Log-linear interpolation

Log-linearly interpolate values between two thresholds.

Usage

loglinear_interpolation(
  x,
  coordinate_one_x,
  coordinate_one_y,
  coordinate_two_x,
  coordinate_two_y
)

Arguments

x

numeric x values for which interpolate y values.

coordinate_one_x

numeric value for lower x-coordinate.

coordinate_one_y

numeric value for lower y-coordinate.

coordinate_two_x

numeric value for upper x-coordinate.

coordinate_two_y

numeric value for upper y-coordinate.

Value

A numeric vector.

Details

Values are log-linearly interpolated at the x-coordinates specified in x using the lower and upper coordinate arguments to define the line. Values lesser or greater than these numbers are assigned the minimum and maximum y coordinates.

Examples

# \dontrun{
# create series of x-values
x <- seq(0, 1000)

# interpolate y-values for the x-values given the two reference points:
# (200, 100) and (900, 15)
y <- loglinear_interpolation(x, 200, 100, 900, 15)

# plot the interpolated values
plot(y ~ x)

# add the reference points to the plot (shown in red)
points(x = c(200, 900), y = c(100, 15), pch = 18, col = "red", cex = 2)


# this function can also be used to calculate representation targets
# following Rodrigues et al. (2014). For example, let's say that
# we had a set of species we were interested in calculating representation
# targets for and we had information on their range sizes (in km^2).
spp_range_size_km2 <- seq(0.01, 15000000, by = 100)

# we can now use this function to calculate representation targets
# (expressed as a percentage of the species' range sizes) using
# the thresholds and cap sizes reported by Rodrigues et al. 2014
spp_target_percentage_rodrigues <- loglinear_interpolation(
    x = spp_range_size_km2,
    coordinate_one_x = 1000,
    coordinate_one_y = 1,
    coordinate_two_x = 250000,
    coordinate_two_y = 0.1
) * 100

# it is also common to apply a cap to the representation targets,
# so let's apply the cap these targets following Butchart et al. (2015)
spp_target_percentage_butchart <- ifelse(
  spp_range_size_km2 >= 10000000,
  (1000000 / spp_range_size_km2) * 100,
  spp_target_percentage_rodrigues
)

# plot species range sizes and representation targets
plot(
  spp_target_percentage_butchart ~ spp_range_size_km2,
  xlab = "Range size km^2" , ylab = "Representation target (%)", type = "l"
)


# plot species range sizes and representation targets on a log10 scale
plot(
  spp_target_percentage_butchart ~ log10(spp_range_size_km2),
  xlab = "Range size km^2" , ylab = "Representation target (%)",
  type = "l", xaxt = "n"
)
axis(
  1, pretty(log10(spp_range_size_km2)),
  10^pretty(log10(spp_range_size_km2))
)

# }