使用离散数据分析生物体的生长模式
Analysing the pattern in the growth of organisms using discrete data
我有特定植物物种 200 个个体大小的数据。但是尺寸是通过间接方式测量的，在总共 14 个月中每月计算叶子的数量（离散数据）。植物的发芽、生长和死亡非常不规则，有的植物寿命长，有的植物死得快，而且发芽时间也不规律：新植物在整个研究期间不断发芽并纳入研究.这是我的数据示例（单元格内的数字指的是叶子的数量）：
Month.1
Month.2
Month.3
Month.4
Month.5
Month.6
Month.7
plant.1
3
21
15
-
-
-
-
plant.2
-
7
14
-
-
-
-
plant.3
-
8
12
10
-
-
-
plant.4
-
-
1
3
5
-
-
plant.5
-
3
6
18
13
4
-
.....
...
...
...
...
...
...
...
根据 Shibaprasadb 的建议，这是我的数据的一个子集，已经转换为长格式：
df <- dput(df)
structure(list(plant = c(1L, 1L, 1L, 1L, 1L, 2L, 3L, 3L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 28L, 29L, 29L, 29L, 30L, 31L, 32L, 32L,
32L, 32L, 32L, 62L, 62L, 63L, 64L, 65L, 65L, 65L, 65L, 66L, 67L,
67L, 67L), month = c(4L, 5L, 6L, 7L, 8L, 4L, 7L, 8L, 2L, 3L,
4L, 5L, 6L, 7L, 8L, 7L, 6L, 7L, 8L, 6L, 7L, 4L, 5L, 6L, 7L, 8L,
5L, 6L, 6L, 6L, 5L, 6L, 7L, 8L, 8L, 2L, 3L, 4L), time = c(0L,
1L, 2L, 3L, 4L, 0L, 0L, 1L, 0L, 1L, 2L, 3L, 4L, 5L, 6L, 0L, 0L,
1L, 2L, 0L, 0L, 0L, 1L, 2L, 3L, 4L, 0L, 1L, 0L, 0L, 0L, 1L, 2L,
3L, 0L, 0L, 1L, 2L), leaves = c(6L, 18L, 9L, 24L, 6L, 12L, 6L,
6L, 63L, 66L, 15L, 9L, 15L, 21L, 12L, 12L, 3L, 42L, 12L, 9L,
3L, 15L, 21L, 18L, 27L, 15L, 21L, 36L, 24L, 21L, 3L, 12L, 18L,
6L, 3L, 15L, 3L, 3L), tray = c(1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L), soil_nutrient = c(62.4,
71, 13.6, 37.6, 13.8, 62.4, 37.6, 13.8, 47.6, 51.8, 62.4, 71,
13.6, 37.6, 13.8, 25.4, 14.2, 25.4, 17, 14.2, 25.4, 51.6, 72.6,
14.2, 25.4, 17, 148.2, 29.4, 29.4, 29.4, 148.2, 29.4, 103.6,
122.4, 122.4, 116.2, 141, 117.6), watering = c(81.6, 89, 10.6,
57.8, 1.2, 81.6, 57.8, 1.2, 46, 48.6, 81.6, 89, 10.6, 57.8, 1.2,
57.8, 10.6, 57.8, 1.2, 10.6, 57.8, 81.6, 89, 10.6, 57.8, 1.2,
89, 10.6, 10.6, 10.6, 89, 10.6, 57.8, 1.2, 1.2, 46, 48.6, 81.6
), UV_treatment = c("n", "n", "n", "n", "n", "n", "n", "n", "n",
"n", "n", "n", "n", "n", "n", "n", "n", "n", "n", "n", "n", "n",
"n", "n", "n", "n", "n", "y", "y", "y", "n", "y", "n", "n", "n",
"n", "n", "n")), class = "data.frame", row.names = c(NA, -38L
))
df
plant month time leaves tray soil_nutrient watering UV_treatment
1 1 4 0 6 1 62.4 81.6 n
2 1 5 1 18 1 71.0 89.0 n
3 1 6 2 9 1 13.6 10.6 n
4 1 7 3 24 1 37.6 57.8 n
5 1 8 4 6 1 13.8 1.2 n
6 2 4 0 12 1 62.4 81.6 n
7 3 7 0 6 1 37.6 57.8 n
8 3 8 1 6 1 13.8 1.2 n
9 4 2 0 63 1 47.6 46.0 n
10 4 3 1 66 1 51.8 48.6 n
11 4 4 2 15 1 62.4 81.6 n
12 4 5 3 9 1 71.0 89.0 n
13 4 6 4 15 1 13.6 10.6 n
14 4 7 5 21 1 37.6 57.8 n
15 4 8 6 12 1 13.8 1.2 n
16 28 7 0 12 3 25.4 57.8 n
17 29 6 0 3 3 14.2 10.6 n
18 29 7 1 42 3 25.4 57.8 n
19 29 8 2 12 3 17.0 1.2 n
20 30 6 0 9 3 14.2 10.6 n
21 31 7 0 3 3 25.4 57.8 n
22 32 4 0 15 3 51.6 81.6 n
23 32 5 1 21 3 72.6 89.0 n
24 32 6 2 18 3 14.2 10.6 n
25 32 7 3 27 3 25.4 57.8 n
26 32 8 4 15 3 17.0 1.2 n
27 62 5 0 21 7 148.2 89.0 n
28 62 6 1 36 7 29.4 10.6 y
29 63 6 0 24 7 29.4 10.6 y
30 64 6 0 21 7 29.4 10.6 y
31 65 5 0 3 7 148.2 89.0 n
32 65 6 1 12 7 29.4 10.6 y
33 65 7 2 18 7 103.6 57.8 n
34 65 8 3 6 7 122.4 1.2 n
35 66 8 0 3 7 122.4 1.2 n
36 67 2 0 15 7 116.2 46.0 n
37 67 3 1 3 7 141.0 48.6 n
38 67 4 2 3 7 117.6 81.6 n
- 植物 = 每株植物的识别编号。
- 月 = 植物发芽的月份。
- 时间 = 类似月，但每株从零开始。
- 叶子 = 每株植物的叶子数。
- 托盘 = 每株植物所在的托盘；总共有 10 个托盘，每个托盘包含不同类型的土壤。
- soil_nutrient = 每个月每个托盘的营养总量。
- 浇水 = 每个月每个托盘的加水量。
- UV_treatment = 我们有兴趣探索其对植物的影响的侵蚀性紫外线处理。
我有兴趣检查它们的生长是否有某种模式，我的意思是它们是否首先显示叶子数量增加，然后是否稳定，然后突然死亡或逐渐减少数量死前的叶子。
我一直在寻找 R 中的物候分析，但到目前为止我发现的主要与气候变化、全球参数等有关。另一方面，考虑时间序列的增长分析主要集中在特定变量的长数据序列，而不是几个个体。
library(tidyverse)
library(ggpubr)
library(lmerTest)
#> Loading required package: lme4
#> Loading required package: Matrix
#>
#> Attaching package: 'Matrix'
#> The following objects are masked from 'package:tidyr':
#>
#> expand, pack, unpack
#>
#> Attaching package: 'lmerTest'
#> The following object is masked from 'package:lme4':
#>
#> lmer
#> The following object is masked from 'package:stats':
#>
#> step
data <- tibble::tribble(
~Plant, ~Month.1, ~Moßnth.2, ~Month.3, ~Month.4, ~Month.5, ~Month.6, ~Month.7,
"plant.1", "3", "21", "15", "-", "-", "-", "-",
"plant.2", "-", "7", "14", "-", "-", "-", "-",
"plant.3", "-", "8", "12", "10", "-", "-", "-",
"plant.4", "-", "-", "1", "3", "5", "-", "-",
"plant.5", "-", "3", "6", "18", "13", "4", "-"
)
data <-
data %>%
pivot_longer(-Plant, names_to = "Month", values_to = "n_leafs") %>%
mutate(
n_leafs = n_leafs %>% as.numeric(),
Month = Month %>% str_extract("[0-9]+$") %>% as.numeric(),
Plant = Plant %>% str_extract("[0-9]+$") %>% as.numeric()
) %>%
# Normalization: Just count the number of months since seeding for each Plant
group_by(Plant) %>%
mutate(Month = Month - min(Month)) %>%
ungroup()
#> Warning in n_leafs %>% as.numeric(): NAs introduced by coercion
#
# The overall trend is that the number of leaves are getting lesser over time.
# However, this is not significant.
#
data %>%
ggplot(aes(Month, n_leafs, color = Plant)) +
geom_point() +
stat_smooth(method = "lm") +
stat_cor()
#> `geom_smooth()` using formula 'y ~ x'
#> Warning: Removed 19 rows containing non-finite values (stat_smooth).
#> Warning: Removed 19 rows containing non-finite values (stat_cor).
#> Warning: Removed 19 rows containing missing values (geom_point).
#
# The number of leaves are not significantly different between the months
#
data %>%
ggplot(aes(factor(Month), n_leafs)) +
geom_boxplot() +
stat_compare_means()
#> Warning: Removed 19 rows containing non-finite values (stat_boxplot).
#> Warning: Removed 19 rows containing non-finite values (stat_compare_means).
#
# There is still no significance after controlling for the different plants
#
lmer(n_leafs ~ Month + (1|Plant), data = data) %>%
summary()
#> Linear mixed model fit by REML. t-tests use Satterthwaite's method [
#> lmerModLmerTest]
#> Formula: n_leafs ~ Month + (1 | Plant)
#> Data: data
#>
#> REML criterion at convergence: 96.8
#>
#> Scaled residuals:
#> Min 1Q Median 3Q Max
#> -1.1084 -0.7883 -0.2424 0.6603 1.8827
#>
#> Random effects:
#> Groups Name Variance Std.Dev.
#> Plant (Intercept) 4.789 2.188
#> Residual 34.943 5.911
#> Number of obs: 16, groups: Plant, 5
#>
#> Fixed effects:
#> Estimate Std. Error df t value Pr(>|t|)
#> (Intercept) 8.2657 3.2163 9.1434 2.570 0.0298 *
#> Month 0.3186 1.2149 13.4746 0.262 0.7971
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Correlation of Fixed Effects:
#> (Intr)
#> Month -0.831
由 reprex package (v2.0.1)
于 2021-09-26 创建
我有特定植物物种 200 个个体大小的数据。但是尺寸是通过间接方式测量的，在总共 14 个月中每月计算叶子的数量（离散数据）。植物的发芽、生长和死亡非常不规则，有的植物寿命长，有的植物死得快，而且发芽时间也不规律：新植物在整个研究期间不断发芽并纳入研究.这是我的数据示例（单元格内的数字指的是叶子的数量）：
| Month.1 | Month.2 | Month.3 | Month.4 | Month.5 | Month.6 | Month.7 | |
|---|---|---|---|---|---|---|---|
| plant.1 | 3 | 21 | 15 | - | - | - | - |
| plant.2 | - | 7 | 14 | - | - | - | - |
| plant.3 | - | 8 | 12 | 10 | - | - | - |
| plant.4 | - | - | 1 | 3 | 5 | - | - |
| plant.5 | - | 3 | 6 | 18 | 13 | 4 | - |
| ..... | ... | ... | ... | ... | ... | ... | ... |
根据 Shibaprasadb 的建议，这是我的数据的一个子集，已经转换为长格式：
df <- dput(df)
structure(list(plant = c(1L, 1L, 1L, 1L, 1L, 2L, 3L, 3L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 28L, 29L, 29L, 29L, 30L, 31L, 32L, 32L,
32L, 32L, 32L, 62L, 62L, 63L, 64L, 65L, 65L, 65L, 65L, 66L, 67L,
67L, 67L), month = c(4L, 5L, 6L, 7L, 8L, 4L, 7L, 8L, 2L, 3L,
4L, 5L, 6L, 7L, 8L, 7L, 6L, 7L, 8L, 6L, 7L, 4L, 5L, 6L, 7L, 8L,
5L, 6L, 6L, 6L, 5L, 6L, 7L, 8L, 8L, 2L, 3L, 4L), time = c(0L,
1L, 2L, 3L, 4L, 0L, 0L, 1L, 0L, 1L, 2L, 3L, 4L, 5L, 6L, 0L, 0L,
1L, 2L, 0L, 0L, 0L, 1L, 2L, 3L, 4L, 0L, 1L, 0L, 0L, 0L, 1L, 2L,
3L, 0L, 0L, 1L, 2L), leaves = c(6L, 18L, 9L, 24L, 6L, 12L, 6L,
6L, 63L, 66L, 15L, 9L, 15L, 21L, 12L, 12L, 3L, 42L, 12L, 9L,
3L, 15L, 21L, 18L, 27L, 15L, 21L, 36L, 24L, 21L, 3L, 12L, 18L,
6L, 3L, 15L, 3L, 3L), tray = c(1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L), soil_nutrient = c(62.4,
71, 13.6, 37.6, 13.8, 62.4, 37.6, 13.8, 47.6, 51.8, 62.4, 71,
13.6, 37.6, 13.8, 25.4, 14.2, 25.4, 17, 14.2, 25.4, 51.6, 72.6,
14.2, 25.4, 17, 148.2, 29.4, 29.4, 29.4, 148.2, 29.4, 103.6,
122.4, 122.4, 116.2, 141, 117.6), watering = c(81.6, 89, 10.6,
57.8, 1.2, 81.6, 57.8, 1.2, 46, 48.6, 81.6, 89, 10.6, 57.8, 1.2,
57.8, 10.6, 57.8, 1.2, 10.6, 57.8, 81.6, 89, 10.6, 57.8, 1.2,
89, 10.6, 10.6, 10.6, 89, 10.6, 57.8, 1.2, 1.2, 46, 48.6, 81.6
), UV_treatment = c("n", "n", "n", "n", "n", "n", "n", "n", "n",
"n", "n", "n", "n", "n", "n", "n", "n", "n", "n", "n", "n", "n",
"n", "n", "n", "n", "n", "y", "y", "y", "n", "y", "n", "n", "n",
"n", "n", "n")), class = "data.frame", row.names = c(NA, -38L
))
df
plant month time leaves tray soil_nutrient watering UV_treatment
1 1 4 0 6 1 62.4 81.6 n
2 1 5 1 18 1 71.0 89.0 n
3 1 6 2 9 1 13.6 10.6 n
4 1 7 3 24 1 37.6 57.8 n
5 1 8 4 6 1 13.8 1.2 n
6 2 4 0 12 1 62.4 81.6 n
7 3 7 0 6 1 37.6 57.8 n
8 3 8 1 6 1 13.8 1.2 n
9 4 2 0 63 1 47.6 46.0 n
10 4 3 1 66 1 51.8 48.6 n
11 4 4 2 15 1 62.4 81.6 n
12 4 5 3 9 1 71.0 89.0 n
13 4 6 4 15 1 13.6 10.6 n
14 4 7 5 21 1 37.6 57.8 n
15 4 8 6 12 1 13.8 1.2 n
16 28 7 0 12 3 25.4 57.8 n
17 29 6 0 3 3 14.2 10.6 n
18 29 7 1 42 3 25.4 57.8 n
19 29 8 2 12 3 17.0 1.2 n
20 30 6 0 9 3 14.2 10.6 n
21 31 7 0 3 3 25.4 57.8 n
22 32 4 0 15 3 51.6 81.6 n
23 32 5 1 21 3 72.6 89.0 n
24 32 6 2 18 3 14.2 10.6 n
25 32 7 3 27 3 25.4 57.8 n
26 32 8 4 15 3 17.0 1.2 n
27 62 5 0 21 7 148.2 89.0 n
28 62 6 1 36 7 29.4 10.6 y
29 63 6 0 24 7 29.4 10.6 y
30 64 6 0 21 7 29.4 10.6 y
31 65 5 0 3 7 148.2 89.0 n
32 65 6 1 12 7 29.4 10.6 y
33 65 7 2 18 7 103.6 57.8 n
34 65 8 3 6 7 122.4 1.2 n
35 66 8 0 3 7 122.4 1.2 n
36 67 2 0 15 7 116.2 46.0 n
37 67 3 1 3 7 141.0 48.6 n
38 67 4 2 3 7 117.6 81.6 n
- 植物 = 每株植物的识别编号。
- 月 = 植物发芽的月份。
- 时间 = 类似月，但每株从零开始。
- 叶子 = 每株植物的叶子数。
- 托盘 = 每株植物所在的托盘；总共有 10 个托盘，每个托盘包含不同类型的土壤。
- soil_nutrient = 每个月每个托盘的营养总量。
- 浇水 = 每个月每个托盘的加水量。
- UV_treatment = 我们有兴趣探索其对植物的影响的侵蚀性紫外线处理。
我有兴趣检查它们的生长是否有某种模式，我的意思是它们是否首先显示叶子数量增加，然后是否稳定，然后突然死亡或逐渐减少数量死前的叶子。
我一直在寻找 R 中的物候分析，但到目前为止我发现的主要与气候变化、全球参数等有关。另一方面，考虑时间序列的增长分析主要集中在特定变量的长数据序列，而不是几个个体。
library(tidyverse)
library(ggpubr)
library(lmerTest)
#> Loading required package: lme4
#> Loading required package: Matrix
#>
#> Attaching package: 'Matrix'
#> The following objects are masked from 'package:tidyr':
#>
#> expand, pack, unpack
#>
#> Attaching package: 'lmerTest'
#> The following object is masked from 'package:lme4':
#>
#> lmer
#> The following object is masked from 'package:stats':
#>
#> step
data <- tibble::tribble(
~Plant, ~Month.1, ~Moßnth.2, ~Month.3, ~Month.4, ~Month.5, ~Month.6, ~Month.7,
"plant.1", "3", "21", "15", "-", "-", "-", "-",
"plant.2", "-", "7", "14", "-", "-", "-", "-",
"plant.3", "-", "8", "12", "10", "-", "-", "-",
"plant.4", "-", "-", "1", "3", "5", "-", "-",
"plant.5", "-", "3", "6", "18", "13", "4", "-"
)
data <-
data %>%
pivot_longer(-Plant, names_to = "Month", values_to = "n_leafs") %>%
mutate(
n_leafs = n_leafs %>% as.numeric(),
Month = Month %>% str_extract("[0-9]+$") %>% as.numeric(),
Plant = Plant %>% str_extract("[0-9]+$") %>% as.numeric()
) %>%
# Normalization: Just count the number of months since seeding for each Plant
group_by(Plant) %>%
mutate(Month = Month - min(Month)) %>%
ungroup()
#> Warning in n_leafs %>% as.numeric(): NAs introduced by coercion
#
# The overall trend is that the number of leaves are getting lesser over time.
# However, this is not significant.
#
data %>%
ggplot(aes(Month, n_leafs, color = Plant)) +
geom_point() +
stat_smooth(method = "lm") +
stat_cor()
#> `geom_smooth()` using formula 'y ~ x'
#> Warning: Removed 19 rows containing non-finite values (stat_smooth).
#> Warning: Removed 19 rows containing non-finite values (stat_cor).
#> Warning: Removed 19 rows containing missing values (geom_point).
#
# The number of leaves are not significantly different between the months
#
data %>%
ggplot(aes(factor(Month), n_leafs)) +
geom_boxplot() +
stat_compare_means()
#> Warning: Removed 19 rows containing non-finite values (stat_boxplot).
#> Warning: Removed 19 rows containing non-finite values (stat_compare_means).
#
# There is still no significance after controlling for the different plants
#
lmer(n_leafs ~ Month + (1|Plant), data = data) %>%
summary()
#> Linear mixed model fit by REML. t-tests use Satterthwaite's method [
#> lmerModLmerTest]
#> Formula: n_leafs ~ Month + (1 | Plant)
#> Data: data
#>
#> REML criterion at convergence: 96.8
#>
#> Scaled residuals:
#> Min 1Q Median 3Q Max
#> -1.1084 -0.7883 -0.2424 0.6603 1.8827
#>
#> Random effects:
#> Groups Name Variance Std.Dev.
#> Plant (Intercept) 4.789 2.188
#> Residual 34.943 5.911
#> Number of obs: 16, groups: Plant, 5
#>
#> Fixed effects:
#> Estimate Std. Error df t value Pr(>|t|)
#> (Intercept) 8.2657 3.2163 9.1434 2.570 0.0298 *
#> Month 0.3186 1.2149 13.4746 0.262 0.7971
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Correlation of Fixed Effects:
#> (Intr)
#> Month -0.831
由 reprex package (v2.0.1)
于 2021-09-26 创建