SongEvo simulates the cultural evolution of quantitative traits of bird song. SongEvo is an individual- (agent-) based model. SongEvo is spatially-explicit and can be parameterized with, and tested against, measured song data. Functions are available for model implementation, sensitivity analyses, parameter optimization, model validation, and hypothesis testing.
SongEvo
implements the modelpar.sens
allows sensitivity analysespar.opt
allows parameter optimizationmod.val
allows model validationh.test
allows hypothesis testingSongEvo
implements the model par.sens
allows sensitivity analyses par.opt
allows parameter
optimization mod.val
allows model validation
h.test
allows hypothesis testing
To explore the SongEvo package, we will use a database of songs from Nuttall’s white-crowned sparrow (Zonotrichia leucophrys nuttalli) recorded at three locations in 1969 and 2005.
Examine global parameters. Global parameters describe our
understanding of the system and may be measured or hypothesized. They
are called “global” because they are used by many many functions and
subroutines within functions. For descriptions of all adjustable
parameters, see ?song.data
.
data("glo.parms")
glo.parms$mortality.a.m <- glo.parms$mortality.a.f <- glo.parms$mortality.a
glo.parms$mortality.j.m <- glo.parms$mortality.j.f <- glo.parms$mortality.j
glo.parms$male.fledge.n.mean <- glo.parms$male.fledge.n.mean*2
glo.parms$male.fledge.n.sd <- glo.parms$male.fledge.n.sd*2
glo.parms <- glo.parms[!names(glo.parms) %in% c("mortality.a","mortality.j")]
str(glo.parms)
#> List of 17
#> $ learning.error.d : num 0
#> $ learning.error.sd : num 430
#> $ n.territories : num 40
#> $ lifespan : num 2.08
#> $ phys.lim.min : num 1559
#> $ phys.lim.max : num 4364
#> $ male.fledge.n.mean: num 2.7
#> $ male.fledge.n.sd : num 1
#> $ disp.age : num 2
#> $ disp.distance.mean: num 110
#> $ disp.distance.sd : num 100
#> $ terr.turnover : num 0.5
#> $ male.fledge.n : num [1:40] 1 1 2 1 0 2 2 2 2 1 ...
#> $ mortality.a.f : num 0.468
#> $ mortality.a.m : num 0.468
#> $ mortality.j.f : num 0.5
#> $ mortality.j.m : num 0.5
Share global parameters with the global environment. We make these parameters available in the global environment so that we can access them with minimal code.
Data include the population name (Bear Valley, PRBO, or Schooner), year of song recording (1969 or 2005), and the frequency bandwidth of the trill.
SongEvo()
In this example, we use songs from individual birds recorded in one
population (PRBO) in the year 1969, which we will call
starting.trait
.
We want a starting population of 40 individuals, so we generate additional trait values to complement those from the existing 30 individuals. Then we create a data frame that includes a row for each individual; we add identification numbers, ages, and geographical coordinates for each individual.
starting.trait2 <- c(starting.trait, rnorm(n.territories-length(starting.trait),
mean=mean(starting.trait), sd=sd(starting.trait)))
init.inds <- data.frame(id = seq(1:n.territories), age = 2, trait = starting.trait2)
init.inds$x1 <- round(runif(n.territories, min=-122.481858, max=-122.447270), digits=8)
init.inds$y1 <- round(runif(n.territories, min=37.787768, max=37.805645), digits=8)
SongEvo()
includes several settings, which we specify
before running the model. For this example, we run the model for 10
iterations, over 36 years (i.e. 1969–2005). When conducting research
with SongEvo()
, users will want to increase the number
iterations (e.g. to 100 or 1000). Each timestep is one year in this
model (i.e. individuals complete all components of the model in 1 year).
We specify territory turnover rate here as an example of how to adjust
parameter values. We could adjust any other parameter value here also.
The learning method specifies that individuals integrate songs heard
from adults within the specified integration distance (intigrate.dist,
in kilometers). In this example, we do not includ a lifespan, so we
assign it NA. In this example, we do not model competition for mates, so
specify it as FALSE. Last, specify all as TRUE in order to save data for
every single simulated individual because we will use those data later
for mapping. If we do not need data for each individual, we set all to
FALSE because the all.inds data.frame becomes very large!
iteration <- 10
years <- 36
timestep <- 1
terr.turnover <- 0.5
integrate.dist <- 0.1
lifespan <- NA
mate.comp <- FALSE
prin <- FALSE
all <- TRUE
Now we call SongEvo with our specifications and save it in an object called SongEvo1.
SongEvo1 <- SongEvo(init.inds = init.inds, females = 1.0, iteration = iteration, steps = years,
timestep = timestep, n.territories = n.territories, terr.turnover = terr.turnover,
integrate.dist = integrate.dist,
learning.error.d = learning.error.d, learning.error.sd = learning.error.sd,
mortality.a.m = mortality.a.m, mortality.a.f = mortality.a.f,
mortality.j.m = mortality.j.m, mortality.j.f = mortality.j.f, lifespan = lifespan,
phys.lim.min = phys.lim.min, phys.lim.max = phys.lim.max,
male.fledge.n.mean = male.fledge.n.mean, male.fledge.n.sd = male.fledge.n.sd, male.fledge.n = male.fledge.n,
disp.age = disp.age, disp.distance.mean = disp.distance.mean, disp.distance.sd = disp.distance.sd,
mate.comp = mate.comp, prin = prin, all = TRUE)
The model required the following time to run on your computer:
Three main objects hold data regarding the SongEvo model. Additional objects are used temporarily within modules of the model.
First, currently alive individuals are stored in a data frame called “inds.” Values within “inds” are updated throughout each of the iterations of the model, and “inds” can be viewed after the model is completed.
head(SongEvo1$inds, min(5,nrow(SongEvo1$inds)))
#> coordinates id age trait x1 y1
#> M1528 (-122.4476, 37.79043) 1528 9 2789.953 -122.4476 37.79043
#> M1729 (-122.4846, 37.78023) 1729 6 3470.873 -122.4846 37.78023
#> M1763 (-122.4493, 37.79083) 1763 5 2763.244 -122.4493 37.79083
#> M1765 (-122.4867, 37.78252) 1765 5 3100.426 -122.4867 37.78252
#> M1773 (-122.4827, 37.78406) 1773 5 3252.713 -122.4827 37.78406
#> male.fledglings female.fledglings territory father sex fitness learn.dir
#> M1528 2 1 1 1359 M 1 0
#> M1729 0 0 0 1655 M 1 0
#> M1763 0 0 0 1647 M 1 0
#> M1765 1 1 1 1655 M 1 0
#> M1773 0 0 1 1708 M 1 0
#> x0 y0
#> M1528 -122.4459 37.79239
#> M1729 -122.4865 37.78322
#> M1763 -122.4497 37.78890
#> M1765 -122.4865 37.78322
#> M1773 -122.4819 37.78442
Second, an array (i.e. a multi-dimensional table) entitled “summary.results” includes population summary values for each time step (dimension 1) in each iteration (dimension 2) of the model. Population summary values are contained in five additional dimensions: population size for each time step of each iteration (“sample.n”), the population mean and variance of the song feature studied (“trait.pop.mean” and “trait.pop.variance”), with associated lower (“lci”) and upper (“uci”) confidence intervals.
dimnames(SongEvo1$summary.results)
#> $iteration
#> [1] "iteration 1" "iteration 2" "iteration 3" "iteration 4" "iteration 5"
#> [6] "iteration 6" "iteration 7" "iteration 8" "iteration 9" "iteration 10"
#>
#> $step
#> [1] "1" "2" "3" "4" "5" "6" "7" "8" "9" "10" "11" "12" "13" "14" "15"
#> [16] "16" "17" "18" "19" "20" "21" "22" "23" "24" "25" "26" "27" "28" "29" "30"
#> [31] "31" "32" "33" "34" "35" "36"
#>
#> $feature
#> [1] "sample.n" "trait.pop.mean" "trait.pop.variance"
#> [4] "lci" "uci"
Third, individual values may optionally be concatenated and saved to one data frame entitled “all.inds.” all.inds can become quite large, and is therefore only recommended if additional data analyses are desired.
head(SongEvo1$all.inds, min(5,nrow(SongEvo1$all.inds)))
#> coordinates id age trait x1 y1 male.fledglings
#> I1.T1.1 (-122.4602, 37.78831) 1 2 4004.8 -122.4602 37.78831 1
#> I1.T1.2 (-122.4747, 37.78894) 2 2 3765.0 -122.4747 37.78894 0
#> I1.T1.3 (-122.4643, 37.80173) 3 2 3237.4 -122.4643 37.80173 1
#> I1.T1.4 (-122.455, 37.78949) 4 2 3621.1 -122.4550 37.78949 0
#> I1.T1.5 (-122.4522, 37.80261) 5 2 3285.4 -122.4522 37.80261 0
#> female.fledglings territory father sex fitness learn.dir x0 y0 timestep
#> I1.T1.1 0 1 0 M 1 0 0 0 1
#> I1.T1.2 1 1 0 M 1 0 0 0 1
#> I1.T1.3 1 1 0 M 1 0 0 0 1
#> I1.T1.4 1 1 0 M 1 0 0 0 1
#> I1.T1.5 0 1 0 M 1 0 0 0 1
#> iteration
#> I1.T1.1 1
#> I1.T1.2 1
#> I1.T1.3 1
#> I1.T1.4 1
#> I1.T1.5 1
We see that the simulated population size remains relatively stable over the course of 36 years. This code uses the summary.results array.
plot(SongEvo1$summary.results[1, , "sample.n"], xlab="Year", ylab="Abundance", type="n",
xaxt="n", ylim=c(0, max(SongEvo1$summary.results[, , "sample.n"], na.rm=TRUE)))
axis(side=1, at=seq(0, 40, by=5), labels=seq(1970, 2010, by=5))
for(p in 1:iteration){
lines(SongEvo1$summary.results[p, , "sample.n"], col="light gray")
}
n.mean <- apply(SongEvo1$summary.results[, , "sample.n"], 2, mean, na.rm=TRUE)
lines(n.mean, col="red")
#Plot 95% quantiles
quant.means <- apply (SongEvo1$summary.results[, , "sample.n"], MARGIN=2, quantile,
probs=c(0.975, 0.025), R=600, na.rm=TRUE)
lines(quant.means[1,], col="red", lty=2)
lines(quant.means[2,], col="red", lty=2)
Load Hmisc package for plotting functions.
We see that the mean trait values per iteration varied widely, though mean trait values over all iterations remained relatively stable. This code uses the summary.results array.
plot(SongEvo1$summary.results[1, , "trait.pop.mean"], xlab="Year", ylab="Bandwidth (Hz)",
xaxt="n", type="n", xlim=c(-0.5, 36),
ylim=c(min(SongEvo1$summary.results[, , "trait.pop.mean"], na.rm=TRUE),
max(SongEvo1$summary.results[, , "trait.pop.mean"], na.rm=TRUE)))
for(p in 1:iteration){
lines(SongEvo1$summary.results[p, , "trait.pop.mean"], col="light gray")
}
freq.mean <- apply(SongEvo1$summary.results[, , "trait.pop.mean"], 2, mean, na.rm=TRUE)
lines(freq.mean, col="blue")
axis(side=1, at=seq(0, 35, by=5), labels=seq(1970, 2005, by=5))#, tcl=-0.25, mgp=c(2,0.5,0))
#Plot 95% quantiles
quant.means <- apply (SongEvo1$summary.results[, , "trait.pop.mean"], MARGIN=2, quantile,
probs=c(0.95, 0.05), R=600, na.rm=TRUE)
lines(quant.means[1,], col="blue", lty=2)
lines(quant.means[2,], col="blue", lty=2)
#plot mean and CI for historic songs.
#plot original song values
library("boot")
sample.mean <- function(d, x) {
mean(d[x])
}
boot_hist <- boot(starting.trait, statistic=sample.mean, R=100)#, strata=mn.res$iteration)
ci.hist <- boot.ci(boot_hist, conf=0.95, type="basic")
low <- ci.hist$basic[4]
high <- ci.hist$basic[5]
points(0, mean(starting.trait), pch=20, cex=0.6, col="black")
errbar(x=0, y=mean(starting.trait), high, low, add=TRUE)
#text and arrows
text(x=5, y=2720, labels="Historical songs", pos=1)
arrows(x0=5, y0=2750, x1=0.4, y1=mean(starting.trait), length=0.1)
We see that variance for each iteration per year increased in the first few years and then stabilized. This code uses the summary.results array.
#plot variance for each iteration per year
plot(SongEvo1$summary.results[1, , "trait.pop.variance"], xlab="Year",
ylab="Bandwidth Variance (Hz)", type="n", xaxt="n",
ylim=c(min(SongEvo1$summary.results[, , "trait.pop.variance"], na.rm=TRUE),
max(SongEvo1$summary.results[, , "trait.pop.variance"], na.rm=TRUE)))
axis(side=1, at=seq(0, 40, by=5), labels=seq(1970, 2010, by=5))
for(p in 1:iteration){
lines(SongEvo1$summary.results[p, , "trait.pop.variance"], col="light gray")
}
n.mean <- apply(SongEvo1$summary.results[, , "trait.pop.variance"], 2, mean, na.rm=TRUE)
lines(n.mean, col="green")
#Plot 95% quantiles
quant.means <- apply (SongEvo1$summary.results[, , "trait.pop.variance"], MARGIN=2, quantile,
probs=c(0.975, 0.025), R=600, na.rm=TRUE)
lines(quant.means[1,], col="green", lty=2)
lines(quant.means[2,], col="green", lty=2)
The simulation results include geographical coordinates and are in a standard spatial data format, thus allowing calculation of a wide variety of spatial statistics.
Load packages for making maps.
Convert data frame from long to wide format. This is necessary for making a multi-panel plot.
all.inds1 <- subset(SongEvo1$all.inds, SongEvo1$all.inds$iteration==1)
w <- dcast(as.data.frame(all.inds1), id ~ timestep, value.var="trait", fill=0)
all.inds1w <- merge(all.inds1, w, by="id")
years.SongEvo1 <- (dim(w)[2]-1 )
names(all.inds1w@data)[-(1:length(all.inds1@data))] <-paste("Ts", 1:(dim(w)[2]-1 ), sep="")
Create a function to generate a continuous color palette–we will use the palette in the next call to make color ramp to represent the trait value.
rbPal <- colorRampPalette(c('blue','red')) #Create a function to generate a continuous color palette
Plot maps, including a separate panel for each timestep (each of 36 years). Our example shows that individuals move across the landscape and that regional dialects evolve and move. The x-axis is longitude, the y-axis is latitude, and the color ramp indicates trill bandwidth in Hz.
spplot(all.inds1w[,-c(1:ncol(all.inds1))], as.table=TRUE,
cuts=c(0, seq(from=1500, to=4500, by=10)), ylab="",
col.regions=c("transparent", rbPal(1000)),
#cuts specifies that the first level (e.g. <1500) is transparent.
colorkey=list(
right=list(
fun=draw.colorkey,
args=list(
key=list(
at=seq(1500, 4500, 10),
col=rbPal(1000),
labels=list(
at=c(1500, 2000, 2500, 3000, 3500, 4000, 4500),
labels=c("1500", "2000", "2500", "3000", "3500", "4000", "4500")
)
)
)
)
)
)
In addition, you can plot simpler multi-panel maps that do not take advantage of the spatial data class.
#Lattice plot (not as a spatial frame)
it1 <- subset(SongEvo1$all.inds, iteration==1)
rbPal <- colorRampPalette(c('blue','red')) #Create a function to generate a continuous color palette
it1$Col <- rbPal(10)[as.numeric(cut(it1$trait, breaks = 10))]
xyplot(it1$y1~it1$x1 | it1$timestep, groups=it1$trait, asp="iso", col=it1$Col,
xlab="Longitude", ylab="Latitude")
par.sens()
This function allows testing the sensitivity of SongEvo to different parameter values.
par.sens()
Here we test the sensitivity of the Acquire a Territory submodel to variation in territory turnover rates, ranging from 0.8–1.2 times the published rate (40–60% of territories turned over). The call for the par.sens function has a format similar to SongEvo. The user specifies the parameter to test and the range of values for that parameter. The function currently allows examination of only one parameter at a time and requires at least two iterations.
Now we call the par.sens function with our specifications.
extra_parms <- list(init.inds = init.inds,
females = 1, # New in SongEvo v2
timestep = 1,
n.territories = nrow(init.inds),
integrate.dist = 0.1,
lifespan = NA,
terr.turnover = 0.5,
mate.comp = FALSE,
prin = FALSE,
all = TRUE,
# New in SongEvo v2
selectivity = 3,
content.bias = FALSE,
n.content.bias.loc = "all",
content.bias.loc = FALSE,
content.bias.loc.ranges = FALSE,
affected.traits = FALSE,
conformity.bias = FALSE,
prestige.bias=FALSE,
learn.m="default",
learn.f="default",
learning.error.d=0,
learning.error.sd=200)
global_parms_key <- which(!names(glo.parms) %in% names(extra_parms))
extra_parms[names(glo.parms[global_parms_key])]=glo.parms[global_parms_key]
par.sens1 <- par.sens(parm = parm, par.range = par.range,
iteration = iteration, steps = years, mate.comp = FALSE,
fixed_parms=extra_parms[names(extra_parms)!=parm], all = TRUE)
#> [1] "terr.turnover = 0.4"
#> [1] "terr.turnover = 0.425"
#> [1] "terr.turnover = 0.45"
#> [1] "terr.turnover = 0.475"
#> [1] "terr.turnover = 0.5"
#> [1] "terr.turnover = 0.525"
#> [1] "terr.turnover = 0.55"
#> [1] "terr.turnover = 0.575"
#> [1] "terr.turnover = 0.6"
Examine results objects, which include two arrays:
The first array, sens.results
, contains the SongEvo
model results for each parameter. It has the following dimensions:
dimnames(par.sens1$sens.results)
#> [[1]]
#> [1] "iteration 1" "iteration 2" "iteration 3" "iteration 4" "iteration 5"
#> [6] "iteration 6" "iteration 7" "iteration 8" "iteration 9" "iteration 10"
#>
#> [[2]]
#> [1] "1" "2" "3" "4" "5" "6" "7" "8" "9" "10" "11" "12" "13" "14" "15"
#> [16] "16" "17" "18" "19" "20" "21" "22" "23" "24" "25" "26" "27" "28" "29" "30"
#> [31] "31" "32" "33" "34" "35" "36"
#>
#> [[3]]
#> [1] "sample.n" "trait.pop.mean" "trait.pop.variance"
#> [4] "lci" "uci"
#>
#> [[4]]
#> [1] "par.val 0.4" "par.val 0.425" "par.val 0.45" "par.val 0.475"
#> [5] "par.val 0.5" "par.val 0.525" "par.val 0.55" "par.val 0.575"
#> [9] "par.val 0.6"
The second array, sens.results.diff
contains the
quantile range of trait values across iterations within a parameter
value. It has the following dimensions:
dimnames(par.sens1$sens.results.diff)
#> [[1]]
#> [1] "par.val 0.4" "par.val 0.425" "par.val 0.45" "par.val 0.475"
#> [5] "par.val 0.5" "par.val 0.525" "par.val 0.55" "par.val 0.575"
#> [9] "par.val 0.6"
#>
#> [[2]]
#> [1] "Quantile diff 1" "Quantile diff 2" "Quantile diff 3" "Quantile diff 4"
#> [5] "Quantile diff 5" "Quantile diff 6" "Quantile diff 7" "Quantile diff 8"
#> [9] "Quantile diff 9" "Quantile diff 10" "Quantile diff 11" "Quantile diff 12"
#> [13] "Quantile diff 13" "Quantile diff 14" "Quantile diff 15" "Quantile diff 16"
#> [17] "Quantile diff 17" "Quantile diff 18" "Quantile diff 19" "Quantile diff 20"
#> [21] "Quantile diff 21" "Quantile diff 22" "Quantile diff 23" "Quantile diff 24"
#> [25] "Quantile diff 25" "Quantile diff 26" "Quantile diff 27" "Quantile diff 28"
#> [29] "Quantile diff 29" "Quantile diff 30" "Quantile diff 31" "Quantile diff 32"
#> [33] "Quantile diff 33" "Quantile diff 34" "Quantile diff 35" "Quantile diff 36"
To assess sensitivity of SongEvo to a range of parameter values, plot the range in trait quantiles per year by the parameter value. We see that territory turnover values of 0.4–0.6 provided means and quantile ranges of trill bandwidths that are similar to those obtained with the published estimate of 0.5, indicating that the Acquire a Territory submodel is robust to realistic variation in those parameter values.
In the figure, solid gray and black lines show the quantile range of song frequency per year over all iterations as parameterized with the published territory turnover rate (0.5; thick black line) and a range of values from 0.4 to 0.6 (in steps of 0.05, light to dark gray). Orange lines show the mean and 2.5th and 97.5th quantiles of all quantile ranges.
#plot of range in trait quantiles by year by parameter value
plot(1:years, par.sens1$sens.results.diff[1,], ylim=c(min(par.sens1$sens.results.diff,
na.rm=TRUE), max(par.sens1$sens.results.diff, na.rm=TRUE)), type="l",
ylab="Quantile range (Hz)", xlab="Year", col="transparent", xaxt="n")
axis(side=1, at=seq(0, 35, by=5), labels=seq(1970, 2005, by=5))
#Make a continuous color ramp from gray to black
grbkPal <- colorRampPalette(c('gray','black'))
#Plot a line for each parameter value
for(i in 1:length(par.range)){
lines(1:years, par.sens1$sens.results.diff[i,], type="l",
col=grbkPal(length(par.range))[i])
}
#Plot values from published parameter values
lines(1:years, par.sens1$sens.results.diff[2,], type="l", col="black", lwd=4)
#Calculate and plot mean and quantiles
quant.mean <- apply(par.sens1$sens.results.diff, 2, mean, na.rm=TRUE)
lines(quant.mean, col="orange")
#Plot 95% quantiles (which are similar to credible intervals)
#95% quantiles of population means (narrower)
quant.means <- apply (par.sens1$sens.results.diff, MARGIN=2, quantile,
probs=c(0.975, 0.025), R=600, na.rm=TRUE)
lines(quant.means[1,], col="orange", lty=2)
lines(quant.means[2,], col="orange", lty=2)
par.opt()
This function follows par.sens to help users optimize values for imperfectly known parameters for SongEvo. The goals are to maximize accuracy and precision of model prediction. Accuracy is quantified by three different approaches: i) the mean of absolute residuals of the predicted population mean values in relation to target data (e.g. observed or hypothetical values (smaller absolute residuals indicate a more accurate model)), ii) the difference between the bootstrapped mean of predicted population means and the mean of the target data, and iii) the proportion of simulated population trait means that fall within (i.e. are “contained by”) the confidence intervals of the target data (a higher proportion indicates greater accuracy). Precision is measured with the residuals of the predicted population variance to the variance of target data (smaller residuals indicate a more precise model).
par.opt()
Users specify the timestep (“ts”) at which to compare simulated trait
values to target trait data (“target.data”) and save the results in an
object (called par.opt1
here).
ts <- years
par.opt1 <- par.opt(sens.results=par.sens1$sens.results, ts=ts,
target.data=target.data, par.range=par.range)
Examine results objects (residuals and target match).
par.opt1$Residuals
#> , , Residuals of mean
#>
#> Iteration 1 Iteration 2 Iteration 3 Iteration 4 Iteration 5
#> par.val 0.4 423.832929 9.072603 220.01363 157.5111 327.92873
#> par.val 0.425 17.414232 179.799740 198.27723 324.6101 309.26890
#> par.val 0.45 360.922983 208.739367 107.36239 467.0985 23.33257
#> par.val 0.475 3.002444 338.446644 329.96314 311.6260 315.47123
#> par.val 0.5 341.488030 201.403363 537.93143 150.5028 447.10296
#> par.val 0.525 48.990549 4.716653 84.59006 248.0517 34.04253
#> par.val 0.55 200.512859 405.570797 407.15971 132.2251 220.14958
#> par.val 0.575 67.261911 42.186316 162.43372 206.6027 239.75274
#> par.val 0.6 150.811345 381.295382 171.25321 208.1720 38.38828
#> Iteration 6 Iteration 7 Iteration 8 Iteration 9 Iteration 10
#> par.val 0.4 188.0418805 259.409848 101.07989 306.98292 268.24544
#> par.val 0.425 76.1139092 243.176975 262.11944 16.48896 76.02736
#> par.val 0.45 383.0761086 375.910563 252.16602 503.62474 323.32619
#> par.val 0.475 153.2608278 28.727254 141.17831 309.86060 221.06166
#> par.val 0.5 99.4218135 3.951095 272.47274 320.36094 17.62708
#> par.val 0.525 312.9364931 250.340011 24.43407 327.93556 342.19469
#> par.val 0.55 0.5390983 263.765862 382.95820 211.45151 506.97215
#> par.val 0.575 318.7519610 163.869580 153.41187 284.50814 226.04219
#> par.val 0.6 123.6396871 102.360795 408.96077 175.26647 122.70636
#>
#> , , Residuals of variance
#>
#> Iteration 1 Iteration 2 Iteration 3 Iteration 4 Iteration 5
#> par.val 0.4 2515.863 174.677 308.593 7942.1285 12035.771
#> par.val 0.425 10017.516 6831.015 15853.671 7922.4563 13192.871
#> par.val 0.45 1593.826 3603.625 10946.393 9493.4430 5722.825
#> par.val 0.475 29326.766 14049.239 6683.842 6075.8750 7398.454
#> par.val 0.5 2252.965 5008.545 8220.947 3904.8427 15041.659
#> par.val 0.525 16246.213 4985.730 2583.530 1494.4725 1153.909
#> par.val 0.55 12505.949 3790.839 3751.787 3554.9732 8349.303
#> par.val 0.575 10729.690 5888.646 4653.696 18446.0970 2108.804
#> par.val 0.6 2678.177 10986.184 12812.079 381.5835 6387.349
#> Iteration 6 Iteration 7 Iteration 8 Iteration 9 Iteration 10
#> par.val 0.4 5660.699 745.1856 2455.0148 10604.891 6587.2905
#> par.val 0.425 8724.015 6092.3161 8211.8084 10462.553 8426.1971
#> par.val 0.45 15458.684 11808.1302 3453.4660 16422.832 1918.9196
#> par.val 0.475 11394.772 11449.7729 2677.1872 5761.245 7357.4517
#> par.val 0.5 3504.654 42385.3601 21120.2672 17558.363 21909.3151
#> par.val 0.525 8086.326 1175.7755 633.1128 6163.405 9007.2104
#> par.val 0.55 22058.056 8688.4754 5270.3232 14535.844 7420.0998
#> par.val 0.575 6963.664 10890.7865 1026.5676 1593.142 965.6395
#> par.val 0.6 1461.935 4864.1629 25620.6497 2764.837 6627.8493
par.opt1$Target.match
#> Difference in means Proportion contained
#> par.val 0.4 174.3299 0.1
#> par.val 0.425 166.8468 0.2
#> par.val 0.45 300.5559 0.1
#> par.val 0.475 215.2598 0.2
#> par.val 0.5 239.2262 0.2
#> par.val 0.525 162.9364 0.4
#> par.val 0.55 273.1305 0.1
#> par.val 0.575 173.0297 0.2
#> par.val 0.6 167.8133 0.1
par.opt()
par.opt()
plot(par.range, par.opt1$Target.match[,1], type="l", xlab="Parameter range",
ylab="Difference in means (Hz)")
plot(par.range, par.opt1$Prop.contained, type="l", xlab="Parameter range",
ylab="Proportion contained")
res.mean.means <- apply(par.opt1$Residuals[, , 1], MARGIN=1, mean, na.rm=TRUE)
res.mean.quants <- apply (par.opt1$Residuals[, , 1], MARGIN=1, quantile,
probs=c(0.975, 0.025), R=600, na.rm=TRUE)
plot(par.range, res.mean.means, col="orange", ylim=c(min(par.opt1$Residuals[,,1],
na.rm=TRUE), max(par.opt1$Residuals[,,1], na.rm=TRUE)), type="b",
xlab="Parameter value (territory turnover rate)",
ylab="Residual of trait mean (trill bandwidth, Hz)")
points(par.range, res.mean.quants[1,], col="orange")
points(par.range, res.mean.quants[2,], col="orange")
lines(par.range, res.mean.quants[1,], col="orange", lty=2)
lines(par.range, res.mean.quants[2,], col="orange", lty=2)
par.opt()
#Calculate and plot mean and quantiles of residuals of variance of trait values
res.var.mean <- apply(par.opt1$Residuals[, , 2], MARGIN=1, mean, na.rm=TRUE)
res.var.quants <- apply (par.opt1$Residuals[, , 2], MARGIN=1, quantile,
probs=c(0.975, 0.025), R=600, na.rm=TRUE)
plot(par.range, res.var.mean, col="purple",
ylim=c(min(par.opt1$Residuals[,,2], na.rm=TRUE),
max(par.opt1$Residuals[,,2], na.rm=TRUE)), type="b",
xlab="Parameter value (territory turnover rate)",
ylab="Residual of trait variance (trill bandwidth, Hz)")
points(par.range, res.var.quants[1,], col="purple")
points(par.range, res.var.quants[2,], col="purple")
lines(par.range, res.var.quants[1,], col="purple", lty=2)
lines(par.range, res.var.quants[2,], col="purple", lty=2)
par.opt()
: plot trait values for range of parameterspar(mfcol=c(3,2),
mar=c(2.1, 2.1, 0.1, 0.1),
cex=0.8)
for(i in 1:length(par.range)){
plot(par.sens1$sens.results[ , , "trait.pop.mean", ], xlab="Year", ylab="Bandwidth (Hz)",
xaxt="n", type="n", xlim=c(-0.5, years),
ylim=c(min(par.sens1$sens.results[ , , "trait.pop.mean", ], na.rm=TRUE),
max(par.sens1$sens.results[ , , "trait.pop.mean", ], na.rm=TRUE)))
for(p in 1:iteration){
lines(par.sens1$sens.results[p, , "trait.pop.mean", i], col="light gray")
}
freq.mean <- apply(par.sens1$sens.results[, , "trait.pop.mean", i], 2, mean, na.rm=TRUE)
lines(freq.mean, col="blue")
axis(side=1, at=seq(0, 35, by=5), labels=seq(1970, 2005, by=5))
#Plot 95% quantiles
quant.means <- apply (par.sens1$sens.results[, , "trait.pop.mean", i], MARGIN=2, quantile,
probs=c(0.95, 0.05), R=600, na.rm=TRUE)
lines(quant.means[1,], col="blue", lty=2)
lines(quant.means[2,], col="blue", lty=2)
#plot mean and CI for historic songs.
#plot original song values
library("boot")
sample.mean <- function(d, x) {
mean(d[x])
}
boot_hist <- boot(starting.trait, statistic=sample.mean, R=100)#, strata=mn.res$iteration)
ci.hist <- boot.ci(boot_hist, conf=0.95, type="basic")
low <- ci.hist$basic[4]
high <- ci.hist$basic[5]
points(0, mean(starting.trait), pch=20, cex=0.6, col="black")
library("Hmisc")
errbar(x=0, y=mean(starting.trait), high, low, add=TRUE)
#plot current song values
library("boot")
sample.mean <- function(d, x) {
mean(d[x])
}
boot_curr <- boot(target.data, statistic=sample.mean, R=100)#, strata=mn.res$iteration)
ci.curr <- boot.ci(boot_curr, conf=0.95, type="basic")
low <- ci.curr$basic[4]
high <- ci.curr$basic[5]
points(years, mean(target.data), pch=20, cex=0.6, col="black")
library("Hmisc")
errbar(x=years, y=mean(target.data), high, low, add=TRUE)
#plot panel title
text(x=3, y=max(par.sens1$sens.results[ , , "trait.pop.mean", ], na.rm=TRUE)-100,
labels=paste("Par = ", par.range[i], sep=""))
}
mod.val()
This function allows users to assess the validity of the specified
model by testing model performance with a population different from the
population used to build the model. The user first runs SongEvo with
initial trait values from the validation population.
mod.val()
uses the summary.results array from SongEvo,
along with target values from a specified timestep, to calculate the
same three measures of accuracy and one measure of precision that are
calculated in par.opt.
We parameterized SongEvo with initial song data from Schooner Bay, CA in 1969, and then compared simulated data to target (i.e. observed) data in 2005.
Prepare initial song data for Schooner Bay.
starting.trait <- subset(song.data, Population=="Schooner" & Year==1969)$Trill.FBW
starting.trait2 <- c(starting.trait, rnorm(n.territories-length(starting.trait),
mean=mean(starting.trait), sd=sd(starting.trait)))
init.inds <- data.frame(id = seq(1:n.territories), age = 2, trait = starting.trait2)
init.inds$x1 <- round(runif(n.territories, min=-122.481858, max=-122.447270), digits=8)
init.inds$y1 <- round(runif(n.territories, min=37.787768, max=37.805645), digits=8)
Specify and call SongEvo() with validation data
iteration <- 10
years <- 36
timestep <- 1
terr.turnover <- 0.5
SongEvo2 <- SongEvo(init.inds = init.inds, females = 1.0, iteration = iteration, steps = years,
timestep = timestep, n.territories = n.territories, terr.turnover = terr.turnover,
integrate.dist = integrate.dist,
learning.error.d = learning.error.d, learning.error.sd = learning.error.sd,
mortality.a.m = mortality.a.m, mortality.a.f = mortality.a.f,
mortality.j.m = mortality.j.m, mortality.j.f = mortality.j.f, lifespan = lifespan,
phys.lim.min = phys.lim.min, phys.lim.max = phys.lim.max,
male.fledge.n.mean = male.fledge.n.mean, male.fledge.n.sd = male.fledge.n.sd, male.fledge.n = male.fledge.n,
disp.age = disp.age, disp.distance.mean = disp.distance.mean, disp.distance.sd = disp.distance.sd,
mate.comp = mate.comp, prin = prin, all = TRUE)
Specify and call mod.val()
ts <- 36
target.data <- subset(song.data, Population=="Schooner" & Year==2005)$Trill.FBW
mod.val1 <- mod.val(summary.results=SongEvo2$summary.results, ts=ts,
target.data=target.data)
Plot results from mod.val()
plot(SongEvo2$summary.results[1, , "trait.pop.mean"], xlab="Year", ylab="Bandwidth (Hz)",
xaxt="n", type="n", xlim=c(-0.5, 36.5),
ylim=c(min(SongEvo2$summary.results[, , "trait.pop.mean"], na.rm=TRUE),
max(SongEvo2$summary.results[, , "trait.pop.mean"], na.rm=TRUE)))
for(p in 1:iteration){
lines(SongEvo2$summary.results[p, , "trait.pop.mean"], col="light gray")
}
freq.mean <- apply(SongEvo2$summary.results[, , "trait.pop.mean"], 2, mean, na.rm=TRUE)
lines(freq.mean, col="blue")
axis(side=1, at=seq(0, 35, by=5), labels=seq(1970, 2005, by=5))
#Plot 95% quantiles
quant.means <- apply (SongEvo2$summary.results[, , "trait.pop.mean"], MARGIN=2, quantile,
probs=c(0.95, 0.05), R=600, na.rm=TRUE)
lines(quant.means[1,], col="blue", lty=2)
lines(quant.means[2,], col="blue", lty=2)
#plot mean and CI for historic songs.
#plot original song values
library("boot")
sample.mean <- function(d, x) {
mean(d[x])
}
boot_hist <- boot(starting.trait, statistic=sample.mean, R=100)
ci.hist <- boot.ci(boot_hist, conf=0.95, type="basic")
low <- ci.hist$basic[4]
high <- ci.hist$basic[5]
points(0, mean(starting.trait), pch=20, cex=0.6, col="black")
library("Hmisc")
errbar(x=0, y=mean(starting.trait), high, low, add=TRUE)
#text and arrows
text(x=5, y=2720, labels="Historical songs", pos=1)
arrows(x0=5, y0=2750, x1=0.4, y1=mean(starting.trait), length=0.1)
#plot current song values
library("boot")
sample.mean <- function(d, x) {
mean(d[x])
}
boot_curr <- boot(target.data, statistic=sample.mean, R=100)
ci.curr <- boot.ci(boot_curr, conf=0.95, type="basic")
low <- ci.curr$basic[4]
high <- ci.curr$basic[5]
points(years, mean(target.data), pch=20, cex=0.6, col="black")
library("Hmisc")
errbar(x=years, y=mean(target.data), high, low, add=TRUE)
#text and arrows
text(x=25, y=3100, labels="Current songs", pos=3)
arrows(x0=25, y0=3300, x1=36, y1=mean(target.data), length=0.1)
The model did reasonably well predicting trait evolution in the
validation population, suggesting that it is valid for our purposes: the
mean bandwidth was abs(mean(target.data)-freq.mean)
Hz from
the observed values, ~21% of predicted population means fell within the
95% confidence intervals of the observed data, and residuals of means
(~545 Hz) and variances (~415181 Hz) were similar to those produced by
the training data set.
h.test()
This function allows hypothesis testing with SongEvo. To test if measured songs from two time points evolved through mechanisms described in the model (e.g. drift or selection), users initialize the model with historical data, parameterize the model based on their understanding of the mechanisms, and test if subsequently observed or predicted data match the simulated data. The output data list includes two measures of accuracy: the proportion of observed points that fall within the confidence intervals of the simulated data and the residuals between simulated and observed population trait means. Precision is measured as the residuals between simulated and observed population trait variances. We tested the hypothesis that songs of Z. l. nuttalli in Bear Valley, CA evolved through cultural drift from 1969 to 2005.
Prepare initial song data for Bear Valley.
starting.trait <- subset(song.data, Population=="Bear Valley" & Year==1969)$Trill.FBW
starting.trait2 <- c(starting.trait, rnorm(n.territories-length(starting.trait),
mean=mean(starting.trait), sd=sd(starting.trait)))
init.inds <- data.frame(id = seq(1:n.territories), age = 2, trait = starting.trait2)
init.inds$x1 <- round(runif(n.territories, min=-122.481858, max=-122.447270), digits=8)
init.inds$y1 <- round(runif(n.territories, min=37.787768, max=37.805645), digits=8)
Specify and call SongEvo() with test data
SongEvo3 <- SongEvo(init.inds = init.inds, females = 1.0, iteration = iteration, steps = years,
timestep = timestep, n.territories = n.territories, terr.turnover = terr.turnover,
integrate.dist = integrate.dist,
learning.error.d = learning.error.d, learning.error.sd = learning.error.sd,
mortality.a.m = mortality.a.m, mortality.a.f = mortality.a.f,
mortality.j.m = mortality.j.m, mortality.j.f = mortality.j.f, lifespan = lifespan,
phys.lim.min = phys.lim.min, phys.lim.max = phys.lim.max,
male.fledge.n.mean = male.fledge.n.mean, male.fledge.n.sd = male.fledge.n.sd, male.fledge.n = male.fledge.n,
disp.age = disp.age, disp.distance.mean = disp.distance.mean, disp.distance.sd = disp.distance.sd,
mate.comp = mate.comp, prin = prin, all = TRUE)
Specify and call h.test()
target.data <- subset(song.data, Population=="Bear Valley" & Year==2005)$Trill.FBW
h.test1 <- h.test(summary.results=SongEvo3$summary.results, ts=ts,
target.data=target.data)
The output data list includes two measures of accuracy: the proportion of observed points that fall within the confidence intervals of the simulated data and the residuals between simulated and observed population trait means. Precision is measured as the residuals between simulated and observed population trait variances.
Eighty percent of the observed data fell within the central 95% of the simulated values, providing support for the hypothesis that cultural drift as described in this model is sufficient to describe the evolution of trill frequency bandwidth in this population.
h.test1
#> $Residuals
#> Residuals of mean Residuals of variance
#> Iteration 1 570.5283 1766.702
#> Iteration 2 897.4296 27905.781
#> Iteration 3 363.7918 34670.479
#> Iteration 4 842.5410 33374.746
#> Iteration 5 714.8821 29906.828
#> Iteration 6 521.8058 43487.935
#> Iteration 7 563.2237 59290.204
#> Iteration 8 428.2495 44896.769
#> Iteration 9 438.2434 15331.006
#> Iteration 10 117.8777 61258.778
#>
#> $Prop.contained
#> [1] 0.4
We can plot simulated data in relation to measured data.
#Plot
plot(SongEvo3$summary.results[1, , "trait.pop.mean"], xlab="Year", ylab="Bandwidth (Hz)",
xaxt="n", type="n", xlim=c(-0.5, 35.5),
ylim=c(min(SongEvo3$summary.results[, , "trait.pop.mean"], na.rm=TRUE),
max(SongEvo3$summary.results[, , "trait.pop.mean"], na.rm=TRUE)))
for(p in 1:iteration){
lines(SongEvo3$summary.results[p, , "trait.pop.mean"], col="light gray")
}
freq.mean <- apply(SongEvo3$summary.results[, , "trait.pop.mean"], 2, mean, na.rm=TRUE)
lines(freq.mean, col="blue")
axis(side=1, at=seq(0, 35, by=5), labels=seq(1970, 2005, by=5))#, tcl=-0.25, mgp=c(2,0.5,0))
#Plot 95% quantiles (which are similar to credible intervals)
quant.means <- apply (SongEvo3$summary.results[, , "trait.pop.mean"], MARGIN=2, quantile,
probs=c(0.95, 0.05), R=600, na.rm=TRUE)
lines(quant.means[1,], col="blue", lty=2)
lines(quant.means[2,], col="blue", lty=2)
#plot original song values
library("boot")
sample.mean <- function(d, x) {
mean(d[x])
}
boot_hist <- boot(starting.trait, statistic=sample.mean, R=100)#, strata=mn.res$iteration)
ci.hist <- boot.ci(boot_hist, conf=0.95, type="basic")
low <- ci.hist$basic[4]
high <- ci.hist$basic[5]
points(0, mean(starting.trait), pch=20, cex=0.6, col="black")
library("Hmisc")
errbar(x=0, y=mean(starting.trait), high, low, add=TRUE)
#plot current song values
points(rep(ts, length(target.data)), target.data)
library("boot")
sample.mean <- function(d, x) {
mean(d[x])
}
boot_curr <- boot(target.data, statistic=sample.mean, R=100)#, strata=mn.res$iteration)
ci.curr <- boot.ci(boot_curr, conf=0.95, type="basic")
low <- ci.curr$basic[4]
high <- ci.curr$basic[5]
points(years, mean(target.data), pch=20, cex=0.6, col="black")
library("Hmisc")
errbar(x=years, y=mean(target.data), high, low, add=TRUE)
#text and arrows
text(x=11, y=2850, labels="Historical songs", pos=1)
arrows(x0=5, y0=2750, x1=0.4, y1=mean(starting.trait), length=0.1)
text(x=25, y=2900, labels="Current songs", pos=1)
arrows(x0=25, y0=2920, x1=years, y1=mean(target.data), length=0.1)