Introducing the bSims R package for simulating bird point counts

The bSims R package is a highly scientific and utterly addictive bird point count simulator. Highly scientific, because it implements a spatially explicit mechanistic simulation that is based on statistical models widely used in bird point count analysis (i.e. removal models, distance sampling), and utterly addictive because the implementation is designed to allow rapid interactive exploration (via shiny apps) and efficient simulation (supporting various parallel backends), thus elevating the user experience.

The goals of the package are to:

1. allow easy testing of statistical assumptions and explore effects of violating these assumptions,
2. aid survey design by comparing different options,
3. and most importantly, to have fun while doing it via an intuitive and interactive user interface.

The simulation interface was designed with the following principles in mind:

1. isolation: the spatial scale is small (local point count scale) so that we can treat individual landscapes as more or less homogeneous units (but see below how certain stratified designs and edge effects can be incorporated) and independent independent in space and time;
2. realism: the implementation of biological mechanisms and observation processes are realistic, defaults are chosen to reflect common practice and assumptions;
3. efficiency: implementation is computationally efficient utilizing parallel computing backends when available;
4. extensibility: the package functionality is well documented and easily extensible.

This documents outlines the major functionality of the package. First we describe the motivation for the simulation and the details of the layers. Then we outline an interactive workflow to design simulation studies and describe how to run efficient simulation experiments. Finally we present some of the current limitations of the framework and how to extend the existing functionality of the package to incorporate more of the biological realism into the simulations.

Simulation layers

Introductory stats books begin with the coin flip to introduce the binomial distribution. In R we can easily simulate an outcome from such a random variable (Y \sim Binomial(1, p)) doing something like this:

p <- 0.5

Y <- rbinom(1, size = 1, prob = p)

But a coin flip in reality is a lot more complicated: we might consider the initial force, the height of the toss, the spin, and the weight of the coin.

Bird behavior combined with the observation process presents a more complicated system, that is often treated as a mixture of a count distribution and a detection/nondetection process, e.g.:

D <- 2 # individuals / unit area
A <- 1 # area
p <- 0.8 # probability of availability given presence
q <- 0.5 # probability of detection given availability

N <- rpois(1, lambda = A * D)
Y <- rbinom(1, size = N, prob = p * q)

This looks not too complicated, corresponding to the true abundance being a random variables (N \sim Poisson(DA)), while the observed count being (Y \sim Binomial(N, pq)). This is the exact simulation that we need when we want to make sure that an estimator is capable of estimating the model parameters (lambda and prob here). But such probabilistic simulations are not very useful when we are interested how well the model captures important aspects of reality.

Going back to the Poisson–Binomial example, N would be a result of all the factors influencing bird abundance, such as geographical location, season, habitat suitability, number of conspecifics, competitors, or predators. Y however would largely depend on how the birds behave depending on timing, or how an observer might detect or miss the different individuals, or count the same individual twice, etc.

Therefore the package has layers, that by default are conditionally independent of each other. This design decision is meant to facilitate the comparison of certain settings while keeping all the underlying realizations identical, thus helping to pinpoint effects without the extra variability introduced by all the other effects.

The conditionally independent layers of a bSims realization are the following, with the corresponding function:

1. landscape (bsims_init),
2. population (bsims_populate),
3. behavior with movement and vocalization events (bsims_animate),
4. the physical side of the observation process (bsims_detect), and
5. the human aspect of the observation process (bsims_transcribe).

This example is a sneak peek go to the package vebsite where the vignette describes all the arguments.

library(bSims)
## Loading required package: intrval
## Loading required package: mefa4
## Loading required package: Matrix
## mefa4 0.3-6   2019-06-20
## Loading required package: MASS
## Loading required package: deldir
## deldir 0.1-23
## bSims 0.2-1   2019-12-16      chik-chik

phi <- 0.5                 # singing rate
tau <- 1:3                 # detection distances by strata
tbr <- c(3, 5, 10)         # time intervals
rbr <- c(0.5, 1, 1.5)      # count radii

l <- bsims_init(10,        # landscape
  road=0.25, edge=0.5)
p <- bsims_populate(l,     # population
  density=c(1, 1, 0))
e <- bsims_animate(p,      # events
  vocal_rate=phi,
  move_rate=1, movement=0.2)
d <- bsims_detect(e,       # detections
  tau=tau)
x <- bsims_transcribe(d,   # transcription
  tint=tbr, rint=rbr)

get_table(x) # removal table
##          0-3min 3-5min 5-10min
## 0-50m         0      0       0
## 50-100m       1      0       0
## 100-150m      1      0       0

op <- par(mfrow=c(2,3), cex.main=2)
plot(l, main="Initialize")
plot(p, main="Populate")
plot(e, main="Animate")
plot(d, main="Detect")
plot(x, main="Transcribe")
par(op)

Statistical validity of the simulations

We can test the validity of the simulations when all of the assumptions are met (that is the default) in the homogeneous habitat case. We set singing rate (phi), detection distance (tau), and density (Den) for the simulations. Density is in this case unrealistically high, because we are not using replication only a single landscape. This will help with the estimation.

phi <- 0.5 # singing rate
tau <- 2   # detection distance
Den <- 10  # density

set.seed(1)
l <- bsims_init()
a <- bsims_populate(l, density=Den)
b <- bsims_animate(a, vocal_rate=phi)
o <- bsims_detect(b, tau=tau)

tint <- c(1, 2, 3, 4, 5)
rint <- c(0.5, 1, 1.5, 2) # truncated at 200 m
(x <- bsims_transcribe(o, tint=tint, rint=rint))
## bSims transcript
##   1 km x 1 km
##   stratification: H
##   total abundance: 1014
##   duration: 10 min
##   detected: 259 heard
##   1st event detected by breaks:
##     [0, 1, 2, 3, 4, 5 min]
##     [0, 50, 100, 150, 200 m]
(y <- get_table(x, "removal")) # binned new individuals
##          0-1min 1-2min 2-3min 3-4min 4-5min
## 0-50m         1      3      1      2      0
## 50-100m       7      3      5      1      1
## 100-150m     12      2      2      1      2
## 150-200m     13      8      2      1      1
colSums(y)
## 0-1min 1-2min 2-3min 3-4min 4-5min 
##     33     16     10      5      4
rowSums(y)
##    0-50m  50-100m 100-150m 150-200m 
##        7       17       19       25

We use the detect package to fit removal model and distance sampling model to the simulated output. This is handily implemented in the estimate method for the transcription objects. First we estimate singing rate, effective detection distance, and density based on truncated distance counts:

library(detect)
## Loading required package: Formula
## Loading required package: stats4
## Loading required package: pbapply
## detect 0.4-2      2018-08-29
cbind(true = c(phi=phi, tau=tau, D=Den), 
  estimate = estimate(x))
##     true  estimate
## phi  0.5 0.5768794
## tau  2.0 2.2733052
## D   10.0 8.2330714

Next we estimate singing rate, effective detection distance, and density based on unlimited distance counts:

rint <- c(0.5, 1, 1.5, 2, Inf) # unlimited

(x <- bsims_transcribe(o, tint=tint, rint=rint))
## bSims transcript
##   1 km x 1 km
##   stratification: H
##   total abundance: 1014
##   duration: 10 min
##   detected: 259 heard
##   1st event detected by breaks:
##     [0, 1, 2, 3, 4, 5 min]
##     [0, 50, 100, 150, 200, Inf m]
(y <- get_table(x, "removal")) # binned new individuals
##          0-1min 1-2min 2-3min 3-4min 4-5min
## 0-50m         1      3      1      2      0
## 50-100m       7      3      5      1      1
## 100-150m     12      2      2      1      2
## 150-200m     13      8      2      1      1
## 200+m        15      9      6      6      2
colSums(y)
## 0-1min 1-2min 2-3min 3-4min 4-5min 
##     48     25     16     11      6
rowSums(y)
##    0-50m  50-100m 100-150m 150-200m    200+m 
##        7       17       19       25       38

cbind(true = c(phi=phi, tau=tau, D=Den), 
  estimate = estimate(x))
##     true  estimate
## phi  0.5 0.5128359
## tau  2.0 1.9928785
## D   10.0 9.2041636

Simulation workflow

Deviations from the assumptions and bias in density estimation can be explored systematically by evaluating the simulations settings. We recommend exploring the simulation settings interactively in the shiny apps using run_app("distfunH") app for the homogeneous habitat case and the run_app("distfunHER") app for the stratified habitat case. The apps represent the simulation layers as tabs, the last tab presenting the settings that can be copied onto the clipboard and pasted into the R session or code. In simple situations, comparing results from a few different settings might be enough.

Let us consider the following simple comparison: we want to see how much of an effect does roads have when the only effect is that the road stratum is unsuitable. Otherwise there are no behavioral or detectability effects of the road.

tint <- c(2, 4, 6, 8, 10)
rint <- c(0.5, 1, 1.5, 2, Inf) # unlimited

## no road
b1 <- bsims_all(
  road = 0,
  density = c(1, 1, 0),
  tint = tint,
  rint = rint)
## road
b2 <- bsims_all(
  road = 0.5,
  density = c(1, 1, 0),
  tint = tint,
  rint = rint)
b1
## bSims wrapper object with settings:
##   road   : 0
##   density: 1, 1, 0
##   tint   : 2, 4, 6, 8, 10
##   rint   : 0.5, 1, 1.5, 2, Inf
b2
## bSims wrapper object with settings:
##   road   : 0.5
##   density: 1, 1, 0
##   tint   : 2, 4, 6, 8, 10
##   rint   : 0.5, 1, 1.5, 2, Inf

The bsims_all function accepts all the arguments we discussed before for the simulation layers. Unspecified arguments will be taken to be the default value. However, bsims_all does not evaluate these arguments, but it creates a closure with the settings. Realizations can be drawn as:

b1$new()
## bSims transcript
##   1 km x 1 km
##   stratification: H
##   total abundance: 75
##   duration: 10 min
##   detected: 12 heard
##   1st event detected by breaks:
##     [0, 2, 4, 6, 8, 10 min]
##     [0, 50, 100, 150, 200, Inf m]
b2$new()
## bSims transcript
##   1 km x 1 km
##   stratification: HR
##   total abundance: 95
##   duration: 10 min
##   detected: 4 heard
##   1st event detected by breaks:
##     [0, 2, 4, 6, 8, 10 min]
##     [0, 50, 100, 150, 200, Inf m]

Run multiple realizations is done as:

B <- 25  # number of runs
bb1 <- b1$replicate(B)
bb2 <- b2$replicate(B)

The replicate function takes an argument for the number of replicates (B) and returns a list of transcript objects with (B) elements. The cl argument can be used to parallelize the work, it can be a numeric value on Unix/Linux/OSX, or a cluster object on any OS. The recover = TRUE argument allows to run simulations with error catching.

Simulated objects returned by bsims_all will contain different realizations and all the conditionally independent layers. Use a customized layered approach if former layers are meant to be kept identical across runs.

In more complex situations the shiny apps will help identifying corner cases that are used to define a gradient of settings for single or multiple simulation options. Let us consider the following scenario: we would like to evaluate how the estimates are changing with increasing road width. We will use the expand_list function which creates a list from all combinations of the supplied inputs. Note that we need to wrap vectors inside list() to avoid interpreting those as values to iterate over.

s <- expand_list(
  road = c(0, 0.5, 1),
  density = list(c(1, 1, 0)),
  tint = list(tint),
  rint = list(rint))
str(s)
## List of 3
##  $ :List of 4
##   ..$ road   : num 0
##   ..$ density: num [1:3] 1 1 0
##   ..$ tint   : num [1:5] 2 4 6 8 10
##   ..$ rint   : num [1:5] 0.5 1 1.5 2 Inf
##  $ :List of 4
##   ..$ road   : num 0.5
##   ..$ density: num [1:3] 1 1 0
##   ..$ tint   : num [1:5] 2 4 6 8 10
##   ..$ rint   : num [1:5] 0.5 1 1.5 2 Inf
##  $ :List of 4
##   ..$ road   : num 1
##   ..$ density: num [1:3] 1 1 0
##   ..$ tint   : num [1:5] 2 4 6 8 10
##   ..$ rint   : num [1:5] 0.5 1 1.5 2 Inf

We now can use this list of settings to run simulations for each. The following illustrates the use of multiple cores:

b <- lapply(s, bsims_all)
nc <- 4 # number of cores to use
library(parallel)
cl <- makeCluster(nc)
bb <- lapply(b, function(z) z$replicate(B, cl=cl))
stopCluster(cl)

In some cases, we want to evaluate crossed effects of multiple settings. For example road width and spatial pattern (random vs. clustered):

s <- expand_list(
  road = c(0, 0.5),
  xy_fun = list(
    NULL,
    function(d) exp(-d^2/1^2) + 0.5*(1-exp(-d^2/4^2))),
  density = list(c(1, 1, 0)),
  tint = list(tint),
  rint = list(rint))
str(s)
## List of 4
##  $ :List of 5
##   ..$ road   : num 0
##   ..$ xy_fun : NULL
##   ..$ density: num [1:3] 1 1 0
##   ..$ tint   : num [1:5] 2 4 6 8 10
##   ..$ rint   : num [1:5] 0.5 1 1.5 2 Inf
##  $ :List of 5
##   ..$ road   : num 0.5
##   ..$ xy_fun : NULL
##   ..$ density: num [1:3] 1 1 0
##   ..$ tint   : num [1:5] 2 4 6 8 10
##   ..$ rint   : num [1:5] 0.5 1 1.5 2 Inf
##  $ :List of 5
##   ..$ road   : num 0
##   ..$ xy_fun :function (d)  
##   .. ..- attr(*, "srcref")= 'srcref' int [1:8] 5 5 5 53 5 53 5 5
##   .. .. ..- attr(*, "srcfile")=Classes 'srcfilecopy', 'srcfile' <environment: 0x7feb60723270> 
##   ..$ density: num [1:3] 1 1 0
##   ..$ tint   : num [1:5] 2 4 6 8 10
##   ..$ rint   : num [1:5] 0.5 1 1.5 2 Inf
##  $ :List of 5
##   ..$ road   : num 0.5
##   ..$ xy_fun :function (d)  
##   .. ..- attr(*, "srcref")= 'srcref' int [1:8] 5 5 5 53 5 53 5 5
##   .. .. ..- attr(*, "srcfile")=Classes 'srcfilecopy', 'srcfile' <environment: 0x7feb60723270> 
##   ..$ density: num [1:3] 1 1 0
##   ..$ tint   : num [1:5] 2 4 6 8 10
##   ..$ rint   : num [1:5] 0.5 1 1.5 2 Inf

The package considers simulations as independent in space and time. When larger landscapes need to be simulated, there might be several options: (1) simulate a larger extent and put multiple independent observers into the landscape; or (2) simulate independent landscapes in isolation. The latter approach can also address spatial and temporal heterogeneity in density, behavior, etc. E.g. if singing rate is changing as a function of time of day, one can define the vocal_rate values as a function of time, and simulate independent animation layers. When the density varies in space, one can simulate independent population layers.

Next steps

The package currently is a snapshot of all that it can be. I am saying this because it was written as an interactive tool for a workshop about point count data analysis (see it the material here). What it will become largely depends on its user base and people willing to take it to the next level via PRs with additional features (see the code of conduct).

If you have ideas, let me know in the issues or comments!