRUE) / sqrt(length(.))))))

print(df3)
     Genotype    variable responsive_value_Mean responsive_value_SD responsive_value_n responsive_value_se
1  Genotype_A Fertilizer1            0.40429958          0.18678735                  4          0.09339368
2  Genotype_A Fertilizer2            0.27184466          0.19261643                  4          0.09630821
3  Genotype_A Fertilizer3            0.03467406          0.20157613                  4          0.10078807
4  Genotype_B Fertilizer1            0.08898722          0.22356907                  4          0.11178453
5  Genotype_B Fertilizer2            0.04424779          0.22774865                  4          0.11387433
6  Genotype_B Fertilizer3            0.06784661          0.16724697                  4          0.08362349
7  Genotype_C Fertilizer1           -0.04728790          0.15442957                  4          0.07721479
8  Genotype_C Fertilizer2            0.03616134          0.16801000                  4          0.08400500
9  Genotype_C Fertilizer3            0.03940658          0.09945565                  4          0.04972782
10 Genotype_D Fertilizer1            0.02422285          0.10233126                  4          0.05116563
11 Genotype_D Fertilizer2           -0.06863141          0.17988747                  4          0.08994374
12 Genotype_D Fertilizer3           -0.01090028          0.18341009                  4          0.09170505

Second, I will generate the figure.

if(!require(remotes)) install.packages("ggplot2")
library(ggplot2)

Fig2=ggplot(data=df3, aes(x=variable, y=responsive_value_Mean, fill=Genotype)) +
  geom_bar(stat="identity",position="dodge", width=0.9, size=1) +
  geom_errorbar(aes(ymin=responsive_value_Mean-responsive_value_se, ymax=responsive_value_Mean+responsive_value_se),
                position=position_dodge(0.5), width=0.5) +
  scale_fill_manual(values=c("grey25","grey35","grey45","grey55"))+
  scale_y_continuous(breaks = seq(-0.6, 0.6, 0.3), limits = c(-0.6, 0.6)) +
  geom_hline(yintercept=0, linetype="dashed", color="red", size=1) +
  facet_wrap(~ Genotype, scales="free") +
  labs(x="Fertilizer", y="Yield") +
  theme_classic(base_size= 15, base_family = "serif") +
  theme(legend.position="none",
        legend.title=element_blank(),
        legend.key=element_rect(color="white", fill=alpha(0.5)),
        legend.text=element_text(family="serif", face="plain",
                                 size=13, color="black"),
        legend.background= element_rect(fill=alpha(0.5)),
        panel.border= element_rect(color="black", fill=NA, linewidth=0.5),
        axis.line= element_line(linewidth= 0.5, colour= "black"),
        strip.background=element_rect(color="white", 
                                      linewidth=0.5, linetype="solid"))
Fig2+windows(width=9, height= 5)

ggsave("C:/Users/agron/Fig2.jpg", 
       Fig2, width=9*2.54, height=5*2.54, units="cm", dpi=1000)

This graph illustrates how yield at different fertilizer levels responds relative to the control. Compared with the previous graph, it clearly highlights the yield differences from the control for each genotype. Genotype A appears to show greater responsiveness at Fertilizer 1 and 2, suggesting that Fertilizers 1 and 2 are beneficial for improving yield in Genotype A. In contrast, the fertilizer effect is minimal in Genotypes B, C, and D.