Can´t set the numerical range for the colors in tile plot

I am using this code to create a tile plot in which each color should show a given numerical data range through a color code. The problem is that my data have a wide numerical range and most of numbers are low. I dont´want to use data transformation, instead I´m trying to set in the code the intervals in which the colors should be used. In values I tried to set the limits to each color but the final plot is not showing what I need.

mean_data <- aggregate(variacao_proporcional ~ causa_variacao_turb + tipo_ambiente, data, mean)

num_breaks <- 9

breaks <- quantile(data$variacao_proporcional, probs = seq(0, 1, length.out = num_breaks ))

breaks_mean <- quantile(mean_data$variacao_proporcional, probs = seq(0, 1, length.out = num_breaks))

print(breaks_mean)
      0%      12.5%        25%      37.5%        50%      62.5%        75%      87.5% 
0.026250   0.795000   1.252750   1.873750   2.473750   3.348333   5.824375  25.951250 
    100% 
401.860000


values <- c(0.02, 0.8, 1.2, 1.8, 2.5, 3.5, 5.9, 26, 402)

colors <- colorRampPalette(c("green", "lightgreen", "gray", "yellow", "gold", "orange", "darkorange", "red", "darkred"))(length(values) - 1)

ggplot(mean_data, aes(x = tipo_ambiente, y = causa_variacao_turb, fill = variacao_proporcional)) +
geom_tile() +
scale_fill_gradientn(colors = colors, breaks = breaks_mean, values = values) +
theme_classic() 

As you can see from my data distribution, i have very low values. I created a gradient that shows the lower values in green colors and all values above 0.8 should be shown in gray while values higher than 1 should appear from yellow to dark green.

Any ideas on how can I make this plot?

I think you want to make categories from your continuous variacao_proporcional variable to make it discrete, and you want your discrete fill to span a range of colors you specify. Here's an example with data from the ggplot2 package. I used the cut command to make an ordered (discrete) factor price_cat.

values <- c(0, 300, 500, 800, 1000, 1500, 3000, 12000, 20000)
colors <- colorRampPalette(c("green", "lightgreen", "gray", "yellow", "gold", "orange", "darkorange", "red", "darkred"))(length(values) - 1)
diamonds2 <- diamonds
diamonds2$price_cat = cut(diamonds2$price, breaks = values) 


ggplot(diamonds2, aes(x = cut, y = carat, fill = price_cat)) +
  geom_jitter(shape = 21, color = "white", stroke = 0.1) +
  scale_fill_manual(values = colors) +
  theme_classic() 

If you want to use a continuous scale like in your code and picture, a transformation would be helpful. You note you don't want to use one, but it seems useful here to me -- note that we can apply it to the mapping without manually altering any of the underlying values. Note that the color legend still refers to the underlying values (not transformations of them), but the mapping itself is transformed to segment the data range more evenly, giving about the same amount of color space to 500-2000 as 5000-15000.

ggplot(diamonds, aes(x = cut, y = carat, fill = price)) +
  geom_jitter(shape = 21, color = "white", stroke = 0.1) +
  scale_fill_gradientn(colors = colors, 
                       breaks = c(200, 500, 1000, 2000, 5000, 15000),
                       trans = scales::pseudo_log_trans(sigma = 100)) +
  theme_classic()