Function that estimates flow between points or zones using the radiation model

Source: R/radiate.R

This is an implementation of the radiation model proposed in a paper by Simini et al. (2012).

od_radiation(p, pop_var = "population", proportion = 1)

Arguments

p

A SpatialPoints dataframe, the first column of which contains a unique ID
pop_var

A character string representing the variable that corresponds to the population of the zone or point
proportion

A number representing the proportion of the population who commute (1, the default, means 100 percent of the population commute to work)

References

Simini, F., Gonzalez, M.C., Maritan, A., Barabasi, A.L., 2012. A universal model for mobility and migration patterns. Nature. doi:10.1038/nature10856

Examples

# load some points data
data(cents)
# plot the points to check they make sense
plot(cents)
class(cents)
#> [1] "SpatialPointsDataFrame"
#> attr(,"package")
#> [1] "sp"
# Create test population to model flows
set.seed(2050)
cents$population <- runif(n = nrow(cents), min = 100, max = 1000)
# estimate
flowlines_radiation <- od_radiation(cents, pop_var = "population")
#> Transforming to CRS +proj=aeqd +lat_0=53.81056376 +lon_0=-1.52916207 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.80951653 +lon_0=-1.54646278 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.80680749 +lon_0=-1.53533373 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.80951653 +lon_0=-1.54646278 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.81696834 +lon_0=-1.54863463 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.80951653 +lon_0=-1.54646278 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.8189947 +lon_0=-1.54103979 +x_0=0 +y_0=0 +ellps=WGS84
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#> Transforming to CRS +proj=aeqd +lat_0=53.80951653 +lon_0=-1.54646278 +x_0=0 +y_0=0 +ellps=WGS84
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#> Transforming to CRS +proj=aeqd +lat_0=53.80951653 +lon_0=-1.54646278 +x_0=0 +y_0=0 +ellps=WGS84
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#> Transforming to CRS +proj=aeqd +lat_0=53.81161098 +lon_0=-1.51186137 +x_0=0 +y_0=0 +ellps=WGS84
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#> Transforming to CRS +proj=aeqd +lat_0=53.81161098 +lon_0=-1.51186137 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.82004192 +lon_0=-1.52373908 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.81161098 +lon_0=-1.51186137 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.82024254 +lon_0=-1.51429754 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.81161098 +lon_0=-1.51186137 +x_0=0 +y_0=0 +ellps=WGS84
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#> Transforming to CRS +proj=aeqd +lat_0=53.81161098 +lon_0=-1.51186137 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.81458358 +lon_0=-1.52128684 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.81161098 +lon_0=-1.51186137 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.80680749 +lon_0=-1.53533373 +x_0=0 +y_0=0 +ellps=WGS84
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#> Transforming to CRS +proj=aeqd +lat_0=53.80409845 +lon_0=-1.52420469 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.8142593 +lon_0=-1.53750559 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.80409845 +lon_0=-1.52420469 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.81628566 +lon_0=-1.52991074 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.80409845 +lon_0=-1.52420469 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.81648627 +lon_0=-1.5204692 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.80409845 +lon_0=-1.52420469 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.80994724 +lon_0=-1.5217611 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.80409845 +lon_0=-1.52420469 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.81082732 +lon_0=-1.5274585 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.80409845 +lon_0=-1.52420469 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.81696834 +lon_0=-1.54863463 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.82442015 +lon_0=-1.55080649 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.81801557 +lon_0=-1.53133393 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.82442015 +lon_0=-1.55080649 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.8142593 +lon_0=-1.53750559 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.82442015 +lon_0=-1.55080649 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.82644651 +lon_0=-1.54321164 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.82442015 +lon_0=-1.55080649 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.82664712 +lon_0=-1.5337701 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.82442015 +lon_0=-1.55080649 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.82010809 +lon_0=-1.535062 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.82442015 +lon_0=-1.55080649 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.82098817 +lon_0=-1.5407594 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.82442015 +lon_0=-1.55080649 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.8189947 +lon_0=-1.54103979 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.82847286 +lon_0=-1.5356168 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.82004192 +lon_0=-1.52373908 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.82847286 +lon_0=-1.5356168 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.81628566 +lon_0=-1.52991074 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.82847286 +lon_0=-1.5356168 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.82644651 +lon_0=-1.54321164 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.82847286 +lon_0=-1.5356168 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.82867348 +lon_0=-1.52617525 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.82847286 +lon_0=-1.5356168 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.82213445 +lon_0=-1.52746715 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.82847286 +lon_0=-1.5356168 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.82301452 +lon_0=-1.53316455 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.82847286 +lon_0=-1.5356168 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.81919531 +lon_0=-1.53159824 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.82887409 +lon_0=-1.51673371 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.82024254 +lon_0=-1.51429754 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.82887409 +lon_0=-1.51673371 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.81648627 +lon_0=-1.5204692 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.82887409 +lon_0=-1.51673371 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.82664712 +lon_0=-1.5337701 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.82887409 +lon_0=-1.51673371 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.82867348 +lon_0=-1.52617525 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.82887409 +lon_0=-1.51673371 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.82233506 +lon_0=-1.51802561 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.82887409 +lon_0=-1.51673371 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.82321514 +lon_0=-1.52372301 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.82887409 +lon_0=-1.51673371 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.81265628 +lon_0=-1.53289014 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.81579603 +lon_0=-1.51931751 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.81370351 +lon_0=-1.51558944 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.81579603 +lon_0=-1.51931751 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.80994724 +lon_0=-1.5217611 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.81579603 +lon_0=-1.51931751 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.82010809 +lon_0=-1.535062 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.81579603 +lon_0=-1.51931751 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.82213445 +lon_0=-1.52746715 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.81579603 +lon_0=-1.51931751 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.82233506 +lon_0=-1.51802561 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.81579603 +lon_0=-1.51931751 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.81667611 +lon_0=-1.52501491 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.81579603 +lon_0=-1.51931751 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.81353636 +lon_0=-1.53858754 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.81755618 +lon_0=-1.53071231 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.81458358 +lon_0=-1.52128684 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.81755618 +lon_0=-1.53071231 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.81082732 +lon_0=-1.5274585 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.81755618 +lon_0=-1.53071231 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.82098817 +lon_0=-1.5407594 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.81755618 +lon_0=-1.53071231 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.82301452 +lon_0=-1.53316455 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.81755618 +lon_0=-1.53071231 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.82321514 +lon_0=-1.52372301 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.81755618 +lon_0=-1.53071231 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.81667611 +lon_0=-1.52501491 +x_0=0 +y_0=0 +ellps=WGS84
#> Transforming to CRS +proj=aeqd +lat_0=53.81755618 +lon_0=-1.53071231 +x_0=0 +y_0=0 +ellps=WGS84
flowlines_radiation$flow
#>  [1]          NA  28.5716171 199.1483930  45.6047446   7.5864754  21.5568487
#>  [7]  41.2170441 105.2684494  24.7449354          NA 118.5268678  10.1879935
#> [13]   4.3086722  57.4515754 259.3003676  15.9131245  44.3764656 293.7173517
#> [19]          NA   9.8773421   7.1271190  35.3137167  81.5452128  15.4279029
#> [25]  85.4088485   5.9374332   8.8651941          NA  84.9504273  35.9825242
#> [31]  26.8695174  53.6173692   1.8104829   1.2293437   0.7982433  84.9504273
#> [37]          NA  19.6809596   2.7914752   1.2033517  27.3885572 106.4446453
#> [43]  44.4324793  34.6086394 100.2158728          NA 220.5555702  36.7618461
#> [49]  13.8249960 259.3003676  59.2543662   6.1879080   3.8213690  34.8945124
#> [55]          NA  22.4008006  10.4091206   4.4967751   1.7164989   1.3797507
#> [61]   4.7760711   2.0211245 102.2283795          NA
sum(flowlines_radiation$flow, na.rm = TRUE) # the total flow in the system
#> [1] 2937.987
sum(cents$population) # the total inter-zonal flow
#> [1] 3450.191
plot(flowlines_radiation, lwd = flowlines_radiation$flow / 100)
points(cents, cex = cents$population / 100)