R/diversity_through_time.R
In thauffe/simGDM: simGDM
Defines functions
diversity_through_time
Documented in
diversity_through_time
#' @title Island diversity and events through time
#'
#' @description This function calculates the the number of colonization,
#' speciation, extinction, and emmigration events through the trajectory
#' of island evolution. This results in the total diversity of endemics
#' and non-endemics at each moment in time.
#'
#' @param Elevation Vector of island elevation through time
#' @param Topography Vector of island topography through time
#' @param Area Vector of island area through time
#' @param Vs Probability of a vicariance event when topography equals 1
#' @param S0 The per species probability of adaptive speciation at maximum empty niche space
#' @param E0 The per-species probability of extinction when richness equals Kmax
#' @param Ms Species richness of the mainland source pool
#' @param Iso_t A descriptor of island isolation in arbitrary units
#' @param Imm The probability of one species arriving from the mainland per time step
#' @param C0 The per-species probability of successful colonization at full empty niche space
#' @param Ana The per-species probability of anagenesis per time step
#' @param Emi Probability of recolonization of the source area per time step
#' @param Z The exponent of the species-area relationship between the island and the source area
#' @param Ma The realized size of the source area that provides new species
#' @param Msa Power exponent controlling the abundance distribution of the source
#' @param DivDep TRUE (default) Diversity dependence acting on immigration, extinction and in-situ speciation
#' @param TargetEffect FALSE (default) No effect of island area on the immigration probability
#' @param EnvirFilt FALSE (default) No effect of island elevation as proxy for habitat diversity on the immigration probability
#'
#' @details Using the parameters in Table 1 of Borregard et al. (2016) with the
#' \code{\link{Island}} dataset results in slightly different diversity trajectories
#' than Borregard's Figure 4a. The example below recreates this figure as closely as possible,
#' but uses a different size of the source area (Ma) and probability of anagenesis (Ana).
#' Reasons for the differences could be the manually digitalized properties of the
#' island itself because Figure S3 (Borregard et al. 2016) containes no y-axis scale.
#' Moreover, the original R script of Borregard et al. (2016) hard-codes many parameters.
#'
#' Rates can be plotted in units of events per time (as in Borregard et al. 2016)
#' or in units of events per lineage per time (as in many phylogenetic studies).
#' This largely removes the hump-shaped extinction trajectory.
#'
#' @return The output is a dataframe containing diversity and rates per time step.
#' \item{Richness}{ Native species richness}
#' \item{NonEndemics}{ Non-endemic species richness}
#' \item{Endemics}{ Endemic species richness}
#' \item{Kmax}{ Carrying capacity}
#' \item{EndemicsClado}{ Endemic species evolved via in-situ cladogenesis}
#' \item{EndemicsAna}{ Endemic species evolved via in-situ anagenesis}
#' \item{Immigrants}{ Species immigrating at that time step to the island}
#' \item{NewViaClado}{ Species evolved via in-situ cladogenesis at that time step}
#' \item{NewViaNonadaptClado}{ Species evolved via non-adaptive in-situ cladogenesis at that time step}
#' \item{NewViaAdaptClado}{ Species evolved via adaptive in-situ cladogenesis at that time step}
#' \item{NewViaAna}{ Species evolved via in-situ anagenesis at that time step}
#' \item{Extinctions}{ Species going extinct at that time step}
#' \item{Emigrants}{ Species emigrating from the island to the mainland}
#'
#' @author Torsten Hauffe
#'
#' @references Borregaard, M. K., T. J. Matthews and R. J. Whittaker (2016).
#' The general dynamic model: towards a unified theory of island biogeography?
#' Global Ecology and Biogeography, 25(7), 805-816.
#'
#' Hauffe, T., D. Delicado, R.S. Etienne and L. Valente (submitted).
#' Lake expansion increases equilibrium diversity via the target effect of island biogeography
#'
#'@examples
#' # Reproduce Figure 4a (Borregaard et al., 2016)
#' data(Island)
#'
#' Dtt <- diversity_through_time(Elevation = Island$Elevation,
#' Topography = Island$Topography,
#' Area = Island$Area,
#' Vs = 0.0005,
#' S0 = 0.0025,
#' E0 = 0.001,
#' Ms = 500,
#' Iso_t = 0.3,
#' Imm = 0.002,
#' C0 = 0.5,
#' Ana = 0.0003,
#' Emi = 0.0002,
#' Z = 0.25,
#' Ma = 200,
#' Msa = 0.3,
#' DivDep = TRUE,
#' TargetEffect = FALSE,
#' EnvirFilt = FALSE)
#'
#' ColRich <- rgb(170, 99, 42, maxColorValue = 255)
#' ColNonEnd <- rgb(249, 195, 91, maxColorValue = 255)
#' ColEnd <- rgb(191, 11, 189, maxColorValue = 255)
#' ColEx <- rgb(211, 0, 0, maxColorValue = 255)
#' ColAna <- rgb(255, 144, 235, maxColorValue = 255)
#' ColClado <- rgb(64, 197, 253, maxColorValue = 255)
#'
#' # Diversities
#' par(las = 1, mar = c(4, 6, 0.1, 0.5))
#' plot(1:nrow(Dtt), Dtt[, "Kmax"], type = "l", col = "black",
#' xlim = c(-1, 5000), ylim = c(0, 160),
#' xaxs = "i", yaxs = "i",
#' xaxt = "n", xlab = "Time (Ma)",
#' ylab = "Species")
#' axis(side = 1, at = c(0, 1000, 2000, 3000, 4000, 5000), labels = c(5, 4, 3, 2, 1, 0))
#' lines(1:nrow(Dtt), Dtt[, "Richness"], type = "l", col = ColRich)
#' lines(1:nrow(Dtt), Dtt[, "NonEndemics"], type = "l", col = ColNonEnd)
#' lines(1:nrow(Dtt), Dtt[, "Endemics"], type = "l", col = ColEnd)
#' legend("topright",
#' legend = c("Carrying capacity", "Total species richness", "Non-endemics", "Endemics"),
#' col = c("black", ColRich, ColNonEnd, ColEnd), lty = 1, bty = "n", cex = 0.7)
#'
#' # Rates
#' plot(1:nrow(Dtt), Dtt[, "Immigrants"], type = "l", col = ColNonEnd,
#' xlim = c(-1, 5000), ylim = c(0, 0.15),
#' xaxs = "i", yaxs = "i",
#' xaxt = "n", xlab = "Time (Ma)",
#' ylab = expression(atop(paste("Rate"), "(events"%.%"time step"^-1*")")))
#' axis(side = 1, at = c(0, 1000, 2000, 3000, 4000, 5000), labels = c(5, 4, 3, 2, 1, 0))
#' lines(1:nrow(Dtt), Dtt[, "Extinctions"], col = ColEx)
#' lines(1:nrow(Dtt), Dtt[, "NewViaAna"], col = ColAna)
#' lines(1:nrow(Dtt), Dtt[, "NewViaClado"], type = "l", col = ColClado)
#' legend("topright",
#' legend = c("Colonization", "Extinction", "Anagenesis", "Cladogenesis"),
#' col = c(ColNonEnd, ColEx, ColAna, ColClado), lty = 1, bty = "n", cex = 0.7)
#'
#' # Divide by island richness and multiply by 1000
#' # to obtain rates in units of events per island species per 1 million years
#' plot(1:nrow(Dtt), 1000 * Dtt[, "Immigrants"] / Dtt[, "Richness"], type = "l", col = ColNonEnd,
#' xlim = c(-1, 5000), ylim = c(0, 1.3),
#' xaxs = "i", yaxs = "i",
#' xaxt = "n", xlab = "Time (Ma)",
#' ylab = expression(atop(paste("Rate"), "(events"%.%"species"^-1%.%"my"^-1*")")))
#' axis(side = 1, at = c(0, 1000, 2000, 3000, 4000, 5000), labels = c(5, 4, 3, 2, 1, 0))
#' lines(1:nrow(Dtt), 1000 * Dtt[, "Extinctions"] / Dtt[, "Richness"], col = ColEx)
#' lines(1:nrow(Dtt), 1000 * Dtt[, "NewViaAna"] / Dtt[, "Richness"], col = ColAna)
#' lines(1:nrow(Dtt), 1000 * Dtt[, "NewViaClado"] / Dtt[, "Richness"], type = "l", col = ColClado)
#' legend("topright",
#' legend = c("Colonization", "Extinction", "Anagenesis", "Cladogenesis"),
#' col = c(ColNonEnd, ColEx, ColAna, ColClado), lty = 1, bty = "n", cex = 0.7)
#'
#' # Figure 4 of Hauffe et al.
#' TimeSteps <- 4000
#' X <- 1:TimeSteps
#' Island <- 1/( 1+exp(-(0.0001 + 0.004*X[1:3000])) )
#' Island <- Island - min(Island)
#' Island <- Island / max(Island)
#' Island <- Island / 2
#' Island <- c(Island, Island[length(Island)] + Island[1:1000])
#' Clado <- 0.00007
#' DttTar <- diversity_through_time(Elevation = Island,
#' Topography = Island,
#' Area = Island,
#' Vs = 0.9 * Clado,
#' S0 = 0.1 * Clado,
#' E0 = 0.00095,
#' Ms = 300,
#' Iso_t = 0.3,
#' Imm = 0.00019,
#' C0 = 1,
#' Ana = 0.00034,
#' Emi = 0,
#' Z = 0.25,
#' Ma = 200,
#' Msa = 0.3,
#' DivDep = FALSE,
#' TargetEffect = TRUE,
#' EnvirFilt = FALSE)
#'
#' # Plot island ontogeny
#' plot(X, Island, type = "l",
#' ylim = c(0, 1), xlim = c(-1, max(X)),
#' xaxs = "i", yaxs = "i",
#' xaxt = "n", xlab = "Time (Ma)",
#' ylab = "Elevation Area Topography (%)")
#' axis(side = 1, at = c(0, 1000, 2000, 3000, 4000), labels = c(4, 3, 2, 1, 0))
#'
#' # Diversities
#' plot(1:nrow(DttTar), DttTar[, "Richness"], type = "l", col = ColRich,
#' xlim = c(-1, max(X)), ylim = c(0, 80),
#' xaxs = "i", yaxs = "i",
#' xaxt = "n", xlab = "Time (Ma)",
#' ylab = "Species")
#' axis(side = 1, at = c(0, 1000, 2000, 3000, 4000), labels = c(4, 3, 2, 1, 0))
#' lines(1:nrow(DttTar), DttTar[, "NonEndemics"], type = "l", col = ColNonEnd)
#' lines(1:nrow(DttTar), DttTar[, "EndemicsAna"], type = "l", col = ColAna)
#' lines(1:nrow(DttTar), DttTar[, "EndemicsClado"], type = "l", col = ColClado)
#' legend("topleft",
#' legend = c("Total species richness", "Non-endemics",
#' "Endemics evolved via cladogenesis",
#' "Endemics via anagenesis"),
#' col = c(ColRich, ColNonEnd, ColAna, ColClado), lty = 1, bty = "n", cex = 0.7)
#'
#' @export diversity_through_time
diversity_through_time <- function(Elevation,
Topography,
Area,
Vs,
S0,
E0,
Ms,
Iso_t,
Imm,
C0,
Ana,
Emi,
Z,
Ma,
Msa,
DivDep = TRUE,
TargetEffect = FALSE,
EnvirFilt = FALSE){
S <- as.data.frame(matrix(NA_real_, nrow = length(Elevation), ncol = 13))
colnames(S) <- c("Richness", "NonEndemics", "Endemics", "Kmax", "EndemicsClado", "EndemicsAna",
"Immigrants", "NewViaClado", "NewViaNonadaptClado", "NewViaAdaptClado",
"NewViaAna", "Extinctions", "Emigrants")
S[1, ] <- 0
for(i in 2:length(Elevation)){
S[i, ] <- calc_diversity(Elevation_t = Elevation[i-1],
Topography_t = Topography[i-1],
Area_t = Area[i-1],
Nat_tm1 = S[i-1, 2],
End_tm1 = S[i-1, 3],
Clado_tm1 = S[i-1, 5],
Ana_tm1 = S[i-1, 6],
Vs = Vs,
S0 = S0,
E0 = E0,
Ms = Ms,
Iso_t = Iso_t,
Imm = Imm,
C0 = C0,
Ana = Ana,
Emi = Emi,
Z = Z,
Ma = Ma,
Msa = Msa,
DivDep = DivDep,
TargetEffect = TargetEffect,
EnvirFilt = EnvirFilt)
}
return(S)
}
thauffe/simGDM documentation built on Feb. 19, 2020, 5:10 p.m.
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Defines functions diversity_through_time
Documented in diversity_through_time
#' @title Island diversity and events through time
#'
#' @description This function calculates the the number of colonization,
#' speciation, extinction, and emmigration events through the trajectory
#' of island evolution. This results in the total diversity of endemics
#' and non-endemics at each moment in time.
#'
#' @param Elevation Vector of island elevation through time
#' @param Topography Vector of island topography through time
#' @param Area Vector of island area through time
#' @param Vs Probability of a vicariance event when topography equals 1
#' @param S0 The per species probability of adaptive speciation at maximum empty niche space
#' @param E0 The per-species probability of extinction when richness equals Kmax
#' @param Ms Species richness of the mainland source pool
#' @param Iso_t A descriptor of island isolation in arbitrary units
#' @param Imm The probability of one species arriving from the mainland per time step
#' @param C0 The per-species probability of successful colonization at full empty niche space
#' @param Ana The per-species probability of anagenesis per time step
#' @param Emi Probability of recolonization of the source area per time step
#' @param Z The exponent of the species-area relationship between the island and the source area
#' @param Ma The realized size of the source area that provides new species
#' @param Msa Power exponent controlling the abundance distribution of the source
#' @param DivDep TRUE (default) Diversity dependence acting on immigration, extinction and in-situ speciation
#' @param TargetEffect FALSE (default) No effect of island area on the immigration probability
#' @param EnvirFilt FALSE (default) No effect of island elevation as proxy for habitat diversity on the immigration probability
#'
#' @details Using the parameters in Table 1 of Borregard et al. (2016) with the
#' \code{\link{Island}} dataset results in slightly different diversity trajectories
#' than Borregard's Figure 4a. The example below recreates this figure as closely as possible,
#' but uses a different size of the source area (Ma) and probability of anagenesis (Ana).
#' Reasons for the differences could be the manually digitalized properties of the
#' island itself because Figure S3 (Borregard et al. 2016) containes no y-axis scale.
#' Moreover, the original R script of Borregard et al. (2016) hard-codes many parameters.
#'
#' Rates can be plotted in units of events per time (as in Borregard et al. 2016)
#' or in units of events per lineage per time (as in many phylogenetic studies).
#' This largely removes the hump-shaped extinction trajectory.
#'
#' @return The output is a dataframe containing diversity and rates per time step.
#' \item{Richness}{ Native species richness}
#' \item{NonEndemics}{ Non-endemic species richness}
#' \item{Endemics}{ Endemic species richness}
#' \item{Kmax}{ Carrying capacity}
#' \item{EndemicsClado}{ Endemic species evolved via in-situ cladogenesis}
#' \item{EndemicsAna}{ Endemic species evolved via in-situ anagenesis}
#' \item{Immigrants}{ Species immigrating at that time step to the island}
#' \item{NewViaClado}{ Species evolved via in-situ cladogenesis at that time step}
#' \item{NewViaNonadaptClado}{ Species evolved via non-adaptive in-situ cladogenesis at that time step}
#' \item{NewViaAdaptClado}{ Species evolved via adaptive in-situ cladogenesis at that time step}
#' \item{NewViaAna}{ Species evolved via in-situ anagenesis at that time step}
#' \item{Extinctions}{ Species going extinct at that time step}
#' \item{Emigrants}{ Species emigrating from the island to the mainland}
#'
#' @author Torsten Hauffe
#'
#' @references Borregaard, M. K., T. J. Matthews and R. J. Whittaker (2016).
#' The general dynamic model: towards a unified theory of island biogeography?
#' Global Ecology and Biogeography, 25(7), 805-816.
#'
#' Hauffe, T., D. Delicado, R.S. Etienne and L. Valente (submitted).
#' Lake expansion increases equilibrium diversity via the target effect of island biogeography
#'
#'@examples
#' # Reproduce Figure 4a (Borregaard et al., 2016)
#' data(Island)
#'
#' Dtt <- diversity_through_time(Elevation = Island$Elevation,
#' Topography = Island$Topography,
#' Area = Island$Area,
#' Vs = 0.0005,
#' S0 = 0.0025,
#' E0 = 0.001,
#' Ms = 500,
#' Iso_t = 0.3,
#' Imm = 0.002,
#' C0 = 0.5,
#' Ana = 0.0003,
#' Emi = 0.0002,
#' Z = 0.25,
#' Ma = 200,
#' Msa = 0.3,
#' DivDep = TRUE,
#' TargetEffect = FALSE,
#' EnvirFilt = FALSE)
#'
#' ColRich <- rgb(170, 99, 42, maxColorValue = 255)
#' ColNonEnd <- rgb(249, 195, 91, maxColorValue = 255)
#' ColEnd <- rgb(191, 11, 189, maxColorValue = 255)
#' ColEx <- rgb(211, 0, 0, maxColorValue = 255)
#' ColAna <- rgb(255, 144, 235, maxColorValue = 255)
#' ColClado <- rgb(64, 197, 253, maxColorValue = 255)
#'
#' # Diversities
#' par(las = 1, mar = c(4, 6, 0.1, 0.5))
#' plot(1:nrow(Dtt), Dtt[, "Kmax"], type = "l", col = "black",
#' xlim = c(-1, 5000), ylim = c(0, 160),
#' xaxs = "i", yaxs = "i",
#' xaxt = "n", xlab = "Time (Ma)",
#' ylab = "Species")
#' axis(side = 1, at = c(0, 1000, 2000, 3000, 4000, 5000), labels = c(5, 4, 3, 2, 1, 0))
#' lines(1:nrow(Dtt), Dtt[, "Richness"], type = "l", col = ColRich)
#' lines(1:nrow(Dtt), Dtt[, "NonEndemics"], type = "l", col = ColNonEnd)
#' lines(1:nrow(Dtt), Dtt[, "Endemics"], type = "l", col = ColEnd)
#' legend("topright",
#' legend = c("Carrying capacity", "Total species richness", "Non-endemics", "Endemics"),
#' col = c("black", ColRich, ColNonEnd, ColEnd), lty = 1, bty = "n", cex = 0.7)
#'
#' # Rates
#' plot(1:nrow(Dtt), Dtt[, "Immigrants"], type = "l", col = ColNonEnd,
#' xlim = c(-1, 5000), ylim = c(0, 0.15),
#' xaxs = "i", yaxs = "i",
#' xaxt = "n", xlab = "Time (Ma)",
#' ylab = expression(atop(paste("Rate"), "(events"%.%"time step"^-1*")")))
#' axis(side = 1, at = c(0, 1000, 2000, 3000, 4000, 5000), labels = c(5, 4, 3, 2, 1, 0))
#' lines(1:nrow(Dtt), Dtt[, "Extinctions"], col = ColEx)
#' lines(1:nrow(Dtt), Dtt[, "NewViaAna"], col = ColAna)
#' lines(1:nrow(Dtt), Dtt[, "NewViaClado"], type = "l", col = ColClado)
#' legend("topright",
#' legend = c("Colonization", "Extinction", "Anagenesis", "Cladogenesis"),
#' col = c(ColNonEnd, ColEx, ColAna, ColClado), lty = 1, bty = "n", cex = 0.7)
#'
#' # Divide by island richness and multiply by 1000
#' # to obtain rates in units of events per island species per 1 million years
#' plot(1:nrow(Dtt), 1000 * Dtt[, "Immigrants"] / Dtt[, "Richness"], type = "l", col = ColNonEnd,
#' xlim = c(-1, 5000), ylim = c(0, 1.3),
#' xaxs = "i", yaxs = "i",
#' xaxt = "n", xlab = "Time (Ma)",
#' ylab = expression(atop(paste("Rate"), "(events"%.%"species"^-1%.%"my"^-1*")")))
#' axis(side = 1, at = c(0, 1000, 2000, 3000, 4000, 5000), labels = c(5, 4, 3, 2, 1, 0))
#' lines(1:nrow(Dtt), 1000 * Dtt[, "Extinctions"] / Dtt[, "Richness"], col = ColEx)
#' lines(1:nrow(Dtt), 1000 * Dtt[, "NewViaAna"] / Dtt[, "Richness"], col = ColAna)
#' lines(1:nrow(Dtt), 1000 * Dtt[, "NewViaClado"] / Dtt[, "Richness"], type = "l", col = ColClado)
#' legend("topright",
#' legend = c("Colonization", "Extinction", "Anagenesis", "Cladogenesis"),
#' col = c(ColNonEnd, ColEx, ColAna, ColClado), lty = 1, bty = "n", cex = 0.7)
#'
#' # Figure 4 of Hauffe et al.
#' TimeSteps <- 4000
#' X <- 1:TimeSteps
#' Island <- 1/( 1+exp(-(0.0001 + 0.004*X[1:3000])) )
#' Island <- Island - min(Island)
#' Island <- Island / max(Island)
#' Island <- Island / 2
#' Island <- c(Island, Island[length(Island)] + Island[1:1000])
#' Clado <- 0.00007
#' DttTar <- diversity_through_time(Elevation = Island,
#' Topography = Island,
#' Area = Island,
#' Vs = 0.9 * Clado,
#' S0 = 0.1 * Clado,
#' E0 = 0.00095,
#' Ms = 300,
#' Iso_t = 0.3,
#' Imm = 0.00019,
#' C0 = 1,
#' Ana = 0.00034,
#' Emi = 0,
#' Z = 0.25,
#' Ma = 200,
#' Msa = 0.3,
#' DivDep = FALSE,
#' TargetEffect = TRUE,
#' EnvirFilt = FALSE)
#'
#' # Plot island ontogeny
#' plot(X, Island, type = "l",
#' ylim = c(0, 1), xlim = c(-1, max(X)),
#' xaxs = "i", yaxs = "i",
#' xaxt = "n", xlab = "Time (Ma)",
#' ylab = "Elevation Area Topography (%)")
#' axis(side = 1, at = c(0, 1000, 2000, 3000, 4000), labels = c(4, 3, 2, 1, 0))
#'
#' # Diversities
#' plot(1:nrow(DttTar), DttTar[, "Richness"], type = "l", col = ColRich,
#' xlim = c(-1, max(X)), ylim = c(0, 80),
#' xaxs = "i", yaxs = "i",
#' xaxt = "n", xlab = "Time (Ma)",
#' ylab = "Species")
#' axis(side = 1, at = c(0, 1000, 2000, 3000, 4000), labels = c(4, 3, 2, 1, 0))
#' lines(1:nrow(DttTar), DttTar[, "NonEndemics"], type = "l", col = ColNonEnd)
#' lines(1:nrow(DttTar), DttTar[, "EndemicsAna"], type = "l", col = ColAna)
#' lines(1:nrow(DttTar), DttTar[, "EndemicsClado"], type = "l", col = ColClado)
#' legend("topleft",
#' legend = c("Total species richness", "Non-endemics",
#' "Endemics evolved via cladogenesis",
#' "Endemics via anagenesis"),
#' col = c(ColRich, ColNonEnd, ColAna, ColClado), lty = 1, bty = "n", cex = 0.7)
#'
#' @export diversity_through_time
diversity_through_time <- function(Elevation,
Topography,
Area,
Vs,
S0,
E0,
Ms,
Iso_t,
Imm,
C0,
Ana,
Emi,
Z,
Ma,
Msa,
DivDep = TRUE,
TargetEffect = FALSE,
EnvirFilt = FALSE){
S <- as.data.frame(matrix(NA_real_, nrow = length(Elevation), ncol = 13))
colnames(S) <- c("Richness", "NonEndemics", "Endemics", "Kmax", "EndemicsClado", "EndemicsAna",
"Immigrants", "NewViaClado", "NewViaNonadaptClado", "NewViaAdaptClado",
"NewViaAna", "Extinctions", "Emigrants")
S[1, ] <- 0
for(i in 2:length(Elevation)){
S[i, ] <- calc_diversity(Elevation_t = Elevation[i-1],
Topography_t = Topography[i-1],
Area_t = Area[i-1],
Nat_tm1 = S[i-1, 2],
End_tm1 = S[i-1, 3],
Clado_tm1 = S[i-1, 5],
Ana_tm1 = S[i-1, 6],
Vs = Vs,
S0 = S0,
E0 = E0,
Ms = Ms,
Iso_t = Iso_t,
Imm = Imm,
C0 = C0,
Ana = Ana,
Emi = Emi,
Z = Z,
Ma = Ma,
Msa = Msa,
DivDep = DivDep,
TargetEffect = TargetEffect,
EnvirFilt = EnvirFilt)
}
return(S)
}
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