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Parasitoid Dispersal Model

Parasitoid wasp drift-diffusion model with Bayesian data modeling framework

Please note: This code will only run in Python version 3.5 or greater.

Publication DOI:
2017 Journal of the Royal Society Interface, "Inferring stratified parasitoid dispersal mechanisms and parameters from coarse data using mathematical and Bayesian methods": DOI

Acknowledements: This material was based upon work partially supported by the National Science Foundation under Grant DMS-1127914 to the Statistical and Applied Mathematical Sciences Institute. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

Dependencies: Numpy Scipy Matplotlib Pillow (if plotting satellite imagery) py.test (if running tests) Reikna (if running on a GPU. Requres CUDA libraries and PyCUDA.) PyMC (if running Bayesian model fitting) PyTables (if running Bayesian model fitting - used by hdf5 PyMC backend) Pandas (if running Bayesian model fitting)


This code consists of two parts: the first is the drift-diffusion model, which itself can be run either as a probabilistic model or as a population model, while the second is a Bayesian modeling framework for fitting the drift-diffusion model parameters to data. Which file you want to run depends on the functionality you would like to access.

Drift-diffusion model

The drift-diffusion probability model can be run simply by typing "python" into a terminal window while within this directory. Given appropriate wind data, this model simulates the spatial probability of a single parasitoid's location after each day assuming that it was released from a central point at midnight.

The population model can be run by typing "python --pop" into a terminal window. This model requires additional information about the number of parasitoids released along with the duration and timing of the release. It simulates the expected value of the parasitoid population after each day inside within each spatial cell of the domain.

Both models accept flags and keyword arguments which will be described below. If a file named "config.txt" is present, will read it for keyword arguments as well. These should be of the form "parameter = value". Anything following a # on a line will be ignored as a comment. Any options passed via the terminal will override the defaults specified in config.txt.

Saved model results can be plotted by typing "python [filename]" where [filename] is the path to the saved simulation data, with or without the file extension. This program features an interactive menu with options including plotting single simulation days, plotting all simulation days in succession, plotting in black and white, saving model visualizations and a user specified size and dpi, and saving all simulation days to an mp4 video file.

The plotting routine is capable of displaying satellite images from Bing or Google maps as a backdrop to the model results. For this functionality to operate, the release coordinates must be specified and a Bing or Google maps key must be provided in config.txt. You can obtain a Bing maps key for free at and a Google maps key for free at The syntax for specifying a map key in config.txt is "map_key = ". An internet connection is required; no maps are cached between calls to the plotting routine. You must specify which service you are using via the maps_service variable - the default is currently Google.

All tests can be run by calling py.test from the terminal.

The model makes use of the Reikna and PyCUDA libraries to run on the GPU. If these libraries are not installed, or if the gloabl cuda flag has been set to False, the model will run on the CPU only.

The model also makes use of Python's multiprocessing library to simulate each day in parallel. Performance will depend on the specifics of your machine, and there is a variable one can set specifying a lower limit on the number of simulated flight days, below which parallelism will not be used.

Bayesian model and parameter fitting

Due to the inevitable varience between datasets - including format, data collection techniques, etc. - it is impractical to expect a specific dataset structure from which code can automatically parse the necessary information. Instead, we leave it to the user to supply Pandas code that will properly parse the data and return expected data structures. This Pandas code should be pasted directly into, which has been heavily commented to provide guidence on exactly what is needed where. Assuming everything is set up properly, implements the LocInfo class which returns an object containing data in a format that can be compared to model results through the Bayesian framework specified in (which specifies priors, runs the simulations, and does the MCMC sampling), (which also specifies priors and runs the simulations, but does so for maximum a posteriori or normal approximation estimates), and (which models data collection and parasitoid emergence based on the simulated population densities).

Once everything is properly specified, MCMC samples can be taken by typing "python" into a terminal. These samples will be saved to an hdf5 database allowing for later inspection or additional sampling.

Parasitoid Drift-Diffusion Model

All model parameters for both the probability model and the population model are specified in the Params class whose implemenation is located in, except for the Bing/Google maps key which is always only specified in config.txt (this is for re-distribution purposes). The Params class implemenation can be edited directly to specify different defaults, and machine specific defaults can also be specified in config.txt. All parameters and flags can also be specified on a per-run basis by using keyword options or flags at the command line. The following is a list of these options. command line options/parameters

Current defaults are specified with brackets where appropriate.

General flags and simulation options

  • --pop, --popmodel, --pop_model, or prob_model=False: Run the drift-diffusion population model (rather than the probability model).
  • --prob, --probmodel, --prob_model, or prob_model=True: Run the drift-diffusion probability model. This is currently the default behavior.
  • --no_output, [--output], output=False/[True]: Turn off/on saving of model results. If on, model results will be saved in a NumPy .npz ZipFile and the model parameters will be saved in a json file of the same name. Saved simulation results can be visualized by typing "python " where is the path to the saved simulation file, with or without the file extension.
  • --no_plot, [--plot], plot=False/[True]: Turn off/on plotting of results after the simulation is finished.
  • --no_cuda, [--cuda], cuda=False/[True]: Whether or not to use CUDA libraries. If CUDA/PyCUDA is not installed, the simulation will be run without CUDA automatically, regardless of this flag.
  • --carnarvon, [--kalbar]: Load location specific parameters for a known location. These include:
    • dataset (name of location)
    • site_name (path to data ...clearly these were named backwards. oh well.)
    • start_time (time at which wind data started recording)
    • coord (release coordinates)
    • r_dur (release duration)
    • r_dist (release time distribution)
    • r_start (time of day release started)
    • r_number (number of wasps released) See below for information on each of these.
  • ndays=: Number of days to run simulation. This should not exceed the number of days you have wind data for. If you would like to run the simulation for all the days for which you have data, you can enter a value of "-1".
  • domain_info=(distance in meters, cell count): This defines the domain for the simulation. Specify the meters from the release point to an edge of the domain, and the number of cells from release to the edge. This will result in a domain with 2*(cells) + 1 number of cells along each edge, with a cell area of (meters/cells)**2.
  • outfile=: Name to use when saving simulation data (include path, if any). Default behavior is to save in a subdirectory named "output" using the name specified by the "dataset" parameter with the time information appended along with "pop" if the population simulation was run.
  • min_ndays=: Minimum number of days requried in a simulation for multiprocessing to kick in. Depending on your machine, there may be a threshold where very short simulations run slower on multiple processors because of overhead.

Location specific variables

  • dataset=: name for this data
  • site_name=: path and name for all the necessary data to run the simulation. This usually looks something like 'data/'. The simulation will then try to load a file named 'data/wind.txt' to get the wind data, which should be specified in units of m/s. If running Bayes, you will also need 'data/releasegrid.txt' and 'data/fields.txt'.
  • coord=(latitude,longitude): Lat/long coordinates of the release point. Needed for satellite images.
  • r_dur=: Number of days the release was conducted. Needed for population model.
  • start_time=00:00/00:30: Time the wind data started. Either midnight (00:00) or 30 min after. Needed for population model.
  • r_start=<number between 0 and 1>: Time of day the release was started. Units are days. Needed for population model.
  • r_number=: Number of wasps released. Needed for population model.

Model parameters

  • g_params=(center,scale): Parameters for wind logistic function g. First one centers the logistic, the second on scales it.
  • f_params=(center,scale,center,scale): Parameters for take-off probability mass function f, which is based on time of day. First two parameters are the morning logistic (center, scale), the second two are for the evening logistic (center, scale).
  • Dparams=(sig_x,sig_y,correlation): Covarience parameters for diffusion in wind. Provide the standard deviation in the x-direction and y-direction, and the correlation.
  • Dlparams=(sig_x,sig_y,correlation): Covarience parameters for local diffusion. The mean is assumed to be zero; provide the standard deviation in the x-direction and y-direction, and the correlation.
  • lam=lambda: lambda parameter describing the probability of wind-based flight during the day assuming ideal conditions
  • mu_r=mu_r: mu parameter scaling flight distance to average wind speed
  • n_periods=: number of wind vector points per flight. This number times the time frequency of the interpolated wind data gives the total flight time (see interp_num).


  • interp_num=: Number of interpolation points to make between wind data collection points as loaded from the data file. The resulting frequency of wind vector points is crucial in determining how long each wasp will fly (see n_periods).
  • maps_key=key: Bing or Google static maps key. Probably best to set this in config.txt.
  • maps_service='Bing' or 'Google' Set in config.txt to match where you got your key.

Running in a terminal (python will result in an interactive menu allowing you to load saved simulations and visualize them in a variety of ways. Journal quality images may be saved using this menu (color or black/white), and video output is also an option.

When run from the terminal, this module plots all grid sample points (using different colors depending on number of leaves sampled) and both the outline and filled cells of each sentinel field. This is a great way to make sure that these locations have been imported correctly.

This module is meant to be loaded into an IPython session and used interactively. Its functions plot the various pieces of the analytic model so that one can easily inspect what is happening "under the hood" for different parameter choices.

Bayesian model

The exact form of the Bayesian model will depend on the specifics of your data collection. LocInfo in handles the loading and the parsing of the data. specifies priors, runs the model, and calls functions to connect the model results to data. It is also the file to run if you want to do MCMC sampling or inspect the results. is similar to (in fact, much of it is just a direct copy), but runs pymc to find the maximum a posteriori estimate instead. does the job of projecting parasitoid emergence from population model results, as well as gathering the expected number of wasps at grid points and cardinal direction sample points. contains functions for plotting traces and posterior distributions from mcmc samples.

All functionality is provided via interactive menus in and, though Bayes_MAP can can also be run via command line arguments (pass the -h flag to see options). MCMC samples from Bayes_Run are saved in hdf5 database which allow for later inspection and resuming of sampling.

At this time the Bayesian modules are only set up and tested for the Kalbar dataset, and thus Kalbar is hard coded into the modules and In Bayes_MAP, it is necessary to specify a value in the dict prior_eps for each stochastic parameter. This tells the solver what step size to use when discretizing derivatives.

Running in a terminal (a valid hdf5 database name must be provided as the first argument) results in an interactive menu allowing the user to plot various posterior distributions along with the traces and Geweke plots. If the needed module name is known, it can also be passed as an argument. Functionality includes plotting posterior distributions formed from a particular piece of the trace by specifying a start and stop point. It may also be useful to import Bayes_Plot into an IPython session to load the database and run these modules and inspect the database directly via pymc (a menu item in also provides the option to launch an IPython session to gain access to the open database).

Running in a terminal (a valid hdf5 database name must be provided as the first argument) results in plots as generated for our publication. Option flags may be passed to produce different kinds of plots.

Running this module in a terminal produces a plot visualizing field locations, average wind direction and speed, and diffusion as specified by the current parameters in


Parasitoid wasp drift-diffusion model with Bayesian inference







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