patter.jl: particle algorithms for animal movement

Particle filters, smoothers and sampling algorithms for animal movement modelling in Julia

Patter.jl provides particle filtering, smoothing and sampling algorithms for animal movement modelling, with a focus on passive acoustic telemetry systems. The package is heavily based on the ParticleFish package developed by Andreas Scheidegger. Patter.jl forms the backend for the patter R package.

Note: Patter.jl is a new Julia package. Like all new packages, you should use it with a degree of caution. Please share feedback and issues.

Highlights

Patter.jl is designed to reconstruct movement paths and emergent patterns of space use from animal tracking data. A powerful, flexible, process-orientated, particle-based framework is used for this purpose. The essential functions are particle_filter() and two_filter_smoother():

• particle_filter() is the particle filter. This simulates the possible locations of an individual moving forwards in time, accounting for all of the data (for example, acoustic observations, depth observations and any other observations) up to each time point and the animal’s movement (a partial marginal distribution).
• two_filter_smoother() is a particle smoothing algorithm. At each time step, the smoother accounts for all of the data from both the past and the future (the full marginal distribution) and substantially refines maps of space use.

We hope to add backward sampling algorithms to the package in due course.

Installation

• Install Julia ≥ v.1.9;

• Install Patter.jl:

  • Use ] in the Julia REPL to open the package manager;
  • Use add https://github.com/edwardlavender/Patter.jl to install Patter.jl;

You can also Patter.jl via the patter R wrapper.

Functionality

Abstract types

Patter.jl is based on three Abstract Types, defined in Julia:

• State structures hold the state (location) of an animal at a given time step;
• ModelMove structures hold movement model, used to simulate new states;
• ModelObs structures hold observation model parameters, used to evaluate the correspondence between simulated states and observations;

Simulation

To simulate datasets, use:

• sim_path_walk() to simulate a movement path from a walk model (via ModelMove);
• sim_observations() to simulate observational time series (via ModelObs);

Real-world datasets

To collate real-world datasets, use:

• assemble_yobs() to assemble a hash-table of observations and observation model parameters;

This function expects a Vector of DataFrames, one for each data type, that comprise a timeline of observations and associated model parameters, and a corresponding Vector of observation model (ModelObs) sub-types.

Modelling

To simulate initial states (i.e., locations) for the particle filter, use:

• simulate_states_init() to simulate states uniformally across an area;

To define a movement model, see:

• ?ModelMove to create a movement model instance;

For available observation models, see:

• ?ModelObs

To implement the particle filter, use:

• particle_filter() to run the filter;

To implement the two-filter smoother, use:

• two_filter_smoother() to run the smoother;

Usage

Set up

This is the basic Patter.jl workflow to reconstruct movement paths and patterns of space use from animal tracking data. First, we load some essential packages:

# Activate project
using Pkg
Pkg.activate(".")

# Load packages
using Patter
import CSV
using DataFrames
using Dates
using Distributions
import GeoArrays
using Plots
import Random
using RCall

Next, we set the seed to ensure reproducibility of our simulations and check the number of threads:

# Set seed
Random.seed!(123);

# Check threads
Threads.nthreads()
#> 1

Third, we define the properties of our study area; namely, a GeoArray of our study area that defines the environment within which movements are possible and the timeline over which we will model movements:

# Read a UTM bathymetry raster that defines the 'environment' within which movements occurred
env = GeoArrays.read(joinpath("data", "bathymetry.tif"));

# Define a timeline for the analysis
# * This specifies the time period and resolution of the analysis
timeline = collect(DateTime("2016-03-17T01:50:00"):Minute(2):DateTime("2016-03-18T01:48:00"));

Movement

We will reconstruct the movements of a tagged flapper skate (Dipturus intermedius) within a study area off the west coast of Scotland, based on electronic tagging and tracking data. To do so, we need a model for the individual’s movements and a series of observation models that connect movements to observations. In this example, we are interested in the two-dimensional (x, y) location of our animal through time (that is, the animal’s ‘state’ is an object of type StateXY). The animal can move up to 750 m in two minutes, which is the resolution at which we will model movement, and we formulate a random walk model (using a ModelMove structure) accordingly based on step lengths and turning angles:

# Formulate a movement model
model_move = ModelMoveXY(env, 
                         truncated(Gamma(1, 250.0), upper = 750.0), 
                         Uniform(-pi, pi));

# Simulate realisation(s) of the movement model
path = simulate_path_walk(xinit = [StateXY(67.87914, 708817.4, 6259203)], 
                          model_move = model_move, 
                          timeline = timeline)
#> 1×720 Matrix{StateXY}:
#>  StateXY(67.8791, 7.08817e5, 6.2592e6)  …  StateXY(21.1177, 7.04308e5, 6.26325e6)

# Extract x and y coordinates for visualisation
x = [path[1, i].x for i in 1:size(path, 2)];
y = [path[1, i].y for i in 1:size(path, 2)];

# Visualise the simulated movement path
p = plot(env, xticks = 5, yticks = 5);
scatter!(p, x, y, color = :red, label = false);
display(p)

See ?State and ?ModelMove for built-in States and movement models. Define a custom sub-type via struct StateCustom <: Patter.State or struct ModelMoveCustom <: Patter.ModelMove and see the help files for the additional methods that need to be provided.

Observations

We have collected acoustic and archival (depth) observations from tagged flapper skate. Here, we load the time series for a selected individual. For analysis using Patter.jl, each dataset must comprise: a timestamp column, that defines the time of an observation; a sensor_id that distinguishes sensors (such as acoustic receivers), an obs column that defines the observation (0 or 1 in the case of acoustic observations); and additional columns that define the parameters of an observation model (ModelObs) structure that links movement to the observations. The wrapper patter package contains helper routines for the assembly of these datasets, if required.

# Read acoustic (0, 1) observations
acoustics = CSV.read(joinpath("data", "acoustics.csv"), DataFrame);
first(acoustics, 6)
#> 6×8 DataFrame
#>  Row │ timestamp            sensor_id  obs    receiver_x  receiver_y  receiver ⋯
#>      │ String31             Int64      Int64  Float64     Float64     Int64    ⋯
#> ─────┼──────────────────────────────────────────────────────────────────────────
#>    1 │ 2016-03-17 01:50:00          3      0   7.06442e5   6.25401e6           ⋯
#>    2 │ 2016-03-17 01:50:00          4      0   7.09742e5   6.26771e6
#>    3 │ 2016-03-17 01:50:00          7      0   7.08742e5   6.26911e6
#>    4 │ 2016-03-17 01:50:00          9      0   7.06042e5   6.25431e6
#>    5 │ 2016-03-17 01:50:00         11      0   7.07542e5   6.26771e6           ⋯
#>    6 │ 2016-03-17 01:50:00         12      0   7.10042e5   6.26731e6
#>                                                                3 columns omitted

# Read archival (depth) observations
archival = CSV.read(joinpath("data", "archival.csv"), DataFrame);
first(archival, 6)
#> 6×5 DataFrame
#>  Row │ timestamp            sensor_id  obs      depth_sigma  depth_deep_eps
#>      │ String31             Int64      Float64  Int64        Int64
#> ─────┼──────────────────────────────────────────────────────────────────────
#>    1 │ 2016-03-17 01:50:00          1    73.78           50              30
#>    2 │ 2016-03-17 01:52:00          1    73.32           50              30
#>    3 │ 2016-03-17 01:54:00          1    73.32           50              30
#>    4 │ 2016-03-17 01:56:00          1    73.32           50              30
#>    5 │ 2016-03-17 01:58:00          1    73.55           50              30
#>    6 │ 2016-03-17 02:00:00          1    68.7            50              30

Individual movements are connected to the observations by models of the observation process for each dataset. Without going into details, here we bundle together the observations with the parameters of the observation models in a typed dictionary for analysis:

# Process time stamps
acoustics.timestamp = DateTime.(acoustics.timestamp, "yyyy-mm-dd HH:MM:SS");
archival.timestamp = DateTime.(archival.timestamp, "yyyy-mm-dd HH:MM:SS");

# Collate datasets & associated `ModelObs` instances into a typed dictionary 
yobs = assemble_yobs(datasets = [acoustics, archival], 
                     model_obs_types = [ModelObsAcousticLogisTrunc, ModelObsDepthNormalTrunc]);

Of course, you do not need acoustic and archival data to implement the algorithms: these are just the data we have collected from flapper skate and they are convenient to illustrate because we have built-in corresponding ModelObs sub-types into the package. However, other datasets can be incorporated almost as easily via custom ModelObs sub-types (that is, struct ModelObsCustom <: Patter.ModelObs) and some supporting methods (see the package help files for details). To simulate observations instead, see simulate_yobs().

Particle filter

We are now in a position to run the particle filter. This runs a simulation forwards (or backwards) in time, sampling states (locations, termed ‘particles’) that are consistent with the movement model and the observations up to and including each time point. We end up with a time series (Matrix) of particles (State instances) that approximate the partial marginal distribution for the location of the animal at each time step:

# Simulate initial states for the forward filter
xinit = simulate_states_init(state_type = StateXY,
                             model_move = model_move, 
                             n = 200_000, 
                             xlim = (705842.1, 710642.1), 
                             ylim = (6249007, 6269707));

# Run the forward filter
fwd = particle_filter(timeline = timeline,
                      xinit = xinit,
                      yobs = yobs,
                      model_move = model_move,
                      n_record = 500,
                      direction = "forward");

# Simulate initial states for the backward filter
xinit = simulate_states_init(state_type = StateXY, 
                             model_move = model_move,
                             n = 200_000, 
                             xlim = (705842.1, 710642.1), 
                             ylim = (6249007, 6269707));

# Run the backward filter
bwd = particle_filter(timeline = timeline,
                      xinit = xinit,
                      yobs = yobs,
                      model_move = model_move,
                      n_record = 500,
                      direction = "backward");

The filter returns a NamedTuple that defines the time steps of the simulation, the simulated States and other algorithm diagnostics

summary(fwd)
#> "@NamedTuple{timesteps::Vector{Int64}, timestamps::Vector{DateTime}, state::Matrix{StateXY}, direction::String, ess::Vector{Float64}, maxlp::Vector{Float64}, convergence::Bool}"

Particle smoother

Particle smoothers refine the outputs from the particle filter. Smoothed particles approximate the full marginal distribution for the location of the individual at each time step (accounting for all of the data before and after each step):

n_particle = 100;
smo = two_filter_smoother(timeline = timeline,
                                 xfwd = fwd.state[1:n_particle, :],
                                 xbwd = bwd.state[1:n_particle, :],
                                 model_move = model_move,
                                 n_sim = 100);

Mapping

Particles can be used to reconstruct movement paths and patterns of space use. At the time of writing, Patter.jl focuses entirely on the provision of fast particle algorithms and lacks supporting routines for mapping and visualisation. However, we can easily estimate a utilisation distribution from Julia using the wrapper patter R package via RCall. This is the R code:

# Load & attach packages
library(patter, quietly = TRUE)
library(spatstat.explore, quietly = TRUE, warn.conflicts = FALSE)
#> Warning: package 'spatstat.explore' was built under R version
#> 4.3.3
#> Warning: package 'spatstat.data' was built under R version 4.3.3
#> Warning: package 'spatstat.univar' was built under R version 4.3.3
#> Warning: package 'spatstat.geom' was built under R version 4.3.3
#> Warning: package 'spatstat.random' was built under R version 4.3.3
#> Warning: package 'nlme' was built under R version 4.3.3
op <- options(terra.pal = rev(terrain.colors(256)))
              
# Read map 
map <- terra::rast(file.path("data", "bathymetry.tif"))

# Convert smoothed particles from `Julia` into a `pf_particles` object
smo <- patter:::pf_particles(.xinit = NULL, .pf_obj = "smo")

# Estimate UD
ud <- map_dens(.map = map,
               .coord = smo$states,
               sigma = spatstat.explore::bw.diggle, 
               .verbose = FALSE)$ud

# Add home range
map_hr_home(ud, .add = TRUE)
mtext(side = 4, "Probability density", line = -3)

options(op)

This basic workflow is highly customisable. You have the flexibility to define species-specific movement models, include any type of observational dataset and implement system-specific observation models. See the function examples for further details and reach out with queries.

Resources

For full details on the methods, see the references below.

For further information of the Patter.jl package, see:

• The online package documentation;
• ?patter::particle_filter() for information on specific functions;

For additional resources, see the documentation for the patter R package.

Disclaimer and troubleshooting

Patter is a new Julia package. All routines are experimental. Researchers interested in using the package are encouraged to get in touch while the methods and package remain at an early stage of evolution ([email protected]).

Citation

To cite patter in publications, please use:

• Lavender, E. et al. (2023). An integrative modelling framework for passive acoustic telemetry. Methods in Ecology and Evolution. https://doi.org/10.1111/2041-210X.14193
• Lavender, E. et al. (in prep). Particle algorithms for animal movement modelling in autonomous receiver networks.
• Lavender, E. et al. (in prep). Particle algorithms for animal tracking in R and Julia. https://doi.org/10.1101/2024.07.30.605733
• Lavender, E. et al. (in prep). Particle filtering reveals patterns of space use in a Critically Endangered elasmobranch.

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Please note that patter is released with a Contributor Code of Conduct. By contributing to this project, you agree to abide by its terms.