diversity_through_time: Island diversity and events through time
In thauffe/simGDM: simGDM
Description
Usage
Arguments
Details
Value
Author(s)
References
Examples
View source: R/diversity_through_time.R
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.
Usage
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diversity_through_time(Elevation, Topography, Area, Vs, S0, E0, Ms, Iso_t,
Imm, C0, Ana, Emi, Z, Ma, Msa, DivDep = TRUE, TargetEffect = FALSE,
EnvirFilt = FALSE)
Arguments
Elevation
Vector of island elevation through time
Topography
Vector of island topography through time
Area
Vector of island area through time
Vs
Probability of a vicariance event when topography equals 1
S0
The per species probability of adaptive speciation at maximum empty niche space
E0
The per-species probability of extinction when richness equals Kmax
Ms
Species richness of the mainland source pool
Iso_t
A descriptor of island isolation in arbitrary units
Imm
The probability of one species arriving from the mainland per time step
C0
The per-species probability of successful colonization at full empty niche space
Ana
The per-species probability of anagenesis per time step
Emi
Probability of recolonization of the source area per time step
Z
The exponent of the species-area relationship between the island and the source area
Ma
The realized size of the source area that provides new species
Msa
Power exponent controlling the abundance distribution of the source
DivDep
TRUE (default) Diversity dependence acting on immigration, extinction and in-situ speciation
TargetEffect
FALSE (default) No effect of island area on the immigration probability
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
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.
Value
The output is a dataframe containing diversity and rates per time step.
Richness
Native species richness
NonEndemics
Non-endemic species richness
Endemics
Endemic species richness
Kmax
Carrying capacity
EndemicsClado
Endemic species evolved via in-situ cladogenesis
EndemicsAna
Endemic species evolved via in-situ anagenesis
Immigrants
Species immigrating at that time step to the island
NewViaClado
Species evolved via in-situ cladogenesis at that time step
NewViaNonadaptClado
Species evolved via non-adaptive in-situ cladogenesis at that time step
NewViaAdaptClado
Species evolved via adaptive in-situ cladogenesis at that time step
NewViaAna
Species evolved via in-situ anagenesis at that time step
Extinctions
Species going extinct at that time step
Emigrants
Species emigrating from the island to the mainland
Author(s)
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
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# 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)
thauffe/simGDM documentation built on Feb. 19, 2020, 5:10 p.m.
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Description Usage Arguments Details Value Author(s) References Examples
View source: R/diversity_through_time.R
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.
Usage
1 2 3 | diversity_through_time(Elevation, Topography, Area, Vs, S0, E0, Ms, Iso_t,
Imm, C0, Ana, Emi, Z, Ma, Msa, DivDep = TRUE, TargetEffect = FALSE,
EnvirFilt = FALSE)
|
Arguments
Elevation |
Vector of island elevation through time |
Topography |
Vector of island topography through time |
Area |
Vector of island area through time |
Vs |
Probability of a vicariance event when topography equals 1 |
S0 |
The per species probability of adaptive speciation at maximum empty niche space |
E0 |
The per-species probability of extinction when richness equals Kmax |
Ms |
Species richness of the mainland source pool |
Iso_t |
A descriptor of island isolation in arbitrary units |
Imm |
The probability of one species arriving from the mainland per time step |
C0 |
The per-species probability of successful colonization at full empty niche space |
Ana |
The per-species probability of anagenesis per time step |
Emi |
Probability of recolonization of the source area per time step |
Z |
The exponent of the species-area relationship between the island and the source area |
Ma |
The realized size of the source area that provides new species |
Msa |
Power exponent controlling the abundance distribution of the source |
DivDep |
TRUE (default) Diversity dependence acting on immigration, extinction and in-situ speciation |
TargetEffect |
FALSE (default) No effect of island area on the immigration probability |
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
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.
Value
The output is a dataframe containing diversity and rates per time step.
Richness |
Native species richness |
NonEndemics |
Non-endemic species richness |
Endemics |
Endemic species richness |
Kmax |
Carrying capacity |
EndemicsClado |
Endemic species evolved via in-situ cladogenesis |
EndemicsAna |
Endemic species evolved via in-situ anagenesis |
Immigrants |
Species immigrating at that time step to the island |
NewViaClado |
Species evolved via in-situ cladogenesis at that time step |
NewViaNonadaptClado |
Species evolved via non-adaptive in-situ cladogenesis at that time step |
NewViaAdaptClado |
Species evolved via adaptive in-situ cladogenesis at that time step |
NewViaAna |
Species evolved via in-situ anagenesis at that time step |
Extinctions |
Species going extinct at that time step |
Emigrants |
Species emigrating from the island to the mainland |
Author(s)
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
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 | # 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)
|
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