1 - Running a simple simulation
General presentation of the package
See ?lansdepi for a complete description of the model,
assumptions and available functions. See also the vignette list of parameters for a detailed
description of all model parameters.
Take a quick overview of what landsepi
can do.
Initialisation of simulation parameters
The function createSimulParams() will create a directory
to store simulation outputs, and return an object of class
LandsepiParams that will further contain all simulation
parameters.
In the following, the object simul_params is to be
updated with all simulation parameters using set*()
functions. For some specific parameters already set using
set*() functions, they may be next updated using
update*() functions. To help parameterisation, built-in
parameters are available and may be loaded via load*()
functions.
To avoid dependency issues between functions, we recommend to
parameterise the simulation with the following order (functions
in bold are crucial to run a simulation, others are
optional):
- createSimulParams()
- setSeed()
- setTime()
- setPathogen()
- updateReproSexProb()
- setLandscape()
- setDispersal()
- setGenes()
- setCultivars()
- allocateCultivarGenes()
- allocateCroptypeCultivars()
- setCroptypes()
- allocateLandscapeCroptypes()
- setInoculum()
- updateSurvivalProb()
- setTreatments()
- setOutputs()
- checkSimulParams()
- runSimul()
Setting the seed and time parameters
A seed (for random number generator) is randomly generated when
simul_params is initialised by
createSimulParams(). If a specific seed is required, it can
be set using the function setSeed():
simul_params@Seed
#> [1] 1732344739
simul_params <- setSeed(simul_params, seed = 1)
simul_params@Seed
#> [1] 1The number of cropping seasons to simulate (e.g. 6 years) and the
number of time steps per cropping season (e.g. 120 days/year) can be set
using setTime():
Setting pathogen parameters
Pathogen parameters must be stored in a list of aggressiveness components defined on a susceptible host for a pathogen genotype not adapted to resistance.
Buit-in parameterisation for different pathogens (e.g. rusts of
cereal crops, mildew of grapevine, black sigatoka of banana) are
available using function loadPathogen():
basic_patho_param <- loadPathogen(disease = "rust")
basic_patho_param
#> $name
#> [1] "rust"
#>
#> $survival_prob
#> [1] 1e-04
#>
#> $repro_sex_prob
#> [1] 0
#>
#> $infection_rate
#> [1] 0.4
#>
#> $propagule_prod_rate
#> [1] 3.125
#>
#> $latent_period_mean
#> [1] 10
#>
#> $latent_period_var
#> [1] 9
#>
#> $infectious_period_mean
#> [1] 24
#>
#> $infectious_period_var
#> [1] 105
#>
#> $sigmoid_kappa
#> [1] 5.333
#>
#> $sigmoid_sigma
#> [1] 3
#>
#> $sigmoid_plateau
#> [1] 1
#>
#> $sex_propagule_viability_limit
#> [1] 1
#>
#> $sex_propagule_release_mean
#> [1] 1
#>
#> $clonal_propagule_gradual_release
#> [1] 0
basic_patho_param <- loadPathogen(disease = "mildew")
basic_patho_param
#> $name
#> [1] "mildew"
#>
#> $survival_prob
#> [1] 1e-04
#>
#> $repro_sex_prob
#> [1] 0
#>
#> $infection_rate
#> [1] 0.9
#>
#> $propagule_prod_rate
#> [1] 2
#>
#> $latent_period_mean
#> [1] 7
#>
#> $latent_period_var
#> [1] 8
#>
#> $infectious_period_mean
#> [1] 14
#>
#> $infectious_period_var
#> [1] 22
#>
#> $sigmoid_kappa
#> [1] 5.333
#>
#> $sigmoid_sigma
#> [1] 3
#>
#> $sigmoid_plateau
#> [1] 1
#>
#> $sex_propagule_viability_limit
#> [1] 5
#>
#> $sex_propagule_release_mean
#> [1] 1
#>
#> $clonal_propagule_gradual_release
#> [1] 1
basic_patho_param <- loadPathogen(disease = "sigatoka")
basic_patho_param
#> $name
#> [1] "sigatoka"
#>
#> $survival_prob
#> [1] 0.5
#>
#> $repro_sex_prob
#> [1] 0
#>
#> $infection_rate
#> [1] 0.02
#>
#> $propagule_prod_rate
#> [1] 90.9
#>
#> $latent_period_mean
#> [1] 25.5
#>
#> $latent_period_var
#> [1] 1.5
#>
#> $infectious_period_mean
#> [1] 22
#>
#> $infectious_period_var
#> [1] 14
#>
#> $sigmoid_kappa
#> [1] 5.333
#>
#> $sigmoid_sigma
#> [1] 3
#>
#> $sigmoid_plateau
#> [1] 1
#>
#> $sex_propagule_viability_limit
#> [1] 1
#>
#> $sex_propagule_release_mean
#> [1] 1
#>
#> $clonal_propagule_gradual_release
#> [1] 0This list may be updated to change a specific parameter. For instance, to change the infection rate to 50%:
basic_patho_param <- loadPathogen("rust")
basic_patho_param$infection_rate <- 0.5
basic_patho_param
#> $name
#> [1] "rust"
#>
#> $survival_prob
#> [1] 1e-04
#>
#> $repro_sex_prob
#> [1] 0
#>
#> $infection_rate
#> [1] 0.5
#>
#> $propagule_prod_rate
#> [1] 3.125
#>
#> $latent_period_mean
#> [1] 10
#>
#> $latent_period_var
#> [1] 9
#>
#> $infectious_period_mean
#> [1] 24
#>
#> $infectious_period_var
#> [1] 105
#>
#> $sigmoid_kappa
#> [1] 5.333
#>
#> $sigmoid_sigma
#> [1] 3
#>
#> $sigmoid_plateau
#> [1] 1
#>
#> $sex_propagule_viability_limit
#> [1] 1
#>
#> $sex_propagule_release_mean
#> [1] 1
#>
#> $clonal_propagule_gradual_release
#> [1] 0Alternatively, the list may be generated manually to control all parameters:
basic_patho_param <- list(infection_rate = 0.4
, latent_period_mean = 10
, latent_period_var = 9
, propagule_prod_rate = 3.125
, infectious_period_mean = 24
, infectious_period_var = 105
, survival_prob = 1e-4
, repro_sex_prob = 0
, sigmoid_kappa = 5.333
, sigmoid_sigma = 3
, sigmoid_plateau = 1
, sex_propagule_viability_limit = 1
, sex_propagule_release_mean = 1
, clonal_propagule_gradual_release = 0)Then, the list is used to fuel the object simul_params
via the function setPathogen():
simul_params <- setPathogen(simul_params, patho_params = basic_patho_param)
simul_params@Pathogen
#> $infection_rate
#> [1] 0.4
#>
#> $latent_period_mean
#> [1] 10
#>
#> $latent_period_var
#> [1] 9
#>
#> $propagule_prod_rate
#> [1] 3.125
#>
#> $infectious_period_mean
#> [1] 24
#>
#> $infectious_period_var
#> [1] 105
#>
#> $survival_prob
#> [1] 1e-04
#>
#> $repro_sex_prob
#> [1] 0
#>
#> $sigmoid_kappa
#> [1] 5.333
#>
#> $sigmoid_sigma
#> [1] 3
#>
#> $sigmoid_plateau
#> [1] 1
#>
#> $sex_propagule_viability_limit
#> [1] 1
#>
#> $sex_propagule_release_mean
#> [1] 1
#>
#> $clonal_propagule_gradual_release
#> [1] 0Setting the landscape and pathogen dispersal
The landscape (i.e. boundaries of fields) must be in shapefile
format. Five built-in landscapes of about 150 fields are available using
the function loadLandscape():
landscape <- loadLandscape(id = 1)
length(landscape)
#> [1] 155
plot(landscape, main = "Landscape structure")
See also tutorial on how to parameterise landscape and dispersal to use your own landscape and compute your own dispersal matrices.
Dispersal is given by a vectorised matrix giving the probability of
dispersal from any field of the landscape to any other field. The size
of the matrix must be the square of the number of fields in the
landscape. It is thus specific to both the pathogen and the landscape.
For rusts pathogens, a built-in dispersal matrix is available for each
landscape using the function loadDispersalPathogen():
disp_patho_clonal <- loadDispersalPathogen(id = 1)[[1]]
head(disp_patho_clonal)
#> [1] 8.814254e-01 9.525884e-04 7.079895e-10 1.594379e-10 3.285800e-06
#> [6] 3.634297e-11
length(landscape)^2 == length(disp_patho_clonal)
#> [1] TRUEThen, the object simul_params is updated with the
landscape and dispersal matrix via the functions
setLandscape() and setDispersalPathogen(),
respectively:
Setting croptypes, cultivars and resistance genes
Fields of the landscape are cultivated with different croptypes that can rotate through time; each croptype is composed of a pure cultivar or a mixture; and each cultivar may carry one or several resistance genes.
Cultivars
Characteristics of each host genotype (i.e. cultivar) are summarised
in a dataframe, which contains parameters representing the cultivar as
if it was cultivated in a pure crop. Note that the name of the
cultivar cannot accept spaces.
A buit-in parameterisation for classical types of cultivars is available
using loadCultivar() to generate each line of the
dataframe. Type “nonCrop” allows the simulation of forest, fallows, etc.
i.e. everything that is not planted, does not cost anything and does not
yield anything (with regard to the subject of the study).
It is advised to implement a susceptible cultivar at first line
of the dataframe to allow pathogen initial inoculation in default
parameterisation.
cultivar1 <- loadCultivar(name = "Susceptible", type = "wheat")
cultivar2 <- loadCultivar(name = "Resistant1", type = "wheat")
cultivar3 <- loadCultivar(name = "Resistant2", type = "banana")
cultivar4 <- loadCultivar(name = "Resistant3", type = "pepper")
cultivar5 <- loadCultivar(name = "Forest", type = "nonCrop")
cultivars <- data.frame(rbind(cultivar1, cultivar2, cultivar3, cultivar4, cultivar5)
, stringsAsFactors = FALSE)
cultivars
#> cultivarName initial_density max_density growth_rate reproduction_rate
#> 1 Susceptible 0.10 2.00 0.10 0
#> 2 Resistant1 0.10 2.00 0.10 0
#> 3 Resistant2 0.90 1.80 0.02 0
#> 4 Resistant3 1.75 1.75 0.00 0
#> 5 Forest 0.00 2.00 0.00 0
#> yield_H yield_L yield_I yield_R planting_cost market_value
#> 1 2.5 0.0 0 0 225 200
#> 2 2.5 0.0 0 0 225 200
#> 3 46.8 46.8 0 0 0 0
#> 4 0.5 0.5 0 0 0 0
#> 5 0.0 0.0 0 0 0 0Similarly as pathogen parameters, characteristics of the cultivars may be updated as required. For example, to change the growth rate of the susceptible cultivar:
cultivars[cultivars$cultivarName == "Susceptible", "growth_rate"] <- 0.2
cultivars
#> cultivarName initial_density max_density growth_rate reproduction_rate
#> 1 Susceptible 0.10 2.00 0.20 0
#> 2 Resistant1 0.10 2.00 0.10 0
#> 3 Resistant2 0.90 1.80 0.02 0
#> 4 Resistant3 1.75 1.75 0.00 0
#> 5 Forest 0.00 2.00 0.00 0
#> yield_H yield_L yield_I yield_R planting_cost market_value
#> 1 2.5 0.0 0 0 225 200
#> 2 2.5 0.0 0 0 225 200
#> 3 46.8 46.8 0 0 0 0
#> 4 0.5 0.5 0 0 0 0
#> 5 0.0 0.0 0 0 0 0Finally, the dataframe cultivars can also be generated
entirely from scratch:
cultivars_new <- data.frame(cultivarName = c("Susceptible", "Resistant"),
initial_density = c(0.1, 0.2),
max_density = c(2.0, 3.0),
growth_rate = c(0.1, 0.2),
reproduction_rate = c(0.0, 0.0),
yield_H = c(2.5, 2.0),
yield_L = c(0.0, 0.0),
yield_I = c(0.0, 0.0),
yield_R = c(0.0, 0.0),
planting_cost = c(225, 300),
market_value = c(200, 150),
stringsAsFactors = FALSE)
cultivars_new
#> cultivarName initial_density max_density growth_rate reproduction_rate
#> 1 Susceptible 0.1 2 0.1 0
#> 2 Resistant 0.2 3 0.2 0
#> yield_H yield_L yield_I yield_R planting_cost market_value
#> 1 2.5 0 0 0 225 200
#> 2 2.0 0 0 0 300 150Note, assuming that only healthy hosts (state H) contribute to host growth, the production of healthy biomass between t and t + 1 is computed using the following logistic equation: $$H_{t+1} = H_{t} \times \left[1 + growth\_rate \times (1-\frac{N_{t}}{K})\right]$$ with Nt the total number of individual hosts at time-step t and K the carrying capacity.
Resistance genes
This part can be skipped if no resistance gene is to be simulated.
Characteristics of each plant resistance gene and each corresponding
pathogenicity gene are summarised in a dataframe.
A built-in parameterisation for classical resistance sources is
available using loadGene() to generate each line of the
dataframe. Type “majorGene” is for completely efficient resistance to
which pathogen may adapt via a single mutation.
Type “APR” stands for Adult Plant Resistance, i.e. a major gene which
activates after a delay after planting, and type “QTL” is a partially
efficient resistance source to which the pathogen may adapt gradually.
The type “immunity” code for a completely efficient resistance gene that
cannot be overcome, in such a way that infection is totally impossible;
it is helpful to parameterise non-host cultivars.
gene1 <- loadGene(name = "MG 1", type = "majorGene")
gene2 <- loadGene(name = "Lr34", type = "APR")
gene3 <- loadGene(name = "gene 3", type = "QTL")
gene4 <- loadGene(name = "nonhost resistance", type = "immunity")
genes <- data.frame(rbind(gene1, gene2, gene3, gene4), stringsAsFactors = FALSE)
genes
#> geneName efficiency age_of_activ_mean age_of_activ_var
#> 1 MG 1 1.0 0 0
#> 2 Lr34 1.0 30 30
#> 3 gene 3 0.5 0 0
#> 4 nonhost resistance 1.0 0 0
#> mutation_prob Nlevels_aggressiveness adaptation_cost relative_advantage
#> 1 1e-07 2 0.5 0.5
#> 2 1e-07 2 0.5 0.5
#> 3 1e-04 6 0.5 0.5
#> 4 0e+00 1 0.0 0.0
#> tradeoff_strength target_trait recombination_sd
#> 1 1 IR 1.00
#> 2 1 IR 1.00
#> 3 1 IR 0.27
#> 4 1 IR 1.00Similarly as pathogen parameters, characteristics of the genes may be updated as required. For example, to change the mutation probability of the pathogen with regard to its adaptation to “MG 1”:
genes[genes$geneName == "MG 1", "mutation_prob"] <- 1e-3
genes
#> geneName efficiency age_of_activ_mean age_of_activ_var
#> 1 MG 1 1.0 0 0
#> 2 Lr34 1.0 30 30
#> 3 gene 3 0.5 0 0
#> 4 nonhost resistance 1.0 0 0
#> mutation_prob Nlevels_aggressiveness adaptation_cost relative_advantage
#> 1 1e-03 2 0.5 0.5
#> 2 1e-07 2 0.5 0.5
#> 3 1e-04 6 0.5 0.5
#> 4 0e+00 1 0.0 0.0
#> tradeoff_strength target_trait recombination_sd
#> 1 1 IR 1.00
#> 2 1 IR 1.00
#> 3 1 IR 0.27
#> 4 1 IR 1.00Alternatively, the dataframe genes can also be generated
entirely from scratch:
genes_new <- data.frame(geneName = c("MG1", "MG2"),
efficiency = c(1.0 , 0.8 ),
age_of_activ_mean = c(0.0 , 0.0 ),
age_of_activ_var = c(0.0 , 0.0 ),
mutation_prob = c(1E-7 , 1E-4),
Nlevels_aggressiveness = c(2 , 2 ),
adaptation_cost = c(0.50 , 0.75 ),
relative_advantage = c(0.50 , 0.75 ),
tradeoff_strength = c(1.0 , 1.0 ),
target_trait = c("IR" , "LAT"),
recombination_sd = c(1.0,1.0),
stringsAsFactors = FALSE)
genes_new
#> geneName efficiency age_of_activ_mean age_of_activ_var mutation_prob
#> 1 MG1 1.0 0 0 1e-07
#> 2 MG2 0.8 0 0 1e-04
#> Nlevels_aggressiveness adaptation_cost relative_advantage tradeoff_strength
#> 1 2 0.50 0.50 1
#> 2 2 0.75 0.75 1
#> target_trait recombination_sd
#> 1 IR 1
#> 2 LAT 1Note that the column “efficiency” refers to the percentage of reduction of the targeted aggressiveness component on hosts carrying the gene. For example, a 80% efficient resistance against infection rate (target_trait = “IR”) means that the infection rate of a non-adapted pathogen is reduced by 80% on a resistant host compared to what it is on a susceptible host. For resistances targeting the latent period, the percentage of reduction is applied to the inverse of the latent period in such a way that latent period is higher in resistant than in susceptible hosts.
Allocating genes to cultivars
The object simul_params can be updated with
setGenes() and setCultivars():
simul_params <- setGenes(simul_params, dfGenes = genes)
simul_params <- setCultivars(simul_params, dfCultivars = cultivars)
simul_params@Genes
#> geneName efficiency age_of_activ_mean
#> MG 1 MG 1 1.0 0
#> Lr34 Lr34 1.0 30
#> gene 3 gene 3 0.5 0
#> nonhost resistance nonhost resistance 1.0 0
#> age_of_activ_var mutation_prob Nlevels_aggressiveness
#> MG 1 0 1e-03 2
#> Lr34 30 1e-07 2
#> gene 3 0 1e-04 6
#> nonhost resistance 0 0e+00 1
#> adaptation_cost relative_advantage tradeoff_strength
#> MG 1 0.5 0.5 1
#> Lr34 0.5 0.5 1
#> gene 3 0.5 0.5 1
#> nonhost resistance 0.0 0.0 1
#> target_trait recombination_sd
#> MG 1 IR 1.00
#> Lr34 IR 1.00
#> gene 3 IR 0.27
#> nonhost resistance IR 1.00
simul_params@Cultivars
#> cultivarName initial_density max_density growth_rate
#> Susceptible Susceptible 0.10 2.00 0.20
#> Resistant1 Resistant1 0.10 2.00 0.10
#> Resistant2 Resistant2 0.90 1.80 0.02
#> Resistant3 Resistant3 1.75 1.75 0.00
#> Forest Forest 0.00 2.00 0.00
#> reproduction_rate yield_H yield_L yield_I yield_R planting_cost
#> Susceptible 0 2.5 0.0 0 0 225
#> Resistant1 0 2.5 0.0 0 0 225
#> Resistant2 0 46.8 46.8 0 0 0
#> Resistant3 0 0.5 0.5 0 0 0
#> Forest 0 0.0 0.0 0 0 0
#> market_value
#> Susceptible 200
#> Resistant1 200
#> Resistant2 0
#> Resistant3 0
#> Forest 0Then the function allocateCultivarGenes() allows the
attribution of resistance genes to cultivars:
simul_params <- allocateCultivarGenes(simul_params
, cultivarName = "Resistant1"
, listGenesNames = c("MG 1"))
simul_params <- allocateCultivarGenes(simul_params
, cultivarName = "Resistant2"
, listGenesNames = c("Lr34", "gene 3"))
simul_params <- allocateCultivarGenes(simul_params
, cultivarName = "Resistant3"
, listGenesNames = c("nonhost resistance"))
simul_params@CultivarsGenes
#> MG 1 Lr34 gene 3 nonhost resistance
#> Susceptible 0 0 0 0
#> Resistant1 1 0 0 0
#> Resistant2 0 1 1 0
#> Resistant3 0 0 0 1
#> Forest 0 0 0 0With this example of parameterisation:
- “Susceptible” is a susceptible cultivar (initially infected by a
wild-type pathogen)
- “Resistant1” is a mono-resistant cultivar
- “Resistant2” is a pyramided cultivar
- “Resistant3” is a nonhost cultivar
- “Forest” is not a crop.
Infection is impossible on both “Resistance3” and “Forest”, but the
former will be considered for host growth, yield and planting costs,
whereas the latter won’t.
Allocating cultivars to croptypes
Characteristics of each croptype (a croptype is a set of hosts
cultivated in a field with specific proportions) are summarised in a
dataframe.
A buit-in parameterisation for classical croptypes is available using
loadCroptypes() to generate the whole table filled with
zeros:
croptypes <- loadCroptypes(simul_params, names = c("Susceptible crop"
, "Pure resistant crop"
, "Mixture"
, "Other"))
croptypes
#> croptypeID croptypeName Susceptible Resistant1 Resistant2 Resistant3
#> 1 0 Susceptible crop 0 0 0 0
#> 2 1 Pure resistant crop 0 0 0 0
#> 3 2 Mixture 0 0 0 0
#> 4 3 Other 0 0 0 0
#> Forest
#> 1 0
#> 2 0
#> 3 0
#> 4 0Then croptypes is updated by
allocateCroptypeCultivars() to specify the composition of
every croptype with regard to cultivars (and proportion for
mixtures):
croptypes <- allocateCroptypeCultivars(croptypes
, croptypeName = "Susceptible crop"
, cultivarsInCroptype = "Susceptible")
croptypes <- allocateCroptypeCultivars(croptypes
, croptypeName = "Pure resistant crop"
, cultivarsInCroptype = "Resistant1")
croptypes <- allocateCroptypeCultivars(croptypes
, croptypeName = "Mixture"
, cultivarsInCroptype = c("Resistant2","Resistant3")
, prop = c(0.4, 0.6))
croptypes <- allocateCroptypeCultivars(croptypes
, croptypeName = "Other"
, cultivarsInCroptype = "Forest")
croptypes
#> croptypeID croptypeName Susceptible Resistant1 Resistant2 Resistant3
#> 1 0 Susceptible crop 1 0 0.0 0.0
#> 2 1 Pure resistant crop 0 1 0.0 0.0
#> 3 2 Mixture 0 0 0.4 0.6
#> 4 3 Other 0 0 0.0 0.0
#> Forest
#> 1 0
#> 2 0
#> 3 0
#> 4 1Finally the object simul_params is updated using
setCroptypes():
simul_params <- setCroptypes(simul_params, dfCroptypes = croptypes)
simul_params@Croptypes
#> croptypeID croptypeName Susceptible Resistant1 Resistant2 Resistant3
#> 0 0 Susceptible crop 1 0 0.0 0.0
#> 1 1 Pure resistant crop 0 1 0.0 0.0
#> 2 2 Mixture 0 0 0.4 0.6
#> 3 3 Other 0 0 0.0 0.0
#> Forest
#> 0 0
#> 1 0
#> 2 0
#> 3 1Alternatively, the dataframe croptypes can be generated
from scratch:
croptypes <- data.frame(croptypeID = c(0, 1, 2, 3) ## must start at 0 and match with values from landscape "croptypeID" layer
, croptypeName = c("Susceptible crop"
, "Pure resistant crop"
, "Mixture"
, "Other")
, Susceptible = c(1,0,0 ,0)
, Resistant1 = c(0,1,0 ,0)
, Resistant2 = c(0,0,0.5,0)
, Resistant3 = c(0,0,0.5,0)
, Forest = c(0,0,0 ,1)
, stringsAsFactors = FALSE)
simul_params <- setCroptypes(simul_params, croptypes)Allocating croptypes to fields of the landscape
The function allocateLandscapeCroptypes() manages the
allocation of croptypes in time (for rotations of different croptypes on
the same fields) and space (for mosaic of fields cultivated with
different croptypes). See ?allocateLandscapeCroptypes for
help in parameters.
Briefly, a rotation sequence is defined by a list. Each element of this
list is a vector containing the indices of the croptypes that are
cultivated simultaneously in the landscape. The “rotation_period”
parameter defines the duration before switching from one element of
“rotation_sequence” to the next. For each element of “rotation_sequence”
is associated a vector of proportions of each croptype in the landscape
(parameter “prop”). The parameter “aggreg” controls the level of spatial
aggregation between croptypes.
For example, to generate a landscape whose surface is composed of 1/3 of forests, 1/3 of susceptible crop, and 1/3 of fields where a pure resistant crop is alternated with a mixture every two years:
# croptypeIDs cultivated in each element of the rotation sequence:
rotation_sequence <- list(c(0,1,3), c(0,2,3))
rotation_period <- 2 # number of years before rotation of the landscape
prop <- list(rep(1/3, 3), rep(1/3, 3)) # proportion (in surface) of each croptype
aggreg <-1 # level of spatial aggregation
simul_params <- allocateLandscapeCroptypes(simul_params
, rotation_period = rotation_period
, rotation_sequence = rotation_sequence
, prop = prop
, aggreg = aggreg
, graphic = TRUE)
# plot(simul_params@Landscape)Setting the inoculum
To set the inoculum, the function setInoculum() is used.
Several scenarios may be simulated and are summarized below. For the
default scenario (see below), the function is simply parameterised with
the probability for individual hosts to be infectious (i.e. at state
‘I’) at the beginning of the simulation (i.e. at t=0).
For more complex scenarios (i.e. to specify the location and genetic
structure of the inoculum), the function setInoculum() can
be used with a 3D-array of dimensions (Nhost, Npatho, Npoly) indicating
the initial probability to be infectious, for each cultivar, pathogen
genotype and polygon, respectively. To define this array, the functions
getMatrixGenePatho(),
getMatrixCultivarPatho(),
getMatrixCroptypePatho() and
getMatrixPolyPatho() acknowledge which pathogen genotypes
can infect which genes, cultivars, croptypes and polygons respectively.
Each function returns a matrix indicating if there is compatibility
(value of 1, i.e. infection is possible) or not (value of 0, i.e. the
cultivar is not present, or protected by a fully efficient resistance
gene targeting the infection rate from the beginning of the cropping
season).
getMatrixGenePatho(simul_params)
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11]
#> MG 1 0 0 0 0 0 0 0 0 0 0 0
#> Lr34 1 1 1 1 1 1 1 1 1 1 1
#> gene 3 1 1 1 1 1 1 1 1 1 1 1
#> nonhost resistance 0 0 0 0 0 0 0 0 0 0 0
#> [,12] [,13] [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21]
#> MG 1 0 1 1 1 1 1 1 1 1 1
#> Lr34 1 1 1 1 1 1 1 1 1 1
#> gene 3 1 1 1 1 1 1 1 1 1 1
#> nonhost resistance 0 0 0 0 0 0 0 0 0 0
#> [,22] [,23] [,24]
#> MG 1 1 1 1
#> Lr34 1 1 1
#> gene 3 1 1 1
#> nonhost resistance 0 0 0
getMatrixCultivarPatho(simul_params)
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12]
#> Susceptible 1 1 1 1 1 1 1 1 1 1 1 1
#> Resistant1 0 0 0 0 0 0 0 0 0 0 0 0
#> Resistant2 1 1 1 1 1 1 1 1 1 1 1 1
#> Resistant3 0 0 0 0 0 0 0 0 0 0 0 0
#> Forest 0 0 0 0 0 0 0 0 0 0 0 0
#> [,13] [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23]
#> Susceptible 1 1 1 1 1 1 1 1 1 1 1
#> Resistant1 1 1 1 1 1 1 1 1 1 1 1
#> Resistant2 1 1 1 1 1 1 1 1 1 1 1
#> Resistant3 0 0 0 0 0 0 0 0 0 0 0
#> Forest 0 0 0 0 0 0 0 0 0 0 0
#> [,24]
#> Susceptible 1
#> Resistant1 1
#> Resistant2 1
#> Resistant3 0
#> Forest 0
getMatrixCroptypePatho(simul_params)
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11]
#> Susceptible crop 1 1 1 1 1 1 1 1 1 1 1
#> Pure resistant crop 0 0 0 0 0 0 0 0 0 0 0
#> Mixture 1 1 1 1 1 1 1 1 1 1 1
#> Other 0 0 0 0 0 0 0 0 0 0 0
#> [,12] [,13] [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21]
#> Susceptible crop 1 1 1 1 1 1 1 1 1 1
#> Pure resistant crop 0 1 1 1 1 1 1 1 1 1
#> Mixture 1 1 1 1 1 1 1 1 1 1
#> Other 0 0 0 0 0 0 0 0 0 0
#> [,22] [,23] [,24]
#> Susceptible crop 1 1 1
#> Pure resistant crop 1 1 1
#> Mixture 1 1 1
#> Other 0 0 0
getMatrixPolyPatho(simul_params)[1:10,]
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
#> [1,] 0 0 0 0 0 0 0 0 0 0 0 0 0
#> [2,] 0 0 0 0 0 0 0 0 0 0 0 0 0
#> [3,] 1 1 1 1 1 1 1 1 1 1 1 1 1
#> [4,] 0 0 0 0 0 0 0 0 0 0 0 0 1
#> [5,] 0 0 0 0 0 0 0 0 0 0 0 0 1
#> [6,] 0 0 0 0 0 0 0 0 0 0 0 0 1
#> [7,] 1 1 1 1 1 1 1 1 1 1 1 1 1
#> [8,] 0 0 0 0 0 0 0 0 0 0 0 0 1
#> [9,] 0 0 0 0 0 0 0 0 0 0 0 0 1
#> [10,] 1 1 1 1 1 1 1 1 1 1 1 1 1
#> [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24]
#> [1,] 0 0 0 0 0 0 0 0 0 0 0
#> [2,] 0 0 0 0 0 0 0 0 0 0 0
#> [3,] 1 1 1 1 1 1 1 1 1 1 1
#> [4,] 1 1 1 1 1 1 1 1 1 1 1
#> [5,] 1 1 1 1 1 1 1 1 1 1 1
#> [6,] 1 1 1 1 1 1 1 1 1 1 1
#> [7,] 1 1 1 1 1 1 1 1 1 1 1
#> [8,] 1 1 1 1 1 1 1 1 1 1 1
#> [9,] 1 1 1 1 1 1 1 1 1 1 1
#> [10,] 1 1 1 1 1 1 1 1 1 1 1Finally, the function loadInoculum() helps build the
inoculum array as follows:
Let ϕv, p, i
be the probability for an individual of cultivar v to be infected by pathogen
genotype p in field i at the beginning of the
simulation. This probability is computed as follows: ϕv, p, i = ϕ0 × ϕvhost × ϕppatho × ϕipoly × Iv, ipresent × Iv, pcompatible
with:
ϕhost
the vector of probabilities for every host (parameter
pI0_host),
ϕpatho
the vector of probabilities for every pathogen genotype (parameter
pI0_patho),
ϕpoly
the vector of probabilities for every polygon (parameter
pI0_poly),
ϕ0 a multiplicative
constant (parameter pI0_all).
Iv, ipresent
a binary variable equal to 1 if cultivar v is grown in field i (and 0 otherwise),
Iv, pcompatible
a binary variable equal to 1 if pathogen genotype p can infect cultivar v at the beginning of the cropping
season (and 0 otherwise).
Scenario 1 (default). Only the avirulent pathogen on the susceptible cultivar in all fields (global inoculum)
The default scenario is the presence of a pathogen genotype not adapted to any resistance gene, and present in all fields of the landscape where a susceptible cultivar is grown. In this situation, it is important that the susceptible cultivar is entered at the first line of the table cultivars. Then, one can simply use:
# Option 1: simply use the default parameterisation
simul_params <- setInoculum(simul_params, 5E-4)
# Option 2: use loadInoculum()
Npatho <- prod(simul_params@Genes$Nlevels_aggressiveness)
Nhost <- nrow(simul_params@Cultivars)
pI0 <- loadInoculum(simul_params, pI0_all=5E-4, pI0_host=c(1,rep(0, Nhost-1)), pI0_patho=c(1,rep(0, Npatho-1)))
simul_params <- setInoculum(simul_params, pI0)Scenario 2. Only the avirulent pathogen on the susceptible cultivar in only some fields (local inoculum)
To specify the location of the inoculum, the parameters
pI0_host, pI0_patho and pI0_poly
are filled with values of 1 and 0 indicating if the cultivar, pathogen
genotype and field are inoculated or not. The probability is given by
the constant pI0_all. In this example, 5 fields in the
landscape are randomly chosen among those cultivated with the
susceptible cultivar:
Npatho <- prod(simul_params@Genes$Nlevels_aggressiveness) ## Nb of pathogen genotypes
Nhost <- nrow(simul_params@Cultivars) ## Nb of cultivars
Npoly <- nrow(simul_params@Landscape) ## Nb of polygons in the landscape
Npoly_inoc <- 5 ## number of inoculated polygons
compatible_poly <- getMatrixPolyPatho(simul_params)[,1] ## whether the avr pathogen can infect the polygons
id_poly <- sample(grep(1, compatible_poly), Npoly_inoc) ## random polygon picked among compatible ones
pI0_poly <- as.numeric(1:Npoly %in% id_poly)
pI0 <- loadInoculum(simul_params, pI0_all=5E-4, pI0_host=c(1,rep(0, Nhost-1)), pI0_patho=c(1,rep(0, Npatho-1)),
pI0_poly=pI0_poly)
simul_params <- setInoculum(simul_params, pI0)Scenario 3. A diversity of pathogen genotypes in the inoculum, in all fields (global inoculum)
This scenario matches with situations where several pathogen
genotypes (including those adapted to resistance) are initially present
in the landscape at the beginning of the simulation. In this example,
different probabilities are given to the different pathogen genotypes
using the parameters pI0_patho (the same rationale can be
used for different probabilities on the different hosts using
pI0_host).
Scenario 4. A diversity of pathogen genotypes in the inoculum, in some fields only (local inoculum)
Here, the example is similar as the previous one but only 5 fields are inoculated:
Npoly <- nrow(simul_params@Landscape)
Npoly_inoc <- 5 ## number of inoculated polygons
id_poly <- sample(1:Npoly, Npoly_inoc) ## random polygon
pI0_poly <- as.numeric(1:Npoly %in% id_poly)
pI0 <- loadInoculum(simul_params, pI0_patho=c(1E-3,1E-4,1E-4,1E-5), pI0_host=c(1,1), pI0_poly=pI0_poly)
simul_params <- setInoculum(simul_params, pI0)Scenario 5. Custom 3D array to define the inoculum
At last, if one wants to run a simulation with a custom inoculum on
the whole landscape, it can simply be entered in the function
setInoculum() as an array of dimension (Nhost, Npatho,
Npoly). Note that in this situation, host individuals may be infected
regardless the resistance gene they carry.
## example with 2 cultivars, 4 pathogen genotypes and 5 fields
Nhost=2
Npatho=4
Npoly=5
pI0 <- array(data = 1:40 / 100, dim = c(Nhost, Npatho, Npoly))
simul_params <- setInoculum(simul_params, pI0)To generate an array that accounts for the fact that (i) the
cultivars are not grown in all polygons, and (ii) cultivars may carry a
resistance gene that prevent initial infection by some pathogen
genotypes, one can use the function loadInoculum() as
follows:
Visualization
The 3D-array inoculum can be vizualised using the function
inoculumToMatrix():
inoculumToMatrix(simul_params)[,,1:5]
#> , , 1
#>
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12]
#> Susceptible 0 0 0 0 0 0 0 0 0 0 0 0
#> Resistant1 0 0 0 0 0 0 0 0 0 0 0 0
#> Resistant2 0 0 0 0 0 0 0 0 0 0 0 0
#> Resistant3 0 0 0 0 0 0 0 0 0 0 0 0
#> Forest 0 0 0 0 0 0 0 0 0 0 0 0
#> [,13] [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23]
#> Susceptible 0 0 0 0 0 0 0 0 0 0 0
#> Resistant1 0 0 0 0 0 0 0 0 0 0 0
#> Resistant2 0 0 0 0 0 0 0 0 0 0 0
#> Resistant3 0 0 0 0 0 0 0 0 0 0 0
#> Forest 0 0 0 0 0 0 0 0 0 0 0
#> [,24]
#> Susceptible 0
#> Resistant1 0
#> Resistant2 0
#> Resistant3 0
#> Forest 0
#>
#> , , 2
#>
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12]
#> Susceptible 0 0 0 0 0 0 0 0 0 0 0 0
#> Resistant1 0 0 0 0 0 0 0 0 0 0 0 0
#> Resistant2 0 0 0 0 0 0 0 0 0 0 0 0
#> Resistant3 0 0 0 0 0 0 0 0 0 0 0 0
#> Forest 0 0 0 0 0 0 0 0 0 0 0 0
#> [,13] [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23]
#> Susceptible 0 0 0 0 0 0 0 0 0 0 0
#> Resistant1 0 0 0 0 0 0 0 0 0 0 0
#> Resistant2 0 0 0 0 0 0 0 0 0 0 0
#> Resistant3 0 0 0 0 0 0 0 0 0 0 0
#> Forest 0 0 0 0 0 0 0 0 0 0 0
#> [,24]
#> Susceptible 0
#> Resistant1 0
#> Resistant2 0
#> Resistant3 0
#> Forest 0
#>
#> , , 3
#>
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12]
#> Susceptible 5e-04 0 0 0 0 0 0 0 0 0 0 0
#> Resistant1 0e+00 0 0 0 0 0 0 0 0 0 0 0
#> Resistant2 0e+00 0 0 0 0 0 0 0 0 0 0 0
#> Resistant3 0e+00 0 0 0 0 0 0 0 0 0 0 0
#> Forest 0e+00 0 0 0 0 0 0 0 0 0 0 0
#> [,13] [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23]
#> Susceptible 0 0 0 0 0 0 0 0 0 0 0
#> Resistant1 0 0 0 0 0 0 0 0 0 0 0
#> Resistant2 0 0 0 0 0 0 0 0 0 0 0
#> Resistant3 0 0 0 0 0 0 0 0 0 0 0
#> Forest 0 0 0 0 0 0 0 0 0 0 0
#> [,24]
#> Susceptible 0
#> Resistant1 0
#> Resistant2 0
#> Resistant3 0
#> Forest 0
#>
#> , , 4
#>
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12]
#> Susceptible 0 0 0 0 0 0 0 0 0 0 0 0
#> Resistant1 0 0 0 0 0 0 0 0 0 0 0 0
#> Resistant2 0 0 0 0 0 0 0 0 0 0 0 0
#> Resistant3 0 0 0 0 0 0 0 0 0 0 0 0
#> Forest 0 0 0 0 0 0 0 0 0 0 0 0
#> [,13] [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23]
#> Susceptible 0 0 0 0 0 0 0 0 0 0 0
#> Resistant1 0 0 0 0 0 0 0 0 0 0 0
#> Resistant2 0 0 0 0 0 0 0 0 0 0 0
#> Resistant3 0 0 0 0 0 0 0 0 0 0 0
#> Forest 0 0 0 0 0 0 0 0 0 0 0
#> [,24]
#> Susceptible 0
#> Resistant1 0
#> Resistant2 0
#> Resistant3 0
#> Forest 0
#>
#> , , 5
#>
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12]
#> Susceptible 0 0 0 0 0 0 0 0 0 0 0 0
#> Resistant1 0 0 0 0 0 0 0 0 0 0 0 0
#> Resistant2 0 0 0 0 0 0 0 0 0 0 0 0
#> Resistant3 0 0 0 0 0 0 0 0 0 0 0 0
#> Forest 0 0 0 0 0 0 0 0 0 0 0 0
#> [,13] [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23]
#> Susceptible 0 0 0 0 0 0 0 0 0 0 0
#> Resistant1 0 0 0 0 0 0 0 0 0 0 0
#> Resistant2 0 0 0 0 0 0 0 0 0 0 0
#> Resistant3 0 0 0 0 0 0 0 0 0 0 0
#> Forest 0 0 0 0 0 0 0 0 0 0 0
#> [,24]
#> Susceptible 0
#> Resistant1 0
#> Resistant2 0
#> Resistant3 0
#> Forest 0Updating the survival probability during the off-season
At the end of each cropping season, pathogens experience a bottleneck
representing the off-season. The probability for a pathogen propagule to
survive the off-season depends on the capacity of the “green bridge” to
host the pathogen. This green bridge can, for example, be a wild
reservoir or volunteer plants remaining in the field (e.g. owing to
seedlings or incomplete harvest). It is assumed that the probability of
survival is the same every year and in every polygon, but this
assumption can be relaxed by updating the probability with a matrix
indicating a probability for every croptype and every year. This
simulates different management strategies or agronomic practices during
the off-season. The function updateSurvivalProb() creates
this matrix as follows:
Let λy, c
be the probability for a pathogen propagule to survive the off-season
between year y and year y + 1 in a polygon cultivated with
croptype c. Unless the matrix
is directly entered via the parameter mat, it is computed
by λy, c = λy × λc
with:
λy the
vector of probabilities for every year (parameter
mat_year),
λc the
vector of probabilities for every croptype (parameter
mat_croptype).
Ncroptypes <- nrow(simul_params@Croptypes)
Nyears <- simul_params@TimeParam$Nyears
## Same probability in every croptype:
simul_params <- updateSurvivalProb(simul_params, mat_year=1:Nyears/100)
simul_params@Pathogen
#> $infection_rate
#> [1] 0.4
#>
#> $latent_period_mean
#> [1] 10
#>
#> $latent_period_var
#> [1] 9
#>
#> $propagule_prod_rate
#> [1] 3.125
#>
#> $infectious_period_mean
#> [1] 24
#>
#> $infectious_period_var
#> [1] 105
#>
#> $survival_prob
#> [1] 0.01 0.02 0.03 0.04 0.05 0.06 0.01 0.02 0.03 0.04 0.05 0.06 0.01 0.02 0.03
#> [16] 0.04 0.05 0.06 0.01 0.02 0.03 0.04 0.05 0.06
#>
#> $repro_sex_prob
#> [1] 0
#>
#> $sigmoid_kappa
#> [1] 5.333
#>
#> $sigmoid_sigma
#> [1] 3
#>
#> $sigmoid_plateau
#> [1] 1
#>
#> $sex_propagule_viability_limit
#> [1] 1
#>
#> $sex_propagule_release_mean
#> [1] 1
#>
#> $clonal_propagule_gradual_release
#> [1] 0
## Same probability every year:
simul_params <- updateSurvivalProb(simul_params, mat_croptype=1:Ncroptypes/10)
simul_params@Pathogen
#> $infection_rate
#> [1] 0.4
#>
#> $latent_period_mean
#> [1] 10
#>
#> $latent_period_var
#> [1] 9
#>
#> $propagule_prod_rate
#> [1] 3.125
#>
#> $infectious_period_mean
#> [1] 24
#>
#> $infectious_period_var
#> [1] 105
#>
#> $survival_prob
#> [1] 0.1 0.1 0.1 0.1 0.1 0.1 0.2 0.2 0.2 0.2 0.2 0.2 0.3 0.3 0.3 0.3 0.3 0.3 0.4
#> [20] 0.4 0.4 0.4 0.4 0.4
#>
#> $repro_sex_prob
#> [1] 0
#>
#> $sigmoid_kappa
#> [1] 5.333
#>
#> $sigmoid_sigma
#> [1] 3
#>
#> $sigmoid_plateau
#> [1] 1
#>
#> $sex_propagule_viability_limit
#> [1] 1
#>
#> $sex_propagule_release_mean
#> [1] 1
#>
#> $clonal_propagule_gradual_release
#> [1] 0
## specific probability for different croptypes and years:
simul_params <- updateSurvivalProb(simul_params, mat_year=1:Nyears/100, mat_croptype=1:Ncroptypes/10)
simul_params@Pathogen
#> $infection_rate
#> [1] 0.4
#>
#> $latent_period_mean
#> [1] 10
#>
#> $latent_period_var
#> [1] 9
#>
#> $propagule_prod_rate
#> [1] 3.125
#>
#> $infectious_period_mean
#> [1] 24
#>
#> $infectious_period_var
#> [1] 105
#>
#> $survival_prob
#> [1] 0.001 0.002 0.003 0.004 0.005 0.006 0.002 0.004 0.006 0.008 0.010 0.012
#> [13] 0.003 0.006 0.009 0.012 0.015 0.018 0.004 0.008 0.012 0.016 0.020 0.024
#>
#> $repro_sex_prob
#> [1] 0
#>
#> $sigmoid_kappa
#> [1] 5.333
#>
#> $sigmoid_sigma
#> [1] 3
#>
#> $sigmoid_plateau
#> [1] 1
#>
#> $sex_propagule_viability_limit
#> [1] 1
#>
#> $sex_propagule_release_mean
#> [1] 1
#>
#> $clonal_propagule_gradual_release
#> [1] 0
## One probability per year and per croptype:
simul_params <- updateSurvivalProb(simul_params, mat=matrix(runif(Nyears*Ncroptypes), ncol=Ncroptypes))
simul_params@Pathogen
#> $infection_rate
#> [1] 0.4
#>
#> $latent_period_mean
#> [1] 10
#>
#> $latent_period_var
#> [1] 9
#>
#> $propagule_prod_rate
#> [1] 3.125
#>
#> $infectious_period_mean
#> [1] 24
#>
#> $infectious_period_var
#> [1] 105
#>
#> $survival_prob
#> [1] 0.33532076 0.63790872 0.82920106 0.70897520 0.34855035 0.12832787
#> [7] 0.38807849 0.92817755 0.80439077 0.75869681 0.95724989 0.99391388
#> [13] 0.60644099 0.02937717 0.33644536 0.27765809 0.11719755 0.04321826
#> [19] 0.37030979 0.33687831 0.17365255 0.62177328 0.39784363 0.95567577
#>
#> $repro_sex_prob
#> [1] 0
#>
#> $sigmoid_kappa
#> [1] 5.333
#>
#> $sigmoid_sigma
#> [1] 3
#>
#> $sigmoid_plateau
#> [1] 1
#>
#> $sex_propagule_viability_limit
#> [1] 1
#>
#> $sex_propagule_release_mean
#> [1] 1
#>
#> $clonal_propagule_gradual_release
#> [1] 0Visualization
The matrix of survival probabilities for every year and croptype, as
well as for every polygon and year, can be vizualised using the function
survivalProbToMatrix():
survivalProbToMatrix(simul_params)
#> $survival_prob
#> Susceptible crop Pure resistant crop Mixture Other
#> year_1 0.3353208 0.3880785 0.60644099 0.3703098
#> year_2 0.6379087 0.9281775 0.02937717 0.3368783
#> year_3 0.8292011 0.8043908 0.33644536 0.1736526
#> year_4 0.7089752 0.7586968 0.27765809 0.6217733
#> year_5 0.3485504 0.9572499 0.11719755 0.3978436
#> year_6 0.1283279 0.9939139 0.04321826 0.9556758
#>
#> $survival_prob_poly
#> year_1 year_2 year_3 year_4 year_5 year_6
#> poly_1 0.3703098 0.3368783 0.1736526 0.6217733 0.3978436 0.9556758
#> poly_2 0.3703098 0.3368783 0.1736526 0.6217733 0.3978436 0.9556758
#> poly_3 0.3353208 0.6379087 0.8292011 0.7089752 0.3485504 0.1283279
#> poly_4 0.3880785 0.9281775 0.3364454 0.2776581 0.9572499 0.9939139
#> poly_5 0.3880785 0.9281775 0.3364454 0.2776581 0.9572499 0.9939139
#> poly_6 0.3880785 0.9281775 0.3364454 0.2776581 0.9572499 0.9939139
#> poly_7 0.3353208 0.6379087 0.8292011 0.7089752 0.3485504 0.1283279
#> poly_8 0.3880785 0.9281775 0.3364454 0.2776581 0.9572499 0.9939139
#> poly_9 0.3880785 0.9281775 0.3364454 0.2776581 0.9572499 0.9939139
#> poly_10 0.3353208 0.6379087 0.8292011 0.7089752 0.3485504 0.1283279
#> poly_11 0.3353208 0.6379087 0.8292011 0.7089752 0.3485504 0.1283279
#> poly_12 0.3880785 0.9281775 0.3364454 0.2776581 0.9572499 0.9939139
#> poly_13 0.3880785 0.9281775 0.3364454 0.2776581 0.9572499 0.9939139
#> poly_14 0.3703098 0.3368783 0.1736526 0.6217733 0.3978436 0.9556758
#> poly_15 0.3880785 0.9281775 0.3364454 0.2776581 0.9572499 0.9939139
#> poly_16 0.3703098 0.3368783 0.1736526 0.6217733 0.3978436 0.9556758
#> poly_17 0.3703098 0.3368783 0.1736526 0.6217733 0.3978436 0.9556758
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#> poly_155 0.3880785 0.9281775 0.3364454 0.2776581 0.9572499 0.9939139Setting chemical treatments
This part can be skipped if no chemical treatment is to be simulated.
Cultivars may be treated with chemicals which reduce the pathogen
infection rate. Treatment efficiency is maximum (i.e. equal to the
parameter treatment_efficiency) at the time of treatment
application (noted t*); then it decreases
with time (i.e. natural pesticide degradation) and host growth (i.e. new
biomass is not protected by treatments):
$$IR(t) = IR_{max} \times \left(1 - \frac{treatment\_efficiency}{1+e^{4.0- 8.5 \times C(t)}}\right)$$ C(t) = C1 × C2 is the treatment concentration at t, which depends on:
- the timelag Δt = t − t*
passed since the time of treatment application t* (i.e. natural
pesticide degradation via the parameter
treatment_degradation_rate)
C1 = e−treatment_degradation_rate × Δt
- the newly produced host biomass, which is not protected by treatments (N(t*) and N(t) are host biomass at the time of treatment application and at time t, respectively)
C2 = min(1.0, N(t*)/N(t))
Cultivars to be treated with chemicals and dates of (possible)
applications are defined with parameters
treatment_cultivars and treatment_timesteps,
and are the same for all polygons cultivated with the cultivars to be
treated. However, the chemicals are applied in a polygon only if the
disease severity (i.e. I(t*)/N(t*))
at the application date is higher than a given threshold, defined by
treatment_application_threshold. The cost of a single
treatment application (monetary units/ha) is defined by
treatment_cost and will impact the economic outputs.
Treatment parameters can be loaded via the function
loadTreatment and next set via the function
setTreatment:
## Via function loadTreatment:
treatment <- loadTreatment(disease="mildew")
## Direct implementation:
treatment <- list(treatment_degradation_rate = 0.1,
treatment_efficiency = 0.8,
treatment_timesteps = seq(1,120,14) ,
treatment_cultivars = c(0),
treatment_cost = 0,
treatment_application_threshold = c(0.0))
## Set the parameters
simul_params <- setTreatment(simul_params, treatment)
#> Warning in checkTreatment(params): Simulation with chemical treatment
#> applicationsChoosing output variables
Several epidemiological, evolutionary and economic outputs can be
generated by landsepi and represented in text files
(writeTXT=TRUE), graphics (graphic=TRUE) and a
video (videoMP4=TRUE).
See equation below, as well as ?epid_output and
?evol_output for details on the different output
variables.
Possible epidemiological outputs include:
- “audpc” : Area Under Disease Progress Curve (average number of diseased hosts per square meter, AUDPCv, y)
- “audpc_rel” : relative Area Under Disease Progress Curve (average proportion of diseased hosts relative to the total number of existing hosts, AUDPCv, yr)
- “gla” : Green Leaf Area (average number of healthy hosts per square meter, GLAv, y)
- “gla_rel” : relative Green Leaf Area (average proportion of healthy hosts relative to the total number of existing hosts, GLAv, yr)
- “eco_yield” : total crop yield (in weight or volume units per ha, Yieldv, y)
- “eco_cost” : operational crop costs (in monetary units per ha, Operational_costv, y)
- “eco_product” : total crop products (in monetary units per ha, Productv, y)
- “eco_margin” : margin (products - operational costs, in monetary units per ha, Marginv, y)
- “contrib”: contribution of pathogen genotypes to LIR dynamics (Contribp, v, y) - “HLIR_dynamics”, “H_dynamics”, “L_dynamics”, “IR_dynamics”, “HLI_dynamics”, etc.: Epidemic dynamics related to the specified sanitary status (H, L, I or R and all their combinations). Graphics only, works only if graphic=TRUE.
- “all” : compute all these outputs (default)
- ““ : none of these outputs will be generated.
Possible evolutionary outputs, based on the computation of genotype frequencies (freq(I)p, t) include:
- “evol_patho”: evolution of pathogen genotypes
- “evol_aggr”: evolution of pathogen aggressiveness (i.e. phenotype)
- “durability”: durability of resistance genes
- “all”: compute all these outputs (default)
- ““: none of these outputs will be generated.
Equations
In the following equations, Hi, v, t, Li, v, p, t, Ii, v, p, t and Ri, v, p, t respectively denote the number of healthy, latent, infectious and removed host individuals, respectively, in field i (i = 1, …, J), for cultivar v (v = 1, …, V) at time step t (t = 1, …, T × Y with Y the total number of cropping seasons and T the number of time-steps per season).
$AUDPC_{v,y} = \frac{\sum_{t=t^0(y)}^{t^f(y)} \sum_{i=1}^{J} \sum_{p=1}^{P} \{I_{i,v,p,t}+R_{i,v,p,t}\}}{T \times \sum_{i=1}^{J} A_i}$
$AUDPC^r_{v,y} = \frac{\sum_{t=t^0(y)}^{t^f(y)} \sum_{i=1}^{J} \sum_{p=1}^{P} \{I_{i,v,p,t}+R_{i,v,p,t}\}}{\sum_{t=t^0(y)}^{t^f(y)} \sum_{i=1}^{J} \left(H_{i,v,t}+\sum_{p=1}^{P} \{L_{i,v,p,t}+I_{i,v,p,t}+R_{i,v,p,t}\}\right)}$
$GLA_{v,y} = \frac{\sum_{t=t^0(y)}^{t^f(y)} \sum_{i=1}^{J} H_{i,v,t}}{T \times \sum_{i=1}^{J} A_i}$
$GLA^r_{v,y} = \frac{\sum_{t=t^0(y)}^{t^f(y)} \sum_{i=1}^{J} H_{i,v,t}}{\sum_{t=t^0(y)}^{t^f(y)} \sum_{i=1}^{J} \left(H_{i,v,t}+\sum_{p=1}^{P} \{L_{i,v,p,t}+I_{i,v,p,t}+R_{i,v,p,t}\}\right)}$
$Yield_{v,y} = \frac{\sum_{t=t^0(y)}^{t^f(y)} \sum_{i=1}^{J} \left( y_{H,v} \times H_{i,v,t} + \sum_{p=1}^{P} \{y_{L,v} \times L_{i,v,p,t} + y_{I,v} \times I_{i,v,p,t} + y_{R,v} \times R_{i,v,p,t}\} \right)} {\sum_{t=t^0(y)}^{t^f(y)} \sum_{i=1}^{J} H^*_{i,v,t}}$ with yH, v, yL, v, yI, v and yR, v the theoretical yield of cultivar v in pure crop (in weight or volume unit/ha/season) associated with the sanitary statuses ‘H’, ‘L’, ‘I’ and ‘R’, respectively. Hi, v, t* is the number of healthy hosts in a pure crop and in absence of disease.
$Operational\_cost_{v,y}=planting\_cost_v \times \frac{\sum_{i \in \Omega_{v,y}}(area_i \times prop_{v,i})} {\sum_{i \in \Omega_{v,y}}area_i} + treatment\_cost \times \frac{\sum_{i \in \Omega_{v,y}}(TFI_{i,v,y} \times area_i \times prop_{v,i})} {\sum_{i \in \Omega_{v,y}}area_i}$ with Ωv, y the set of polygon indices where cultivar v is cultivated at year y, and propv, i the proportion of cultivar v in polygon i (for mixtures). TFI stands for the Treatment Frequency Indicator (number of treatment applications per ha).
Productv, y = yieldv, y × market_value
Marginv, y = Productv, y − Operational_Costv, y
$Contrib_{p,v,y} = \frac{\sum_{t=t^0(y)}^{t^f(y)} \sum_{i=1}^{J} \{L_{i,v,p,t}+I_{i,v,p,t}+R_{i,v,p,t}\}} {\sum_{t=t^0(y)}^{t^f(y)} \sum_{i=1}^{J} \sum_{p=1}^{P} \{L_{i,v,p,t}+I_{i,v,p,t}+R_{i,v,p,t}\}}$
$freq(I)_{p,t} = \frac{\sum_{i=1}^{J} \sum_{v=1}^{V} I_{i,v,p,t}} {\sum_{p=1}^{P} \sum_{i=1}^{J} \sum_{v=1}^{V} I_{i,v,p,t}}$
With respect to evolutionary outputs, for each pathogen genotype
(evol_patho) or phenotype (evol_aggr, note
that different pathogen genotypes may lead to the same phenotype on a
resistant host, i.e. level of aggressiveness), several computations are
performed:
- appearance: time to first appearance (as propagule);
- R_infection: time to first true infection of a resistant host;
- R_invasion: time to invasion, when the number of infections of
resistant hosts reaches thres_breakdown, above which the
genotype or phenotype is unlikely to go extinct.
The value Nyears + 1 time step is used if the genotype or
phenotype never appeared/infected/invaded.
Durability is defined as the time to invasion of completely adapted
pathogen individuals.
Parameterisation
A list of outputs can be generated using
loadOutputs():
outputlist <- loadOutputs(epid_outputs = "all", evol_outputs = "all", disease="rust")
outputlist
#> $epid_outputs
#> [1] "all"
#>
#> $evol_outputs
#> [1] "all"
#>
#> $thres_breakdown
#> [1] 50000
#>
#> $audpc100S
#> [1] 0.76Among the elements of outputList, “audpc100S” is the
audpc in a fully susceptible landscape (used as reference value for
graphics). If necessary, the function compute_audpc100S
helps compute this value in a single 1-km^2 field:
audpc100S <- compute_audpc100S("rust", "wheat", area=1E6)
#> Computing audpc100S for rust in a single susceptible field of 1e+06 m^2 during 120 time steps
#> [1] "Run the C++ model"
#>
#> *** SPATIOTEMPORAL MODEL SIMULATING THE SPREAD AND EVOLUTION OF A PATHOGEN IN A LANDSCAPE ***
#>
#> ----------------------------- YEAR 1 -----------------------------
#> ----------------------------- YEAR 2 -----------------------------
#> ----------------------------- YEAR 3 -----------------------------
#> ----------------------------- YEAR 4 -----------------------------
#> ----------------------------- YEAR 5 -----------------------------
#> total computational time 0 seconds.
#> [1] "Compute model outputs"
#> [1] "remove binary files"
#> [1] "model outputs stored in : /tmp/RtmpgF2VTd/Rbuildfdd6e14d076/landsepi/vignettes"
audpc100S <- compute_audpc100S("mildew", "grapevine", area=1E6)
#> Computing audpc100S for mildew in a single susceptible field of 1e+06 m^2 during 120 time steps
#> [1] "Run the C++ model"
#>
#> *** SPATIOTEMPORAL MODEL SIMULATING THE SPREAD AND EVOLUTION OF A PATHOGEN IN A LANDSCAPE ***
#>
#> ----------------------------- YEAR 1 -----------------------------
#> ----------------------------- YEAR 2 -----------------------------
#> ----------------------------- YEAR 3 -----------------------------
#> ----------------------------- YEAR 4 -----------------------------
#> ----------------------------- YEAR 5 -----------------------------
#> total computational time 4 seconds.
#> [1] "Compute model outputs"
#> [1] "remove binary files"
#> [1] "model outputs stored in : /tmp/RtmpgF2VTd/Rbuildfdd6e14d076/landsepi/vignettes"
audpc100S <- compute_audpc100S("sigatoka", "banana", area=1E6, nTSpY=182)
#> Computing audpc100S for sigatoka in a single susceptible field of 1e+06 m^2 during 182 time steps
#> [1] "Run the C++ model"
#>
#> *** SPATIOTEMPORAL MODEL SIMULATING THE SPREAD AND EVOLUTION OF A PATHOGEN IN A LANDSCAPE ***
#>
#> ----------------------------- YEAR 1 -----------------------------
#> ----------------------------- YEAR 2 -----------------------------
#> ----------------------------- YEAR 3 -----------------------------
#> ----------------------------- YEAR 4 -----------------------------
#> ----------------------------- YEAR 5 -----------------------------
#> total computational time 1 seconds.
#> [1] "Compute model outputs"
#> [1] "remove binary files"
#> [1] "model outputs stored in : /tmp/RtmpgF2VTd/Rbuildfdd6e14d076/landsepi/vignettes"Then simul_params can be updated via
setOutputs():
See also tutorial on how to run a numerical experimental design to compute your own output variables and to run several simulations within an experimental design
Running the simulation
The functions checkSimulParams() and
saveDeploymentStrategy() check simulation parameters and
save the object simul_params (which contains all parameters
associated with the deployment strategy) into a GPKG file,
respectively.
Then, the function runSimul() launches the simulation.
Use ?runSimul to get all available options.
- General presentation of the package
- Initialisation of simulation parameters
- Setting the seed and time parameters
- Setting pathogen parameters
- Setting the landscape and pathogen dispersal
- Setting croptypes, cultivars and resistance genes
- Setting the inoculum
- Updating the survival probability during the off-season
- Setting chemical treatments
- Choosing output variables
- Running the simulation