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<div id="header">
<h1 class="title toc-ignore">Tutorial 3: Dynamic landscapes and movement
paths</h1>
</div>
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<p>In this tutorial, we show how to simulate population response to
dynamic changes in the landscape. Additionally, we explore possibilities
to analyse individual path data from the Stochastic Movement Simulator
(SMS) dispersal model and compare different SMS specifications.</p>
<p>To this end, two settings of landscape dynamics are covered:</p>
<ol style="list-style-type: decimal">
<li>Road scenario: a patch-matrix landscape is getting fragmented by the
construction of a road</li>
<li>Land abandonment scenario: a cell-based landscape with continuous
shifts in the proportional cover of different land use types</li>
</ol>
<div id="getting-started" class="section level1" number="1">
<h1><span class="header-section-number">1</span> Getting started:</h1>
<div id="create-a-rs-directory" class="section level2" number="1.1">
<h2><span class="header-section-number">1.1</span> Create a RS
directory</h2>
<p>First of all, load <code>RangeShiftR</code> and other required
packages and set the relative path from your current working directory
to the RS directory.</p>
<pre class="r"><code># load packages
library(RangeShiftR)
library(tidyr)
library(ggplot2)
library(terra)
library(gridExtra)
library(RColorBrewer)
# relative path from current working directory:
dirpath = "Tutorial_03/"</code></pre>
<p>As already shown in the previous tutorials, we need the three
sub-folders ‘Inputs’, ‘Outputs’ and ‘Output_Maps’, which can be created
from within R if they don’t exist already:</p>
<pre class="r"><code>dir.create(paste0(dirpath,"Inputs"), showWarnings = TRUE)
dir.create(paste0(dirpath,"Outputs"), showWarnings = TRUE)
dir.create(paste0(dirpath,"Output_Maps"), showWarnings = TRUE)</code></pre>
<p>Copy the input files provided for exercise 3 into the ‘Inputs’
folder. The files can be downloaded <a
href="files/Tutorial3_Inputs.zip">here</a>. All dynamic landscapes from
Tutorial 3 were created using the package <code>NLMR</code> <span
class="citation">(Sciaini et al. 2018)</span>.</p>
</div>
</div>
<div id="road-scenario" class="section level1" number="2">
<h1><span class="header-section-number">2</span> Road scenario</h1>
<p>In this scenario, we simulate a patch-matrix landscape that is
getting fragmented by the construction of a road. With this example we
show some possible ways to analyse the optional SMS paths output.</p>
<div id="artificial-maps" class="section level2" number="2.1">
<h2><span class="header-section-number">2.1</span> Artificial Maps</h2>
<p>We created a series of four maps (<em>map_01.asc</em> to
<em>map_04.asc</em>) that represent different time steps in which a
landscape mosaic of woodland and grassland patches in an agricultural
matrix gets increasingly disturbed by woodland clearing and the
construction of a road.</p>
<p>We choose land type <em>2</em> to be the matrix and the others
(<em>1</em>,<em>3</em>,<em>4</em>) to be different forms of habitat. The
road is denoted by its own code <em>5</em> and will be assigned higher
dispersal costs. The land types are:</p>
<ol style="list-style-type: decimal">
<li>semi-natural grassland</li>
<li>arable</li>
<li>woodland</li>
<li>improved grassland</li>
<li>road</li>
</ol>
<p>Load all habitat maps into R and plot them together:</p>
<pre class="r"><code>habitat_maps <- terra::rast(sapply(1:4, FUN=function(n){terra::rast(paste0(dirpath,"Inputs/map_0",n,".asc"))}))
mycol_terrain <- c("#D0C096","#E2E2E2","#027C1E","#97A753","dark red")
plot(habitat_maps,
col=mycol_terrain,
breaks = 0:5+.5, type="continuous", axes=F)</code></pre>
<p><img src="tutorial_3_files/figure-html/unnamed-chunk-4-1.png" width="672" /></p>
<p>The patches are defined by cohesive regions of habitat, confined by
the matrix. Thus, a patch can be made up of up to three different
habitat types. As we have already seen in <a
href="tutorial_02.html">Tutorial 2</a>, we also need to explicitly
define the patch IDs. The patch files should have the same extent and
resolution as the habitat map, and each cell contains a unique patch ID
that indicates to which patch it belongs. As the patches do not change
between habitat maps 3 and 4, we only need three different patch
files.</p>
<pre class="r"><code>patches <- terra::rast(sapply(1:3, FUN=function(n){terra::rast(paste0(dirpath,"Inputs/patches_0",n,".asc"))}))
# Plot the patches in different colours:
plot(patches, breaks=c(0:230), legend=F,
col = c('black',rep(brewer.pal(n = 12, name = "Paired"),5)), axes = F, type ="continuous")</code></pre>
<p><img src="tutorial_3_files/figure-html/unnamed-chunk-5-1.png" width="672" /></p>
<p>As the last input map, we look at the initial distribution of our
model species. According to this map, a few large patches will be
initialised at the beginning of the simulation time:</p>
<pre class="r"><code>plot(terra::rast(paste0(dirpath,"Inputs/init_dist.asc")), type="continuous")</code></pre>
<p><img src="tutorial_3_files/figure-html/unnamed-chunk-7-1.png" width="672" /></p>
</div>
<div id="rangeshiftr-setup" class="section level2" number="2.2">
<h2><span class="header-section-number">2.2</span> RangeShiftR
setup</h2>
<p>We aim to simulate a population at equilibrium with the environment
before road construction starts. Landscape clearing and road
construction then increasingly disrupt individual movement in the
landscape. In order to set up the simulation, we need to specify the
species’ demography parameters, the landscape parameters and the
dispersal parameters.</p>
<div id="demographic-parameters" class="section level3" number="2.2.1">
<h3><span class="header-section-number">2.2.1</span> Demographic
parameters</h3>
<p>We choose to model a long-lived, stage-structured population with
four stages and a simple form of mate limitation
(<code>ReproductionType = 1</code>). The transition matrix is set up so
that new-borns (stage 0) always develop to juveniles (stage 1), meaning
that new-born mortality is accounted for within the fecundity. Juveniles
(stage 1) do not reproduce and develop to sub-adult (stage 2) quickly,
with a rate of ca. <em>6/7</em>. Sub-adult (stage 2) have a little
slower development than juveniles. Only the adults (stage 3) reproduce
and have a high survival rate.</p>
<pre class="r"><code>( TraMa <- matrix( c(0,1,0,0, 0,.10,.60,0, 0,0,0.2,0.45, 5,0,0,.85), ncol = 4) )</code></pre>
<pre><code>## [,1] [,2] [,3] [,4]
## [1,] 0 0.0 0.00 5.00
## [2,] 1 0.1 0.00 0.00
## [3,] 0 0.6 0.20 0.00
## [4,] 0 0.0 0.45 0.85</code></pre>
<p>Furthermore, we assume density-dependence in fecundity and survival,
where the density dependence in survival is lower than in fecundity
(controlled by <code>SurvDensCoeff</code>). Finally, we assume that
individuals in patches that get destroyed will not die instantly but
will be able to disperse to new patches (controlled by the parameter
<code>PostDestructn</code>).</p>
<pre class="r"><code>demog <- Demography(ReproductionType = 1,
StageStruct = StageStructure(Stages = 4,
TransMatrix = TraMa,
FecDensDep = T,
SurvDensDep = T,
SurvDensCoeff = 0.4,
PostDestructn = T))</code></pre>
</div>
<div id="set-landscape-and-explore-equilibrium-population-size"
class="section level3" number="2.2.2">
<h3><span class="header-section-number">2.2.2</span> Set landscape and
explore equilibrium population size</h3>
<p>Next, we need to define the landscape object (using
<code>ImportedLandscape()</code>). You may remember from the previous
tutorials that the strength of density dependence (<em>1/b</em>) is also
specified in the landscape object via the argument
<code>K_or_DensDep</code>. (Note that <code>K_or_DensDep</code> holds
the carrying capacities <em>K</em> in case of a non-structured
population and <em>1/b</em> in case of a stage-structured population,
like in this example.)</p>
<p>Specifically, for each land cover type, we need to set <em>1/b</em>,
the strength of density dependence, which will affect the equilibrium
population size. To this end, we give a vector to
<code>K_or_DensDep</code> that holds the values of <em>1/b</em> for each
land type. Since we’d like to simulate a woodland species we set the
lowest density dependence <em>b</em> (i.e. highest <em>1/b</em>) for
forest (land type <em>3</em>). To characterise the matrix and roads,
<em>1/b</em> is set to <em>0</em>, denoting non-habitat.</p>
<p>As <em>b</em> affects the equilibrium population size, it will also
affect the maximum abundance that we could observe in a patch and stage.
To explore the potential effect of <em>b</em> on equilibrium population
sizes before running the simulation, we implemented the function
<code>getLocalisedEquilPop()</code>. This allows a better understanding
of reasonable values of <em>1/b</em> for the different land types. In
fact, the function <code>getLocalisedEquilPop()</code> runs a quick
simulation of a closed and localised population (i.e. without dispersal
and in a single idealised patch) for a given vector of potential
<em>1/b</em> values (argument <code>DensDep_values</code>) and based on
our above defined <code>Demography()</code> module (argument
<code>demog</code>).</p>
<p>The <code>getLocalisedEquilPop()</code> function uses absolute values
of individuals in the local population (since there is not spatial
extent), while what we need are relative values of <em>1/b</em> as
individuals per hectare. We choose to simulate a hypothetical patch of
our landscape, and want to determine the value of <em>1/b</em> that is
needed to observe e.g. <em>100</em> individuals (let’s assume this
corresponds to our empirical observation how many individuals were
maximally observed in woodland patches). Thus, we aim to find the
<em>1/b</em> parameter that would yield a maximum local population
abundance of <em>100</em> individuals. We can now assess the localised
equilibrium population size for different values of <em>1/b</em> and see
how the density dependence plays out. By default, the function
<code>getLocalisedEquilPop()</code> will output a barplot illustrating
the equilibrium population sizes for the different levels of
<em>1/b</em>:</p>
<pre class="r"><code>eq_pop <- getLocalisedEquilPop(demog = demog, DensDep_values = seq(50,300,50))</code></pre>
<pre><code>## [1] 50 100 150 200 250 300</code></pre>
<p><img src="tutorial_3_files/figure-html/unnamed-chunk-10-1.png" width="672" /></p>
<p>Here, a <em>1/b</em> of roughly <em>150</em> would yield the desired
result approximately, in a closed and localised population. We choose
the slightly higher value, since dispersal losses are not accounted for.
We thus assume <em>1/b=150</em> for the woodland habitat and lower
<em>1/b</em> for the less suitable grassland patches.</p>
<p>Now, we can specify all parameters in the landscape object, including
the file names of the habitat and patch files, and the years in which
the different landscapes should be loaded in the simulation. Note that
we have to include the patch map 3 twice, in order to match the patch
maps with their corresponding habitat maps.</p>
<pre class="r"><code># define in which simulation year the new habitat maps and patch landscape should be loaded:
year_blocks <- c(0,80,110,140)
# explicitly provide the file names to the landscape object:
landnames <- c("map_01.asc","map_02.asc","map_03.asc","map_04.asc")
land <- ImportedLandscape(LandscapeFile = landnames,
PatchFile = c("patches_01.asc","patches_02.asc","patches_03.asc","patches_03.asc"),
DynamicLandYears = year_blocks,
Nhabitats = 5,
Resolution = 10,
K_or_DensDep = c(125,0,150,75,0),
SpDistFile = "init_dist.asc",
SpDistResolution = 10)</code></pre>
</div>
<div id="dispersal-parameters" class="section level3" number="2.2.3">
<h3><span class="header-section-number">2.2.3</span> Dispersal
parameters</h3>
<p>The next step is to set up the dispersal module. We set a density-
and stage-dependent emigration probability, such that only the juvenile
and sub-adult stages emigrate. As a transfer method we choose the SMS
movement process with a dispersal bias, which gives an individual the
preference to move away from its natal patch. The strength of this bias
decays with the number of steps taken (controlled by the decay rate
<code>AlphaDB</code> and the inflection point <code>BetaDB</code>). In
<code>SMS()</code>, the dispersal resistance of each land type is set by
the argument <code>Costs</code>, and the constant step mortality is
defined by <code>StepMort</code>. The density-dependent emigration
probability is defined by the maximum emigration probability and the
parameters <span class="math inline">\(\alpha\)</span> and <span
class="math inline">\(\beta\)</span>, all of which are provided as
matrix in the argument <code>EmigProb</code>.</p>
<p>The settlement rules include a maximum and minimum number of steps
per dispersal event. Furthermore, we use the option to set a maximum
number of steps per year (<code>MaxStepsYear</code>). If an individual
reaches this limit during dispersal, it halts and waits for the next
year to continue its dispersal event, while being subjected to the
yearly survival probability of its stage. If, in contrast the individual
hits the overall limit on the number of steps, <code>MaxSteps</code>, it
dies.</p>
<p>Additionally, we set the mating requirement (<code>FindMate</code>)
for settlement. This enables an individual to settle in a given patch
only if there is an individual of the opposite sex present.</p>
<pre class="r"><code># density-dependent emigration
disp <- Dispersal(Emigration = Emigration(StageDep = T,
DensDep = T,
EmigProb = cbind(0:3,c(0.55,0.45,0,0), c(5,5,0,0), c(1,1,0,0))),
Transfer = SMS(DP = 1.8, MemSize = 4,
GoalType = 2, GoalBias = 2.5, AlphaDB = .4, BetaDB = 10,
Costs = c(3,5,1,2,30),
StepMort = 0.01),
Settlement = Settlement(MaxSteps = 80, MinSteps = 15, MaxStepsYear = 20,
FindMate = T)
)</code></pre>
<p>We can have a look at the dispersal bias and emigration probability
we parameterised using the generic function
<code>plotProbs()</code>.</p>
<pre class="r"><code>par(mfrow=c(1,2))
plotProbs(disp@Transfer)
plotProbs(disp@Emigration)</code></pre>
<p><img src="tutorial_3_files/figure-html/unnamed-chunk-13-1.png" width="672" /></p>
</div>
<div id="initialisation" class="section level3" number="2.2.4">
<h3><span class="header-section-number">2.2.4</span> Initialisation</h3>
<p>Now we turn to the initial conditions of our simulation. We
initialise every patch with the equilibrium density and proportional
density of stages that we simulated above with the matrix model (with
<code>1/b=150</code>).</p>
<pre class="r"><code># run again for convenience to get local equilibrium population size
# at target value of 1/b:
eq_pop <- getLocalisedEquilPop(demog = demog, DensDep_values = 150, plot=F)
# calculate proportion of all stages excluding the new-born juvenile (stage 0) population,
# which can't be initialised:
prop_stgs <- eq_pop[-1]/sum(eq_pop[-1])
# we initialise at roughly half the 1/b of the most suitable patch
init <- Initialise(InitType = 1, # from loaded species distribution map (see 'land' module)
SpType = 0, # all presence cells (the default)
InitDens = 2, # initial density: user-defined
IndsHaCell = 75, # initial density in inds/ha
PropStages = c(0,prop_stgs), # initial stage distribution
InitAge = 2) # initial age distribution: quasi-equilibrium (the default).</code></pre>
</div>
<div id="simulation" class="section level3" number="2.2.5">
<h3><span class="header-section-number">2.2.5</span> Simulation</h3>
<p>Lastly, we set the number of simulated years and replicates as well
as the types and temporal intervals of produced output.</p>
<p>We request the population output for every 10 years and the range
output for every 5 years.</p>
<p>Since we simulate SMS dispersal, we can enable the paths output to
get the individual dispersal trajectories and their step-wise status by
setting <code>OutIntPaths</code>> 0. Since this output type can
produce large amounts of data when there are many dispersal events
taking place, it can be advantageous to start with large intervals or
few replicates. The results for each replicate will be stored in a
separate file.</p>
<p>Finally, we put together the parameter master with all the settings
we have made in this section and a set seed.</p>
<pre class="r"><code>simul <- Simulation(Simulation = 1,
Years = 200,
Replicates = 20,
OutIntPop = 10,
OutIntRange = 5,
OutIntPaths = 10,
OutIntInd = 10)
s <- RSsim(batchnum = 12, seed = 987, land = land, demog = demog, dispersal = disp, init = init, simul = simul)</code></pre>
</div>
<div id="run-rs" class="section level3" number="2.2.6">
<h3><span class="header-section-number">2.2.6</span> Run RS</h3>
<p>Let’s run the <code>RangeShiftR</code> simulation:</p>
<pre class="r"><code>RunRS(s, dirpath = dirpath)</code></pre>
</div>
</div>
<div id="results" class="section level2" number="2.3">
<h2><span class="header-section-number">2.3</span> Results</h2>
<div id="abundance-and-occupied-patches-over-time"
class="section level3" number="2.3.1">
<h3><span class="header-section-number">2.3.1</span> Abundance and
occupied patches over time</h3>
<p>To get a first impression of our simulation results, we look at the
time series for total abundance and the number of occupied patches.
These functions use the range output; as we set its output interval to 5
years, we get a time series with a temporal resolution of 5 years.</p>
<pre class="r"><code>par(mfrow=c(1,2))
plotAbundance(s, dirpath)
plotOccupancy(s, dirpath)</code></pre>
<p><img src="tutorial_3_files/figure-html/unnamed-chunk-17-1.png" width="672" /></p>
<p>After initialisation, the abundance first drops and then quickly
grows to values around <em>2000</em> individuals. The mean occupancy
plateaus at about <em>20</em> patches, but with a large variance.</p>
</div>
<div id="occupancy-probability-and-time-to-colonisation"
class="section level3" number="2.3.2">
<h3><span class="header-section-number">2.3.2</span> Occupancy
Probability and Time to colonisation</h3>
<p>We use the function <code>ColonisationStats()</code> to get the
occupancy probabilities at given years as well as the time to
colonisation for all patches. With the option <code>maps=T</code>, this
function also returns maps to visualise these quantities.</p>
<p><code>ColonisationStats()</code> uses the population output; as we
set its output interval to 10 years, we can only request the results for
those years. If we don’t specify a year, the last recorded year is used
by default. (In the second scenario below, you can find an example on
how to get the occupancy probabilities for given years.)</p>
<p>The function returns a list with the numeric results and the
maps:</p>
<pre class="r"><code>col <- ColonisationStats(s, dirpath, maps=T)</code></pre>
<pre><code>## Warning: [rast] the first raster was empty and was ignored</code></pre>
<pre class="r"><code>names(col)</code></pre>
<pre><code>## [1] "occ_prob" "col_time" "map_occ_prob" "map_col_time"</code></pre>
<p>Let’s plot the mean occupancy probability in the last recorded year,
year <em>200</em>, over all replicates:</p>
<pre class="r"><code>plot(col$map_occ_prob)</code></pre>
<p><img src="tutorial_3_files/figure-html/unnamed-chunk-19-1.png" width="672" /></p>
<p>We find that larger patches tend to have a higher probability of
being occupied in the last year of a given replicate of our
simulation.</p>
<p>Now, let’s also plot the mean time to colonisation for all
patches:</p>
<pre class="r"><code>plot(col$map_col_time)</code></pre>
<p><img src="tutorial_3_files/figure-html/unnamed-chunk-20-1.png" width="672" /></p>
<p>The darker the color, the earlier a patch was colonised during the
simulation. The initial patches appear in dark blue and the matrix in
white. We find that larger patches tend to get colonised earlier than
smaller ones.</p>
</div>
<div id="local-population-densities-prior-to-landscape-changes"
class="section level3" number="2.3.3">
<h3><span class="header-section-number">2.3.3</span> Local population
densities prior to landscape changes</h3>
<p>To get a spatial view of the population, we load the population
output that contains information on patch-specific and stage-specific
abundance (recorded every 10 years) and map the local population density
onto the four different patch maps. We use the last recorded time step
before the landscape changes occur.</p>
<p>Since the population output lists the absolute abundances for each
patch, larger patches tend to have larger population sizes than smaller
ones. To account for this, we divide the abundances by the number of
cells in its respective patch to get a population density.</p>
<pre class="r"><code># last recorded time step before the landscape changes:
map_years <- c(70,100,130,190)
# We have already read in the patches earlier:
patches <- patches[[c(1:3,3)]]
# initialise raster stacks for population density
map_pop <- patches
names(map_pop) <- paste('Year',map_years)
values(map_pop)[values(map_pop)==0] <- NA
values(map_pop)[values(map_pop) >0] <- 0
# populate stack with values read from Population output (takes a little while to run...)
pop_df <- readPop(s, dirpath)
for(i in 1:length(map_years)){
# mean NInd per Patch over all replicates
Pop_mean_over_reps <- aggregate(NInd~PatchID, data = subset(pop_df,Year==map_years[i],select=c('Rep','PatchID','NInd')), FUN = mean)
# exclude matrix patch
Pop_mean_over_reps <- Pop_mean_over_reps[Pop_mean_over_reps$PatchID>0,]
# get patch sizes
cell_counts <- data.frame(table(values(patches[[i]])))
Pop_mean_over_reps <- merge(Pop_mean_over_reps, cell_counts, by.x = 'PatchID', by.y = 'Var1')
# assign density values to patch map
for (l in 1:nrow(Pop_mean_over_reps) ) {
values(map_pop[[i]])[values(patches[[i]])==Pop_mean_over_reps[l,'PatchID']] <- (Pop_mean_over_reps[l,'NInd']/Pop_mean_over_reps[l,'Freq'])
}
}
# plot density
plot(map_pop, range=c(0,max(values(map_pop), na.rm=T)),type="continuous")</code></pre>
<p><img src="tutorial_3_files/figure-html/unnamed-chunk-21-1.png" width="672" /></p>
<p>In the present example, we find that larger patches tend to have
higher population densities. We encourage you to play around with
different modelling assumptions, for example the density dependence in
survival and emigration probability and explore the effects on local
population densities.</p>
</div>
<div id="dispersal-outcomes" class="section level3" number="2.3.4">
<h3><span class="header-section-number">2.3.4</span> Dispersal
outcomes</h3>
<p>Now we analyse the SMS paths output. There is a separate output file
for each replicate. Let’s look at the paths of the first replicate (note
that counting starts at zero):</p>
<pre class="r"><code># read output file
steps <- read.table(paste0(dirpath,"Outputs/Batch12_Sim1_Land1_Rep1_MovePaths.txt"), header = T)
head(steps)</code></pre>
<pre><code>## Year IndID Step x y Status
## 1 0 3 0 102 115 0
## 2 0 3 1 101 116 1
## 3 0 18 0 101 124 0
## 4 0 18 1 102 123 1
## 5 0 28 0 101 114 0
## 6 0 28 1 100 115 1</code></pre>
<p>The SMS paths files list for each output year (every 10th year) all
currently dispersing individuals with all steps taken by them during
this year. From this file we can easily extract how many steps
individuals took during dispersal in one year.</p>
<pre class="r"><code># we ask how often a step was logged per individual
hist(c(table(steps$IndID)),xlab='Number of steps',main='Steps per dispersing individual')</code></pre>
<p><img src="tutorial_3_files/figure-html/unnamed-chunk-23-1.png" width="672" /></p>
<p>We observe that most individuals disperse for 20 steps within one
year. Note that the natal cell is also included in the MovePaths output,
so an individual taking 20 steps will be recorded 21 times in total.</p>
<p>To reconstruct the individual paths, we need the status information
of each step from the last column of the SMS path files. This variable
codes for 9 different possible states:</p>
<ol start="0" style="list-style-type: decimal">
<li>in natal patch</li>
<li>still dispersing</li>
<li>awaiting settlement in possible suitable patch</li>
<li>waiting between dispersal events</li>
<li>completed settlement</li>
<li>completed settlement in a suitable neighbouring cell</li>
<li>died during transfer by failing to find a suitable patch (includes
exceeding maximum number of steps or crossing absorbing boundary)</li>
<li>died during transfer by constant, step-dependent, habitat-dependent
or distance-dependent mortality</li>
<li>died: failed to survive annual (demographic) mortality (only
available in Individual output)</li>
<li>died: exceeded maximum age (only available in Indidividual
output)</li>
</ol>
<p>The first 7 states are directly related to dispersal and thus are
included in the SMS paths output. The last two states (8 and 9) are
related to annual mortality and age mortality and are therefore only
available in the Individual output.</p>
<p>Let’s look at a specific trajectory.</p>
<pre class="r"><code># find all individuals with a 10-step path:
Inds <- names(which(table(steps$IndID) == 10))
steps_10 <- subset(steps, IndID %in% Inds)
# look at first individual with a starting path
(steps_i <- subset(steps_10, IndID == subset(steps_10, Step == 0)[1,"IndID"]))</code></pre>
<pre><code>## Year IndID Step x y Status
## 223 0 2341 0 76 55 0
## 224 0 2341 1 75 54 1
## 604 0 2341 2 75 53 1
## 850 0 2341 3 74 52 1
## 1096 0 2341 4 73 51 1
## 1342 0 2341 5 72 50 1
## 1587 0 2341 6 71 51 1
## 1827 0 2341 7 72 51 1
## 2067 0 2341 8 71 50 1
## 2306 0 2341 8 71 50 7</code></pre>
<p>This list of steps begins with the starting cell in the natal patch
(status 0), followed by 8 SMS steps that record the intermediate cells,
and ends with the dispersal outcome; in this case the individual died
during dispersal from the set step-mortality (status 7). Note that
<code>x</code> and <code>y</code> refer to the cell count in each
direction, not the actual position in meters.</p>
<p>We look at another 10-step dispersal event, one that already starts
with a step number above the maximum number of steps per year
(<code>MaxStepsYear</code>):</p>
<pre class="r"><code>(steps_i <- subset(steps, IndID == subset(steps_10, Step > 20)[1,"IndID"]) )</code></pre>
<pre><code>## Year IndID Step x y Status
## 4879 10 7930 41 129 117 1
## 5074 10 7930 42 130 116 1
## 5206 10 7930 43 130 115 1
## 5334 10 7930 44 130 116 1
## 5461 10 7930 45 130 115 1
## 5585 10 7930 46 130 114 1
## 5708 10 7930 47 131 113 1
## 5829 10 7930 48 132 113 1
## 5948 10 7930 49 133 113 1
## 6065 10 7930 49 133 113 7</code></pre>
<p>This list doesn’t start with with status 0, so we know that this
event has begun already in an earlier year and is now being continued.
This happens if an individual is forced to wait until the next year to
continue dispersal because it reached the maximum yearly number of steps
(<code>MaxStepsYear</code>). This outcome will be denoted by status 3 at
the end of the previous year. During the wait time, the individual is
subject to annual survival and might die from demographic mortality
(status 8). In above case, settlement terminates successfully (status
4).</p>
<p>Now that we know how to interpret the data, let’s plot some
trajectories. Since a single dispersal event can be allowed to span
multiple years and because we haven’t recorded the SMS steps of every
year but only every 10th year, there might be incomplete trajectories in
the data. We plot all dispersal events that started in year <em>70</em>
(i.e. before the first landscape transition):</p>
<pre class="r"><code># find all dispersing individuals of the last 10 years of the first map
steps_map1 <- subset(steps, Year >= 70 & Year < 80)
Inds <- subset(steps_map1, Status == 0, select = IndID) # Trajectory contains start of path
# trajectory is completed within one year if it starts with status 0 and ends with status 4 or greater
Inds_outcome <- sapply(Inds$IndID, function(Ind){
steps_i <- subset(steps_map1, IndID == Ind)
outcome = steps_i$Status[nrow(steps_i)]
if(outcome %in% c(2,3) ) "wait" else {
if(outcome %in% c(4,5) ) "settle" else {
if(outcome>4) "die"
}
}
})
Inds <- data.frame(IndID = Inds, Outcome = Inds_outcome)
# load raster of first map
map1 <- terra::rast(paste0(dirpath,"Inputs/",landnames[1]))
# multiply x and y counts by map resolution
steps_map1[,c(4,5)] <- steps_map1[,c(4,5)]*res(map1)
# We use ggplot to plot the movement paths
pathplot_1 <- ggplot()+
geom_tile(data = as.data.frame(map1, xy = TRUE), aes(x = x, y = y,fill = factor(map_01))) +
geom_path(data = steps_map1[steps_map1$IndID %in% Inds[Inds$Outcome == "wait",1],], aes(x = x, y = y, group = factor(IndID)), col = "mediumorchid", alpha = .7, lwd=2) +
geom_path(data = steps_map1[steps_map1$IndID %in% Inds[Inds$Outcome == "settle",1],], aes(x = x, y = y, group = factor(IndID)), col = "blue2", alpha = .7, lwd=2) +
geom_path(data = steps_map1[steps_map1$IndID %in% Inds[Inds$Outcome == "die",1],], aes(x = x, y = y, group = factor(IndID)), col = "red", alpha = .7, lwd=2) +
scale_fill_manual(breaks = 1:5, values = mycol_terrain) +
guides(fill = "none", color = "none") +
theme_void()