data(iris)
library(ggplot2)
g <- ggplot(iris, aes(Sepal.Length, Petal.Length)) + geom_point(aes(colour=Species), alpha=0.5) #desired plot

plot(iris$Sepal.Length, iris$Petal.Length, col=iris$Species) #attempt in base graphics

g2 <- ggplot(iris, aes(Sepal.Length, Petal.Length)) + geom_point(aes(colour=Species, alpha=Petal.Width))

getColWithAlpha <- function(colLevel, alphaLevel)
{
  maxAlpha <- max(alphaLevel)
  cols <- rainbow(length(levels(colLevel)))
  res <- cols[colLevel]
  sapply(seq(along.with=res), function(i) adjustcolor(res[i], alphaLevel[i]/maxAlpha) )
}

 plot(iris$Sepal.Length, iris$Petal.Length,
      col = getColWithAlpha(iris$Species, iris$Petal.Width), pch = 20)

COL <- adjustcolor(c("red", "blue", "darkgreen")[iris$Species], alpha.f = 0.5)
plot(iris$Sepal.Length, iris$Petal.Length, col = COL, pch = 19, cex = 1.5) #attempt in base graphics

# Allocate Petal.Length to 7 length categories
seq.pl <- seq(min(iris$Petal.Length)-0.1,max(iris$Petal.Length)+0.1, length.out = 7)

# Define number of alpha groups needed to fill these
cats <- nlevels(cut(iris$Petal.Length, breaks = seq.pl))

# Create alpha mapping
alpha.mapping <- as.numeric(as.character(cut(iris$Petal.Length, breaks = seq.pl, labels = seq(100,255,len = cats))))

# Allocate species by colors
COLS <- as.data.frame(col2rgb(c("red", "blue", "darkgreen")[iris$Species]))

# Combine colors and alpha mapping
COL <- unlist(lapply(1:ncol(COLS), function(i) {
  rgb(red = COLS[1,i], green = COLS[2,i], blue = COLS[3,i], alpha = alpha.mapping[i], maxColorValue = 255)
  }))

# Plot
plot(iris$Sepal.Length, iris$Petal.Length, col = COL, pch = 19, cex = 1.5)