knitr::opts_chunk$set(collapse = TRUE, comment = "#>", tidy = FALSE)
SongEvo simulates the cultural evolution of quantitative traits of bird song. SongEvo is an individual- (agent-) based model. SongEvo is spatially-explicit and can be parameterized with, and tested against, measured song data. Functions are available for model implementation, sensitivity analyses, parameter optimization, model validation, and hypothesis testing.
SongEvo
implements the modelpar.sens
allows sensitivity analysespar.opt
allows parameter optimizationmod.val
allows model validationh.test
allows hypothesis testinglibrary(SongEvo)
SongEvo
implements the model
par.sens
allows sensitivity analyses
par.opt
allows parameter optimization
mod.val
allows model validation
h.test
allows hypothesis testing
To explore the SongEvo package, we will use a database of songs from Nuttall’s white-crowned sparrow (Zonotrichia leucophrys nuttalli) recorded at three locations in 1969 and 2005.
data("song.data")
Examine global parameters. Global parameters describe our understanding of the system and may be measured or hypothesized. They are called "global" because they are used by many many functions and subroutines within functions. For descriptions of all adjustable parameters, see ?song.data
.
data("glo.parms") str(glo.parms)
Share global parameters with the global environment. We make these parameters available in the global environment so that we can access them with minimal code.
list2env(glo.parms, globalenv())
Data include the population name (Bear Valley, PRBO, or Schooner), year of song recording (1969 or 2005), and the frequency bandwidth of the trill.
str(song.data)
SongEvo()
In this example, we use songs from individual birds recorded in one population (PRBO) in the year 1969, which we will call starting.trait
.
starting.trait <- subset(song.data, Population=="PRBO" & Year==1969)$Trill.FBW
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 learning.method <- "integrate" 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, iteration = iteration, steps = years, timestep = timestep, n.territories = n.territories, terr.turnover = terr.turnover, learning.method = learning.method, integrate.dist = integrate.dist, learning.error.d = learning.error.d, learning.error.sd = learning.error.sd, mortality.a = mortality.a, mortality.j = mortality.j, 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)
The model required the following time to run on your computer:
SongEvo1$time
Three main objects hold data regarding the SongEvo model. Additional objects are used temporarily within modules of the model.
First, currently alive individuals are stored in a data frame called “inds.” Values within “inds” are updated throughout each of the iterations of the model, and “inds” can be viewed after the model is completed.
head(SongEvo1$inds, 5)
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$summary.results)
Third, individual values may optionally be concatenated and saved to one data frame entitled “all.inds.” all.inds can become quite large, and is therefore only recommended if additional data analyses are desired.
head(SongEvo1$all.inds, 5)
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$summary.results[, , "sample.n"], MARGIN=2, quantile, probs=c(0.975, 0.025), R=600, na.rm=TRUE) lines(quant.means[1,], col="red", lty=2) lines(quant.means[2,], col="red", lty=2)
Load Hmisc package for plotting functions.
library("Hmisc")
We see that the mean trait values per iteration varied widely, though mean trait values over all iterations remained relatively stable. This code uses the summary.results array.
plot(SongEvo1$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.
library("sp") library("reshape2") library("lattice")
Convert data frame from long to wide format. This is necessary for making a multi-panel plot.
all.inds1 <- subset(SongEvo1$all.inds, iteration==1) w <- dcast(as.data.frame(all.inds1), id ~ timestep, value.var="trait", fill=0) all.inds1w <- merge(all.inds1, w, by="id") names(all.inds1w) <- c(names(all.inds1), paste("Ts", seq(1:years), sep=""))
Create a function to generate a continuous color palette--we will use the palette in the next call to make color ramp to represent the trait value.
rbPal <- colorRampPalette(c('blue','red')) #Create a function to generate a continuous color palette
Plot maps, including a separate panel for each timestep (each of 36 years). Our example shows that individuals move across the landscape and that regional dialects evolve and move. The x-axis is longitude, the y-axis is latitude, and the color ramp indicates trill bandwidth in Hz.
spplot(all.inds1w[,-c(1:ncol(all.inds1))], as.table=TRUE, cuts=c(0, seq(from=1500, to=4500, by=10)), ylab="", col.regions=c("transparent", rbPal(1000)), #cuts specifies that the first level (e.g. <1500) is transparent. colorkey=list( right=list( fun=draw.colorkey, args=list( key=list( at=seq(1500, 4500, 10), col=rbPal(1000), labels=list( at=c(1500, 2000, 2500, 3000, 3500, 4000, 4500), labels=c("1500", "2000", "2500", "3000", "3500", "4000", "4500") ) ) ) ) ) )
In addition, you can plot simpler multi-panel maps that do not take advantage of the spatial data class.
#Lattice plot (not as a spatial frame) it1 <- subset(SongEvo1$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$Col, xlab="Longitude", ylab="Latitude")
par.sens()
This function allows testing the sensitivity of SongEvo to different parameter values.
par.sens()
Here we test the sensitivity of the Acquire a Territory submodel to variation in territory turnover rates, ranging from 0.8–1.2 times the published rate (40–60% of territories turned over). The call for the par.sens function has a format similar to SongEvo. The user specifies the parameter to test and the range of values for that parameter. The function currently allows examination of only one parameter at a time and requires at least two iterations.
parm <- "terr.turnover" par.range = seq(from=0.4, to=0.6, by=0.05) sens.results <- NULL
Now we call the par.sens function with our specifications.
extra_parms <- list(init.inds = init.inds, timestep = 1, n.territories = nrow(init.inds), learning.method = "integrate", integrate.dist = 0.1, lifespan = NA, terr.turnover = 0.5, mate.comp = FALSE, prin = FALSE, all = TRUE) global_parms_key <- which(!names(glo.parms) %in% names(extra_parms)) extra_parms[names(glo.parms[global_parms_key])]=glo.parms[global_parms_key] par.sens1 <- par.sens(parm = parm, par.range = par.range, iteration = iteration, steps = years, mate.comp = FALSE, fixed_parms=extra_parms[names(extra_parms)!=parm], all = TRUE)
Examine results objects, which include two arrays:
The first array, sens.results
, contains the SongEvo model results for each parameter. It has the following dimensions:
dimnames(par.sens1$sens.results)
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$sens.results.diff)
To assess sensitivity of SongEvo to a range of parameter values, plot the range in trait quantiles per year by the parameter value. We see that territory turnover values of 0.4--0.6 provided means and quantile ranges of trill bandwidths that are similar to those obtained with the published estimate of 0.5, indicating that the Acquire a Territory submodel is robust to realistic variation in those parameter values.
In the figure, solid gray and black lines show the quantile range of song frequency per year over all iterations as parameterized with the published territory turnover rate (0.5; thick black line) and a range of values from 0.4 to 0.6 (in steps of 0.05, light to dark gray). Orange lines show the mean and 2.5th and 97.5th quantiles of all quantile ranges.
#plot of range in trait quantiles by year by parameter value plot(1:years, par.sens1$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).
target.data <- subset(song.data, Population=="PRBO" & Year==2005)$Trill.FBW
par.opt()
Users specify the timestep (“ts”) at which to compare simulated trait values to target trait data (“target.data”) and save the results in an object (called par.opt1
here).
ts <- years par.opt1 <- par.opt(sens.results=par.sens1$sens.results, ts=ts, target.data=target.data, par.range=par.range)
Examine results objects (residuals and target match).
par.opt1$Residuals par.opt1$Target.match
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)
#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(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, iteration = iteration, steps = years, timestep = timestep, n.territories = n.territories, terr.turnover = terr.turnover, learning.method = learning.method, integrate.dist = integrate.dist, learning.error.d = learning.error.d, learning.error.sd = learning.error.sd, mortality.a = mortality.a, mortality.j = mortality.j, 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)
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$y1 <- round(runif(n.territories, min=37.787768, max=37.805645), digits=8)
Specify and call SongEvo() with test data
SongEvo3 <- SongEvo(init.inds = init.inds, iteration = iteration, steps = years, timestep = timestep, n.territories = n.territories, terr.turnover = terr.turnover, learning.method = learning.method, integrate.dist = integrate.dist, learning.error.d = learning.error.d, learning.error.sd = learning.error.sd, mortality.a = mortality.a, mortality.j = mortality.j, lifespan = lifespan, phys.lim.min = phys.lim.min, phys.lim.max = phys.lim.max, male.fledge.n.mean = male.fledge.n.mean, male.fledge.n.sd = male.fledge.n.sd, male.fledge.n = male.fledge.n, disp.age = disp.age, disp.distance.mean = disp.distance.mean, disp.distance.sd = disp.distance.sd, mate.comp = mate.comp, prin = prin, all)
Specify and call h.test()
target.data <- subset(song.data, Population=="Bear Valley" & Year==2005)$Trill.FBW h.test1 <- h.test(summary.results=SongEvo3$summary.results, ts=ts, target.data=target.data)
The output data list includes two measures of accuracy: the proportion of observed points that fall within the confidence intervals of the simulated data and the residuals between simulated and observed population trait means. Precision is measured as the residuals between simulated and observed population trait variances.
Eighty percent of the observed data fell within the central 95% of the simulated values, providing support for the hypothesis that cultural drift as described in this model is sufficient to describe the evolution of trill frequency bandwidth in this population.
h.test1
We can plot simulated data in relation to measured data.
#Plot plot(SongEvo3$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)
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