This can be used to simulate fires, seed dispersal, calculation of iterative,
concentric, symmetric (currently) landscape values and many other things.
Essentially, it starts from a collection of cells (`start`

, called "events")
and spreads to neighbours, according to the `directions`

and `spreadProb`

with modifications due to other arguments. **NOTE:**
the `spread`

function is similar, but sometimes slightly faster, but less
robust, and more difficult to use iteratively.

spread2(landscape, start = ncell(landscape)/2 - ncol(landscape)/2, spreadProb = 0.23, asRaster = TRUE, maxSize, exactSize, directions = 8L, iterations = 1000000L, returnDistances = FALSE, returnFrom = FALSE, spreadProbRel = NA_real_, plot.it = FALSE, circle = FALSE, asymmetry = NA_real_, asymmetryAngle = NA_real_, allowOverlap = FALSE, neighProbs = NA_real_, skipChecks = FALSE)

- landscape
Required. A

`RasterLayer`

object. This defines the possible locations for spreading events to start and spread2 into. Required.- start
Required. Either a vector of pixel numbers to initiate spreading, or a data.table that is the output of a previous

`spread2`

. If a vector, they should be cell indices (pixels) on the`landscape`

. If user has x and y coordinates, these can be converted with`cellFromXY`

.- spreadProb
Numeric of length 1 or

`RasterLayer`

. If numeric of length 1, then this is the global (absolute) probability of spreading into each cell from a neighbor. If a raster then this must be the cell-specific (absolute) probability of a "receiving" potential cell. Default is`0.23`

. If relative probabilities are required, use`spreadProbRel`

. If used together, then the relative probabilities will be re-scaled so that the mean relative probability of potential neighbours is equal to the mean of`spreadProb`

of the potential neighbours.- asRaster
Logical, length 1. If

`TRUE`

, the function will return a`Raster`

where raster non NA values indicate the cells that were "active", and the value is the initial starting pixel.- maxSize
Numeric. Maximum number of cells for a single or all events to be spread2. Recycled to match

`start`

length, if it is not as long as`start`

. This will be overridden if`exactSize`

also provided. See section on`Breaking out of spread2 events`

.- exactSize
Numeric vector, length 1 or

`length(start)`

. Similar to`maxSize`

, but these will be the exact final sizes of the events. i.e., the spread2 events will continue until they are`floor(exactSize)`

. This will override`maxSize`

if both provided. See Details.- directions
The number adjacent cells in which to look; default is 8 (Queen case). Can only be 4 or 8.

- iterations
Number of iterations to spread2. Leaving this

`NULL`

allows the spread2 to continue until stops spreading itself (i.e., exhausts itself).- returnDistances
Logical. Should the function include a column with the individual cell distances from the locus where that event started. Default is FALSE. See Details.

- returnFrom
Logical. Should the function return a column with the source, i.e, the lag 1 "from" pixel, for each iteration.

- spreadProbRel
Optional

`RasterLayer`

indicating a surface of relative probabilities useful when using`neighProbs`

(which provides a mechanism for selecting a specific number of cells at each iteration). This indicates the relative probabilities for the selection of successful neighbours.`spreadProb`

will still be evaluated*after*the relative probabilities and`neighProbs`

has been evaluated, i.e., potential cells will be identified, then some could be rejected via`spreadProb`

. If absolute`spreadProb`

is not desired,*be sure to set*`spreadProb = 1`

. Ignored if`neighProbs`

is not provided.- plot.it
If TRUE, then plot the raster at every iteraction, so one can watch the spread2 event grow.

- circle
Logical. If TRUE, then outward spread2 will be by equidistant rings, rather than solely by adjacent cells (via

`directions`

arg.). Default is`FALSE`

. Using`circle = TRUE`

can be dramatically slower for large problems. Note, this will likely create unexpected results if`spreadProb < 1`

.- asymmetry
A numeric or

`RasterLayer`

indicating the ratio of the asymmetry to be used. i.e., 1 is no asymmetry; 2 means that the angles in the direction of the`asymmetryAngle`

are 2x the`spreadProb`

of the angles opposite tot he`asymmetryAngle`

Default is NA, indicating no asymmetry. See details. This is still experimental. Use with caution.- asymmetryAngle
A numeric or

`RasterLayer`

indicating the angle in degrees (0 is "up", as in North on a map), that describes which way the`asymmetry`

is.- allowOverlap
Logical. If TRUE, then individual events can overlap with one another, i.e., they do not interact (this is slower than if allowOverlap = FALSE). Default is FALSE. This can also be

`NA`

, which means that the event can overlap with other events, and also itself. This would be, perhaps, useful for dispersal of, say, insect swarms.- neighProbs
An optional numeric vector, whose sum is 1. It indicates the probabilities that an individual spread iteration will spread to

`1, 2, ..., length(neighProbs)`

neighbours, respectively. If this is used (i.e., something other than NA),`circle`

and`returnDistances`

will not work currently.- skipChecks
Logical. If TRUE, the argument checking (i.e., assertions) will be skipped. This should likely only be used once it is clear that the function arguments are well understood and function speed is of the primary improtance. This is likely most useful in repeated iteration cases i.e., if this call is using the previous output from this same function.

Either a `data.table`

(`asRaster=FALSE`

) or a `RasterLayer`

(`asRaster=TRUE`

, the default).
The `data.table`

will have one attribute named `spreadState`

, which
is a list containing a `data.table`

of current cluster-level information
about the spread events.
If `asRaster=TRUE`

, then the `data.table`

(with its `spreadState`

attribute) will be attached to the `Raster`

as an attribute named `pixel`

as it
provides pixel-level information about the spread events.

The `RasterLayer`

represents every cell in which a successful spread2 event occurred.
For the case of, say, a fire this would represent every cell that burned.
If `allowOverlap`

is `TRUE`

, the return will always be a `data.table`

.

If `asRaster`

is `FALSE`

, then this function returns a
`data.table`

with 3 (or 4 if `returnFrom`

is `TRUE`

) columns:

`initialPixels` |

the initial cell number of that particular spread2 event. |

`pixels` |

The cell indices of cells that have been touched by the spread2 algorithm. |

`state` |

a logical indicating whether the cell is active (i.e., could still be a source for spreading) or not (no spreading will occur from these cells). |

`from` |

The pixel indices that were the immediately preceeding
"source" for each `pixels` , i.e., the lag 1 pixels.
Only returned if `returnFrom` is `TRUE` |

The attribute saved with the name "spreadState" (e.g., `attr(output, "spreadState")`

)
includes a `data.table`

with columns:

`id` |

An arbitrary code, from 1 to `length(start)` for each "event". |

`initialPixels` |

the initial cell number of that particular spread2 event. |

`numRetries` |

The number of re-starts the event did because it got
stuck (normally only because `exactSize` was used
and was not achieved. |

`maxSize` |

The number of pixels that were provided as inputs via
`maxSize` or `exactSize` . |

`size` |

The current size, in pixels, of each event. |

and several other objects that provide significant speed ups in iterative calls to
spread2. If the user runs `spread2`

iteratively, there will likely be significant
speed gains if the `data.table`

passed in to `start`

should have the attribute
attached, or re-attached if it was lost, e.g., via
`setattr(outInput, "spreadState", attr(out, "spreadState"))`

, where `out`

is the
returned `data.table`

from the previous call to `spread2`

, and `outInput`

is
the modified `data.table`

. Currently, the modified `data.table`

**must** have the
same order as `out`

.

There are 2 main underlying algorithms for active cells to "spread" to
nearby cells (adjacent cells): `spreadProb`

and `neighProb`

.
Using `spreadProb`

, every "active" pixel will assess all
neighbours (either 4 or 8, depending on `directions`

), and will "activate"
whichever neighbours successfully pass independent calls to
`runif(1,0,1)<spreadProb`

.
The algorithm will iterate again and again, each time starting from the newly
"activated" cells. Several built-in decisions are as follows.
1. no active cell can active a cell that was already activated by
the same event (i.e., "it won't go backwards"). 2. If `allowOverlap`

is
`FALSE`

, then the previous rule will also apply, regardless of which
"event" caused the pixels to be previously active.

This function can be interrupted before all active cells are exhausted if
the `iterations`

value is reached before there are no more active
cells to spread2 into. The interrupted output (a data.table) can be passed
subsequently as an input to this same function (as `start`

).
This is intended to be used for situations where external events happen during
a spread2 event, or where one or more arguments to the spread2 function
change before a spread2 event is completed.
For example, if it is desired that the `spreadProb`

change before a
spread2 event is completed because, for example, a fire is spreading, and a
new set of conditions arise due to a change in weather.
`asymmetry`

here is slightly different than in the `spread`

function,
so that it can deal with a `RasterLayer`

of `asymmetryAngle`

.
Here, the `spreadProb`

values of a given set of neighbours around each active pixel
are adjusted to create `adjustedSpreadProb`

which is calculated maintain the
following
two qualities: $$mean(spreadProb) = mean(ajustedSpreadProb)$$ and
$$max(spreadProb)/min(spreadProb) = asymmetry$$ along the axis of
`asymmetryAngle`

. NOTE: this means that the 8 neighbours around an active
cell may not fulfill the preceeding equality if `asymmetryAngle`

is not
exactly one of the 8 angles of the 8 neighbours. This means that
$$max(spreadProb)/min(spreadProb)$$ will generally be less than
`asymmetry`

, for the 8 neighbours. The exact adjustment to the spreadProb
is calculated with:
$$angleQuality <- (cos(angles - rad(asymmetryAngle))+1)/2$$
which is multiplied to get an angle-adjusted spreadProb:
$$spreadProbAdj <- actualSpreadProb * angleQuality$$
which is then rescaled:
$$adjustedSpreadProb = (spreadProbAdj - min(spreadProbAdj)) * par2 + par1$$,
where par1 and par2 are parameters calculated internally to make the 2 conditions above true.

If `exactSize`

or `maxSize`

are used, then spreading will continue and stop
before or at `maxSize`

or at `exactSize`

. If `iterations`

is specified,
then the function will end, and the returned `data.table`

will still
may (if `maxSize`

) or will (if `exactSize`

) have at least one active
cell per event that did not already achieve `maxSize`

or `exactSize`

. This
will be very useful to build new, customized higher-level wrapper functions that iteratively
call `spread2`

.

`exactSize`

may not be achieved if there aren't enough cells in the map.
Also, `exactSize`

may not be achieved because the active cells are "stuck",
i.e., they have no unactivated cells to move to; or the `spreadProb`

is low.
In the latter two cases, the algorithm will retry again, but it will only
re-try from the last iterations active cells.
The algorithm will only retry 10 times before quitting.
Currently, there will also be an attempt to "jump" up to four cells away from
the active cells to try to continue spreading.

A common way to use this function is to build wrappers around this, followed
by iterative calls in a `while`

loop. See example.

There are 3 ways for the spread2 to "stop" spreading.
Here, each "event" is defined as all cells that are spawned from each unique
`start`

location.
The ways outlined below are all acting at all times, i.e., they are not
mutually exclusive.
Therefore, it is the user's responsibility to make sure the different rules
are interacting with each other correctly.

`spreadProb` |

Probabilistically, if spreadProb is low enough, active spreading events will stop. In practice, this number generally should be below 0.3 to actually see an event stop |

`maxSize` |

This is the number of cells that are "successfully" turned
on during a spreading event. `spreadProb` will still
be active, so, it is possible that the end size of each event
is smaller than `maxSize` , but they will not be greater
than `maxSize` |

`exactSize` |

This is the number of cells that are "successfully" turned
on during a spreading event. This will override an event that
stops probabilistically via `spreadProb` , but forcing
its last set of active cells to try again to find neighbours.
It will try 10 times per event, before giving up.
During those 10 times, it will try twice to "jump" up to
4 cells outwards from each of the active cells. |

`iterations` |

This is a hard cap on the number of internal iterations to
complete before returning the current state of the system
as a `data.table` . |

This function can be used iteratively, with relatively little overhead compared to using
it non-iteratively. In general, this function can be called with arguments set as user
needs, and with specifying iterations = 1 (say). This means that the function will spread
outwards 1 iteration, then stop. The returned object will be a data.table or `RasterLayer`

that can be passed immediately back as the start argument into a subsequent
call to `spread2`

. This means that every argument can be updated at each iteration.

When using this function iteratively, there are several things to keep in mind.
The output will likely be sorted differently than the input (i.e., the
order of start, if a vector, may not be the same order as that returned).
This means that when passing the same object back into the next iteration of the
function call, `maxSize`

or `exactSize`

may not be in the same order.
To get the same order, the easiest thing to do is sort the initial `start`

objects by their pixel location, increasing.
Then, of course, sorting any vectorized arguments (e.g., `maxSize`

) accordingly.
**NOTE**: the `data.table`

or `RasterLayer`

should not use be altered
when passed back into `spread2`

.

`spread`

for a different implementation of the same alogorithm.
`spread`

is less robust but it is often slightly faster.

library(raster) library(quickPlot) a <- raster(extent(0, 10, 0, 10), res = 1) sams <- sort(sample(ncell(a), 3)) # Simple use -- similar to spread(...) out <- spread2(a, start = sams, 0.225) if (interactive()) { clearPlot() Plot(out) }# Use maxSize -- this gives an upper limit maxSizes <- sort(sample(1:10, size = length(sams))) out <- spread2(a, start = sams, 0.225, maxSize = maxSizes, asRaster = FALSE) # check TRUE using data.table .N out[, .N, by = "initialPixels"]$n <= maxSizes#> logical(0)# Use exactSize -- gives an exact size, if there is enough space on the Raster exactSizes <- maxSizes out <- spread2(a, start = sams, spreadProb = 0.225, exactSize = exactSizes, asRaster = FALSE) out[, .N, by = "initialPixels"]$n == maxSizes # should be TRUE TRUE TRUE#> logical(0)# Use exactSize -- but where it can't be achieved exactSizes <- sort(sample(100:110, size = length(sams))) out <- spread2(a, start = sams, 1, exactSize = exactSizes) # Iterative calling -- create a function with a high escape probability spreadWithEscape <- function(ras, start, escapeProb, spreadProb) { out <- spread2(ras, start = sams, spreadProb = escapeProb, asRaster = FALSE) while (any(out$state == "sourceActive")) { # pass in previous output as start out <- spread2(ras, start = out, spreadProb = spreadProb, asRaster = FALSE, skipChecks = TRUE) # skipChecks for speed } out } set.seed(421) out1 <- spreadWithEscape(a, sams, escapeProb = 0.25, spreadProb = 0.225) set.seed(421) out2 <- spread2(a, sams, 0.225, asRaster = FALSE) # The one with high escape probability is larger (most of the time) NROW(out1) > NROW(out2)#> [1] TRUE## Use neighProbs, with a spreadProb that is a RasterLayer # Create a raster of different values, which will be the relative probabilities # i.e., they are rescaled to relative probabilities within the 8 neighbour choices. # The neighProbs below means 70% of the time, 1 neighbour will be chosen, # 30% of the time 2 neighbours. # The cells with spreadProb of 5 are 5 times more likely than cells with 1 to be chosen, # when they are both within the 8 neighbours sp <- raster(extent(0, 3, 0, 3), res = 1, vals = 1:9) #small raster, simple values # Check neighProbs worked out <- list() # enough replicates to see stabilized probabilities for (i in 1:100) { out[[i]] <- spread2(sp, spreadProbRel = sp, spreadProb = 1, start = 5, iterations = 1, neighProbs = c(1), asRaster = FALSE) } out <- data.table::rbindlist(out)[pixels != 5] # remove starting cell table(sp[out$pixels])#> #> 2 3 4 6 7 8 9 #> 5 11 12 12 16 22 22# should be non-significant -- note no 5 because that was the starting cell # This tests whether the null model is true ... there should be proportions # equivalent to 1:2:3:4:6:7:8:9 ... i.e,. cell 9 should have 9x as many events # spread to it as cell 1. This comes from sp object above which is providing # the relative spread probabilities keep <- c(1:4, 6:9) chisq.test(keep, unname(tabulate(sp[out$pixels], 9)[keep]), simulate.p.value = TRUE)#> #> Pearson's Chi-squared test with simulated p-value (based on 2000 #> replicates) #> #> data: keep and unname(tabulate(sp[out$pixels], 9)[keep]) #> X-squared = 40, df = NA, p-value = 1 #>## Example showing asymmetry sams <- ncell(a) / 4 - ncol(a) / 4 * 3 circs <- spread2(a, spreadProb = 0.213, start = sams, asymmetry = 2, asymmetryAngle = 135, asRaster = TRUE) # ADVANCED: Estimate spreadProb when using asymmetry, such that the expected # event size is the same as without using asymmetry ras <- raster(a) ras[] <- 1 if (interactive()) { n <- 100 sizes <- integer(n) for (i in 1:n) { circs <- spread2(ras, spreadProb = 0.225, start = round(ncell(ras) / 4 - ncol(ras) / 4 * 3), asRaster = FALSE) sizes[i] <- circs[, .N] } goalSize <- mean(sizes) library(parallel) library(DEoptim) cl <- makeCluster(pmin(10, detectCores() - 2)) # only need 10 cores for 10 populations in DEoptim parallel::clusterEvalQ(cl, { library(SpaDES.tools) library(raster) library(fpCompare) }) objFn <- function(sp, n = 20, ras, goalSize) { sizes <- integer(n) for (i in 1:n) { circs <- spread2(ras, spreadProb = sp, start = ncell(ras) / 4 - ncol(ras) / 4 * 3, asymmetry = 2, asymmetryAngle = 135, asRaster = FALSE) sizes[i] <- circs[, .N] } abs(mean(sizes) - goalSize) } aa <- DEoptim(objFn, lower = 0.2, upper = 0.23, control = DEoptim.control(cluster = cl, NP = 10, VTR = 0.02, initialpop = as.matrix(rnorm(10, 0.213, 0.001))), ras = a, goalSize = goalSize) # The value of spreadProb that will give the same expected event sizes to spreadProb = 0.225 is: sp <- aa$optim$bestmem circs <- spread2(ras, spreadProb = sp, start = ncell(ras) / 4 - ncol(ras) / 4 * 3, asymmetry = 2, asymmetryAngle = 135, asRaster = FALSE) stopCluster(cl) }#> #>#> #>#> Iteration: 1 bestvalit: 5.600000 bestmemit: 0.213323 #> 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