Compare with assemblages built using the ‘redundancy’, ‘partitioning’, and ‘expansion’ rules
Redundancy rules
The redundancy rules add species with traits redundant to those previously added. We will start the simulation by ‘seeding’ the assemblage with 5 species at random (before the rule starts).
set.seed(3142)
Sseed = 5
redund_sample <- redundancy(Sseed = Sseed, Smax = Smax, ecospace = ecospace)Note that the number of functionally unique species will not change after the simulation begins in the default rule. Although there are 50 species, there are only 5 functionally unique entities.
## char1 char2 char3 char4 char5 char6 char7 char8 char9
## 1 state2 state4 0.0 state8 state11 0.5 state15 state19 0
## 2 state3 state5 0.5 state8 state11 0.0 state16 state18 1
## 3 state2 state5 1.0 state8 state12 1.0 state16 state20 1
## 4 state3 state4 1.0 state8 state13 1.0 state17 state20 1
## 5 state2 state5 1.0 state9 state12 1.0 state15 state20 1Relax the rule so that new species are on average 95% functionally identical to pre-existing ones:
set.seed(3142)
redund_sample2 <- redundancy(Sseed = Sseed, Smax = Smax,
ecospace = ecospace, strength = 0.95)Plot both ‘redundancy’ assemblages (using PCA with Gower dissimilarity), showing order of assembly. Seed species in red, next 5 in black, remainder in gray. Notice the redundancy models produce an ecospace with discrete clusters of life habits.
## This is vegan 2.5-6pc <- prcomp(FD::gowdis(redund_sample))
plot(pc$x, type = "n",
main = paste("Redundancy model,\n", Smax, "species"))
text(pc$x[,1], pc$x[,2], labels = seq(Smax), col = c(rep("red", Sseed),
rep("black", 5), rep("slategray", (Smax - Sseed - 5))),
pch = c(rep(19, Sseed), rep(21, (Smax - Sseed))), cex = .8)
pc.r <- prcomp(FD::gowdis(redund_sample2))
plot(pc.r$x, type = "n", main =
paste("Redundancy model (95% identical),\n", Smax, "species"))
text(pc.r$x[,1], pc.r$x[,2], labels = seq(Smax), col = c(rep("red",
Sseed), rep("black", 5), rep("slategray", (Smax - Sseed - 5))),
pch = c(rep(19, Sseed), rep(21, (Smax - Sseed))), cex = .8)
Partitioning rules
The partitioning rules add species with traits intermediate to those previously added. We will start the simulation by ‘seeding’ the assemblage with 5 species at random (before the rule starts).
The rules can be implemented in a “strict” (the default) version:
set.seed(3142)
Sseed = 5
partS_sample <- partitioning(Sseed = Sseed, Smax = Smax,
ecospace = ecospace)Or in a “relaxed” version:
set.seed(3142)
Sseed = 5
partR_sample <- partitioning(Sseed = Sseed, Smax = Smax,
ecospace = ecospace, rule = "relaxed")Plot both ‘partitioning’ assemblages, showing order of assembly. Notice both partitioning models produce gradients, with the ‘strict’ version having linear gradients and the ‘relaxed’ version filling the centroid.
pc.ps <- prcomp(FD::gowdis(partS_sample))
plot(pc.ps$x, type = "n",
main = paste("'Strict' partitioning model,\n", Smax, "species"))
text(pc.ps$x[,1], pc$x[,2], labels = seq(Smax),
col = c(rep("red", Sseed), rep("black", 5),
rep("slategray", (Smax - Sseed - 5))),
pch = c(rep(19, Sseed), rep(21, (Smax - Sseed))), cex = .8)
pc.pr <- prcomp(FD::gowdis(partR_sample))
plot(pc.pr$x, type = "n",
main = paste("'Relaxed' partitioning model,\n", Smax, "species"))
text(pc.pr$x[,1], pc.pr$x[,2], labels = seq(Smax),
col = c(rep("red", Sseed), rep("black", 5),
rep("slategray", (Smax - Sseed - 5))),
pch = c(rep(19, Sseed), rep(21, (Smax - Sseed))), cex = .8)
Expansion rules
The expansion rules add species with traits maximally different from those previously added. We will start the simulation by ‘seeding’ the assemblage with 5 species at random (before the rule starts).
Plot the assemblage, showing order of assembly. Notice how later species consistently expand the ecospace, exploring previously unexplored parts of the ecospace.
pc.e <- prcomp(FD::gowdis(exp_sample))
plot(pc.e$x, type = "n",
main = paste("Expansion model,\n", Smax, "species"))
text(pc.e$x[,1], pc$x[,2], labels = seq(Smax),
col = c(rep("red", Sseed), rep("black", 5),
rep("slategray", (Smax - Sseed - 5))),
pch = c(rep(19, Sseed), rep(21, (Smax - Sseed))), cex = .8)
Visually comparing four rules
It is instructive to compare the four models graphically. This is possible here because set.seed() was used when running each simulation, so they all share the same starting configurations. Plotting using vegan:metaMDS in two dimensions for improved visualization of simulation dynamics.
library(vegan, quietly = TRUE)
start <- neutral_sample[1:Sseed,]
neu <- neutral_sample[(Sseed + 1):Smax,]
red <- redund_sample2[(Sseed + 1):Smax,]
par <- partR_sample[(Sseed + 1):Smax,]
exp <- exp_sample[(Sseed + 1):Smax,]
nmds.data <- rbind(start, neu, red, par, exp)
all <- metaMDS(gowdis(nmds.data), zerodist = "add", k = 2, trymax = 10)## Run 0 stress 0.2908926
## Run 1 stress 0.3084162
## Run 2 stress 0.2891901
## ... New best solution
## ... Procrustes: rmse 0.02133373 max resid 0.1671276
## Run 3 stress 0.2904407
## Run 4 stress 0.2916602
## Run 5 stress 0.3010061
## Run 6 stress 0.3032821
## Run 7 stress 0.2979624
## Run 8 stress 0.293234
## Run 9 stress 0.2979938
## Run 10 stress 0.2978477
## Run 11 stress 0.2934677
## Run 12 stress 0.300761
## Run 13 stress 0.2913372
## Run 14 stress 0.2975214
## Run 15 stress 0.2899913
## Run 16 stress 0.3098921
## Run 17 stress 0.3032887
## Run 18 stress 0.2911977
## Run 19 stress 0.2929413
## Run 20 stress 0.3052993
## *** No convergence -- monoMDS stopping criteria:
## 2: no. of iterations >= maxit
## 18: stress ratio > sratmaxplot(all$points[,1], all$points[,2],
col = c(rep("red", Sseed), rep("orange", nrow(neu)),
rep("red", nrow(red)), rep("blue", nrow(par)),
rep("purple", nrow(exp))),
pch = c(rep(19, Sseed), rep(21, nrow(neu)),
rep(22, nrow(red)), rep(23, nrow(par)),
rep(24, nrow(exp))),
main = paste("Combined models,\n", Smax, "species per model"),
xlab = "Axis 1", ylab = "Axis 2", cex = 2, cex.lab = 1.5, lwd = 1)
leg.txt <- c("seed", "neutral", "redundancy", "partitioning",
"expansion")
leg.col <- c("red", "orange", "red", "blue", "purple")
leg.pch <- c(19, 21, 22, 23, 24)
legend("topright", inset = .02, legend = leg.txt, pch = leg.pch,
col = leg.col, cex = .75)
