Referencing previous / next column in call to mutate() - r

Question

My data looks like this:
set.seed(1234)
library(tidyverse)
df <- data.frame(Time = c(1,1,2,2,3,3),
Region = c("A", "B", "A", "B", "A", "B"),
Age_1 = round(rnorm(6, mean = 10),0),
Age_2 = round(rnorm(6, mean = 10),0),
Age_3 = round(rnorm(6, mean = 10),0),
Age_4 = round(rnorm(6, mean = 10),0),
Age_5 = round(rnorm(6, mean = 10),0))
I need to generate ratios of population change for each region and point in time. For instance, Ratio_2 for Time == 2 would be Age_2 (at Time == 2) / Age_1 (at Time == 1), grouped by Region. I could do this manually by typing:
df %>%
group_by(Region) %>%
mutate(Ratio_2 = Age_2 / dplyr::lag(Age_1, order_by = Time),
Ratio_3 = Age_3 / dplyr::lag(Age_2, order_by = Time),
Ratio_4 = Age_4 / dplyr::lag(Age_3, order_by = Time),
Ratio_5 = Age_5 / dplyr::lag(Age_4, order_by = Time))
df
# A tibble: 6 x 11
# Groups: Region [2]
Time Region Age_1 Age_2 Age_3 Age_4 Age_5 Ratio_2 Ratio_3 Ratio_4 Ratio_5
<dbl> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 1 A 11 8 9 9 10 NA NA NA NA
2 1 B 10 9 10 10 11 NA NA NA NA
3 2 A 9 10 9 8 12 0.909 1.12 0.889 1.33
4 2 B 9 10 9 9 9 1 1 0.9 0.9
5 3 A 8 11 9 9 12 1.22 0.9 1 1.5
6 3 B 9 9 9 9 9 1 0.9 1 1
Since my original data has lots of age groups, this procedure involves lots of manual coding. A programmatic solution in my mind could look something like this:
df %>%
group_by(Region) %>%
mutate(across(4:7, ~ . / dplyr::lag(.[?], order_by = Time), .names="Ratio_{.col}"))
The part containing dplyr::lag(.[?]) needs to reference the previous column in the data frame relative to . but I haven't found a method for doing so.
Note: This question is related to a post from yesterday, in which I was trying to solve the problem at hand with the data being in long format. Doing it in wide format is a different question though, which is why I opened this question.

Answer 1

Here is one option with across
library(dplyr)
library(stringr)
df %>%
group_by(Region) %>%
mutate(across(matches('^Age_[2-5]$'),
~ ./lag(get(str_replace(cur_column(), '\\d+',
as.character(readr::parse_number(cur_column())-1))), order_by = Time ),
.names = "Ratio_{.col}" )) %>%
ungroup
Or it can be done in a simplified way
library(purrr)
df[str_c('Region_', 2:5)] <- map2(df[4:7], df[3:6],
~ .x/lag(.y, order_by = df$Time))